Finite Group Databasebeta

← #7087272

Subgroups — #7087272

Order 512.

1740 conjugacy classes of subgroups.

The subgroup lattice has 1479 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45033C211yesmaximal, characteristic, complemented
2#42589C211yesmaximal, characteristic, complemented
3#32533C211yesmaximal, characteristic, complemented
4#32162C211yesmaximal, characteristic, complemented
5#32094C211yesmaximal, characteristic, complemented
6#32061C211yesmaximal, characteristic, complemented
7#30890C211yesmaximal, characteristic, complemented
8#30605C211yesmaximal, characteristic, complemented
9#30444C211yesmaximal, characteristic, complemented
10#30444C211yesmaximal, characteristic, complemented
11#29564C211yesmaximal, characteristic, complemented
12#28950C211yesmaximal, characteristic, complemented
13#28916C211yesmaximal, characteristic, complemented
14#28624C211yesmaximal, characteristic, complemented
15#28458C211yesmaximal, characteristic, complemented
16#28353C211yesmaximal, characteristic, complemented
17#27065C211yesmaximal, characteristic, complemented
18#26619C211yesmaximal, characteristic, complemented
19#26601C211yesmaximal, characteristic, complemented
20#26548C211yesmaximal, characteristic, complemented
21#26254C211yesmaximal, characteristic, complemented
22#26174C211yesmaximal, characteristic, complemented
23#25426C211yesmaximal, characteristic, complemented
24#25364C211yesmaximal, characteristic, complemented
25#25148C211yesmaximal, characteristic, complemented
26#25097C211yesmaximal, characteristic, complemented
27#23810C211yesmaximal, characteristic, complemented
28#23287C211yesmaximal, characteristic, complemented
29#22995C211yesmaximal, characteristic, complemented
30#22868C211yesmaximal, characteristic, complemented
31#22158C211yesmaximal, characteristic, complemented
32C2×#493C2211yescharacteristic
33C2×#493C2211yescharacteristic
34C2×#493C2211yescharacteristic, complemented
35C2×#490C2211yescharacteristic, complemented
36C2×#482C2211yescharacteristic
37C2×#469C2211yescharacteristic
38C2×#469C2211yescharacteristic
39C2×#459C2211yescharacteristic
40C2×#459C2211yescharacteristic
41C2×#459C2211yescharacteristic
42C2×#459C2211yescharacteristic
43C2×#459C2211yescharacteristic, complemented
44C2×#447C2211yescharacteristic
45C2×#447C2211yescharacteristic
46C2×#447C2211yescharacteristic
47C2×#442C2211yescharacteristic
48C2×#442C2211yescharacteristic, complemented
49C2×C4×D8C2211yescharacteristic
50C2×C4×D8C2211yescharacteristic, complemented
51C2×C4×D8C2211yescharacteristic, complemented
52C2×#418C2211yescharacteristic
53#2825—21no—
54#2778—21no—
55#2714—21no—
56#2703—21no—
57#2703—21no—
58#2688—21no—
59#2688—21no—
60#2678—21no—
61#2668—21no—
62#2641C2211yescharacteristic
63#2635—21no—
64#2617—21no—
65#2591—21no—
66#2559—21no—
67#2541C2211yescharacteristic
68#2541C2211yescharacteristic
69#2541C2211yescharacteristic, complemented
70#2513C2211yescharacteristic
71#2512C2211yescharacteristic, complemented
72#2509C2211yescharacteristic, complemented
73#2500C2211yescharacteristic
74#2490C2211yescharacteristic
75#2457—21no—
76#2454C2211yescharacteristic
77#2445C2211yescharacteristic
78#2445C2211yescharacteristic, complemented
79#2433C2211yescharacteristic
80#2433C2211yescharacteristic
81#2428C2211yescharacteristic
82#2428C2211yescharacteristic
83#2428C2211yescharacteristic
84#2428C2211yescharacteristic
85#2424—21no—
86#2420C2211yescharacteristic
87#2416—21no—
88#2401C2211yescharacteristic
89#2366C2211yescharacteristic
90#2366C2211yescharacteristic, complemented
91#2363C2211yescharacteristic
92#2363C2211yescharacteristic
93D4×C4⋊C4C2211yescharacteristic, complemented
94D4×C22⋊C4C2211yescharacteristic
95#2328C2211yescharacteristic
96#2328C2211yescharacteristic, complemented
97#2319C2211yescharacteristic, complemented
98#2094C2211yescharacteristic
99#2092C2211yescharacteristic
100#2092C2211yescharacteristic, complemented
101#2092C2211yescharacteristic, complemented
102#2092C2211yescharacteristic, complemented
103#2088C2211yescharacteristic, complemented
104#2071C2211yescharacteristic, complemented
105#2067C2211yescharacteristic
106#2065C2211yescharacteristic
107#2065C2211yescharacteristic, complemented
108#2059C2211yescharacteristic, complemented
109#2054C2211yescharacteristic
110#2054C2211yescharacteristic
111#2054C2211yescharacteristic
112#2054C2211yescharacteristic, complemented
113#2054C2211yescharacteristic, complemented
114#2054C2211yescharacteristic, complemented
115#2041C2211yescharacteristic
116#2041C2211yescharacteristic
117#2041C2211yescharacteristic
118#2041C2211yescharacteristic, complemented
119#2041C2211yescharacteristic, complemented
120#2041C2211yescharacteristic, complemented
121#2033C2211yescharacteristic
122#2033C2211yescharacteristic
123#2025C2211yescharacteristic, complemented
124#2011C2211yescharacteristic
125#2011C2211yescharacteristic
126#2011C2211yescharacteristic
127#2011C2211yescharacteristic
128#2011C2211yescharacteristic
129#2011C2211yescharacteristic
130#2011C2211yescharacteristic
131#2011C2211yescharacteristic
132#2011C2211yescharacteristic, complemented
133#2011C2211yescharacteristic, complemented
134#1999C2211yescharacteristic
135#1999C2211yescharacteristic
136#1999C2211yescharacteristic
137#1999C2211yescharacteristic
138#1991C2211yescharacteristic, complemented
139#1982C2211yescharacteristic
140#1982C2211yescharacteristic, complemented
141#1972C2211yescharacteristic
142#1972C2211yescharacteristic, complemented
143#1970C2211yescharacteristic
144#1970C2211yescharacteristic
145#1970C2211yescharacteristic
146#1970C2211yescharacteristic, complemented
147#1970C2211yescharacteristic, complemented
148#1961C2211yescharacteristic
149#1957C2211yescharacteristic
150#1949C2211yescharacteristic, complemented
151#1947C2211yescharacteristic, complemented
152#1942C2211yescharacteristic, complemented
153#1941C2211yescharacteristic, complemented
154#1939C2211yescharacteristic, complemented
155#1936C2211yescharacteristic
156#1936C2211yescharacteristic, complemented
157#1934C2211yescharacteristic
158#1934C2211yescharacteristic
159#1934C2211yescharacteristic, complemented
160#1926C2211yescharacteristic
161#1926C2211yescharacteristic
162#1926C2211yescharacteristic, complemented
163#1926C2211yescharacteristic, complemented
164#1925C2211yescharacteristic, complemented
165#1923C2211yescharacteristic
166#1923C2211yescharacteristic
167#1923C2211yescharacteristic
168#1921C2211yescharacteristic, complemented
169#1917C2211yescharacteristic, complemented
170#1917C2211yescharacteristic, complemented
171#1916C2211yescharacteristic, complemented
172#1895C2211yescharacteristic
173#1879C2211yescharacteristic
174#1879C2211yescharacteristic
175#1879C2211yescharacteristic
176#1879C2211yescharacteristic
177#1879C2211yescharacteristic
178#1879C2211yescharacteristic
179#1879C2211yescharacteristic
180#1879C2211yescharacteristic, complemented
181#1879C2211yescharacteristic, complemented
182#1879C2211yescharacteristic, complemented
183#1879C2211yescharacteristic, complemented
184#1879C2211yescharacteristic, complemented
185#1875C2211yescharacteristic
186#1864C2211yescharacteristic, complemented
187#1864C2211yescharacteristic, complemented
188#1864C2211yescharacteristic, complemented
189#1862C2211yescharacteristic
190#1862C2211yescharacteristic
191#1862C2211yescharacteristic, complemented
192#1854C2211yescharacteristic
193#1851C2211yescharacteristic
194#1804C2211yescharacteristic, complemented
195C8×C4⋊C4C2211yescharacteristic, complemented
196C8×C4⋊C4C2211yescharacteristic, complemented
197#1768C2211yescharacteristic, complemented
198C4×#102C2211yescharacteristic
199C4×#102C2211yescharacteristic, complemented
200#1753C2211yescharacteristic
201#1753C2211yescharacteristic
202#1746C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×D8C2311yescharacteristic
205C22×D8C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C22×D8C2311yescharacteristic
211C22×D8C2311yescharacteristic
212C22×D8C2311yescharacteristic
213C22×D8C2311yescharacteristic
214C22×D8C2311yescharacteristic
215C22×D8C2311yescharacteristic
216C22×M16C2311yescharacteristic
217C2×#127C2311yescharacteristic
218C2×#127C2311yescharacteristic
219C2×#127C2311yescharacteristic
220C2×#127C2311yescharacteristic
221C2×#127C2311yescharacteristic
222C2×#127C2311yescharacteristic
223C2×#127C2311yescharacteristic
224C2×#127C2311yescharacteristic
225C2×#126—21no—
226C2×#125C2311yescharacteristic
227C2×#123—21no—
228C2×#123—21no—
229C2×#121—21no—
230C2×#121—21no—
231C2×#121—21no—
232C2×#121—21no—
233C2×#121—21no—
234C2×#121—21no—
235C2×#121—21no—
236C2×#121—21no—
237C2×#121—21no—
238C2×#121—21no—
239C2×#121C2311yescharacteristic
240C2×#121C2311yescharacteristic
241C2×#121C2311yescharacteristic
242C2×#121C2311yescharacteristic
243C2×#121C2311yescharacteristic
244C2×#120—21no—
245C2×#120—21no—
246C2×#120—21no—
247C2×#120—21no—
248C2×C4×D4—21no—
249C2×C4×D4—21no—
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2311yescharacteristic
257C2×C4×D4C2311yescharacteristic
258C2×C4×D4C2311yescharacteristic
259C2×#117C2311yescharacteristic
260C22×C4⋊C4—21no—
261C22×C22⋊C4—21no—
262#493—42no—
263#493—42no—
264#493—42no—
265#490—42no—
266#482—42no—
267#469—42no—
268#469—42no—
269#459—24no—
270#459—24no—
271#459—42no—
272#459—42no—
273#459—42no—
274#447—24no—
275#447—42no—
276#447—42no—
277#442—42no—
278#442—42no—
279C4×D8—42no—
280C4×D8—42no—
281C4×D8—42no—
282C2×#107C2311yescharacteristic
283C2×#107C2311yescharacteristic
284C2×#107C2311yescharacteristic
285C2×#107C2311yescharacteristic
286C2×#106C2311yescharacteristic
287C2×#106C2311yescharacteristic
288C2×#106C2311yescharacteristic
289C2×#106C2311yescharacteristic
290C2×C4⋊C8C2311yescharacteristic
291C2×C4⋊C8C2311yescharacteristic
292C2×C4⋊C8C2311yescharacteristic
293C2×C4⋊C8C2311yescharacteristic
294C2×C4⋊C8C2311yescharacteristic
295#418—42no—
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
317C2×#102C2311yescharacteristic
318C2×#102C2311yescharacteristic
319C2×#102C2311yescharacteristic
320C2×#102C2311yescharacteristic
321C2×#102C2311yescharacteristic
322C2×#102C2311yescharacteristic
323C2×#102C2311yescharacteristic
324C2×#102C2311yescharacteristic
325C2×#102C2311yescharacteristic
326C2×#102C2311yescharacteristic
327C2×#102C2311yescharacteristic
328C2×C22⋊C8C2311yescharacteristic
329C2×C22⋊C8C2311yescharacteristic
330C2×C22⋊C8C2311yescharacteristic
331C2×#97C2311yescharacteristic
332C2×#97C2311yescharacteristic
333C2×C4×C8C2311yescharacteristic
334C2×C4×C8C2311yescharacteristic
335C2×C4×C8C2311yescharacteristic
336C2×C4×C8C2311yescharacteristic
337C2×C4×C8C2311yescharacteristic
338#401D411yescharacteristic
339#400—21no—
340#400—21no—
341#400D411yescharacteristic
342#400D411yescharacteristic
343#400D411yescharacteristic
344#399—21no—
345#397—21no—
346#397—21no—
347#397—21no—
348#397—21no—
349#397—21no—
350#397D411yescharacteristic
351#397D411yescharacteristic
352#397D411yescharacteristic
353#396—21no—
354#396—21no—
355#396D411yescharacteristic
356#394—21no—
357#394—21no—
358#394—21no—
359#394—21no—
360#394—21no—
361#394—21no—
362#394—21no—
363#394—21no—
364#394—21no—
365#394—21no—
366#394—21no—
367#394—21no—
368#394—21no—
369#394—21no—
370#394—21no—
371#394—21no—
372#392—21no—
373#392—21no—
374#392—21no—
375#392—21no—
376#392—21no—
377#392—21no—
378#392—21no—
379#392—21no—
380#392—21no—
381#392—21no—
382#392—21no—
383#392—21no—
384#392—21no—
385#392—21no—
386#390—21no—
387#390—21no—
388#390—21no—
389#390—21no—
390#390—21no—
391#390C2311yescharacteristic
392#390C2311yescharacteristic
393#390C2311yescharacteristic
394#390C2311yescharacteristic
395#390C2311yescharacteristic
396#390C2311yescharacteristic
397#390C2311yescharacteristic
398#390C2311yescharacteristic
399#390C2311yescharacteristic
400#390C2311yescharacteristic
401#390C2311yescharacteristic
402#390C2311yescharacteristic
403#390C2311yescharacteristic
404#390C2311yescharacteristic
405#390C2311yescharacteristic
406#390C2311yescharacteristic
407#390C2311yescharacteristic
408#389—21no—
409#389C2311yescharacteristic
410#389C2311yescharacteristic
411#389C2311yescharacteristic
412#389C2311yescharacteristic
413#389C2311yescharacteristic
414#389C2311yescharacteristic
415#389C2311yescharacteristic
416#388—21no—
417#388—21no—
418#388—21no—
419#388—21no—
420#388—21no—
421#388—21no—
422#388—21no—
423#388—21no—
424#388—21no—
425#388—21no—
426#387—21no—
427#386—21no—
428#386—21no—
429#386—21no—
430#386—21no—
431#386—21no—
432#386—21no—
433#386—21no—
434#386—21no—
435#386—21no—
436#386—21no—
437#386—21no—
438#386—21no—
439#386—21no—
440#386—21no—
441#386—21no—
442#386—21no—
443#386—21no—
444#386—21no—
445#386—21no—
446#386—21no—
447#386—21no—
448#386—21no—
449#386—21no—
450#385—21no—
451#385—21no—
452#385—21no—
453#384C2311yescharacteristic
454#382C2311yescharacteristic
455#382C2311yescharacteristic
456#381—21no—
457#381—21no—
458#380—21no—
459#380—21no—
460#380—21no—
461#380C2311yescharacteristic
462#379—21no—
463C4×C4⋊C4C2311yescharacteristic
464C4×C4⋊C4C2311yescharacteristic
465C4×C4⋊C4C2311yescharacteristic
466C4×C4⋊C4C2311yescharacteristic
467C4×C4⋊C4C2311yescharacteristic
468C4×C4⋊C4C2311yescharacteristic
469C4×C22⋊C4—21no—
470C4×C22⋊C4—21no—
471C4×C22⋊C4C2311yescharacteristic
472C4×C22⋊C4C2311yescharacteristic
473C4×C22⋊C4C2311yescharacteristic
474#376C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499C25—21no—
500C22×D4—22no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—41no—
524C22×D4—41no—
525C22×D4—41no—
526C22×D4—41no—
527C22×D4—41no—
528C22×D4C2411yescharacteristic
529C22×D4C2411yescharacteristic
530C22×D4C2411yescharacteristic
531C22×D4C2411yescharacteristic
532C22×D4C2411yescharacteristic
533C22×D4C2411yescharacteristic
534C22×D4C2411yescharacteristic
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4—21no—
540C23×C4—21no—
541C23×C4—21no—
542C23×C4—21no—
543C23×C4—21no—
544C23×C4C2411yescharacteristic
545C2×D8—22no—
546C2×D8—22no—
547C2×D8—22no—
548C2×D8—22no—
549C2×D8—22no—
550C2×D8—22no—
551C2×D8—22no—
552C2×D8—22no—
553C2×D8—22no—
554C2×D8—22no—
555C2×D8—22no—
556C2×D8—22no—
557C2×D8—22no—
558C2×D8—22no—
559C2×D8—41no—
560C2×D8—41no—
561C2×D8—41no—
562C2×D8—41no—
563C2×D8—41no—
564C2×D8—41no—
565C2×D8—41no—
566C2×D8—41no—
567C2×D8—41no—
568C2×D8—41no—
569C2×D8—41no—
570C2×D8—41no—
571C2×D8—41no—
572C2×D8—41no—
573C2×D8—41no—
574C2×D8—41no—
575C2×D8—41no—
576C2×D8—41no—
577C2×D8—41no—
578C2×D8—41no—
579C2×D8—41no—
580C2×D8—41no—
581C2×M16—22no—
582C2×M16—41no—
583C2×M16—41no—
584C22×C8C2411yescharacteristic
585C22×C8C2411yescharacteristic
586C22×C8C2411yescharacteristic
587C22×C8C2411yescharacteristic
588C22×C8C2411yescharacteristic
589C22×C8C2411yescharacteristic
590C22×C8C2411yescharacteristic
591C22×C8C2411yescharacteristic
592#127—22no—
593#127—22no—
594#127—22no—
595#127—22no—
596#127—41no—
597#127—41no—
598#127—41no—
599#127—41no—
600#127—41no—
601#127—41no—
602#127—41no—
603#127—41no—
604#127—41no—
605#127—41no—
606#127—41no—
607#127—41no—
608#126—82no—
609#125—41no—
610#125—41no—
611#123—82no—
612#123—82no—
613#121—22no—
614#121—22no—
615#121—41no—
616#121—41no—
617#121—41no—
618#121—41no—
619#121—41no—
620#121—41no—
621#121—41no—
622#121—41no—
623#121—82no—
624#121—82no—
625#121—82no—
626#121—82no—
627#121—82no—
628#121—82no—
629#121—82no—
630#121—82no—
631#121—82no—
632#121—82no—
633#120—82no—
634#120—82no—
635#120—82no—
636#120—82no—
637C4×D4—22no—
638C4×D4—22no—
639C4×D4—41no—
640C4×D4—41no—
641C4×D4—41no—
642C4×D4—41no—
643C4×D4—41no—
644C4×D4—41no—
645C4×D4—41no—
646C4×D4—41no—
647C4×D4—41no—
648C4×D4—41no—
649C4×D4—41no—
650C4×D4—41no—
651C4×D4—41no—
652C4×D4—41no—
653C4×D4—41no—
654C4×D4—41no—
655C4×D4—82no—
656C4×D4—82no—
657#117—41no—
658#117—41no—
659C2×C4⋊C4—21no—
660C2×C4⋊C4—21no—
661C2×C4⋊C4—21no—
662C2×C4⋊C4—21no—
663C2×C4⋊C4—21no—
664C2×C4⋊C4—21no—
665C2×C4⋊C4—21no—
666C2×C4⋊C4—21no—
667C2×C4⋊C4—21no—
668C2×C4⋊C4—21no—
669C2×C4⋊C4—21no—
670C2×C4⋊C4—82no—
671C2×C4⋊C4C2×D411yescharacteristic
672C2×C4⋊C4C2×D411yescharacteristic
673C2×C4⋊C4C2×D411yescharacteristic
674C2×C4⋊C4C2×D411yescharacteristic
675C2×C4⋊C4C2×D411yescharacteristic
676C2×C4⋊C4C2×D411yescharacteristic
677C2×C4⋊C4C2411yescharacteristic
678C2×C4⋊C4C2411yescharacteristic
679C2×C4⋊C4C2411yescharacteristic
680C2×C4⋊C4C2411yescharacteristic
681C2×C4⋊C4C2411yescharacteristic
682C2×C4⋊C4C2411yescharacteristic
683C2×C4⋊C4C2411yescharacteristic
684C2×C4⋊C4C2411yescharacteristic
685C2×C4⋊C4C2411yescharacteristic
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—21no—
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—21no—
720C2×C22⋊C4—21no—
721C2×C22⋊C4—21no—
722C2×C22⋊C4—21no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4—21no—
725C2×C22⋊C4—21no—
726C2×C22⋊C4—21no—
727C2×C22⋊C4—21no—
728C2×C22⋊C4—21no—
729C2×C22⋊C4—21no—
730C2×C22⋊C4—21no—
731C2×C22⋊C4—21no—
732C2×C22⋊C4—21no—
733C2×C22⋊C4—21no—
734C2×C22⋊C4—21no—
735C2×C22⋊C4—21no—
736C2×C22⋊C4—82no—
737C2×C22⋊C4C2×D411yescharacteristic
738C2×C22⋊C4C2×D411yescharacteristic
739C2×C22⋊C4C2×D411yescharacteristic
740C2×C22⋊C4C2×D411yescharacteristic
741C2×C22⋊C4C2×D411yescharacteristic
742C2×C22⋊C4C2×D411yescharacteristic
743C2×C42—21no—
744C2×C42—21no—
745C2×C42—21no—
746C2×C42—21no—
747C2×C42C2411yescharacteristic
748C2×C42C2411yescharacteristic
749C2×C42C2411yescharacteristic
750C2×C42C2411yescharacteristic
751C2×C42C2411yescharacteristic
752C2×C42C2411yescharacteristic
753#107—22no—
754#107—41no—
755#107—41no—
756#107—41no—
757#106—22no—
758#106—41no—
759#106—41no—
760#106—41no—
761C4⋊C8—22no—
762C4⋊C8—22no—
763C4⋊C8—22no—
764C4⋊C8—41no—
765C4⋊C8—41no—
766#102—22no—
767#102—22no—
768#102—22no—
769#102—22no—
770#102—22no—
771#102—22no—
772#102—22no—
773#102—22no—
774#102—22no—
775#102—22no—
776#102—22no—
777#102—41no—
778#102—41no—
779#102—41no—
780#102—41no—
781#102—41no—
782#102—41no—
783#102—41no—
784#102—41no—
785#102—41no—
786#102—41no—
787#102—41no—
788#102—41no—
789#102—41no—
790#102—41no—
791#102—41no—
792#102—41no—
793#102—41no—
794#102—41no—
795#102—41no—
796#102—41no—
797#102#4114yes—
798C22⋊C8—22no—
799C22⋊C8—22no—
800C22⋊C8—41no—
801#97—22no—
802#97—41no—
803C4×C8—22no—
804C4×C8—22no—
805C4×C8—41no—
806C4×C8—41no—
807C4×C8—41no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95—21no—
815#95—21no—
816#95—21no—
817#95—21no—
818#95—21no—
819#95—21no—
820#95—21no—
821#95—21no—
822#95—21no—
823#95C2×D411yescharacteristic
824#95C2×D411yescharacteristic
825#95C2×D411yescharacteristic
826#95C2×D411yescharacteristic
827#95C2×D411yescharacteristic
828#95C2×D411yescharacteristic
829#95C2×D411yescharacteristic
830#95C2×D411yescharacteristic
831#95C2×D411yescharacteristic
832#95C2×D411yescharacteristic
833#95C2×D411yescharacteristic
834#95C2×D411yescharacteristic
835#95C2×D411yescharacteristic
836#95C2×D411yescharacteristic
837#95C2×D411yescharacteristic
838#95C2×D411yescharacteristic
839C24—21no—
840C24—21no—
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—42no—
847C24—42no—
848C24—81no—
849C24—81no—
850C24—81no—
851C24—81no—
852C24—81no—
853C24C22×D411yescharacteristic
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—21no—
859C2×D4—21no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—21no—
870C2×D4—21no—
871C2×D4—21no—
872C2×D4—21no—
873C2×D4—21no—
874C2×D4—21no—
875C2×D4—21no—
876C2×D4—21no—
877C2×D4—21no—
878C2×D4—21no—
879C2×D4—21no—
880C2×D4—21no—
881C2×D4—21no—
882C2×D4—21no—
883C2×D4—21no—
884C2×D4—21no—
885C2×D4—21no—
886C2×D4—21no—
887C2×D4—21no—
888C2×D4—21no—
889C2×D4—21no—
890C2×D4—21no—
891C2×D4—21no—
892C2×D4—21no—
893C2×D4—21no—
894C2×D4—42no—
895C2×D4—42no—
896C2×D4—42no—
897C2×D4—42no—
898C2×D4—42no—
899C2×D4—42no—
900C2×D4—42no—
901C2×D4—42no—
902C2×D4—42no—
903C2×D4—42no—
904C2×D4—44no—
905C2×D4—42no—
906C2×D4—42no—
907C2×D4—42no—
908C2×D4—42no—
909C2×D4—42no—
910C2×D4—42no—
911C2×D4—42no—
912C2×D4—42no—
913C2×D4—81no—
914C2×D4—81no—
915C2×D4—81no—
916C2×D4—81no—
917C2×D4—81no—
918C2×D4—81no—
919C2×D4—81no—
920C2×D4—81no—
921C2×D4—81no—
922C2×D4—81no—
923C2×D4—81no—
924C2×D4—81no—
925C2×D4—81no—
926C2×D4—81no—
927C2×D4—81no—
928C2×D4—81no—
929C2×D4—81no—
930C2×D4—81no—
931C2×D4—81no—
932C2×D4—81no—
933C2×D4—81no—
934C2×D4—81no—
935C2×D4—81no—
936C2×D4—81no—
937C2×D4—81no—
938C2×D4—81no—
939C2×D4—81no—
940C2×D4—81no—
941C2×D4—81no—
942C2×D4—81no—
943C2×D4—81no—
944C2×D4—81no—
945C2×D4—81no—
946C2×D4—81no—
947C2×D4—81no—
948C2×D4—81no—
949C2×D4—81no—
950C2×D4—82no—
951C2×D4—82no—
952C2×D4—82no—
953C2×D4—81no—
954C2×D4—81no—
955C2×D4—81no—
956C2×D4—81no—
957C2×D4—81no—
958C2×D4—81no—
959C2×D4—81no—
960C2×D4—81no—
961C2×D4—81no—
962C2×D4—81no—
963C2×D4—81no—
964C2×D4C2×#4112yes—
965C2×D4H(5,𝔽2)12yes—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—21no—
977C22×C4—21no—
978C22×C4—21no—
979C22×C4—21no—
980C22×C4—21no—
981C22×C4—42no—
982C22×C4—42no—
983C22×C4—42no—
984C22×C4—42no—
985C22×C4—42no—
986C22×C4—42no—
987C22×C4—81no—
988C22×C4—81no—
989C22×C4—81no—
990C22×C4—81no—
991C22×C4—81no—
992C22×C4—81no—
993C22×C4—81no—
994C22×C4—81no—
995C22×C4—81no—
996C22×C4—81no—
997C22×C4—81no—
998C22×C4—81no—
999C22×C4—81no—
1000C22×C4—81no—
1001C22×C4—81no—
1002C22×C4—81no—
1003C22×C4—81no—
1004C22×C4—81no—
1005C22×C4—81no—
1006C22×C4—81no—
1007C22×C4—81no—
1008C22×C4C22×D411yescharacteristic
1009C22×C4C22×D411yescharacteristic
1010C22×C4C22×D411yescharacteristic
1011C22×C4C22×D411yescharacteristic
1012C22×C4C22×D411yescharacteristic
1013C22×C4C22×D411yescharacteristic
1014C22×C4C22×D411yescharacteristic
1015C22×C4C22×D411yescharacteristic
1016C22×C4C22×D411yescharacteristic
1017C22×C4C22×D411yescharacteristic
1018C22×C4C22×D411yescharacteristic
1019C22×C4C22×D411yescharacteristic
1020C22×C4C22×D411yescharacteristic
1021C22×C4C2511yescharacteristic
1022D8—44no—
1023D8—44no—
1024D8—44no—
1025D8—44no—
1026D8—44no—
1027D8—82no—
1028D8—82no—
1029D8—82no—
1030D8—82no—
1031D8—82no—
1032D8—82no—
1033D8—82no—
1034M16—82no—
1035C2×C8—21no—
1036C2×C8—21no—
1037C2×C8—21no—
1038C2×C8—21no—
1039C2×C8—21no—
1040C2×C8—21no—
1041C2×C8—21no—
1042C2×C8—21no—
1043C2×C8—21no—
1044C2×C8—21no—
1045C2×C8—21no—
1046C2×C8—21no—
1047C2×C8—21no—
1048C2×C8—21no—
1049C2×C8—21no—
1050C2×C8—21no—
1051C2×C8—21no—
1052C2×C8—21no—
1053C2×C8—21no—
1054C2×C8—21no—
1055C2×C8—21no—
1056C2×C8C2×#4112yes—
1057C2×C8H(5,𝔽2)12yes—
1058C2×C8H(5,𝔽2)12yes—
1059C4⋊C4—22no—
1060C4⋊C4—22no—
1061C4⋊C4—22no—
1062C4⋊C4—22no—
1063C4⋊C4—22no—
1064C4⋊C4—22no—
1065C4⋊C4—21no—
1066C4⋊C4—21no—
1067C4⋊C4—21no—
1068C4⋊C4—21no—
1069C4⋊C4—21no—
1070C4⋊C4—21no—
1071C4⋊C4—21no—
1072C4⋊C4—21no—
1073C4⋊C4—21no—
1074C4⋊C4—21no—
1075C4⋊C4—21no—
1076C4⋊C4—21no—
1077C4⋊C4—21no—
1078C4⋊C4—21no—
1079C4⋊C4—21no—
1080C4⋊C4—21no—
1081C4⋊C4—21no—
1082C4⋊C4—42no—
1083C4⋊C4—42no—
1084C4⋊C4—81no—
1085C4⋊C4—81no—
1086C4⋊C4—81no—
1087C4⋊C4—81no—
1088C4⋊C4—81no—
1089C4⋊C4—81no—
1090C4⋊C4—81no—
1091C4⋊C4—81no—
1092C4⋊C4—81no—
1093C4⋊C4C2×#4112yes—
1094C22⋊C4—22no—
1095C22⋊C4—22no—
1096C22⋊C4—22no—
1097C22⋊C4—41no—
1098C22⋊C4—41no—
1099C22⋊C4—41no—
1100C22⋊C4—42no—
1101C22⋊C4—42no—
1102C22⋊C4—42no—
1103C22⋊C4—42no—
1104C22⋊C4—42no—
1105C22⋊C4—42no—
1106C22⋊C4—42no—
1107C22⋊C4—42no—
1108C22⋊C4—42no—
1109C22⋊C4—42no—
1110C22⋊C4—42no—
1111C22⋊C4—81no—
1112C22⋊C4—81no—
1113C22⋊C4—81no—
1114C22⋊C4—81no—
1115C22⋊C4—81no—
1116C22⋊C4—81no—
1117C22⋊C4—81no—
1118C22⋊C4—81no—
1119C22⋊C4—81no—
1120C22⋊C4—81no—
1121C22⋊C4—81no—
1122C22⋊C4—81no—
1123C22⋊C4—81no—
1124C22⋊C4—81no—
1125C22⋊C4—81no—
1126C22⋊C4—81no—
1127C22⋊C4—81no—
1128C22⋊C4—81no—
1129C22⋊C4—81no—
1130C22⋊C4—81no—
1131C22⋊C4—81no—
1132C22⋊C4—81no—
1133C22⋊C4—81no—
1134C22⋊C4—81no—
1135C22⋊C4—81no—
1136C22⋊C4—81no—
1137C22⋊C4—81no—
1138C22⋊C4—81no—
1139C22⋊C4—81no—
1140C22⋊C4—81no—
1141C22⋊C4—81no—
1142C22⋊C4—81no—
1143C22⋊C4—81no—
1144C22⋊C4—81no—
1145C22⋊C4—81no—
1146C22⋊C4—81no—
1147C22⋊C4—81no—
1148C22⋊C4—81no—
1149C22⋊C4—81no—
1150C42—21no—
1151C42—21no—
1152C42—21no—
1153C42—21no—
1154C42—21no—
1155C42—21no—
1156C42—21no—
1157C42—21no—
1158C42—21no—
1159C42—21no—
1160C42—21no—
1161C42—21no—
1162C42—81no—
1163C42—81no—
1164C42—81no—
1165C42—81no—
1166C23—21no—
1167C23—21no—
1168C23—22no—
1169C23—22no—
1170C23—21no—
1171C23—21no—
1172C23—21no—
1173C23—21no—
1174C23—21no—
1175C23—41no—
1176C23—41no—
1177C23—41no—
1178C23—41no—
1179C23—41no—
1180C23—41no—
1181C23—41no—
1182C23—41no—
1183C23—41no—
1184C23—41no—
1185C23—41no—
1186C23—41no—
1187C23—41no—
1188C23—41no—
1189C23—41no—
1190C23—41no—
1191C23—41no—
1192C23—41no—
1193C23—41no—
1194C23—41no—
1195C23—41no—
1196C23—41no—
1197C23—41no—
1198C23—41no—
1199C23—41no—
1200C23—41no—
1201C23—41no—
1202C23—41no—
1203C23—41no—
1204C23—41no—
1205C23—41no—
1206C23—41no—
1207C23—41no—
1208C23—41no—
1209C23—41no—
1210C23—41no—
1211C23—41no—
1212C23—41no—
1213C23—41no—
1214C23—41no—
1215C23—41no—
1216C23—41no—
1217C23—41no—
1218C23—41no—
1219C23—41no—
1220C23—41no—
1221C23—41no—
1222C23—84no—
1223C23—84no—
1224C23—162no—
1225C23—162no—
1226C23—162no—
1227C23—162no—
1228C23—162no—
1229C23C23×D411yescharacteristic
1230D4—22no—
1231D4—22no—
1232D4—22no—
1233D4—22no—
1234D4—41no—
1235D4—41no—
1236D4—41no—
1237D4—41no—
1238D4—41no—
1239D4—41no—
1240D4—41no—
1241D4—41no—
1242D4—41no—
1243D4—41no—
1244D4—41no—
1245D4—41no—
1246D4—41no—
1247D4—41no—
1248D4—41no—
1249D4—41no—
1250D4—41no—
1251D4—41no—
1252D4—41no—
1253D4—41no—
1254D4—41no—
1255D4—41no—
1256D4—41no—
1257D4—41no—
1258D4—84no—
1259D4—84no—
1260D4—84no—
1261D4—162no—
1262D4—162no—
1263D4—162no—
1264D4—162no—
1265D4—162no—
1266D4—162no—
1267D4—162no—
1268D4—162no—
1269D4—162no—
1270D4—162no—
1271D4—162no—
1272D4—162no—
1273D4—162no—
1274D4—162no—
1275D4—162no—
1276D4—162no—
1277D4—162no—
1278D4—162no—
1279D4—162no—
1280C2×C4—21no—
1281C2×C4—21no—
1282C2×C4—21no—
1283C2×C4—21no—
1284C2×C4—21no—
1285C2×C4—21no—
1286C2×C4—21no—
1287C2×C4—21no—
1288C2×C4—21no—
1289C2×C4—21no—
1290C2×C4—21no—
1291C2×C4—21no—
1292C2×C4—21no—
1293C2×C4—21no—
1294C2×C4—21no—
1295C2×C4—22no—
1296C2×C4—21no—
1297C2×C4—21no—
1298C2×C4—21no—
1299C2×C4—21no—
1300C2×C4—21no—
1301C2×C4—21no—
1302C2×C4—21no—
1303C2×C4—21no—
1304C2×C4—21no—
1305C2×C4—21no—
1306C2×C4—21no—
1307C2×C4—21no—
1308C2×C4—21no—
1309C2×C4—21no—
1310C2×C4—21no—
1311C2×C4—21no—
1312C2×C4—21no—
1313C2×C4—21no—
1314C2×C4—21no—
1315C2×C4—21no—
1316C2×C4—21no—
1317C2×C4—41no—
1318C2×C4—41no—
1319C2×C4—41no—
1320C2×C4—41no—
1321C2×C4—41no—
1322C2×C4—41no—
1323C2×C4—41no—
1324C2×C4—41no—
1325C2×C4—41no—
1326C2×C4—41no—
1327C2×C4—41no—
1328C2×C4—41no—
1329C2×C4—41no—
1330C2×C4—41no—
1331C2×C4—41no—
1332C2×C4—41no—
1333C2×C4—41no—
1334C2×C4—41no—
1335C2×C4—41no—
1336C2×C4—41no—
1337C2×C4—41no—
1338C2×C4—41no—
1339C2×C4—41no—
1340C2×C4—41no—
1341C2×C4—41no—
1342C2×C4—41no—
1343C2×C4—41no—
1344C2×C4—41no—
1345C2×C4—41no—
1346C2×C4—41no—
1347C2×C4—84no—
1348C2×C4—162no—
1349C2×C4—162no—
1350C2×C4—162no—
1351C2×C4—162no—
1352C2×C4—162no—
1353C2×C4—162no—
1354C2×C4—162no—
1355C2×C4—162no—
1356C2×C4#57612yes—
1357C2×C4#57612yes—
1358C2×C4#57612yes—
1359C2×C4C22×#4111yescharacteristic
1360C2×C4C2×H(5,𝔽2)11yescharacteristic
1361C2×C4C2×H(5,𝔽2)11yescharacteristic
1362C2×C4C2×H(5,𝔽2)11yescharacteristic
1363C2×C4#58511yescharacteristic
1364C2×C4#58511yescharacteristic
1365C8—22no—
1366C8—22no—
1367C8—22no—
1368C8—41no—
1369C8—41no—
1370C8—41no—
1371C8—41no—
1372C8—41no—
1373C22—42no—
1374C22—41no—
1375C22—41no—
1376C22—42no—
1377C22—42no—
1378C22—41no—
1379C22—42no—
1380C22—41no—
1381C22—41no—
1382C22—42no—
1383C22—42no—
1384C22—41no—
1385C22—41no—
1386C22—81no—
1387C22—81no—
1388C22—81no—
1389C22—81no—
1390C22—81no—
1391C22—81no—
1392C22—81no—
1393C22—81no—
1394C22—81no—
1395C22—81no—
1396C22—81no—
1397C22—81no—
1398C22—81no—
1399C22—81no—
1400C22—81no—
1401C22—81no—
1402C22—81no—
1403C22—81no—
1404C22—81no—
1405C22—81no—
1406C22—81no—
1407C22—81no—
1408C22—81no—
1409C22—81no—
1410C22—81no—
1411C22—81no—
1412C22—81no—
1413C22—81no—
1414C22—81no—
1415C22—81no—
1416C22—81no—
1417C22—81no—
1418C22—81no—
1419C22—81no—
1420C22—81no—
1421C22—81no—
1422C22—81no—
1423C22—81no—
1424C22—81no—
1425C22—81no—
1426C22—81no—
1427C22—81no—
1428C22—81no—
1429C22—168no—
1430C22D4×#4111yescharacteristic
1431C22#348811yescharacteristic
1432C22#349811yescharacteristic
1433C22C2×#57611yescharacteristic
1434C22C2×#57611yescharacteristic
1435C22C2×#57611yescharacteristic
1436C22#358511yescharacteristic
1437C4—22no—
1438C4—22no—
1439C4—22no—
1440C4—41no—
1441C4—42no—
1442C4—41no—
1443C4—41no—
1444C4—41no—
1445C4—41no—
1446C4—41no—
1447C4—41no—
1448C4—41no—
1449C4—41no—
1450C4—41no—
1451C4—81no—
1452C4—81no—
1453C4—81no—
1454C4—81no—
1455C4—81no—
1456C4—81no—
1457C4—81no—
1458C4—81no—
1459C4#350611yescharacteristic
1460C4#351911yescharacteristic
1461C4#353311yescharacteristic
1462C4#353411yescharacteristic
1463C2—81no—
1464C2—82no—
1465C2—82no—
1466C2—161no—
1467C2—161no—
1468C2—161no—
1469C2—161no—
1470C2—161no—
1471C2#4418411yescharacteristic
1472C2#6148011yescharacteristic
1473C2#6155511yescharacteristic
1474C2#6203111yescharacteristic
1475C2#6205111yescharacteristic
1476C2#6243111yescharacteristic
1477C2#6246311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2401 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #45033C2semidirect
2. #42589C2semidirect
3. #32533C2semidirect
4. #32162C2semidirect
5. #32094C2semidirect
6. #32061C2semidirect
7. #30890C2semidirect
8. #30605C2semidirect
9. #30444C2semidirect
10. #30444C2semidirect
11. #29564C2semidirect
12. #28950C2semidirect
13. #28916C2semidirect
14. #28624C2semidirect
15. #28458C2semidirect
16. #28353C2semidirect
17. #27065C2semidirect
18. #26619C2semidirect
19. #26601C2semidirect
20. #26548C2semidirect
21. #26254C2semidirect
22. #26174C2semidirect
23. #25426C2semidirect
24. #25364C2semidirect
25. #25148C2semidirect
26. #25097C2semidirect
27. #23810C2semidirect
28. #23287C2semidirect
29. #22995C2semidirect
30. #22868C2semidirect
31. #22158C2semidirect
34. C2×#493C22semidirect
35. C2×#490C22semidirect
43. C2×#459C22semidirect
48. C2×#442C22semidirect
50. C2×C4×D8C22semidirect
51. C2×C4×D8C22semidirect
69. #2541C22semidirect
71. #2512C22semidirect
72. #2509C22semidirect
78. #2445C22semidirect
90. #2366C22semidirect
93. D4×C4⋊C4C22semidirect
96. #2328C22semidirect
97. #2319C22semidirect
100. #2092C22semidirect
101. #2092C22semidirect
102. #2092C22semidirect
103. #2088C22semidirect
104. #2071C22semidirect
107. #2065C22semidirect
108. #2059C22semidirect
112. #2054C22semidirect
113. #2054C22semidirect
114. #2054C22semidirect
118. #2041C22semidirect
119. #2041C22semidirect
120. #2041C22semidirect
123. #2025C22semidirect
132. #2011C22semidirect
133. #2011C22semidirect
138. #1991C22semidirect
140. #1982C22semidirect
142. #1972C22semidirect
146. #1970C22semidirect
147. #1970C22semidirect
150. #1949C22semidirect
151. #1947C22semidirect
152. #1942C22semidirect
153. #1941C22semidirect
154. #1939C22semidirect
156. #1936C22semidirect
159. #1934C22semidirect
162. #1926C22semidirect
163. #1926C22semidirect
164. #1925C22semidirect
168. #1921C22semidirect
169. #1917C22semidirect
170. #1917C22semidirect
171. #1916C22semidirect
180. #1879C22semidirect
181. #1879C22semidirect
182. #1879C22semidirect
183. #1879C22semidirect
184. #1879C22semidirect
186. #1864C22semidirect
187. #1864C22semidirect
188. #1864C22semidirect
191. #1862C22semidirect
194. #1804C22semidirect
195. C8×C4⋊C4C22semidirect
196. C8×C4⋊C4C22semidirect
197. #1768C22semidirect
199. C4×#102C22semidirect
202. #1746C22semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#450332
#425892
#325332
#321622
#320942
#320612
#308902
#306052
#304442
#295642
#289502
#289162
#286242
#284582
#283532
#270652
#266192
#266012
#265482
#262542
#261742
#254262
#253642
#251482
#250972
#238102
#232872
#229952
#228682
#221582