Finite Group Databasebeta

← #62309

Subgroups — #62309

Order 256.

899 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3541C211yesmaximal, characteristic, complemented
2#3540C211yesmaximal, characteristic, complemented
3#3357C211yesmaximal, characteristic, complemented
4#3350C211yesmaximal, characteristic, complemented
5#3348C211yesmaximal, characteristic, complemented
6#3342C211yesmaximal, characteristic, complemented
7#3328C211yesmaximal, characteristic, complemented
8#3322C211yesmaximal, characteristic, complemented
9#3321C211yesmaximal, characteristic, complemented
10#3316C211yesmaximal, characteristic, complemented
11#3313C211yesmaximal, characteristic, complemented
12#3311C211yesmaximal, characteristic, complemented
13#3303C211yesmaximal, characteristic, complemented
14#3300C211yesmaximal, characteristic, complemented
15#3282C211yesmaximal, characteristic, complemented
16#3277C211yesmaximal, characteristic, complemented
17#3269C211yesmaximal, characteristic, complemented
18#3266C211yesmaximal, characteristic, complemented
19#3263C211yesmaximal, characteristic, complemented
20#3258C211yesmaximal, characteristic, complemented
21#3202C211yesmaximal, characteristic, complemented
22#3198C211yesmaximal, characteristic, complemented
23#3191C211yesmaximal, characteristic, complemented
24#3190C211yesmaximal, characteristic, complemented
25#3178C211yesmaximal, characteristic, complemented
26#3175C211yesmaximal, characteristic, complemented
27#3063C211yesmaximal, characteristic, complemented
28#3057C211yesmaximal, characteristic, complemented
29#3056C211yesmaximal, characteristic, complemented
30#3054C211yesmaximal, characteristic, complemented
31#2933C211yesmaximal, characteristic, complemented
32C2×#137C2211yescharacteristic
33C2×#137C2211yescharacteristic, complemented
34C2×#135C2211yescharacteristic
35C22×SD16C2211yescharacteristic, complemented
36C2×#131C2211yescharacteristic
37C22×M16C2211yescharacteristic, complemented
38#563—21no—
39#562—21no—
40H(3,𝔽4)—21no—
41#560—21no—
42#559—21no—
43#556C2211yescharacteristic
44#556C2211yescharacteristic
45#556C2211yescharacteristic
46#555C2211yescharacteristic
47#555C2211yescharacteristic
48#554—21no—
49#554C2211yescharacteristic, complemented
50#553—21no—
51#553C2211yescharacteristic
52#552C2211yescharacteristic, complemented
53#551—21no—
54D4×Q8C2211yescharacteristic
55#548C2211yescharacteristic
56#548C2211yescharacteristic
57#548C2211yescharacteristic
58#548C2211yescharacteristic, complemented
59#547C2211yescharacteristic, complemented
60#546C2211yescharacteristic
61#546C2211yescharacteristic
62#542—21no—
63#542—21no—
64#542—21no—
65#542C2211yescharacteristic
66#542C2211yescharacteristic
67#542C2211yescharacteristic, complemented
68#541C2211yescharacteristic, complemented
69#539—21no—
70#538—21no—
71#538—21no—
72#538—21no—
73#538—21no—
74#537C2211yescharacteristic
75#536C2211yescharacteristic
76#536C2211yescharacteristic
77#535C2211yescharacteristic
78#525C2211yescharacteristic
79#525C2211yescharacteristic
80#525C2211yescharacteristic
81#525C2211yescharacteristic, complemented
82C2×C22⋊Q8C2211yescharacteristic, complemented
83#501C2211yescharacteristic, complemented
84#500C2211yescharacteristic, complemented
85#497C2211yescharacteristic, complemented
86#495C2211yescharacteristic, complemented
87#489C2211yescharacteristic, complemented
88#489C2211yescharacteristic, complemented
89#488C2211yescharacteristic, complemented
90#487C2211yescharacteristic, complemented
91#485C2211yescharacteristic, complemented
92#485C2211yescharacteristic, complemented
93#485C2211yescharacteristic, complemented
94#485C2211yescharacteristic, complemented
95#485C2211yescharacteristic, complemented
96#485C2211yescharacteristic, complemented
97#485C2211yescharacteristic, complemented
98#485C2211yescharacteristic, complemented
99#485C2211yescharacteristic, complemented
100#483C2211yescharacteristic, complemented
101#482C2211yescharacteristic
102#482C2211yescharacteristic, complemented
103#482C2211yescharacteristic, complemented
104#481C2211yescharacteristic, complemented
105#480C2211yescharacteristic
106#480C2211yescharacteristic, complemented
107#479C2211yescharacteristic, complemented
108#478C2211yescharacteristic, complemented
109#477C2211yescharacteristic, complemented
110#476C2211yescharacteristic, complemented
111#476C2211yescharacteristic, complemented
112#475C2211yescharacteristic, complemented
113#475C2211yescharacteristic, complemented
114#475C2211yescharacteristic, complemented
115#470C2211yescharacteristic, complemented
116#470C2211yescharacteristic, complemented
117#470C2211yescharacteristic, complemented
118#470C2211yescharacteristic, complemented
119#470C2211yescharacteristic, complemented
120#469C2211yescharacteristic
121#469C2211yescharacteristic
122#468C2211yescharacteristic
123#468C2211yescharacteristic
124#468C2211yescharacteristic
125#468C2211yescharacteristic
126#468C2211yescharacteristic, complemented
127#468C2211yescharacteristic, complemented
128#468C2211yescharacteristic, complemented
129#468C2211yescharacteristic, complemented
130#468C2211yescharacteristic, complemented
131#467C2211yescharacteristic, complemented
132#467C2211yescharacteristic, complemented
133#467C2211yescharacteristic, complemented
134#467C2211yescharacteristic, complemented
135#467C2211yescharacteristic, complemented
136#467C2211yescharacteristic, complemented
137#466C2211yescharacteristic
138#465C2211yescharacteristic
139#465C2211yescharacteristic
140#465C2211yescharacteristic
141#465C2211yescharacteristic
142#465C2211yescharacteristic
143#465C2211yescharacteristic, complemented
144#465C2211yescharacteristic, complemented
145#465C2211yescharacteristic, complemented
146#465C2211yescharacteristic, complemented
147#464C2211yescharacteristic, complemented
148#464C2211yescharacteristic, complemented
149#464C2211yescharacteristic, complemented
150#464C2211yescharacteristic, complemented
151#463C2211yescharacteristic, complemented
152#463C2211yescharacteristic, complemented
153#462C2211yescharacteristic, complemented
154#461C2211yescharacteristic, complemented
155#452C2211yescharacteristic
156#452C2211yescharacteristic
157#452C2211yescharacteristic
158#452C2211yescharacteristic, complemented
159#451C2211yescharacteristic, complemented
160#451C2211yescharacteristic, complemented
161#451C2211yescharacteristic, complemented
162#451C2211yescharacteristic, complemented
163#451C2211yescharacteristic, complemented
164#450C2211yescharacteristic, complemented
165#449C2211yescharacteristic
166#449C2211yescharacteristic
167#449C2211yescharacteristic, complemented
168#449C2211yescharacteristic, complemented
169#448C2211yescharacteristic
170#447C2211yescharacteristic, complemented
171#441C2211yescharacteristic, complemented
172#440C2211yescharacteristic, complemented
173#440C2211yescharacteristic, complemented
174#440C2211yescharacteristic, complemented
175C4×Q16C2211yescharacteristic, complemented
176C4×Q16C2211yescharacteristic, complemented
177C4×SD16C2211yescharacteristic, complemented
178C4×D8C2211yescharacteristic, complemented
179#436C2211yescharacteristic
180#436C2211yescharacteristic, complemented
181#435C2211yescharacteristic
182#435C2211yescharacteristic
183#435C2211yescharacteristic, complemented
184#435C2211yescharacteristic, complemented
185C8×D4C2211yescharacteristic
186C8×D4C2211yescharacteristic, complemented
187#428C2211yescharacteristic, complemented
188#428C2211yescharacteristic, complemented
189#427C2211yescharacteristic, complemented
190#427C2211yescharacteristic, complemented
191#424C2211yescharacteristic, complemented
192#419C2211yescharacteristic, complemented
193#419C2211yescharacteristic, complemented
194#418C2211yescharacteristic, complemented
195#417C2211yescharacteristic
196#416C2211yescharacteristic
197#416C2211yescharacteristic, complemented
198#416C2211yescharacteristic, complemented
199C2×#103C2211yescharacteristic, complemented
200#408C2211yescharacteristic
201C2×C22⋊C8C2211yescharacteristic, complemented
202#405C2211yescharacteristic, complemented
203C2×#41C2311yescharacteristic
204C2×#41C2311yescharacteristic
205C2×#41C2311yescharacteristic
206C2×#41C2311yescharacteristic
207C2×#41C2311yescharacteristic
208C22×Q8C2311yescharacteristic
209C22×Q8C2311yescharacteristic
210C22×Q8C2311yescharacteristic
211C22×D4C2311yescharacteristic
212C23×C4C2311yescharacteristic
213#137—42no—
214#137—42no—
215#135—42no—
216C2×Q16C2311yescharacteristic
217C2×Q16C2311yescharacteristic
218C2×Q16C2311yescharacteristic
219C2×Q16C2311yescharacteristic
220C2×Q16C2311yescharacteristic
221C2×Q16C2311yescharacteristic
222C2×SD16—42no—
223C2×SD16C2311yescharacteristic
224C2×SD16C2311yescharacteristic
225C2×SD16C2311yescharacteristic
226C2×SD16C2311yescharacteristic
227C2×SD16C2311yescharacteristic
228C2×SD16C2311yescharacteristic
229C2×SD16C2311yescharacteristic
230C2×SD16C2311yescharacteristic
231C2×D8C2311yescharacteristic
232C2×D8C2311yescharacteristic
233#131—42no—
234C2×M16—42no—
235C2×M16C2311yescharacteristic
236C2×M16C2311yescharacteristic
237C2×M16C2311yescharacteristic
238C2×M16C2311yescharacteristic
239C2×M16C2311yescharacteristic
240C2×M16C2311yescharacteristic
241C22×C8C2311yescharacteristic
242C22×C8C2311yescharacteristic
243C22×C8C2311yescharacteristic
244C22×C8C2311yescharacteristic
245C22×C8C2311yescharacteristic
246C22×C8C2311yescharacteristic
247C4⋊Q8—21no—
248C4⋊Q8—21no—
249C4⋊Q8—21no—
250C4⋊Q8C2311yescharacteristic
251C4⋊Q8C2311yescharacteristic
252C4⋊Q8C2311yescharacteristic
253C4⋊Q8C2311yescharacteristic
254#127—21no—
255#126—21no—
256#126—21no—
257#126—21no—
258#126—21no—
259#126—21no—
260#126—21no—
261#126—21no—
262#126—21no—
263#126—21no—
264#126—21no—
265#126—21no—
266#126—21no—
267#126—21no—
268#125—21no—
269#125—21no—
270#125—21no—
271#125—21no—
272#125C2311yescharacteristic
273#124—21no—
274#124—21no—
275#124—21no—
276#124—21no—
277#124—21no—
278#124—21no—
279#124—21no—
280#124—21no—
281#124—21no—
282#124—21no—
283#124—21no—
284#124—21no—
285#124—21no—
286#124—21no—
287#124—21no—
288#124—21no—
289#124—21no—
290#124C2311yescharacteristic
291#124C2311yescharacteristic
292#124C2311yescharacteristic
293#123—21no—
294#123—21no—
295#123—21no—
296#123—21no—
297#123—21no—
298#123—21no—
299#123—21no—
300#123—21no—
301#123—21no—
302#123—21no—
303#123—21no—
304#123—21no—
305#123—21no—
306#123—21no—
307#123—21no—
308#123—21no—
309#123D411yescharacteristic
310#123D411yescharacteristic
311C22⋊Q8—21no—
312C22⋊Q8—21no—
313C22⋊Q8—21no—
314C22⋊Q8—21no—
315C22⋊Q8—21no—
316C22⋊Q8—21no—
317C22⋊Q8—21no—
318C22⋊Q8—21no—
319C22⋊Q8—21no—
320C22⋊Q8—21no—
321C22⋊Q8—21no—
322C22⋊Q8—21no—
323C22⋊Q8—21no—
324C22⋊Q8—21no—
325C22⋊Q8D411yescharacteristic
326C22⋊Q8D411yescharacteristic
327C22⋊Q8C2311yescharacteristic
328C22⋊Q8C2311yescharacteristic
329C22⋊Q8C2311yescharacteristic
330C22⋊Q8C2311yescharacteristic
331C22⋊Q8C2311yescharacteristic
332C22⋊Q8C2311yescharacteristic
333C22⋊Q8C2311yescharacteristic
334C22⋊Q8C2311yescharacteristic
335C22⋊Q8C2311yescharacteristic
336C22⋊Q8C2311yescharacteristic
337C22⋊Q8C2311yescharacteristic
338C22⋊Q8C2311yescharacteristic
339C22⋊Q8C2311yescharacteristic
340C22⋊Q8C2311yescharacteristic
341C22⋊Q8C2311yescharacteristic
342#121—21no—
343#121—21no—
344#121—21no—
345#121—21no—
346#121—21no—
347#121—21no—
348#121—21no—
349#121—21no—
350#121—21no—
351#121—21no—
352#121—21no—
353#121—21no—
354#121—21no—
355#121D411yescharacteristic
356#121D411yescharacteristic
357#121C2311yescharacteristic
358#121C2311yescharacteristic
359#121C2311yescharacteristic
360#121C2311yescharacteristic
361#121C2311yescharacteristic
362#121C2311yescharacteristic
363#121C2311yescharacteristic
364#121C2311yescharacteristic
365#121C2311yescharacteristic
366#120—21no—
367#120—21no—
368#120—21no—
369#120—21no—
370#120—21no—
371#120—21no—
372#120—21no—
373#120D411yescharacteristic
374#120D411yescharacteristic
375C4×Q8—21no—
376C4×Q8—21no—
377C4×Q8—21no—
378C4×Q8C2311yescharacteristic
379C4×Q8C2311yescharacteristic
380C4×Q8C2311yescharacteristic
381C4×Q8C2311yescharacteristic
382C4×Q8C2311yescharacteristic
383C4×D4—21no—
384C4×D4—21no—
385C4×D4—21no—
386C4×D4—21no—
387C4×D4—21no—
388C4×D4—21no—
389C4×D4—21no—
390C4×D4—21no—
391C4×D4—21no—
392C4×D4—21no—
393C4×D4—21no—
394C4×D4—21no—
395C4×D4—21no—
396C4×D4C2311yescharacteristic
397C4×D4C2311yescharacteristic
398C4×D4C2311yescharacteristic
399C4×D4C2311yescharacteristic
400C4×D4C2311yescharacteristic
401C4×D4C2311yescharacteristic
402C4×D4C2311yescharacteristic
403#117—21no—
404#117—21no—
405#117—21no—
406#117C2311yescharacteristic
407#117C2311yescharacteristic
408#117C2311yescharacteristic
409#117C2311yescharacteristic
410#117C2311yescharacteristic
411#117C2311yescharacteristic
412#117C2311yescharacteristic
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4C2311yescharacteristic
416C2×C4⋊C4C2311yescharacteristic
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420#107C2311yescharacteristic
421#107C2311yescharacteristic
422#107C2311yescharacteristic
423#107C2311yescharacteristic
424#107C2311yescharacteristic
425#107C2311yescharacteristic
426#107C2311yescharacteristic
427#107C2311yescharacteristic
428#106C2311yescharacteristic
429#106C2311yescharacteristic
430#106C2311yescharacteristic
431#106C2311yescharacteristic
432#106C2311yescharacteristic
433#106C2311yescharacteristic
434#106C2311yescharacteristic
435#106C2311yescharacteristic
436C4⋊C8C2311yescharacteristic
437C4⋊C8C2311yescharacteristic
438C4⋊C8C2311yescharacteristic
439C4⋊C8C2311yescharacteristic
440#103C2311yescharacteristic
441#103C2311yescharacteristic
442#103C2311yescharacteristic
443#103C2311yescharacteristic
444#103C2311yescharacteristic
445#103C2311yescharacteristic
446#103C2311yescharacteristic
447#103C2311yescharacteristic
448#103C2311yescharacteristic
449#103C2311yescharacteristic
450#103C2311yescharacteristic
451#103C2311yescharacteristic
452#103C2311yescharacteristic
453#103C2311yescharacteristic
454#103C2311yescharacteristic
455#103C2311yescharacteristic
456#103C2311yescharacteristic
457#103C2311yescharacteristic
458#103C2311yescharacteristic
459#103C2311yescharacteristic
460#102C2311yescharacteristic
461#102C2311yescharacteristic
462#102C2311yescharacteristic
463#102C2311yescharacteristic
464#102C2311yescharacteristic
465#102C2311yescharacteristic
466#102C2311yescharacteristic
467#102C2311yescharacteristic
468#102C2311yescharacteristic
469#102C2311yescharacteristic
470#102C2311yescharacteristic
471#102C2311yescharacteristic
472C22⋊C8C2311yescharacteristic
473C22⋊C8C2311yescharacteristic
474C22⋊C8C2311yescharacteristic
475C22⋊C8C2311yescharacteristic
476C22⋊C8C2311yescharacteristic
477C22⋊C8C2311yescharacteristic
478C22⋊C8C2311yescharacteristic
479C22⋊C8C2311yescharacteristic
480#97C2311yescharacteristic
481#97C2311yescharacteristic
482C4×C8C2311yescharacteristic
483C4×C8C2311yescharacteristic
484C24—21no—
485C24C2×D411yescharacteristic
486#41—41no—
487#41—41no—
488#41—41no—
489#41—41no—
490#41—41no—
491#41—41no—
492#41—41no—
493#41—41no—
494#41—41no—
495#41—41no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—41no—
503C2×Q8—41no—
504C2×Q8—41no—
505C2×Q8—41no—
506C2×Q8—41no—
507C2×Q8—41no—
508C2×Q8C2×D411yescharacteristic
509C2×Q8C2411yescharacteristic
510C2×Q8C2411yescharacteristic
511C2×Q8C2411yescharacteristic
512C2×Q8C2411yescharacteristic
513C2×Q8C2411yescharacteristic
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—41no—
529C2×D4—41no—
530C2×D4C2×D411yescharacteristic
531C2×D4C2×D411yescharacteristic
532C2×D4C2×D411yescharacteristic
533C2×D4C2×D411yescharacteristic
534C2×D4C2×D411yescharacteristic
535C2×D4C2×D411yescharacteristic
536C2×D4C2×D411yescharacteristic
537C2×D4C2411yescharacteristic
538C2×D4C2411yescharacteristic
539C2×D4C2411yescharacteristic
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4C2×D411yescharacteristic
555C22×C4C2×D411yescharacteristic
556C22×C4C2×D411yescharacteristic
557C22×C4C2411yescharacteristic
558C22×C4C2411yescharacteristic
559C22×C4C2411yescharacteristic
560C22×C4C2411yescharacteristic
561C22×C4C2411yescharacteristic
562Q16—22no—
563Q16—41no—
564Q16—41no—
565Q16—41no—
566Q16—41no—
567Q16—41no—
568SD16—22no—
569SD16—22no—
570SD16—22no—
571SD16—41no—
572SD16—41no—
573SD16—41no—
574SD16—41no—
575SD16—41no—
576D8—41no—
577D8—41no—
578M16—22no—
579M16—22no—
580M16—22no—
581M16—41no—
582M16—41no—
583M16—41no—
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—41no—
587C2×C8—41no—
588C2×C8—41no—
589C2×C8—41no—
590C2×C8C2411yescharacteristic
591C2×C8C2411yescharacteristic
592C2×C8C2411yescharacteristic
593C2×C8C2411yescharacteristic
594C2×C8C2411yescharacteristic
595C2×C8C2411yescharacteristic
596C2×C8C2411yescharacteristic
597C2×C8C2411yescharacteristic
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4C2×D411yescharacteristic
628C4⋊C4C2×D411yescharacteristic
629C4⋊C4C2×D411yescharacteristic
630C4⋊C4C2×D411yescharacteristic
631C4⋊C4C2×D411yescharacteristic
632C4⋊C4C2×D411yescharacteristic
633C4⋊C4C2411yescharacteristic
634C4⋊C4C2411yescharacteristic
635C4⋊C4C2411yescharacteristic
636C4⋊C4C2411yescharacteristic
637C4⋊C4C2411yescharacteristic
638C4⋊C4C2411yescharacteristic
639C4⋊C4C2411yescharacteristic
640C4⋊C4C2411yescharacteristic
641C22⋊C4—21no—
642C22⋊C4—21no—
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4—21no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—21no—
659C22⋊C4—21no—
660C22⋊C4—21no—
661C22⋊C4—21no—
662C22⋊C4—21no—
663C22⋊C4—21no—
664C22⋊C4—21no—
665C22⋊C4—21no—
666C22⋊C4—21no—
667C22⋊C4—21no—
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—21no—
671C22⋊C4—21no—
672C22⋊C4—21no—
673C22⋊C4—21no—
674C22⋊C4—21no—
675C22⋊C4—21no—
676C22⋊C4—21no—
677C22⋊C4—21no—
678C22⋊C4—21no—
679C22⋊C4—21no—
680C22⋊C4C2×D411yescharacteristic
681C22⋊C4C2×D411yescharacteristic
682C22⋊C4C2×D411yescharacteristic
683C22⋊C4C2×D411yescharacteristic
684C22⋊C4C2×D411yescharacteristic
685C22⋊C4C2×D411yescharacteristic
686C22⋊C4C2×D411yescharacteristic
687C22⋊C4C2×D411yescharacteristic
688C22⋊C4C2×D411yescharacteristic
689C22⋊C4C2×D411yescharacteristic
690C42—21no—
691C42—21no—
692C42—21no—
693C42—21no—
694C42—21no—
695C42—21no—
696C42—21no—
697C42—21no—
698C42—21no—
699C42—21no—
700C42—21no—
701C42C2411yescharacteristic
702C42C2411yescharacteristic
703C23—21no—
704C23—21no—
705C23—21no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—81no—
710C23—81no—
711C23—81no—
712C23C22×D411yescharacteristic
713C23C22×D411yescharacteristic
714C23C22×D411yescharacteristic
715C23C22×D411yescharacteristic
716C23C22×D411yescharacteristic
717Q8—21no—
718Q8—21no—
719Q8—21no—
720Q8—21no—
721Q8—21no—
722Q8—21no—
723Q8—21no—
724Q8—21no—
725Q8—21no—
726Q8—21no—
727Q8—41no—
728Q8—81no—
729Q8—81no—
730Q8—81no—
731Q8—81no—
732Q8—81no—
733Q8—81no—
734D4—21no—
735D4—21no—
736D4—21no—
737D4—21no—
738D4—21no—
739D4—21no—
740D4—41no—
741D4—41no—
742D4—41no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—42no—
748D4—81no—
749D4—81no—
750D4—81no—
751D4—81no—
752D4—81no—
753D4—81no—
754D4—81no—
755D4—81no—
756D4—81no—
757D4—81no—
758D4—81no—
759D4—81no—
760D4—81no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—81no—
788C2×C4—81no—
789C2×C4—81no—
790C2×C4—81no—
791C2×C4—81no—
792C2×C4—81no—
793C2×C4—81no—
794C2×C4—81no—
795C2×C4—81no—
796C2×C4—81no—
797C2×C4—81no—
798C2×C4—81no—
799C2×C4C22×D411yescharacteristic
800C2×C4C22×D411yescharacteristic
801C2×C4C22×D411yescharacteristic
802C2×C4C22×D411yescharacteristic
803C2×C4C22×D411yescharacteristic
804C2×C4C22×D411yescharacteristic
805C2×C4C22×D411yescharacteristic
806C2×C4C22×D411yescharacteristic
807C2×C4C22×D411yescharacteristic
808C2×C4C2511yescharacteristic
809C8—21no—
810C8—21no—
811C8—21no—
812C8—21no—
813C8—21no—
814C8—21no—
815C8—21no—
816C8H(5,𝔽2)12yes—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—21no—
827C22—21no—
828C22—21no—
829C22—21no—
830C22—21no—
831C22—21no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—41no—
841C22—82no—
842C22—162no—
843C22C23×D411yescharacteristic
844C4—21no—
845C4—21no—
846C4—21no—
847C4—21no—
848C4—21no—
849C4—21no—
850C4—21no—
851C4—21no—
852C4—21no—
853C4—41no—
854C4—41no—
855C4—41no—
856C4—41no—
857C4—41no—
858C4—41no—
859C4—41no—
860C4—41no—
861C4—41no—
862C4—41no—
863C4—41no—
864C4—41no—
865C4—41no—
866C4C2×H(5,𝔽2)11yescharacteristic
867C4#58511yescharacteristic
868C2—41no—
869C2—41no—
870C2—41no—
871C2—41no—
872C2—41no—
873C2—81no—
874C2—81no—
875C2—81no—
876C2#349611yescharacteristic
877C2#358411yescharacteristic
878C2#358611yescharacteristic
subgroupG/H
center, socleC22C23×D4
commutator, Frattini, cosocleC2×C4C25
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #525 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #3541C2semidirect
2. #3540C2semidirect
3. #3357C2semidirect
4. #3350C2semidirect
5. #3348C2semidirect
6. #3342C2semidirect
7. #3328C2semidirect
8. #3322C2semidirect
9. #3321C2semidirect
10. #3316C2semidirect
11. #3313C2semidirect
12. #3311C2semidirect
13. #3303C2semidirect
14. #3300C2semidirect
15. #3282C2semidirect
16. #3277C2semidirect
17. #3269C2semidirect
18. #3266C2semidirect
19. #3263C2semidirect
20. #3258C2semidirect
21. #3202C2semidirect
22. #3198C2semidirect
23. #3191C2semidirect
24. #3190C2semidirect
25. #3178C2semidirect
26. #3175C2semidirect
27. #3063C2semidirect
28. #3057C2semidirect
29. #3056C2semidirect
30. #3054C2semidirect
31. #2933C2semidirect
33. C2×#137C22semidirect
35. C22×SD16C22semidirect
37. C22×M16C22semidirect
49. #554C22semidirect
52. #552C22semidirect
58. #548C22semidirect
59. #547C22semidirect
67. #542C22semidirect
68. #541C22semidirect
81. #525C22semidirect
82. C2×C22⋊Q8C22semidirect
83. #501C22semidirect
84. #500C22semidirect
85. #497C22semidirect
86. #495C22semidirect
87. #489C22semidirect
88. #489C22semidirect
89. #488C22semidirect
90. #487C22semidirect
91. #485C22semidirect
92. #485C22semidirect
93. #485C22semidirect
94. #485C22semidirect
95. #485C22semidirect
96. #485C22semidirect
97. #485C22semidirect
98. #485C22semidirect
99. #485C22semidirect
100. #483C22semidirect
102. #482C22semidirect
103. #482C22semidirect
104. #481C22semidirect
106. #480C22semidirect
107. #479C22semidirect
108. #478C22semidirect
109. #477C22semidirect
110. #476C22semidirect
111. #476C22semidirect
112. #475C22semidirect
113. #475C22semidirect
114. #475C22semidirect
115. #470C22semidirect
116. #470C22semidirect
117. #470C22semidirect
118. #470C22semidirect
119. #470C22semidirect
126. #468C22semidirect
127. #468C22semidirect
128. #468C22semidirect
129. #468C22semidirect
130. #468C22semidirect
131. #467C22semidirect
132. #467C22semidirect
133. #467C22semidirect
134. #467C22semidirect
135. #467C22semidirect
136. #467C22semidirect
143. #465C22semidirect
144. #465C22semidirect
145. #465C22semidirect
146. #465C22semidirect
147. #464C22semidirect
148. #464C22semidirect
149. #464C22semidirect
150. #464C22semidirect
151. #463C22semidirect
152. #463C22semidirect
153. #462C22semidirect
154. #461C22semidirect
158. #452C22semidirect
159. #451C22semidirect
160. #451C22semidirect
161. #451C22semidirect
162. #451C22semidirect
163. #451C22semidirect
164. #450C22semidirect
167. #449C22semidirect
168. #449C22semidirect
170. #447C22semidirect
171. #441C22semidirect
172. #440C22semidirect
173. #440C22semidirect
174. #440C22semidirect
175. C4×Q16C22semidirect
176. C4×Q16C22semidirect
177. C4×SD16C22semidirect
178. C4×D8C22semidirect
180. #436C22semidirect
183. #435C22semidirect
184. #435C22semidirect
186. C8×D4C22semidirect
187. #428C22semidirect
188. #428C22semidirect
189. #427C22semidirect
190. #427C22semidirect
191. #424C22semidirect
192. #419C22semidirect
193. #419C22semidirect
194. #418C22semidirect
197. #416C22semidirect
198. #416C22semidirect
199. C2×#103C22semidirect
201. C2×C22⋊C8C22semidirect
202. #405C22semidirect

Maximal subgroups

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

subgroupindex
#35412
#35402
#33572
#33502
#33482
#33422
#33282
#33222
#33212
#33162
#33132
#33112
#33032
#33002
#32822
#32772
#32692
#32662
#32632
#32582
#32022
#31982
#31912
#31902
#31782
#31752
#30632
#30572
#30562
#30542
#29332