Finite Group Databasebeta

← #62321

Subgroups — #62321

Order 256.

918 conjugacy classes of subgroups.

The subgroup lattice has 887 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3541C211yesmaximal, characteristic, complemented
2#3536C211yesmaximal, characteristic, complemented
3#3356C211yesmaximal, characteristic, complemented
4#3345C211yesmaximal, characteristic, complemented
5#3344C211yesmaximal, characteristic, complemented
6#3335C211yesmaximal, characteristic, complemented
7#3331C211yesmaximal, characteristic, complemented
8#3323C211yesmaximal, characteristic, complemented
9#3316C211yesmaximal, characteristic, complemented
10#3316C211yesmaximal, characteristic, complemented
11#3311C211yesmaximal, characteristic, complemented
12#3308C211yesmaximal, characteristic, complemented
13#3301C211yesmaximal, characteristic, complemented
14#3298C211yesmaximal, characteristic, complemented
15#3285C211yesmaximal, characteristic, complemented
16#3275C211yesmaximal, characteristic, complemented
17#3270C211yesmaximal, characteristic, complemented
18#3267C211yesmaximal, characteristic, complemented
19#3263C211yesmaximal, characteristic, complemented
20#3258C211yesmaximal, characteristic, complemented
21#3204C211yesmaximal, characteristic, complemented
22#3201C211yesmaximal, characteristic, complemented
23#3190C211yesmaximal, characteristic, complemented
24#3187C211yesmaximal, characteristic, complemented
25#3178C211yesmaximal, characteristic, complemented
26#3173C211yesmaximal, characteristic, complemented
27#3063C211yesmaximal, characteristic, complemented
28#3060C211yesmaximal, characteristic, complemented
29#3055C211yesmaximal, characteristic, complemented
30C2×#470C211yesmaximal, characteristic, complemented
31#2933C211yesmaximal, characteristic, complemented
32C2×#137C2211yescharacteristic, complemented
33C2×AGL(1,ℤ/8)C2211yescharacteristic
34C2×#135C2211yescharacteristic, complemented
35C22×Q16C2211yescharacteristic, complemented
36C2×#131C2211yescharacteristic, complemented
37C22×M16C2211yescharacteristic
38#563—21no—
39#562—21no—
40#562—21no—
41#562—21no—
42#556C2211yescharacteristic
43#554—21no—
44#554C2211yescharacteristic
45#554C2211yescharacteristic
46#554C2211yescharacteristic, complemented
47#553—21no—
48#553C2211yescharacteristic, complemented
49#552C2211yescharacteristic
50D4×Q8C2211yescharacteristic, complemented
51#548C2211yescharacteristic
52#548C2211yescharacteristic
53#548C2211yescharacteristic
54#548C2211yescharacteristic, complemented
55#547C2211yescharacteristic
56#547C2211yescharacteristic
57#547C2211yescharacteristic
58#546—21no—
59#546—21no—
60#546C2211yescharacteristic
61#546C2211yescharacteristic
62#543—21no—
63#542—21no—
64#542C2211yescharacteristic
65#542C2211yescharacteristic
66#542C2211yescharacteristic, complemented
67#541C2211yescharacteristic, complemented
68#539—21no—
69#539—21no—
70#538—21no—
71#538—21no—
72#538—21no—
73#537—21no—
74#537C2211yescharacteristic
75#537C2211yescharacteristic
76#537C2211yescharacteristic, complemented
77#536C2211yescharacteristic, complemented
78#525C2211yescharacteristic
79#525C2211yescharacteristic
80C2×C22⋊Q8C2211yescharacteristic
81C2×C22⋊Q8C2211yescharacteristic
82C2×#121C2211yescharacteristic
83#501C2211yescharacteristic, complemented
84#498C2211yescharacteristic, complemented
85#497C2211yescharacteristic, complemented
86#495C2211yescharacteristic, complemented
87#489C2211yescharacteristic, complemented
88#489C2211yescharacteristic, complemented
89#488C2211yescharacteristic, complemented
90#487C2211yescharacteristic, complemented
91#485C2211yescharacteristic
92#485C2211yescharacteristic
93#485C2211yescharacteristic, complemented
94#484C2211yescharacteristic, complemented
95#483C2211yescharacteristic
96#483C2211yescharacteristic
97#483C2211yescharacteristic, complemented
98#483C2211yescharacteristic, complemented
99#483C2211yescharacteristic, complemented
100#483C2211yescharacteristic, complemented
101#482C2211yescharacteristic, complemented
102#481C2211yescharacteristic
103#481C2211yescharacteristic
104#481C2211yescharacteristic, complemented
105#481C2211yescharacteristic, complemented
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
116#470C2211yescharacteristic
117#470C2211yescharacteristic
118#470C2211yescharacteristic
119#470C2211yescharacteristic, complemented
120#470C2211yescharacteristic, complemented
121#470C2211yescharacteristic, complemented
122#470C2211yescharacteristic, complemented
123#470C2211yescharacteristic, complemented
124#470C2211yescharacteristic, complemented
125#469C2211yescharacteristic
126#469C2211yescharacteristic
127#469C2211yescharacteristic, complemented
128#468C2211yescharacteristic
129#468C2211yescharacteristic
130#468C2211yescharacteristic, complemented
131#467C2211yescharacteristic, complemented
132#467C2211yescharacteristic, complemented
133#467C2211yescharacteristic, complemented
134#466C2211yescharacteristic
135#466C2211yescharacteristic
136#465C2211yescharacteristic
137#465C2211yescharacteristic
138#465C2211yescharacteristic
139#465C2211yescharacteristic
140#465C2211yescharacteristic
141#465C2211yescharacteristic
142#465C2211yescharacteristic, complemented
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, complemented
158#452C2211yescharacteristic, complemented
159#452C2211yescharacteristic, complemented
160#452C2211yescharacteristic, complemented
161#451C2211yescharacteristic, complemented
162#451C2211yescharacteristic, complemented
163#450C2211yescharacteristic
164#450C2211yescharacteristic
165#449C2211yescharacteristic, complemented
166#449C2211yescharacteristic, complemented
167#448C2211yescharacteristic
168#448C2211yescharacteristic
169#448C2211yescharacteristic, complemented
170#448C2211yescharacteristic, complemented
171#442C2211yescharacteristic, complemented
172#441C2211yescharacteristic, complemented
173#441C2211yescharacteristic, complemented
174#440C2211yescharacteristic, complemented
175C4×Q16C2211yescharacteristic, complemented
176C4×SD16C2211yescharacteristic, complemented
177C4×SD16C2211yescharacteristic, complemented
178C4×SD16C2211yescharacteristic, complemented
179#436C2211yescharacteristic
180#436C2211yescharacteristic
181#435C2211yescharacteristic
182#435C2211yescharacteristic
183#435C2211yescharacteristic, complemented
184#435C2211yescharacteristic, complemented
185C8×D4C2211yescharacteristic, complemented
186C8×D4C2211yescharacteristic, complemented
187#428C2211yescharacteristic
188#428C2211yescharacteristic, complemented
189C2×#106C2211yescharacteristic, complemented
190C2×#106C2211yescharacteristic, complemented
191#424C2211yescharacteristic, complemented
192#418C2211yescharacteristic
193#417C2211yescharacteristic
194#417C2211yescharacteristic, complemented
195#417C2211yescharacteristic, complemented
196#416C2211yescharacteristic, complemented
197C2×#103C2211yescharacteristic, complemented
198C2×#103C2211yescharacteristic, complemented
199C2×#103C2211yescharacteristic, complemented
200#408C2211yescharacteristic, complemented
201C2×C22⋊C8C2211yescharacteristic
202#405C2211yescharacteristic, complemented
203C2×#41—21no—
204C2×#41—21no—
205C2×#41C2311yescharacteristic
206C2×#41C2311yescharacteristic
207C2×#41C2311yescharacteristic
208C2×#41C2311yescharacteristic
209C2×#41C2311yescharacteristic
210C22×Q8C2311yescharacteristic
211C22×Q8C2311yescharacteristic
212C22×Q8C2311yescharacteristic
213C22×D4—21no—
214C22×D4C2311yescharacteristic
215C23×C4C2311yescharacteristic
216#137—42no—
217AGL(1,ℤ/8)—42no—
218#135—42no—
219C2×Q16—42no—
220C2×Q16C2311yescharacteristic
221C2×Q16C2311yescharacteristic
222C2×Q16C2311yescharacteristic
223C2×Q16C2311yescharacteristic
224C2×Q16C2311yescharacteristic
225C2×Q16C2311yescharacteristic
226C2×SD16C2311yescharacteristic
227C2×SD16C2311yescharacteristic
228C2×SD16C2311yescharacteristic
229C2×SD16C2311yescharacteristic
230C2×SD16C2311yescharacteristic
231C2×SD16C2311yescharacteristic
232C2×SD16C2311yescharacteristic
233C2×SD16C2311yescharacteristic
234C2×D8C2311yescharacteristic
235C2×D8C2311yescharacteristic
236#131—42no—
237C2×M16—42no—
238C2×M16C2311yescharacteristic
239C2×M16C2311yescharacteristic
240C2×M16C2311yescharacteristic
241C2×M16C2311yescharacteristic
242C2×M16C2311yescharacteristic
243C2×M16C2311yescharacteristic
244C22×C8C2311yescharacteristic
245C22×C8C2311yescharacteristic
246C22×C8C2311yescharacteristic
247C22×C8C2311yescharacteristic
248C22×C8C2311yescharacteristic
249C22×C8C2311yescharacteristic
250C4⋊Q8—21no—
251C4⋊Q8—21no—
252C4⋊Q8C2311yescharacteristic
253C4⋊Q8C2311yescharacteristic
254C4⋊Q8C2311yescharacteristic
255C4⋊Q8C2311yescharacteristic
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#125—21no—
266#125—21no—
267#125—21no—
268#125—21no—
269#125—21no—
270#125—21no—
271#125C2311yescharacteristic
272#124—21no—
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#124C2311yescharacteristic
282#124C2311yescharacteristic
283#124C2311yescharacteristic
284#123—21no—
285#123—21no—
286#123—21no—
287#123—21no—
288#123—21no—
289#123—21no—
290#123—21no—
291#123—21no—
292#123—21no—
293#123—21no—
294#123—21no—
295#123—21no—
296#123—21no—
297#123—21no—
298#123—21no—
299#123—21no—
300#123D411yescharacteristic
301#123D411yescharacteristic
302C22⋊Q8—21no—
303C22⋊Q8—21no—
304C22⋊Q8—21no—
305C22⋊Q8—21no—
306C22⋊Q8—21no—
307C22⋊Q8—21no—
308C22⋊Q8—21no—
309C22⋊Q8—21no—
310C22⋊Q8—21no—
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⋊Q8—21no—
326C22⋊Q8D411yescharacteristic
327C22⋊Q8D411yescharacteristic
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
342C22⋊Q8C2311yescharacteristic
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#121—21no—
356#121—21no—
357#121—21no—
358#121—21no—
359#121—21no—
360#121—21no—
361#121—21no—
362#121D411yescharacteristic
363#121D411yescharacteristic
364#121C2311yescharacteristic
365#121C2311yescharacteristic
366#121C2311yescharacteristic
367#121C2311yescharacteristic
368#121C2311yescharacteristic
369#121C2311yescharacteristic
370#121C2311yescharacteristic
371#121C2311yescharacteristic
372#121C2311yescharacteristic
373#120—21no—
374#120—21no—
375#120—21no—
376#120D411yescharacteristic
377#120D411yescharacteristic
378C4×Q8—21no—
379C4×Q8C2311yescharacteristic
380C4×Q8C2311yescharacteristic
381C4×Q8C2311yescharacteristic
382C4×Q8C2311yescharacteristic
383C4×Q8C2311yescharacteristic
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×D4C2311yescharacteristic
396C4×D4C2311yescharacteristic
397C4×D4C2311yescharacteristic
398C4×D4C2311yescharacteristic
399C4×D4C2311yescharacteristic
400C4×D4C2311yescharacteristic
401C4×D4C2311yescharacteristic
402#117—21no—
403#117C2311yescharacteristic
404#117C2311yescharacteristic
405#117C2311yescharacteristic
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4C2311yescharacteristic
410C2×C4⋊C4C2311yescharacteristic
411C2×C4⋊C4C2311yescharacteristic
412C2×C4⋊C4C2311yescharacteristic
413C2×C4⋊C4C2311yescharacteristic
414C2×C4⋊C4C2311yescharacteristic
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420#107C2311yescharacteristic
421#107C2311yescharacteristic
422#107C2311yescharacteristic
423#107C2311yescharacteristic
424#106C2311yescharacteristic
425#106C2311yescharacteristic
426#106C2311yescharacteristic
427#106C2311yescharacteristic
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—
496#41—82no—
497#41—82no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—41no—
505C2×Q8—41no—
506C2×Q8—41no—
507C2×Q8—41no—
508C2×Q8—41no—
509C2×Q8—41no—
510C2×Q8C2×D411yescharacteristic
511C2×Q8C2411yescharacteristic
512C2×Q8C2411yescharacteristic
513C2×Q8C2411yescharacteristic
514C2×Q8C2411yescharacteristic
515C2×Q8C2411yescharacteristic
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—21no—
529C2×D4—21no—
530C2×D4—41no—
531C2×D4—41no—
532C2×D4—82no—
533C2×D4C2×D411yescharacteristic
534C2×D4C2×D411yescharacteristic
535C2×D4C2×D411yescharacteristic
536C2×D4C2×D411yescharacteristic
537C2×D4C2×D411yescharacteristic
538C2×D4C2×D411yescharacteristic
539C2×D4C2×D411yescharacteristic
540C2×D4C2411yescharacteristic
541C2×D4C2411yescharacteristic
542C2×D4C2411yescharacteristic
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—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—41no—
560C22×C4—41no—
561C22×C4C2×D411yescharacteristic
562C22×C4C2×D411yescharacteristic
563C22×C4C2×D411yescharacteristic
564C22×C4C2411yescharacteristic
565C22×C4C2411yescharacteristic
566C22×C4C2411yescharacteristic
567C22×C4C2411yescharacteristic
568C22×C4C2411yescharacteristic
569Q16—22no—
570Q16—22no—
571Q16—41no—
572Q16—41no—
573Q16—41no—
574Q16—41no—
575SD16—22no—
576SD16—41no—
577SD16—41no—
578SD16—41no—
579SD16—41no—
580SD16—41no—
581SD16—41no—
582SD16—41no—
583D8—22no—
584D8—41no—
585M16—22no—
586M16—22no—
587M16—22no—
588M16—41no—
589M16—41no—
590M16—41no—
591C2×C8—22no—
592C2×C8—22no—
593C2×C8—41no—
594C2×C8—41no—
595C2×C8—41no—
596C2×C8—41no—
597C2×C8C2411yescharacteristic
598C2×C8C2411yescharacteristic
599C2×C8C2411yescharacteristic
600C2×C8C2411yescharacteristic
601C2×C8C2411yescharacteristic
602C2×C8C2411yescharacteristic
603C2×C8C2411yescharacteristic
604C2×C8C2411yescharacteristic
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⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4C2×D411yescharacteristic
639C4⋊C4C2×D411yescharacteristic
640C4⋊C4C2×D411yescharacteristic
641C4⋊C4C2×D411yescharacteristic
642C4⋊C4C2×D411yescharacteristic
643C4⋊C4C2×D411yescharacteristic
644C4⋊C4C2411yescharacteristic
645C4⋊C4C2411yescharacteristic
646C4⋊C4C2411yescharacteristic
647C4⋊C4C2411yescharacteristic
648C4⋊C4C2411yescharacteristic
649C4⋊C4C2411yescharacteristic
650C4⋊C4C2411yescharacteristic
651C4⋊C4C2411yescharacteristic
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⋊C4—21no—
681C22⋊C4—21no—
682C22⋊C4—21no—
683C22⋊C4—21no—
684C22⋊C4—21no—
685C22⋊C4—21no—
686C22⋊C4—21no—
687C22⋊C4C2×D411yescharacteristic
688C22⋊C4C2×D411yescharacteristic
689C22⋊C4C2×D411yescharacteristic
690C22⋊C4C2×D411yescharacteristic
691C22⋊C4C2×D411yescharacteristic
692C22⋊C4C2×D411yescharacteristic
693C22⋊C4C2×D411yescharacteristic
694C22⋊C4C2×D411yescharacteristic
695C22⋊C4C2×D411yescharacteristic
696C22⋊C4C2×D411yescharacteristic
697C42—21no—
698C42—21no—
699C42—21no—
700C42—21no—
701C42—21no—
702C42—21no—
703C42—21no—
704C42C2411yescharacteristic
705C42C2411yescharacteristic
706C23—22no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—41no—
711C23—41no—
712C23—42no—
713C23—81no—
714C23—81no—
715C23C22×D411yescharacteristic
716C23C22×D411yescharacteristic
717C23C22×D411yescharacteristic
718C23C22×D411yescharacteristic
719C23C22×D411yescharacteristic
720Q8—21no—
721Q8—21no—
722Q8—21no—
723Q8—21no—
724Q8—21no—
725Q8—21no—
726Q8—21no—
727Q8—21no—
728Q8—21no—
729Q8—21no—
730Q8—41no—
731Q8—81no—
732Q8—81no—
733Q8—81no—
734Q8—81no—
735Q8—81no—
736Q8—81no—
737D4—22no—
738D4—22no—
739D4—21no—
740D4—21no—
741D4—21no—
742D4—21no—
743D4—21no—
744D4—21no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—41no—
750D4—42no—
751D4—42no—
752D4—42no—
753D4—81no—
754D4—81no—
755D4—81no—
756D4—81no—
757D4—81no—
758D4—81no—
759D4—81no—
760D4—81no—
761D4—81no—
762D4—81no—
763D4—81no—
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—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—42no—
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×C4—81no—
800C2×C4—81no—
801C2×C4—81no—
802C2×C4—81no—
803C2×C4—81no—
804C2×C4—81no—
805C2×C4—81no—
806C2×C4C22×D411yescharacteristic
807C2×C4C22×D411yescharacteristic
808C2×C4C22×D411yescharacteristic
809C2×C4C22×D411yescharacteristic
810C2×C4C22×D411yescharacteristic
811C2×C4C22×D411yescharacteristic
812C2×C4C22×D411yescharacteristic
813C2×C4C22×D411yescharacteristic
814C2×C4C22×D411yescharacteristic
815C2×C4C2511yescharacteristic
816C8—21no—
817C8—21no—
818C8—21no—
819C8—21no—
820C8—21no—
821C8—21no—
822C8—21no—
823C8H(5,𝔽2)12yes—
824C22—21no—
825C22—21no—
826C22—21no—
827C22—21no—
828C22—21no—
829C22—21no—
830C22—21no—
831C22—21no—
832C22—21no—
833C22—21no—
834C22—21no—
835C22—21no—
836C22—21no—
837C22—21no—
838C22—41no—
839C22—41no—
840C22—41no—
841C22—41no—
842C22—41no—
843C22—41no—
844C22—41no—
845C22—41no—
846C22—41no—
847C22—82no—
848C22—162no—
849C22#57712yes—
850C22C23×D411yescharacteristic
851C4—21no—
852C4—21no—
853C4—21no—
854C4—21no—
855C4—21no—
856C4—21no—
857C4—21no—
858C4—21no—
859C4—21no—
860C4—41no—
861C4—41no—
862C4—41no—
863C4—41no—
864C4—41no—
865C4—41no—
866C4—41no—
867C4—41no—
868C4—41no—
869C4—41no—
870C4—41no—
871C4—41no—
872C4—41no—
873C4C2×H(5,𝔽2)11yescharacteristic
874C4#58511yescharacteristic
875C2—22no—
876C2—41no—
877C2—41no—
878C2—41no—
879C2—41no—
880C2—81no—
881C2—81no—
882C2—81no—
883C2#349611yescharacteristic
884C2C2×#57711yescharacteristic
885C2#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. #3536C2semidirect
3. #3356C2semidirect
4. #3345C2semidirect
5. #3344C2semidirect
6. #3335C2semidirect
7. #3331C2semidirect
8. #3323C2semidirect
9. #3316C2semidirect
10. #3316C2semidirect
11. #3311C2semidirect
12. #3308C2semidirect
13. #3301C2semidirect
14. #3298C2semidirect
15. #3285C2semidirect
16. #3275C2semidirect
17. #3270C2semidirect
18. #3267C2semidirect
19. #3263C2semidirect
20. #3258C2semidirect
21. #3204C2semidirect
22. #3201C2semidirect
23. #3190C2semidirect
24. #3187C2semidirect
25. #3178C2semidirect
26. #3173C2semidirect
27. #3063C2semidirect
28. #3060C2semidirect
29. #3055C2semidirect
30. C2×#470C2semidirect
31. #2933C2semidirect
32. C2×#137C22semidirect
34. C2×#135C22semidirect
35. C22×Q16C22semidirect
36. C2×#131C22semidirect
46. #554C22semidirect
48. #553C22semidirect
50. D4×Q8C22semidirect
54. #548C22semidirect
66. #542C22semidirect
67. #541C22semidirect
76. #537C22semidirect
77. #536C22semidirect
83. #501C22semidirect
84. #498C22semidirect
85. #497C22semidirect
86. #495C22semidirect
87. #489C22semidirect
88. #489C22semidirect
89. #488C22semidirect
90. #487C22semidirect
93. #485C22semidirect
94. #484C22semidirect
97. #483C22semidirect
98. #483C22semidirect
99. #483C22semidirect
100. #483C22semidirect
101. #482C22semidirect
104. #481C22semidirect
105. #481C22semidirect
106. #480C22semidirect
107. #479C22semidirect
108. #478C22semidirect
109. #477C22semidirect
110. #476C22semidirect
111. #476C22semidirect
112. #475C22semidirect
113. #475C22semidirect
114. #475C22semidirect
119. #470C22semidirect
120. #470C22semidirect
121. #470C22semidirect
122. #470C22semidirect
123. #470C22semidirect
124. #470C22semidirect
127. #469C22semidirect
130. #468C22semidirect
131. #467C22semidirect
132. #467C22semidirect
133. #467C22semidirect
142. #465C22semidirect
143. #465C22semidirect
144. #465C22semidirect
145. #465C22semidirect
146. #465C22semidirect
147. #464C22semidirect
148. #464C22semidirect
149. #464C22semidirect
150. #464C22semidirect
151. #463C22semidirect
152. #463C22semidirect
153. #462C22semidirect
154. #461C22semidirect
157. #452C22semidirect
158. #452C22semidirect
159. #452C22semidirect
160. #452C22semidirect
161. #451C22semidirect
162. #451C22semidirect
165. #449C22semidirect
166. #449C22semidirect
169. #448C22semidirect
170. #448C22semidirect
171. #442C22semidirect
172. #441C22semidirect
173. #441C22semidirect
174. #440C22semidirect
175. C4×Q16C22semidirect
176. C4×SD16C22semidirect
177. C4×SD16C22semidirect
178. C4×SD16C22semidirect
183. #435C22semidirect
184. #435C22semidirect
185. C8×D4C22semidirect
186. C8×D4C22semidirect
188. #428C22semidirect
189. C2×#106C22semidirect
190. C2×#106C22semidirect
191. #424C22semidirect
194. #417C22semidirect
195. #417C22semidirect
196. #416C22semidirect
197. C2×#103C22semidirect
198. C2×#103C22semidirect
199. C2×#103C22semidirect
200. #408C22semidirect
202. #405C22semidirect

Maximal subgroups

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

subgroupindex
#35412
#35362
#33562
#33452
#33442
#33352
#33312
#33232
#33162
#33112
#33082
#33012
#32982
#32852
#32752
#32702
#32672
#32632
#32582
#32042
#32012
#31902
#31872
#31782
#31732
#30632
#30602
#30552
C2×#4702
#29332