Finite Group Databasebeta

← #62317

Subgroups — #62317

Order 256.

888 conjugacy classes of subgroups.

The subgroup lattice has 863 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3541C211yesmaximal, characteristic
2#3538C211yesmaximal, characteristic, complemented
3#3352C211yesmaximal, characteristic, complemented
4#3349C211yesmaximal, characteristic, complemented
5#3344C211yesmaximal, characteristic, complemented
6#3337C211yesmaximal, characteristic, complemented
7#3328C211yesmaximal, characteristic, complemented
8#3327C211yesmaximal, characteristic, complemented
9#3320C211yesmaximal, characteristic, complemented
10#3315C211yesmaximal, characteristic, complemented
11#3312C211yesmaximal, characteristic, complemented
12#3312C211yesmaximal, characteristic, complemented
13#3300C211yesmaximal, characteristic, complemented
14#3299C211yesmaximal, characteristic, complemented
15D4×Q16C211yesmaximal, characteristic, complemented
16#3276C211yesmaximal, characteristic, complemented
17#3270C211yesmaximal, characteristic, complemented
18#3270C211yesmaximal, characteristic, complemented
19#3261C211yesmaximal, characteristic, complemented
20#3258C211yesmaximal, characteristic, complemented
21#3202C211yesmaximal, characteristic, complemented
22#3201C211yesmaximal, characteristic, complemented
23#3190C211yesmaximal, characteristic, complemented
24#3189C211yesmaximal, characteristic, complemented
25#3178C211yesmaximal, characteristic, complemented
26#3177C211yesmaximal, characteristic, complemented
27#3063C211yesmaximal, characteristic, complemented
28#3059C211yesmaximal, characteristic, complemented
29#3056C211yesmaximal, characteristic, complemented
30C2×#470C211yesmaximal, characteristic, complemented
31#2933C211yesmaximal, characteristic, complemented
32C2×#137C2211yescharacteristic
33C2×#137C2211yescharacteristic, complemented
34C22×Q16C2211yescharacteristic
35C22×Q16C2211yescharacteristic, complemented
36C2×#131C2211yescharacteristic
37C22×M16C2211yescharacteristic
38#563—21no—
39#563—21no—
40#563—21no—
41#562—21no—
42#556C2211yescharacteristic
43#554—21no—
44#554C2211yescharacteristic
45#553—21no—
46#553C2211yescharacteristic
47#552C2211yescharacteristic
48#552C2211yescharacteristic
49#552C2211yescharacteristic
50#552C2211yescharacteristic
51#552C2211yescharacteristic
52#551—21no—
53#551—21no—
54D4×Q8C2211yescharacteristic
55D4×Q8C2211yescharacteristic
56D4×Q8C2211yescharacteristic
57D4×Q8C2211yescharacteristic
58D4×Q8C2211yescharacteristic
59#548C2211yescharacteristic
60#548C2211yescharacteristic
61#547C2211yescharacteristic
62#544—21no—
63#544—21no—
64#542—21no—
65#542C2211yescharacteristic
66#541C2211yescharacteristic
67#541C2211yescharacteristic
68#541C2211yescharacteristic
69#539—21no—
70#539—21no—
71#539—21no—
72#538—21no—
73#538—21no—
74#537C2211yescharacteristic
75#536C2211yescharacteristic
76#536C2211yescharacteristic
77#536C2211yescharacteristic
78#525C2211yescharacteristic
79#525C2211yescharacteristic
80C2×C22⋊Q8C2211yescharacteristic
81C2×C22⋊Q8C2211yescharacteristic
82C2×C22⋊Q8C2211yescharacteristic
83#501C2211yescharacteristic, complemented
84#499C2211yescharacteristic, complemented
85#497C2211yescharacteristic, complemented
86#494C2211yescharacteristic, complemented
87#491C2211yescharacteristic, complemented
88#491C2211yescharacteristic, complemented
89#488C2211yescharacteristic, complemented
90#487C2211yescharacteristic, complemented
91#485C2211yescharacteristic
92#485C2211yescharacteristic
93#485C2211yescharacteristic, complemented
94#485C2211yescharacteristic, complemented
95#485C2211yescharacteristic, complemented
96#485C2211yescharacteristic, complemented
97#485C2211yescharacteristic, complemented
98#484C2211yescharacteristic
99#484C2211yescharacteristic
100#484C2211yescharacteristic
101#484C2211yescharacteristic
102#484C2211yescharacteristic, complemented
103#483C2211yescharacteristic
104#483C2211yescharacteristic, complemented
105#482C2211yescharacteristic, complemented
106#480C2211yescharacteristic
107#479C2211yescharacteristic, complemented
108#479C2211yescharacteristic, complemented
109#479C2211yescharacteristic, complemented
110#479C2211yescharacteristic, complemented
111#479C2211yescharacteristic, complemented
112#478C2211yescharacteristic, complemented
113#477C2211yescharacteristic, complemented
114#475C2211yescharacteristic, complemented
115#470C2211yescharacteristic
116#470C2211yescharacteristic
117#470C2211yescharacteristic
118#470C2211yescharacteristic
119#470C2211yescharacteristic
120#470C2211yescharacteristic
121#470C2211yescharacteristic
122#470C2211yescharacteristic
123#470C2211yescharacteristic
124#470C2211yescharacteristic
125#470C2211yescharacteristic, complemented
126#470C2211yescharacteristic, complemented
127#470C2211yescharacteristic, complemented
128#468C2211yescharacteristic
129#468C2211yescharacteristic
130#468C2211yescharacteristic, complemented
131#467C2211yescharacteristic
132#467C2211yescharacteristic
133#467C2211yescharacteristic
134#467C2211yescharacteristic
135#467C2211yescharacteristic
136#467C2211yescharacteristic
137#467C2211yescharacteristic
138#467C2211yescharacteristic
139#467C2211yescharacteristic, complemented
140#467C2211yescharacteristic, complemented
141#467C2211yescharacteristic, complemented
142#465C2211yescharacteristic
143#465C2211yescharacteristic
144#465C2211yescharacteristic
145#465C2211yescharacteristic
146#465C2211yescharacteristic, complemented
147#464C2211yescharacteristic, complemented
148#464C2211yescharacteristic, complemented
149#462C2211yescharacteristic, complemented
150#462C2211yescharacteristic, complemented
151#462C2211yescharacteristic, complemented
152#462C2211yescharacteristic, complemented
153#462C2211yescharacteristic, complemented
154#461C2211yescharacteristic, complemented
155#452C2211yescharacteristic
156#452C2211yescharacteristic
157#452C2211yescharacteristic, complemented
158#452C2211yescharacteristic, complemented
159#451C2211yescharacteristic
160#451C2211yescharacteristic
161#451C2211yescharacteristic
162#451C2211yescharacteristic
163#451C2211yescharacteristic
164#451C2211yescharacteristic, complemented
165#451C2211yescharacteristic, complemented
166#451C2211yescharacteristic, complemented
167#451C2211yescharacteristic, complemented
168#451C2211yescharacteristic, complemented
169#448C2211yescharacteristic
170#448C2211yescharacteristic, complemented
171#441C2211yescharacteristic, complemented
172#441C2211yescharacteristic, complemented
173#441C2211yescharacteristic, complemented
174#440C2211yescharacteristic, complemented
175C4×Q16C2211yescharacteristic, complemented
176C4×Q16C2211yescharacteristic, complemented
177C4×Q16C2211yescharacteristic, complemented
178C4×SD16C2211yescharacteristic, complemented
179#436C2211yescharacteristic
180#436C2211yescharacteristic
181#435C2211yescharacteristic
182#435C2211yescharacteristic
183#435C2211yescharacteristic
184#435C2211yescharacteristic
185C8×D4C2211yescharacteristic
186C8×D4C2211yescharacteristic
187#428C2211yescharacteristic
188#428C2211yescharacteristic, complemented
189#427C2211yescharacteristic, complemented
190C2×#106C2211yescharacteristic
191#424C2211yescharacteristic
192#419C2211yescharacteristic
193#419C2211yescharacteristic, complemented
194#419C2211yescharacteristic, complemented
195#417C2211yescharacteristic
196#416C2211yescharacteristic, complemented
197C2×#103C2211yescharacteristic
198C2×#103C2211yescharacteristic
199C2×#103C2211yescharacteristic, complemented
200#408C2211yescharacteristic
201C2×C22⋊C8C2211yescharacteristic
202#405C2211yescharacteristic
203C2×#41C2311yescharacteristic
204C2×#41C2311yescharacteristic
205C2×#41C2311yescharacteristic
206C22×Q8C2311yescharacteristic
207C22×Q8C2311yescharacteristic
208C22×Q8C2311yescharacteristic
209C22×Q8C2311yescharacteristic
210C22×Q8C2311yescharacteristic
211C22×Q8C2311yescharacteristic
212C23×C4C2311yescharacteristic
213#137—42no—
214#137—42no—
215C2×Q16—42no—
216C2×Q16—42no—
217C2×Q16C2311yescharacteristic
218C2×Q16C2311yescharacteristic
219C2×Q16C2311yescharacteristic
220C2×Q16C2311yescharacteristic
221C2×Q16C2311yescharacteristic
222C2×Q16C2311yescharacteristic
223C2×Q16C2311yescharacteristic
224C2×Q16C2311yescharacteristic
225C2×Q16C2311yescharacteristic
226C2×Q16C2311yescharacteristic
227C2×Q16C2311yescharacteristic
228C2×Q16C2311yescharacteristic
229C2×SD16C2311yescharacteristic
230C2×SD16C2311yescharacteristic
231C2×SD16C2311yescharacteristic
232C2×SD16C2311yescharacteristic
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⋊Q8—21no—
251C4⋊Q8—21no—
252C4⋊Q8—21no—
253C4⋊Q8—21no—
254C4⋊Q8—21no—
255C4⋊Q8C2311yescharacteristic
256C4⋊Q8C2311yescharacteristic
257C4⋊Q8C2311yescharacteristic
258C4⋊Q8C2311yescharacteristic
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#126—21no—
269#126—21no—
270#126—21no—
271#126—21no—
272#126—21no—
273#126—21no—
274#125—21no—
275#125—21no—
276#125—21no—
277#125—21no—
278#125—21no—
279#125—21no—
280#125—21no—
281#125—21no—
282#125—21no—
283#125—21no—
284#125—21no—
285#125—21no—
286#125C2311yescharacteristic
287#125C2311yescharacteristic
288#125C2311yescharacteristic
289#124—21no—
290#124—21no—
291#124—21no—
292#124—21no—
293#124—21no—
294#124—21no—
295#124—21no—
296#124C2311yescharacteristic
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#123—21no—
310#123—21no—
311#123—21no—
312#123—21no—
313#123D411yescharacteristic
314#123D411yescharacteristic
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⋊Q8—21no—
327C22⋊Q8—21no—
328C22⋊Q8—21no—
329C22⋊Q8—21no—
330C22⋊Q8—21no—
331C22⋊Q8—21no—
332C22⋊Q8—21no—
333C22⋊Q8—21no—
334C22⋊Q8—21no—
335C22⋊Q8—21no—
336C22⋊Q8—21no—
337C22⋊Q8D411yescharacteristic
338C22⋊Q8D411yescharacteristic
339C22⋊Q8C2311yescharacteristic
340C22⋊Q8C2311yescharacteristic
341C22⋊Q8C2311yescharacteristic
342C22⋊Q8C2311yescharacteristic
343C22⋊Q8C2311yescharacteristic
344C22⋊Q8C2311yescharacteristic
345C22⋊Q8C2311yescharacteristic
346C22⋊Q8C2311yescharacteristic
347C22⋊Q8C2311yescharacteristic
348C22⋊Q8C2311yescharacteristic
349C22⋊Q8C2311yescharacteristic
350C22⋊Q8C2311yescharacteristic
351C22⋊Q8C2311yescharacteristic
352C22⋊Q8C2311yescharacteristic
353C22⋊Q8C2311yescharacteristic
354C22⋊Q8C2311yescharacteristic
355C22⋊Q8C2311yescharacteristic
356C22⋊Q8C2311yescharacteristic
357C22⋊Q8C2311yescharacteristic
358C22⋊Q8C2311yescharacteristic
359C22⋊Q8C2311yescharacteristic
360#121—21no—
361#121—21no—
362#121—21no—
363#121—21no—
364#121—21no—
365#121—21no—
366#121—21no—
367#121D411yescharacteristic
368#121D411yescharacteristic
369#121C2311yescharacteristic
370#121C2311yescharacteristic
371#121C2311yescharacteristic
372#120—21no—
373#120D411yescharacteristic
374#120D411yescharacteristic
375C4×Q8—21no—
376C4×Q8C2311yescharacteristic
377C4×Q8C2311yescharacteristic
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×D4C2311yescharacteristic
395C4×D4C2311yescharacteristic
396C4×D4C2311yescharacteristic
397C4×D4C2311yescharacteristic
398C4×D4C2311yescharacteristic
399#117—21no—
400#117—21no—
401#117—21no—
402#117—21no—
403#117—21no—
404#117C2311yescharacteristic
405#117C2311yescharacteristic
406#117C2311yescharacteristic
407#117C2311yescharacteristic
408#117C2311yescharacteristic
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4C2311yescharacteristic
414C2×C4⋊C4C2311yescharacteristic
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#103C2311yescharacteristic
461#103C2311yescharacteristic
462#103C2311yescharacteristic
463#103C2311yescharacteristic
464#103C2311yescharacteristic
465#103C2311yescharacteristic
466#103C2311yescharacteristic
467#103C2311yescharacteristic
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
484C24C2×D411yescharacteristic
485#41—41no—
486#41—41no—
487#41—41no—
488#41—41no—
489#41—41no—
490#41—41no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—41no—
499C2×Q8—41no—
500C2×Q8—41no—
501C2×Q8—41no—
502C2×Q8—41no—
503C2×Q8—41no—
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×Q8C2411yescharacteristic
517C2×Q8C2411yescharacteristic
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4C2×D411yescharacteristic
524C2×D4C2×D411yescharacteristic
525C2×D4C2×D411yescharacteristic
526C2×D4C2×D411yescharacteristic
527C2×D4C2×D411yescharacteristic
528C2×D4C2×D411yescharacteristic
529C2×D4C2×D411yescharacteristic
530C2×D4C2411yescharacteristic
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4C2×D411yescharacteristic
547C22×C4C2×D411yescharacteristic
548C22×C4C2×D411yescharacteristic
549C22×C4C2411yescharacteristic
550C22×C4C2411yescharacteristic
551C22×C4C2411yescharacteristic
552C22×C4C2411yescharacteristic
553C22×C4C2411yescharacteristic
554Q16—22no—
555Q16—22no—
556Q16—22no—
557Q16—41no—
558Q16—41no—
559Q16—41no—
560Q16—41no—
561Q16—41no—
562Q16—41no—
563Q16—41no—
564Q16—41no—
565Q16—41no—
566SD16—22no—
567SD16—41no—
568SD16—41no—
569SD16—41no—
570M16—22no—
571M16—22no—
572M16—22no—
573M16—41no—
574M16—41no—
575M16—41no—
576C2×C8—22no—
577C2×C8—22no—
578C2×C8—41no—
579C2×C8—41no—
580C2×C8—41no—
581C2×C8—41no—
582C2×C8C2411yescharacteristic
583C2×C8C2411yescharacteristic
584C2×C8C2411yescharacteristic
585C2×C8C2411yescharacteristic
586C2×C8C2411yescharacteristic
587C2×C8C2411yescharacteristic
588C2×C8C2411yescharacteristic
589C2×C8C2411yescharacteristic
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
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⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4C2×D411yescharacteristic
636C4⋊C4C2×D411yescharacteristic
637C4⋊C4C2×D411yescharacteristic
638C4⋊C4C2×D411yescharacteristic
639C4⋊C4C2×D411yescharacteristic
640C4⋊C4C2×D411yescharacteristic
641C4⋊C4C2411yescharacteristic
642C4⋊C4C2411yescharacteristic
643C4⋊C4C2411yescharacteristic
644C4⋊C4C2411yescharacteristic
645C4⋊C4C2411yescharacteristic
646C4⋊C4C2411yescharacteristic
647C4⋊C4C2411yescharacteristic
648C4⋊C4C2411yescharacteristic
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—22no—
704C23—21no—
705C23—41no—
706C23—41no—
707C23C22×D411yescharacteristic
708C23C22×D411yescharacteristic
709C23C22×D411yescharacteristic
710C23C22×D411yescharacteristic
711C23C22×D411yescharacteristic
712Q8—21no—
713Q8—21no—
714Q8—21no—
715Q8—21no—
716Q8—21no—
717Q8—21no—
718Q8—21no—
719Q8—21no—
720Q8—21no—
721Q8—21no—
722Q8—21no—
723Q8—21no—
724Q8—21no—
725Q8—21no—
726Q8—41no—
727Q8—81no—
728Q8—81no—
729Q8—81no—
730Q8—81no—
731Q8—81no—
732Q8—81no—
733Q8—81no—
734D4—22no—
735D4—22no—
736D4—21no—
737D4—21no—
738D4—41no—
739D4—41no—
740D4—41no—
741D4—41no—
742D4—41no—
743D4—42no—
744D4—81no—
745D4—81no—
746D4—81no—
747D4—81no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
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—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—81no—
779C2×C4—81no—
780C2×C4—81no—
781C2×C4—81no—
782C2×C4—81no—
783C2×C4—81no—
784C2×C4—81no—
785C2×C4—81no—
786C2×C4—81no—
787C2×C4—81no—
788C2×C4—81no—
789C2×C4C22×D411yescharacteristic
790C2×C4C22×D411yescharacteristic
791C2×C4C22×D411yescharacteristic
792C2×C4C22×D411yescharacteristic
793C2×C4C22×D411yescharacteristic
794C2×C4C22×D411yescharacteristic
795C2×C4C22×D411yescharacteristic
796C2×C4C22×D411yescharacteristic
797C2×C4C22×D411yescharacteristic
798C2×C4C2511yescharacteristic
799C8—21no—
800C8—21no—
801C8—21no—
802C8—21no—
803C8—21no—
804C8—21no—
805C8—21no—
806C8H(5,𝔽2)12yes—
807C22—21no—
808C22—21no—
809C22—21no—
810C22—21no—
811C22—21no—
812C22—21no—
813C22—21no—
814C22—21no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—21no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—82no—
825C22#57812yes—
826C22C23×D411yescharacteristic
827C4—21no—
828C4—21no—
829C4—21no—
830C4—21no—
831C4—21no—
832C4—21no—
833C4—21no—
834C4—21no—
835C4—21no—
836C4—41no—
837C4—41no—
838C4—41no—
839C4—41no—
840C4—41no—
841C4—41no—
842C4—41no—
843C4—41no—
844C4—41no—
845C4—41no—
846C4—41no—
847C4—41no—
848C4—41no—
849C4—41no—
850C4—41no—
851C4C2×H(5,𝔽2)11yescharacteristic
852C4#58511yescharacteristic
853C2—22no—
854C2—41no—
855C2—41no—
856C2—41no—
857C2—41no—
858C2—81no—
859C2#349611yescharacteristic
860C2C2×#57811yescharacteristic
861C2#358611yescharacteristic
subgroupG/H
center, socleC22C23×D4
commutator, Frattini, cosocleC2×C4C25
prime radical#3541C2
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
2. #3538C2semidirect
3. #3352C2semidirect
4. #3349C2semidirect
5. #3344C2semidirect
6. #3337C2semidirect
7. #3328C2semidirect
8. #3327C2semidirect
9. #3320C2semidirect
10. #3315C2semidirect
11. #3312C2semidirect
12. #3312C2semidirect
13. #3300C2semidirect
14. #3299C2semidirect
15. D4×Q16C2semidirect
16. #3276C2semidirect
17. #3270C2semidirect
18. #3270C2semidirect
19. #3261C2semidirect
20. #3258C2semidirect
21. #3202C2semidirect
22. #3201C2semidirect
23. #3190C2semidirect
24. #3189C2semidirect
25. #3178C2semidirect
26. #3177C2semidirect
27. #3063C2semidirect
28. #3059C2semidirect
29. #3056C2semidirect
30. C2×#470C2semidirect
31. #2933C2semidirect
33. C2×#137C22semidirect
35. C22×Q16C22semidirect
83. #501C22semidirect
84. #499C22semidirect
85. #497C22semidirect
86. #494C22semidirect
87. #491C22semidirect
88. #491C22semidirect
89. #488C22semidirect
90. #487C22semidirect
93. #485C22semidirect
94. #485C22semidirect
95. #485C22semidirect
96. #485C22semidirect
97. #485C22semidirect
102. #484C22semidirect
104. #483C22semidirect
105. #482C22semidirect
107. #479C22semidirect
108. #479C22semidirect
109. #479C22semidirect
110. #479C22semidirect
111. #479C22semidirect
112. #478C22semidirect
113. #477C22semidirect
114. #475C22semidirect
125. #470C22semidirect
126. #470C22semidirect
127. #470C22semidirect
130. #468C22semidirect
139. #467C22semidirect
140. #467C22semidirect
141. #467C22semidirect
146. #465C22semidirect
147. #464C22semidirect
148. #464C22semidirect
149. #462C22semidirect
150. #462C22semidirect
151. #462C22semidirect
152. #462C22semidirect
153. #462C22semidirect
154. #461C22semidirect
157. #452C22semidirect
158. #452C22semidirect
164. #451C22semidirect
165. #451C22semidirect
166. #451C22semidirect
167. #451C22semidirect
168. #451C22semidirect
170. #448C22semidirect
171. #441C22semidirect
172. #441C22semidirect
173. #441C22semidirect
174. #440C22semidirect
175. C4×Q16C22semidirect
176. C4×Q16C22semidirect
177. C4×Q16C22semidirect
178. C4×SD16C22semidirect
188. #428C22semidirect
189. #427C22semidirect
193. #419C22semidirect
194. #419C22semidirect
196. #416C22semidirect
199. C2×#103C22semidirect

Maximal subgroups

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

subgroupindex
#35412
#35382
#33522
#33492
#33442
#33372
#33282
#33272
#33202
#33152
#33122
#33002
#32992
D4×Q162
#32762
#32702
#32612
#32582
#32022
#32012
#31902
#31892
#31782
#31772
#30632
#30592
#30562
C2×#4702
#29332