Finite Group Databasebeta

← #49190

Subgroups — #49190

Order 256.

967 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2775C211yesmaximal, characteristic, complemented
2#2764C211yesmaximal, characteristic, complemented
3#2761C211yesmaximal, characteristic, complemented
4#2757C211yesmaximal, characteristic, complemented
5#2756C211yesmaximal, characteristic, complemented
6#2749C211yesmaximal, characteristic, complemented
7#2749C211yesmaximal, characteristic, complemented
8#2729C211yesmaximal, characteristic, complemented
9#2697C211yesmaximal, characteristic, complemented
10#2688C211yesmaximal, characteristic, complemented
11#2681C211yesmaximal, characteristic, complemented
12#2670C211yesmaximal, characteristic, complemented
13#2661C211yesmaximal, characteristic, complemented
14#2640C211yesmaximal, characteristic, complemented
15#2572C211yesmaximal, characteristic, complemented
16#2572C211yesmaximal, characteristic, complemented
17#2557C211yesmaximal, characteristic, complemented
18#2526C211yesmaximal, characteristic, complemented
19#2488C211yesmaximal, characteristic, complemented
20#2483C211yesmaximal, characteristic, complemented
21#2472C211yesmaximal, characteristic, complemented
22#2459C211yesmaximal, characteristic, complemented
23#2459C211yesmaximal, characteristic, complemented
24#2432C211yesmaximal, characteristic, complemented
25#2430C211yesmaximal, characteristic, complemented
26#2424C211yesmaximal, characteristic, complemented
27#2420C211yesmaximal, characteristic, complemented
28#2404C211yesmaximal, characteristic, complemented
29#2379C211yesmaximal, characteristic, complemented
30#2353C211yesmaximal, characteristic, complemented
31#2321C211yesmaximal, characteristic, complemented
32C22×#41C2211yescharacteristic
33C2×C4⋊Q8C2211yescharacteristic, complemented
34C2×#124C2211yescharacteristic
35C2×#124C2211yescharacteristic
36C2×#124C2211yescharacteristic
37C2×#123C2211yescharacteristic
38C2×#123C2211yescharacteristic, complemented
39C2×C22⋊Q8C2211yescharacteristic
40C2×C22⋊Q8C2211yescharacteristic, complemented
41C2×#121C2211yescharacteristic
42C2×#121C2211yescharacteristic
43C2×#121C2211yescharacteristic, complemented
44C2×#120C2211yescharacteristic
45C2×#120C2211yescharacteristic
46C2×#120C2211yescharacteristic
47C2×C4×D4C2211yescharacteristic
48C2×C4×D4C2211yescharacteristic
49C22×C22⋊C4C2211yescharacteristic
50C22×C22⋊C4C2211yescharacteristic
51#400C2211yescharacteristic, complemented
52#400C2211yescharacteristic, complemented
53#400C2211yescharacteristic, complemented
54#400C2211yescharacteristic, complemented
55#398C2211yescharacteristic, complemented
56#398C2211yescharacteristic, complemented
57#398C2211yescharacteristic, complemented
58#397C2211yescharacteristic
59#397C2211yescharacteristic
60#397C2211yescharacteristic
61#397C2211yescharacteristic
62#397C2211yescharacteristic
63#397C2211yescharacteristic
64#397C2211yescharacteristic
65#397C2211yescharacteristic, complemented
66#397C2211yescharacteristic, complemented
67#397C2211yescharacteristic, complemented
68#397C2211yescharacteristic, complemented
69#396C2211yescharacteristic
70#396C2211yescharacteristic
71#396C2211yescharacteristic
72#396C2211yescharacteristic, complemented
73#395C2211yescharacteristic, complemented
74#394C2211yescharacteristic
75#394C2211yescharacteristic
76#394C2211yescharacteristic
77#394C2211yescharacteristic
78#394C2211yescharacteristic
79#394C2211yescharacteristic
80#394C2211yescharacteristic
81#394C2211yescharacteristic
82#394C2211yescharacteristic, complemented
83#394C2211yescharacteristic, complemented
84#394C2211yescharacteristic, complemented
85#394C2211yescharacteristic, complemented
86#393C2211yescharacteristic
87#393C2211yescharacteristic
88#393C2211yescharacteristic
89#393C2211yescharacteristic
90#393C2211yescharacteristic, complemented
91#393C2211yescharacteristic, complemented
92#393C2211yescharacteristic, complemented
93#392C2211yescharacteristic
94#392C2211yescharacteristic
95#392C2211yescharacteristic
96#392C2211yescharacteristic
97#392C2211yescharacteristic
98#392C2211yescharacteristic
99#391C2211yescharacteristic, complemented
100#391C2211yescharacteristic, complemented
101#391C2211yescharacteristic, complemented
102#391C2211yescharacteristic, complemented
103#391C2211yescharacteristic, complemented
104#390C2211yescharacteristic
105#390C2211yescharacteristic
106#390C2211yescharacteristic
107#390C2211yescharacteristic
108#390C2211yescharacteristic
109#390C2211yescharacteristic
110#390C2211yescharacteristic
111#389C2211yescharacteristic, complemented
112#389C2211yescharacteristic, complemented
113#388C2211yescharacteristic
114#388C2211yescharacteristic
115#388C2211yescharacteristic
116#388C2211yescharacteristic
117#388C2211yescharacteristic
118#388C2211yescharacteristic
119#388C2211yescharacteristic
120#388C2211yescharacteristic
121#388C2211yescharacteristic
122#388C2211yescharacteristic
123#388C2211yescharacteristic
124#388C2211yescharacteristic, complemented
125#388C2211yescharacteristic, complemented
126#388C2211yescharacteristic, complemented
127#388C2211yescharacteristic, complemented
128#388C2211yescharacteristic, complemented
129#388C2211yescharacteristic, complemented
130#388C2211yescharacteristic, complemented
131#387C2211yescharacteristic, complemented
132#387C2211yescharacteristic, complemented
133#387C2211yescharacteristic, complemented
134#387C2211yescharacteristic, complemented
135#386C2211yescharacteristic
136#386C2211yescharacteristic
137#386C2211yescharacteristic
138#386C2211yescharacteristic
139#386C2211yescharacteristic
140#386C2211yescharacteristic
141#386C2211yescharacteristic
142#386C2211yescharacteristic
143#386C2211yescharacteristic
144#386C2211yescharacteristic
145#386C2211yescharacteristic
146#386C2211yescharacteristic
147#386C2211yescharacteristic
148#386C2211yescharacteristic
149#386C2211yescharacteristic
150#386C2211yescharacteristic, complemented
151#386C2211yescharacteristic, complemented
152#386C2211yescharacteristic, complemented
153#386C2211yescharacteristic, complemented
154#385C2211yescharacteristic
155#385C2211yescharacteristic
156#385C2211yescharacteristic
157#385C2211yescharacteristic
158#385C2211yescharacteristic
159#385C2211yescharacteristic
160#385C2211yescharacteristic, complemented
161#385C2211yescharacteristic, complemented
162#385C2211yescharacteristic, complemented
163#383C2211yescharacteristic, complemented
164#383C2211yescharacteristic, complemented
165#383C2211yescharacteristic, complemented
166#383C2211yescharacteristic, complemented
167#382C2211yescharacteristic, complemented
168#382C2211yescharacteristic, complemented
169#381C2211yescharacteristic
170#381C2211yescharacteristic
171#381C2211yescharacteristic
172#381C2211yescharacteristic
173#381C2211yescharacteristic
174#381C2211yescharacteristic, complemented
175#381C2211yescharacteristic, complemented
176#380C2211yescharacteristic, complemented
177#379C2211yescharacteristic
178#379C2211yescharacteristic
179C4×C22⋊C4C2211yescharacteristic
180C4×C22⋊C4C2211yescharacteristic
181C4×C22⋊C4C2211yescharacteristic, complemented
182C4×C22⋊C4C2211yescharacteristic, complemented
183C4×C22⋊C4C2211yescharacteristic, complemented
184C4×C22⋊C4C2211yescharacteristic, complemented
185#376C2211yescharacteristic, complemented
186C2×#95C2211yescharacteristic, complemented
187C25C2311yescharacteristic
188C2×#41—42no—
189C2×#41—42no—
190C2×#41—42no—
191C22×Q8C2311yescharacteristic
192C22×Q8C2311yescharacteristic
193C22×Q8C2311yescharacteristic
194C22×D4C2311yescharacteristic
195C22×D4C2311yescharacteristic
196C22×D4C2311yescharacteristic
197C22×D4C2311yescharacteristic
198C22×D4C2311yescharacteristic
199C22×D4C2311yescharacteristic
200C22×D4C2311yescharacteristic
201C22×D4C2311yescharacteristic
202C22×D4C2311yescharacteristic
203C22×D4C2311yescharacteristic
204C22×D4C2311yescharacteristic
205C22×D4C2311yescharacteristic
206C23×C4C2311yescharacteristic
207C23×C4C2311yescharacteristic
208C23×C4C2311yescharacteristic
209C23×C4C2311yescharacteristic
210C23×C4C2311yescharacteristic
211C23×C4C2311yescharacteristic
212C23×C4C2311yescharacteristic
213C23×C4C2311yescharacteristic
214C23×C4C2311yescharacteristic
215C4⋊Q8—42no—
216#124—24no—
217#124—42no—
218#124—42no—
219#123—42no—
220#123—42no—
221C22⋊Q8—42no—
222C22⋊Q8—42no—
223#121—42no—
224#121—42no—
225#121—42no—
226#120—24no—
227#120—42no—
228#120—42no—
229C4×D4—24no—
230C4×D4—42no—
231C2×C4⋊C4C2311yescharacteristic
232C2×C4⋊C4C2311yescharacteristic
233C2×C4⋊C4C2311yescharacteristic
234C2×C4⋊C4C2311yescharacteristic
235C2×C4⋊C4C2311yescharacteristic
236C2×C4⋊C4C2311yescharacteristic
237C2×C4⋊C4C2311yescharacteristic
238C2×C4⋊C4C2311yescharacteristic
239C2×C4⋊C4C2311yescharacteristic
240C2×C4⋊C4C2311yescharacteristic
241C2×C4⋊C4C2311yescharacteristic
242C2×C4⋊C4C2311yescharacteristic
243C2×C4⋊C4C2311yescharacteristic
244C2×C4⋊C4C2311yescharacteristic
245C2×C4⋊C4C2311yescharacteristic
246C2×C4⋊C4C2311yescharacteristic
247C2×C4⋊C4C2311yescharacteristic
248C2×C4⋊C4C2311yescharacteristic
249C2×C4⋊C4C2311yescharacteristic
250C2×C4⋊C4C2311yescharacteristic
251C2×C4⋊C4C2311yescharacteristic
252C2×C22⋊C4—42no—
253C2×C22⋊C4—42no—
254C2×C22⋊C4C2311yescharacteristic
255C2×C22⋊C4C2311yescharacteristic
256C2×C22⋊C4C2311yescharacteristic
257C2×C22⋊C4C2311yescharacteristic
258C2×C22⋊C4C2311yescharacteristic
259C2×C22⋊C4C2311yescharacteristic
260C2×C22⋊C4C2311yescharacteristic
261C2×C22⋊C4C2311yescharacteristic
262C2×C22⋊C4C2311yescharacteristic
263C2×C22⋊C4C2311yescharacteristic
264C2×C22⋊C4C2311yescharacteristic
265C2×C22⋊C4C2311yescharacteristic
266C2×C22⋊C4C2311yescharacteristic
267C2×C22⋊C4C2311yescharacteristic
268C2×C22⋊C4C2311yescharacteristic
269C2×C22⋊C4C2311yescharacteristic
270C2×C22⋊C4C2311yescharacteristic
271C2×C22⋊C4C2311yescharacteristic
272C2×C22⋊C4C2311yescharacteristic
273C2×C22⋊C4C2311yescharacteristic
274C2×C22⋊C4C2311yescharacteristic
275C2×C22⋊C4C2311yescharacteristic
276C2×C22⋊C4C2311yescharacteristic
277C2×C22⋊C4C2311yescharacteristic
278C2×C22⋊C4C2311yescharacteristic
279C2×C22⋊C4C2311yescharacteristic
280C2×C22⋊C4C2311yescharacteristic
281C2×C22⋊C4C2311yescharacteristic
282C2×C22⋊C4C2311yescharacteristic
283C2×C22⋊C4C2311yescharacteristic
284C2×C22⋊C4C2311yescharacteristic
285C2×C22⋊C4C2311yescharacteristic
286C2×C22⋊C4C2311yescharacteristic
287C2×C22⋊C4C2311yescharacteristic
288C2×C22⋊C4C2311yescharacteristic
289C2×C22⋊C4C2311yescharacteristic
290C2×C22⋊C4C2311yescharacteristic
291C2×C22⋊C4C2311yescharacteristic
292C2×C22⋊C4C2311yescharacteristic
293C2×C22⋊C4C2311yescharacteristic
294C2×C22⋊C4C2311yescharacteristic
295C2×C22⋊C4C2311yescharacteristic
296C2×C22⋊C4C2311yescharacteristic
297C2×C22⋊C4C2311yescharacteristic
298C2×C22⋊C4C2311yescharacteristic
299C2×C22⋊C4C2311yescharacteristic
300C2×C22⋊C4C2311yescharacteristic
301C2×C22⋊C4C2311yescharacteristic
302C2×C22⋊C4C2311yescharacteristic
303C2×C22⋊C4C2311yescharacteristic
304C2×C22⋊C4C2311yescharacteristic
305C2×C22⋊C4C2311yescharacteristic
306C2×C22⋊C4C2311yescharacteristic
307C2×C22⋊C4C2311yescharacteristic
308C2×C42C2311yescharacteristic
309C2×C42C2311yescharacteristic
310C2×C42C2311yescharacteristic
311C2×C42C2311yescharacteristic
312C2×C42C2311yescharacteristic
313C2×C42C2311yescharacteristic
314C2×C42C2311yescharacteristic
315C2×C42C2311yescharacteristic
316C2×C42C2311yescharacteristic
317#95C2311yescharacteristic
318#95C2311yescharacteristic
319#95C2311yescharacteristic
320#95C2311yescharacteristic
321#95C2311yescharacteristic
322#95C2311yescharacteristic
323#95C2311yescharacteristic
324#95C2311yescharacteristic
325#95C2311yescharacteristic
326#95C2311yescharacteristic
327#95C2311yescharacteristic
328#95C2311yescharacteristic
329#95C2311yescharacteristic
330#95C2311yescharacteristic
331#95C2311yescharacteristic
332#95C2311yescharacteristic
333#95C2311yescharacteristic
334#95C2311yescharacteristic
335#95C2311yescharacteristic
336#95C2311yescharacteristic
337#95C2311yescharacteristic
338#95C2311yescharacteristic
339#95C2311yescharacteristic
340#95C2311yescharacteristic
341#95C2311yescharacteristic
342#95C2311yescharacteristic
343#95C2311yescharacteristic
344#95C2311yescharacteristic
345#95C2311yescharacteristic
346#95C2311yescharacteristic
347#95C2311yescharacteristic
348#95C2311yescharacteristic
349#95C2311yescharacteristic
350#95C2311yescharacteristic
351#95C2311yescharacteristic
352#95C2311yescharacteristic
353#95C2311yescharacteristic
354#95C2311yescharacteristic
355#95C2311yescharacteristic
356#95C2311yescharacteristic
357#95C2311yescharacteristic
358#95C2311yescharacteristic
359#95C2311yescharacteristic
360#95C2311yescharacteristic
361#95C2311yescharacteristic
362#95C2311yescharacteristic
363C24—22no—
364C24—22no—
365C24—41no—
366C24—41no—
367C24—41no—
368C24—41no—
369C24—41no—
370C24C2411yescharacteristic
371C24C2411yescharacteristic
372C24C2411yescharacteristic
373C24C2411yescharacteristic
374C24C2411yescharacteristic
375C24C2411yescharacteristic
376#41—416no—
377C2×Q8—22no—
378C2×Q8—22no—
379C2×Q8—22no—
380C2×Q8—41no—
381C2×Q8—41no—
382C2×Q8—41no—
383C2×Q8—41no—
384C2×Q8—41no—
385C2×Q8—41no—
386C2×D4—22no—
387C2×D4—22no—
388C2×D4—22no—
389C2×D4—22no—
390C2×D4—22no—
391C2×D4—22no—
392C2×D4—22no—
393C2×D4—22no—
394C2×D4—22no—
395C2×D4—22no—
396C2×D4—22no—
397C2×D4—22no—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—41no—
401C2×D4—41no—
402C2×D4—41no—
403C2×D4—41no—
404C2×D4—41no—
405C2×D4—41no—
406C2×D4—41no—
407C2×D4—41no—
408C2×D4—41no—
409C2×D4—41no—
410C2×D4—41no—
411C2×D4—41no—
412C2×D4—41no—
413C2×D4—41no—
414C2×D4—41no—
415C2×D4—41no—
416C2×D4—41no—
417C2×D4—41no—
418C2×D4—41no—
419C2×D4—41no—
420C2×D4—41no—
421C2×D4—41no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4C2411yescharacteristic
450C22×C4C2411yescharacteristic
451C22×C4C2411yescharacteristic
452C22×C4C2411yescharacteristic
453C22×C4C2411yescharacteristic
454C22×C4C2411yescharacteristic
455C22×C4C2411yescharacteristic
456C22×C4C2411yescharacteristic
457C22×C4C2411yescharacteristic
458C22×C4C2411yescharacteristic
459C22×C4C2411yescharacteristic
460C22×C4C2411yescharacteristic
461C22×C4C2411yescharacteristic
462C22×C4C2411yescharacteristic
463C22×C4C2411yescharacteristic
464C22×C4C2411yescharacteristic
465C22×C4C2411yescharacteristic
466C22×C4C2411yescharacteristic
467C22×C4C2411yescharacteristic
468C22×C4C2411yescharacteristic
469C22×C4C2411yescharacteristic
470C22×C4C2411yescharacteristic
471C22×C4C2411yescharacteristic
472C22×C4C2411yescharacteristic
473C22×C4C2411yescharacteristic
474C4⋊C4—22no—
475C4⋊C4—22no—
476C4⋊C4—41no—
477C4⋊C4—41no—
478C4⋊C4—41no—
479C4⋊C4—41no—
480C4⋊C4—41no—
481C4⋊C4—41no—
482C4⋊C4—41no—
483C4⋊C4—41no—
484C4⋊C4—41no—
485C4⋊C4—41no—
486C4⋊C4—41no—
487C4⋊C4—41no—
488C4⋊C4—41no—
489C4⋊C4—41no—
490C4⋊C4—41no—
491C4⋊C4—41no—
492C4⋊C4—41no—
493C4⋊C4—41no—
494C4⋊C4—41no—
495C22⋊C4—22no—
496C22⋊C4—22no—
497C22⋊C4—22no—
498C22⋊C4—22no—
499C22⋊C4—22no—
500C22⋊C4—22no—
501C22⋊C4—22no—
502C22⋊C4—22no—
503C22⋊C4—22no—
504C22⋊C4—22no—
505C22⋊C4—22no—
506C22⋊C4—22no—
507C22⋊C4—22no—
508C22⋊C4—22no—
509C22⋊C4—41no—
510C22⋊C4—41no—
511C22⋊C4—41no—
512C22⋊C4—41no—
513C22⋊C4—41no—
514C22⋊C4—41no—
515C22⋊C4—41no—
516C22⋊C4—41no—
517C22⋊C4—41no—
518C22⋊C4—41no—
519C22⋊C4—41no—
520C22⋊C4—41no—
521C22⋊C4—41no—
522C22⋊C4—41no—
523C22⋊C4—41no—
524C22⋊C4—41no—
525C22⋊C4—41no—
526C22⋊C4—41no—
527C22⋊C4—41no—
528C22⋊C4—41no—
529C22⋊C4—41no—
530C22⋊C4—41no—
531C22⋊C4—41no—
532C22⋊C4—41no—
533C22⋊C4—41no—
534C22⋊C4—41no—
535C22⋊C4—41no—
536C22⋊C4—41no—
537C22⋊C4—41no—
538C22⋊C4—41no—
539C22⋊C4—41no—
540C22⋊C4—41no—
541C22⋊C4—41no—
542C22⋊C4—41no—
543C22⋊C4—41no—
544C22⋊C4—41no—
545C22⋊C4—41no—
546C22⋊C4—41no—
547C22⋊C4—41no—
548C22⋊C4#4114yescomplemented
549C42—22no—
550C42—22no—
551C42—22no—
552C42—41no—
553C42—41no—
554C42—41no—
555C42—41no—
556C42—41no—
557C42—41no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—44no—
598C23—44no—
599C23—82no—
600C23—82no—
601C23—82no—
602C23—82no—
603C23—82no—
604C23C2×#4112yes—
605C23H(5,𝔽2)12yes—
606C23H(5,𝔽2)12yes—
607C23C2511yescharacteristic
608Q8—44no—
609Q8—82no—
610Q8—82no—
611D4—44no—
612D4—44no—
613D4—44no—
614D4—44no—
615D4—44no—
616D4—82no—
617D4—82no—
618D4—82no—
619D4—82no—
620D4—82no—
621D4—82no—
622D4—82no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—44no—
696C2×C4—44no—
697C2×C4—44no—
698C2×C4—82no—
699C2×C4—82no—
700C2×C4—82no—
701C2×C4—82no—
702C2×C4—82no—
703C2×C4—82no—
704C2×C4C2×#4112yes—
705C2×C4C2×#4112yes—
706C2×C4H(5,𝔽2)12yes—
707C22—22no—
708C22—22no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—88no—
750C22C22×#4111yescharacteristic
751C22C2×H(5,𝔽2)11yescharacteristic
752C22C2×H(5,𝔽2)11yescharacteristic
753C22C2×H(5,𝔽2)11yescharacteristic
754C22#58511yescharacteristic
755C22#58511yescharacteristic
756C22#58511yescharacteristic
757C4—22no—
758C4—22no—
759C4—22no—
760C4—41no—
761C4—41no—
762C4—41no—
763C4—41no—
764C4—41no—
765C4—41no—
766C4—41no—
767C4—41no—
768C4—41no—
769C4—41no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—41no—
774C4—41no—
775C4—41no—
776C4—41no—
777C4—41no—
778C4—41no—
779C4—41no—
780C4—41no—
781C4—41no—
782C2—42no—
783C2—42no—
784C2—42no—
785C2—81no—
786C2—81no—
787C2—81no—
788C2#349411yescharacteristic
789C2#351311yescharacteristic
790C2#351411yescharacteristic
791C2#353211yescharacteristic
792C2#353311yescharacteristic
793C2#354511yescharacteristic
794C2#355111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C25
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #2775C2semidirect
2. #2764C2semidirect
3. #2761C2semidirect
4. #2757C2semidirect
5. #2756C2semidirect
6. #2749C2semidirect
7. #2749C2semidirect
8. #2729C2semidirect
9. #2697C2semidirect
10. #2688C2semidirect
11. #2681C2semidirect
12. #2670C2semidirect
13. #2661C2semidirect
14. #2640C2semidirect
15. #2572C2semidirect
16. #2572C2semidirect
17. #2557C2semidirect
18. #2526C2semidirect
19. #2488C2semidirect
20. #2483C2semidirect
21. #2472C2semidirect
22. #2459C2semidirect
23. #2459C2semidirect
24. #2432C2semidirect
25. #2430C2semidirect
26. #2424C2semidirect
27. #2420C2semidirect
28. #2404C2semidirect
29. #2379C2semidirect
30. #2353C2semidirect
31. #2321C2semidirect
33. C2×C4⋊Q8C22semidirect
38. C2×#123C22semidirect
40. C2×C22⋊Q8C22semidirect
43. C2×#121C22semidirect
51. #400C22semidirect
52. #400C22semidirect
53. #400C22semidirect
54. #400C22semidirect
55. #398C22semidirect
56. #398C22semidirect
57. #398C22semidirect
65. #397C22semidirect
66. #397C22semidirect
67. #397C22semidirect
68. #397C22semidirect
72. #396C22semidirect
73. #395C22semidirect
82. #394C22semidirect
83. #394C22semidirect
84. #394C22semidirect
85. #394C22semidirect
90. #393C22semidirect
91. #393C22semidirect
92. #393C22semidirect
99. #391C22semidirect
100. #391C22semidirect
101. #391C22semidirect
102. #391C22semidirect
103. #391C22semidirect
111. #389C22semidirect
112. #389C22semidirect
124. #388C22semidirect
125. #388C22semidirect
126. #388C22semidirect
127. #388C22semidirect
128. #388C22semidirect
129. #388C22semidirect
130. #388C22semidirect
131. #387C22semidirect
132. #387C22semidirect
133. #387C22semidirect
134. #387C22semidirect
150. #386C22semidirect
151. #386C22semidirect
152. #386C22semidirect
153. #386C22semidirect
160. #385C22semidirect
161. #385C22semidirect
162. #385C22semidirect
163. #383C22semidirect
164. #383C22semidirect
165. #383C22semidirect
166. #383C22semidirect
167. #382C22semidirect
168. #382C22semidirect
174. #381C22semidirect
175. #381C22semidirect
176. #380C22semidirect
181. C4×C22⋊C4C22semidirect
182. C4×C22⋊C4C22semidirect
183. C4×C22⋊C4C22semidirect
184. C4×C22⋊C4C22semidirect
185. #376C22semidirect
186. C2×#95C22semidirect
548. C22⋊C4#41semidirect

Maximal subgroups

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

subgroupindex
#27752
#27642
#27612
#27572
#27562
#27492
#27292
#26972
#26882
#26812
#26702
#26612
#26402
#25722
#25572
#25262
#24882
#24832
#24722
#24592
#24322
#24302
#24242
#24202
#24042
#23792
#23532
#23212