Finite Group Databasebeta

← #40686

Subgroups — #40686

Order 256.

919 conjugacy classes of subgroups.

The subgroup lattice has 789 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2837C211yesmaximal, characteristic, complemented
2#2829C211yesmaximal, characteristic, complemented
3#2705C211yesmaximal, characteristic, complemented
4#2697C211yesmaximal, characteristic, complemented
5#2694C211yesmaximal, characteristic, complemented
6#2693C211yesmaximal, characteristic, complemented
7#2687C211yesmaximal, characteristic, complemented
8#2685C211yesmaximal, characteristic, complemented
9#2670C211yesmaximal, characteristic, complemented
10#2668C211yesmaximal, characteristic, complemented
11#2664C211yesmaximal, characteristic, complemented
12#2661C211yesmaximal, characteristic, complemented
13#2661C211yesmaximal, characteristic, complemented
14#2654C211yesmaximal, characteristic, complemented
15#2635C211yesmaximal, characteristic, complemented
16#2597C211yesmaximal, characteristic, complemented
17#2593C211yesmaximal, characteristic, complemented
18#2554C211yesmaximal, characteristic, complemented
19#2554C211yesmaximal, characteristic, complemented
20#2539C211yesmaximal, characteristic, complemented
21#2521C211yesmaximal, characteristic, complemented
22#2516C211yesmaximal, characteristic, complemented
23#2490C211yesmaximal, characteristic, complemented
24#2461C211yesmaximal, characteristic, complemented
25#2448C211yesmaximal, characteristic, complemented
26#2426C211yesmaximal, characteristic, complemented
27#2411C211yesmaximal, characteristic, complemented
28#2396C211yesmaximal, characteristic, complemented
29#2374C211yesmaximal, characteristic, complemented
30#2363C211yesmaximal, characteristic, complemented
31#2312C211yesmaximal, characteristic, complemented
32C2×#126C2211yescharacteristic
33C2×#126C2211yescharacteristic, complemented
34C2×#125C2211yescharacteristic, complemented
35C2×#124C2211yescharacteristic
36C2×#124C2211yescharacteristic
37C2×#123C2211yescharacteristic
38C2×#123C2211yescharacteristic
39C2×#123C2211yescharacteristic
40C2×#123C2211yescharacteristic
41C2×#123C2211yescharacteristic, complemented
42C2×C22⋊Q8C2211yescharacteristic, complemented
43C2×#121C2211yescharacteristic
44C2×#121C2211yescharacteristic
45C2×#121C2211yescharacteristic
46C2×#120C2211yescharacteristic
47C2×#120C2211yescharacteristic
48C2×#120C2211yescharacteristic
49C2×C4×Q8C2211yescharacteristic, complemented
50C2×C4×D4C2211yescharacteristic, complemented
51C2×#117C2211yescharacteristic
52C22×C22⋊C4C2211yescharacteristic
53#400C2211yescharacteristic, complemented
54#400C2211yescharacteristic, complemented
55#400C2211yescharacteristic, complemented
56#400C2211yescharacteristic, complemented
57#399C2211yescharacteristic
58#399C2211yescharacteristic
59#399C2211yescharacteristic
60#399C2211yescharacteristic
61#399C2211yescharacteristic, complemented
62#399C2211yescharacteristic, complemented
63#398C2211yescharacteristic, complemented
64#398C2211yescharacteristic, complemented
65#398C2211yescharacteristic, complemented
66#398C2211yescharacteristic, complemented
67#398C2211yescharacteristic, complemented
68#398C2211yescharacteristic, complemented
69#397C2211yescharacteristic
70#397C2211yescharacteristic
71#397C2211yescharacteristic
72#397C2211yescharacteristic
73#397C2211yescharacteristic, complemented
74#397C2211yescharacteristic, complemented
75#397C2211yescharacteristic, complemented
76#397C2211yescharacteristic, complemented
77#396C2211yescharacteristic
78#396C2211yescharacteristic
79#396C2211yescharacteristic
80#396C2211yescharacteristic
81#396C2211yescharacteristic
82#396C2211yescharacteristic, complemented
83#396C2211yescharacteristic, complemented
84#396C2211yescharacteristic, complemented
85#395C2211yescharacteristic, complemented
86#394C2211yescharacteristic
87#394C2211yescharacteristic
88#394C2211yescharacteristic
89#394C2211yescharacteristic
90#394C2211yescharacteristic
91#394C2211yescharacteristic
92#394C2211yescharacteristic
93#394C2211yescharacteristic
94#394C2211yescharacteristic
95#394C2211yescharacteristic
96#394C2211yescharacteristic
97#394C2211yescharacteristic
98#394C2211yescharacteristic, complemented
99#394C2211yescharacteristic, complemented
100#394C2211yescharacteristic, complemented
101#393C2211yescharacteristic
102#392C2211yescharacteristic
103#392C2211yescharacteristic
104#392C2211yescharacteristic
105#392C2211yescharacteristic
106#392C2211yescharacteristic
107#392C2211yescharacteristic
108#392C2211yescharacteristic, complemented
109#391C2211yescharacteristic, complemented
110#390C2211yescharacteristic
111#390C2211yescharacteristic
112#390C2211yescharacteristic
113#390C2211yescharacteristic
114#390C2211yescharacteristic
115#390C2211yescharacteristic
116#390C2211yescharacteristic
117#390C2211yescharacteristic
118#390C2211yescharacteristic
119#390C2211yescharacteristic
120#390C2211yescharacteristic
121#390C2211yescharacteristic, complemented
122#390C2211yescharacteristic, complemented
123#390C2211yescharacteristic, complemented
124#389C2211yescharacteristic, complemented
125#389C2211yescharacteristic, complemented
126#389C2211yescharacteristic, complemented
127#388C2211yescharacteristic
128#388C2211yescharacteristic
129#388C2211yescharacteristic
130#388C2211yescharacteristic
131#388C2211yescharacteristic
132#388C2211yescharacteristic
133#388C2211yescharacteristic
134#388C2211yescharacteristic
135#388C2211yescharacteristic
136#388C2211yescharacteristic
137#388C2211yescharacteristic
138#388C2211yescharacteristic
139#388C2211yescharacteristic
140#388C2211yescharacteristic
141#388C2211yescharacteristic
142#388C2211yescharacteristic
143#388C2211yescharacteristic
144#388C2211yescharacteristic, complemented
145#388C2211yescharacteristic, complemented
146#388C2211yescharacteristic, complemented
147#388C2211yescharacteristic, complemented
148#388C2211yescharacteristic, complemented
149#388C2211yescharacteristic, complemented
150#388C2211yescharacteristic, complemented
151#388C2211yescharacteristic, complemented
152#388C2211yescharacteristic, complemented
153#387C2211yescharacteristic, complemented
154#387C2211yescharacteristic, complemented
155#387C2211yescharacteristic, complemented
156#387C2211yescharacteristic, complemented
157#386C2211yescharacteristic
158#386C2211yescharacteristic
159#386C2211yescharacteristic
160#386C2211yescharacteristic
161#386C2211yescharacteristic
162#386C2211yescharacteristic
163#386C2211yescharacteristic
164#386C2211yescharacteristic, complemented
165#385C2211yescharacteristic
166#385C2211yescharacteristic, complemented
167#381C2211yescharacteristic, complemented
168#380C2211yescharacteristic
169#380C2211yescharacteristic
170#380C2211yescharacteristic, complemented
171#379C2211yescharacteristic
172#379C2211yescharacteristic
173#379C2211yescharacteristic
174C4×C4⋊C4C2211yescharacteristic, complemented
175C4×C4⋊C4C2211yescharacteristic, complemented
176C4×C4⋊C4C2211yescharacteristic, complemented
177C4×C4⋊C4C2211yescharacteristic, complemented
178C4×C4⋊C4C2211yescharacteristic, complemented
179C4×C4⋊C4C2211yescharacteristic, complemented
180C4×C22⋊C4C2211yescharacteristic
181C4×C22⋊C4C2211yescharacteristic
182C4×C22⋊C4C2211yescharacteristic
183C4×C22⋊C4C2211yescharacteristic, complemented
184C4×C22⋊C4C2211yescharacteristic, complemented
185C4×C22⋊C4C2211yescharacteristic, complemented
186C4×C22⋊C4C2211yescharacteristic, complemented
187C25C2311yescharacteristic
188C22×Q8C2311yescharacteristic
189C22×D4C2311yescharacteristic
190C22×D4C2311yescharacteristic
191C22×D4C2311yescharacteristic
192C22×D4C2311yescharacteristic
193C22×D4C2311yescharacteristic
194C22×D4C2311yescharacteristic
195C22×D4C2311yescharacteristic
196C22×D4C2311yescharacteristic
197C22×D4C2311yescharacteristic
198C22×D4C2311yescharacteristic
199C22×D4C2311yescharacteristic
200C22×D4C2311yescharacteristic
201C23×C4C2311yescharacteristic
202C23×C4C2311yescharacteristic
203C23×C4C2311yescharacteristic
204C23×C4C2311yescharacteristic
205C23×C4C2311yescharacteristic
206#126—42no—
207#126—42no—
208#125—42no—
209#124—42no—
210#124—42no—
211#123—24no—
212#123—42no—
213#123—42no—
214#123—42no—
215#123—42no—
216C22⋊Q8—42no—
217#121—24no—
218#121—42no—
219#121—42no—
220#120—42no—
221#120—42no—
222#120—42no—
223C4×Q8—42no—
224C4×D4—42no—
225#117—42no—
226C2×C4⋊C4C2311yescharacteristic
227C2×C4⋊C4C2311yescharacteristic
228C2×C4⋊C4C2311yescharacteristic
229C2×C4⋊C4C2311yescharacteristic
230C2×C4⋊C4C2311yescharacteristic
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×C4⋊C4C2311yescharacteristic
253C2×C4⋊C4C2311yescharacteristic
254C2×C4⋊C4C2311yescharacteristic
255C2×C4⋊C4C2311yescharacteristic
256C2×C4⋊C4C2311yescharacteristic
257C2×C22⋊C4—24no—
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×C22⋊C4C2311yescharacteristic
309C2×C22⋊C4C2311yescharacteristic
310C2×C22⋊C4C2311yescharacteristic
311C2×C22⋊C4C2311yescharacteristic
312C2×C22⋊C4C2311yescharacteristic
313C2×C22⋊C4C2311yescharacteristic
314C2×C22⋊C4C2311yescharacteristic
315C2×C22⋊C4C2311yescharacteristic
316C2×C42C2311yescharacteristic
317C2×C42C2311yescharacteristic
318C2×C42C2311yescharacteristic
319C2×C42C2311yescharacteristic
320C2×C42C2311yescharacteristic
321C2×C42C2311yescharacteristic
322C2×C42C2311yescharacteristic
323C2×C42C2311yescharacteristic
324C2×C42C2311yescharacteristic
325C2×C42C2311yescharacteristic
326C2×C42C2311yescharacteristic
327C2×C42C2311yescharacteristic
328C2×C42C2311yescharacteristic
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—41no—
365C24—41no—
366C24—41no—
367C24—41no—
368C24—41no—
369C24—41no—
370C24C2411yescharacteristic
371C24C2411yescharacteristic
372C24C2411yescharacteristic
373C24C2411yescharacteristic
374C24C2411yescharacteristic
375C24C2411yescharacteristic
376C2×Q8—22no—
377C2×Q8—22no—
378C2×Q8—41no—
379C2×D4—22no—
380C2×D4—22no—
381C2×D4—22no—
382C2×D4—22no—
383C2×D4—22no—
384C2×D4—22no—
385C2×D4—22no—
386C2×D4—41no—
387C2×D4—41no—
388C2×D4—41no—
389C2×D4—41no—
390C2×D4—41no—
391C2×D4—41no—
392C2×D4—41no—
393C2×D4—41no—
394C2×D4—41no—
395C2×D4—41no—
396C2×D4—41no—
397C2×D4—41no—
398C2×D4—41no—
399C2×D4—41no—
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—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—41no—
419C22×C4—41no—
420C22×C4—41no—
421C22×C4—41no—
422C22×C4—41no—
423C22×C4—41no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4#4114yes—
430C22×C4C2411yescharacteristic
431C22×C4C2411yescharacteristic
432C22×C4C2411yescharacteristic
433C22×C4C2411yescharacteristic
434C22×C4C2411yescharacteristic
435C22×C4C2411yescharacteristic
436C22×C4C2411yescharacteristic
437C22×C4C2411yescharacteristic
438C22×C4C2411yescharacteristic
439C22×C4C2411yescharacteristic
440C22×C4C2411yescharacteristic
441C22×C4C2411yescharacteristic
442C22×C4C2411yescharacteristic
443C22×C4C2411yescharacteristic
444C22×C4C2411yescharacteristic
445C22×C4C2411yescharacteristic
446C22×C4C2411yescharacteristic
447C22×C4C2411yescharacteristic
448C22×C4C2411yescharacteristic
449C22×C4C2411yescharacteristic
450C22×C4C2411yescharacteristic
451C22×C4C2411yescharacteristic
452C22×C4C2411yescharacteristic
453C22×C4C2411yescharacteristic
454C22×C4C2411yescharacteristic
455C4⋊C4—22no—
456C4⋊C4—22no—
457C4⋊C4—22no—
458C4⋊C4—22no—
459C4⋊C4—22no—
460C4⋊C4—22no—
461C4⋊C4—22no—
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4—22no—
465C4⋊C4—22no—
466C4⋊C4—41no—
467C4⋊C4—41no—
468C4⋊C4—41no—
469C4⋊C4—41no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C4⋊C4—41no—
474C4⋊C4—41no—
475C4⋊C4—41no—
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—
486C22⋊C4—22no—
487C22⋊C4—22no—
488C22⋊C4—22no—
489C22⋊C4—22no—
490C22⋊C4—22no—
491C22⋊C4—22no—
492C22⋊C4—22no—
493C22⋊C4—22no—
494C22⋊C4—22no—
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—41no—
506C22⋊C4—41no—
507C22⋊C4—41no—
508C22⋊C4—41no—
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—
544C42—22no—
545C42—22no—
546C42—41no—
547C42—41no—
548C42—41no—
549C42—41no—
550C42—41no—
551C42—41no—
552C42—41no—
553C42—41no—
554C42—41no—
555C42—41no—
556C42—41no—
557C23—21no—
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—21no—
598C23—44no—
599C23—82no—
600C23—82no—
601C23—82no—
602C23—82no—
603C23—82no—
604C23—82no—
605C23C2×#4112yes—
606C23C2511yescharacteristic
607Q8—44no—
608D4—44no—
609D4—82no—
610D4—82no—
611D4—82no—
612D4—82no—
613D4—82no—
614D4—82no—
615D4—82no—
616D4—82no—
617D4—82no—
618D4—82no—
619D4—82no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
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—44no—
691C2×C4—82no—
692C2×C4—82no—
693C2×C4—82no—
694C2×C4—82no—
695C2×C4C2×#4112yes—
696C2×C4C2×#4112yes—
697C2×C4H(5,𝔽2)12yes—
698C2×C4H(5,𝔽2)12yes—
699C2×C4H(5,𝔽2)12yes—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
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—88no—
743C22C22×#4111yescharacteristic
744C22C2×H(5,𝔽2)11yescharacteristic
745C22C2×H(5,𝔽2)11yescharacteristic
746C22C2×H(5,𝔽2)11yescharacteristic
747C22#58511yescharacteristic
748C22#58511yescharacteristic
749C22#58511yescharacteristic
750C4—22no—
751C4—22no—
752C4—22no—
753C4—22no—
754C4—22no—
755C4—41no—
756C4—41no—
757C4—41no—
758C4—41no—
759C4—41no—
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—
775C2—42no—
776C2—81no—
777C2—81no—
778C2—81no—
779C2—81no—
780C2—81no—
781C2#345511yescharacteristic
782C2#350511yescharacteristic
783C2#350811yescharacteristic
784C2#353411yescharacteristic
785C2#354511yescharacteristic
786C2#354611yescharacteristic
787C2#356211yescharacteristic
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. #2837C2semidirect
2. #2829C2semidirect
3. #2705C2semidirect
4. #2697C2semidirect
5. #2694C2semidirect
6. #2693C2semidirect
7. #2687C2semidirect
8. #2685C2semidirect
9. #2670C2semidirect
10. #2668C2semidirect
11. #2664C2semidirect
12. #2661C2semidirect
13. #2661C2semidirect
14. #2654C2semidirect
15. #2635C2semidirect
16. #2597C2semidirect
17. #2593C2semidirect
18. #2554C2semidirect
19. #2554C2semidirect
20. #2539C2semidirect
21. #2521C2semidirect
22. #2516C2semidirect
23. #2490C2semidirect
24. #2461C2semidirect
25. #2448C2semidirect
26. #2426C2semidirect
27. #2411C2semidirect
28. #2396C2semidirect
29. #2374C2semidirect
30. #2363C2semidirect
31. #2312C2semidirect
33. C2×#126C22semidirect
34. C2×#125C22semidirect
41. C2×#123C22semidirect
42. C2×C22⋊Q8C22semidirect
49. C2×C4×Q8C22semidirect
50. C2×C4×D4C22semidirect
53. #400C22semidirect
54. #400C22semidirect
55. #400C22semidirect
56. #400C22semidirect
61. #399C22semidirect
62. #399C22semidirect
63. #398C22semidirect
64. #398C22semidirect
65. #398C22semidirect
66. #398C22semidirect
67. #398C22semidirect
68. #398C22semidirect
73. #397C22semidirect
74. #397C22semidirect
75. #397C22semidirect
76. #397C22semidirect
82. #396C22semidirect
83. #396C22semidirect
84. #396C22semidirect
85. #395C22semidirect
98. #394C22semidirect
99. #394C22semidirect
100. #394C22semidirect
108. #392C22semidirect
109. #391C22semidirect
121. #390C22semidirect
122. #390C22semidirect
123. #390C22semidirect
124. #389C22semidirect
125. #389C22semidirect
126. #389C22semidirect
144. #388C22semidirect
145. #388C22semidirect
146. #388C22semidirect
147. #388C22semidirect
148. #388C22semidirect
149. #388C22semidirect
150. #388C22semidirect
151. #388C22semidirect
152. #388C22semidirect
153. #387C22semidirect
154. #387C22semidirect
155. #387C22semidirect
156. #387C22semidirect
164. #386C22semidirect
166. #385C22semidirect
167. #381C22semidirect
170. #380C22semidirect
174. C4×C4⋊C4C22semidirect
175. C4×C4⋊C4C22semidirect
176. C4×C4⋊C4C22semidirect
177. C4×C4⋊C4C22semidirect
178. C4×C4⋊C4C22semidirect
179. C4×C4⋊C4C22semidirect
183. C4×C22⋊C4C22semidirect
184. C4×C22⋊C4C22semidirect
185. C4×C22⋊C4C22semidirect
186. C4×C22⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
#28372
#28292
#27052
#26972
#26942
#26932
#26872
#26852
#26702
#26682
#26642
#26612
#26542
#26352
#25972
#25932
#25542
#25392
#25212
#25162
#24902
#24612
#24482
#24262
#24112
#23962
#23742
#23632
#23122