Finite Group Databasebeta

← #57196

Subgroups — #57196

Order 256.

1064 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2825C211yesmaximal, characteristic, complemented
2#2825C211yesmaximal, characteristic, complemented
3#2818C211yesmaximal, characteristic, complemented
4#2778C211yesmaximal, characteristic, complemented
5#2759C211yesmaximal, characteristic, complemented
6#2715C211yesmaximal, characteristic, complemented
7#2714C211yesmaximal, characteristic, complemented
8#2714C211yesmaximal, characteristic, complemented
9#2714C211yesmaximal, characteristic, complemented
10#2714C211yesmaximal, characteristic, complemented
11#2705C211yesmaximal, characteristic, complemented
12#2691C211yesmaximal, characteristic, complemented
13#2684C211yesmaximal, characteristic, complemented
14#2678C211yesmaximal, characteristic, complemented
15#2678C211yesmaximal, characteristic, complemented
16#2670C211yesmaximal, characteristic, complemented
17#2669C211yesmaximal, characteristic, complemented
18#2669C211yesmaximal, characteristic, complemented
19#2668C211yesmaximal, characteristic, complemented
20#2662C211yesmaximal, characteristic, complemented
21#2653C211yesmaximal, characteristic, complemented
22#2615C211yesmaximal, characteristic, complemented
23#2559C211yesmaximal, characteristic, complemented
24#2554C211yesmaximal, characteristic, complemented
25#2521C211yesmaximal, characteristic, complemented
26#2510C211yesmaximal, characteristic, complemented
27#2431C211yesmaximal, characteristic, complemented
28#2431C211yesmaximal, characteristic, complemented
29#2431C211yesmaximal, characteristic, complemented
30#2430C211yesmaximal, characteristic, complemented
31#2430C211yesmaximal, characteristic, complemented
32C22×#41C2211yescharacteristic, complemented
33C22×#41C2211yescharacteristic, complemented
34C2×#127C2211yescharacteristic
35C2×#127C2211yescharacteristic
36C2×#126C2211yescharacteristic, complemented
37C2×#126C2211yescharacteristic, complemented
38C2×#126C2211yescharacteristic, complemented
39C2×#126C2211yescharacteristic, complemented
40C2×#124C2211yescharacteristic
41C2×#124C2211yescharacteristic
42C2×#124C2211yescharacteristic
43C2×#123C2211yescharacteristic
44C2×#123C2211yescharacteristic
45C2×#121C2211yescharacteristic
46C2×#121C2211yescharacteristic
47C2×#121C2211yescharacteristic
48C2×#121C2211yescharacteristic
49C2×#121C2211yescharacteristic
50C2×#121C2211yescharacteristic
51C2×#121C2211yescharacteristic
52C2×#121C2211yescharacteristic
53C2×#120C2211yescharacteristic
54C2×#120C2211yescharacteristic
55C2×#120C2211yescharacteristic
56C2×#120C2211yescharacteristic
57C2×#120C2211yescharacteristic
58#401C2211yescharacteristic, complemented
59#401C2211yescharacteristic, complemented
60#400C2211yescharacteristic, complemented
61#399C2211yescharacteristic
62#398C2211yescharacteristic, complemented
63#397C2211yescharacteristic
64#397C2211yescharacteristic
65#397C2211yescharacteristic
66#397C2211yescharacteristic
67#397C2211yescharacteristic
68#397C2211yescharacteristic
69#397C2211yescharacteristic, complemented
70#397C2211yescharacteristic, complemented
71#397C2211yescharacteristic, complemented
72#396C2211yescharacteristic
73#396C2211yescharacteristic
74#396C2211yescharacteristic, complemented
75#396C2211yescharacteristic, complemented
76#395C2211yescharacteristic, complemented
77#395C2211yescharacteristic, complemented
78#394C2211yescharacteristic
79#394C2211yescharacteristic
80#394C2211yescharacteristic
81#394C2211yescharacteristic
82#394C2211yescharacteristic
83#394C2211yescharacteristic
84#394C2211yescharacteristic
85#394C2211yescharacteristic
86#394C2211yescharacteristic
87#394C2211yescharacteristic
88#394C2211yescharacteristic
89#394C2211yescharacteristic
90#394C2211yescharacteristic
91#394C2211yescharacteristic
92#394C2211yescharacteristic, complemented
93#394C2211yescharacteristic, complemented
94#394C2211yescharacteristic, complemented
95#394C2211yescharacteristic, complemented
96#393C2211yescharacteristic
97#393C2211yescharacteristic
98#393C2211yescharacteristic
99#393C2211yescharacteristic, complemented
100#392C2211yescharacteristic
101#392C2211yescharacteristic
102#392C2211yescharacteristic
103#392C2211yescharacteristic
104#392C2211yescharacteristic
105#392C2211yescharacteristic
106#392C2211yescharacteristic
107#392C2211yescharacteristic
108#392C2211yescharacteristic
109#392C2211yescharacteristic
110#392C2211yescharacteristic
111#392C2211yescharacteristic
112#392C2211yescharacteristic
113#392C2211yescharacteristic
114#392C2211yescharacteristic
115#392C2211yescharacteristic
116#392C2211yescharacteristic, complemented
117#392C2211yescharacteristic, complemented
118#392C2211yescharacteristic, complemented
119#392C2211yescharacteristic, complemented
120#392C2211yescharacteristic, complemented
121#392C2211yescharacteristic, complemented
122#391C2211yescharacteristic, complemented
123#391C2211yescharacteristic, complemented
124#391C2211yescharacteristic, complemented
125#390C2211yescharacteristic
126#390C2211yescharacteristic
127#390C2211yescharacteristic
128#390C2211yescharacteristic
129#390C2211yescharacteristic
130#390C2211yescharacteristic
131#390C2211yescharacteristic, complemented
132#390C2211yescharacteristic, complemented
133#390C2211yescharacteristic, complemented
134#390C2211yescharacteristic, complemented
135#389C2211yescharacteristic, complemented
136#388C2211yescharacteristic
137#388C2211yescharacteristic
138#388C2211yescharacteristic
139#388C2211yescharacteristic
140#388C2211yescharacteristic
141#388C2211yescharacteristic
142#388C2211yescharacteristic
143#388C2211yescharacteristic
144#388C2211yescharacteristic
145#388C2211yescharacteristic
146#388C2211yescharacteristic, complemented
147#388C2211yescharacteristic, complemented
148#387C2211yescharacteristic, complemented
149#387C2211yescharacteristic, complemented
150#387C2211yescharacteristic, complemented
151#387C2211yescharacteristic, complemented
152#386C2211yescharacteristic
153#386C2211yescharacteristic
154#386C2211yescharacteristic
155#386C2211yescharacteristic
156#386C2211yescharacteristic
157#386C2211yescharacteristic
158#386C2211yescharacteristic
159#386C2211yescharacteristic
160#386C2211yescharacteristic
161#386C2211yescharacteristic
162#386C2211yescharacteristic
163#386C2211yescharacteristic, complemented
164#386C2211yescharacteristic, complemented
165#386C2211yescharacteristic, complemented
166#386C2211yescharacteristic, complemented
167#386C2211yescharacteristic, complemented
168#386C2211yescharacteristic, complemented
169#386C2211yescharacteristic, complemented
170#386C2211yescharacteristic, complemented
171#385C2211yescharacteristic, complemented
172#385C2211yescharacteristic, complemented
173#385C2211yescharacteristic, complemented
174#385C2211yescharacteristic, complemented
175#385C2211yescharacteristic, complemented
176#383C2211yescharacteristic, complemented
177#380C2211yescharacteristic, complemented
178#380C2211yescharacteristic, complemented
179#380C2211yescharacteristic, complemented
180#379C2211yescharacteristic
181#379C2211yescharacteristic
182C4×C4⋊C4C2211yescharacteristic, complemented
183C4×C22⋊C4C2211yescharacteristic, complemented
184C4×C22⋊C4C2211yescharacteristic, complemented
185C4×C22⋊C4C2211yescharacteristic, complemented
186C2×#95C2211yescharacteristic, complemented
187C25C2311yescharacteristic
188C2×#41—42no—
189C2×#41—42no—
190C2×#41—42no—
191C2×#41—42no—
192C2×#41—42no—
193C2×#41—42no—
194C22×Q8C2311yescharacteristic
195C22×Q8C2311yescharacteristic
196C22×D4C2311yescharacteristic
197C22×D4C2311yescharacteristic
198C22×D4C2311yescharacteristic
199C22×D4C2311yescharacteristic
200C22×D4C2311yescharacteristic
201C22×D4C2311yescharacteristic
202C22×D4C2311yescharacteristic
203C22×D4C2311yescharacteristic
204C22×D4C2311yescharacteristic
205C22×D4C2311yescharacteristic
206C22×D4C2311yescharacteristic
207C22×D4C2311yescharacteristic
208C22×D4C2311yescharacteristic
209C22×D4C2311yescharacteristic
210C22×D4C2311yescharacteristic
211C22×D4C2311yescharacteristic
212C22×D4C2311yescharacteristic
213C22×D4C2311yescharacteristic
214C22×D4C2311yescharacteristic
215C22×D4C2311yescharacteristic
216C22×D4C2311yescharacteristic
217C22×D4C2311yescharacteristic
218C22×D4C2311yescharacteristic
219C22×D4C2311yescharacteristic
220C22×D4C2311yescharacteristic
221C23×C4C2311yescharacteristic
222C23×C4C2311yescharacteristic
223C23×C4C2311yescharacteristic
224C23×C4C2311yescharacteristic
225C23×C4C2311yescharacteristic
226C23×C4C2311yescharacteristic
227C23×C4C2311yescharacteristic
228#127—42no—
229#127—42no—
230#126—42no—
231#126—42no—
232#126—42no—
233#126—42no—
234#124—42no—
235#124—42no—
236#124—42no—
237#123—42no—
238#123—42no—
239#121—42no—
240#121—42no—
241#121—42no—
242#121—42no—
243#121—42no—
244#121—42no—
245#121—42no—
246#121—42no—
247#120—42no—
248#120—42no—
249#120—42no—
250#120—42no—
251#120—42no—
252C2×C4⋊C4C2311yescharacteristic
253C2×C4⋊C4C2311yescharacteristic
254C2×C4⋊C4C2311yescharacteristic
255C2×C4⋊C4C2311yescharacteristic
256C2×C4⋊C4C2311yescharacteristic
257C2×C4⋊C4C2311yescharacteristic
258C2×C4⋊C4C2311yescharacteristic
259C2×C4⋊C4C2311yescharacteristic
260C2×C4⋊C4C2311yescharacteristic
261C2×C4⋊C4C2311yescharacteristic
262C2×C4⋊C4C2311yescharacteristic
263C2×C4⋊C4C2311yescharacteristic
264C2×C4⋊C4C2311yescharacteristic
265C2×C4⋊C4C2311yescharacteristic
266C2×C4⋊C4C2311yescharacteristic
267C2×C4⋊C4C2311yescharacteristic
268C2×C4⋊C4C2311yescharacteristic
269C2×C4⋊C4C2311yescharacteristic
270C2×C4⋊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×C22⋊C4C2311yescharacteristic
317C2×C22⋊C4C2311yescharacteristic
318C2×C22⋊C4C2311yescharacteristic
319C2×C22⋊C4C2311yescharacteristic
320C2×C22⋊C4C2311yescharacteristic
321C2×C22⋊C4C2311yescharacteristic
322C2×C22⋊C4C2311yescharacteristic
323C2×C22⋊C4C2311yescharacteristic
324C2×C22⋊C4C2311yescharacteristic
325C2×C22⋊C4C2311yescharacteristic
326C2×C22⋊C4C2311yescharacteristic
327C2×C22⋊C4C2311yescharacteristic
328C2×C22⋊C4C2311yescharacteristic
329C2×C22⋊C4C2311yescharacteristic
330C2×C22⋊C4C2311yescharacteristic
331C2×C42C2311yescharacteristic
332C2×C42C2311yescharacteristic
333C2×C42C2311yescharacteristic
334C2×C42C2311yescharacteristic
335C2×C42C2311yescharacteristic
336C2×C42C2311yescharacteristic
337C2×C42C2311yescharacteristic
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
363#95C2311yescharacteristic
364#95C2311yescharacteristic
365#95C2311yescharacteristic
366#95C2311yescharacteristic
367#95C2311yescharacteristic
368#95C2311yescharacteristic
369#95C2311yescharacteristic
370#95C2311yescharacteristic
371#95C2311yescharacteristic
372C24—41no—
373C24—41no—
374C24—41no—
375C24—41no—
376C24—41no—
377C24—41no—
378C24—41no—
379C24C2411yescharacteristic
380C24C2411yescharacteristic
381C24C2411yescharacteristic
382C24C2411yescharacteristic
383C24C2411yescharacteristic
384C24C2411yescharacteristic
385C24C2411yescharacteristic
386C24C2411yescharacteristic
387#41—416no—
388#41—416no—
389C2×Q8—22no—
390C2×Q8—22no—
391C2×Q8—22no—
392C2×Q8—41no—
393C2×Q8—41no—
394C2×Q8—41no—
395C2×D4—22no—
396C2×D4—22no—
397C2×D4—22no—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—22no—
401C2×D4—22no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—22no—
405C2×D4—22no—
406C2×D4—22no—
407C2×D4—22no—
408C2×D4—22no—
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—
422C2×D4—41no—
423C2×D4—41no—
424C2×D4—41no—
425C2×D4—41no—
426C2×D4—41no—
427C2×D4—41no—
428C2×D4—41no—
429C2×D4—41no—
430C2×D4—41no—
431C2×D4—41no—
432C2×D4—41no—
433C2×D4—41no—
434C2×D4—41no—
435C2×D4—41no—
436C2×D4—41no—
437C2×D4—41no—
438C2×D4—41no—
439C2×D4—41no—
440C2×D4—41no—
441C2×D4—41no—
442C2×D4—41no—
443C2×D4—41no—
444C2×D4—41no—
445C2×D4—41no—
446C2×D4—41no—
447C2×D4—41no—
448C2×D4—41no—
449C2×D4—41no—
450C2×D4—41no—
451C2×D4—41no—
452C2×D4—41no—
453C2×D4—41no—
454C2×D4—41no—
455C2×D4—41no—
456C2×D4—41no—
457C2×D4—41no—
458C2×D4—41no—
459C2×D4—41no—
460C2×D4—41no—
461C2×D4—41no—
462C2×D4—41no—
463C2×D4—41no—
464C2×D4—41no—
465C2×D4—41no—
466C2×D4—41no—
467C2×D4—41no—
468C2×D4—41no—
469C2×D4—41no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—41no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4—41no—
486C22×C4—41no—
487C22×C4—41no—
488C22×C4—41no—
489C22×C4—41no—
490C22×C4—41no—
491C22×C4C2411yescharacteristic
492C22×C4C2411yescharacteristic
493C22×C4C2411yescharacteristic
494C22×C4C2411yescharacteristic
495C22×C4C2411yescharacteristic
496C22×C4C2411yescharacteristic
497C22×C4C2411yescharacteristic
498C22×C4C2411yescharacteristic
499C22×C4C2411yescharacteristic
500C22×C4C2411yescharacteristic
501C22×C4C2411yescharacteristic
502C22×C4C2411yescharacteristic
503C22×C4C2411yescharacteristic
504C22×C4C2411yescharacteristic
505C22×C4C2411yescharacteristic
506C22×C4C2411yescharacteristic
507C22×C4C2411yescharacteristic
508C22×C4C2411yescharacteristic
509C22×C4C2411yescharacteristic
510C22×C4C2411yescharacteristic
511C22×C4C2411yescharacteristic
512C22×C4C2411yescharacteristic
513C22×C4C2411yescharacteristic
514C4⋊C4—22no—
515C4⋊C4—22no—
516C4⋊C4—22no—
517C4⋊C4—22no—
518C4⋊C4—22no—
519C4⋊C4—22no—
520C4⋊C4—41no—
521C4⋊C4—41no—
522C4⋊C4—41no—
523C4⋊C4—41no—
524C4⋊C4—41no—
525C4⋊C4—41no—
526C4⋊C4—41no—
527C4⋊C4—41no—
528C4⋊C4—41no—
529C4⋊C4—41no—
530C4⋊C4—41no—
531C4⋊C4—41no—
532C4⋊C4—41no—
533C22⋊C4—22no—
534C22⋊C4—22no—
535C22⋊C4—22no—
536C22⋊C4—22no—
537C22⋊C4—22no—
538C22⋊C4—22no—
539C22⋊C4—22no—
540C22⋊C4—22no—
541C22⋊C4—22no—
542C22⋊C4—22no—
543C22⋊C4—22no—
544C22⋊C4—22no—
545C22⋊C4—41no—
546C22⋊C4—41no—
547C22⋊C4—41no—
548C22⋊C4—41no—
549C22⋊C4—41no—
550C22⋊C4—41no—
551C22⋊C4—41no—
552C22⋊C4—41no—
553C22⋊C4—41no—
554C22⋊C4—41no—
555C22⋊C4—41no—
556C22⋊C4—41no—
557C22⋊C4—41no—
558C22⋊C4—41no—
559C22⋊C4—41no—
560C22⋊C4—41no—
561C22⋊C4—41no—
562C22⋊C4—41no—
563C22⋊C4—41no—
564C22⋊C4—41no—
565C22⋊C4—41no—
566C22⋊C4—41no—
567C22⋊C4—41no—
568C22⋊C4—41no—
569C22⋊C4—41no—
570C22⋊C4—41no—
571C22⋊C4—41no—
572C22⋊C4—41no—
573C22⋊C4—41no—
574C22⋊C4—41no—
575C22⋊C4—41no—
576C22⋊C4—41no—
577C22⋊C4—41no—
578C22⋊C4—41no—
579C22⋊C4—41no—
580C22⋊C4—41no—
581C22⋊C4—41no—
582C22⋊C4—41no—
583C22⋊C4—41no—
584C22⋊C4—41no—
585C22⋊C4—41no—
586C22⋊C4—41no—
587C22⋊C4—41no—
588C22⋊C4—41no—
589C22⋊C4—41no—
590C22⋊C4—41no—
591C22⋊C4—41no—
592C22⋊C4—41no—
593C42—22no—
594C42—22no—
595C42—41no—
596C42—41no—
597C42—41no—
598C42—41no—
599C42—41no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—82no—
656C23—82no—
657C23—82no—
658C23—82no—
659C23—82no—
660C23—82no—
661C23—82no—
662C23H(5,𝔽2)12yes—
663C23C2511yescharacteristic
664Q8—44no—
665Q8—44no—
666D4—44no—
667D4—44no—
668D4—44no—
669D4—44no—
670D4—44no—
671D4—44no—
672D4—82no—
673D4—82no—
674D4—82no—
675D4—82no—
676D4—82no—
677D4—82no—
678D4—82no—
679D4—82no—
680D4—82no—
681D4—82no—
682D4—82no—
683D4—82no—
684D4—82no—
685D4—82no—
686D4—82no—
687D4—82no—
688D4—82no—
689D4—82no—
690D4—82no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
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—44no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—44no—
760C2×C4—44no—
761C2×C4—44no—
762C2×C4—82no—
763C2×C4H(5,𝔽2)12yes—
764C2×C4H(5,𝔽2)12yes—
765C2×C4H(5,𝔽2)12yes—
766C2×C4H(5,𝔽2)12yes—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—88no—
824C22C2×H(5,𝔽2)11yescharacteristic
825C22C2×H(5,𝔽2)11yescharacteristic
826C22C2×H(5,𝔽2)11yescharacteristic
827C22C2×H(5,𝔽2)11yescharacteristic
828C22C2×H(5,𝔽2)11yescharacteristic
829C22#58511yescharacteristic
830C22#58511yescharacteristic
831C4—22no—
832C4—22no—
833C4—22no—
834C4—22no—
835C4—41no—
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—
851C4—41no—
852C4—41no—
853C4—41no—
854C2—42no—
855C2—81no—
856C2—81no—
857C2—81no—
858C2—81no—
859C2—81no—
860C2—81no—
861C2—81no—
862C2#353211yescharacteristic
863C2#353211yescharacteristic
864C2#354611yescharacteristic
865C2#354611yescharacteristic
866C2#354611yescharacteristic
867C2#354611yescharacteristic
868C2#356011yescharacteristic
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. #2825C2semidirect
2. #2825C2semidirect
3. #2818C2semidirect
4. #2778C2semidirect
5. #2759C2semidirect
6. #2715C2semidirect
7. #2714C2semidirect
8. #2714C2semidirect
9. #2714C2semidirect
10. #2714C2semidirect
11. #2705C2semidirect
12. #2691C2semidirect
13. #2684C2semidirect
14. #2678C2semidirect
15. #2678C2semidirect
16. #2670C2semidirect
17. #2669C2semidirect
18. #2669C2semidirect
19. #2668C2semidirect
20. #2662C2semidirect
21. #2653C2semidirect
22. #2615C2semidirect
23. #2559C2semidirect
24. #2554C2semidirect
25. #2521C2semidirect
26. #2510C2semidirect
27. #2431C2semidirect
28. #2431C2semidirect
29. #2431C2semidirect
30. #2430C2semidirect
31. #2430C2semidirect
32. C22×#41C22semidirect
33. C22×#41C22semidirect
36. C2×#126C22semidirect
37. C2×#126C22semidirect
38. C2×#126C22semidirect
39. C2×#126C22semidirect
58. #401C22semidirect
59. #401C22semidirect
60. #400C22semidirect
62. #398C22semidirect
69. #397C22semidirect
70. #397C22semidirect
71. #397C22semidirect
74. #396C22semidirect
75. #396C22semidirect
76. #395C22semidirect
77. #395C22semidirect
92. #394C22semidirect
93. #394C22semidirect
94. #394C22semidirect
95. #394C22semidirect
99. #393C22semidirect
116. #392C22semidirect
117. #392C22semidirect
118. #392C22semidirect
119. #392C22semidirect
120. #392C22semidirect
121. #392C22semidirect
122. #391C22semidirect
123. #391C22semidirect
124. #391C22semidirect
131. #390C22semidirect
132. #390C22semidirect
133. #390C22semidirect
134. #390C22semidirect
135. #389C22semidirect
146. #388C22semidirect
147. #388C22semidirect
148. #387C22semidirect
149. #387C22semidirect
150. #387C22semidirect
151. #387C22semidirect
163. #386C22semidirect
164. #386C22semidirect
165. #386C22semidirect
166. #386C22semidirect
167. #386C22semidirect
168. #386C22semidirect
169. #386C22semidirect
170. #386C22semidirect
171. #385C22semidirect
172. #385C22semidirect
173. #385C22semidirect
174. #385C22semidirect
175. #385C22semidirect
176. #383C22semidirect
177. #380C22semidirect
178. #380C22semidirect
179. #380C22semidirect
182. C4×C4⋊C4C22semidirect
183. C4×C22⋊C4C22semidirect
184. C4×C22⋊C4C22semidirect
185. C4×C22⋊C4C22semidirect
186. C2×#95C22semidirect

Maximal subgroups

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

subgroupindex
#28252
#28182
#27782
#27592
#27152
#27142
#27052
#26912
#26842
#26782
#26702
#26692
#26682
#26622
#26532
#26152
#25592
#25542
#25212
#25102
#24312
#24302