Finite Group Databasebeta

← #57487

Subgroups — #57487

Order 256.

1064 conjugacy classes of subgroups.

The subgroup lattice has 873 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2826C211yesmaximal, characteristic, complemented
2#2825C211yesmaximal, characteristic, complemented
3#2812C211yesmaximal, characteristic, complemented
4#2787C211yesmaximal, characteristic, complemented
5#2779C211yesmaximal, characteristic, complemented
6#2778C211yesmaximal, characteristic, complemented
7#2761C211yesmaximal, characteristic, complemented
8#2735C211yesmaximal, characteristic, complemented
9#2714C211yesmaximal, characteristic, complemented
10#2708C211yesmaximal, characteristic, complemented
11#2706C211yesmaximal, characteristic, complemented
12#2691C211yesmaximal, characteristic, complemented
13#2682C211yesmaximal, characteristic, complemented
14#2678C211yesmaximal, characteristic, complemented
15#2678C211yesmaximal, characteristic, complemented
16#2673C211yesmaximal, characteristic, complemented
17#2673C211yesmaximal, characteristic, complemented
18#2671C211yesmaximal, characteristic, complemented
19#2669C211yesmaximal, characteristic, complemented
20#2636C211yesmaximal, characteristic, complemented
21#2635C211yesmaximal, characteristic, complemented
22#2624C211yesmaximal, characteristic, complemented
23#2602C211yesmaximal, characteristic, complemented
24#2476C211yesmaximal, characteristic, complemented
25#2464C211yesmaximal, characteristic, complemented
26#2418C211yesmaximal, characteristic, complemented
27#2412C211yesmaximal, characteristic, complemented
28#2411C211yesmaximal, characteristic, complemented
29#2410C211yesmaximal, characteristic, complemented
30#2410C211yesmaximal, characteristic, complemented
31#2408C211yesmaximal, characteristic, complemented
32C23×D4C2211yescharacteristic
33C2×#127C2211yescharacteristic, complemented
34C2×#126C2211yescharacteristic, complemented
35C2×#123C2211yescharacteristic
36C2×#123C2211yescharacteristic, complemented
37C2×#123C2211yescharacteristic, complemented
38C2×#123C2211yescharacteristic, complemented
39C2×#123C2211yescharacteristic, complemented
40C2×#121C2211yescharacteristic
41C2×#121C2211yescharacteristic
42C2×#121C2211yescharacteristic
43C2×#121C2211yescharacteristic
44C2×#121C2211yescharacteristic
45C2×#121C2211yescharacteristic
46C2×#121C2211yescharacteristic
47C2×#121C2211yescharacteristic, complemented
48C2×#121C2211yescharacteristic, complemented
49C2×#120C2211yescharacteristic
50C2×#120C2211yescharacteristic
51C2×#120C2211yescharacteristic
52C2×#120C2211yescharacteristic
53C2×#120C2211yescharacteristic
54C2×#120C2211yescharacteristic
55C2×C4×D4C2211yescharacteristic
56C2×C4×D4C2211yescharacteristic, complemented
57C2×#117C2211yescharacteristic, complemented
58C22×C22⋊C4C2211yescharacteristic
59C22×C22⋊C4C2211yescharacteristic
60#401C2211yescharacteristic, complemented
61#400C2211yescharacteristic, complemented
62#400C2211yescharacteristic, complemented
63#400C2211yescharacteristic, complemented
64#399C2211yescharacteristic, complemented
65#399C2211yescharacteristic, complemented
66#399C2211yescharacteristic, complemented
67#398C2211yescharacteristic, complemented
68#398C2211yescharacteristic, complemented
69#398C2211yescharacteristic, complemented
70#397C2211yescharacteristic
71#397C2211yescharacteristic
72#397C2211yescharacteristic
73#397C2211yescharacteristic, complemented
74#397C2211yescharacteristic, complemented
75#397C2211yescharacteristic, complemented
76#397C2211yescharacteristic, complemented
77#397C2211yescharacteristic, complemented
78#397C2211yescharacteristic, complemented
79#397C2211yescharacteristic, complemented
80#396C2211yescharacteristic
81#396C2211yescharacteristic, complemented
82#396C2211yescharacteristic, complemented
83#396C2211yescharacteristic, complemented
84#396C2211yescharacteristic, complemented
85#396C2211yescharacteristic, complemented
86#394C2211yescharacteristic
87#394C2211yescharacteristic
88#394C2211yescharacteristic
89#394C2211yescharacteristic
90#394C2211yescharacteristic
91#394C2211yescharacteristic
92#394C2211yescharacteristic
93#394C2211yescharacteristic
94#394C2211yescharacteristic
95#394C2211yescharacteristic
96#394C2211yescharacteristic, complemented
97#394C2211yescharacteristic, complemented
98#394C2211yescharacteristic, complemented
99#394C2211yescharacteristic, complemented
100#394C2211yescharacteristic, complemented
101#394C2211yescharacteristic, complemented
102#394C2211yescharacteristic, complemented
103#394C2211yescharacteristic, complemented
104#394C2211yescharacteristic, complemented
105#394C2211yescharacteristic, complemented
106#394C2211yescharacteristic, complemented
107#394C2211yescharacteristic, complemented
108#394C2211yescharacteristic, complemented
109#392C2211yescharacteristic
110#392C2211yescharacteristic
111#392C2211yescharacteristic
112#392C2211yescharacteristic
113#392C2211yescharacteristic
114#392C2211yescharacteristic
115#392C2211yescharacteristic
116#392C2211yescharacteristic
117#392C2211yescharacteristic, complemented
118#392C2211yescharacteristic, complemented
119#392C2211yescharacteristic, complemented
120#392C2211yescharacteristic, complemented
121#392C2211yescharacteristic, complemented
122#392C2211yescharacteristic, complemented
123#392C2211yescharacteristic, complemented
124#390C2211yescharacteristic
125#390C2211yescharacteristic
126#390C2211yescharacteristic
127#390C2211yescharacteristic, complemented
128#390C2211yescharacteristic, complemented
129#390C2211yescharacteristic, complemented
130#390C2211yescharacteristic, complemented
131#389C2211yescharacteristic, complemented
132#389C2211yescharacteristic, complemented
133#388C2211yescharacteristic
134#388C2211yescharacteristic
135#388C2211yescharacteristic
136#388C2211yescharacteristic, complemented
137#388C2211yescharacteristic, complemented
138#388C2211yescharacteristic, complemented
139#388C2211yescharacteristic, complemented
140#388C2211yescharacteristic, complemented
141#388C2211yescharacteristic, complemented
142#388C2211yescharacteristic, complemented
143#388C2211yescharacteristic, complemented
144#388C2211yescharacteristic, complemented
145#388C2211yescharacteristic, complemented
146#387C2211yescharacteristic, complemented
147#387C2211yescharacteristic, complemented
148#387C2211yescharacteristic, complemented
149#387C2211yescharacteristic, complemented
150#386C2211yescharacteristic
151#386C2211yescharacteristic
152#386C2211yescharacteristic
153#386C2211yescharacteristic
154#386C2211yescharacteristic
155#386C2211yescharacteristic
156#386C2211yescharacteristic, complemented
157#386C2211yescharacteristic, complemented
158#386C2211yescharacteristic, complemented
159#386C2211yescharacteristic, complemented
160#386C2211yescharacteristic, complemented
161#386C2211yescharacteristic, complemented
162#386C2211yescharacteristic, complemented
163#386C2211yescharacteristic, complemented
164#386C2211yescharacteristic, complemented
165#386C2211yescharacteristic, complemented
166#386C2211yescharacteristic, complemented
167#385C2211yescharacteristic
168#385C2211yescharacteristic
169#385C2211yescharacteristic, complemented
170#385C2211yescharacteristic, complemented
171#385C2211yescharacteristic, complemented
172#385C2211yescharacteristic, complemented
173#385C2211yescharacteristic, complemented
174#385C2211yescharacteristic, complemented
175#385C2211yescharacteristic, complemented
176#382C2211yescharacteristic, complemented
177#381C2211yescharacteristic, complemented
178#380C2211yescharacteristic
179#380C2211yescharacteristic, complemented
180#380C2211yescharacteristic, complemented
181#380C2211yescharacteristic, complemented
182#379C2211yescharacteristic
183#379C2211yescharacteristic
184#379C2211yescharacteristic
185#379C2211yescharacteristic
186C4×C22⋊C4C2211yescharacteristic, complemented
187C25C2311yescharacteristic
188C25C2311yescharacteristic
189C22×D4—42no—
190C22×D4—42no—
191C22×D4—42no—
192C22×D4C2311yescharacteristic
193C22×D4C2311yescharacteristic
194C22×D4C2311yescharacteristic
195C22×D4C2311yescharacteristic
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
214C23×C4C2311yescharacteristic
215C23×C4C2311yescharacteristic
216C23×C4C2311yescharacteristic
217C23×C4C2311yescharacteristic
218C23×C4C2311yescharacteristic
219C23×C4C2311yescharacteristic
220C23×C4C2311yescharacteristic
221C23×C4C2311yescharacteristic
222#127—42no—
223#126—42no—
224#123—42no—
225#123—42no—
226#123—42no—
227#123—42no—
228#123—42no—
229#121—42no—
230#121—42no—
231#121—42no—
232#121—42no—
233#121—42no—
234#121—42no—
235#121—42no—
236#121—42no—
237#121—42no—
238#120—42no—
239#120—42no—
240#120—42no—
241#120—42no—
242#120—42no—
243#120—42no—
244C4×D4—42no—
245C4×D4—42no—
246#117—42no—
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×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⋊C4—42no—
272C2×C22⋊C4—42no—
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×C22⋊C4C2311yescharacteristic
332C2×C22⋊C4C2311yescharacteristic
333C2×C22⋊C4C2311yescharacteristic
334C2×C22⋊C4C2311yescharacteristic
335C2×C42C2311yescharacteristic
336C2×C42C2311yescharacteristic
337C2×C42C2311yescharacteristic
338C2×C42C2311yescharacteristic
339C2×C42C2311yescharacteristic
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—22no—
373C24—22no—
374C24—22no—
375C24—22no—
376C24—41no—
377C24—41no—
378C24—41no—
379C24—41no—
380C24—41no—
381C24—41no—
382C24—41no—
383C24—41no—
384C24—41no—
385C24—41no—
386C24C2411yescharacteristic
387C24C2411yescharacteristic
388C24C2411yescharacteristic
389C24C2411yescharacteristic
390C24C2411yescharacteristic
391C24C2411yescharacteristic
392C24C2411yescharacteristic
393C24C2411yescharacteristic
394C2×D4—22no—
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—22no—
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—416no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—41no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4—41no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4C2411yescharacteristic
486C22×C4C2411yescharacteristic
487C22×C4C2411yescharacteristic
488C22×C4C2411yescharacteristic
489C22×C4C2411yescharacteristic
490C22×C4C2411yescharacteristic
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
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—41no—
513C4⋊C4—41no—
514C4⋊C4—41no—
515C4⋊C4—41no—
516C4⋊C4—41no—
517C4⋊C4—41no—
518C4⋊C4—41no—
519C4⋊C4—41no—
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—
532C22⋊C4—22no—
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—22no—
546C22⋊C4—22no—
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—
593C22⋊C4—41no—
594C42—22no—
595C42—41no—
596C42—41no—
597C42—41no—
598C42—41no—
599C23—21no—
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—44no—
653C23—44no—
654C23—44no—
655C23—44no—
656C23—82no—
657C23—82no—
658C23—82no—
659C23—82no—
660C23—82no—
661C23—82no—
662C23—82no—
663C23—82no—
664C23—82no—
665C23—82no—
666C23H(5,𝔽2)12yes—
667C23H(5,𝔽2)12yes—
668C23H(5,𝔽2)12yes—
669C23C2511yescharacteristic
670D4—44no—
671D4—44no—
672D4—44no—
673D4—44no—
674D4—44no—
675D4—44no—
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—
691D4—82no—
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—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—44no—
760C2×C4—44no—
761C2×C4—82no—
762C2×C4—82no—
763C2×C4—82no—
764C2×C4—82no—
765C2×C4—82no—
766C2×C4—82no—
767C2×C4H(5,𝔽2)12yes—
768C2×C4H(5,𝔽2)12yes—
769C22—22no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
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—41no—
824C22—41no—
825C22—88no—
826C22—88no—
827C22C2×H(5,𝔽2)11yescharacteristic
828C22C2×H(5,𝔽2)11yescharacteristic
829C22C2×H(5,𝔽2)11yescharacteristic
830C22C2×H(5,𝔽2)11yescharacteristic
831C22C2×H(5,𝔽2)11yescharacteristic
832C22#58511yescharacteristic
833C22#58511yescharacteristic
834C4—22no—
835C4—22no—
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—
854C4—41no—
855C4—41no—
856C4—41no—
857C2—42no—
858C2—42no—
859C2—42no—
860C2—81no—
861C2—81no—
862C2—81no—
863C2—81no—
864C2—81no—
865C2#353211yescharacteristic
866C2#353311yescharacteristic
867C2#353411yescharacteristic
868C2#353411yescharacteristic
869C2#353711yescharacteristic
870C2#354211yescharacteristic
871C2#354611yescharacteristic
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. #2826C2semidirect
2. #2825C2semidirect
3. #2812C2semidirect
4. #2787C2semidirect
5. #2779C2semidirect
6. #2778C2semidirect
7. #2761C2semidirect
8. #2735C2semidirect
9. #2714C2semidirect
10. #2708C2semidirect
11. #2706C2semidirect
12. #2691C2semidirect
13. #2682C2semidirect
14. #2678C2semidirect
15. #2678C2semidirect
16. #2673C2semidirect
17. #2673C2semidirect
18. #2671C2semidirect
19. #2669C2semidirect
20. #2636C2semidirect
21. #2635C2semidirect
22. #2624C2semidirect
23. #2602C2semidirect
24. #2476C2semidirect
25. #2464C2semidirect
26. #2418C2semidirect
27. #2412C2semidirect
28. #2411C2semidirect
29. #2410C2semidirect
30. #2410C2semidirect
31. #2408C2semidirect
33. C2×#127C22semidirect
34. C2×#126C22semidirect
36. C2×#123C22semidirect
37. C2×#123C22semidirect
38. C2×#123C22semidirect
39. C2×#123C22semidirect
47. C2×#121C22semidirect
48. C2×#121C22semidirect
56. C2×C4×D4C22semidirect
57. C2×#117C22semidirect
60. #401C22semidirect
61. #400C22semidirect
62. #400C22semidirect
63. #400C22semidirect
64. #399C22semidirect
65. #399C22semidirect
66. #399C22semidirect
67. #398C22semidirect
68. #398C22semidirect
69. #398C22semidirect
73. #397C22semidirect
74. #397C22semidirect
75. #397C22semidirect
76. #397C22semidirect
77. #397C22semidirect
78. #397C22semidirect
79. #397C22semidirect
81. #396C22semidirect
82. #396C22semidirect
83. #396C22semidirect
84. #396C22semidirect
85. #396C22semidirect
96. #394C22semidirect
97. #394C22semidirect
98. #394C22semidirect
99. #394C22semidirect
100. #394C22semidirect
101. #394C22semidirect
102. #394C22semidirect
103. #394C22semidirect
104. #394C22semidirect
105. #394C22semidirect
106. #394C22semidirect
107. #394C22semidirect
108. #394C22semidirect
117. #392C22semidirect
118. #392C22semidirect
119. #392C22semidirect
120. #392C22semidirect
121. #392C22semidirect
122. #392C22semidirect
123. #392C22semidirect
127. #390C22semidirect
128. #390C22semidirect
129. #390C22semidirect
130. #390C22semidirect
131. #389C22semidirect
132. #389C22semidirect
136. #388C22semidirect
137. #388C22semidirect
138. #388C22semidirect
139. #388C22semidirect
140. #388C22semidirect
141. #388C22semidirect
142. #388C22semidirect
143. #388C22semidirect
144. #388C22semidirect
145. #388C22semidirect
146. #387C22semidirect
147. #387C22semidirect
148. #387C22semidirect
149. #387C22semidirect
156. #386C22semidirect
157. #386C22semidirect
158. #386C22semidirect
159. #386C22semidirect
160. #386C22semidirect
161. #386C22semidirect
162. #386C22semidirect
163. #386C22semidirect
164. #386C22semidirect
165. #386C22semidirect
166. #386C22semidirect
169. #385C22semidirect
170. #385C22semidirect
171. #385C22semidirect
172. #385C22semidirect
173. #385C22semidirect
174. #385C22semidirect
175. #385C22semidirect
176. #382C22semidirect
177. #381C22semidirect
179. #380C22semidirect
180. #380C22semidirect
181. #380C22semidirect
186. C4×C22⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
#28262
#28252
#28122
#27872
#27792
#27782
#27612
#27352
#27142
#27082
#27062
#26912
#26822
#26782
#26732
#26712
#26692
#26362
#26352
#26242
#26022
#24762
#24642
#24182
#24122
#24112
#24102
#24082