Finite Group Databasebeta

← #48550

Subgroups — #48550

Order 256.

1072 conjugacy classes of subgroups.

The subgroup lattice has 841 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2778C211yesmaximal, characteristic, complemented
2#2764C211yesmaximal, characteristic, complemented
3#2760C211yesmaximal, characteristic, complemented
4#2759C211yesmaximal, characteristic, complemented
5#2749C211yesmaximal, characteristic, complemented
6#2746C211yesmaximal, characteristic, complemented
7#2712C211yesmaximal, characteristic, complemented
8#2699C211yesmaximal, characteristic, complemented
9#2696C211yesmaximal, characteristic, complemented
10#2692C211yesmaximal, characteristic, complemented
11#2669C211yesmaximal, characteristic, complemented
12#2668C211yesmaximal, characteristic, complemented
13#2639C211yesmaximal, characteristic, complemented
14#2631C211yesmaximal, characteristic, complemented
15#2572C211yesmaximal, characteristic, complemented
16#2572C211yesmaximal, characteristic, complemented
17#2557C211yesmaximal, characteristic, complemented
18#2510C211yesmaximal, characteristic, complemented
19#2472C211yesmaximal, characteristic, complemented
20#2464C211yesmaximal, characteristic, complemented
21#2456C211yesmaximal, characteristic, complemented
22#2444C211yesmaximal, characteristic, complemented
23#2431C211yesmaximal, characteristic, complemented
24#2430C211yesmaximal, characteristic, complemented
25#2412C211yesmaximal, characteristic, complemented
26#2407C211yesmaximal, characteristic, complemented
27#2404C211yesmaximal, characteristic, complemented
28#2404C211yesmaximal, characteristic, complemented
29#2380C211yesmaximal, characteristic, complemented
30#2339C211yesmaximal, characteristic, complemented
31#2321C211yesmaximal, characteristic, complemented
32C22×#41C2211yescharacteristic
33C22×#41C2211yescharacteristic
34C2×#127C2211yescharacteristic
35C2×#124C2211yescharacteristic
36C2×#124C2211yescharacteristic, complemented
37C2×#123C2211yescharacteristic
38C2×#123C2211yescharacteristic, complemented
39C2×C22⋊Q8C2211yescharacteristic
40C2×C22⋊Q8C2211yescharacteristic, complemented
41C2×#121C2211yescharacteristic
42C2×#121C2211yescharacteristic
43C2×#121C2211yescharacteristic
44C2×#121C2211yescharacteristic
45C2×#121C2211yescharacteristic, complemented
46C2×#120C2211yescharacteristic
47C2×#120C2211yescharacteristic
48C2×#120C2211yescharacteristic
49C2×#120C2211yescharacteristic
50C2×C4×D4C2211yescharacteristic
51C2×C4×D4C2211yescharacteristic, complemented
52C2×C4×D4C2211yescharacteristic, complemented
53C22×C22⋊C4C2211yescharacteristic
54C22×C22⋊C4C2211yescharacteristic
55#401C2211yescharacteristic, complemented
56#401C2211yescharacteristic, complemented
57#400C2211yescharacteristic, complemented
58#400C2211yescharacteristic, complemented
59#400C2211yescharacteristic, complemented
60#400C2211yescharacteristic, complemented
61#399C2211yescharacteristic
62#398C2211yescharacteristic, complemented
63#398C2211yescharacteristic, complemented
64#397C2211yescharacteristic
65#397C2211yescharacteristic
66#397C2211yescharacteristic
67#397C2211yescharacteristic
68#397C2211yescharacteristic
69#397C2211yescharacteristic, complemented
70#397C2211yescharacteristic, complemented
71#397C2211yescharacteristic, complemented
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#393C2211yescharacteristic
84#393C2211yescharacteristic
85#393C2211yescharacteristic
86#393C2211yescharacteristic
87#393C2211yescharacteristic
88#393C2211yescharacteristic, complemented
89#393C2211yescharacteristic, complemented
90#393C2211yescharacteristic, complemented
91#393C2211yescharacteristic, complemented
92#392C2211yescharacteristic
93#392C2211yescharacteristic
94#392C2211yescharacteristic
95#392C2211yescharacteristic
96#392C2211yescharacteristic
97#392C2211yescharacteristic
98#392C2211yescharacteristic
99#392C2211yescharacteristic
100#392C2211yescharacteristic
101#392C2211yescharacteristic, complemented
102#392C2211yescharacteristic, complemented
103#391C2211yescharacteristic, complemented
104#391C2211yescharacteristic, complemented
105#391C2211yescharacteristic, complemented
106#391C2211yescharacteristic, complemented
107#391C2211yescharacteristic, complemented
108#390C2211yescharacteristic
109#390C2211yescharacteristic
110#390C2211yescharacteristic
111#390C2211yescharacteristic, complemented
112#388C2211yescharacteristic
113#388C2211yescharacteristic
114#388C2211yescharacteristic
115#388C2211yescharacteristic
116#388C2211yescharacteristic
117#388C2211yescharacteristic
118#388C2211yescharacteristic
119#388C2211yescharacteristic
120#388C2211yescharacteristic, complemented
121#388C2211yescharacteristic, complemented
122#388C2211yescharacteristic, complemented
123#388C2211yescharacteristic, complemented
124#387C2211yescharacteristic, complemented
125#387C2211yescharacteristic, complemented
126#387C2211yescharacteristic, complemented
127#386C2211yescharacteristic
128#386C2211yescharacteristic
129#386C2211yescharacteristic
130#386C2211yescharacteristic
131#386C2211yescharacteristic
132#386C2211yescharacteristic
133#386C2211yescharacteristic
134#386C2211yescharacteristic
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
151#386C2211yescharacteristic
152#386C2211yescharacteristic, complemented
153#386C2211yescharacteristic, complemented
154#386C2211yescharacteristic, complemented
155#386C2211yescharacteristic, complemented
156#386C2211yescharacteristic, complemented
157#386C2211yescharacteristic, complemented
158#386C2211yescharacteristic, complemented
159#386C2211yescharacteristic, complemented
160#386C2211yescharacteristic, complemented
161#385C2211yescharacteristic
162#385C2211yescharacteristic
163#385C2211yescharacteristic, complemented
164#385C2211yescharacteristic, complemented
165#385C2211yescharacteristic, complemented
166#385C2211yescharacteristic, complemented
167#383C2211yescharacteristic, complemented
168#383C2211yescharacteristic, complemented
169#383C2211yescharacteristic, complemented
170#383C2211yescharacteristic, complemented
171#381C2211yescharacteristic
172#381C2211yescharacteristic
173#381C2211yescharacteristic
174#381C2211yescharacteristic, complemented
175#381C2211yescharacteristic, complemented
176#381C2211yescharacteristic, complemented
177#380C2211yescharacteristic
178#380C2211yescharacteristic
179#380C2211yescharacteristic, complemented
180#379C2211yescharacteristic
181C4×C22⋊C4C2211yescharacteristic
182C4×C22⋊C4C2211yescharacteristic
183C4×C22⋊C4C2211yescharacteristic, complemented
184C4×C22⋊C4C2211yescharacteristic, complemented
185C2×#95C2211yescharacteristic, complemented
186C2×#95C2211yescharacteristic, complemented
187C25C2311yescharacteristic
188C2×#41—24no—
189C2×#41—42no—
190C2×#41—42no—
191C2×#41—42no—
192C2×#41—42no—
193C2×#41—42no—
194C22×Q8C2311yescharacteristic
195C22×Q8C2311yescharacteristic
196C22×Q8C2311yescharacteristic
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
215C23×C4C2311yescharacteristic
216C23×C4C2311yescharacteristic
217C23×C4C2311yescharacteristic
218C23×C4C2311yescharacteristic
219C23×C4C2311yescharacteristic
220C23×C4C2311yescharacteristic
221C23×C4C2311yescharacteristic
222C23×C4C2311yescharacteristic
223C23×C4C2311yescharacteristic
224C23×C4C2311yescharacteristic
225C23×C4C2311yescharacteristic
226C23×C4C2311yescharacteristic
227#127—24no—
228#124—42no—
229#124—42no—
230#123—42no—
231#123—42no—
232C22⋊Q8—42no—
233C22⋊Q8—42no—
234#121—42no—
235#121—42no—
236#121—42no—
237#121—42no—
238#121—42no—
239#120—24no—
240#120—42no—
241#120—42no—
242#120—42no—
243C4×D4—42no—
244C4×D4—42no—
245C4×D4—42no—
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×C4⋊C4C2311yescharacteristic
258C2×C4⋊C4C2311yescharacteristic
259C2×C4⋊C4C2311yescharacteristic
260C2×C4⋊C4C2311yescharacteristic
261C2×C22⋊C4—42no—
262C2×C22⋊C4—42no—
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×C22⋊C4C2311yescharacteristic
317C2×C42C2311yescharacteristic
318C2×C42C2311yescharacteristic
319C2×C42C2311yescharacteristic
320C2×C42C2311yescharacteristic
321C2×C42C2311yescharacteristic
322C2×C42C2311yescharacteristic
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
363#95C2311yescharacteristic
364#95C2311yescharacteristic
365#95C2311yescharacteristic
366#95C2311yescharacteristic
367#95C2311yescharacteristic
368#95C2311yescharacteristic
369C24—22no—
370C24—22no—
371C24—41no—
372C24—41no—
373C24—41no—
374C24—41no—
375C24—41no—
376C24C2411yescharacteristic
377C24C2411yescharacteristic
378C24C2411yescharacteristic
379C24C2411yescharacteristic
380C24C2411yescharacteristic
381C24C2411yescharacteristic
382C24C2411yescharacteristic
383#41—416no—
384#41—416no—
385C2×Q8—22no—
386C2×Q8—22no—
387C2×Q8—22no—
388C2×Q8—41no—
389C2×Q8—41no—
390C2×Q8—41no—
391C2×Q8—41no—
392C2×Q8—41no—
393C2×Q8—41no—
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—22no—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—22no—
414C2×D4—22no—
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#4114yescomplemented
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—41no—
459C22×C4—41no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—41no—
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×C4C2411yescharacteristic
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—41no—
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—
523C22⋊C4—22no—
524C22⋊C4—22no—
525C22⋊C4—22no—
526C22⋊C4—22no—
527C22⋊C4—22no—
528C22⋊C4—22no—
529C22⋊C4—22no—
530C22⋊C4—22no—
531C22⋊C4—22no—
532C22⋊C4—22no—
533C22⋊C4—22no—
534C22⋊C4—22no—
535C22⋊C4—22no—
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—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—
577C42—22no—
578C42—22no—
579C42—41no—
580C42—41no—
581C42—41no—
582C42—41no—
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—21no—
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—44no—
629C23—44no—
630C23—82no—
631C23—82no—
632C23—82no—
633C23—82no—
634C23—82no—
635C23C2×#4112yes—
636C23C2×#4112yes—
637C23H(5,𝔽2)12yes—
638C23H(5,𝔽2)12yes—
639C23C2511yescharacteristic
640Q8—44no—
641Q8—44no—
642Q8—82no—
643D4—28no—
644D4—44no—
645D4—44no—
646D4—44no—
647D4—44no—
648D4—44no—
649D4—44no—
650D4—82no—
651D4—82no—
652D4—82no—
653D4—82no—
654D4—82no—
655D4—82no—
656D4—82no—
657D4—82no—
658D4—82no—
659D4—82no—
660D4—82no—
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—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—44no—
731C2×C4—44no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—82no—
737C2×C4—82no—
738C2×C4—82no—
739C2×C4—82no—
740C2×C4—82no—
741C2×C4—82no—
742C2×C4C2×#4112yes—
743C2×C4H(5,𝔽2)12yes—
744C2×C4H(5,𝔽2)12yes—
745C22—22no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—22no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
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—88no—
795C22C22×#4111yescharacteristic
796C22C2×H(5,𝔽2)11yescharacteristic
797C22C2×H(5,𝔽2)11yescharacteristic
798C22C2×H(5,𝔽2)11yescharacteristic
799C22C2×H(5,𝔽2)11yescharacteristic
800C22#58511yescharacteristic
801C22#58511yescharacteristic
802C4—22no—
803C4—22no—
804C4—22no—
805C4—41no—
806C4—41no—
807C4—41no—
808C4—41no—
809C4—41no—
810C4—41no—
811C4—41no—
812C4—41no—
813C4—41no—
814C4—41no—
815C4—41no—
816C4—41no—
817C4—41no—
818C4—41no—
819C4—41no—
820C4—41no—
821C4—41no—
822C4—41no—
823C4—41no—
824C4—41no—
825C4—41no—
826C2—42no—
827C2—42no—
828C2—42no—
829C2—42no—
830C2—81no—
831C2—81no—
832C2—81no—
833C2#349011yescharacteristic
834C2#351311yescharacteristic
835C2#351411yescharacteristic
836C2#353211yescharacteristic
837C2#354211yescharacteristic
838C2#354611yescharacteristic
839C2#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. #2778C2semidirect
2. #2764C2semidirect
3. #2760C2semidirect
4. #2759C2semidirect
5. #2749C2semidirect
6. #2746C2semidirect
7. #2712C2semidirect
8. #2699C2semidirect
9. #2696C2semidirect
10. #2692C2semidirect
11. #2669C2semidirect
12. #2668C2semidirect
13. #2639C2semidirect
14. #2631C2semidirect
15. #2572C2semidirect
16. #2572C2semidirect
17. #2557C2semidirect
18. #2510C2semidirect
19. #2472C2semidirect
20. #2464C2semidirect
21. #2456C2semidirect
22. #2444C2semidirect
23. #2431C2semidirect
24. #2430C2semidirect
25. #2412C2semidirect
26. #2407C2semidirect
27. #2404C2semidirect
28. #2404C2semidirect
29. #2380C2semidirect
30. #2339C2semidirect
31. #2321C2semidirect
36. C2×#124C22semidirect
38. C2×#123C22semidirect
40. C2×C22⋊Q8C22semidirect
45. C2×#121C22semidirect
51. C2×C4×D4C22semidirect
52. C2×C4×D4C22semidirect
55. #401C22semidirect
56. #401C22semidirect
57. #400C22semidirect
58. #400C22semidirect
59. #400C22semidirect
60. #400C22semidirect
62. #398C22semidirect
63. #398C22semidirect
69. #397C22semidirect
70. #397C22semidirect
71. #397C22semidirect
72. #396C22semidirect
73. #395C22semidirect
82. #394C22semidirect
88. #393C22semidirect
89. #393C22semidirect
90. #393C22semidirect
91. #393C22semidirect
101. #392C22semidirect
102. #392C22semidirect
103. #391C22semidirect
104. #391C22semidirect
105. #391C22semidirect
106. #391C22semidirect
107. #391C22semidirect
111. #390C22semidirect
120. #388C22semidirect
121. #388C22semidirect
122. #388C22semidirect
123. #388C22semidirect
124. #387C22semidirect
125. #387C22semidirect
126. #387C22semidirect
152. #386C22semidirect
153. #386C22semidirect
154. #386C22semidirect
155. #386C22semidirect
156. #386C22semidirect
157. #386C22semidirect
158. #386C22semidirect
159. #386C22semidirect
160. #386C22semidirect
163. #385C22semidirect
164. #385C22semidirect
165. #385C22semidirect
166. #385C22semidirect
167. #383C22semidirect
168. #383C22semidirect
169. #383C22semidirect
170. #383C22semidirect
174. #381C22semidirect
175. #381C22semidirect
176. #381C22semidirect
179. #380C22semidirect
183. C4×C22⋊C4C22semidirect
184. C4×C22⋊C4C22semidirect
185. C2×#95C22semidirect
186. C2×#95C22semidirect
447. C2×D4#41semidirect

Maximal subgroups

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

subgroupindex
#27782
#27642
#27602
#27592
#27492
#27462
#27122
#26992
#26962
#26922
#26692
#26682
#26392
#26312
#25722
#25572
#25102
#24722
#24642
#24562
#24442
#24312
#24302
#24122
#24072
#24042
#23802
#23392
#23212