Finite Group Databasebeta

← #47855

Subgroups — #47855

Order 256.

1047 conjugacy classes of subgroups.

The subgroup lattice has 769 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#563C211yesmaximal, characteristic, complemented
2C2×#543C211yesmaximal, characteristic, complemented
3#2729C211yesmaximal, characteristic, complemented
4#2728C211yesmaximal, characteristic, complemented
5#2723C211yesmaximal, characteristic, complemented
6#2704C211yesmaximal, characteristic, complemented
7#2702C211yesmaximal, characteristic, complemented
8#2700C211yesmaximal, characteristic, complemented
9#2698C211yesmaximal, characteristic, complemented
10#2692C211yesmaximal, characteristic, complemented
11#2690C211yesmaximal, characteristic, complemented
12#2689C211yesmaximal, characteristic, complemented
13#2687C211yesmaximal, characteristic, complemented
14#2677C211yesmaximal, characteristic, complemented
15#2663C211yesmaximal, characteristic, complemented
16#2621C211yesmaximal, characteristic, complemented
17#2561C211yesmaximal, characteristic, complemented
18#2560C211yesmaximal, characteristic, complemented
19#2560C211yesmaximal, characteristic, complemented
20#2556C211yesmaximal, characteristic, complemented
21#2536C211yesmaximal, characteristic, complemented
22#2492C211yesmaximal, characteristic, complemented
23#2489C211yesmaximal, characteristic, complemented
24#2480C211yesmaximal, characteristic, complemented
25#2480C211yesmaximal, characteristic, complemented
26#2472C211yesmaximal, characteristic
27#2452C211yesmaximal, characteristic, complemented
28#2429C211yesmaximal, characteristic, complemented
29#2418C211yesmaximal, characteristic
30#2411C211yesmaximal, characteristic
31#2362C211yesmaximal, characteristic, complemented
32#563—28no—
33#543—28no—
34C2×C4⋊Q8C2211yescharacteristic, complemented
35C2×C4⋊Q8C2211yescharacteristic, complemented
36C2×C4⋊Q8C2211yescharacteristic, complemented
37C2×#126C2211yescharacteristic
38C2×#126C2211yescharacteristic
39C2×#126C2211yescharacteristic, complemented
40C2×#126C2211yescharacteristic, complemented
41C2×#125C2211yescharacteristic, complemented
42C2×#125C2211yescharacteristic, complemented
43C2×#124C2211yescharacteristic
44C2×#123C2211yescharacteristic
45C2×#123C2211yescharacteristic
46C2×C22⋊Q8C2211yescharacteristic
47C2×C22⋊Q8C2211yescharacteristic
48C2×C22⋊Q8C2211yescharacteristic
49C2×C22⋊Q8C2211yescharacteristic
50C2×C22⋊Q8C2211yescharacteristic
51C2×C22⋊Q8C2211yescharacteristic
52C2×C22⋊Q8C2211yescharacteristic
53C2×C22⋊Q8C2211yescharacteristic
54C2×C22⋊Q8C2211yescharacteristic
55C2×C22⋊Q8C2211yescharacteristic
56C2×C22⋊Q8C2211yescharacteristic
57C2×C22⋊Q8C2211yescharacteristic
58C2×C22⋊Q8C2211yescharacteristic
59C2×C22⋊Q8C2211yescharacteristic
60C2×C22⋊Q8C2211yescharacteristic, complemented
61C2×C22⋊Q8C2211yescharacteristic, complemented
62C2×#120C2211yescharacteristic
63C2×C4×Q8C2211yescharacteristic, complemented
64C2×C4×D4C2211yescharacteristic
65C2×#117C2211yescharacteristic
66C22×C22⋊C4C2211yescharacteristic
67C22×C22⋊C4C2211yescharacteristic
68C22×C22⋊C4C2211yescharacteristic
69#400C2211yescharacteristic, complemented
70#400C2211yescharacteristic, complemented
71#400C2211yescharacteristic, complemented
72#400C2211yescharacteristic, complemented
73#400C2211yescharacteristic, complemented
74#399C2211yescharacteristic
75#399C2211yescharacteristic, complemented
76#398C2211yescharacteristic, complemented
77#398C2211yescharacteristic, complemented
78#398C2211yescharacteristic, complemented
79#398C2211yescharacteristic, complemented
80#398C2211yescharacteristic, complemented
81#398C2211yescharacteristic, complemented
82#398C2211yescharacteristic, complemented
83#398C2211yescharacteristic, complemented
84#398C2211yescharacteristic, complemented
85#397C2211yescharacteristic
86#397C2211yescharacteristic
87#397C2211yescharacteristic
88#397C2211yescharacteristic
89#397C2211yescharacteristic
90#397C2211yescharacteristic
91#397C2211yescharacteristic
92#397C2211yescharacteristic
93#397C2211yescharacteristic
94#397C2211yescharacteristic
95#397C2211yescharacteristic, complemented
96#396C2211yescharacteristic
97#396C2211yescharacteristic
98#396C2211yescharacteristic
99#396C2211yescharacteristic
100#396C2211yescharacteristic, complemented
101#395C2211yescharacteristic, complemented
102#395C2211yescharacteristic, complemented
103#395C2211yescharacteristic, complemented
104#395C2211yescharacteristic, complemented
105#394C2211yescharacteristic
106#394C2211yescharacteristic
107#394C2211yescharacteristic
108#394C2211yescharacteristic
109#394C2211yescharacteristic
110#394C2211yescharacteristic
111#393C2211yescharacteristic
112#393C2211yescharacteristic
113#393C2211yescharacteristic
114#393C2211yescharacteristic, complemented
115#393C2211yescharacteristic, complemented
116#393C2211yescharacteristic, complemented
117#391C2211yescharacteristic, complemented
118#391C2211yescharacteristic, complemented
119#391C2211yescharacteristic, complemented
120#391C2211yescharacteristic, complemented
121#391C2211yescharacteristic, complemented
122#391C2211yescharacteristic, complemented
123#391C2211yescharacteristic, complemented
124#391C2211yescharacteristic, complemented
125#390C2211yescharacteristic
126#390C2211yescharacteristic
127#390C2211yescharacteristic
128#389C2211yescharacteristic, complemented
129#389C2211yescharacteristic, complemented
130#389C2211yescharacteristic, complemented
131#389C2211yescharacteristic, complemented
132#389C2211yescharacteristic, complemented
133#389C2211yescharacteristic, complemented
134#388C2211yescharacteristic
135#388C2211yescharacteristic
136#388C2211yescharacteristic
137#388C2211yescharacteristic
138#388C2211yescharacteristic
139#388C2211yescharacteristic
140#388C2211yescharacteristic
141#388C2211yescharacteristic
142#388C2211yescharacteristic
143#388C2211yescharacteristic
144#388C2211yescharacteristic
145#388C2211yescharacteristic
146#388C2211yescharacteristic
147#388C2211yescharacteristic
148#388C2211yescharacteristic
149#388C2211yescharacteristic
150#388C2211yescharacteristic, complemented
151#388C2211yescharacteristic, complemented
152#388C2211yescharacteristic, complemented
153#388C2211yescharacteristic, complemented
154#387C2211yescharacteristic, complemented
155#387C2211yescharacteristic, complemented
156#387C2211yescharacteristic, complemented
157#387C2211yescharacteristic, complemented
158#387C2211yescharacteristic, complemented
159#386C2211yescharacteristic
160#386C2211yescharacteristic
161#386C2211yescharacteristic
162#386C2211yescharacteristic
163#386C2211yescharacteristic
164#385C2211yescharacteristic
165#385C2211yescharacteristic
166#385C2211yescharacteristic
167#385C2211yescharacteristic
168#385C2211yescharacteristic
169#385C2211yescharacteristic
170#385C2211yescharacteristic, complemented
171#382C2211yescharacteristic, complemented
172#382C2211yescharacteristic, complemented
173#381C2211yescharacteristic
174#381C2211yescharacteristic
175#380C2211yescharacteristic
176#380C2211yescharacteristic
177#380C2211yescharacteristic
178#380C2211yescharacteristic, complemented
179#379C2211yescharacteristic
180#379C2211yescharacteristic
181#379C2211yescharacteristic
182C4×C4⋊C4C2211yescharacteristic, complemented
183C4×C4⋊C4C2211yescharacteristic, complemented
184C4×C4⋊C4C2211yescharacteristic, complemented
185C4×C22⋊C4C2211yescharacteristic
186C4×C22⋊C4C2211yescharacteristic
187C4×C22⋊C4C2211yescharacteristic
188C4×C22⋊C4C2211yescharacteristic
189C25C2311yescharacteristic
190C22×Q8C2311yescharacteristic
191C22×Q8C2311yescharacteristic
192C22×Q8C2311yescharacteristic
193C22×Q8C2311yescharacteristic
194C22×Q8C2311yescharacteristic
195C22×Q8C2311yescharacteristic
196C22×D4C2311yescharacteristic
197C22×D4C2311yescharacteristic
198C22×D4C2311yescharacteristic
199C23×C4C2311yescharacteristic
200C23×C4C2311yescharacteristic
201C23×C4C2311yescharacteristic
202C23×C4C2311yescharacteristic
203C23×C4C2311yescharacteristic
204C23×C4C2311yescharacteristic
205C23×C4C2311yescharacteristic
206C4⋊Q8—24no—
207C4⋊Q8—24no—
208C4⋊Q8—42no—
209#126—24no—
210#126—24no—
211#126—24no—
212#126—24no—
213#125—24no—
214#125—24no—
215#124—24no—
216#123—24no—
217#123—24no—
218C22⋊Q8—24no—
219C22⋊Q8—24no—
220C22⋊Q8—24no—
221C22⋊Q8—24no—
222C22⋊Q8—24no—
223C22⋊Q8—24no—
224C22⋊Q8—24no—
225C22⋊Q8—24no—
226C22⋊Q8—24no—
227C22⋊Q8—24no—
228C22⋊Q8—24no—
229C22⋊Q8—24no—
230C22⋊Q8—24no—
231C22⋊Q8—24no—
232C22⋊Q8—42no—
233C22⋊Q8D418yescomplemented
234#120—42no—
235C4×Q8—42no—
236C4×D4—42no—
237#117—42no—
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×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×C4⋊C4C2311yescharacteristic
272C2×C4⋊C4C2311yescharacteristic
273C2×C4⋊C4C2311yescharacteristic
274C2×C4⋊C4C2311yescharacteristic
275C2×C4⋊C4C2311yescharacteristic
276C2×C4⋊C4C2311yescharacteristic
277C2×C4⋊C4C2311yescharacteristic
278C2×C4⋊C4C2311yescharacteristic
279C2×C22⋊C4—24no—
280C2×C22⋊C4—24no—
281C2×C22⋊C4—24no—
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×C42C2311yescharacteristic
327C2×C42C2311yescharacteristic
328C2×C42C2311yescharacteristic
329C2×C42C2311yescharacteristic
330C2×C42C2311yescharacteristic
331C2×C42C2311yescharacteristic
332C2×C42C2311yescharacteristic
333C2×C42C2311yescharacteristic
334C2×C42C2311yescharacteristic
335C2×C42C2311yescharacteristic
336C2×C42C2311yescharacteristic
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
369#95C2311yescharacteristic
370#95C2311yescharacteristic
371#95C2311yescharacteristic
372#95C2311yescharacteristic
373#95C2311yescharacteristic
374#95C2311yescharacteristic
375#95C2311yescharacteristic
376#95C2311yescharacteristic
377#95C2311yescharacteristic
378#95C2311yescharacteristic
379C24—22no—
380C24—22no—
381C24—22no—
382C24—41no—
383C24—41no—
384C24—41no—
385C24—41no—
386C24C2411yescharacteristic
387C24C2411yescharacteristic
388C24C2411yescharacteristic
389C24C2411yescharacteristic
390C2×Q8—22no—
391C2×Q8—22no—
392C2×Q8—22no—
393C2×Q8—22no—
394C2×Q8—22no—
395C2×Q8—41no—
396C2×Q8—41no—
397C2×Q8—41no—
398C2×Q8—41no—
399C2×Q8—41no—
400C2×Q8—41no—
401C2×Q8—41no—
402C2×Q8—41no—
403C2×Q8—41no—
404C2×Q8—41no—
405C2×Q8—41no—
406C2×Q8—41no—
407C2×Q8C2×D414yes—
408C2×D4—22no—
409C2×D4—22no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—41no—
413C2×D4—41no—
414C2×D4—41no—
415C2×D4—41no—
416C2×D4—41no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—41no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4C2×D414yes—
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
455C22×C4C2411yescharacteristic
456C22×C4C2411yescharacteristic
457C22×C4C2411yescharacteristic
458C22×C4C2411yescharacteristic
459C22×C4C2411yescharacteristic
460C22×C4C2411yescharacteristic
461C22×C4C2411yescharacteristic
462C22×C4C2411yescharacteristic
463C22×C4C2411yescharacteristic
464C22×C4C2411yescharacteristic
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—22no—
468C4⋊C4—22no—
469C4⋊C4—22no—
470C4⋊C4—22no—
471C4⋊C4—22no—
472C4⋊C4—22no—
473C4⋊C4—22no—
474C4⋊C4—22no—
475C4⋊C4—22no—
476C4⋊C4—22no—
477C4⋊C4—22no—
478C4⋊C4—22no—
479C4⋊C4—22no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—41no—
492C4⋊C4—41no—
493C4⋊C4—41no—
494C4⋊C4—41no—
495C4⋊C4—41no—
496C4⋊C4—41no—
497C4⋊C4—41no—
498C4⋊C4—41no—
499C4⋊C4—41no—
500C4⋊C4—41no—
501C4⋊C4—41no—
502C4⋊C4—41no—
503C4⋊C4C2×D414yes—
504C4⋊C4C2×D414yes—
505C4⋊C4C2×D414yes—
506C22⋊C4—22no—
507C22⋊C4—22no—
508C22⋊C4—22no—
509C22⋊C4—22no—
510C22⋊C4—22no—
511C22⋊C4—22no—
512C22⋊C4—22no—
513C22⋊C4—22no—
514C22⋊C4—22no—
515C22⋊C4—22no—
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—22no—
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—41no—
533C22⋊C4—41no—
534C22⋊C4—41no—
535C22⋊C4—41no—
536C22⋊C4—41no—
537C22⋊C4—41no—
538C22⋊C4—41no—
539C22⋊C4—41no—
540C22⋊C4—41no—
541C22⋊C4—41no—
542C22⋊C4—41no—
543C22⋊C4—41no—
544C22⋊C4—41no—
545C22⋊C4—41no—
546C22⋊C4—41no—
547C22⋊C4—41no—
548C22⋊C4C2×D414yes—
549C22⋊C4C2×D414yes—
550C42—22no—
551C42—22no—
552C42—22no—
553C42—22no—
554C42—22no—
555C42—41no—
556C42—41no—
557C42—41no—
558C42—41no—
559C42—41no—
560C42—41no—
561C23—28no—
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—82no—
588C23—82no—
589C23—82no—
590C23—82no—
591C23—82no—
592C23—82no—
593C23C22×D412yes—
594C232−1+412yes—
595C232−1+412yes—
596C23C2511yescharacteristic
597Q8—44no—
598Q8—82no—
599Q8—82no—
600Q8—82no—
601Q8—82no—
602Q8—82no—
603D4—44no—
604D4—82no—
605D4—82no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
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—44no—
681C2×C4—82no—
682C2×C4—82no—
683C2×C4—82no—
684C2×C4—82no—
685C2×C4—82no—
686C2×C4—82no—
687C2×C4C22×D412yes—
688C2×C4C22×D412yes—
689C2×C4C22×D412yes—
690C2×C4C22×D412yes—
691C2×C4C22×D412yes—
692C2×C4C22×D412yes—
693C2×C4H(5,𝔽2)12yes—
694C22—22no—
695C22—22no—
696C22—22no—
697C22—22no—
698C22—22no—
699C22—22no—
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—88no—
723C22C23×D411yescharacteristic
724C22C2×H(5,𝔽2)11yescharacteristic
725C22C2×2−1+411yescharacteristic
726C22C2×2−1+411yescharacteristic
727C22#58511yescharacteristic
728C22#58511yescharacteristic
729C22#58511yescharacteristic
730C4—22no—
731C4—22no—
732C4—22no—
733C4—22no—
734C4—22no—
735C4—22no—
736C4—22no—
737C4—41no—
738C4—41no—
739C4—41no—
740C4—41no—
741C4—41no—
742C4—41no—
743C4—41no—
744C4—41no—
745C4—41no—
746C4—41no—
747C4—41no—
748C4—41no—
749C4—41no—
750C4—41no—
751C4—41no—
752C4—41no—
753C4—41no—
754C4—41no—
755C4—41no—
756C4—41no—
757C2—42no—
758C2—42no—
759C2—42no—
760C2—81no—
761C2#348611yescharacteristic
762C2#349611yescharacteristic
763C2#350011yescharacteristic
764C2#353511yescharacteristic
765C2#356111yescharacteristic
766C2#356411yescharacteristic
767C2#356411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C25
prime radicalC2×#120C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#563C2semidirect
2. C2×#543C2semidirect
3. #2729C2semidirect
4. #2728C2semidirect
5. #2723C2semidirect
6. #2704C2semidirect
7. #2702C2semidirect
8. #2700C2semidirect
9. #2698C2semidirect
10. #2692C2semidirect
11. #2690C2semidirect
12. #2689C2semidirect
13. #2687C2semidirect
14. #2677C2semidirect
15. #2663C2semidirect
16. #2621C2semidirect
17. #2561C2semidirect
18. #2560C2semidirect
19. #2560C2semidirect
20. #2556C2semidirect
21. #2536C2semidirect
22. #2492C2semidirect
23. #2489C2semidirect
24. #2480C2semidirect
25. #2480C2semidirect
27. #2452C2semidirect
28. #2429C2semidirect
31. #2362C2semidirect
34. C2×C4⋊Q8C22semidirect
35. C2×C4⋊Q8C22semidirect
36. C2×C4⋊Q8C22semidirect
39. C2×#126C22semidirect
40. C2×#126C22semidirect
41. C2×#125C22semidirect
42. C2×#125C22semidirect
60. C2×C22⋊Q8C22semidirect
61. C2×C22⋊Q8C22semidirect
63. C2×C4×Q8C22semidirect
69. #400C22semidirect
70. #400C22semidirect
71. #400C22semidirect
72. #400C22semidirect
73. #400C22semidirect
75. #399C22semidirect
76. #398C22semidirect
77. #398C22semidirect
78. #398C22semidirect
79. #398C22semidirect
80. #398C22semidirect
81. #398C22semidirect
82. #398C22semidirect
83. #398C22semidirect
84. #398C22semidirect
95. #397C22semidirect
100. #396C22semidirect
101. #395C22semidirect
102. #395C22semidirect
103. #395C22semidirect
104. #395C22semidirect
114. #393C22semidirect
115. #393C22semidirect
116. #393C22semidirect
117. #391C22semidirect
118. #391C22semidirect
119. #391C22semidirect
120. #391C22semidirect
121. #391C22semidirect
122. #391C22semidirect
123. #391C22semidirect
124. #391C22semidirect
128. #389C22semidirect
129. #389C22semidirect
130. #389C22semidirect
131. #389C22semidirect
132. #389C22semidirect
133. #389C22semidirect
150. #388C22semidirect
151. #388C22semidirect
152. #388C22semidirect
153. #388C22semidirect
154. #387C22semidirect
155. #387C22semidirect
156. #387C22semidirect
157. #387C22semidirect
158. #387C22semidirect
170. #385C22semidirect
171. #382C22semidirect
172. #382C22semidirect
178. #380C22semidirect
182. C4×C4⋊C4C22semidirect
183. C4×C4⋊C4C22semidirect
184. C4×C4⋊C4C22semidirect
233. C22⋊Q8D4semidirect

Maximal subgroups

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

subgroupindex
C2×#5632
C2×#5432
#27292
#27282
#27232
#27042
#27022
#27002
#26982
#26922
#26902
#26892
#26872
#26772
#26632
#26212
#25612
#25602
#25562
#25362
#24922
#24892
#24802
#24722
#24522
#24292
#24182
#24112
#23622