Finite Group Databasebeta

← #43935

Subgroups — #43935

Order 256.

1120 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#552C211yesmaximal, characteristic, complemented
2C2×#551C211yesmaximal, characteristic
3#2725C211yesmaximal, characteristic, complemented
4#2725C211yesmaximal, characteristic, complemented
5#2721C211yesmaximal, characteristic, complemented
6#2720C211yesmaximal, characteristic, complemented
7#2718C211yesmaximal, characteristic, complemented
8#2715C211yesmaximal, characteristic, complemented
9#2695C211yesmaximal, characteristic, complemented
10#2674C211yesmaximal, characteristic, complemented
11#2534C211yesmaximal, characteristic
12#2484C211yesmaximal, characteristic, complemented
13#2482C211yesmaximal, characteristic, complemented
14#2475C211yesmaximal, characteristic, complemented
15#2470C211yesmaximal, characteristic, complemented
16#2469C211yesmaximal, characteristic, complemented
17#2466C211yesmaximal, characteristic, complemented
18#2449C211yesmaximal, characteristic, complemented
19#2441C211yesmaximal, characteristic, complemented
20#2440C211yesmaximal, characteristic, complemented
21#2438C211yesmaximal, characteristic, complemented
22#2437C211yesmaximal, characteristic, complemented
23#2429C211yesmaximal, characteristic, complemented
24#2419C211yesmaximal, characteristic, complemented
25#2418C211yesmaximal, characteristic
26#2413C211yesmaximal, characteristic, complemented
27C2×#396C211yesmaximal, characteristic, complemented
28D4×C4⋊C4C211yesmaximal, characteristic, complemented
29#2342C211yesmaximal, characteristic, complemented
30#2322C211yesmaximal, characteristic, complemented
31#2316C211yesmaximal, characteristic, complemented
32#552—28no—
33#551—28no—
34C2×C4⋊Q8C2211yescharacteristic, complemented
35C2×#126C2211yescharacteristic
36C2×#126C2211yescharacteristic
37C2×#126C2211yescharacteristic, complemented
38C2×#126C2211yescharacteristic, complemented
39C2×#125C2211yescharacteristic, complemented
40C2×#125C2211yescharacteristic, complemented
41C2×#125C2211yescharacteristic, complemented
42C2×#124C2211yescharacteristic
43C2×#123C2211yescharacteristic
44C2×#123C2211yescharacteristic
45C2×#123C2211yescharacteristic
46C2×#123C2211yescharacteristic
47C2×#123C2211yescharacteristic
48C2×C22⋊Q8C2211yescharacteristic
49C2×C22⋊Q8C2211yescharacteristic
50C2×C22⋊Q8C2211yescharacteristic
51C2×C22⋊Q8C2211yescharacteristic
52C2×C22⋊Q8C2211yescharacteristic, complemented
53C2×#120C2211yescharacteristic
54C2×C4×Q8C2211yescharacteristic, complemented
55C2×C4×D4C2211yescharacteristic
56C2×C4×D4C2211yescharacteristic
57C2×C4×D4C2211yescharacteristic
58C2×C4×D4C2211yescharacteristic
59C2×#117C2211yescharacteristic
60C2×#117C2211yescharacteristic
61C2×#117C2211yescharacteristic
62C2×#117C2211yescharacteristic
63C2×#117C2211yescharacteristic, complemented
64C22×C4⋊C4C2211yescharacteristic
65C22×C4⋊C4C2211yescharacteristic
66C22×C4⋊C4C2211yescharacteristic
67C22×C4⋊C4C2211yescharacteristic, complemented
68C22×C22⋊C4C2211yescharacteristic
69C22×C22⋊C4C2211yescharacteristic
70C22×C22⋊C4C2211yescharacteristic
71C22×C22⋊C4C2211yescharacteristic
72#400C2211yescharacteristic, complemented
73#400C2211yescharacteristic, complemented
74#400C2211yescharacteristic, complemented
75#400C2211yescharacteristic, complemented
76#399C2211yescharacteristic
77#399C2211yescharacteristic
78#399C2211yescharacteristic
79#399C2211yescharacteristic
80#398C2211yescharacteristic, complemented
81#398C2211yescharacteristic, complemented
82#398C2211yescharacteristic, complemented
83#398C2211yescharacteristic, complemented
84#398C2211yescharacteristic, complemented
85#398C2211yescharacteristic, complemented
86#398C2211yescharacteristic, complemented
87#397C2211yescharacteristic
88#397C2211yescharacteristic
89#397C2211yescharacteristic
90#397C2211yescharacteristic, complemented
91#397C2211yescharacteristic, complemented
92#396C2211yescharacteristic
93#396C2211yescharacteristic
94#396C2211yescharacteristic
95#396C2211yescharacteristic
96#396C2211yescharacteristic
97#396C2211yescharacteristic
98#396C2211yescharacteristic
99#396C2211yescharacteristic
100#396C2211yescharacteristic
101#396C2211yescharacteristic
102#396C2211yescharacteristic
103#396C2211yescharacteristic
104#395C2211yescharacteristic, complemented
105#395C2211yescharacteristic, complemented
106#395C2211yescharacteristic, complemented
107#394C2211yescharacteristic
108#394C2211yescharacteristic
109#394C2211yescharacteristic
110#394C2211yescharacteristic
111#393C2211yescharacteristic
112#391C2211yescharacteristic, complemented
113#389C2211yescharacteristic, complemented
114#389C2211yescharacteristic, complemented
115#389C2211yescharacteristic, complemented
116#389C2211yescharacteristic, complemented
117#389C2211yescharacteristic, complemented
118#389C2211yescharacteristic, complemented
119#389C2211yescharacteristic, complemented
120#389C2211yescharacteristic, complemented
121#389C2211yescharacteristic, complemented
122#389C2211yescharacteristic, complemented
123#389C2211yescharacteristic, complemented
124#389C2211yescharacteristic, complemented
125#389C2211yescharacteristic, complemented
126#389C2211yescharacteristic, complemented
127#389C2211yescharacteristic, complemented
128#388C2211yescharacteristic
129#388C2211yescharacteristic
130#388C2211yescharacteristic
131#388C2211yescharacteristic
132#388C2211yescharacteristic
133#388C2211yescharacteristic
134#388C2211yescharacteristic
135#388C2211yescharacteristic
136#388C2211yescharacteristic
137#388C2211yescharacteristic
138#388C2211yescharacteristic
139#388C2211yescharacteristic
140#388C2211yescharacteristic, complemented
141#388C2211yescharacteristic, complemented
142#387C2211yescharacteristic, complemented
143#387C2211yescharacteristic, complemented
144#387C2211yescharacteristic, complemented
145#387C2211yescharacteristic, complemented
146#387C2211yescharacteristic, complemented
147#387C2211yescharacteristic, complemented
148#387C2211yescharacteristic, complemented
149#387C2211yescharacteristic, complemented
150#387C2211yescharacteristic, complemented
151#387C2211yescharacteristic, complemented
152#386C2211yescharacteristic
153#386C2211yescharacteristic
154#386C2211yescharacteristic
155#386C2211yescharacteristic
156#385C2211yescharacteristic
157#385C2211yescharacteristic
158#385C2211yescharacteristic
159#385C2211yescharacteristic
160#385C2211yescharacteristic
161#385C2211yescharacteristic
162#385C2211yescharacteristic
163#385C2211yescharacteristic
164#385C2211yescharacteristic
165#385C2211yescharacteristic, complemented
166#385C2211yescharacteristic, complemented
167#385C2211yescharacteristic, complemented
168#385C2211yescharacteristic, complemented
169#385C2211yescharacteristic, complemented
170#384C2211yescharacteristic, complemented
171#384C2211yescharacteristic, complemented
172#381C2211yescharacteristic
173#381C2211yescharacteristic
174#381C2211yescharacteristic
175#381C2211yescharacteristic, complemented
176#380C2211yescharacteristic
177#380C2211yescharacteristic
178#380C2211yescharacteristic
179#380C2211yescharacteristic
180#380C2211yescharacteristic
181#380C2211yescharacteristic, complemented
182#379C2211yescharacteristic
183#379C2211yescharacteristic
184C4×C4⋊C4C2211yescharacteristic, complemented
185C4×C22⋊C4C2211yescharacteristic
186C4×C22⋊C4C2211yescharacteristic
187C4×C22⋊C4C2211yescharacteristic
188C2×#95C2211yescharacteristic
189C25C2311yescharacteristic
190C22×Q8C2311yescharacteristic
191C22×Q8C2311yescharacteristic
192C22×D4C2311yescharacteristic
193C22×D4C2311yescharacteristic
194C22×D4C2311yescharacteristic
195C23×C4C2311yescharacteristic
196C23×C4C2311yescharacteristic
197C23×C4C2311yescharacteristic
198C23×C4C2311yescharacteristic
199C23×C4C2311yescharacteristic
200C23×C4C2311yescharacteristic
201C23×C4C2311yescharacteristic
202C23×C4C2311yescharacteristic
203C23×C4C2311yescharacteristic
204C23×C4C2311yescharacteristic
205C23×C4C2311yescharacteristic
206C4⋊Q8—42no—
207#126—24no—
208#126—24no—
209#126—24no—
210#126—24no—
211#125—24no—
212#125—24no—
213#125—24no—
214#124—24no—
215#123—24no—
216#123—24no—
217#123—24no—
218#123—42no—
219#123D418yes—
220C22⋊Q8—24no—
221C22⋊Q8—24no—
222C22⋊Q8—24no—
223C22⋊Q8—24no—
224C22⋊Q8—42no—
225#120—24no—
226C4×Q8—24no—
227C4×D4—24no—
228C4×D4—24no—
229C4×D4—24no—
230C4×D4—24no—
231#117—24no—
232#117—24no—
233#117—24no—
234#117—24no—
235#117—24no—
236C2×C4⋊C4—24no—
237C2×C4⋊C4—24no—
238C2×C4⋊C4—42no—
239C2×C4⋊C4—42no—
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×C4⋊C4C2311yescharacteristic
280C2×C4⋊C4C2311yescharacteristic
281C2×C4⋊C4C2311yescharacteristic
282C2×C4⋊C4C2311yescharacteristic
283C2×C4⋊C4C2311yescharacteristic
284C2×C4⋊C4C2311yescharacteristic
285C2×C4⋊C4C2311yescharacteristic
286C2×C4⋊C4C2311yescharacteristic
287C2×C4⋊C4C2311yescharacteristic
288C2×C4⋊C4C2311yescharacteristic
289C2×C22⋊C4—24no—
290C2×C22⋊C4—24no—
291C2×C22⋊C4—24no—
292C2×C22⋊C4—42no—
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×C42C2311yescharacteristic
334C2×C42C2311yescharacteristic
335C2×C42C2311yescharacteristic
336C2×C42C2311yescharacteristic
337C2×C42C2311yescharacteristic
338C2×C42C2311yescharacteristic
339C2×C42C2311yescharacteristic
340C2×C42C2311yescharacteristic
341C2×C42C2311yescharacteristic
342C2×C42C2311yescharacteristic
343C2×C42C2311yescharacteristic
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
379#95C2311yescharacteristic
380#95C2311yescharacteristic
381#95C2311yescharacteristic
382C24—22no—
383C24—22no—
384C24—22no—
385C24—22no—
386C24—41no—
387C24—41no—
388C24—41no—
389C24C2411yescharacteristic
390C24C2411yescharacteristic
391C24C2411yescharacteristic
392C24C2411yescharacteristic
393C2×Q8—22no—
394C2×Q8—22no—
395C2×Q8—22no—
396C2×Q8—41no—
397C2×Q8—41no—
398C2×Q8—41no—
399C2×D4—22no—
400C2×D4—22no—
401C2×D4—22no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—41no—
405C2×D4—41no—
406C2×D4—41no—
407C2×D4C2×D414yes—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
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×C4—41no—
438C22×C4—41no—
439C22×C4C2×D414yes—
440C22×C4#4114yes—
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
465C22×C4C2411yescharacteristic
466C22×C4C2411yescharacteristic
467C22×C4C2411yescharacteristic
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—22no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—22no—
497C4⋊C4—41no—
498C4⋊C4—41no—
499C4⋊C4—41no—
500C4⋊C4—41no—
501C4⋊C4—41no—
502C4⋊C4—41no—
503C4⋊C4—41no—
504C4⋊C4—41no—
505C4⋊C4—41no—
506C4⋊C4—41no—
507C4⋊C4—41no—
508C4⋊C4—41no—
509C4⋊C4—41no—
510C4⋊C4—41no—
511C4⋊C4—41no—
512C4⋊C4—41no—
513C4⋊C4—41no—
514C4⋊C4—41no—
515C4⋊C4C2×D414yes—
516C4⋊C4C2×D414yes—
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—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—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⋊C4C2×D414yes—
555C22⋊C4C2×D414yes—
556C22⋊C4C2×D414yes—
557C42—22no—
558C42—22no—
559C42—22no—
560C42—22no—
561C42—22no—
562C42—22no—
563C42—22no—
564C42—22no—
565C42—22no—
566C42—41no—
567C42—41no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—44no—
592C23—44no—
593C23—44no—
594C23—44no—
595C23—82no—
596C23—82no—
597C23—82no—
598C23C22×D412yes—
599C23C22×D412yes—
600C23C2×#4112yes—
601C232−1+412yes—
602C232−1+412yes—
603C23C2511yescharacteristic
604Q8—44no—
605Q8—82no—
606D4—28no—
607D4—44no—
608D4—82no—
609C2×C4—28no—
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—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—44no—
684C2×C4—44no—
685C2×C4—44no—
686C2×C4—44no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—82no—
690C2×C4—82no—
691C2×C4—82no—
692C2×C4—82no—
693C2×C4C22×D412yes—
694C2×C4C22×D412yes—
695C2×C4C22×D412yes—
696C2×C4C22×D412yes—
697C2×C4C22×D412yes—
698C2×C4C2×#4112yes—
699C2×C4C2×#4112yes—
700C2×C4H(5,𝔽2)12yes—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—88no—
729C22#54714yes—
730C22C23×D411yescharacteristic
731C22C22×#4111yescharacteristic
732C22C2×H(5,𝔽2)11yescharacteristic
733C22C2×2−1+411yescharacteristic
734C22C2×2−1+411yescharacteristic
735C22#58511yescharacteristic
736C22#58511yescharacteristic
737C4—22no—
738C4—22no—
739C4—22no—
740C4—22no—
741C4—22no—
742C4—22no—
743C4—22no—
744C4—22no—
745C4—41no—
746C4—41no—
747C4—41no—
748C4—41no—
749C4—41no—
750C4—41no—
751C4—41no—
752C4—41no—
753C4—41no—
754C4—41no—
755C4—41no—
756C4—41no—
757C4—41no—
758C4—41no—
759C4—41no—
760C4—41no—
761C4—41no—
762C4—41no—
763C4—41no—
764C2—24no—
765C2—42no—
766C2—42no—
767C2—81no—
768C2C2×#54711yescharacteristic
769C2#348811yescharacteristic
770C2#348911yescharacteristic
771C2#349511yescharacteristic
772C2#350511yescharacteristic
773C2#353811yescharacteristic
774C2#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×#552C2semidirect
3. #2725C2semidirect
4. #2725C2semidirect
5. #2721C2semidirect
6. #2720C2semidirect
7. #2718C2semidirect
8. #2715C2semidirect
9. #2695C2semidirect
10. #2674C2semidirect
12. #2484C2semidirect
13. #2482C2semidirect
14. #2475C2semidirect
15. #2470C2semidirect
16. #2469C2semidirect
17. #2466C2semidirect
18. #2449C2semidirect
19. #2441C2semidirect
20. #2440C2semidirect
21. #2438C2semidirect
22. #2437C2semidirect
23. #2429C2semidirect
24. #2419C2semidirect
26. #2413C2semidirect
27. C2×#396C2semidirect
28. D4×C4⋊C4C2semidirect
29. #2342C2semidirect
30. #2322C2semidirect
31. #2316C2semidirect
34. C2×C4⋊Q8C22semidirect
37. C2×#126C22semidirect
38. C2×#126C22semidirect
39. C2×#125C22semidirect
40. C2×#125C22semidirect
41. C2×#125C22semidirect
52. C2×C22⋊Q8C22semidirect
54. C2×C4×Q8C22semidirect
63. C2×#117C22semidirect
67. C22×C4⋊C4C22semidirect
72. #400C22semidirect
73. #400C22semidirect
74. #400C22semidirect
75. #400C22semidirect
80. #398C22semidirect
81. #398C22semidirect
82. #398C22semidirect
83. #398C22semidirect
84. #398C22semidirect
85. #398C22semidirect
86. #398C22semidirect
90. #397C22semidirect
91. #397C22semidirect
104. #395C22semidirect
105. #395C22semidirect
106. #395C22semidirect
112. #391C22semidirect
113. #389C22semidirect
114. #389C22semidirect
115. #389C22semidirect
116. #389C22semidirect
117. #389C22semidirect
118. #389C22semidirect
119. #389C22semidirect
120. #389C22semidirect
121. #389C22semidirect
122. #389C22semidirect
123. #389C22semidirect
124. #389C22semidirect
125. #389C22semidirect
126. #389C22semidirect
127. #389C22semidirect
140. #388C22semidirect
141. #388C22semidirect
142. #387C22semidirect
143. #387C22semidirect
144. #387C22semidirect
145. #387C22semidirect
146. #387C22semidirect
147. #387C22semidirect
148. #387C22semidirect
149. #387C22semidirect
150. #387C22semidirect
151. #387C22semidirect
165. #385C22semidirect
166. #385C22semidirect
167. #385C22semidirect
168. #385C22semidirect
169. #385C22semidirect
170. #384C22semidirect
171. #384C22semidirect
175. #381C22semidirect
181. #380C22semidirect
184. C4×C4⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
C2×#5522
C2×#5512
#27252
#27212
#27202
#27182
#27152
#26952
#26742
#25342
#24842
#24822
#24752
#24702
#24692
#24662
#24492
#24412
#24402
#24382
#24372
#24292
#24192
#24182
#24132
C2×#3962
D4×C4⋊C42
#23422
#23222
#23162