Finite Group Databasebeta

← #38422

Subgroups — #38422

Order 256.

1122 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#554C211yesmaximal, characteristic, complemented
2C2×#551C211yesmaximal, characteristic
3#2857C211yesmaximal, characteristic, complemented
4#2721C211yesmaximal, characteristic, complemented
5#2716C211yesmaximal, characteristic, complemented
6#2700C211yesmaximal, characteristic, complemented
7#2690C211yesmaximal, characteristic, complemented
8#2687C211yesmaximal, characteristic, complemented
9#2680C211yesmaximal, characteristic, complemented
10#2677C211yesmaximal, characteristic, complemented
11#2674C211yesmaximal, characteristic, complemented
12#2664C211yesmaximal, characteristic, complemented
13#2663C211yesmaximal, characteristic, complemented
14#2611C211yesmaximal, characteristic, complemented
15#2604C211yesmaximal, characteristic, complemented
16#2583C211yesmaximal, characteristic, complemented
17#2561C211yesmaximal, characteristic, complemented
18#2438C211yesmaximal, characteristic, complemented
19#2438C211yesmaximal, characteristic, complemented
20#2437C211yesmaximal, characteristic, complemented
21#2437C211yesmaximal, characteristic, complemented
22#2419C211yesmaximal, characteristic, complemented
23#2419C211yesmaximal, characteristic, complemented
24#2418C211yesmaximal, characteristic
25#2418C211yesmaximal, characteristic
26#2415C211yesmaximal, characteristic, complemented
27#2413C211yesmaximal, characteristic, complemented
28#2323C211yesmaximal, characteristic, complemented
29#2322C211yesmaximal, characteristic, complemented
30#2290C211yesmaximal, characteristic, complemented
31C2×#388C211yesmaximal, characteristic, complemented
32#554—28no—
33#551—28no—
34C2×C4⋊Q8C2211yescharacteristic, complemented
35C2×C4⋊Q8C2211yescharacteristic, complemented
36C2×#126C2211yescharacteristic
37C2×#126C2211yescharacteristic
38C2×#125C2211yescharacteristic, complemented
39C2×#125C2211yescharacteristic, complemented
40C2×#124C2211yescharacteristic
41C2×#123C2211yescharacteristic
42C2×#123C2211yescharacteristic
43C2×#123C2211yescharacteristic
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, complemented
54C2×C22⋊Q8C2211yescharacteristic, complemented
55C2×C22⋊Q8C2211yescharacteristic, complemented
56C2×#120C2211yescharacteristic
57C2×C4×Q8C2211yescharacteristic, complemented
58C2×C4×D4C2211yescharacteristic
59C2×C4×D4C2211yescharacteristic
60C2×C4×D4C2211yescharacteristic
61C2×C4×D4C2211yescharacteristic
62C2×#117C2211yescharacteristic
63C2×#117C2211yescharacteristic
64C2×#117C2211yescharacteristic, complemented
65C22×C4⋊C4C2211yescharacteristic
66C22×C4⋊C4C2211yescharacteristic, complemented
67C22×C22⋊C4C2211yescharacteristic
68C22×C22⋊C4C2211yescharacteristic
69C22×C22⋊C4C2211yescharacteristic
70C22×C22⋊C4C2211yescharacteristic
71C22×C42C2211yescharacteristic
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#398C2211yescharacteristic, complemented
88#397C2211yescharacteristic
89#397C2211yescharacteristic
90#397C2211yescharacteristic
91#397C2211yescharacteristic
92#397C2211yescharacteristic, complemented
93#397C2211yescharacteristic, complemented
94#397C2211yescharacteristic, complemented
95#397C2211yescharacteristic, complemented
96#396C2211yescharacteristic
97#396C2211yescharacteristic
98#396C2211yescharacteristic
99#396C2211yescharacteristic
100#395C2211yescharacteristic, complemented
101#395C2211yescharacteristic, complemented
102#395C2211yescharacteristic, complemented
103#395C2211yescharacteristic, complemented
104#394C2211yescharacteristic
105#394C2211yescharacteristic
106#394C2211yescharacteristic
107#394C2211yescharacteristic
108#393C2211yescharacteristic
109#393C2211yescharacteristic
110#393C2211yescharacteristic
111#393C2211yescharacteristic
112#391C2211yescharacteristic, complemented
113#391C2211yescharacteristic, complemented
114#391C2211yescharacteristic, complemented
115#391C2211yescharacteristic, 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#388C2211yescharacteristic
127#388C2211yescharacteristic
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
141#388C2211yescharacteristic
142#388C2211yescharacteristic, complemented
143#388C2211yescharacteristic, 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#387C2211yescharacteristic, complemented
153#387C2211yescharacteristic, complemented
154#386C2211yescharacteristic
155#386C2211yescharacteristic
156#386C2211yescharacteristic
157#386C2211yescharacteristic
158#385C2211yescharacteristic
159#385C2211yescharacteristic
160#385C2211yescharacteristic
161#385C2211yescharacteristic
162#385C2211yescharacteristic
163#385C2211yescharacteristic
164#385C2211yescharacteristic
165#385C2211yescharacteristic
166#385C2211yescharacteristic
167#385C2211yescharacteristic
168#385C2211yescharacteristic, complemented
169#385C2211yescharacteristic, complemented
170#384C2211yescharacteristic, complemented
171#381C2211yescharacteristic
172#381C2211yescharacteristic
173#381C2211yescharacteristic, complemented
174#381C2211yescharacteristic, complemented
175#380C2211yescharacteristic
176#380C2211yescharacteristic
177#380C2211yescharacteristic
178#380C2211yescharacteristic
179#380C2211yescharacteristic
180#380C2211yescharacteristic
181#379C2211yescharacteristic
182#379C2211yescharacteristic
183C4×C4⋊C4C2211yescharacteristic, complemented
184C4×C22⋊C4C2211yescharacteristic
185C4×C22⋊C4C2211yescharacteristic, complemented
186#376C2211yescharacteristic, complemented
187C2×#95C2211yescharacteristic
188C2×#95C2211yescharacteristic
189C25C2311yescharacteristic
190C22×Q8C2311yescharacteristic
191C22×Q8C2311yescharacteristic
192C22×Q8C2311yescharacteristic
193C22×Q8C2311yescharacteristic
194C22×D4C2311yescharacteristic
195C22×D4C2311yescharacteristic
196C22×D4C2311yescharacteristic
197C23×C4C2311yescharacteristic
198C23×C4C2311yescharacteristic
199C23×C4C2311yescharacteristic
200C23×C4C2311yescharacteristic
201C23×C4C2311yescharacteristic
202C23×C4C2311yescharacteristic
203C23×C4C2311yescharacteristic
204C23×C4C2311yescharacteristic
205C23×C4C2311yescharacteristic
206C23×C4C2311yescharacteristic
207C23×C4C2311yescharacteristic
208C4⋊Q8—24no—
209C4⋊Q8—42no—
210#126—24no—
211#126—24no—
212#125—24no—
213#125—24no—
214#124—24no—
215#123—24no—
216#123—24no—
217#123—24no—
218#123—24no—
219#123—42no—
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—42no—
230#120—24no—
231C4×Q8—24no—
232C4×D4—24no—
233C4×D4—24no—
234C4×D4—24no—
235C4×D4D418yes—
236#117—24no—
237#117—24no—
238#117—42no—
239C2×C4⋊C4—24no—
240C2×C4⋊C4—24no—
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×C22⋊C4—24no—
285C2×C22⋊C4—24no—
286C2×C22⋊C4—24no—
287C2×C22⋊C4—42no—
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×C42—42no—
329C2×C42C2311yescharacteristic
330C2×C42C2311yescharacteristic
331C2×C42C2311yescharacteristic
332C2×C42C2311yescharacteristic
333C2×C42C2311yescharacteristic
334C2×C42C2311yescharacteristic
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
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—22no—
397C2×Q8—22no—
398C2×Q8—41no—
399C2×Q8—41no—
400C2×Q8—41no—
401C2×Q8—41no—
402C2×Q8—41no—
403C2×Q8—41no—
404C2×Q8—41no—
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×D4C2×D414yes—
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—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
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×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4C2×D414yes—
446C22×C4C2×D414yes—
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
468C22×C4C2411yescharacteristic
469C22×C4C2411yescharacteristic
470C22×C4C2411yescharacteristic
471C22×C4C2411yescharacteristic
472C22×C4C2411yescharacteristic
473C22×C4C2411yescharacteristic
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—22no—
498C4⋊C4—22no—
499C4⋊C4—22no—
500C4⋊C4—22no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—22no—
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⋊C4—41no—
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⋊C4#4114yes—
557C42—22no—
558C42—22no—
559C42—22no—
560C42—22no—
561C42—22no—
562C42—22no—
563C42—41no—
564C42—41no—
565C42—41no—
566C42—41no—
567C42C2×D414yes—
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—
606Q8—82no—
607Q8—82no—
608D4—28no—
609D4—44no—
610D4—82no—
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—21no—
684C2×C4—44no—
685C2×C4—44no—
686C2×C4—44no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—44no—
690C2×C4—44no—
691C2×C4—44no—
692C2×C4—82no—
693C2×C4—82no—
694C2×C4—82no—
695C2×C4C22×D412yes—
696C2×C4C22×D412yes—
697C2×C4C22×D412yes—
698C2×C4C22×D412yes—
699C2×C4C22×D412yes—
700C2×C4C2×#4112yes—
701C2×C4C2×#4112yes—
702C2×C4H(5,𝔽2)12yes—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—22no—
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—41no—
729C22—41no—
730C22—88no—
731C22#53614yes—
732C22C23×D411yescharacteristic
733C22C22×#4111yescharacteristic
734C22C2×H(5,𝔽2)11yescharacteristic
735C22C2×2−1+411yescharacteristic
736C22C2×2−1+411yescharacteristic
737C22#58511yescharacteristic
738C22#58511yescharacteristic
739C4—22no—
740C4—22no—
741C4—22no—
742C4—22no—
743C4—22no—
744C4—22no—
745C4—22no—
746C4—22no—
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—
764C4—41no—
765C4—41no—
766C2—24no—
767C2—42no—
768C2—42no—
769C2—81no—
770C2C2×#53611yescharacteristic
771C2D4×#4111yescharacteristic
772C2#349511yescharacteristic
773C2#349611yescharacteristic
774C2#352011yescharacteristic
775C2#353511yescharacteristic
776C2#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×#554C2semidirect
3. #2857C2semidirect
4. #2721C2semidirect
5. #2716C2semidirect
6. #2700C2semidirect
7. #2690C2semidirect
8. #2687C2semidirect
9. #2680C2semidirect
10. #2677C2semidirect
11. #2674C2semidirect
12. #2664C2semidirect
13. #2663C2semidirect
14. #2611C2semidirect
15. #2604C2semidirect
16. #2583C2semidirect
17. #2561C2semidirect
18. #2438C2semidirect
19. #2438C2semidirect
20. #2437C2semidirect
21. #2437C2semidirect
22. #2419C2semidirect
23. #2419C2semidirect
26. #2415C2semidirect
27. #2413C2semidirect
28. #2323C2semidirect
29. #2322C2semidirect
30. #2290C2semidirect
31. C2×#388C2semidirect
34. C2×C4⋊Q8C22semidirect
35. C2×C4⋊Q8C22semidirect
38. C2×#125C22semidirect
39. C2×#125C22semidirect
53. C2×C22⋊Q8C22semidirect
54. C2×C22⋊Q8C22semidirect
55. C2×C22⋊Q8C22semidirect
57. C2×C4×Q8C22semidirect
64. C2×#117C22semidirect
66. 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
87. #398C22semidirect
92. #397C22semidirect
93. #397C22semidirect
94. #397C22semidirect
95. #397C22semidirect
100. #395C22semidirect
101. #395C22semidirect
102. #395C22semidirect
103. #395C22semidirect
112. #391C22semidirect
113. #391C22semidirect
114. #391C22semidirect
115. #391C22semidirect
116. #389C22semidirect
117. #389C22semidirect
118. #389C22semidirect
119. #389C22semidirect
120. #389C22semidirect
121. #389C22semidirect
122. #389C22semidirect
123. #389C22semidirect
124. #389C22semidirect
125. #389C22semidirect
142. #388C22semidirect
143. #388C22semidirect
144. #387C22semidirect
145. #387C22semidirect
146. #387C22semidirect
147. #387C22semidirect
148. #387C22semidirect
149. #387C22semidirect
150. #387C22semidirect
151. #387C22semidirect
152. #387C22semidirect
153. #387C22semidirect
168. #385C22semidirect
169. #385C22semidirect
170. #384C22semidirect
173. #381C22semidirect
174. #381C22semidirect
183. C4×C4⋊C4C22semidirect
185. C4×C22⋊C4C22semidirect
186. #376C22semidirect

Maximal subgroups

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

subgroupindex
C2×#5542
C2×#5512
#28572
#27212
#27162
#27002
#26902
#26872
#26802
#26772
#26742
#26642
#26632
#26112
#26042
#25832
#25612
#24382
#24372
#24192
#24182
#24152
#24132
#23232
#23222
#22902
C2×#3882