Finite Group Databasebeta

← #43110

Subgroups — #43110

Order 256.

1238 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
1C2×#559C211yesmaximal, characteristic, complemented
2C2×#547C211yesmaximal, characteristic, complemented
3#2710C211yesmaximal, characteristic, complemented
4#2710C211yesmaximal, characteristic, complemented
5#2701C211yesmaximal, characteristic, complemented
6#2700C211yesmaximal, characteristic, complemented
7#2682C211yesmaximal, characteristic, complemented
8#2676C211yesmaximal, characteristic, complemented
9#2674C211yesmaximal, characteristic, complemented
10#2673C211yesmaximal, characteristic, complemented
11#2579C211yesmaximal, characteristic, complemented
12#2557C211yesmaximal, characteristic, complemented
13#2465C211yesmaximal, characteristic, complemented
14#2464C211yesmaximal, characteristic, complemented
15#2461C211yesmaximal, characteristic, complemented
16#2461C211yesmaximal, characteristic, complemented
17#2459C211yesmaximal, characteristic, complemented
18#2459C211yesmaximal, characteristic, complemented
19#2458C211yesmaximal, characteristic, complemented
20#2455C211yesmaximal, characteristic, complemented
21#2451C211yesmaximal, characteristic, complemented
22#2449C211yesmaximal, characteristic, complemented
23#2443C211yesmaximal, characteristic, complemented
24#2431C211yesmaximal, characteristic, complemented
25#2407C211yesmaximal, characteristic, complemented
26#2406C211yesmaximal, characteristic, complemented
27#2388C211yesmaximal, characteristic, complemented
28#2361C211yesmaximal, characteristic, complemented
29#2360C211yesmaximal, characteristic, complemented
30#2335C211yesmaximal, characteristic, complemented
31#2322C211yesmaximal, characteristic, complemented
32C22×#41C2211yescharacteristic
33C22×#41C2211yescharacteristic
34#559—28no—
35#547—28no—
36C2×C4⋊Q8C2211yescharacteristic
37C2×#127C2211yescharacteristic
38C2×#124C2211yescharacteristic
39C2×#124C2211yescharacteristic
40C2×#124C2211yescharacteristic
41C2×#124C2211yescharacteristic
42C2×#124C2211yescharacteristic
43C2×#123C2211yescharacteristic
44C2×#123C2211yescharacteristic
45C2×#123C2211yescharacteristic
46C2×#123C2211yescharacteristic
47C2×#123C2211yescharacteristic
48C2×#123C2211yescharacteristic
49C2×#123C2211yescharacteristic
50C2×#123C2211yescharacteristic
51C2×#123C2211yescharacteristic
52C2×C22⋊Q8C2211yescharacteristic
53C2×C22⋊Q8C2211yescharacteristic
54C2×C22⋊Q8C2211yescharacteristic
55C2×C22⋊Q8C2211yescharacteristic
56C2×#121C2211yescharacteristic
57C2×#121C2211yescharacteristic
58C2×#121C2211yescharacteristic
59C2×#121C2211yescharacteristic
60C2×#121C2211yescharacteristic
61C2×C4×Q8C2211yescharacteristic
62C2×C4×Q8C2211yescharacteristic
63C2×C4×D4C2211yescharacteristic
64C2×C4×D4C2211yescharacteristic
65C2×C4×D4C2211yescharacteristic
66C2×C4×D4C2211yescharacteristic
67C2×C4×D4C2211yescharacteristic
68C2×C4×D4C2211yescharacteristic
69C2×C4×D4C2211yescharacteristic
70C2×C4×D4C2211yescharacteristic
71C22×C4⋊C4C2211yescharacteristic
72C22×C4⋊C4C2211yescharacteristic
73C22×C4⋊C4C2211yescharacteristic
74#399C2211yescharacteristic
75#399C2211yescharacteristic
76#398C2211yescharacteristic
77#398C2211yescharacteristic
78#398C2211yescharacteristic
79#397C2211yescharacteristic
80#397C2211yescharacteristic
81#397C2211yescharacteristic
82#396C2211yescharacteristic
83#396C2211yescharacteristic
84#396C2211yescharacteristic
85#396C2211yescharacteristic
86#395C2211yescharacteristic
87#395C2211yescharacteristic
88#395C2211yescharacteristic
89#395C2211yescharacteristic
90#394C2211yescharacteristic
91#394C2211yescharacteristic
92#394C2211yescharacteristic
93#394C2211yescharacteristic
94#394C2211yescharacteristic
95#394C2211yescharacteristic
96#394C2211yescharacteristic
97#394C2211yescharacteristic
98#394C2211yescharacteristic
99#394C2211yescharacteristic
100#394C2211yescharacteristic
101#393C2211yescharacteristic
102#393C2211yescharacteristic
103#393C2211yescharacteristic
104#393C2211yescharacteristic
105#392C2211yescharacteristic
106#392C2211yescharacteristic
107#392C2211yescharacteristic
108#392C2211yescharacteristic
109#392C2211yescharacteristic
110#392C2211yescharacteristic
111#392C2211yescharacteristic
112#392C2211yescharacteristic
113#392C2211yescharacteristic
114#391C2211yescharacteristic
115#391C2211yescharacteristic
116#391C2211yescharacteristic
117#391C2211yescharacteristic
118#391C2211yescharacteristic
119#390C2211yescharacteristic
120#390C2211yescharacteristic
121#390C2211yescharacteristic
122#390C2211yescharacteristic
123#390C2211yescharacteristic
124#389C2211yescharacteristic
125#389C2211yescharacteristic
126#389C2211yescharacteristic
127#389C2211yescharacteristic
128#389C2211yescharacteristic
129#389C2211yescharacteristic
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
143#388C2211yescharacteristic
144#387C2211yescharacteristic
145#387C2211yescharacteristic
146#387C2211yescharacteristic
147#387C2211yescharacteristic
148#387C2211yescharacteristic
149#387C2211yescharacteristic
150#387C2211yescharacteristic
151#387C2211yescharacteristic
152#386C2211yescharacteristic
153#386C2211yescharacteristic
154#386C2211yescharacteristic
155#386C2211yescharacteristic
156#386C2211yescharacteristic
157#386C2211yescharacteristic
158#386C2211yescharacteristic
159#386C2211yescharacteristic
160#386C2211yescharacteristic
161#386C2211yescharacteristic
162#386C2211yescharacteristic
163#386C2211yescharacteristic
164#386C2211yescharacteristic
165#385C2211yescharacteristic
166#385C2211yescharacteristic
167#385C2211yescharacteristic
168#385C2211yescharacteristic
169#385C2211yescharacteristic
170#385C2211yescharacteristic
171#385C2211yescharacteristic
172#385C2211yescharacteristic
173#385C2211yescharacteristic
174#385C2211yescharacteristic
175#385C2211yescharacteristic
176#385C2211yescharacteristic
177#385C2211yescharacteristic
178#381C2211yescharacteristic
179#381C2211yescharacteristic
180#380C2211yescharacteristic
181C4×C4⋊C4C2211yescharacteristic
182C4×C4⋊C4C2211yescharacteristic
183C4×C22⋊C4C2211yescharacteristic
184C4×C22⋊C4C2211yescharacteristic
185C4×C22⋊C4C2211yescharacteristic
186C4×C22⋊C4C2211yescharacteristic
187C4×C22⋊C4C2211yescharacteristic
188C4×C22⋊C4C2211yescharacteristic
189C2×#41—24no—
190C2×#41—24no—
191C2×#41—42no—
192C2×#41—42no—
193C2×#41—42no—
194C2×#41—42no—
195C22×Q8C2311yescharacteristic
196C22×Q8C2311yescharacteristic
197C22×Q8C2311yescharacteristic
198C22×Q8C2311yescharacteristic
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
222C23×C4C2311yescharacteristic
223C23×C4C2311yescharacteristic
224C23×C4C2311yescharacteristic
225C23×C4C2311yescharacteristic
226C4⋊Q8—24no—
227#127—24no—
228#124—24no—
229#124—24no—
230#124—24no—
231#124—24no—
232#124—42no—
233#123—24no—
234#123—24no—
235#123—24no—
236#123—24no—
237#123—24no—
238#123—24no—
239#123—24no—
240#123—42no—
241#123D418yescomplemented
242C22⋊Q8—24no—
243C22⋊Q8—24no—
244C22⋊Q8—24no—
245C22⋊Q8—42no—
246#121—24no—
247#121—24no—
248#121—24no—
249#121—42no—
250#121—42no—
251C4×Q8—24no—
252C4×Q8—24no—
253C4×D4—24no—
254C4×D4—24no—
255C4×D4—24no—
256C4×D4—24no—
257C4×D4—24no—
258C4×D4—24no—
259C4×D4—42no—
260C4×D4—42no—
261C2×C4⋊C4—24no—
262C2×C4⋊C4—24no—
263C2×C4⋊C4—42no—
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×C4⋊C4C2311yescharacteristic
290C2×C4⋊C4C2311yescharacteristic
291C2×C4⋊C4C2311yescharacteristic
292C2×C4⋊C4C2311yescharacteristic
293C2×C4⋊C4C2311yescharacteristic
294C2×C4⋊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×C22⋊C4C2311yescharacteristic
336C2×C22⋊C4C2311yescharacteristic
337C2×C22⋊C4C2311yescharacteristic
338C2×C22⋊C4C2311yescharacteristic
339C2×C22⋊C4C2311yescharacteristic
340C2×C22⋊C4C2311yescharacteristic
341C2×C22⋊C4C2311yescharacteristic
342C2×C22⋊C4C2311yescharacteristic
343C2×C42C2311yescharacteristic
344C2×C42C2311yescharacteristic
345C2×C42C2311yescharacteristic
346C2×C42C2311yescharacteristic
347C2×C42C2311yescharacteristic
348C2×C42C2311yescharacteristic
349C2×C42C2311yescharacteristic
350C2×C42C2311yescharacteristic
351C2×C42C2311yescharacteristic
352C2×C42C2311yescharacteristic
353C2×C42C2311yescharacteristic
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
382#95C2311yescharacteristic
383#95C2311yescharacteristic
384#95C2311yescharacteristic
385#95C2311yescharacteristic
386#95C2311yescharacteristic
387#95C2311yescharacteristic
388C24C2411yescharacteristic
389C24C2411yescharacteristic
390C24C2411yescharacteristic
391C24C2411yescharacteristic
392C24C2411yescharacteristic
393C24C2411yescharacteristic
394#41—416no—
395#41—416no—
396C2×Q8—22no—
397C2×Q8—22no—
398C2×Q8—22no—
399C2×Q8—22no—
400C2×Q8—22no—
401C2×Q8—22no—
402C2×Q8—22no—
403C2×Q8—22no—
404C2×Q8—41no—
405C2×Q8—41no—
406C2×Q8—41no—
407C2×Q8—41no—
408C2×D4—22no—
409C2×D4—22no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—22no—
421C2×D4—22no—
422C2×D4—22no—
423C2×D4—22no—
424C2×D4—22no—
425C2×D4—22no—
426C2×D4—22no—
427C2×D4—22no—
428C2×D4—22no—
429C2×D4—22no—
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×D4C2×D414yes—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
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×C4—41no—
486C22×C4—41no—
487C22×C4—41no—
488C22×C4C2×D414yes—
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
508C22×C4C2411yescharacteristic
509C22×C4C2411yescharacteristic
510C22×C4C2411yescharacteristic
511C22×C4C2411yescharacteristic
512C22×C4C2411yescharacteristic
513C22×C4C2411yescharacteristic
514C4⋊C4—22no—
515C4⋊C4—22no—
516C4⋊C4—22no—
517C4⋊C4—22no—
518C4⋊C4—22no—
519C4⋊C4—22no—
520C4⋊C4—22no—
521C4⋊C4—22no—
522C4⋊C4—22no—
523C4⋊C4—22no—
524C4⋊C4—22no—
525C4⋊C4—22no—
526C4⋊C4—22no—
527C4⋊C4—22no—
528C4⋊C4—22no—
529C4⋊C4—22no—
530C4⋊C4—22no—
531C4⋊C4—41no—
532C4⋊C4—41no—
533C4⋊C4—41no—
534C4⋊C4—41no—
535C4⋊C4—41no—
536C4⋊C4—41no—
537C4⋊C4—41no—
538C4⋊C4—41no—
539C4⋊C4—41no—
540C4⋊C4—41no—
541C4⋊C4—41no—
542C4⋊C4C2×D414yes—
543C4⋊C4C2×D414yes—
544C4⋊C4#4114yescomplemented
545C22⋊C4—22no—
546C22⋊C4—22no—
547C22⋊C4—22no—
548C22⋊C4—22no—
549C22⋊C4—22no—
550C22⋊C4—22no—
551C22⋊C4—22no—
552C22⋊C4—22no—
553C22⋊C4—22no—
554C22⋊C4—22no—
555C22⋊C4—22no—
556C22⋊C4—22no—
557C22⋊C4—22no—
558C22⋊C4—22no—
559C22⋊C4—22no—
560C22⋊C4—22no—
561C22⋊C4—22no—
562C22⋊C4—22no—
563C22⋊C4—22no—
564C22⋊C4—22no—
565C22⋊C4—22no—
566C22⋊C4—22no—
567C22⋊C4—22no—
568C22⋊C4—22no—
569C22⋊C4—22no—
570C22⋊C4—22no—
571C22⋊C4—22no—
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⋊C4C2×D414yes—
591C22⋊C4C2×D414yes—
592C22⋊C4C2×D414yes—
593C42—22no—
594C42—22no—
595C42—22no—
596C42—22no—
597C42—22no—
598C42—22no—
599C42—41no—
600C42—41no—
601C42—41no—
602C42—41no—
603C42—41no—
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—
643C23C22×D412yes—
644C23C22×D412yes—
645C23H(5,𝔽2)12yes—
646C23C2511yescharacteristic
647Q8—44no—
648Q8—44no—
649Q8—44no—
650Q8—44no—
651D4—28no—
652D4—44no—
653D4—44no—
654D4—44no—
655D4—44no—
656D4—44no—
657D4—44no—
658D4—44no—
659D4—44no—
660D4—44no—
661D4—44no—
662D4—44no—
663D4—82no—
664D4—82no—
665D4—82no—
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—21no—
731C2×C4—44no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—82no—
741C2×C4—82no—
742C2×C4—82no—
743C2×C4C22×D412yes—
744C2×C4C22×D412yes—
745C2×C4C22×D412yes—
746C2×C4C22×D412yes—
747C2×C4C22×D412yes—
748C2×C4C2×#4112yes—
749C2×C4C2×#4112yes—
750C2×C4C2×#4112yes—
751C2×C4H(5,𝔽2)12yes—
752C2×C42−1+412yes—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—22no—
760C22—22no—
761C22—22no—
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—41no—
795C22C23×D411yescharacteristic
796C22C22×#4111yescharacteristic
797C22C2×H(5,𝔽2)11yescharacteristic
798C22C2×H(5,𝔽2)11yescharacteristic
799C22C2×2−1+411yescharacteristic
800C22#58511yescharacteristic
801C22#58511yescharacteristic
802C4—22no—
803C4—22no—
804C4—22no—
805C4—22no—
806C4—22no—
807C4—22no—
808C4—22no—
809C4—22no—
810C4—22no—
811C4—22no—
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—
826C4—41no—
827C2—42no—
828C2—42no—
829C2—42no—
830C2—81no—
831C2—81no—
832C2—81no—
833C2D4×#4111yescharacteristic
834C2#348411yescharacteristic
835C2#348911yescharacteristic
836C2#350611yescharacteristic
837C2#352211yescharacteristic
838C2#353311yescharacteristic
839C2#355411yescharacteristic
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. C2×#559C2semidirect
2. C2×#547C2semidirect
3. #2710C2semidirect
4. #2710C2semidirect
5. #2701C2semidirect
6. #2700C2semidirect
7. #2682C2semidirect
8. #2676C2semidirect
9. #2674C2semidirect
10. #2673C2semidirect
11. #2579C2semidirect
12. #2557C2semidirect
13. #2465C2semidirect
14. #2464C2semidirect
15. #2461C2semidirect
16. #2461C2semidirect
17. #2459C2semidirect
18. #2459C2semidirect
19. #2458C2semidirect
20. #2455C2semidirect
21. #2451C2semidirect
22. #2449C2semidirect
23. #2443C2semidirect
24. #2431C2semidirect
25. #2407C2semidirect
26. #2406C2semidirect
27. #2388C2semidirect
28. #2361C2semidirect
29. #2360C2semidirect
30. #2335C2semidirect
31. #2322C2semidirect
241. #123D4semidirect
544. C4⋊C4#41semidirect

Maximal subgroups

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

subgroupindex
C2×#5592
C2×#5472
#27102
#27012
#27002
#26822
#26762
#26742
#26732
#25792
#25572
#24652
#24642
#24612
#24592
#24582
#24552
#24512
#24492
#24432
#24312
#24072
#24062
#23882
#23612
#23602
#23352
#23222