Finite Group Databasebeta

← #39870

Subgroups — #39870

Order 256.

1084 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#551C211yesmaximal, characteristic, complemented
2C2×#529C211yesmaximal, characteristic, complemented
3#2853C211yesmaximal, characteristic, complemented
4#2724C211yesmaximal, characteristic, complemented
5#2710C211yesmaximal, characteristic, complemented
6#2706C211yesmaximal, characteristic, complemented
7#2701C211yesmaximal, characteristic, complemented
8#2700C211yesmaximal, characteristic, complemented
9#2697C211yesmaximal, characteristic, complemented
10#2680C211yesmaximal, characteristic, complemented
11#2678C211yesmaximal, characteristic
12#2638C211yesmaximal, characteristic, complemented
13#2637C211yesmaximal, characteristic, complemented
14#2609C211yesmaximal, characteristic, complemented
15#2602C211yesmaximal, characteristic, complemented
16#2601C211yesmaximal, characteristic, complemented
17#2600C211yesmaximal, characteristic, complemented
18#2560C211yesmaximal, characteristic, complemented
19#2556C211yesmaximal, characteristic, complemented
20#2519C211yesmaximal, characteristic, complemented
21#2512C211yesmaximal, characteristic, complemented
22#2499C211yesmaximal, characteristic, complemented
23#2482C211yesmaximal, characteristic, complemented
24#2480C211yesmaximal, characteristic, complemented
25#2478C211yesmaximal, characteristic, complemented
26#2474C211yesmaximal, characteristic, complemented
27#2472C211yesmaximal, characteristic, complemented
28#2357C211yesmaximal, characteristic, complemented
29#2323C211yesmaximal, characteristic, complemented
30#2321C211yesmaximal, characteristic, complemented
31C4×#123C211yesmaximal, characteristic, complemented
32#551—28no—
33#529—28no—
34C2×#126C2211yescharacteristic
35C2×#126C2211yescharacteristic
36C2×#126C2211yescharacteristic
37C2×#126C2211yescharacteristic, complemented
38C2×#125C2211yescharacteristic, complemented
39C2×#124C2211yescharacteristic
40C2×#124C2211yescharacteristic
41C2×#123C2211yescharacteristic
42C2×#123C2211yescharacteristic
43C2×#123C2211yescharacteristic
44C2×#123C2211yescharacteristic
45C2×#123C2211yescharacteristic
46C2×#123C2211yescharacteristic, complemented
47C2×C22⋊Q8C2211yescharacteristic
48C2×C22⋊Q8C2211yescharacteristic
49C2×C22⋊Q8C2211yescharacteristic
50C2×C22⋊Q8C2211yescharacteristic, complemented
51C2×#121C2211yescharacteristic
52C2×#120C2211yescharacteristic
53C2×#120C2211yescharacteristic
54C2×C4×Q8C2211yescharacteristic, complemented
55C2×C4×D4C2211yescharacteristic
56C2×C4×D4C2211yescharacteristic
57C2×C4×D4C2211yescharacteristic
58C2×C4×D4C2211yescharacteristic, complemented
59C2×#117C2211yescharacteristic
60C2×#117C2211yescharacteristic
61C2×#117C2211yescharacteristic
62C2×#117C2211yescharacteristic, complemented
63C22×C22⋊C4C2211yescharacteristic
64C22×C22⋊C4C2211yescharacteristic
65C22×C42C2211yescharacteristic, complemented
66#399C2211yescharacteristic
67#399C2211yescharacteristic
68#398C2211yescharacteristic, complemented
69#398C2211yescharacteristic, complemented
70#398C2211yescharacteristic, complemented
71#398C2211yescharacteristic, complemented
72#398C2211yescharacteristic, complemented
73#398C2211yescharacteristic, complemented
74#397C2211yescharacteristic
75#397C2211yescharacteristic
76#397C2211yescharacteristic
77#397C2211yescharacteristic
78#397C2211yescharacteristic
79#397C2211yescharacteristic
80#397C2211yescharacteristic
81#397C2211yescharacteristic
82#397C2211yescharacteristic
83#397C2211yescharacteristic, complemented
84#397C2211yescharacteristic, complemented
85#397C2211yescharacteristic, complemented
86#396C2211yescharacteristic
87#396C2211yescharacteristic
88#396C2211yescharacteristic
89#396C2211yescharacteristic
90#396C2211yescharacteristic, complemented
91#396C2211yescharacteristic, complemented
92#395C2211yescharacteristic, complemented
93#395C2211yescharacteristic, complemented
94#394C2211yescharacteristic
95#394C2211yescharacteristic
96#394C2211yescharacteristic
97#394C2211yescharacteristic
98#394C2211yescharacteristic
99#394C2211yescharacteristic
100#394C2211yescharacteristic, complemented
101#394C2211yescharacteristic, complemented
102#393C2211yescharacteristic
103#393C2211yescharacteristic, complemented
104#392C2211yescharacteristic
105#392C2211yescharacteristic
106#391C2211yescharacteristic, complemented
107#391C2211yescharacteristic, complemented
108#391C2211yescharacteristic, complemented
109#390C2211yescharacteristic
110#390C2211yescharacteristic
111#390C2211yescharacteristic
112#390C2211yescharacteristic
113#390C2211yescharacteristic
114#390C2211yescharacteristic
115#389C2211yescharacteristic, complemented
116#389C2211yescharacteristic, complemented
117#389C2211yescharacteristic, complemented
118#389C2211yescharacteristic, complemented
119#389C2211yescharacteristic, complemented
120#388C2211yescharacteristic
121#388C2211yescharacteristic
122#388C2211yescharacteristic
123#388C2211yescharacteristic
124#388C2211yescharacteristic
125#388C2211yescharacteristic
126#388C2211yescharacteristic
127#388C2211yescharacteristic
128#388C2211yescharacteristic
129#388C2211yescharacteristic
130#388C2211yescharacteristic
131#388C2211yescharacteristic
132#388C2211yescharacteristic
133#388C2211yescharacteristic
134#388C2211yescharacteristic
135#388C2211yescharacteristic
136#388C2211yescharacteristic, complemented
137#388C2211yescharacteristic, complemented
138#388C2211yescharacteristic, complemented
139#388C2211yescharacteristic, complemented
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#386C2211yescharacteristic
157#386C2211yescharacteristic
158#386C2211yescharacteristic
159#386C2211yescharacteristic
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#382C2211yescharacteristic, complemented
172#382C2211yescharacteristic, complemented
173#381C2211yescharacteristic
174#381C2211yescharacteristic, complemented
175#381C2211yescharacteristic, complemented
176#380C2211yescharacteristic
177#379C2211yescharacteristic
178#379C2211yescharacteristic
179#379C2211yescharacteristic
180C4×C4⋊C4C2211yescharacteristic, complemented
181C4×C4⋊C4C2211yescharacteristic, complemented
182C4×C4⋊C4C2211yescharacteristic, complemented
183C4×C4⋊C4C2211yescharacteristic, complemented
184C4×C4⋊C4C2211yescharacteristic, complemented
185C4×C22⋊C4C2211yescharacteristic
186C4×C22⋊C4C2211yescharacteristic
187C4×C22⋊C4C2211yescharacteristic
188C4×C22⋊C4C2211yescharacteristic, complemented
189C25C2311yescharacteristic
190C22×Q8C2311yescharacteristic
191C22×Q8C2311yescharacteristic
192C22×D4C2311yescharacteristic
193C22×D4C2311yescharacteristic
194C22×D4C2311yescharacteristic
195C22×D4C2311yescharacteristic
196C22×D4C2311yescharacteristic
197C22×D4C2311yescharacteristic
198C22×D4C2311yescharacteristic
199C23×C4C2311yescharacteristic
200C23×C4C2311yescharacteristic
201C23×C4C2311yescharacteristic
202C23×C4C2311yescharacteristic
203C23×C4C2311yescharacteristic
204C23×C4C2311yescharacteristic
205C23×C4C2311yescharacteristic
206C23×C4C2311yescharacteristic
207#126—24no—
208#126—24no—
209#126—24no—
210#126—24no—
211#125—24no—
212#124—24no—
213#124—24no—
214#123—24no—
215#123—24no—
216#123—24no—
217#123—24no—
218#123—24no—
219#123—24no—
220C22⋊Q8—24no—
221C22⋊Q8—24no—
222C22⋊Q8—24no—
223C22⋊Q8—24no—
224#121—24no—
225#120—24no—
226#120—24no—
227C4×Q8—24no—
228C4×D4—24no—
229C4×D4—24no—
230C4×D4—24no—
231C4×D4D418yescomplemented
232#117—24no—
233#117—24no—
234#117—24no—
235#117—24no—
236C2×C4⋊C4C2311yescharacteristic
237C2×C4⋊C4C2311yescharacteristic
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×C22⋊C4—24no—
272C2×C22⋊C4—24no—
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×C22⋊C4C2311yescharacteristic
318C2×C22⋊C4C2311yescharacteristic
319C2×C22⋊C4C2311yescharacteristic
320C2×C22⋊C4C2311yescharacteristic
321C2×C22⋊C4C2311yescharacteristic
322C2×C22⋊C4C2311yescharacteristic
323C2×C42—24no—
324C2×C42C2311yescharacteristic
325C2×C42C2311yescharacteristic
326C2×C42C2311yescharacteristic
327C2×C42C2311yescharacteristic
328C2×C42C2311yescharacteristic
329C2×C42C2311yescharacteristic
330C2×C42C2311yescharacteristic
331C2×C42C2311yescharacteristic
332C2×C42C2311yescharacteristic
333C2×C42C2311yescharacteristic
334C2×C42C2311yescharacteristic
335C2×C42C2311yescharacteristic
336C2×C42C2311yescharacteristic
337C2×C42C2311yescharacteristic
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
376C24—22no—
377C24—22no—
378C24—41no—
379C24—41no—
380C24—41no—
381C24—41no—
382C24—41no—
383C24C2411yescharacteristic
384C24C2411yescharacteristic
385C24C2411yescharacteristic
386C24C2411yescharacteristic
387C24C2411yescharacteristic
388C2×Q8—22no—
389C2×Q8—22no—
390C2×Q8—22no—
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—41no—
403C2×D4—41no—
404C2×D4—41no—
405C2×D4—41no—
406C2×D4—41no—
407C2×D4—41no—
408C2×D4—41no—
409C2×D4—41no—
410C2×D4—41no—
411C2×D4—41no—
412C2×D4—41no—
413C2×D4—41no—
414C2×D4C2×D414yes—
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—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×C4C2×D414yes—
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—41no—
487C4⋊C4—41no—
488C4⋊C4—41no—
489C4⋊C4—41no—
490C4⋊C4—41no—
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⋊C4C2×D414yes—
500C22⋊C4—22no—
501C22⋊C4—22no—
502C22⋊C4—22no—
503C22⋊C4—22no—
504C22⋊C4—22no—
505C22⋊C4—22no—
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—41no—
526C22⋊C4—41no—
527C22⋊C4—41no—
528C22⋊C4—41no—
529C22⋊C4—41no—
530C22⋊C4—41no—
531C22⋊C4—41no—
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⋊C4C2×D414yes—
548C22⋊C4C2×D414yes—
549C22⋊C4#4114yes—
550C42—22no—
551C42—22no—
552C42—22no—
553C42—22no—
554C42—22no—
555C42—22no—
556C42—22no—
557C42—41no—
558C42—41no—
559C42—41no—
560C42—41no—
561C42—41no—
562C42—41no—
563C42C2×D414yes—
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—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—44no—
597C23—44no—
598C23—82no—
599C23—82no—
600C23—82no—
601C23—82no—
602C23—82no—
603C23C22×D412yes—
604C23C22×D412yes—
605C23C2×#4112yes—
606C23C2511yescharacteristic
607Q8—44no—
608Q8—82no—
609D4—44no—
610D4—44no—
611D4—44no—
612D4—44no—
613D4—82no—
614D4—82no—
615D4—82no—
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—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—44no—
690C2×C4—44no—
691C2×C4—44no—
692C2×C4—44no—
693C2×C4—44no—
694C2×C4—82no—
695C2×C4C22×D412yes—
696C2×C4C22×D412yes—
697C2×C4C22×D412yes—
698C2×C4C22×D412yes—
699C2×C4C22×D412yes—
700C2×C4C2×#4112yes—
701C2×C4C2×#4112yes—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—22no—
710C22—22no—
711C22—41no—
712C22—41no—
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—41no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—88no—
738C22C23×D411yescharacteristic
739C22C22×#4111yescharacteristic
740C22#58511yescharacteristic
741C22#58511yescharacteristic
742C22#58511yescharacteristic
743C22#58511yescharacteristic
744C22#58511yescharacteristic
745C4—22no—
746C4—22no—
747C4—22no—
748C4—22no—
749C4—22no—
750C4—22no—
751C4—22no—
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—
766C4—41no—
767C4—41no—
768C4—41no—
769C4—41no—
770C4—41no—
771C2—42no—
772C2—42no—
773C2—42no—
774C2—81no—
775C2—81no—
776C2#344911yescharacteristic
777C2D4×#4111yescharacteristic
778C2#348511yescharacteristic
779C2#351011yescharacteristic
780C2#352111yescharacteristic
781C2#356611yescharacteristic
782C2#356611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C25
prime radical#2678C2
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×#551C2semidirect
2. C2×#529C2semidirect
3. #2853C2semidirect
4. #2724C2semidirect
5. #2710C2semidirect
6. #2706C2semidirect
7. #2701C2semidirect
8. #2700C2semidirect
9. #2697C2semidirect
10. #2680C2semidirect
12. #2638C2semidirect
13. #2637C2semidirect
14. #2609C2semidirect
15. #2602C2semidirect
16. #2601C2semidirect
17. #2600C2semidirect
18. #2560C2semidirect
19. #2556C2semidirect
20. #2519C2semidirect
21. #2512C2semidirect
22. #2499C2semidirect
23. #2482C2semidirect
24. #2480C2semidirect
25. #2478C2semidirect
26. #2474C2semidirect
27. #2472C2semidirect
28. #2357C2semidirect
29. #2323C2semidirect
30. #2321C2semidirect
31. C4×#123C2semidirect
37. C2×#126C22semidirect
38. C2×#125C22semidirect
46. C2×#123C22semidirect
50. C2×C22⋊Q8C22semidirect
54. C2×C4×Q8C22semidirect
58. C2×C4×D4C22semidirect
62. C2×#117C22semidirect
65. C22×C42C22semidirect
68. #398C22semidirect
69. #398C22semidirect
70. #398C22semidirect
71. #398C22semidirect
72. #398C22semidirect
73. #398C22semidirect
83. #397C22semidirect
84. #397C22semidirect
85. #397C22semidirect
90. #396C22semidirect
91. #396C22semidirect
92. #395C22semidirect
93. #395C22semidirect
100. #394C22semidirect
101. #394C22semidirect
103. #393C22semidirect
106. #391C22semidirect
107. #391C22semidirect
108. #391C22semidirect
115. #389C22semidirect
116. #389C22semidirect
117. #389C22semidirect
118. #389C22semidirect
119. #389C22semidirect
136. #388C22semidirect
137. #388C22semidirect
138. #388C22semidirect
139. #388C22semidirect
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. #382C22semidirect
172. #382C22semidirect
174. #381C22semidirect
175. #381C22semidirect
180. C4×C4⋊C4C22semidirect
181. C4×C4⋊C4C22semidirect
182. C4×C4⋊C4C22semidirect
183. C4×C4⋊C4C22semidirect
184. C4×C4⋊C4C22semidirect
188. C4×C22⋊C4C22semidirect
231. C4×D4D4semidirect

Maximal subgroups

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

subgroupindex
C2×#5512
C2×#5292
#28532
#27242
#27102
#27062
#27012
#27002
#26972
#26802
#26782
#26382
#26372
#26092
#26022
#26012
#26002
#25602
#25562
#25192
#25122
#24992
#24822
#24802
#24782
#24742
#24722
#23572
#23232
#23212
C4×#1232