Finite Group Databasebeta

← #43501

Subgroups — #43501

Order 256.

1076 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×#552C211yesmaximal, characteristic, complemented
2C2×#538C211yesmaximal, characteristic
3#2720C211yesmaximal, characteristic, complemented
4#2708C211yesmaximal, characteristic, complemented
5#2700C211yesmaximal, characteristic, complemented
6#2698C211yesmaximal, characteristic, complemented
7#2697C211yesmaximal, characteristic, complemented
8#2694C211yesmaximal, characteristic, complemented
9#2685C211yesmaximal, characteristic, complemented
10#2672C211yesmaximal, characteristic, complemented
11#2591C211yesmaximal, characteristic, complemented
12#2558C211yesmaximal, characteristic, complemented
13#2521C211yesmaximal, characteristic, complemented
14#2519C211yesmaximal, characteristic, complemented
15#2500C211yesmaximal, characteristic, complemented
16#2496C211yesmaximal, characteristic, complemented
17#2489C211yesmaximal, characteristic, complemented
18#2480C211yesmaximal, characteristic, complemented
19#2476C211yesmaximal, characteristic, complemented
20#2474C211yesmaximal, characteristic, complemented
21#2474C211yesmaximal, characteristic, complemented
22#2472C211yesmaximal, characteristic, complemented
23#2469C211yesmaximal, characteristic, complemented
24#2460C211yesmaximal, characteristic, complemented
25#2420C211yesmaximal, characteristic, complemented
26#2418C211yesmaximal, characteristic, complemented
27#2395C211yesmaximal, characteristic, complemented
28#2374C211yesmaximal, characteristic, complemented
29#2367C211yesmaximal, characteristic, complemented
30#2342C211yesmaximal, characteristic, complemented
31#2322C211yesmaximal, characteristic, complemented
32#552—28no—
33#538—28no—
34C2×#126C2211yescharacteristic
35C2×#126C2211yescharacteristic
36C2×#126C2211yescharacteristic
37C2×#126C2211yescharacteristic
38C2×#125C2211yescharacteristic, complemented
39C2×#125C2211yescharacteristic, complemented
40C2×#125C2211yescharacteristic, complemented
41C2×#124C2211yescharacteristic
42C2×#124C2211yescharacteristic
43C2×#124C2211yescharacteristic
44C2×#123C2211yescharacteristic
45C2×#123C2211yescharacteristic
46C2×#123C2211yescharacteristic
47C2×#123C2211yescharacteristic
48C2×C22⋊Q8C2211yescharacteristic
49C2×C22⋊Q8C2211yescharacteristic
50C2×C22⋊Q8C2211yescharacteristic, complemented
51C2×#121C2211yescharacteristic
52C2×#121C2211yescharacteristic
53C2×#121C2211yescharacteristic
54C2×#120C2211yescharacteristic
55C2×#120C2211yescharacteristic
56C2×C4×Q8C2211yescharacteristic, complemented
57C2×C4×D4C2211yescharacteristic
58C2×C4×D4C2211yescharacteristic
59C2×C4×D4C2211yescharacteristic
60C2×#117C2211yescharacteristic
61C2×#117C2211yescharacteristic, complemented
62C2×#117C2211yescharacteristic, complemented
63C22×C4⋊C4C2211yescharacteristic, complemented
64C22×C22⋊C4C2211yescharacteristic
65C22×C22⋊C4C2211yescharacteristic
66#400C2211yescharacteristic, complemented
67#400C2211yescharacteristic, complemented
68#400C2211yescharacteristic, complemented
69#400C2211yescharacteristic, complemented
70#399C2211yescharacteristic
71#399C2211yescharacteristic
72#399C2211yescharacteristic, complemented
73#398C2211yescharacteristic, complemented
74#398C2211yescharacteristic, complemented
75#398C2211yescharacteristic, complemented
76#397C2211yescharacteristic
77#397C2211yescharacteristic
78#397C2211yescharacteristic
79#397C2211yescharacteristic
80#397C2211yescharacteristic
81#397C2211yescharacteristic
82#397C2211yescharacteristic
83#397C2211yescharacteristic, complemented
84#397C2211yescharacteristic, complemented
85#396C2211yescharacteristic
86#396C2211yescharacteristic
87#396C2211yescharacteristic
88#396C2211yescharacteristic
89#396C2211yescharacteristic, complemented
90#395C2211yescharacteristic, complemented
91#395C2211yescharacteristic, complemented
92#395C2211yescharacteristic, complemented
93#394C2211yescharacteristic
94#394C2211yescharacteristic
95#394C2211yescharacteristic
96#394C2211yescharacteristic
97#394C2211yescharacteristic
98#394C2211yescharacteristic
99#394C2211yescharacteristic
100#394C2211yescharacteristic
101#394C2211yescharacteristic
102#394C2211yescharacteristic
103#394C2211yescharacteristic, complemented
104#394C2211yescharacteristic, complemented
105#393C2211yescharacteristic
106#391C2211yescharacteristic, complemented
107#391C2211yescharacteristic, complemented
108#391C2211yescharacteristic, complemented
109#390C2211yescharacteristic
110#390C2211yescharacteristic
111#390C2211yescharacteristic
112#390C2211yescharacteristic
113#389C2211yescharacteristic, complemented
114#389C2211yescharacteristic, complemented
115#389C2211yescharacteristic, complemented
116#389C2211yescharacteristic, complemented
117#388C2211yescharacteristic
118#388C2211yescharacteristic
119#388C2211yescharacteristic
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, complemented
134#388C2211yescharacteristic, complemented
135#388C2211yescharacteristic, complemented
136#388C2211yescharacteristic, complemented
137#388C2211yescharacteristic, complemented
138#388C2211yescharacteristic, complemented
139#388C2211yescharacteristic, complemented
140#388C2211yescharacteristic, complemented
141#387C2211yescharacteristic, complemented
142#387C2211yescharacteristic, complemented
143#387C2211yescharacteristic, complemented
144#387C2211yescharacteristic, complemented
145#387C2211yescharacteristic, complemented
146#387C2211yescharacteristic, complemented
147#387C2211yescharacteristic, complemented
148#386C2211yescharacteristic
149#386C2211yescharacteristic
150#386C2211yescharacteristic
151#386C2211yescharacteristic
152#386C2211yescharacteristic
153#386C2211yescharacteristic
154#386C2211yescharacteristic, complemented
155#386C2211yescharacteristic, complemented
156#385C2211yescharacteristic
157#385C2211yescharacteristic
158#385C2211yescharacteristic
159#385C2211yescharacteristic
160#385C2211yescharacteristic
161#385C2211yescharacteristic, complemented
162#385C2211yescharacteristic, complemented
163#385C2211yescharacteristic, complemented
164#384C2211yescharacteristic, complemented
165#382C2211yescharacteristic, complemented
166#382C2211yescharacteristic, complemented
167#381C2211yescharacteristic
168#381C2211yescharacteristic, complemented
169#380C2211yescharacteristic
170#380C2211yescharacteristic
171#380C2211yescharacteristic
172#380C2211yescharacteristic, complemented
173#379C2211yescharacteristic
174#379C2211yescharacteristic
175#379C2211yescharacteristic
176C4×C4⋊C4C2211yescharacteristic, complemented
177C4×C4⋊C4C2211yescharacteristic, complemented
178C4×C4⋊C4C2211yescharacteristic, complemented
179C4×C4⋊C4C2211yescharacteristic, complemented
180C4×C4⋊C4C2211yescharacteristic, complemented
181C4×C22⋊C4C2211yescharacteristic
182C4×C22⋊C4C2211yescharacteristic
183C4×C22⋊C4C2211yescharacteristic
184C4×C22⋊C4C2211yescharacteristic
185C4×C22⋊C4C2211yescharacteristic
186C4×C22⋊C4C2211yescharacteristic, complemented
187C4×C22⋊C4C2211yescharacteristic, complemented
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#125—24no—
213#125—24no—
214#124—24no—
215#124—24no—
216#124—24no—
217#123—24no—
218#123—24no—
219#123—24no—
220#123D418yes—
221C22⋊Q8—24no—
222C22⋊Q8—24no—
223C22⋊Q8—24no—
224#121—24no—
225#121—24no—
226#121—24no—
227#120—24no—
228#120—24no—
229C4×Q8—24no—
230C4×D4—24no—
231C4×D4—24no—
232C4×D4—24no—
233#117—24no—
234#117—24no—
235#117—24no—
236C2×C4⋊C4—24no—
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×C4⋊C4C2311yescharacteristic
272C2×C22⋊C4—24no—
273C2×C22⋊C4—24no—
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×C22⋊C4C2311yescharacteristic
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—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×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—41no—
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⋊C4C2×D414yes—
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—41no—
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⋊C4C2×D414yes—
547C22⋊C4C2×D414yes—
548C22⋊C4C2×D414yes—
549C22⋊C4#4114yes—
550C42—22no—
551C42—22no—
552C42—22no—
553C42—22no—
554C42—22no—
555C42—22no—
556C42—22no—
557C42—22no—
558C42—41no—
559C42—41no—
560C42—41no—
561C42—41no—
562C42—41no—
563C42—41no—
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—82no—
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—82no—
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—
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—
776C2D4×#4111yescharacteristic
777C2#348511yescharacteristic
778C2#349311yescharacteristic
779C2#350011yescharacteristic
780C2#352111yescharacteristic
781C2#356611yescharacteristic
782C2#356611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C25
prime radicalC2×#538C2
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. #2720C2semidirect
4. #2708C2semidirect
5. #2700C2semidirect
6. #2698C2semidirect
7. #2697C2semidirect
8. #2694C2semidirect
9. #2685C2semidirect
10. #2672C2semidirect
11. #2591C2semidirect
12. #2558C2semidirect
13. #2521C2semidirect
14. #2519C2semidirect
15. #2500C2semidirect
16. #2496C2semidirect
17. #2489C2semidirect
18. #2480C2semidirect
19. #2476C2semidirect
20. #2474C2semidirect
21. #2474C2semidirect
22. #2472C2semidirect
23. #2469C2semidirect
24. #2460C2semidirect
25. #2420C2semidirect
26. #2418C2semidirect
27. #2395C2semidirect
28. #2374C2semidirect
29. #2367C2semidirect
30. #2342C2semidirect
31. #2322C2semidirect
38. C2×#125C22semidirect
39. C2×#125C22semidirect
40. C2×#125C22semidirect
50. C2×C22⋊Q8C22semidirect
56. C2×C4×Q8C22semidirect
61. C2×#117C22semidirect
62. C2×#117C22semidirect
63. C22×C4⋊C4C22semidirect
66. #400C22semidirect
67. #400C22semidirect
68. #400C22semidirect
69. #400C22semidirect
72. #399C22semidirect
73. #398C22semidirect
74. #398C22semidirect
75. #398C22semidirect
83. #397C22semidirect
84. #397C22semidirect
89. #396C22semidirect
90. #395C22semidirect
91. #395C22semidirect
92. #395C22semidirect
103. #394C22semidirect
104. #394C22semidirect
106. #391C22semidirect
107. #391C22semidirect
108. #391C22semidirect
113. #389C22semidirect
114. #389C22semidirect
115. #389C22semidirect
116. #389C22semidirect
133. #388C22semidirect
134. #388C22semidirect
135. #388C22semidirect
136. #388C22semidirect
137. #388C22semidirect
138. #388C22semidirect
139. #388C22semidirect
140. #388C22semidirect
141. #387C22semidirect
142. #387C22semidirect
143. #387C22semidirect
144. #387C22semidirect
145. #387C22semidirect
146. #387C22semidirect
147. #387C22semidirect
154. #386C22semidirect
155. #386C22semidirect
161. #385C22semidirect
162. #385C22semidirect
163. #385C22semidirect
164. #384C22semidirect
165. #382C22semidirect
166. #382C22semidirect
168. #381C22semidirect
172. #380C22semidirect
176. C4×C4⋊C4C22semidirect
177. C4×C4⋊C4C22semidirect
178. C4×C4⋊C4C22semidirect
179. C4×C4⋊C4C22semidirect
180. C4×C4⋊C4C22semidirect
186. C4×C22⋊C4C22semidirect
187. C4×C22⋊C4C22semidirect
188. C4×C22⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
C2×#5522
C2×#5382
#27202
#27082
#27002
#26982
#26972
#26942
#26852
#26722
#25912
#25582
#25212
#25192
#25002
#24962
#24892
#24802
#24762
#24742
#24722
#24692
#24602
#24202
#24182
#23952
#23742
#23672
#23422
#23222