Finite Group Databasebeta

← #37740

Subgroups — #37740

Order 256.

1089 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#538C211yesmaximal, characteristic
2C2×#529C211yesmaximal, characteristic, complemented
3#2853C211yesmaximal, characteristic, complemented
4#2721C211yesmaximal, characteristic, complemented
5#2717C211yesmaximal, characteristic, complemented
6#2717C211yesmaximal, characteristic, complemented
7#2708C211yesmaximal, characteristic, complemented
8#2701C211yesmaximal, characteristic, complemented
9#2697C211yesmaximal, characteristic, complemented
10#2690C211yesmaximal, characteristic, complemented
11#2684C211yesmaximal, characteristic, complemented
12#2663C211yesmaximal, characteristic, complemented
13#2638C211yesmaximal, characteristic, complemented
14#2521C211yesmaximal, characteristic, complemented
15#2496C211yesmaximal, characteristic, complemented
16#2480C211yesmaximal, characteristic, complemented
17#2478C211yesmaximal, characteristic, complemented
18#2474C211yesmaximal, characteristic, complemented
19#2469C211yesmaximal, characteristic, complemented
20#2466C211yesmaximal, characteristic, complemented
21#2465C211yesmaximal, characteristic, complemented
22#2447C211yesmaximal, characteristic, complemented
23#2444C211yesmaximal, characteristic, complemented
24#2422C211yesmaximal, characteristic, complemented
25#2419C211yesmaximal, characteristic, complemented
26#2418C211yesmaximal, characteristic, complemented
27#2418C211yesmaximal, characteristic, complemented
28#2359C211yesmaximal, characteristic, complemented
29#2342C211yesmaximal, characteristic, complemented
30#2333C211yesmaximal, characteristic, complemented
31C4×#123C211yesmaximal, characteristic, complemented
32#538—28no—
33#529—28no—
34C2×#126C2211yescharacteristic
35C2×#126C2211yescharacteristic
36C2×#126C2211yescharacteristic
37C2×#126C2211yescharacteristic, complemented
38C2×#125C2211yescharacteristic, complemented
39C2×#124C2211yescharacteristic
40C2×#124C2211yescharacteristic
41C2×#124C2211yescharacteristic
42C2×#123C2211yescharacteristic
43C2×#123C2211yescharacteristic
44C2×#123C2211yescharacteristic
45C2×#123C2211yescharacteristic
46C2×#123C2211yescharacteristic
47C2×#123C2211yescharacteristic, complemented
48C2×C22⋊Q8C2211yescharacteristic
49C2×C22⋊Q8C2211yescharacteristic, complemented
50C2×#121C2211yescharacteristic
51C2×#121C2211yescharacteristic
52C2×#121C2211yescharacteristic
53C2×#120C2211yescharacteristic
54C2×#120C2211yescharacteristic
55C2×C4×Q8C2211yescharacteristic, complemented
56C2×C4×D4C2211yescharacteristic
57C2×C4×D4C2211yescharacteristic
58C2×C4×D4C2211yescharacteristic
59C2×C4×D4C2211yescharacteristic
60C2×C4×D4C2211yescharacteristic, complemented
61C2×#117C2211yescharacteristic
62C2×#117C2211yescharacteristic, complemented
63C22×C22⋊C4C2211yescharacteristic
64C22×C22⋊C4C2211yescharacteristic
65C22×C42C2211yescharacteristic, complemented
66#400C2211yescharacteristic, complemented
67#400C2211yescharacteristic, complemented
68#400C2211yescharacteristic, complemented
69#399C2211yescharacteristic
70#399C2211yescharacteristic
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#397C2211yescharacteristic, complemented
87#397C2211yescharacteristic, complemented
88#397C2211yescharacteristic, complemented
89#396C2211yescharacteristic
90#396C2211yescharacteristic
91#396C2211yescharacteristic
92#395C2211yescharacteristic, complemented
93#395C2211yescharacteristic, complemented
94#395C2211yescharacteristic, complemented
95#395C2211yescharacteristic, complemented
96#394C2211yescharacteristic
97#394C2211yescharacteristic
98#394C2211yescharacteristic
99#394C2211yescharacteristic
100#394C2211yescharacteristic
101#394C2211yescharacteristic
102#394C2211yescharacteristic
103#394C2211yescharacteristic
104#393C2211yescharacteristic
105#393C2211yescharacteristic
106#391C2211yescharacteristic, complemented
107#391C2211yescharacteristic, complemented
108#390C2211yescharacteristic
109#390C2211yescharacteristic, complemented
110#389C2211yescharacteristic, complemented
111#389C2211yescharacteristic, complemented
112#389C2211yescharacteristic, complemented
113#389C2211yescharacteristic, complemented
114#389C2211yescharacteristic, complemented
115#388C2211yescharacteristic
116#388C2211yescharacteristic
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, complemented
131#387C2211yescharacteristic, complemented
132#387C2211yescharacteristic, complemented
133#387C2211yescharacteristic, complemented
134#387C2211yescharacteristic, complemented
135#387C2211yescharacteristic, complemented
136#387C2211yescharacteristic, complemented
137#387C2211yescharacteristic, complemented
138#387C2211yescharacteristic, complemented
139#387C2211yescharacteristic, complemented
140#387C2211yescharacteristic, complemented
141#387C2211yescharacteristic, complemented
142#387C2211yescharacteristic, complemented
143#387C2211yescharacteristic, complemented
144#386C2211yescharacteristic
145#386C2211yescharacteristic
146#386C2211yescharacteristic
147#386C2211yescharacteristic
148#386C2211yescharacteristic
149#386C2211yescharacteristic
150#386C2211yescharacteristic
151#386C2211yescharacteristic
152#386C2211yescharacteristic
153#386C2211yescharacteristic, complemented
154#385C2211yescharacteristic
155#385C2211yescharacteristic
156#385C2211yescharacteristic
157#385C2211yescharacteristic
158#385C2211yescharacteristic
159#385C2211yescharacteristic
160#385C2211yescharacteristic, complemented
161#385C2211yescharacteristic, complemented
162#385C2211yescharacteristic, complemented
163#385C2211yescharacteristic, complemented
164#385C2211yescharacteristic, complemented
165#385C2211yescharacteristic, complemented
166#384C2211yescharacteristic, complemented
167#381C2211yescharacteristic
168#381C2211yescharacteristic, complemented
169#381C2211yescharacteristic, complemented
170#381C2211yescharacteristic, complemented
171#380C2211yescharacteristic
172#380C2211yescharacteristic
173#380C2211yescharacteristic
174#380C2211yescharacteristic
175#380C2211yescharacteristic, complemented
176#379C2211yescharacteristic
177#379C2211yescharacteristic
178#379C2211yescharacteristic
179C4×C4⋊C4C2211yescharacteristic, complemented
180C4×C4⋊C4C2211yescharacteristic, complemented
181C4×C4⋊C4C2211yescharacteristic, complemented
182C4×C22⋊C4C2211yescharacteristic
183C4×C22⋊C4C2211yescharacteristic
184C4×C22⋊C4C2211yescharacteristic
185C4×C22⋊C4C2211yescharacteristic
186C4×C22⋊C4C2211yescharacteristic, complemented
187C4×C22⋊C4C2211yescharacteristic, complemented
188C2×#95C2211yescharacteristic, 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
207C23×C4C2311yescharacteristic
208C23×C4C2311yescharacteristic
209#126—24no—
210#126—24no—
211#126—24no—
212#126—24no—
213#125—24no—
214#124—24no—
215#124—24no—
216#124—24no—
217#123—24no—
218#123—24no—
219#123—24no—
220#123—24no—
221#123—24no—
222#123—24no—
223C22⋊Q8—24no—
224C22⋊Q8—24no—
225#121—24no—
226#121—24no—
227#121D418yes—
228#120—24no—
229#120—24no—
230C4×Q8—24no—
231C4×D4—24no—
232C4×D4—24no—
233C4×D4—24no—
234C4×D4—24no—
235C4×D4—24no—
236#117—24no—
237#117—24no—
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×C42—24no—
322C2×C42C2311yescharacteristic
323C2×C42C2311yescharacteristic
324C2×C42C2311yescharacteristic
325C2×C42C2311yescharacteristic
326C2×C42C2311yescharacteristic
327C2×C42C2311yescharacteristic
328C2×C42C2311yescharacteristic
329C2×C42C2311yescharacteristic
330C2×C42C2311yescharacteristic
331C2×C42C2311yescharacteristic
332C2×C42C2311yescharacteristic
333C2×C42C2311yescharacteristic
334#95C2311yescharacteristic
335#95C2311yescharacteristic
336#95C2311yescharacteristic
337#95C2311yescharacteristic
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—41no—
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—41no—
401C2×D4—41no—
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×D4C2×D414yes—
413C2×D4C2×D414yes—
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—22no—
425C22×C4—22no—
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×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4C2×D414yes—
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
468C22×C4C2411yescharacteristic
469C22×C4C2411yescharacteristic
470C22×C4C2411yescharacteristic
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—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⋊C4—41no—
500C4⋊C4—41no—
501C4⋊C4—41no—
502C4⋊C4—41no—
503C4⋊C4C2×D414yes—
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—22no—
526C22⋊C4—22no—
527C22⋊C4—22no—
528C22⋊C4—22no—
529C22⋊C4—22no—
530C22⋊C4—22no—
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⋊C4—41no—
548C22⋊C4—41no—
549C22⋊C4C2×D414yes—
550C22⋊C4C2×D414yes—
551C22⋊C4#4114yes—
552C42—22no—
553C42—22no—
554C42—22no—
555C42—22no—
556C42—22no—
557C42—22no—
558C42—22no—
559C42—22no—
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—44no—
596C23—44no—
597C23—82no—
598C23—82no—
599C23—82no—
600C23—82no—
601C23—82no—
602C23C22×D412yes—
603C23C22×D412yes—
604C23C22×D412yes—
605C23C2×#4112yes—
606C23C2511yescharacteristic
607Q8—44no—
608Q8—82no—
609D4—44no—
610D4—44no—
611D4—44no—
612D4—44no—
613D4—44no—
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—21no—
688C2×C4—44no—
689C2×C4—44no—
690C2×C4—44no—
691C2×C4—44no—
692C2×C4—44no—
693C2×C4—82no—
694C2×C4—82no—
695C2×C4—82no—
696C2×C4—82no—
697C2×C4—82no—
698C2×C4C22×D412yes—
699C2×C4C22×D412yes—
700C2×C4C22×D412yes—
701C2×C4C22×D412yes—
702C2×C4C2×#4112yes—
703C2×C4C2×#4112yes—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
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—41no—
738C22—41no—
739C22—88no—
740C22C23×D411yescharacteristic
741C22C22×#4111yescharacteristic
742C22#58511yescharacteristic
743C22#58511yescharacteristic
744C22#58511yescharacteristic
745C22#58511yescharacteristic
746C22#58511yescharacteristic
747C4—22no—
748C4—22no—
749C4—22no—
750C4—22no—
751C4—22no—
752C4—22no—
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—
771C4—41no—
772C4—41no—
773C2—42no—
774C2—42no—
775C2—42no—
776C2—42no—
777C2—81no—
778C2#345511yescharacteristic
779C2D4×#4111yescharacteristic
780C2#348511yescharacteristic
781C2#348511yescharacteristic
782C2#352111yescharacteristic
783C2#356611yescharacteristic
784C2#356811yescharacteristic
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
2. C2×#529C2semidirect
3. #2853C2semidirect
4. #2721C2semidirect
5. #2717C2semidirect
6. #2717C2semidirect
7. #2708C2semidirect
8. #2701C2semidirect
9. #2697C2semidirect
10. #2690C2semidirect
11. #2684C2semidirect
12. #2663C2semidirect
13. #2638C2semidirect
14. #2521C2semidirect
15. #2496C2semidirect
16. #2480C2semidirect
17. #2478C2semidirect
18. #2474C2semidirect
19. #2469C2semidirect
20. #2466C2semidirect
21. #2465C2semidirect
22. #2447C2semidirect
23. #2444C2semidirect
24. #2422C2semidirect
25. #2419C2semidirect
26. #2418C2semidirect
27. #2418C2semidirect
28. #2359C2semidirect
29. #2342C2semidirect
30. #2333C2semidirect
31. C4×#123C2semidirect
37. C2×#126C22semidirect
38. C2×#125C22semidirect
47. C2×#123C22semidirect
49. C2×C22⋊Q8C22semidirect
55. C2×C4×Q8C22semidirect
60. C2×C4×D4C22semidirect
62. C2×#117C22semidirect
65. C22×C42C22semidirect
66. #400C22semidirect
67. #400C22semidirect
68. #400C22semidirect
71. #398C22semidirect
72. #398C22semidirect
73. #398C22semidirect
83. #397C22semidirect
84. #397C22semidirect
85. #397C22semidirect
86. #397C22semidirect
87. #397C22semidirect
88. #397C22semidirect
92. #395C22semidirect
93. #395C22semidirect
94. #395C22semidirect
95. #395C22semidirect
106. #391C22semidirect
107. #391C22semidirect
109. #390C22semidirect
110. #389C22semidirect
111. #389C22semidirect
112. #389C22semidirect
113. #389C22semidirect
114. #389C22semidirect
130. #388C22semidirect
131. #387C22semidirect
132. #387C22semidirect
133. #387C22semidirect
134. #387C22semidirect
135. #387C22semidirect
136. #387C22semidirect
137. #387C22semidirect
138. #387C22semidirect
139. #387C22semidirect
140. #387C22semidirect
141. #387C22semidirect
142. #387C22semidirect
143. #387C22semidirect
153. #386C22semidirect
160. #385C22semidirect
161. #385C22semidirect
162. #385C22semidirect
163. #385C22semidirect
164. #385C22semidirect
165. #385C22semidirect
166. #384C22semidirect
168. #381C22semidirect
169. #381C22semidirect
170. #381C22semidirect
175. #380C22semidirect
179. C4×C4⋊C4C22semidirect
180. C4×C4⋊C4C22semidirect
181. C4×C4⋊C4C22semidirect
186. C4×C22⋊C4C22semidirect
187. C4×C22⋊C4C22semidirect
188. C2×#95C22semidirect

Maximal subgroups

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

subgroupindex
C2×#5382
C2×#5292
#28532
#27212
#27172
#27082
#27012
#26972
#26902
#26842
#26632
#26382
#25212
#24962
#24802
#24782
#24742
#24692
#24662
#24652
#24472
#24442
#24222
#24192
#24182
#23592
#23422
#23332
C4×#1232