Finite Group Databasebeta

← #59169

Subgroups — #59169

Order 256.

1125 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#552C211yesmaximal, characteristic, complemented
2C22×#126C211yesmaximal, characteristic, complemented
3#2721C211yesmaximal, characteristic, complemented
4#2702C211yesmaximal, characteristic, complemented
5#2698C211yesmaximal, characteristic, complemented
6#2695C211yesmaximal, characteristic, complemented
7#2604C211yesmaximal, characteristic, complemented
8#2601C211yesmaximal, characteristic, complemented
9#2553C211yesmaximal, characteristic, complemented
10#2519C211yesmaximal, characteristic, complemented
11#2519C211yesmaximal, characteristic, complemented
12#2496C211yesmaximal, characteristic, complemented
13#2481C211yesmaximal, characteristic, complemented
14#2480C211yesmaximal, characteristic, complemented
15#2479C211yesmaximal, characteristic, complemented
16#2478C211yesmaximal, characteristic, complemented
17#2473C211yesmaximal, characteristic, complemented
18#2473C211yesmaximal, characteristic, complemented
19#2468C211yesmaximal, characteristic, complemented
20#2449C211yesmaximal, characteristic, complemented
21#2442C211yesmaximal, characteristic, complemented
22#2437C211yesmaximal, characteristic, complemented
23#2418C211yesmaximal, characteristic
24#2418C211yesmaximal, characteristic
25#2373C211yesmaximal, characteristic, complemented
26#2358C211yesmaximal, characteristic
27#2352C211yesmaximal, characteristic, complemented
28D4×C4⋊C4C211yesmaximal, characteristic, complemented
29#2342C211yesmaximal, characteristic, complemented
30C4×C22⋊Q8C211yesmaximal, characteristic, complemented
31#2290C211yesmaximal, characteristic, complemented
32#552—28no—
33C2×#126—28no—
34C2×#126C2211yescharacteristic
35C2×#126C2211yescharacteristic
36C2×#126C2211yescharacteristic
37C2×#126C2211yescharacteristic
38C2×#126C2211yescharacteristic
39C2×#126C2211yescharacteristic
40C2×#126C2211yescharacteristic
41C2×#126C2211yescharacteristic
42C2×#126C2211yescharacteristic
43C2×#125C2211yescharacteristic, complemented
44C2×#125C2211yescharacteristic, complemented
45C2×#125C2211yescharacteristic, complemented
46C2×#123C2211yescharacteristic
47C2×#123C2211yescharacteristic
48C2×C22⋊Q8C2211yescharacteristic
49C2×C22⋊Q8C2211yescharacteristic
50C2×C22⋊Q8C2211yescharacteristic, complemented
51C2×#120C2211yescharacteristic
52C2×C4×Q8C2211yescharacteristic, complemented
53C2×C4×D4C2211yescharacteristic
54C2×C4×D4C2211yescharacteristic
55C2×C4×D4C2211yescharacteristic
56C2×C4×D4C2211yescharacteristic
57C2×#117C2211yescharacteristic
58C2×#117C2211yescharacteristic, complemented
59C2×#117C2211yescharacteristic, complemented
60C22×C4⋊C4C2211yescharacteristic
61C22×C4⋊C4C2211yescharacteristic
62C22×C4⋊C4C2211yescharacteristic
63C22×C4⋊C4C2211yescharacteristic, complemented
64C22×C22⋊C4C2211yescharacteristic
65C22×C22⋊C4C2211yescharacteristic
66C22×C22⋊C4C2211yescharacteristic
67C22×C22⋊C4C2211yescharacteristic
68C22×C42C2211yescharacteristic
69#400C2211yescharacteristic, complemented
70#400C2211yescharacteristic, complemented
71#400C2211yescharacteristic, complemented
72#400C2211yescharacteristic, complemented
73#399C2211yescharacteristic
74#399C2211yescharacteristic
75#399C2211yescharacteristic
76#399C2211yescharacteristic, complemented
77#398C2211yescharacteristic, complemented
78#398C2211yescharacteristic, complemented
79#398C2211yescharacteristic, complemented
80#398C2211yescharacteristic, complemented
81#398C2211yescharacteristic, complemented
82#398C2211yescharacteristic, complemented
83#398C2211yescharacteristic, complemented
84#398C2211yescharacteristic, complemented
85#398C2211yescharacteristic, complemented
86#397C2211yescharacteristic
87#397C2211yescharacteristic
88#397C2211yescharacteristic
89#397C2211yescharacteristic
90#397C2211yescharacteristic
91#396C2211yescharacteristic
92#396C2211yescharacteristic
93#396C2211yescharacteristic
94#396C2211yescharacteristic, complemented
95#395C2211yescharacteristic, complemented
96#394C2211yescharacteristic
97#394C2211yescharacteristic
98#394C2211yescharacteristic
99#394C2211yescharacteristic
100#393C2211yescharacteristic
101#391C2211yescharacteristic, complemented
102#390C2211yescharacteristic
103#389C2211yescharacteristic, complemented
104#389C2211yescharacteristic, complemented
105#389C2211yescharacteristic, complemented
106#389C2211yescharacteristic, complemented
107#389C2211yescharacteristic, complemented
108#389C2211yescharacteristic, complemented
109#389C2211yescharacteristic, complemented
110#389C2211yescharacteristic, complemented
111#388C2211yescharacteristic
112#388C2211yescharacteristic
113#388C2211yescharacteristic
114#388C2211yescharacteristic
115#388C2211yescharacteristic
116#388C2211yescharacteristic
117#388C2211yescharacteristic
118#388C2211yescharacteristic
119#388C2211yescharacteristic
120#388C2211yescharacteristic
121#388C2211yescharacteristic
122#388C2211yescharacteristic
123#388C2211yescharacteristic
124#388C2211yescharacteristic, complemented
125#388C2211yescharacteristic, complemented
126#388C2211yescharacteristic, complemented
127#388C2211yescharacteristic, complemented
128#387C2211yescharacteristic, complemented
129#387C2211yescharacteristic, complemented
130#387C2211yescharacteristic, 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#386C2211yescharacteristic
140#386C2211yescharacteristic
141#386C2211yescharacteristic
142#386C2211yescharacteristic
143#386C2211yescharacteristic
144#386C2211yescharacteristic
145#386C2211yescharacteristic
146#385C2211yescharacteristic
147#385C2211yescharacteristic
148#385C2211yescharacteristic
149#385C2211yescharacteristic
150#385C2211yescharacteristic
151#385C2211yescharacteristic
152#385C2211yescharacteristic
153#385C2211yescharacteristic
154#385C2211yescharacteristic
155#385C2211yescharacteristic
156#385C2211yescharacteristic
157#385C2211yescharacteristic
158#385C2211yescharacteristic, complemented
159#385C2211yescharacteristic, complemented
160#385C2211yescharacteristic, complemented
161#384C2211yescharacteristic, complemented
162#382C2211yescharacteristic, complemented
163#382C2211yescharacteristic, complemented
164#381C2211yescharacteristic
165#380C2211yescharacteristic
166#380C2211yescharacteristic
167#380C2211yescharacteristic
168#380C2211yescharacteristic
169#380C2211yescharacteristic
170#380C2211yescharacteristic
171#380C2211yescharacteristic, complemented
172#380C2211yescharacteristic, complemented
173#379C2211yescharacteristic
174#379C2211yescharacteristic
175C4×C4⋊C4C2211yescharacteristic, complemented
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
187C4×C22⋊C4C2211yescharacteristic, complemented
188#376C2211yescharacteristic, complemented
189C25C2311yescharacteristic
190C22×Q8C2311yescharacteristic
191C22×D4C2311yescharacteristic
192C22×D4C2311yescharacteristic
193C22×D4C2311yescharacteristic
194C23×C4C2311yescharacteristic
195C23×C4C2311yescharacteristic
196C23×C4C2311yescharacteristic
197C23×C4C2311yescharacteristic
198C23×C4C2311yescharacteristic
199C23×C4C2311yescharacteristic
200C23×C4C2311yescharacteristic
201C23×C4C2311yescharacteristic
202C23×C4C2311yescharacteristic
203C23×C4C2311yescharacteristic
204C23×C4C2311yescharacteristic
205#126—24no—
206#126—24no—
207#126—24no—
208#126—24no—
209#126—24no—
210#126—24no—
211#126—24no—
212#126—24no—
213#126D418yescomplemented
214#125—24no—
215#125—24no—
216#125—24no—
217#123—24no—
218#123—24no—
219C22⋊Q8—24no—
220C22⋊Q8—24no—
221C22⋊Q8—24no—
222#120—24no—
223C4×Q8—24no—
224C4×D4—24no—
225C4×D4—24no—
226C4×D4—24no—
227C4×D4—24no—
228#117—24no—
229#117—24no—
230#117—24no—
231C2×C4⋊C4—24no—
232C2×C4⋊C4—24no—
233C2×C4⋊C4—24no—
234C2×C4⋊C4—24no—
235C2×C4⋊C4C2311yescharacteristic
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×C4⋊C4C2311yescharacteristic
272C2×C4⋊C4C2311yescharacteristic
273C2×C4⋊C4C2311yescharacteristic
274C2×C4⋊C4C2311yescharacteristic
275C2×C4⋊C4C2311yescharacteristic
276C2×C4⋊C4C2311yescharacteristic
277C2×C4⋊C4C2311yescharacteristic
278C2×C4⋊C4C2311yescharacteristic
279C2×C22⋊C4—24no—
280C2×C22⋊C4—24no—
281C2×C22⋊C4—24no—
282C2×C22⋊C4—24no—
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
338C2×C42C2311yescharacteristic
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
376#95C2311yescharacteristic
377#95C2311yescharacteristic
378#95C2311yescharacteristic
379C24—22no—
380C24—22no—
381C24—22no—
382C24—22no—
383C24—41no—
384C24—41no—
385C24—41no—
386C24C2411yescharacteristic
387C24C2411yescharacteristic
388C24C2411yescharacteristic
389C24C2411yescharacteristic
390C2×Q8—22no—
391C2×Q8—22no—
392C2×Q8—41no—
393C2×D4—22no—
394C2×D4—22no—
395C2×D4—22no—
396C2×D4—22no—
397C2×D4—22no—
398C2×D4—41no—
399C2×D4—41no—
400C2×D4—41no—
401C2×D4#4114yes—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
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—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×C4C2411yescharacteristic
436C22×C4C2411yescharacteristic
437C22×C4C2411yescharacteristic
438C22×C4C2411yescharacteristic
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
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4—22no—
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—22no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—22no—
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—
504C4⋊C4C2×D414yes—
505C4⋊C4C2×D414yes—
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—22no—
532C22⋊C4—22no—
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⋊C4C2×D414yes—
543C22⋊C4C2×D414yes—
544C22⋊C4C2×D414yes—
545C22⋊C4#4114yes—
546C42—22no—
547C42—22no—
548C42—22no—
549C42—22no—
550C42—22no—
551C42—22no—
552C42—22no—
553C42—22no—
554C42—22no—
555C42—22no—
556C42—41no—
557C42—41no—
558C42—41no—
559C42—41no—
560C42C2×D414yes—
561C23—21no—
562C23—21no—
563C23—21no—
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—44no—
585C23—44no—
586C23—44no—
587C23—44no—
588C23—82no—
589C23—82no—
590C23—82no—
591C23C22×D412yes—
592C23C2×#4112yes—
593C23C2×#4112yes—
594C23C2×#4112yes—
595C232−1+412yes—
596C23C2511yescharacteristic
597Q8—44no—
598D4—28no—
599D4—44no—
600D4—82no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
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—44no—
674C2×C4—44no—
675C2×C4—44no—
676C2×C4—44no—
677C2×C4—44no—
678C2×C4—44no—
679C2×C4—44no—
680C2×C4—44no—
681C2×C4—44no—
682C2×C4—44no—
683C2×C4—82no—
684C2×C4C22×D412yes—
685C2×C4C22×D412yes—
686C2×C4C22×D412yes—
687C2×C4C22×D412yes—
688C2×C4C22×D412yes—
689C2×C4C22×D412yes—
690C2×C4C2×#4112yes—
691C2×C4C2×#4112yes—
692C2×C4C2×#4112yes—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—22no—
697C22—22no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—88no—
721C22#55214yescomplemented
722C22C23×D411yescharacteristic
723C22C22×#4111yescharacteristic
724C22C22×#4111yescharacteristic
725C22C2×2−1+411yescharacteristic
726C22#58511yescharacteristic
727C22#58511yescharacteristic
728C22#58511yescharacteristic
729C4—22no—
730C4—22no—
731C4—22no—
732C4—22no—
733C4—22no—
734C4—22no—
735C4—22no—
736C4—22no—
737C4—22no—
738C4—41no—
739C4—41no—
740C4—41no—
741C4—41no—
742C4—41no—
743C4—41no—
744C4—41no—
745C4—41no—
746C4—41no—
747C4—41no—
748C4—41no—
749C4—41no—
750C4—41no—
751C4—41no—
752C4—41no—
753C4—41no—
754C4—41no—
755C4—41no—
756C2—24no—
757C2—42no—
758C2—42no—
759C2—81no—
760C2D4×#4111yescharacteristic
761C2D4×#4111yescharacteristic
762C2C2×#55211yescharacteristic
763C2#348911yescharacteristic
764C2#352111yescharacteristic
765C2#352111yescharacteristic
766C2#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×#552C2semidirect
2. C22×#126C2semidirect
3. #2721C2semidirect
4. #2702C2semidirect
5. #2698C2semidirect
6. #2695C2semidirect
7. #2604C2semidirect
8. #2601C2semidirect
9. #2553C2semidirect
10. #2519C2semidirect
11. #2519C2semidirect
12. #2496C2semidirect
13. #2481C2semidirect
14. #2480C2semidirect
15. #2479C2semidirect
16. #2478C2semidirect
17. #2473C2semidirect
18. #2473C2semidirect
19. #2468C2semidirect
20. #2449C2semidirect
21. #2442C2semidirect
22. #2437C2semidirect
25. #2373C2semidirect
27. #2352C2semidirect
28. D4×C4⋊C4C2semidirect
29. #2342C2semidirect
30. C4×C22⋊Q8C2semidirect
31. #2290C2semidirect
43. C2×#125C22semidirect
44. C2×#125C22semidirect
45. C2×#125C22semidirect
50. C2×C22⋊Q8C22semidirect
52. C2×C4×Q8C22semidirect
58. C2×#117C22semidirect
59. C2×#117C22semidirect
63. C22×C4⋊C4C22semidirect
69. #400C22semidirect
70. #400C22semidirect
71. #400C22semidirect
72. #400C22semidirect
76. #399C22semidirect
77. #398C22semidirect
78. #398C22semidirect
79. #398C22semidirect
80. #398C22semidirect
81. #398C22semidirect
82. #398C22semidirect
83. #398C22semidirect
84. #398C22semidirect
85. #398C22semidirect
94. #396C22semidirect
95. #395C22semidirect
101. #391C22semidirect
103. #389C22semidirect
104. #389C22semidirect
105. #389C22semidirect
106. #389C22semidirect
107. #389C22semidirect
108. #389C22semidirect
109. #389C22semidirect
110. #389C22semidirect
124. #388C22semidirect
125. #388C22semidirect
126. #388C22semidirect
127. #388C22semidirect
128. #387C22semidirect
129. #387C22semidirect
130. #387C22semidirect
131. #387C22semidirect
132. #387C22semidirect
133. #387C22semidirect
134. #387C22semidirect
135. #387C22semidirect
136. #387C22semidirect
137. #387C22semidirect
138. #387C22semidirect
158. #385C22semidirect
159. #385C22semidirect
160. #385C22semidirect
161. #384C22semidirect
162. #382C22semidirect
163. #382C22semidirect
171. #380C22semidirect
172. #380C22semidirect
175. C4×C4⋊C4C22semidirect
176. C4×C4⋊C4C22semidirect
177. C4×C4⋊C4C22semidirect
178. C4×C4⋊C4C22semidirect
179. C4×C4⋊C4C22semidirect
180. C4×C4⋊C4C22semidirect
187. C4×C22⋊C4C22semidirect
188. #376C22semidirect
213. #126D4semidirect
721. C22#552semidirect

Maximal subgroups

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

subgroupindex
C2×#5522
C22×#1262
#27212
#27022
#26982
#26952
#26042
#26012
#25532
#25192
#24962
#24812
#24802
#24792
#24782
#24732
#24682
#24492
#24422
#24372
#24182
#23732
#23582
#23522
D4×C4⋊C42
#23422
C4×C22⋊Q82
#22902