Finite Group Databasebeta

← #38557

Subgroups — #38557

Order 256.

988 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2854C211yesmaximal, characteristic, complemented
2#2800C211yesmaximal, characteristic, complemented
3#2796C211yesmaximal, characteristic, complemented
4#2710C211yesmaximal, characteristic, complemented
5#2708C211yesmaximal, characteristic, complemented
6#2704C211yesmaximal, characteristic, complemented
7#2703C211yesmaximal, characteristic, complemented
8#2697C211yesmaximal, characteristic, complemented
9#2678C211yesmaximal, characteristic, complemented
10#2650C211yesmaximal, characteristic, complemented
11#2630C211yesmaximal, characteristic, complemented
12#2587C211yesmaximal, characteristic, complemented
13#2555C211yesmaximal, characteristic, complemented
14#2531C211yesmaximal, characteristic, complemented
15#2531C211yesmaximal, characteristic, complemented
16#2526C211yesmaximal, characteristic, complemented
17#2490C211yesmaximal, characteristic, complemented
18#2472C211yesmaximal, characteristic, complemented
19#2471C211yesmaximal, characteristic, complemented
20#2464C211yesmaximal, characteristic, complemented
21#2460C211yesmaximal, characteristic, complemented
22#2457C211yesmaximal, characteristic, complemented
23#2427C211yesmaximal, characteristic, complemented
24#2424C211yesmaximal, characteristic, complemented
25#2424C211yesmaximal, characteristic, complemented
26#2372C211yesmaximal, characteristic, complemented
27#2342C211yesmaximal, characteristic, complemented
28#2335C211yesmaximal, characteristic, complemented
29#2321C211yesmaximal, characteristic, complemented
30C4×#121C211yesmaximal, characteristic, complemented
31#2290C211yesmaximal, characteristic, complemented
32C2×#125C2211yescharacteristic, complemented
33C2×#124C2211yescharacteristic
34C2×#124C2211yescharacteristic, complemented
35C2×#123C2211yescharacteristic
36C2×#123C2211yescharacteristic
37C2×#123C2211yescharacteristic, complemented
38C2×#123C2211yescharacteristic, complemented
39C2×C22⋊Q8C2211yescharacteristic
40C2×#121C2211yescharacteristic
41C2×#121C2211yescharacteristic
42C2×#121C2211yescharacteristic
43C2×#121C2211yescharacteristic
44C2×#121C2211yescharacteristic
45C2×#120C2211yescharacteristic
46C2×#120C2211yescharacteristic
47C2×#120C2211yescharacteristic
48C2×C4×D4C2211yescharacteristic
49C2×C4×D4C2211yescharacteristic
50C2×C4×D4C2211yescharacteristic
51C2×C4×D4C2211yescharacteristic, complemented
52C2×#117C2211yescharacteristic
53C22×C22⋊C4C2211yescharacteristic
54C22×C22⋊C4C2211yescharacteristic
55C22×C42C2211yescharacteristic, complemented
56#400C2211yescharacteristic, complemented
57#400C2211yescharacteristic, complemented
58#400C2211yescharacteristic, complemented
59#399C2211yescharacteristic, complemented
60#398C2211yescharacteristic, complemented
61#398C2211yescharacteristic, complemented
62#398C2211yescharacteristic, complemented
63#397C2211yescharacteristic
64#397C2211yescharacteristic
65#397C2211yescharacteristic
66#397C2211yescharacteristic
67#397C2211yescharacteristic, complemented
68#397C2211yescharacteristic, complemented
69#397C2211yescharacteristic, complemented
70#397C2211yescharacteristic, complemented
71#397C2211yescharacteristic, complemented
72#396C2211yescharacteristic
73#396C2211yescharacteristic
74#396C2211yescharacteristic
75#396C2211yescharacteristic
76#396C2211yescharacteristic
77#396C2211yescharacteristic, complemented
78#395C2211yescharacteristic, complemented
79#394C2211yescharacteristic
80#394C2211yescharacteristic
81#394C2211yescharacteristic
82#394C2211yescharacteristic
83#394C2211yescharacteristic
84#394C2211yescharacteristic
85#394C2211yescharacteristic
86#394C2211yescharacteristic
87#394C2211yescharacteristic
88#394C2211yescharacteristic
89#394C2211yescharacteristic, complemented
90#393C2211yescharacteristic
91#392C2211yescharacteristic
92#392C2211yescharacteristic
93#392C2211yescharacteristic
94#392C2211yescharacteristic
95#392C2211yescharacteristic, complemented
96#391C2211yescharacteristic, complemented
97#391C2211yescharacteristic, complemented
98#390C2211yescharacteristic
99#390C2211yescharacteristic
100#390C2211yescharacteristic
101#390C2211yescharacteristic
102#390C2211yescharacteristic
103#390C2211yescharacteristic
104#390C2211yescharacteristic
105#390C2211yescharacteristic
106#390C2211yescharacteristic, complemented
107#389C2211yescharacteristic, complemented
108#389C2211yescharacteristic, complemented
109#389C2211yescharacteristic, complemented
110#389C2211yescharacteristic, complemented
111#389C2211yescharacteristic, complemented
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
125#388C2211yescharacteristic
126#388C2211yescharacteristic
127#388C2211yescharacteristic, complemented
128#388C2211yescharacteristic, complemented
129#388C2211yescharacteristic, complemented
130#388C2211yescharacteristic, complemented
131#388C2211yescharacteristic, complemented
132#388C2211yescharacteristic, complemented
133#388C2211yescharacteristic, complemented
134#388C2211yescharacteristic, complemented
135#388C2211yescharacteristic, 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
154#386C2211yescharacteristic
155#386C2211yescharacteristic
156#386C2211yescharacteristic, complemented
157#386C2211yescharacteristic, complemented
158#386C2211yescharacteristic, complemented
159#385C2211yescharacteristic
160#385C2211yescharacteristic
161#385C2211yescharacteristic
162#385C2211yescharacteristic
163#385C2211yescharacteristic
164#385C2211yescharacteristic, complemented
165#385C2211yescharacteristic, complemented
166#381C2211yescharacteristic
167#380C2211yescharacteristic
168#380C2211yescharacteristic, complemented
169#380C2211yescharacteristic, complemented
170#380C2211yescharacteristic, complemented
171#380C2211yescharacteristic, complemented
172#379C2211yescharacteristic
173#379C2211yescharacteristic
174C4×C4⋊C4C2211yescharacteristic, complemented
175C4×C4⋊C4C2211yescharacteristic, complemented
176C4×C22⋊C4C2211yescharacteristic
177C4×C22⋊C4C2211yescharacteristic
178C4×C22⋊C4C2211yescharacteristic
179C4×C22⋊C4C2211yescharacteristic
180C4×C22⋊C4C2211yescharacteristic
181C4×C22⋊C4C2211yescharacteristic, complemented
182C4×C22⋊C4C2211yescharacteristic, complemented
183C4×C22⋊C4C2211yescharacteristic, complemented
184C4×C22⋊C4C2211yescharacteristic, complemented
185#376C2211yescharacteristic, complemented
186#376C2211yescharacteristic, complemented
187C25C2311yescharacteristic
188C22×Q8C2311yescharacteristic
189C22×D4C2311yescharacteristic
190C22×D4C2311yescharacteristic
191C22×D4C2311yescharacteristic
192C22×D4C2311yescharacteristic
193C22×D4C2311yescharacteristic
194C22×D4C2311yescharacteristic
195C22×D4C2311yescharacteristic
196C22×D4C2311yescharacteristic
197C22×D4C2311yescharacteristic
198C22×D4C2311yescharacteristic
199C22×D4C2311yescharacteristic
200C22×D4C2311yescharacteristic
201C23×C4C2311yescharacteristic
202C23×C4C2311yescharacteristic
203C23×C4C2311yescharacteristic
204C23×C4C2311yescharacteristic
205C23×C4C2311yescharacteristic
206C23×C4C2311yescharacteristic
207C23×C4C2311yescharacteristic
208C23×C4C2311yescharacteristic
209C23×C4C2311yescharacteristic
210#125—42no—
211#124—24no—
212#124—42no—
213#123—24no—
214#123—42no—
215#123—42no—
216#123—42no—
217C22⋊Q8—42no—
218#121—24no—
219#121—42no—
220#121—42no—
221#121—42no—
222#121—42no—
223#120—24no—
224#120—42no—
225#120—42no—
226C4×D4—24no—
227C4×D4—42no—
228C4×D4—42no—
229C4×D4—42no—
230#117—42no—
231C2×C4⋊C4C2311yescharacteristic
232C2×C4⋊C4C2311yescharacteristic
233C2×C4⋊C4C2311yescharacteristic
234C2×C4⋊C4C2311yescharacteristic
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×C22⋊C4—24no—
259C2×C22⋊C4—42no—
260C2×C22⋊C4C2311yescharacteristic
261C2×C22⋊C4C2311yescharacteristic
262C2×C22⋊C4C2311yescharacteristic
263C2×C22⋊C4C2311yescharacteristic
264C2×C22⋊C4C2311yescharacteristic
265C2×C22⋊C4C2311yescharacteristic
266C2×C22⋊C4C2311yescharacteristic
267C2×C22⋊C4C2311yescharacteristic
268C2×C22⋊C4C2311yescharacteristic
269C2×C22⋊C4C2311yescharacteristic
270C2×C22⋊C4C2311yescharacteristic
271C2×C22⋊C4C2311yescharacteristic
272C2×C22⋊C4C2311yescharacteristic
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×C42—42no—
315C2×C42C2311yescharacteristic
316C2×C42C2311yescharacteristic
317C2×C42C2311yescharacteristic
318C2×C42C2311yescharacteristic
319C2×C42C2311yescharacteristic
320C2×C42C2311yescharacteristic
321C2×C42C2311yescharacteristic
322C2×C42C2311yescharacteristic
323C2×C42C2311yescharacteristic
324C2×C42C2311yescharacteristic
325C2×C42C2311yescharacteristic
326C2×C42C2311yescharacteristic
327C2×C42C2311yescharacteristic
328#95C2311yescharacteristic
329#95C2311yescharacteristic
330#95C2311yescharacteristic
331#95C2311yescharacteristic
332#95C2311yescharacteristic
333#95C2311yescharacteristic
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
366C24—22no—
367C24—22no—
368C24—41no—
369C24—41no—
370C24—41no—
371C24—41no—
372C24—41no—
373C24C2411yescharacteristic
374C24C2411yescharacteristic
375C24C2411yescharacteristic
376C24C2411yescharacteristic
377C24C2411yescharacteristic
378C24C2411yescharacteristic
379C2×Q8—22no—
380C2×Q8—41no—
381C2×Q8—41no—
382C2×D4—22no—
383C2×D4—22no—
384C2×D4—22no—
385C2×D4—22no—
386C2×D4—22no—
387C2×D4—22no—
388C2×D4—22no—
389C2×D4—22no—
390C2×D4—22no—
391C2×D4—22no—
392C2×D4—22no—
393C2×D4—22no—
394C2×D4—22no—
395C2×D4—22no—
396C2×D4—22no—
397C2×D4—41no—
398C2×D4—41no—
399C2×D4—41no—
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×D4—41no—
413C2×D4—41no—
414C2×D4—41no—
415C2×D4—41no—
416C2×D4—41no—
417C2×D4—41no—
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—22no—
427C22×C4—22no—
428C22×C4—22no—
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×C4—41no—
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
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—41no—
480C4⋊C4—41no—
481C4⋊C4—41no—
482C4⋊C4—41no—
483C4⋊C4—41no—
484C4⋊C4—41no—
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—
497C22⋊C4—22no—
498C22⋊C4—22no—
499C22⋊C4—22no—
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—41no—
519C22⋊C4—41no—
520C22⋊C4—41no—
521C22⋊C4—41no—
522C22⋊C4—41no—
523C22⋊C4—41no—
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⋊C4—41no—
547C22⋊C4—41no—
548C22⋊C4—41no—
549C22⋊C4#4114yes—
550C22⋊C4#4114yes—
551C42—22no—
552C42—22no—
553C42—22no—
554C42—22no—
555C42—41no—
556C42—41no—
557C42—41no—
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—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—44no—
604C23—44no—
605C23—82no—
606C23—82no—
607C23—82no—
608C23—82no—
609C23—82no—
610C23C2×#4112yes—
611C23C2×#4112yes—
612C23H(5,𝔽2)12yes—
613C23C2511yescharacteristic
614Q8—82no—
615D4—44no—
616D4—44no—
617D4—44no—
618D4—44no—
619D4—82no—
620D4—82no—
621D4—82no—
622D4—82no—
623D4—82no—
624D4—82no—
625D4—82no—
626D4—82no—
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—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—44no—
697C2×C4—44no—
698C2×C4—44no—
699C2×C4—44no—
700C2×C4—82no—
701C2×C4—82no—
702C2×C4—82no—
703C2×C4—82no—
704C2×C4—82no—
705C2×C4C2×#4112yes—
706C2×C4C2×#4112yes—
707C2×C4C2×#4112yes—
708C2×C4C2×#4112yes—
709C2×C4H(5,𝔽2)12yes—
710C2×C4H(5,𝔽2)12yes—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—22no—
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—41no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—88no—
754C22C22×#4111yescharacteristic
755C22C22×#4111yescharacteristic
756C22C2×H(5,𝔽2)11yescharacteristic
757C22C2×H(5,𝔽2)11yescharacteristic
758C22C2×H(5,𝔽2)11yescharacteristic
759C22#58511yescharacteristic
760C22#58511yescharacteristic
761C4—22no—
762C4—22no—
763C4—22no—
764C4—22no—
765C4—22no—
766C4—22no—
767C4—41no—
768C4—41no—
769C4—41no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—41no—
774C4—41no—
775C4—41no—
776C4—41no—
777C4—41no—
778C4—41no—
779C4—41no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—41no—
784C4—41no—
785C4—41no—
786C2—42no—
787C2—42no—
788C2—42no—
789C2—81no—
790C2—81no—
791C2—81no—
792C2#345511yescharacteristic
793C2#348111yescharacteristic
794C2#349411yescharacteristic
795C2#351411yescharacteristic
796C2#351911yescharacteristic
797C2#353411yescharacteristic
798C2#354211yescharacteristic
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. #2854C2semidirect
2. #2800C2semidirect
3. #2796C2semidirect
4. #2710C2semidirect
5. #2708C2semidirect
6. #2704C2semidirect
7. #2703C2semidirect
8. #2697C2semidirect
9. #2678C2semidirect
10. #2650C2semidirect
11. #2630C2semidirect
12. #2587C2semidirect
13. #2555C2semidirect
14. #2531C2semidirect
15. #2531C2semidirect
16. #2526C2semidirect
17. #2490C2semidirect
18. #2472C2semidirect
19. #2471C2semidirect
20. #2464C2semidirect
21. #2460C2semidirect
22. #2457C2semidirect
23. #2427C2semidirect
24. #2424C2semidirect
25. #2424C2semidirect
26. #2372C2semidirect
27. #2342C2semidirect
28. #2335C2semidirect
29. #2321C2semidirect
30. C4×#121C2semidirect
31. #2290C2semidirect
32. C2×#125C22semidirect
34. C2×#124C22semidirect
37. C2×#123C22semidirect
38. C2×#123C22semidirect
51. C2×C4×D4C22semidirect
55. C22×C42C22semidirect
56. #400C22semidirect
57. #400C22semidirect
58. #400C22semidirect
59. #399C22semidirect
60. #398C22semidirect
61. #398C22semidirect
62. #398C22semidirect
67. #397C22semidirect
68. #397C22semidirect
69. #397C22semidirect
70. #397C22semidirect
71. #397C22semidirect
77. #396C22semidirect
78. #395C22semidirect
89. #394C22semidirect
95. #392C22semidirect
96. #391C22semidirect
97. #391C22semidirect
106. #390C22semidirect
107. #389C22semidirect
108. #389C22semidirect
109. #389C22semidirect
110. #389C22semidirect
111. #389C22semidirect
127. #388C22semidirect
128. #388C22semidirect
129. #388C22semidirect
130. #388C22semidirect
131. #388C22semidirect
132. #388C22semidirect
133. #388C22semidirect
134. #388C22semidirect
135. #388C22semidirect
136. #387C22semidirect
137. #387C22semidirect
138. #387C22semidirect
139. #387C22semidirect
140. #387C22semidirect
141. #387C22semidirect
142. #387C22semidirect
143. #387C22semidirect
156. #386C22semidirect
157. #386C22semidirect
158. #386C22semidirect
164. #385C22semidirect
165. #385C22semidirect
168. #380C22semidirect
169. #380C22semidirect
170. #380C22semidirect
171. #380C22semidirect
174. C4×C4⋊C4C22semidirect
175. C4×C4⋊C4C22semidirect
181. C4×C22⋊C4C22semidirect
182. C4×C22⋊C4C22semidirect
183. C4×C22⋊C4C22semidirect
184. C4×C22⋊C4C22semidirect
185. #376C22semidirect
186. #376C22semidirect

Maximal subgroups

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

subgroupindex
#28542
#28002
#27962
#27102
#27082
#27042
#27032
#26972
#26782
#26502
#26302
#25872
#25552
#25312
#25262
#24902
#24722
#24712
#24642
#24602
#24572
#24272
#24242
#23722
#23422
#23352
#23212
C4×#1212
#22902