Finite Group Databasebeta

← #59195

Subgroups — #59195

Order 256.

1094 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2746C211yesmaximal, characteristic, complemented
2#2743C211yesmaximal, characteristic, complemented
3#2740C211yesmaximal, characteristic, complemented
4#2737C211yesmaximal, characteristic, complemented
5#2576C211yesmaximal, characteristic, complemented
6#2572C211yesmaximal, characteristic, complemented
7#2564C211yesmaximal, characteristic, complemented
8#2561C211yesmaximal, characteristic, complemented
9#2526C211yesmaximal, characteristic, complemented
10#2516C211yesmaximal, characteristic, complemented
11#2510C211yesmaximal, characteristic, complemented
12#2510C211yesmaximal, characteristic, complemented
13#2498C211yesmaximal, characteristic, complemented
14#2493C211yesmaximal, characteristic, complemented
15#2493C211yesmaximal, characteristic, complemented
16#2488C211yesmaximal, characteristic, complemented
17#2483C211yesmaximal, characteristic, complemented
18#2482C211yesmaximal, characteristic, complemented
19#2438C211yesmaximal, characteristic, complemented
20#2437C211yesmaximal, characteristic, complemented
21#2419C211yesmaximal, characteristic, complemented
22#2405C211yesmaximal, characteristic
23#2359C211yesmaximal, characteristic, complemented
24#2353C211yesmaximal, characteristic, complemented
25#2343C211yesmaximal, characteristic, complemented
26#2342C211yesmaximal, characteristic, complemented
27#2342C211yesmaximal, characteristic, complemented
28D4×C22⋊C4C211yesmaximal, characteristic
29C2×#386C211yesmaximal, characteristic
30#2280C211yesmaximal, characteristic, complemented
31C2×#381C211yesmaximal, characteristic, complemented
32C23×D4C2211yescharacteristic
33C24×C4C2211yescharacteristic
34C2×#123C2211yescharacteristic
35C2×#123C2211yescharacteristic
36C2×C22⋊Q8C2211yescharacteristic
37C2×C22⋊Q8C2211yescharacteristic, complemented
38C2×C4×D4C2211yescharacteristic
39C2×C4×D4C2211yescharacteristic
40C2×#117C2211yescharacteristic
41C2×#117C2211yescharacteristic
42C2×#117C2211yescharacteristic, complemented
43C22×C22⋊C4C2211yescharacteristic
44C22×C22⋊C4C2211yescharacteristic
45C22×C22⋊C4C2211yescharacteristic
46C22×C22⋊C4C2211yescharacteristic
47C22×C22⋊C4C2211yescharacteristic
48C22×C22⋊C4C2211yescharacteristic
49#401C2211yescharacteristic, complemented
50#401C2211yescharacteristic, complemented
51#400C2211yescharacteristic, complemented
52#400C2211yescharacteristic, complemented
53#400C2211yescharacteristic, complemented
54#400C2211yescharacteristic, complemented
55#400C2211yescharacteristic, complemented
56#400C2211yescharacteristic, complemented
57#400C2211yescharacteristic, complemented
58#399C2211yescharacteristic, complemented
59#399C2211yescharacteristic, complemented
60#399C2211yescharacteristic, complemented
61#398C2211yescharacteristic, complemented
62#398C2211yescharacteristic, complemented
63#397C2211yescharacteristic, complemented
64#397C2211yescharacteristic, complemented
65#397C2211yescharacteristic, complemented
66#397C2211yescharacteristic, complemented
67#397C2211yescharacteristic, complemented
68#397C2211yescharacteristic, complemented
69#397C2211yescharacteristic, complemented
70#397C2211yescharacteristic, complemented
71#396C2211yescharacteristic, complemented
72#396C2211yescharacteristic, complemented
73#395C2211yescharacteristic, complemented
74#394C2211yescharacteristic
75#394C2211yescharacteristic
76#394C2211yescharacteristic
77#394C2211yescharacteristic
78#393C2211yescharacteristic, complemented
79#393C2211yescharacteristic, complemented
80#393C2211yescharacteristic, complemented
81#391C2211yescharacteristic, complemented
82#390C2211yescharacteristic
83#390C2211yescharacteristic
84#389C2211yescharacteristic, complemented
85#388C2211yescharacteristic, complemented
86#388C2211yescharacteristic, complemented
87#388C2211yescharacteristic, complemented
88#388C2211yescharacteristic, complemented
89#388C2211yescharacteristic, complemented
90#388C2211yescharacteristic, complemented
91#388C2211yescharacteristic, complemented
92#388C2211yescharacteristic, complemented
93#388C2211yescharacteristic, complemented
94#388C2211yescharacteristic, complemented
95#388C2211yescharacteristic, complemented
96#388C2211yescharacteristic, complemented
97#388C2211yescharacteristic, complemented
98#388C2211yescharacteristic, complemented
99#388C2211yescharacteristic, complemented
100#388C2211yescharacteristic, complemented
101#387C2211yescharacteristic, complemented
102#387C2211yescharacteristic, complemented
103#387C2211yescharacteristic, complemented
104#387C2211yescharacteristic, complemented
105#387C2211yescharacteristic, complemented
106#387C2211yescharacteristic, complemented
107#387C2211yescharacteristic, complemented
108#387C2211yescharacteristic, complemented
109#387C2211yescharacteristic, complemented
110#387C2211yescharacteristic, complemented
111#387C2211yescharacteristic, complemented
112#387C2211yescharacteristic, complemented
113#386C2211yescharacteristic
114#386C2211yescharacteristic
115#386C2211yescharacteristic
116#386C2211yescharacteristic
117#386C2211yescharacteristic
118#386C2211yescharacteristic
119#386C2211yescharacteristic
120#386C2211yescharacteristic
121#386C2211yescharacteristic
122#386C2211yescharacteristic
123#386C2211yescharacteristic
124#386C2211yescharacteristic
125#386C2211yescharacteristic
126#386C2211yescharacteristic
127#385C2211yescharacteristic
128#385C2211yescharacteristic
129#385C2211yescharacteristic
130#385C2211yescharacteristic
131#385C2211yescharacteristic
132#385C2211yescharacteristic
133#385C2211yescharacteristic, complemented
134#385C2211yescharacteristic, complemented
135#385C2211yescharacteristic, complemented
136#385C2211yescharacteristic, complemented
137#385C2211yescharacteristic, complemented
138#385C2211yescharacteristic, complemented
139#383C2211yescharacteristic, complemented
140#383C2211yescharacteristic, complemented
141#383C2211yescharacteristic, complemented
142#382C2211yescharacteristic, complemented
143#381C2211yescharacteristic
144#381C2211yescharacteristic
145#381C2211yescharacteristic
146#381C2211yescharacteristic
147#381C2211yescharacteristic
148#381C2211yescharacteristic
149#381C2211yescharacteristic, complemented
150#381C2211yescharacteristic, complemented
151#381C2211yescharacteristic, complemented
152#381C2211yescharacteristic, complemented
153#381C2211yescharacteristic, complemented
154#381C2211yescharacteristic, complemented
155#381C2211yescharacteristic, complemented
156#380C2211yescharacteristic
157#380C2211yescharacteristic
158#380C2211yescharacteristic, complemented
159#380C2211yescharacteristic, complemented
160#380C2211yescharacteristic, complemented
161#380C2211yescharacteristic, complemented
162#380C2211yescharacteristic, complemented
163#380C2211yescharacteristic, complemented
164#379C2211yescharacteristic
165#379C2211yescharacteristic
166#379C2211yescharacteristic
167#379C2211yescharacteristic
168#379C2211yescharacteristic
169C4×C4⋊C4C2211yescharacteristic, complemented
170C4×C22⋊C4C2211yescharacteristic
171C4×C22⋊C4C2211yescharacteristic
172C4×C22⋊C4C2211yescharacteristic
173C4×C22⋊C4C2211yescharacteristic, complemented
174C4×C22⋊C4C2211yescharacteristic, complemented
175C4×C22⋊C4C2211yescharacteristic, complemented
176C4×C22⋊C4C2211yescharacteristic, complemented
177C4×C22⋊C4C2211yescharacteristic, complemented
178C4×C22⋊C4C2211yescharacteristic, complemented
179C4×C22⋊C4C2211yescharacteristic, complemented
180#376C2211yescharacteristic, complemented
181C2×#95C2211yescharacteristic
182C2×#95C2211yescharacteristic
183C2×#95C2211yescharacteristic, complemented
184C2×#95C2211yescharacteristic, complemented
185C2×#95C2211yescharacteristic, complemented
186C2×#95C2211yescharacteristic, complemented
187C25C2311yescharacteristic
188C25C2311yescharacteristic
189C22×Q8C2311yescharacteristic
190C22×D4—24no—
191C22×D4—24no—
192C22×D4—42no—
193C22×D4C2311yescharacteristic
194C22×D4C2311yescharacteristic
195C22×D4C2311yescharacteristic
196C22×D4C2311yescharacteristic
197C23×C4—24no—
198C23×C4—24no—
199C23×C4—42no—
200C23×C4C2311yescharacteristic
201C23×C4C2311yescharacteristic
202C23×C4C2311yescharacteristic
203C23×C4C2311yescharacteristic
204C23×C4C2311yescharacteristic
205C23×C4C2311yescharacteristic
206C23×C4C2311yescharacteristic
207C23×C4C2311yescharacteristic
208C23×C4C2311yescharacteristic
209C23×C4C2311yescharacteristic
210C23×C4C2311yescharacteristic
211C23×C4C2311yescharacteristic
212C23×C4C2311yescharacteristic
213C23×C4C2311yescharacteristic
214C23×C4C2311yescharacteristic
215#123—24no—
216#123—42no—
217C22⋊Q8—42no—
218C22⋊Q8—42no—
219C4×D4—24no—
220C4×D4—42no—
221#117—24no—
222#117—42no—
223#117—42no—
224C2×C4⋊C4C2311yescharacteristic
225C2×C4⋊C4C2311yescharacteristic
226C2×C4⋊C4C2311yescharacteristic
227C2×C4⋊C4C2311yescharacteristic
228C2×C4⋊C4C2311yescharacteristic
229C2×C4⋊C4C2311yescharacteristic
230C2×C4⋊C4C2311yescharacteristic
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×C22⋊C4—24no—
248C2×C22⋊C4—24no—
249C2×C22⋊C4—42no—
250C2×C22⋊C4—42no—
251C2×C22⋊C4—42no—
252C2×C22⋊C4—42no—
253C2×C22⋊C4C2311yescharacteristic
254C2×C22⋊C4C2311yescharacteristic
255C2×C22⋊C4C2311yescharacteristic
256C2×C22⋊C4C2311yescharacteristic
257C2×C22⋊C4C2311yescharacteristic
258C2×C22⋊C4C2311yescharacteristic
259C2×C22⋊C4C2311yescharacteristic
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×C42C2311yescharacteristic
300C2×C42C2311yescharacteristic
301C2×C42C2311yescharacteristic
302C2×C42C2311yescharacteristic
303C2×C42C2311yescharacteristic
304C2×C42C2311yescharacteristic
305C2×C42C2311yescharacteristic
306C2×C42C2311yescharacteristic
307C2×C42C2311yescharacteristic
308C2×C42C2311yescharacteristic
309#95C2311yescharacteristic
310#95C2311yescharacteristic
311#95C2311yescharacteristic
312#95C2311yescharacteristic
313#95C2311yescharacteristic
314#95C2311yescharacteristic
315#95C2311yescharacteristic
316#95C2311yescharacteristic
317#95C2311yescharacteristic
318#95C2311yescharacteristic
319#95C2311yescharacteristic
320#95C2311yescharacteristic
321#95C2311yescharacteristic
322#95C2311yescharacteristic
323#95C2311yescharacteristic
324#95C2311yescharacteristic
325#95C2311yescharacteristic
326#95C2311yescharacteristic
327#95C2311yescharacteristic
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
363C24—22no—
364C24—22no—
365C24—22no—
366C24—22no—
367C24—22no—
368C24—22no—
369C24—22no—
370C24—22no—
371C24—41no—
372C24—41no—
373C24—41no—
374C24—41no—
375C24—41no—
376C24#4114yes—
377C24C2411yescharacteristic
378C24C2411yescharacteristic
379C24C2411yescharacteristic
380C24C2411yescharacteristic
381C24C2411yescharacteristic
382C2×Q8—41no—
383C2×Q8—41no—
384C2×Q8—41no—
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—41no—
395C2×D4—41no—
396C2×D4—416no—
397C2×D4#4114yes—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
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—41no—
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×C4—41no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—416no—
443C22×C4#4114yes—
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
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—41no—
476C4⋊C4—41no—
477C4⋊C4—41no—
478C4⋊C4—41no—
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—
493C22⋊C4—22no—
494C22⋊C4—22no—
495C22⋊C4—22no—
496C22⋊C4—22no—
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—41no—
517C22⋊C4—41no—
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—
539C42—22no—
540C42—22no—
541C42—22no—
542C42—41no—
543C42—41no—
544C42—41no—
545C42—41no—
546C42—41no—
547C42—41no—
548C42—41no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—28no—
558C23—28no—
559C23—21no—
560C23—21no—
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—44no—
579C23—44no—
580C23—44no—
581C23—44no—
582C23—44no—
583C23—44no—
584C23—44no—
585C23—44no—
586C23—44no—
587C23—82no—
588C23—82no—
589C23—82no—
590C23C2×#4112yes—
591C23C2×#4112yes—
592C23C2×#4112yes—
593C23C2×#4112yes—
594C23C2×#4112yes—
595C23C2×#4112yes—
596C23H(5,𝔽2)12yes—
597C23H(5,𝔽2)12yes—
598C23C2511yescharacteristic
599Q8—82no—
600D4—28no—
601D4—44no—
602D4—44no—
603D4—44no—
604C2×C4—28no—
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—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—44no—
681C2×C4—44no—
682C2×C4—44no—
683C2×C4—44no—
684C2×C4—44no—
685C2×C4—44no—
686C2×C4—44no—
687C2×C4—82no—
688C2×C4—82no—
689C2×C4—82no—
690C2×C4—82no—
691C2×C4—82no—
692C2×C4—82no—
693C2×C4—82no—
694C2×C4C2×#4112yes—
695C2×C4C2×#4112yes—
696C2×C4C2×#4112yes—
697C22—22no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—416no—
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—88no—
732C22#55114yes—
733C22#55114yes—
734C22C22×#4111yescharacteristic
735C22C22×#4111yescharacteristic
736C22C22×#4111yescharacteristic
737C22C2×H(5,𝔽2)11yescharacteristic
738C22C2×H(5,𝔽2)11yescharacteristic
739C22#58511yescharacteristic
740C22#58511yescharacteristic
741C4—22no—
742C4—22no—
743C4—22no—
744C4—41no—
745C4—41no—
746C4—41no—
747C4—41no—
748C4—41no—
749C4—41no—
750C4—41no—
751C4—41no—
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—
767C2—24no—
768C2—24no—
769C2—42no—
770C2—42no—
771C2—81no—
772C2C2×#55111yescharacteristic
773C2C2×#55111yescharacteristic
774C2#347511yescharacteristic
775C2#349111yescharacteristic
776C2#349411yescharacteristic
777C2#351311yescharacteristic
778C2#353411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C25
prime radicalC23×D4C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #2746C2semidirect
2. #2743C2semidirect
3. #2740C2semidirect
4. #2737C2semidirect
5. #2576C2semidirect
6. #2572C2semidirect
7. #2564C2semidirect
8. #2561C2semidirect
9. #2526C2semidirect
10. #2516C2semidirect
11. #2510C2semidirect
12. #2510C2semidirect
13. #2498C2semidirect
14. #2493C2semidirect
15. #2493C2semidirect
16. #2488C2semidirect
17. #2483C2semidirect
18. #2482C2semidirect
19. #2438C2semidirect
20. #2437C2semidirect
21. #2419C2semidirect
23. #2359C2semidirect
24. #2353C2semidirect
25. #2343C2semidirect
26. #2342C2semidirect
27. #2342C2semidirect
30. #2280C2semidirect
31. C2×#381C2semidirect
37. C2×C22⋊Q8C22semidirect
42. C2×#117C22semidirect
49. #401C22semidirect
50. #401C22semidirect
51. #400C22semidirect
52. #400C22semidirect
53. #400C22semidirect
54. #400C22semidirect
55. #400C22semidirect
56. #400C22semidirect
57. #400C22semidirect
58. #399C22semidirect
59. #399C22semidirect
60. #399C22semidirect
61. #398C22semidirect
62. #398C22semidirect
63. #397C22semidirect
64. #397C22semidirect
65. #397C22semidirect
66. #397C22semidirect
67. #397C22semidirect
68. #397C22semidirect
69. #397C22semidirect
70. #397C22semidirect
71. #396C22semidirect
72. #396C22semidirect
73. #395C22semidirect
78. #393C22semidirect
79. #393C22semidirect
80. #393C22semidirect
81. #391C22semidirect
84. #389C22semidirect
85. #388C22semidirect
86. #388C22semidirect
87. #388C22semidirect
88. #388C22semidirect
89. #388C22semidirect
90. #388C22semidirect
91. #388C22semidirect
92. #388C22semidirect
93. #388C22semidirect
94. #388C22semidirect
95. #388C22semidirect
96. #388C22semidirect
97. #388C22semidirect
98. #388C22semidirect
99. #388C22semidirect
100. #388C22semidirect
101. #387C22semidirect
102. #387C22semidirect
103. #387C22semidirect
104. #387C22semidirect
105. #387C22semidirect
106. #387C22semidirect
107. #387C22semidirect
108. #387C22semidirect
109. #387C22semidirect
110. #387C22semidirect
111. #387C22semidirect
112. #387C22semidirect
133. #385C22semidirect
134. #385C22semidirect
135. #385C22semidirect
136. #385C22semidirect
137. #385C22semidirect
138. #385C22semidirect
139. #383C22semidirect
140. #383C22semidirect
141. #383C22semidirect
142. #382C22semidirect
149. #381C22semidirect
150. #381C22semidirect
151. #381C22semidirect
152. #381C22semidirect
153. #381C22semidirect
154. #381C22semidirect
155. #381C22semidirect
158. #380C22semidirect
159. #380C22semidirect
160. #380C22semidirect
161. #380C22semidirect
162. #380C22semidirect
163. #380C22semidirect
169. C4×C4⋊C4C22semidirect
173. C4×C22⋊C4C22semidirect
174. C4×C22⋊C4C22semidirect
175. C4×C22⋊C4C22semidirect
176. C4×C22⋊C4C22semidirect
177. C4×C22⋊C4C22semidirect
178. C4×C22⋊C4C22semidirect
179. C4×C22⋊C4C22semidirect
180. #376C22semidirect
183. C2×#95C22semidirect
184. C2×#95C22semidirect
185. C2×#95C22semidirect
186. C2×#95C22semidirect

Maximal subgroups

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

subgroupindex
#27462
#27432
#27402
#27372
#25762
#25722
#25642
#25612
#25262
#25162
#25102
#24982
#24932
#24882
#24832
#24822
#24382
#24372
#24192
#24052
#23592
#23532
#23432
#23422
D4×C22⋊C42
C2×#3862
#22802
C2×#3812