Finite Group Databasebeta

← #40356

Subgroups — #40356

Order 256.

1048 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2849C211yesmaximal, characteristic, complemented
2#2782C211yesmaximal, characteristic, complemented
3#2748C211yesmaximal, characteristic, complemented
4#2746C211yesmaximal, characteristic, complemented
5#2735C211yesmaximal, characteristic, complemented
6#2688C211yesmaximal, characteristic, complemented
7#2678C211yesmaximal, characteristic, complemented
8#2668C211yesmaximal, characteristic, complemented
9#2668C211yesmaximal, characteristic, complemented
10#2652C211yesmaximal, characteristic, complemented
11#2636C211yesmaximal, characteristic, complemented
12#2597C211yesmaximal, characteristic, complemented
13#2579C211yesmaximal, characteristic, complemented
14#2576C211yesmaximal, characteristic, complemented
15#2576C211yesmaximal, characteristic, complemented
16#2575C211yesmaximal, characteristic, complemented
17#2553C211yesmaximal, characteristic, complemented
18#2535C211yesmaximal, characteristic, complemented
19#2517C211yesmaximal, characteristic, complemented
20#2467C211yesmaximal, characteristic, complemented
21#2457C211yesmaximal, characteristic, complemented
22#2457C211yesmaximal, characteristic, complemented
23#2456C211yesmaximal, characteristic, complemented
24#2443C211yesmaximal, characteristic, complemented
25#2419C211yesmaximal, characteristic, complemented
26#2364C211yesmaximal, characteristic, complemented
27#2361C211yesmaximal, characteristic, complemented
28#2333C211yesmaximal, characteristic, complemented
29#2325C211yesmaximal, characteristic, complemented
30C4×#120C211yesmaximal, characteristic, complemented
31C4×#120C211yesmaximal, characteristic, complemented
32C24×C4C2211yescharacteristic
33C2×#126C2211yescharacteristic, complemented
34C2×#123C2211yescharacteristic
35C2×#123C2211yescharacteristic
36C2×#123C2211yescharacteristic
37C2×#121C2211yescharacteristic
38C2×#121C2211yescharacteristic
39C2×#121C2211yescharacteristic
40C2×#121C2211yescharacteristic
41C2×#121C2211yescharacteristic
42C2×#120C2211yescharacteristic
43C2×#120C2211yescharacteristic
44C2×#120C2211yescharacteristic
45C2×C4×D4C2211yescharacteristic
46C2×C4×D4C2211yescharacteristic
47C2×C4×D4C2211yescharacteristic
48C2×C4×D4C2211yescharacteristic
49C2×C4×D4C2211yescharacteristic
50C2×C4×D4C2211yescharacteristic
51C2×C4×D4C2211yescharacteristic, complemented
52C2×C4×D4C2211yescharacteristic, complemented
53C22×C4⋊C4C2211yescharacteristic, complemented
54#401C2211yescharacteristic, complemented
55#400C2211yescharacteristic, complemented
56#400C2211yescharacteristic, complemented
57#400C2211yescharacteristic, complemented
58#400C2211yescharacteristic, complemented
59#400C2211yescharacteristic, complemented
60#399C2211yescharacteristic
61#399C2211yescharacteristic
62#399C2211yescharacteristic
63#399C2211yescharacteristic, complemented
64#398C2211yescharacteristic, complemented
65#398C2211yescharacteristic, complemented
66#398C2211yescharacteristic, complemented
67#397C2211yescharacteristic
68#397C2211yescharacteristic
69#397C2211yescharacteristic
70#397C2211yescharacteristic
71#397C2211yescharacteristic
72#397C2211yescharacteristic
73#397C2211yescharacteristic
74#397C2211yescharacteristic
75#397C2211yescharacteristic, complemented
76#397C2211yescharacteristic, complemented
77#396C2211yescharacteristic
78#396C2211yescharacteristic
79#396C2211yescharacteristic
80#396C2211yescharacteristic, complemented
81#396C2211yescharacteristic, complemented
82#394C2211yescharacteristic
83#394C2211yescharacteristic
84#394C2211yescharacteristic
85#394C2211yescharacteristic
86#394C2211yescharacteristic
87#394C2211yescharacteristic
88#394C2211yescharacteristic, complemented
89#392C2211yescharacteristic
90#392C2211yescharacteristic
91#392C2211yescharacteristic
92#392C2211yescharacteristic
93#392C2211yescharacteristic, complemented
94#390C2211yescharacteristic
95#390C2211yescharacteristic
96#390C2211yescharacteristic, complemented
97#389C2211yescharacteristic, complemented
98#388C2211yescharacteristic
99#388C2211yescharacteristic
100#388C2211yescharacteristic
101#388C2211yescharacteristic
102#388C2211yescharacteristic
103#388C2211yescharacteristic
104#388C2211yescharacteristic
105#388C2211yescharacteristic, complemented
106#388C2211yescharacteristic, complemented
107#388C2211yescharacteristic, complemented
108#388C2211yescharacteristic, complemented
109#388C2211yescharacteristic, complemented
110#388C2211yescharacteristic, complemented
111#387C2211yescharacteristic, complemented
112#387C2211yescharacteristic, complemented
113#387C2211yescharacteristic, complemented
114#387C2211yescharacteristic, complemented
115#387C2211yescharacteristic, complemented
116#387C2211yescharacteristic, complemented
117#387C2211yescharacteristic, complemented
118#387C2211yescharacteristic, complemented
119#387C2211yescharacteristic, complemented
120#387C2211yescharacteristic, complemented
121#387C2211yescharacteristic, complemented
122#387C2211yescharacteristic, complemented
123#387C2211yescharacteristic, complemented
124#386C2211yescharacteristic
125#386C2211yescharacteristic
126#386C2211yescharacteristic
127#386C2211yescharacteristic
128#386C2211yescharacteristic
129#386C2211yescharacteristic
130#386C2211yescharacteristic
131#386C2211yescharacteristic
132#386C2211yescharacteristic
133#386C2211yescharacteristic
134#386C2211yescharacteristic
135#386C2211yescharacteristic
136#386C2211yescharacteristic
137#386C2211yescharacteristic
138#386C2211yescharacteristic
139#386C2211yescharacteristic
140#386C2211yescharacteristic
141#386C2211yescharacteristic
142#386C2211yescharacteristic
143#386C2211yescharacteristic, complemented
144#386C2211yescharacteristic, complemented
145#386C2211yescharacteristic, complemented
146#386C2211yescharacteristic, complemented
147#386C2211yescharacteristic, complemented
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#385C2211yescharacteristic, complemented
162#382C2211yescharacteristic, complemented
163#382C2211yescharacteristic, complemented
164#382C2211yescharacteristic, complemented
165#381C2211yescharacteristic
166#381C2211yescharacteristic
167#381C2211yescharacteristic, complemented
168#381C2211yescharacteristic, complemented
169#380C2211yescharacteristic, complemented
170#380C2211yescharacteristic, complemented
171#380C2211yescharacteristic, complemented
172#380C2211yescharacteristic, complemented
173#379C2211yescharacteristic
174#379C2211yescharacteristic
175#379C2211yescharacteristic
176C4×C4⋊C4C2211yescharacteristic, complemented
177C4×C22⋊C4C2211yescharacteristic
178C4×C22⋊C4C2211yescharacteristic
179C4×C22⋊C4C2211yescharacteristic
180C4×C22⋊C4C2211yescharacteristic
181C4×C22⋊C4C2211yescharacteristic
182C4×C22⋊C4C2211yescharacteristic
183C4×C22⋊C4C2211yescharacteristic, complemented
184C4×C22⋊C4C2211yescharacteristic, complemented
185C4×C22⋊C4C2211yescharacteristic, complemented
186C2×#95C2211yescharacteristic, complemented
187C25C2311yescharacteristic
188C22×D4C2311yescharacteristic
189C22×D4C2311yescharacteristic
190C22×D4C2311yescharacteristic
191C22×D4C2311yescharacteristic
192C22×D4C2311yescharacteristic
193C22×D4C2311yescharacteristic
194C22×D4C2311yescharacteristic
195C22×D4C2311yescharacteristic
196C22×D4C2311yescharacteristic
197C22×D4C2311yescharacteristic
198C22×D4C2311yescharacteristic
199C22×D4C2311yescharacteristic
200C23×C4—42no—
201C23×C4—42no—
202C23×C4—42no—
203C23×C4C2311yescharacteristic
204C23×C4C2311yescharacteristic
205C23×C4C2311yescharacteristic
206C23×C4C2311yescharacteristic
207C23×C4C2311yescharacteristic
208C23×C4C2311yescharacteristic
209C23×C4C2311yescharacteristic
210C23×C4C2311yescharacteristic
211C23×C4C2311yescharacteristic
212C23×C4C2311yescharacteristic
213C23×C4C2311yescharacteristic
214C23×C4C2311yescharacteristic
215C23×C4C2311yescharacteristic
216#126—42no—
217#123—42no—
218#123—42no—
219#123—42no—
220#121—24no—
221#121—24no—
222#121—24no—
223#121—24no—
224#121—42no—
225#120—24no—
226#120—24no—
227#120—42no—
228C4×D4—42no—
229C4×D4—42no—
230C4×D4—42no—
231C4×D4—42no—
232C4×D4—42no—
233C4×D4—42no—
234C4×D4—42no—
235C4×D4—42no—
236C2×C4⋊C4—42no—
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×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×C42C2311yescharacteristic
314C2×C42C2311yescharacteristic
315C2×C42C2311yescharacteristic
316C2×C42C2311yescharacteristic
317C2×C42C2311yescharacteristic
318C2×C42C2311yescharacteristic
319C2×C42C2311yescharacteristic
320C2×C42C2311yescharacteristic
321C2×C42C2311yescharacteristic
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
363#95C2311yescharacteristic
364#95C2311yescharacteristic
365#95C2311yescharacteristic
366C24—22no—
367C24—22no—
368C24—22no—
369C24—41no—
370C24—41no—
371C24—41no—
372C24—41no—
373C24C2411yescharacteristic
374C24C2411yescharacteristic
375C24C2411yescharacteristic
376C24C2411yescharacteristic
377C24C2411yescharacteristic
378C24C2411yescharacteristic
379C2×D4—22no—
380C2×D4—22no—
381C2×D4—22no—
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—41no—
395C2×D4—41no—
396C2×D4—41no—
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#4114yes—
414C2×D4#4114yes—
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—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×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—41no—
454C22×C4—416no—
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
471C22×C4C2411yescharacteristic
472C22×C4C2411yescharacteristic
473C22×C4C2411yescharacteristic
474C22×C4C2411yescharacteristic
475C22×C4C2411yescharacteristic
476C22×C4C2411yescharacteristic
477C22×C4C2411yescharacteristic
478C22×C4C2411yescharacteristic
479C22×C4C2411yescharacteristic
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—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⋊C4—41no—
499C4⋊C4—41no—
500C4⋊C4—41no—
501C4⋊C4—41no—
502C4⋊C4—41no—
503C4⋊C4—41no—
504C4⋊C4—41no—
505C4⋊C4—41no—
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—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—41no—
550C22⋊C4—41no—
551C22⋊C4—41no—
552C22⋊C4—41no—
553C22⋊C4—41no—
554C22⋊C4—41no—
555C22⋊C4—41no—
556C42—22no—
557C42—22no—
558C42—41no—
559C42—41no—
560C42—41no—
561C42—41no—
562C42—41no—
563C42—41no—
564C42—41no—
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—44no—
603C23—44no—
604C23—44no—
605C23—44no—
606C23—44no—
607C23—44no—
608C23—44no—
609C23C2×#4112yes—
610C23C2×#4112yes—
611C23C2×#4112yes—
612C23C2×#4112yes—
613C23H(5,𝔽2)12yes—
614C23C2511yescharacteristic
615D4—44no—
616D4—44no—
617D4—44no—
618D4—44no—
619D4—44no—
620D4—44no—
621D4—44no—
622D4—44no—
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—21no—
697C2×C4—21no—
698C2×C4—44no—
699C2×C4—44no—
700C2×C4—44no—
701C2×C4—44no—
702C2×C4—44no—
703C2×C4—44no—
704C2×C4—44no—
705C2×C4—82no—
706C2×C4—82no—
707C2×C4—82no—
708C2×C4—82no—
709C2×C4—82no—
710C2×C4—82no—
711C2×C4C2×#4112yes—
712C2×C4C2×#4112yes—
713C2×C4H(5,𝔽2)12yes—
714C2×C4H(5,𝔽2)12yes—
715C22—22no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—22no—
729C22—22no—
730C22—416no—
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—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22C22×#4111yescharacteristic
759C22C22×#4111yescharacteristic
760C22C2×H(5,𝔽2)11yescharacteristic
761C22C2×H(5,𝔽2)11yescharacteristic
762C22C2×H(5,𝔽2)11yescharacteristic
763C22#58511yescharacteristic
764C22#58511yescharacteristic
765C4—22no—
766C4—22no—
767C4—22no—
768C4—22no—
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—
786C4—41no—
787C4—41no—
788C4—41no—
789C4—41no—
790C2—42no—
791C2—42no—
792C2—42no—
793C2—42no—
794C2—42no—
795C2—81no—
796C2#345911yescharacteristic
797C2#348111yescharacteristic
798C2#350511yescharacteristic
799C2#351311yescharacteristic
800C2#351311yescharacteristic
801C2#353211yescharacteristic
802C2#353911yescharacteristic
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. #2849C2semidirect
2. #2782C2semidirect
3. #2748C2semidirect
4. #2746C2semidirect
5. #2735C2semidirect
6. #2688C2semidirect
7. #2678C2semidirect
8. #2668C2semidirect
9. #2668C2semidirect
10. #2652C2semidirect
11. #2636C2semidirect
12. #2597C2semidirect
13. #2579C2semidirect
14. #2576C2semidirect
15. #2576C2semidirect
16. #2575C2semidirect
17. #2553C2semidirect
18. #2535C2semidirect
19. #2517C2semidirect
20. #2467C2semidirect
21. #2457C2semidirect
22. #2457C2semidirect
23. #2456C2semidirect
24. #2443C2semidirect
25. #2419C2semidirect
26. #2364C2semidirect
27. #2361C2semidirect
28. #2333C2semidirect
29. #2325C2semidirect
30. C4×#120C2semidirect
31. C4×#120C2semidirect
33. C2×#126C22semidirect
51. C2×C4×D4C22semidirect
52. C2×C4×D4C22semidirect
53. C22×C4⋊C4C22semidirect
54. #401C22semidirect
55. #400C22semidirect
56. #400C22semidirect
57. #400C22semidirect
58. #400C22semidirect
59. #400C22semidirect
63. #399C22semidirect
64. #398C22semidirect
65. #398C22semidirect
66. #398C22semidirect
75. #397C22semidirect
76. #397C22semidirect
80. #396C22semidirect
81. #396C22semidirect
88. #394C22semidirect
93. #392C22semidirect
96. #390C22semidirect
97. #389C22semidirect
105. #388C22semidirect
106. #388C22semidirect
107. #388C22semidirect
108. #388C22semidirect
109. #388C22semidirect
110. #388C22semidirect
111. #387C22semidirect
112. #387C22semidirect
113. #387C22semidirect
114. #387C22semidirect
115. #387C22semidirect
116. #387C22semidirect
117. #387C22semidirect
118. #387C22semidirect
119. #387C22semidirect
120. #387C22semidirect
121. #387C22semidirect
122. #387C22semidirect
123. #387C22semidirect
143. #386C22semidirect
144. #386C22semidirect
145. #386C22semidirect
146. #386C22semidirect
147. #386C22semidirect
158. #385C22semidirect
159. #385C22semidirect
160. #385C22semidirect
161. #385C22semidirect
162. #382C22semidirect
163. #382C22semidirect
164. #382C22semidirect
167. #381C22semidirect
168. #381C22semidirect
169. #380C22semidirect
170. #380C22semidirect
171. #380C22semidirect
172. #380C22semidirect
176. C4×C4⋊C4C22semidirect
183. C4×C22⋊C4C22semidirect
184. C4×C22⋊C4C22semidirect
185. C4×C22⋊C4C22semidirect
186. C2×#95C22semidirect

Maximal subgroups

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

subgroupindex
#28492
#27822
#27482
#27462
#27352
#26882
#26782
#26682
#26522
#26362
#25972
#25792
#25762
#25752
#25532
#25352
#25172
#24672
#24572
#24562
#24432
#24192
#23642
#23612
#23332
#23252
C4×#1202