Finite Group Databasebeta

← #43212

Subgroups — #43212

Order 256.

995 conjugacy classes of subgroups.

The subgroup lattice has 801 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2778C211yesmaximal, characteristic, complemented
2#2765C211yesmaximal, characteristic, complemented
3#2761C211yesmaximal, characteristic, complemented
4#2749C211yesmaximal, characteristic, complemented
5#2707C211yesmaximal, characteristic, complemented
6#2688C211yesmaximal, characteristic, complemented
7#2682C211yesmaximal, characteristic, complemented
8#2678C211yesmaximal, characteristic, complemented
9#2595C211yesmaximal, characteristic, complemented
10#2576C211yesmaximal, characteristic, complemented
11#2573C211yesmaximal, characteristic, complemented
12#2566C211yesmaximal, characteristic, complemented
13#2534C211yesmaximal, characteristic, complemented
14#2500C211yesmaximal, characteristic, complemented
15#2497C211yesmaximal, characteristic, complemented
16#2470C211yesmaximal, characteristic, complemented
17#2470C211yesmaximal, characteristic, complemented
18#2460C211yesmaximal, characteristic, complemented
19#2457C211yesmaximal, characteristic, complemented
20#2456C211yesmaximal, characteristic, complemented
21#2425C211yesmaximal, characteristic, complemented
22#2424C211yesmaximal, characteristic, complemented
23#2424C211yesmaximal, characteristic, complemented
24#2412C211yesmaximal, characteristic, complemented
25#2392C211yesmaximal, characteristic, complemented
26#2364C211yesmaximal, characteristic, complemented
27#2363C211yesmaximal, characteristic, complemented
28#2358C211yesmaximal, characteristic, complemented
29#2342C211yesmaximal, characteristic, complemented
30#2333C211yesmaximal, characteristic, complemented
31#2318C211yesmaximal, characteristic, complemented
32C2×#125C2211yescharacteristic, complemented
33C2×#123C2211yescharacteristic
34C2×#123C2211yescharacteristic
35C2×#123C2211yescharacteristic
36C2×#123C2211yescharacteristic, complemented
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, complemented
51C2×#117C2211yescharacteristic
52C2×#117C2211yescharacteristic, complemented
53C22×C22⋊C4C2211yescharacteristic
54C22×C22⋊C4C2211yescharacteristic
55C22×C22⋊C4C2211yescharacteristic
56#401C2211yescharacteristic, complemented
57#400C2211yescharacteristic, complemented
58#400C2211yescharacteristic, complemented
59#400C2211yescharacteristic, complemented
60#400C2211yescharacteristic, complemented
61#398C2211yescharacteristic, complemented
62#398C2211yescharacteristic, complemented
63#397C2211yescharacteristic
64#397C2211yescharacteristic
65#397C2211yescharacteristic
66#397C2211yescharacteristic, complemented
67#397C2211yescharacteristic, complemented
68#397C2211yescharacteristic, complemented
69#397C2211yescharacteristic, complemented
70#396C2211yescharacteristic
71#396C2211yescharacteristic
72#396C2211yescharacteristic
73#396C2211yescharacteristic
74#396C2211yescharacteristic
75#396C2211yescharacteristic, complemented
76#396C2211yescharacteristic, complemented
77#396C2211yescharacteristic, complemented
78#396C2211yescharacteristic, complemented
79#396C2211yescharacteristic, complemented
80#394C2211yescharacteristic
81#394C2211yescharacteristic
82#394C2211yescharacteristic
83#394C2211yescharacteristic
84#394C2211yescharacteristic
85#394C2211yescharacteristic
86#394C2211yescharacteristic
87#394C2211yescharacteristic
88#394C2211yescharacteristic
89#394C2211yescharacteristic
90#394C2211yescharacteristic, complemented
91#392C2211yescharacteristic
92#392C2211yescharacteristic
93#392C2211yescharacteristic
94#392C2211yescharacteristic
95#392C2211yescharacteristic, complemented
96#390C2211yescharacteristic
97#390C2211yescharacteristic
98#390C2211yescharacteristic
99#390C2211yescharacteristic
100#390C2211yescharacteristic
101#390C2211yescharacteristic, complemented
102#390C2211yescharacteristic, complemented
103#389C2211yescharacteristic, complemented
104#389C2211yescharacteristic, complemented
105#389C2211yescharacteristic, complemented
106#389C2211yescharacteristic, complemented
107#388C2211yescharacteristic
108#388C2211yescharacteristic
109#388C2211yescharacteristic
110#388C2211yescharacteristic
111#388C2211yescharacteristic
112#388C2211yescharacteristic
113#388C2211yescharacteristic
114#388C2211yescharacteristic
115#388C2211yescharacteristic
116#388C2211yescharacteristic
117#388C2211yescharacteristic
118#388C2211yescharacteristic, complemented
119#388C2211yescharacteristic, complemented
120#388C2211yescharacteristic, complemented
121#388C2211yescharacteristic, complemented
122#388C2211yescharacteristic, complemented
123#388C2211yescharacteristic, complemented
124#388C2211yescharacteristic, complemented
125#387C2211yescharacteristic, complemented
126#387C2211yescharacteristic, complemented
127#387C2211yescharacteristic, complemented
128#387C2211yescharacteristic, complemented
129#387C2211yescharacteristic, complemented
130#387C2211yescharacteristic, complemented
131#387C2211yescharacteristic, complemented
132#387C2211yescharacteristic, complemented
133#387C2211yescharacteristic, complemented
134#386C2211yescharacteristic
135#386C2211yescharacteristic
136#386C2211yescharacteristic
137#386C2211yescharacteristic
138#386C2211yescharacteristic
139#386C2211yescharacteristic
140#386C2211yescharacteristic
141#386C2211yescharacteristic
142#386C2211yescharacteristic
143#386C2211yescharacteristic
144#386C2211yescharacteristic
145#386C2211yescharacteristic
146#386C2211yescharacteristic
147#386C2211yescharacteristic, complemented
148#386C2211yescharacteristic, complemented
149#386C2211yescharacteristic, complemented
150#386C2211yescharacteristic, complemented
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#384C2211yescharacteristic, complemented
163#383C2211yescharacteristic, complemented
164#382C2211yescharacteristic, complemented
165#382C2211yescharacteristic, complemented
166#381C2211yescharacteristic
167#381C2211yescharacteristic
168#381C2211yescharacteristic
169#381C2211yescharacteristic, complemented
170#380C2211yescharacteristic
171#380C2211yescharacteristic
172#380C2211yescharacteristic
173#380C2211yescharacteristic
174#379C2211yescharacteristic
175C4×C4⋊C4C2211yescharacteristic, complemented
176C4×C4⋊C4C2211yescharacteristic, complemented
177C4×C22⋊C4C2211yescharacteristic
178C4×C22⋊C4C2211yescharacteristic
179C4×C22⋊C4C2211yescharacteristic
180C4×C22⋊C4C2211yescharacteristic
181C4×C22⋊C4C2211yescharacteristic
182C4×C22⋊C4C2211yescharacteristic, complemented
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×C4C2311yescharacteristic
201C23×C4C2311yescharacteristic
202C23×C4C2311yescharacteristic
203C23×C4C2311yescharacteristic
204C23×C4C2311yescharacteristic
205C23×C4C2311yescharacteristic
206C23×C4C2311yescharacteristic
207C23×C4C2311yescharacteristic
208C23×C4C2311yescharacteristic
209C23×C4C2311yescharacteristic
210C23×C4C2311yescharacteristic
211#125—42no—
212#123—42no—
213#123—42no—
214#123—42no—
215#123—42no—
216#121—24no—
217#121—24no—
218#121—24no—
219#121—42no—
220#121—42no—
221#120—24no—
222#120—42no—
223#120—42no—
224C4×D4—24no—
225C4×D4—42no—
226C4×D4—42no—
227C4×D4—42no—
228C4×D4—42no—
229C4×D4—42no—
230#117—42no—
231#117—42no—
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×C4⋊C4C2311yescharacteristic
259C2×C4⋊C4C2311yescharacteristic
260C2×C22⋊C4—24no—
261C2×C22⋊C4—42no—
262C2×C22⋊C4—42no—
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×C22⋊C4C2311yescharacteristic
315C2×C42C2311yescharacteristic
316C2×C42C2311yescharacteristic
317C2×C42C2311yescharacteristic
318C2×C42C2311yescharacteristic
319C2×C42C2311yescharacteristic
320C2×C42C2311yescharacteristic
321C2×C42C2311yescharacteristic
322C2×C42C2311yescharacteristic
323C2×C42C2311yescharacteristic
324C2×C42C2311yescharacteristic
325C2×C42C2311yescharacteristic
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—41no—
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—41no—
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—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—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
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
471C22×C4C2411yescharacteristic
472C22×C4C2411yescharacteristic
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—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—
497C4⋊C4—41no—
498C4⋊C4—41no—
499C4⋊C4—41no—
500C4⋊C4—41no—
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—22no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—22no—
523C22⋊C4—22no—
524C22⋊C4—22no—
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—41no—
550C22⋊C4—41no—
551C22⋊C4—41no—
552C22⋊C4#4114yes—
553C42—22no—
554C42—22no—
555C42—22no—
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—44no—
603C23—44no—
604C23—44no—
605C23—82no—
606C23—82no—
607C23—82no—
608C23—82no—
609C23C2×#4112yes—
610C23C2×#4112yes—
611C23C2×#4112yes—
612C23H(5,𝔽2)12yes—
613C23C2511yescharacteristic
614D4—44no—
615D4—44no—
616D4—44no—
617D4—44no—
618D4—44no—
619D4—44no—
620D4—82no—
621D4—82no—
622D4—82no—
623D4—82no—
624D4—82no—
625D4—82no—
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—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—82no—
699C2×C4—82no—
700C2×C4—82no—
701C2×C4—82no—
702C2×C4—82no—
703C2×C4—82no—
704C2×C4—82no—
705C2×C4—82no—
706C2×C4—82no—
707C2×C4C2×#4112yes—
708C2×C4C2×#4112yes—
709C2×C4C2×#4112yes—
710C2×C4H(5,𝔽2)12yes—
711C2×C4H(5,𝔽2)12yes—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
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—41no—
754C22—88no—
755C22C22×#4111yescharacteristic
756C22C22×#4111yescharacteristic
757C22C2×H(5,𝔽2)11yescharacteristic
758C22C2×H(5,𝔽2)11yescharacteristic
759C22C2×H(5,𝔽2)11yescharacteristic
760C22#58511yescharacteristic
761C22#58511yescharacteristic
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—
786C4—41no—
787C2—42no—
788C2—42no—
789C2—42no—
790C2—42no—
791C2—81no—
792C2—81no—
793C2#347511yescharacteristic
794C2#350511yescharacteristic
795C2#351311yescharacteristic
796C2#351911yescharacteristic
797C2#351911yescharacteristic
798C2#354211yescharacteristic
799C2#356011yescharacteristic
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. #2778C2semidirect
2. #2765C2semidirect
3. #2761C2semidirect
4. #2749C2semidirect
5. #2707C2semidirect
6. #2688C2semidirect
7. #2682C2semidirect
8. #2678C2semidirect
9. #2595C2semidirect
10. #2576C2semidirect
11. #2573C2semidirect
12. #2566C2semidirect
13. #2534C2semidirect
14. #2500C2semidirect
15. #2497C2semidirect
16. #2470C2semidirect
17. #2470C2semidirect
18. #2460C2semidirect
19. #2457C2semidirect
20. #2456C2semidirect
21. #2425C2semidirect
22. #2424C2semidirect
23. #2424C2semidirect
24. #2412C2semidirect
25. #2392C2semidirect
26. #2364C2semidirect
27. #2363C2semidirect
28. #2358C2semidirect
29. #2342C2semidirect
30. #2333C2semidirect
31. #2318C2semidirect
32. C2×#125C22semidirect
36. C2×#123C22semidirect
50. C2×C4×D4C22semidirect
52. C2×#117C22semidirect
56. #401C22semidirect
57. #400C22semidirect
58. #400C22semidirect
59. #400C22semidirect
60. #400C22semidirect
61. #398C22semidirect
62. #398C22semidirect
66. #397C22semidirect
67. #397C22semidirect
68. #397C22semidirect
69. #397C22semidirect
75. #396C22semidirect
76. #396C22semidirect
77. #396C22semidirect
78. #396C22semidirect
79. #396C22semidirect
90. #394C22semidirect
95. #392C22semidirect
101. #390C22semidirect
102. #390C22semidirect
103. #389C22semidirect
104. #389C22semidirect
105. #389C22semidirect
106. #389C22semidirect
118. #388C22semidirect
119. #388C22semidirect
120. #388C22semidirect
121. #388C22semidirect
122. #388C22semidirect
123. #388C22semidirect
124. #388C22semidirect
125. #387C22semidirect
126. #387C22semidirect
127. #387C22semidirect
128. #387C22semidirect
129. #387C22semidirect
130. #387C22semidirect
131. #387C22semidirect
132. #387C22semidirect
133. #387C22semidirect
147. #386C22semidirect
148. #386C22semidirect
149. #386C22semidirect
150. #386C22semidirect
158. #385C22semidirect
159. #385C22semidirect
160. #385C22semidirect
161. #385C22semidirect
162. #384C22semidirect
163. #383C22semidirect
164. #382C22semidirect
165. #382C22semidirect
169. #381C22semidirect
175. C4×C4⋊C4C22semidirect
176. C4×C4⋊C4C22semidirect
182. C4×C22⋊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
#27782
#27652
#27612
#27492
#27072
#26882
#26822
#26782
#25952
#25762
#25732
#25662
#25342
#25002
#24972
#24702
#24602
#24572
#24562
#24252
#24242
#24122
#23922
#23642
#23632
#23582
#23422
#23332
#23182