Finite Group Databasebeta

← #43048

Subgroups — #43048

Order 256.

985 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
1#2786C211yesmaximal, characteristic, complemented
2#2782C211yesmaximal, characteristic, complemented
3#2746C211yesmaximal, characteristic, complemented
4#2745C211yesmaximal, characteristic, complemented
5#2739C211yesmaximal, characteristic, complemented
6#2736C211yesmaximal, characteristic, complemented
7#2735C211yesmaximal, characteristic, complemented
8#2723C211yesmaximal, characteristic, complemented
9#2597C211yesmaximal, characteristic, complemented
10#2595C211yesmaximal, characteristic, complemented
11#2578C211yesmaximal, characteristic, complemented
12#2575C211yesmaximal, characteristic, complemented
13#2564C211yesmaximal, characteristic, complemented
14#2515C211yesmaximal, characteristic, complemented
15#2510C211yesmaximal, characteristic, complemented
16#2498C211yesmaximal, characteristic, complemented
17#2488C211yesmaximal, characteristic, complemented
18#2482C211yesmaximal, characteristic, complemented
19#2481C211yesmaximal, characteristic, complemented
20#2480C211yesmaximal, characteristic, complemented
21#2477C211yesmaximal, characteristic, complemented
22#2437C211yesmaximal, characteristic, complemented
23#2419C211yesmaximal, characteristic, complemented
24#2405C211yesmaximal, characteristic
25C2×#397C211yesmaximal, characteristic, complemented
26#2359C211yesmaximal, characteristic, complemented
27#2352C211yesmaximal, characteristic, complemented
28#2342C211yesmaximal, characteristic, complemented
29D4×C22⋊C4C211yesmaximal, characteristic
30#2312C211yesmaximal, characteristic, complemented
31#2308C211yesmaximal, characteristic
32C23×D4C2211yescharacteristic
33C2×#126C2211yescharacteristic, complemented
34C2×#123C2211yescharacteristic
35C2×#123C2211yescharacteristic
36C2×C22⋊Q8C2211yescharacteristic, complemented
37C2×C22⋊Q8C2211yescharacteristic, complemented
38C2×C4×D4C2211yescharacteristic
39C2×C4×D4C2211yescharacteristic
40C2×#117C2211yescharacteristic, complemented
41C2×#117C2211yescharacteristic, complemented
42C22×C4⋊C4C2211yescharacteristic, complemented
43C22×C22⋊C4C2211yescharacteristic
44C22×C22⋊C4C2211yescharacteristic
45C22×C22⋊C4C2211yescharacteristic
46C22×C22⋊C4C2211yescharacteristic
47C22×C22⋊C4C2211yescharacteristic
48#401C2211yescharacteristic, complemented
49#400C2211yescharacteristic, complemented
50#400C2211yescharacteristic, complemented
51#400C2211yescharacteristic, complemented
52#400C2211yescharacteristic, complemented
53#400C2211yescharacteristic, complemented
54#400C2211yescharacteristic, complemented
55#400C2211yescharacteristic, complemented
56#400C2211yescharacteristic, complemented
57#399C2211yescharacteristic
58#399C2211yescharacteristic, complemented
59#399C2211yescharacteristic, complemented
60#398C2211yescharacteristic, complemented
61#398C2211yescharacteristic, complemented
62#397C2211yescharacteristic
63#397C2211yescharacteristic
64#397C2211yescharacteristic
65#397C2211yescharacteristic
66#397C2211yescharacteristic, complemented
67#397C2211yescharacteristic, complemented
68#397C2211yescharacteristic, complemented
69#397C2211yescharacteristic, complemented
70#397C2211yescharacteristic, complemented
71#397C2211yescharacteristic, complemented
72#397C2211yescharacteristic, complemented
73#397C2211yescharacteristic, complemented
74#397C2211yescharacteristic, complemented
75#397C2211yescharacteristic, complemented
76#397C2211yescharacteristic, complemented
77#396C2211yescharacteristic
78#396C2211yescharacteristic
79#396C2211yescharacteristic, complemented
80#395C2211yescharacteristic, complemented
81#394C2211yescharacteristic
82#394C2211yescharacteristic
83#394C2211yescharacteristic
84#394C2211yescharacteristic
85#393C2211yescharacteristic
86#393C2211yescharacteristic, complemented
87#393C2211yescharacteristic, complemented
88#391C2211yescharacteristic, complemented
89#390C2211yescharacteristic
90#390C2211yescharacteristic
91#389C2211yescharacteristic, complemented
92#388C2211yescharacteristic
93#388C2211yescharacteristic
94#388C2211yescharacteristic
95#388C2211yescharacteristic
96#388C2211yescharacteristic
97#388C2211yescharacteristic
98#388C2211yescharacteristic
99#388C2211yescharacteristic
100#388C2211yescharacteristic, complemented
101#388C2211yescharacteristic, complemented
102#388C2211yescharacteristic, complemented
103#388C2211yescharacteristic, complemented
104#388C2211yescharacteristic, complemented
105#388C2211yescharacteristic, complemented
106#388C2211yescharacteristic, complemented
107#388C2211yescharacteristic, complemented
108#388C2211yescharacteristic, complemented
109#388C2211yescharacteristic, complemented
110#388C2211yescharacteristic, complemented
111#388C2211yescharacteristic, complemented
112#388C2211yescharacteristic, complemented
113#388C2211yescharacteristic, complemented
114#388C2211yescharacteristic, 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#387C2211yescharacteristic, complemented
125#387C2211yescharacteristic, complemented
126#387C2211yescharacteristic, complemented
127#387C2211yescharacteristic, complemented
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#385C2211yescharacteristic
143#385C2211yescharacteristic
144#385C2211yescharacteristic, complemented
145#385C2211yescharacteristic, complemented
146#385C2211yescharacteristic, complemented
147#385C2211yescharacteristic, complemented
148#385C2211yescharacteristic, complemented
149#385C2211yescharacteristic, complemented
150#385C2211yescharacteristic, complemented
151#385C2211yescharacteristic, complemented
152#385C2211yescharacteristic, complemented
153#385C2211yescharacteristic, complemented
154#383C2211yescharacteristic, complemented
155#382C2211yescharacteristic, complemented
156#382C2211yescharacteristic, complemented
157#381C2211yescharacteristic
158#381C2211yescharacteristic
159#381C2211yescharacteristic, complemented
160#381C2211yescharacteristic, complemented
161#380C2211yescharacteristic
162#380C2211yescharacteristic, complemented
163#380C2211yescharacteristic, complemented
164#380C2211yescharacteristic, complemented
165#380C2211yescharacteristic, complemented
166#380C2211yescharacteristic, complemented
167#380C2211yescharacteristic, complemented
168#379C2211yescharacteristic
169#379C2211yescharacteristic
170#379C2211yescharacteristic
171#379C2211yescharacteristic
172#379C2211yescharacteristic
173#379C2211yescharacteristic
174#379C2211yescharacteristic
175C4×C4⋊C4C2211yescharacteristic, complemented
176C4×C4⋊C4C2211yescharacteristic, complemented
177C4×C22⋊C4C2211yescharacteristic
178C4×C22⋊C4C2211yescharacteristic, complemented
179C4×C22⋊C4C2211yescharacteristic, complemented
180C4×C22⋊C4C2211yescharacteristic, complemented
181C4×C22⋊C4C2211yescharacteristic, complemented
182C4×C22⋊C4C2211yescharacteristic, complemented
183C4×C22⋊C4C2211yescharacteristic, 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×C4C2311yescharacteristic
198C23×C4C2311yescharacteristic
199C23×C4C2311yescharacteristic
200C23×C4C2311yescharacteristic
201C23×C4C2311yescharacteristic
202C23×C4C2311yescharacteristic
203C23×C4C2311yescharacteristic
204C23×C4C2311yescharacteristic
205C23×C4C2311yescharacteristic
206C23×C4C2311yescharacteristic
207C23×C4C2311yescharacteristic
208#126—42no—
209#123—24no—
210#123—42no—
211C22⋊Q8—42no—
212C22⋊Q8—42no—
213C4×D4—24no—
214C4×D4—42no—
215#117—42no—
216#117—42no—
217C2×C4⋊C4—42no—
218C2×C4⋊C4C2311yescharacteristic
219C2×C4⋊C4C2311yescharacteristic
220C2×C4⋊C4C2311yescharacteristic
221C2×C4⋊C4C2311yescharacteristic
222C2×C4⋊C4C2311yescharacteristic
223C2×C4⋊C4C2311yescharacteristic
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×C22⋊C4—24no—
246C2×C22⋊C4—24no—
247C2×C22⋊C4—42no—
248C2×C22⋊C4—42no—
249C2×C22⋊C4—42no—
250C2×C22⋊C4C2311yescharacteristic
251C2×C22⋊C4C2311yescharacteristic
252C2×C22⋊C4C2311yescharacteristic
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×C22⋊C4C2311yescharacteristic
300C2×C42C2311yescharacteristic
301C2×C42C2311yescharacteristic
302C2×C42C2311yescharacteristic
303C2×C42C2311yescharacteristic
304C2×C42C2311yescharacteristic
305C2×C42C2311yescharacteristic
306C2×C42C2311yescharacteristic
307C2×C42C2311yescharacteristic
308C2×C42C2311yescharacteristic
309C2×C42C2311yescharacteristic
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
360C24—22no—
361C24—22no—
362C24—22no—
363C24—22no—
364C24—41no—
365C24—41no—
366C24—41no—
367C24—41no—
368C24—41no—
369C24—41no—
370C24—41no—
371C24—41no—
372C24—41no—
373C24#4114yes—
374C24C2411yescharacteristic
375C24C2411yescharacteristic
376C24C2411yescharacteristic
377C24C2411yescharacteristic
378C24C2411yescharacteristic
379C2×Q8—41no—
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—41no—
392C2×D4—41no—
393C2×D4—416no—
394C2×D4#4114yes—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
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—41no—
409C22×C4—41no—
410C22×C4—41no—
411C22×C4—41no—
412C22×C4—41no—
413C22×C4—41no—
414C22×C4—41no—
415C22×C4—41no—
416C22×C4—41no—
417C22×C4—41no—
418C22×C4—41no—
419C22×C4—41no—
420C22×C4—41no—
421C22×C4—41no—
422C22×C4—41no—
423C22×C4—41no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4C2411yescharacteristic
429C22×C4C2411yescharacteristic
430C22×C4C2411yescharacteristic
431C22×C4C2411yescharacteristic
432C22×C4C2411yescharacteristic
433C22×C4C2411yescharacteristic
434C22×C4C2411yescharacteristic
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
454C4⋊C4—22no—
455C4⋊C4—22no—
456C4⋊C4—22no—
457C4⋊C4—22no—
458C4⋊C4—22no—
459C4⋊C4—22no—
460C4⋊C4—22no—
461C4⋊C4—41no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4—41no—
468C4⋊C4—41no—
469C4⋊C4—41no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C4⋊C4—41no—
474C4⋊C4—41no—
475C4⋊C4—41no—
476C4⋊C4—41no—
477C4⋊C4—41no—
478C4⋊C4—41no—
479C4⋊C4—41no—
480C4⋊C4—41no—
481C22⋊C4—22no—
482C22⋊C4—22no—
483C22⋊C4—22no—
484C22⋊C4—22no—
485C22⋊C4—22no—
486C22⋊C4—22no—
487C22⋊C4—22no—
488C22⋊C4—22no—
489C22⋊C4—22no—
490C22⋊C4—22no—
491C22⋊C4—22no—
492C22⋊C4—22no—
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—41no—
502C22⋊C4—41no—
503C22⋊C4—41no—
504C22⋊C4—41no—
505C22⋊C4—41no—
506C22⋊C4—41no—
507C22⋊C4—41no—
508C22⋊C4—41no—
509C22⋊C4—41no—
510C22⋊C4—41no—
511C22⋊C4—41no—
512C22⋊C4—41no—
513C22⋊C4—41no—
514C22⋊C4—41no—
515C22⋊C4—41no—
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—
531C42—22no—
532C42—41no—
533C42—41no—
534C42—41no—
535C42—41no—
536C42—41no—
537C42—41no—
538C42—41no—
539C42—41no—
540C42—41no—
541C23—21no—
542C23—21no—
543C23—21no—
544C23—21no—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—28no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—44no—
572C23—44no—
573C23—44no—
574C23—44no—
575C23—82no—
576C23—82no—
577C23—82no—
578C23—82no—
579C23—82no—
580C23—82no—
581C23—82no—
582C23—82no—
583C23—82no—
584C23C2×#4112yes—
585C23C2×#4112yes—
586C23C2×#4112yes—
587C23C2×#4112yes—
588C23C2×#4112yes—
589C23H(5,𝔽2)12yes—
590C23C2511yescharacteristic
591Q8—82no—
592D4—28no—
593D4—44no—
594D4—44no—
595D4—44no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
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—44no—
673C2×C4—44no—
674C2×C4—44no—
675C2×C4—44no—
676C2×C4—82no—
677C2×C4—82no—
678C2×C4—82no—
679C2×C4—82no—
680C2×C4—82no—
681C2×C4—82no—
682C2×C4—82no—
683C2×C4C2×#4112yes—
684C2×C4H(5,𝔽2)12yes—
685C22—22no—
686C22—22no—
687C22—22no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—22no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—22no—
697C22—22no—
698C22—22no—
699C22—22no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—41no—
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—88no—
720C22—88no—
721C22#55114yes—
722C22C22×#4111yescharacteristic
723C22C22×#4111yescharacteristic
724C22C2×H(5,𝔽2)11yescharacteristic
725C22C2×H(5,𝔽2)11yescharacteristic
726C22#58511yescharacteristic
727C22#58511yescharacteristic
728C22#58511yescharacteristic
729C4—22no—
730C4—22no—
731C4—41no—
732C4—41no—
733C4—41no—
734C4—41no—
735C4—41no—
736C4—41no—
737C4—41no—
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—
755C2—24no—
756C2—42no—
757C2—42no—
758C2—42no—
759C2—81no—
760C2C2×#55111yescharacteristic
761C2#349111yescharacteristic
762C2#350511yescharacteristic
763C2#351311yescharacteristic
764C2#352111yescharacteristic
765C2#355811yescharacteristic
766C2#356011yescharacteristic
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. #2786C2semidirect
2. #2782C2semidirect
3. #2746C2semidirect
4. #2745C2semidirect
5. #2739C2semidirect
6. #2736C2semidirect
7. #2735C2semidirect
8. #2723C2semidirect
9. #2597C2semidirect
10. #2595C2semidirect
11. #2578C2semidirect
12. #2575C2semidirect
13. #2564C2semidirect
14. #2515C2semidirect
15. #2510C2semidirect
16. #2498C2semidirect
17. #2488C2semidirect
18. #2482C2semidirect
19. #2481C2semidirect
20. #2480C2semidirect
21. #2477C2semidirect
22. #2437C2semidirect
23. #2419C2semidirect
25. C2×#397C2semidirect
26. #2359C2semidirect
27. #2352C2semidirect
28. #2342C2semidirect
30. #2312C2semidirect
33. C2×#126C22semidirect
36. C2×C22⋊Q8C22semidirect
37. C2×C22⋊Q8C22semidirect
40. C2×#117C22semidirect
41. C2×#117C22semidirect
42. C22×C4⋊C4C22semidirect
48. #401C22semidirect
49. #400C22semidirect
50. #400C22semidirect
51. #400C22semidirect
52. #400C22semidirect
53. #400C22semidirect
54. #400C22semidirect
55. #400C22semidirect
56. #400C22semidirect
58. #399C22semidirect
59. #399C22semidirect
60. #398C22semidirect
61. #398C22semidirect
66. #397C22semidirect
67. #397C22semidirect
68. #397C22semidirect
69. #397C22semidirect
70. #397C22semidirect
71. #397C22semidirect
72. #397C22semidirect
73. #397C22semidirect
74. #397C22semidirect
75. #397C22semidirect
76. #397C22semidirect
79. #396C22semidirect
80. #395C22semidirect
86. #393C22semidirect
87. #393C22semidirect
88. #391C22semidirect
91. #389C22semidirect
100. #388C22semidirect
101. #388C22semidirect
102. #388C22semidirect
103. #388C22semidirect
104. #388C22semidirect
105. #388C22semidirect
106. #388C22semidirect
107. #388C22semidirect
108. #388C22semidirect
109. #388C22semidirect
110. #388C22semidirect
111. #388C22semidirect
112. #388C22semidirect
113. #388C22semidirect
114. #388C22semidirect
115. #387C22semidirect
116. #387C22semidirect
117. #387C22semidirect
118. #387C22semidirect
119. #387C22semidirect
120. #387C22semidirect
121. #387C22semidirect
122. #387C22semidirect
123. #387C22semidirect
124. #387C22semidirect
125. #387C22semidirect
126. #387C22semidirect
127. #387C22semidirect
144. #385C22semidirect
145. #385C22semidirect
146. #385C22semidirect
147. #385C22semidirect
148. #385C22semidirect
149. #385C22semidirect
150. #385C22semidirect
151. #385C22semidirect
152. #385C22semidirect
153. #385C22semidirect
154. #383C22semidirect
155. #382C22semidirect
156. #382C22semidirect
159. #381C22semidirect
160. #381C22semidirect
162. #380C22semidirect
163. #380C22semidirect
164. #380C22semidirect
165. #380C22semidirect
166. #380C22semidirect
167. #380C22semidirect
175. C4×C4⋊C4C22semidirect
176. C4×C4⋊C4C22semidirect
178. C4×C22⋊C4C22semidirect
179. C4×C22⋊C4C22semidirect
180. C4×C22⋊C4C22semidirect
181. C4×C22⋊C4C22semidirect
182. C4×C22⋊C4C22semidirect
183. C4×C22⋊C4C22semidirect
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
#27862
#27822
#27462
#27452
#27392
#27362
#27352
#27232
#25972
#25952
#25782
#25752
#25642
#25152
#25102
#24982
#24882
#24822
#24812
#24802
#24772
#24372
#24192
#24052
C2×#3972
#23592
#23522
#23422
D4×C22⋊C42
#23122
#23082