Finite Group Databasebeta

← #36331

Subgroups — #36331

Order 256.

1082 conjugacy classes of subgroups.

The subgroup lattice has 777 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2854C211yesmaximal, characteristic, complemented
2#2852C211yesmaximal, characteristic, complemented
3#2849C211yesmaximal, characteristic, complemented
4#2608C211yesmaximal, characteristic, complemented
5#2602C211yesmaximal, characteristic, complemented
6#2597C211yesmaximal, characteristic, complemented
7#2595C211yesmaximal, characteristic, complemented
8#2587C211yesmaximal, characteristic, complemented
9#2573C211yesmaximal, characteristic, complemented
10#2559C211yesmaximal, characteristic, complemented
11#2554C211yesmaximal, characteristic, complemented
12#2526C211yesmaximal, characteristic, complemented
13#2518C211yesmaximal, characteristic, complemented
14#2505C211yesmaximal, characteristic, complemented
15#2480C211yesmaximal, characteristic, complemented
16#2470C211yesmaximal, characteristic, complemented
17#2466C211yesmaximal, characteristic, complemented
18#2444C211yesmaximal, characteristic, complemented
19#2424C211yesmaximal, characteristic
20#2411C211yesmaximal, characteristic, complemented
21#2411C211yesmaximal, characteristic, complemented
22#2374C211yesmaximal, characteristic, complemented
23#2373C211yesmaximal, characteristic, complemented
24#2363C211yesmaximal, characteristic, complemented
25#2359C211yesmaximal, characteristic, complemented
26#2359C211yesmaximal, characteristic, complemented
27#2357C211yesmaximal, characteristic, complemented
28C4×#120C211yesmaximal, characteristic, complemented
29#2296C211yesmaximal, characteristic, complemented
30#2290C211yesmaximal, characteristic, complemented
31C2×C4×C22⋊C4C211yesmaximal, characteristic, complemented
32C24×C4C2211yescharacteristic
33C2×#126C2211yescharacteristic
34C2×#126C2211yescharacteristic, complemented
35C2×#123C2211yescharacteristic
36C2×#123C2211yescharacteristic
37C2×#123C2211yescharacteristic
38C2×#123C2211yescharacteristic
39C2×#121C2211yescharacteristic
40C2×#121C2211yescharacteristic
41C2×#120C2211yescharacteristic
42C2×#120C2211yescharacteristic
43C2×C4×D4C2211yescharacteristic
44C2×C4×D4C2211yescharacteristic
45C2×C4×D4C2211yescharacteristic
46C2×C4×D4C2211yescharacteristic
47C2×#117C2211yescharacteristic
48C2×#117C2211yescharacteristic
49C2×#117C2211yescharacteristic, complemented
50C22×C22⋊C4C2211yescharacteristic
51C22×C22⋊C4C2211yescharacteristic
52C22×C42C2211yescharacteristic
53C22×C42C2211yescharacteristic
54#400C2211yescharacteristic, complemented
55#400C2211yescharacteristic, complemented
56#400C2211yescharacteristic, complemented
57#400C2211yescharacteristic, complemented
58#398C2211yescharacteristic, complemented
59#397C2211yescharacteristic
60#397C2211yescharacteristic
61#397C2211yescharacteristic
62#397C2211yescharacteristic, complemented
63#397C2211yescharacteristic, complemented
64#396C2211yescharacteristic
65#396C2211yescharacteristic
66#396C2211yescharacteristic
67#396C2211yescharacteristic
68#396C2211yescharacteristic
69#396C2211yescharacteristic
70#394C2211yescharacteristic
71#394C2211yescharacteristic
72#394C2211yescharacteristic
73#394C2211yescharacteristic
74#394C2211yescharacteristic
75#394C2211yescharacteristic
76#394C2211yescharacteristic, complemented
77#392C2211yescharacteristic
78#390C2211yescharacteristic
79#390C2211yescharacteristic
80#390C2211yescharacteristic
81#390C2211yescharacteristic
82#390C2211yescharacteristic
83#390C2211yescharacteristic, complemented
84#390C2211yescharacteristic, complemented
85#389C2211yescharacteristic, complemented
86#389C2211yescharacteristic, complemented
87#389C2211yescharacteristic, complemented
88#389C2211yescharacteristic, complemented
89#389C2211yescharacteristic, complemented
90#389C2211yescharacteristic, complemented
91#389C2211yescharacteristic, complemented
92#389C2211yescharacteristic, complemented
93#389C2211yescharacteristic, complemented
94#388C2211yescharacteristic
95#388C2211yescharacteristic
96#388C2211yescharacteristic
97#388C2211yescharacteristic
98#388C2211yescharacteristic
99#388C2211yescharacteristic
100#388C2211yescharacteristic
101#388C2211yescharacteristic
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#388C2211yescharacteristic, 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, complemented
140#385C2211yescharacteristic
141#385C2211yescharacteristic
142#385C2211yescharacteristic
143#385C2211yescharacteristic
144#385C2211yescharacteristic
145#385C2211yescharacteristic
146#385C2211yescharacteristic
147#385C2211yescharacteristic
148#385C2211yescharacteristic
149#385C2211yescharacteristic
150#385C2211yescharacteristic
151#385C2211yescharacteristic
152#385C2211yescharacteristic, complemented
153#385C2211yescharacteristic, complemented
154#383C2211yescharacteristic, complemented
155#382C2211yescharacteristic, complemented
156#381C2211yescharacteristic
157#381C2211yescharacteristic
158#381C2211yescharacteristic, complemented
159#380C2211yescharacteristic
160#379C2211yescharacteristic
161#379C2211yescharacteristic
162C4×C4⋊C4C2211yescharacteristic, complemented
163C4×C4⋊C4C2211yescharacteristic, complemented
164C4×C4⋊C4C2211yescharacteristic, complemented
165C4×C4⋊C4C2211yescharacteristic, complemented
166C4×C4⋊C4C2211yescharacteristic, complemented
167C4×C4⋊C4C2211yescharacteristic, complemented
168C4×C4⋊C4C2211yescharacteristic, complemented
169C4×C22⋊C4C2211yescharacteristic
170C4×C22⋊C4C2211yescharacteristic
171C4×C22⋊C4C2211yescharacteristic
172C4×C22⋊C4C2211yescharacteristic
173C4×C22⋊C4C2211yescharacteristic
174C4×C22⋊C4C2211yescharacteristic
175C4×C22⋊C4C2211yescharacteristic
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
184#376C2211yescharacteristic, complemented
185C2×#95C2211yescharacteristic
186C2×#95C2211yescharacteristic
187C25C2311yescharacteristic
188C22×D4C2311yescharacteristic
189C22×D4C2311yescharacteristic
190C22×D4C2311yescharacteristic
191C22×D4C2311yescharacteristic
192C22×D4C2311yescharacteristic
193C22×D4C2311yescharacteristic
194C22×D4C2311yescharacteristic
195C23×C4—24no—
196C23×C4—42no—
197C23×C4—42no—
198C23×C4C2311yescharacteristic
199C23×C4C2311yescharacteristic
200C23×C4C2311yescharacteristic
201C23×C4C2311yescharacteristic
202C23×C4C2311yescharacteristic
203C23×C4C2311yescharacteristic
204C23×C4C2311yescharacteristic
205C23×C4C2311yescharacteristic
206C23×C4C2311yescharacteristic
207C23×C4C2311yescharacteristic
208C23×C4C2311yescharacteristic
209C23×C4C2311yescharacteristic
210#126—24no—
211#126—42no—
212#123—24no—
213#123—24no—
214#123—24no—
215#123—42no—
216#121—24no—
217#121—42no—
218#120—24no—
219#120—42no—
220C4×D4—24no—
221C4×D4—24no—
222C4×D4—42no—
223C4×D4—42no—
224#117—24no—
225#117—42no—
226#117—42no—
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×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×C22⋊C4—24no—
257C2×C22⋊C4—24no—
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×C22⋊C4C2311yescharacteristic
301C2×C22⋊C4C2311yescharacteristic
302C2×C22⋊C4C2311yescharacteristic
303C2×C22⋊C4C2311yescharacteristic
304C2×C42—42no—
305C2×C42—42no—
306C2×C42C2311yescharacteristic
307C2×C42C2311yescharacteristic
308C2×C42C2311yescharacteristic
309C2×C42C2311yescharacteristic
310C2×C42C2311yescharacteristic
311C2×C42C2311yescharacteristic
312C2×C42C2311yescharacteristic
313C2×C42C2311yescharacteristic
314C2×C42C2311yescharacteristic
315C2×C42C2311yescharacteristic
316C2×C42C2311yescharacteristic
317C2×C42C2311yescharacteristic
318C2×C42C2311yescharacteristic
319C2×C42C2311yescharacteristic
320C2×C42C2311yescharacteristic
321C2×C42C2311yescharacteristic
322C2×C42C2311yescharacteristic
323C2×C42C2311yescharacteristic
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—22no—
370C24—22no—
371C24—41no—
372C24—41no—
373C24C2411yescharacteristic
374C24C2411yescharacteristic
375C24C2411yescharacteristic
376C24C2411yescharacteristic
377C24C2411yescharacteristic
378C2×D4—22no—
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—41no—
392C2×D4—41no—
393C2×D4—41no—
394C2×D4—41no—
395C2×D4—41no—
396C2×D4—41no—
397C2×D4—41no—
398C2×D4—41no—
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—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×C4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4—41no—
433C22×C4—416no—
434C22×C4#4114yes—
435C22×C4#4114yes—
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
454C22×C4C2411yescharacteristic
455C22×C4C2411yescharacteristic
456C22×C4C2411yescharacteristic
457C22×C4C2411yescharacteristic
458C22×C4C2411yescharacteristic
459C22×C4C2411yescharacteristic
460C22×C4C2411yescharacteristic
461C22×C4C2411yescharacteristic
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4—22no—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—22no—
468C4⋊C4—22no—
469C4⋊C4—22no—
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—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—
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—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—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#4114yes—
536C22⋊C4#4114yes—
537C42—22no—
538C42—22no—
539C42—22no—
540C42—22no—
541C42—22no—
542C42—22no—
543C42—22no—
544C42—41no—
545C42—41no—
546C42—41no—
547C42—41no—
548C42—41no—
549C42—41no—
550C42—41no—
551C42—41no—
552C42—41no—
553C42—41no—
554C42—41no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—28no—
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—21no—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—44no—
587C23—44no—
588C23—44no—
589C23—44no—
590C23—44no—
591C23—44no—
592C23C2×#4112yes—
593C23C2×#4112yes—
594C23C2×#4112yes—
595C23C2×#4112yes—
596C23H(5,𝔽2)12yes—
597C23C2511yescharacteristic
598D4—44no—
599D4—44no—
600D4—44no—
601D4—44no—
602D4—82no—
603D4—82no—
604D4—82no—
605C2×C4—28no—
606C2×C4—28no—
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—44no—
677C2×C4—44no—
678C2×C4—44no—
679C2×C4—44no—
680C2×C4—44no—
681C2×C4—44no—
682C2×C4—44no—
683C2×C4—44no—
684C2×C4—44no—
685C2×C4—82no—
686C2×C4C2×#4112yes—
687C2×C4C2×#4112yes—
688C2×C4C2×#4112yes—
689C2×C4C2×#4112yes—
690C2×C4C2×#4112yes—
691C2×C4C2×#4112yes—
692C2×C4C2×#4112yes—
693C2×C4C2×#4112yes—
694C2×C4H(5,𝔽2)12yes—
695C22—22no—
696C22—22no—
697C22—22no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—416no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
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#55314yes—
731C22C22×#4111yescharacteristic
732C22C22×#4111yescharacteristic
733C22C22×#4111yescharacteristic
734C22C22×#4111yescharacteristic
735C22C2×H(5,𝔽2)11yescharacteristic
736C22C2×H(5,𝔽2)11yescharacteristic
737C22#58511yescharacteristic
738C4—22no—
739C4—22no—
740C4—22no—
741C4—22no—
742C4—22no—
743C4—22no—
744C4—22no—
745C4—22no—
746C4—22no—
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—
764C2—24no—
765C2—42no—
766C2—42no—
767C2—81no—
768C2—81no—
769C2#344411yescharacteristic
770C2C2×#55311yescharacteristic
771C2#347511yescharacteristic
772C2#348111yescharacteristic
773C2#349011yescharacteristic
774C2#350611yescharacteristic
775C2#351311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C25
prime radical#2424C2
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. #2852C2semidirect
3. #2849C2semidirect
4. #2608C2semidirect
5. #2602C2semidirect
6. #2597C2semidirect
7. #2595C2semidirect
8. #2587C2semidirect
9. #2573C2semidirect
10. #2559C2semidirect
11. #2554C2semidirect
12. #2526C2semidirect
13. #2518C2semidirect
14. #2505C2semidirect
15. #2480C2semidirect
16. #2470C2semidirect
17. #2466C2semidirect
18. #2444C2semidirect
20. #2411C2semidirect
21. #2411C2semidirect
22. #2374C2semidirect
23. #2373C2semidirect
24. #2363C2semidirect
25. #2359C2semidirect
26. #2359C2semidirect
27. #2357C2semidirect
28. C4×#120C2semidirect
29. #2296C2semidirect
30. #2290C2semidirect
31. C2×C4×C22⋊C4C2semidirect
34. C2×#126C22semidirect
49. C2×#117C22semidirect
54. #400C22semidirect
55. #400C22semidirect
56. #400C22semidirect
57. #400C22semidirect
58. #398C22semidirect
62. #397C22semidirect
63. #397C22semidirect
76. #394C22semidirect
83. #390C22semidirect
84. #390C22semidirect
85. #389C22semidirect
86. #389C22semidirect
87. #389C22semidirect
88. #389C22semidirect
89. #389C22semidirect
90. #389C22semidirect
91. #389C22semidirect
92. #389C22semidirect
93. #389C22semidirect
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. #388C22semidirect
116. #387C22semidirect
117. #387C22semidirect
118. #387C22semidirect
119. #387C22semidirect
120. #387C22semidirect
121. #387C22semidirect
122. #387C22semidirect
123. #387C22semidirect
124. #387C22semidirect
125. #387C22semidirect
126. #387C22semidirect
127. #387C22semidirect
139. #386C22semidirect
152. #385C22semidirect
153. #385C22semidirect
154. #383C22semidirect
155. #382C22semidirect
158. #381C22semidirect
162. C4×C4⋊C4C22semidirect
163. C4×C4⋊C4C22semidirect
164. C4×C4⋊C4C22semidirect
165. C4×C4⋊C4C22semidirect
166. C4×C4⋊C4C22semidirect
167. C4×C4⋊C4C22semidirect
168. C4×C4⋊C4C22semidirect
181. C4×C22⋊C4C22semidirect
182. C4×C22⋊C4C22semidirect
183. C4×C22⋊C4C22semidirect
184. #376C22semidirect

Maximal subgroups

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

subgroupindex
#28542
#28522
#28492
#26082
#26022
#25972
#25952
#25872
#25732
#25592
#25542
#25262
#25182
#25052
#24802
#24702
#24662
#24442
#24242
#24112
#23742
#23732
#23632
#23592
#23572
C4×#1202
#22962
#22902
C2×C4×C22⋊C42