Finite Group Databasebeta

← #40888

Subgroups — #40888

Order 256.

973 conjugacy classes of subgroups.

The subgroup lattice has 773 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2830C211yesmaximal, characteristic, complemented
2#2827C211yesmaximal, characteristic, complemented
3#2800C211yesmaximal, characteristic, complemented
4#2788C211yesmaximal, characteristic, complemented
5#2781C211yesmaximal, characteristic, complemented
6#2768C211yesmaximal, characteristic, complemented
7#2735C211yesmaximal, characteristic, complemented
8#2735C211yesmaximal, characteristic, complemented
9#2727C211yesmaximal, characteristic, complemented
10#2702C211yesmaximal, characteristic, complemented
11#2652C211yesmaximal, characteristic, complemented
12#2651C211yesmaximal, characteristic, complemented
13#2649C211yesmaximal, characteristic, complemented
14#2626C211yesmaximal, characteristic, complemented
15#2623C211yesmaximal, characteristic, complemented
16#2587C211yesmaximal, characteristic, complemented
17#2561C211yesmaximal, characteristic, complemented
18#2488C211yesmaximal, characteristic, complemented
19#2486C211yesmaximal, characteristic, complemented
20#2482C211yesmaximal, characteristic, complemented
21#2481C211yesmaximal, characteristic, complemented
22#2480C211yesmaximal, characteristic, complemented
23#2480C211yesmaximal, characteristic, complemented
24#2449C211yesmaximal, characteristic, complemented
25#2413C211yesmaximal, characteristic, complemented
26#2405C211yesmaximal, characteristic
27#2405C211yesmaximal, characteristic
28C2×#396C211yesmaximal, characteristic, complemented
29#2359C211yesmaximal, characteristic, complemented
30D4×C22⋊C4C211yesmaximal, characteristic
31#2322C211yesmaximal, characteristic, complemented
32C23×D4C2211yescharacteristic
33C2×#126C2211yescharacteristic, complemented
34C2×#126C2211yescharacteristic, complemented
35C2×#123C2211yescharacteristic
36C2×#123C2211yescharacteristic
37C2×#123C2211yescharacteristic
38C2×#123C2211yescharacteristic
39C2×C22⋊Q8C2211yescharacteristic, complemented
40C2×C22⋊Q8C2211yescharacteristic, complemented
41C2×C4×D4C2211yescharacteristic
42C2×C4×D4C2211yescharacteristic
43C2×#117C2211yescharacteristic, complemented
44C22×C4⋊C4C2211yescharacteristic, complemented
45C22×C4⋊C4C2211yescharacteristic, complemented
46C22×C4⋊C4C2211yescharacteristic, complemented
47C22×C22⋊C4C2211yescharacteristic
48C22×C22⋊C4C2211yescharacteristic
49C22×C22⋊C4C2211yescharacteristic
50C22×C22⋊C4C2211yescharacteristic
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#399C2211yescharacteristic, complemented
61#399C2211yescharacteristic, complemented
62#398C2211yescharacteristic, complemented
63#398C2211yescharacteristic, complemented
64#398C2211yescharacteristic, complemented
65#398C2211yescharacteristic, complemented
66#398C2211yescharacteristic, complemented
67#398C2211yescharacteristic, complemented
68#398C2211yescharacteristic, complemented
69#397C2211yescharacteristic
70#397C2211yescharacteristic
71#397C2211yescharacteristic
72#397C2211yescharacteristic, complemented
73#397C2211yescharacteristic, complemented
74#397C2211yescharacteristic, complemented
75#397C2211yescharacteristic, complemented
76#397C2211yescharacteristic, complemented
77#397C2211yescharacteristic, complemented
78#397C2211yescharacteristic, complemented
79#397C2211yescharacteristic, complemented
80#397C2211yescharacteristic, complemented
81#397C2211yescharacteristic, complemented
82#396C2211yescharacteristic
83#396C2211yescharacteristic
84#396C2211yescharacteristic
85#396C2211yescharacteristic
86#396C2211yescharacteristic
87#396C2211yescharacteristic, complemented
88#396C2211yescharacteristic, complemented
89#396C2211yescharacteristic, complemented
90#396C2211yescharacteristic, complemented
91#396C2211yescharacteristic, complemented
92#396C2211yescharacteristic, complemented
93#396C2211yescharacteristic, complemented
94#396C2211yescharacteristic, complemented
95#395C2211yescharacteristic, complemented
96#394C2211yescharacteristic
97#394C2211yescharacteristic
98#394C2211yescharacteristic
99#394C2211yescharacteristic
100#394C2211yescharacteristic
101#394C2211yescharacteristic
102#394C2211yescharacteristic
103#394C2211yescharacteristic
104#393C2211yescharacteristic
105#393C2211yescharacteristic, complemented
106#393C2211yescharacteristic, complemented
107#391C2211yescharacteristic, complemented
108#390C2211yescharacteristic
109#390C2211yescharacteristic
110#389C2211yescharacteristic, complemented
111#389C2211yescharacteristic, complemented
112#389C2211yescharacteristic, complemented
113#389C2211yescharacteristic, complemented
114#389C2211yescharacteristic, complemented
115#389C2211yescharacteristic, complemented
116#389C2211yescharacteristic, complemented
117#389C2211yescharacteristic, complemented
118#388C2211yescharacteristic
119#388C2211yescharacteristic
120#388C2211yescharacteristic
121#388C2211yescharacteristic
122#388C2211yescharacteristic
123#388C2211yescharacteristic
124#388C2211yescharacteristic, complemented
125#388C2211yescharacteristic, complemented
126#388C2211yescharacteristic, complemented
127#388C2211yescharacteristic, complemented
128#388C2211yescharacteristic, complemented
129#388C2211yescharacteristic, complemented
130#388C2211yescharacteristic, complemented
131#388C2211yescharacteristic, complemented
132#388C2211yescharacteristic, complemented
133#388C2211yescharacteristic, complemented
134#388C2211yescharacteristic, complemented
135#388C2211yescharacteristic, complemented
136#388C2211yescharacteristic, complemented
137#388C2211yescharacteristic, complemented
138#387C2211yescharacteristic, complemented
139#387C2211yescharacteristic, complemented
140#387C2211yescharacteristic, complemented
141#387C2211yescharacteristic, complemented
142#387C2211yescharacteristic, complemented
143#387C2211yescharacteristic, complemented
144#387C2211yescharacteristic, complemented
145#386C2211yescharacteristic
146#386C2211yescharacteristic
147#386C2211yescharacteristic
148#386C2211yescharacteristic
149#386C2211yescharacteristic
150#386C2211yescharacteristic
151#386C2211yescharacteristic
152#386C2211yescharacteristic
153#385C2211yescharacteristic
154#385C2211yescharacteristic
155#385C2211yescharacteristic
156#385C2211yescharacteristic
157#385C2211yescharacteristic, complemented
158#385C2211yescharacteristic, complemented
159#385C2211yescharacteristic, complemented
160#385C2211yescharacteristic, complemented
161#385C2211yescharacteristic, complemented
162#385C2211yescharacteristic, complemented
163#385C2211yescharacteristic, complemented
164#385C2211yescharacteristic, complemented
165#382C2211yescharacteristic, complemented
166#381C2211yescharacteristic, complemented
167#381C2211yescharacteristic, complemented
168#381C2211yescharacteristic, complemented
169#380C2211yescharacteristic
170#380C2211yescharacteristic, complemented
171#380C2211yescharacteristic, complemented
172#380C2211yescharacteristic, complemented
173#379C2211yescharacteristic
174#379C2211yescharacteristic
175#379C2211yescharacteristic
176#379C2211yescharacteristic
177#379C2211yescharacteristic
178#379C2211yescharacteristic
179#379C2211yescharacteristic
180#379C2211yescharacteristic
181C4×C4⋊C4C2211yescharacteristic, complemented
182C4×C22⋊C4C2211yescharacteristic
183C4×C22⋊C4C2211yescharacteristic, complemented
184C4×C22⋊C4C2211yescharacteristic, complemented
185C4×C22⋊C4C2211yescharacteristic, complemented
186C2×#95C2211yescharacteristic, complemented
187C25C2311yescharacteristic
188C25C2311yescharacteristic
189C22×Q8C2311yescharacteristic
190C22×D4—24no—
191C22×D4—42no—
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
206#126—42no—
207#126—42no—
208#123—24no—
209#123—24no—
210#123—42no—
211#123—42no—
212C22⋊Q8—42no—
213C22⋊Q8—42no—
214C4×D4—42no—
215C4×D4—42no—
216#117—42no—
217C2×C4⋊C4—42no—
218C2×C4⋊C4—42no—
219C2×C4⋊C4—42no—
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×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×C22⋊C4—42no—
258C2×C22⋊C4—42no—
259C2×C22⋊C4—42no—
260C2×C22⋊C4—42no—
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×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
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—41no—
370C24—41no—
371C24—41no—
372C24—41no—
373C24—41no—
374C24—41no—
375C24—41no—
376C24—41no—
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—41no—
393C2×D4—41no—
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—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×C4C2411yescharacteristic
426C22×C4C2411yescharacteristic
427C22×C4C2411yescharacteristic
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
451C4⋊C4—22no—
452C4⋊C4—22no—
453C4⋊C4—22no—
454C4⋊C4—22no—
455C4⋊C4—22no—
456C4⋊C4—22no—
457C4⋊C4—22no—
458C4⋊C4—22no—
459C4⋊C4—41no—
460C4⋊C4—41no—
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—
481C4⋊C4—41no—
482C4⋊C4—41no—
483C4⋊C4—41no—
484C4⋊C4—41no—
485C4⋊C4—41no—
486C4⋊C4—41no—
487C4⋊C4—41no—
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—22no—
502C22⋊C4—22no—
503C22⋊C4—22no—
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—
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—
540C42—41no—
541C42—41no—
542C42—41no—
543C42—41no—
544C42—41no—
545C42—41no—
546C42—41no—
547C42—41no—
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—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—82no—
585C23—82no—
586C23—82no—
587C23—82no—
588C23—82no—
589C23—82no—
590C23—82no—
591C23—82no—
592C23C2×#4112yes—
593C23C2×#4112yes—
594C23H(5,𝔽2)12yes—
595C23H(5,𝔽2)12yes—
596C232−1+412yes—
597C23C2511yescharacteristic
598Q8—82no—
599D4—28no—
600D4—44no—
601D4—44no—
602D4—44no—
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—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—44no—
680C2×C4—44no—
681C2×C4—44no—
682C2×C4—44no—
683C2×C4—44no—
684C2×C4—82no—
685C2×C4—82no—
686C2×C4—82no—
687C2×C4—82no—
688C2×C4C2×#4112yes—
689C2×C4H(5,𝔽2)12yes—
690C22—22no—
691C22—22no—
692C22—22no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—22no—
697C22—22no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
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—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—88no—
725C22—88no—
726C22#53814yes—
727C22C22×#4111yescharacteristic
728C22C2×H(5,𝔽2)11yescharacteristic
729C22C2×H(5,𝔽2)11yescharacteristic
730C22C2×H(5,𝔽2)11yescharacteristic
731C22C2×2−1+411yescharacteristic
732C22#58511yescharacteristic
733C22#58511yescharacteristic
734C4—22no—
735C4—22no—
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—
755C4—41no—
756C4—41no—
757C4—41no—
758C4—41no—
759C4—41no—
760C2—24no—
761C2—42no—
762C2—42no—
763C2—81no—
764C2—81no—
765C2C2×#53811yescharacteristic
766C2#352011yescharacteristic
767C2#352111yescharacteristic
768C2#353411yescharacteristic
769C2#353511yescharacteristic
770C2#353511yescharacteristic
771C2#354211yescharacteristic
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. #2830C2semidirect
2. #2827C2semidirect
3. #2800C2semidirect
4. #2788C2semidirect
5. #2781C2semidirect
6. #2768C2semidirect
7. #2735C2semidirect
8. #2735C2semidirect
9. #2727C2semidirect
10. #2702C2semidirect
11. #2652C2semidirect
12. #2651C2semidirect
13. #2649C2semidirect
14. #2626C2semidirect
15. #2623C2semidirect
16. #2587C2semidirect
17. #2561C2semidirect
18. #2488C2semidirect
19. #2486C2semidirect
20. #2482C2semidirect
21. #2481C2semidirect
22. #2480C2semidirect
23. #2480C2semidirect
24. #2449C2semidirect
25. #2413C2semidirect
28. C2×#396C2semidirect
29. #2359C2semidirect
31. #2322C2semidirect
33. C2×#126C22semidirect
34. C2×#126C22semidirect
39. C2×C22⋊Q8C22semidirect
40. C2×C22⋊Q8C22semidirect
43. C2×#117C22semidirect
44. C22×C4⋊C4C22semidirect
45. C22×C4⋊C4C22semidirect
46. C22×C4⋊C4C22semidirect
51. #400C22semidirect
52. #400C22semidirect
53. #400C22semidirect
54. #400C22semidirect
55. #400C22semidirect
56. #400C22semidirect
58. #399C22semidirect
59. #399C22semidirect
60. #399C22semidirect
61. #399C22semidirect
62. #398C22semidirect
63. #398C22semidirect
64. #398C22semidirect
65. #398C22semidirect
66. #398C22semidirect
67. #398C22semidirect
68. #398C22semidirect
72. #397C22semidirect
73. #397C22semidirect
74. #397C22semidirect
75. #397C22semidirect
76. #397C22semidirect
77. #397C22semidirect
78. #397C22semidirect
79. #397C22semidirect
80. #397C22semidirect
81. #397C22semidirect
87. #396C22semidirect
88. #396C22semidirect
89. #396C22semidirect
90. #396C22semidirect
91. #396C22semidirect
92. #396C22semidirect
93. #396C22semidirect
94. #396C22semidirect
95. #395C22semidirect
105. #393C22semidirect
106. #393C22semidirect
107. #391C22semidirect
110. #389C22semidirect
111. #389C22semidirect
112. #389C22semidirect
113. #389C22semidirect
114. #389C22semidirect
115. #389C22semidirect
116. #389C22semidirect
117. #389C22semidirect
124. #388C22semidirect
125. #388C22semidirect
126. #388C22semidirect
127. #388C22semidirect
128. #388C22semidirect
129. #388C22semidirect
130. #388C22semidirect
131. #388C22semidirect
132. #388C22semidirect
133. #388C22semidirect
134. #388C22semidirect
135. #388C22semidirect
136. #388C22semidirect
137. #388C22semidirect
138. #387C22semidirect
139. #387C22semidirect
140. #387C22semidirect
141. #387C22semidirect
142. #387C22semidirect
143. #387C22semidirect
144. #387C22semidirect
157. #385C22semidirect
158. #385C22semidirect
159. #385C22semidirect
160. #385C22semidirect
161. #385C22semidirect
162. #385C22semidirect
163. #385C22semidirect
164. #385C22semidirect
165. #382C22semidirect
166. #381C22semidirect
167. #381C22semidirect
168. #381C22semidirect
170. #380C22semidirect
171. #380C22semidirect
172. #380C22semidirect
181. 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
#28302
#28272
#28002
#27882
#27812
#27682
#27352
#27272
#27022
#26522
#26512
#26492
#26262
#26232
#25872
#25612
#24882
#24862
#24822
#24812
#24802
#24492
#24132
#24052
C2×#3962
#23592
D4×C22⋊C42
#23222