Finite Group Databasebeta

← #7625823

Subgroups — #7625823

Order 512.

11006 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
1C2×#3487C211yesmaximal, characteristic
2C2×C4×2−1+4C211yesmaximal, characteristic, complemented
3C2×#3428C211yesmaximal, characteristic, complemented
4#34313C214yesmaximal, complemented
5#34312C214yesmaximal, complemented
6#34295C214yesmaximal, complemented
7#34295C214yesmaximal, complemented
8#34294C214yesmaximal, complemented
9#34293C214yesmaximal, complemented
10#34275C216yesmaximal, complemented
11#34269C216yesmaximal, complemented
12#34257C211yesmaximal, characteristic, complemented
13#34249C211yesmaximal, characteristic, complemented
14#34202C216yesmaximal, complemented
15C4×#550C214yesmaximal, complemented
16C4×#548C214yesmaximal, complemented
17#34136C216yesmaximal, complemented
18C2×#2341C211yesmaximal, characteristic, complemented
19C4×#519C211yesmaximal, characteristic, complemented
20C22×2−1+4C2211yescharacteristic
21C23×#41C2211yescharacteristic
22#3487C4132yescomplemented
23C2×#550C2214yes—
24C2×#550C2214yes—
25C2×#548C2214yes—
26C2×#548C2214yes—
27C2×#535C2216yes—
28C2×#525C2216yes—
29C4×2−1+4—216no—
30#3428—216no—
31C2×#520C2214yes—
32C2×#520C2214yes—
33C2×#520C2216yes—
34C2×#520C2214yescomplemented
35C2×#519C2211yescharacteristic
36C2×#519C2211yescharacteristic
37C2×#519C2211yescharacteristic
38C2×#519C2214yescomplemented
39C2×#518C2216yes—
40C2×C4×#41C2216yes—
41C2×C4×#41C2214yes—
42C2×C4×#41C2214yes—
43C2×C4×#41C2214yescomplemented
44C22×C4×Q8C2211yescharacteristic
45C22×C4×Q8C2211yescharacteristic
46C22×C4×Q8C2214yescomplemented
47C22×#117C2216yes—
48#2367C22112yescomplemented
49#2367C22112yescomplemented
50#2366C22112yescomplemented
51#2366C22112yescomplemented
52#2363C22112yescomplemented
53#2363C2216yescomplemented
54#2363C2216yescomplemented
55#2363C22112yescomplemented
56#2362C2216yescomplemented
57#2362C2216yescomplemented
58#2361C2216yescomplemented
59#2361C22112yescomplemented
60#2361C2216yescomplemented
61#2361C22112yescomplemented
62#2360C2216yescomplemented
63#2360C2216yescomplemented
64#2359C2214yes—
65#2359C22112yes—
66#2358C22112yes—
67#2358C22112yes—
68#2358C22124yes—
69#2354C22112yescomplemented
70#2352C22112yescomplemented
71#2352C22112yescomplemented
72#2351C2214yescomplemented
73#2351C2214yescomplemented
74Q8×C4⋊C4C2214yescomplemented
75Q8×C4⋊C4C2214yescomplemented
76D4×C4⋊C4C22112yescomplemented
77#2341C2214yes—
78#2341C2214yes—
79#2341C2214yes—
80#2341C2214yes—
81#2341C2214yescomplemented
82#2341C2214yescomplemented
83Q8×C22⋊C4C2214yescomplemented
84Q8×C22⋊C4C2214yescomplemented
85#2328C22112yescomplemented
86#2326C22112yescomplemented
87#2324C22112yescomplemented
88#2324C22112yescomplemented
89#2324C22112yescomplemented
90#2323C22112yescomplemented
91#2317C2216yes—
92#2311C2216yes—
93C4×#127C22112yescomplemented
94C4×#124C22112yescomplemented
95C4×C22⋊Q8C22112yescomplemented
96C4×#121C22112yescomplemented
97C4×#121C22112yescomplemented
98C4×#121C22112yescomplemented
99#2297C2216yes—
100#2296C2216yes—
101#2293C22112yescomplemented
102C2×#390C2213yes—
103C2×#390C2213yes—
104#2290C22112yescomplemented
105#2290C22112yescomplemented
106C2×#380C2213yes—
107#2276C2214yescomplemented
108#2276C2214yescomplemented
109#2274C2216yes—
110C42×Q8C2214yescomplemented
111C42×Q8C2214yescomplemented
112C42×D4C22112yescomplemented
113C4×#117C2216yes—
114C2×C4×C22⋊C4C2213yes—
115C2×2−1+4—28no—
116C2×2−1+4—28no—
117C2×2−1+4C2×C4116yescomplemented
118C22×#41—28no—
119C22×#41—28no—
120C22×#41C2×C4116yescomplemented
121C22×#41C2314yes—
122C22×#41C2314yes—
123C22×#41C2316yes—
124C22×#41C2314yes—
125C23×Q8C2314yes—
126C23×Q8C2311yescharacteristic
127C23×D4C2313yes—
128C24×C4C2313yes—
129#550C2×C4164yescomplemented
130#550C2×C4164yescomplemented
131#548C2×C4164yescomplemented
132#548C2×C4164yescomplemented
133#535C2×C4196yescomplemented
134C2×#127C23112yes—
135C2×#124C23112yes—
136#525C2×C4196yescomplemented
137C2×#123C2314yes—
138C2×C22⋊Q8C2316yes—
139C2×C22⋊Q8C2316yes—
140C2×#121C2316yes—
141C2×#121C23112yes—
142C2×#121C23112yes—
143C2×#121C2316yes—
144C2×#120C23112yes—
145#520—232no—
146#520—232no—
147#520—232no—
148#520—248no—
149#519—28no—
150#519—232no—
151#519C2×C4116yescomplemented
152#519D4116yescomplemented
153#518—248no—
154C4×#41—232no—
155C4×#41—232no—
156C4×#41—232no—
157C4×#41—248no—
158C2×C4×Q8—28no—
159C2×C4×Q8—28no—
160C2×C4×Q8—232no—
161C2×C4×Q8C23112yes—
162C2×C4×Q8C2314yes—
163C2×C4×Q8C2314yes—
164C2×C4×Q8C2314yes—
165C2×C4×Q8C2314yes—
166C2×C4×Q8C2314yes—
167C2×C4×Q8C2314yes—
168C2×C4×Q8C2316yes—
169C2×C4×Q8C2316yes—
170C2×C4×Q8C2314yes—
171C2×C4×Q8C2314yes—
172C2×C4×Q8C2314yes—
173C2×C4×Q8C2314yes—
174C2×C4×D4C23112yes—
175C2×C4×D4C23112yes—
176C2×C4×D4C23112yes—
177C2×C4×D4C2314yes—
178C2×C4×D4C23112yes—
179C2×C4×D4C23112yes—
180C2×C4×D4C2316yes—
181C2×C4×D4C2316yes—
182C2×C4×D4C23112yes—
183C2×C4×D4C23112yes—
184C2×C4×D4C23112yes—
185C2×C4×D4C23124yes—
186C2×C4×D4C23112yes—
187C2×C4×D4C23112yes—
188C2×#117—248no—
189C2×#117C2316yes—
190C2×#117C23112yes—
191C2×#117C23112yes—
192C2×#117C2316yes—
193C2×#117C23112yes—
194C2×#117C2316yes—
195C2×#117C2314yes—
196C2×#117C2316yes—
197C2×#117C2316yes—
198C22×C4⋊C4C2313yes—
199C22×C4⋊C4C2313yes—
200C22×C4⋊C4C2316yes—
201C22×C4⋊C4C23112yes—
202C22×C4⋊C4C2316yes—
203C22×C22⋊C4C23112yes—
204C22×C22⋊C4C2313yes—
205C22×C22⋊C4C2313yes—
206C22×C22⋊C4C2316yes—
207C22×C42C23112yes—
208C22×C42C2313yes—
209C22×C42C2313yes—
210C22×C42C23112yes—
211#391C23112yes—
212#391C2316yes—
213#391C2316yes—
214#390C2316yes—
215#390C23112yes—
216#390C23124yes—
217#390C23112yes—
218#390C23112yes—
219#390C23112yes—
220#390C23112yes—
221#390C23112yes—
222#390C2316yes—
223#390C23112yes—
224#389C23112yes—
225#389C23112yes—
226#389C23112yes—
227#389C2316yes—
228#389C2316yes—
229#389C2316yes—
230#389C2316yes—
231#389C2314yes—
232#388C23124yes—
233#388C23124yes—
234#388C23112yes—
235#388C23112yes—
236#388C23112yes—
237#388C23112yes—
238#388C23112yes—
239#388C23112yes—
240#388C2314yes—
241#388C2314yes—
242#387C23112yes—
243#387C23112yes—
244#387C2314yes—
245#387C2314yes—
246#386C23112yes—
247#386C23112yes—
248#386C23124yes—
249#386C23124yes—
250#386C23112yes—
251#386C23112yes—
252#386C2314yes—
253#386C23112yes—
254#385C23112yes—
255#385C23112yes—
256#385C23112yes—
257#385C23124yes—
258#385C23112yes—
259#385C2314yes—
260#385C2314yes—
261#384C23112yes—
262#382C23112yes—
263#380C23112yes—
264#380C23112yes—
265#380C23112yes—
266#380C23112yes—
267C4×C4⋊C4C23112yes—
268C4×C4⋊C4C23112yes—
269C4×C4⋊C4C23112yes—
270C4×C4⋊C4C23112yes—
271C4×C4⋊C4C23112yes—
272C4×C4⋊C4C23112yes—
273C4×C4⋊C4C23112yes—
274C4×C4⋊C4C2314yes—
275C4×C4⋊C4C2316yes—
276C4×C4⋊C4C2316yes—
277C4×C4⋊C4C2316yes—
278C4×C4⋊C4C2316yes—
279C4×C22⋊C4C23112yes—
280C4×C22⋊C4C23112yes—
281C4×C22⋊C4C2316yes—
282C4×C22⋊C4C2316yes—
283C4×C22⋊C4C2316yes—
284C4×C22⋊C4C2316yes—
285C4×C22⋊C4C23112yes—
286C4×C22⋊C4C23124yes—
287C4×C22⋊C4C2314yes—
288C4×C22⋊C4C23112yes—
289C4×C22⋊C4C23112yes—
290C4×C22⋊C4C23112yes—
291C4×C22⋊C4C2314yes—
292#376C23112yes—
293C2×#95C2311yescharacteristic
294C2×#95C2313yes—
295C43C23112yes—
296C25C2413yes—
2972−1+4—2128no—
298C2×#41—2128no—
299C2×#41—216no—
300C2×#41—216no—
301C2×#41—216no—
302C2×#41—216no—
303C2×#41—216no—
304C2×#41—216no—
305C2×#41—224no—
306C2×#41—224no—
307C2×#41C22×C4148yes—
308C2×#41C22×C4132yes—
309C2×#41C22×C4132yes—
310C2×#41C22×C4132yes—
311C22×Q8—216no—
312C22×Q8—216no—
313C22×Q8C22×C4132yes—
314C22×Q8C22×C418yes—
315C22×Q8C2×D418yes—
316C22×Q8#4118yes—
317C22×Q8C2416yes—
318C22×Q8C2414yes—
319C22×D4—212no—
320C22×D4—212no—
321C22×D4C22×C4124yes—
322C22×D4C2414yes—
323C22×D4C24112yes—
324C22×D4C2416yes—
325C22×D4C24112yes—
326C22×D4C24112yes—
327C23×C4—212no—
328C23×C4—212no—
329C23×C4C22×C4124yes—
330C23×C4C2411yescharacteristic
331C23×C4C2411yescharacteristic
332C23×C4C2414yes—
333C23×C4C2416yes—
334C23×C4C24112yes—
335C23×C4C2411yescharacteristic
336C23×C4C2416yes—
337C23×C4C2413yes—
338C23×C4C2413yes—
339C23×C4C24112yes—
340C23×C4C24112yes—
341C23×C4C24112yes—
342C23×C4C2413yes—
343#127C22×C4196yes—
344#124C22×C4196yes—
345#123C22×C4132yes—
346C22⋊Q8C22×C4148yes—
347C22⋊Q8C22×C4148yes—
348#121C22×C4148yes—
349#121C22×C4148yes—
350#121C22×C4196yes—
351#121C22×C4196yes—
352#120C22×C4196yes—
353C4×Q8—216no—
354C4×Q8—216no—
355C4×Q8—216no—
356C4×Q8—216no—
357C4×Q8—216no—
358C4×Q8—216no—
359C4×Q8—224no—
360C4×Q8—224no—
361C4×Q8—248no—
362C4×Q8C22×C4132yes—
363C4×Q8C22×C4132yes—
364C4×Q8C2×D4132yes—
365C4×Q8C2×D4132yes—
366C4×D4—224no—
367C4×D4—248no—
368C4×D4—248no—
369C4×D4—224no—
370C4×D4—216no—
371C4×D4—248no—
372C4×D4—248no—
373C4×D4—248no—
374C4×D4—248no—
375C4×D4—424no—
376C4×D4—424no—
377C4×D4—824no—
378C4×D4C22×C4196yes—
379C4×D4C22×C4196yes—
380#117—224no—
381#117—224no—
382#117—224no—
383#117—248no—
384#117—216no—
385#117—248no—
386#117—248no—
387#117C22×C4148yes—
388#117C2×D4148yes—
389C2×C4⋊C4—212no—
390C2×C4⋊C4—212no—
391C2×C4⋊C4—224no—
392C2×C4⋊C4—224no—
393C2×C4⋊C4—248no—
394C2×C4⋊C4C2414yes—
395C2×C4⋊C4C2414yes—
396C2×C4⋊C4C24112yes—
397C2×C4⋊C4C24112yes—
398C2×C4⋊C4C2416yes—
399C2×C4⋊C4C2416yes—
400C2×C4⋊C4C24112yes—
401C2×C4⋊C4C2414yes—
402C2×C4⋊C4C2414yes—
403C2×C4⋊C4C24112yes—
404C2×C4⋊C4C24112yes—
405C2×C4⋊C4C2414yes—
406C2×C4⋊C4C2416yes—
407C2×C4⋊C4C2416yes—
408C2×C4⋊C4C2414yes—
409C2×C4⋊C4C2414yes—
410C2×C4⋊C4C2416yes—
411C2×C4⋊C4C2416yes—
412C2×C22⋊C4—248no—
413C2×C22⋊C4—46no—
414C2×C22⋊C4—46no—
415C2×C22⋊C4—86no—
416C2×C22⋊C4C2414yes—
417C2×C22⋊C4C24112yes—
418C2×C22⋊C4C24112yes—
419C2×C22⋊C4C2416yes—
420C2×C22⋊C4C2416yes—
421C2×C22⋊C4C2414yes—
422C2×C22⋊C4C24112yes—
423C2×C22⋊C4C2414yes—
424C2×C22⋊C4C24124yes—
425C2×C22⋊C4C2416yes—
426C2×C22⋊C4C2416yes—
427C2×C22⋊C4C24112yes—
428C2×C22⋊C4C24112yes—
429C2×C22⋊C4C2414yes—
430C2×C22⋊C4C2414yes—
431C2×C22⋊C4C2414yes—
432C2×C22⋊C4C2414yes—
433C2×C22⋊C4C24112yes—
434C2×C22⋊C4C24112yes—
435C2×C22⋊C4C2414yes—
436C2×C42—212no—
437C2×C42—212no—
438C2×C42—248no—
439C2×C42—248no—
440C2×C42C2414yes—
441C2×C42C2414yes—
442C2×C42C24112yes—
443C2×C42C24112yes—
444C2×C42C2416yes—
445C2×C42C2414yes—
446C2×C42C2414yes—
447C2×C42C2416yes—
448C2×C42C2416yes—
449C2×C42C2416yes—
450C2×C42C24112yes—
451C2×C42C24112yes—
452C2×C42C2414yes—
453C2×C42C24112yes—
454C2×C42C24112yes—
455#95C2411yescharacteristic
456#95C2411yescharacteristic
457#95C2411yescharacteristic
458#95C2411yescharacteristic
459#95C2416yes—
460#95C2416yes—
461#95C2414yes—
462#95C2414yes—
463#95C24112yes—
464#95C24112yes—
465#95C2414yes—
466#95C2414yes—
467#95C24112yes—
468#95C2414yes—
469#95C24112yes—
470#95C24112yes—
471#95C24112yes—
472#95C2414yes—
473C24—26no—
474C24—26no—
475C24—43no—
476C24—43no—
477C24—43no—
478C24—43no—
479C24C23×C4112yes—
480C24C2516yes—
481C24C2514yes—
482C24C2511yescharacteristic
483#41—2128no—
484#41—2128no—
485#41—2128no—
486#41—2192no—
487C2×Q8—2128no—
488C2×Q8—212no—
489C2×Q8—212no—
490C2×Q8C4×D4164yescomplemented
491C2×Q8C23×C4124yes—
492C2×Q8C23×C4116yes—
493C2×Q8C22×D4116yes—
494C2×Q8C2×#41116yes—
495C2×D4—28no—
496C2×D4—28no—
497C2×D4—296no—
498C2×D4—224no—
499C2×D4—212no—
500C2×D4—224no—
501C2×D4—212no—
502C2×D4—412no—
503C2×D4—412no—
504C2×D4—412no—
505C2×D4—412no—
506C2×D4C23×C4116yes—
507C2×D4C23×C4148yes—
508C2×D4C23×C4124yes—
509C2×D4C23×C4148yes—
510C2×D4C23×C4148yes—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—296no—
514C22×C4—212no—
515C22×C4—224no—
516C22×C4—212no—
517C22×C4—212no—
518C22×C4—212no—
519C22×C4—224no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—26no—
523C22×C4—26no—
524C22×C4—28no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—28no—
528C22×C4—224no—
529C22×C4—224no—
530C22×C4—224no—
531C22×C4—41no—
532C22×C4—44no—
533C22×C4—41no—
534C22×C4—43no—
535C22×C4—43no—
536C22×C4—43no—
537C22×C4—43no—
538C22×C4—412no—
539C22×C4—412no—
540C22×C4—412no—
541C22×C4—412no—
542C22×C4—412no—
543C22×C4—412no—
544C22×C4C23×C4148yes—
545C22×C4C23×C4124yes—
546C22×C4C23×C4124yes—
547C22×C4C23×C414yes—
548C22×C4C23×C4112yes—
549C22×C4C22×D4112yes—
550C22×C4C2×#41112yes—
551C22×C4C2511yescharacteristic
552C22×C4C2516yes—
553C22×C4C2514yes—
554C22×C4C2511yescharacteristic
555C22×C4C2514yes—
556C22×C4C2516yes—
557C22×C4C2511yescharacteristic
558C22×C4C2514yes—
559C22×C4C2514yes—
560C22×C4C2514yes—
561C22×C4C2511yescharacteristic
562C22×C4C2514yes—
563C22×C4C2514yes—
564C22×C4C2511yescharacteristic
565C22×C4C2511yescharacteristic
566C22×C4C2516yes—
567C4⋊C4—28no—
568C4⋊C4—28no—
569C4⋊C4—224no—
570C4⋊C4—224no—
571C4⋊C4—212no—
572C4⋊C4—212no—
573C4⋊C4—28no—
574C4⋊C4—224no—
575C4⋊C4—28no—
576C4⋊C4—44no—
577C4⋊C4—412no—
578C4⋊C4—412no—
579C4⋊C4C23×C4124yes—
580C4⋊C4C23×C4124yes—
581C4⋊C4C23×C4116yes—
582C4⋊C4C23×C4116yes—
583C4⋊C4C22×D4124yes—
584C4⋊C4C22×D4124yes—
585C22⋊C4—28no—
586C22⋊C4—224no—
587C22⋊C4—224no—
588C22⋊C4—28no—
589C22⋊C4—224no—
590C22⋊C4—212no—
591C22⋊C4—212no—
592C22⋊C4—28no—
593C22⋊C4—46no—
594C22⋊C4—46no—
595C22⋊C4—424no—
596C22⋊C4—44no—
597C22⋊C4—412no—
598C22⋊C4—412no—
599C22⋊C4C23×C4116yes—
600C22⋊C4C23×C4116yes—
601C22⋊C4C23×C4116yes—
602C22⋊C4C23×C4148yes—
603C22⋊C4C23×C4148yes—
604C22⋊C4C22×D4116yes—
605C42—28no—
606C42—28no—
607C42—28no—
608C42—212no—
609C42—224no—
610C42—224no—
611C42—212no—
612C42—212no—
613C42—212no—
614C42—28no—
615C42—44no—
616C42—412no—
617C42—412no—
618C42C23×C4148yes—
619C42C22×D4148yes—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—24no—
625C23—26no—
626C23—24no—
627C23—26no—
628C23—26no—
629C23—26no—
630C23—24no—
631C23—24no—
632C23—26no—
633C23—24no—
634C23—24no—
635C23—26no—
636C23—224no—
637C23—412no—
638C23—412no—
639C23—86no—
640C23—86no—
641C23—86no—
642C23—86no—
643C23C24×C4112yes—
644C23C24×C418yes—
645C23C24×C412yes—
646C23C23×D412yes—
647C23C22×#4112yes—
648C23C2611yescharacteristic
649Q8—248no—
650Q8C2×C4×D4164yes—
651D4—232no—
652D4—296no—
653D4—248no—
654D4—448no—
655D4—448no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—24no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—21no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—21no—
674C2×C4—28no—
675C2×C4—248no—
676C2×C4—248no—
677C2×C4—296no—
678C2×C4—21no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—26no—
682C2×C4—21no—
683C2×C4—26no—
684C2×C4—26no—
685C2×C4—26no—
686C2×C4—24no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—24no—
690C2×C4—26no—
691C2×C4—26no—
692C2×C4—24no—
693C2×C4—21no—
694C2×C4—24no—
695C2×C4—21no—
696C2×C4—416no—
697C2×C4—44no—
698C2×C4—44no—
699C2×C4—824no—
700C2×C4—824no—
701C2×C4—824no—
702C2×C4—86no—
703C2×C4—86no—
704C2×C4C2×C4×D4148yes—
705C2×C4C24×C418yes—
706C2×C4C24×C418yes—
707C2×C4C24×C418yes—
708C2×C4C24×C412yes—
709C2×C4C24×C412yes—
710C2×C4C24×C4112yes—
711C2×C4C23×D418yes—
712C2×C4C23×D418yes—
713C2×C4C23×D4112yes—
714C2×C4C22×#41112yes—
715C2×C4#58512yes—
716C2×C4#58512yes—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—28no—
724C22—212no—
725C22—28no—
726C22—212no—
727C22—28no—
728C22—212no—
729C22—44no—
730C22—46no—
731C22—44no—
732C22—46no—
733C22—44no—
734C22—46no—
735C22—44no—
736C22—46no—
737C22—824no—
738C22C22×C4×D414yes—
739C22C25×C411yescharacteristic
740C22C24×D411yescharacteristic
741C22C23×#4111yescharacteristic
742C22C2×#58511yescharacteristic
743C22C2×#58511yescharacteristic
744C22H(7,𝔽2)11yescharacteristic
745C222−1+611yescharacteristic
746C4—22no—
747C4—28no—
748C4—28no—
749C4—22no—
750C4—22no—
751C4—22no—
752C4—28no—
753C4—28no—
754C4—28no—
755C4—41no—
756C4—44no—
757C4—44no—
758C4—46no—
759C4—41no—
760C4—46no—
761C4C22×C4×D4124yes—
762C2—24no—
763C2—48no—
764C2—412no—
765C2C23×C4×D411yescharacteristic
766C2C4×#58511yescharacteristic
767C2#6265411yescharacteristic
768C2#6300211yescharacteristic
769C2#6300311yescharacteristic
770C2#6300511yescharacteristic
771C2#6300611yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC23C26
commutatorC22C25×C4
prime radicalC2×#3487C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×C4×2−1+4C2semidirect
3. C2×#3428C2semidirect
4. #34313C2semidirect
5. #34312C2semidirect
6. #34295C2semidirect
7. #34295C2semidirect
8. #34294C2semidirect
9. #34293C2semidirect
10. #34275C2semidirect
11. #34269C2semidirect
12. #34257C2semidirect
13. #34249C2semidirect
14. #34202C2semidirect
15. C4×#550C2semidirect
16. C4×#548C2semidirect
17. #34136C2semidirect
18. C2×#2341C2semidirect
19. C4×#519C2semidirect
22. #3487C4semidirect
34. C2×#520C22semidirect
38. C2×#519C22semidirect
43. C2×C4×#41C22semidirect
46. C22×C4×Q8C22semidirect
48. #2367C22semidirect
49. #2367C22semidirect
50. #2366C22semidirect
51. #2366C22semidirect
52. #2363C22semidirect
53. #2363C22semidirect
54. #2363C22semidirect
55. #2363C22semidirect
56. #2362C22semidirect
57. #2362C22semidirect
58. #2361C22semidirect
59. #2361C22semidirect
60. #2361C22semidirect
61. #2361C22semidirect
62. #2360C22semidirect
63. #2360C22semidirect
69. #2354C22semidirect
70. #2352C22semidirect
71. #2352C22semidirect
72. #2351C22semidirect
73. #2351C22semidirect
74. Q8×C4⋊C4C22semidirect
75. Q8×C4⋊C4C22semidirect
76. D4×C4⋊C4C22semidirect
81. #2341C22semidirect
82. #2341C22semidirect
83. Q8×C22⋊C4C22semidirect
84. Q8×C22⋊C4C22semidirect
85. #2328C22semidirect
86. #2326C22semidirect
87. #2324C22semidirect
88. #2324C22semidirect
89. #2324C22semidirect
90. #2323C22semidirect
93. C4×#127C22semidirect
94. C4×#124C22semidirect
95. C4×C22⋊Q8C22semidirect
96. C4×#121C22semidirect
97. C4×#121C22semidirect
98. C4×#121C22semidirect
101. #2293C22semidirect
104. #2290C22semidirect
105. #2290C22semidirect
107. #2276C22semidirect
108. #2276C22semidirect
110. C42×Q8C22semidirect
111. C42×Q8C22semidirect
112. C42×D4C22semidirect
117. C2×2−1+4C2×C4semidirect
120. C22×#41C2×C4semidirect
129. #550C2×C4semidirect
130. #550C2×C4semidirect
131. #548C2×C4semidirect
132. #548C2×C4semidirect
133. #535C2×C4semidirect
136. #525C2×C4semidirect
151. #519C2×C4semidirect
152. #519D4semidirect
490. C2×Q8C4×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#34872
C2×C4×2−1+42
C2×#34282
#343132
#343122
#342952
#342942
#342932
#342752
#342692
#342572
#342492
#342022
C4×#5502
C4×#5482
#341362
C2×#23412
C4×#5192