Finite Group Databasebeta

← #7626604

Subgroups — #7626604

Order 512.

6974 conjugacy classes of subgroups.

The subgroup lattice has 811 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#552C211yesmaximal, characteristic
2#34482C218yesmaximal, complemented
3#34465C218yesmaximal, complemented
4#34462C218yesmaximal, complemented
5#34381C214yesmaximal, complemented
6#34378C214yesmaximal, complemented
7#34376C214yesmaximal
8#34314C218yesmaximal, complemented
9#34217C212yesmaximal, complemented
10#34203C212yesmaximal, complemented
11#34203C212yesmaximal, complemented
12#34182C211yesmaximal, characteristic, complemented
13#34180C214yesmaximal, complemented
14#34179C211yesmaximal, characteristic, complemented
15#34178C211yesmaximal, characteristic, complemented
16D4×#117C212yesmaximal
17#34059C211yesmaximal, characteristic, complemented
18#34052C211yesmaximal, characteristic, complemented
19C2×#2316C211yesmaximal, characteristic, complemented
20C2×#552C4132yescomplemented
21C2×#552C2214yes—
22C2×#552C2214yes—
23C2×#552C2214yes—
24C2×#552C2214yes—
25C22×#126C2212yes—
26C22×#125C2212yes—
27C22×#125C2211yescharacteristic
28C22×#123C2212yes—
29C22×C22⋊Q8C2211yescharacteristic
30C22×C22⋊Q8C2211yescharacteristic
31C2×#519C2212yes—
32C22×C4×Q8C2211yescharacteristic
33C22×C4×D4C2211yescharacteristic
34C22×#117C2212yes—
35C22×#117C2212yes—
36C22×#117C2211yescharacteristic
37C22×#117C2212yes—
38C23×C4⋊C4C2211yescharacteristic
39#2383C22116yescomplemented
40#2382C22116yescomplemented
41#2376C22116yes—
42#2373C22116yescomplemented
43#2370C22116yescomplemented
44#2370C2218yescomplemented
45#2370C2218yescomplemented
46#2362C2218yescomplemented
47#2362C2218yescomplemented
48#2360C2218yescomplemented
49#2360C2218yescomplemented
50#2359C22116yes—
51#2354C2214yes—
52#2352C2214yes—
53#2352C2214yes—
54#2351C2218yescomplemented
55Q8×C4⋊C4C2218yescomplemented
56D4×C4⋊C4C2214yes—
57#2347C2218yescomplemented
58#2347C2218yescomplemented
59#2346C2218yescomplemented
60#2346C2218yescomplemented
61#2345C2218yes—
62#2345C2218yes—
63#2345C2218yescomplemented
64#2344C2214yes—
65#2344C2218yes—
66#2344C2218yes—
67#2344C2218yescomplemented
68#2343C2218yescomplemented
69#2343C2218yescomplemented
70#2342C2218yes—
71#2342C2218yes—
72#2342C2214yes—
73#2342C2214yes—
74D4×C22⋊C4C2214yes—
75#2336C22116yescomplemented
76#2335C22116yes—
77#2334C22116yescomplemented
78#2334C22116yescomplemented
79#2330C22116yescomplemented
80#2330C2218yescomplemented
81#2323C2218yescomplemented
82#2323C2218yescomplemented
83#2322C22116yes—
84#2320C2218yescomplemented
85#2317C2218yescomplemented
86#2317C2218yescomplemented
87#2316C2211yescharacteristic
88#2316C2214yes—
89#2316C2211yescharacteristic
90#2316C2212yes—
91#2316C2211yescharacteristic
92#2316C2212yes—
93#2316C2211yescharacteristic
94#2316C2214yes—
95#2316C2218yescomplemented
96#2315C2214yes—
97#2314C2218yescomplemented
98#2314C2218yescomplemented
99#2313C2214yes—
100#2313C2214yes—
101#2312C2214yes—
102#2310C2212yes—
103C4×#125C2218yescomplemented
104C4×C22⋊Q8C2218yescomplemented
105C4×C22⋊Q8C2218yescomplemented
106#2296C2218yescomplemented
107#2295C2218yescomplemented
108#2293C2214yes—
109C2×#389C2218yescomplemented
110#2290C2214yes—
111#2290C2214yes—
112#2285C2214yes—
113#2285C2212yes—
114#2285C2214yes—
115#2283C2214yes—
116#2283C2214yes—
117#2280C2214yes—
118#2280C2212yes—
119#2280C2212yes—
120C2×#380C2214yes—
121#2274C2212yes—
122#2274C2212yes—
123#2274C2218yescomplemented
124C42×D4C2214yes—
125C4×#117C2212yes—
126C23×Q8C2311yescharacteristic
127C23×D4C2311yescharacteristic
128C24×C4C2311yescharacteristic
129C24×C4C2311yescharacteristic
130C24×C4C2312yes—
131#552C2×C4164yescomplemented
132#552C2×C4164yescomplemented
133#552C2×C4164yescomplemented
134#552C2×C4164yescomplemented
135C2×#126C2×C4132yescomplemented
136C2×#126C2318yes—
137C2×#126C2318yes—
138C2×#125C2×C4132yescomplemented
139C2×#125C2×C4116yescomplemented
140C2×#125C2314yes—
141C2×#125C2314yes—
142C2×#125C2318yes—
143C2×#125C2318yes—
144C2×#123C2×C4132yes—
145C2×#123C2318yes—
146C2×#123C2318yes—
147C2×C22⋊Q8C2×C4116yescomplemented
148C2×C22⋊Q8C2×C4116yescomplemented
149C2×C22⋊Q8C2314yes—
150C2×C22⋊Q8C2314yes—
151C2×C22⋊Q8C2314yes—
152C2×C22⋊Q8C2314yes—
153#519—48no—
154C2×C4×Q8C2×C4116yescomplemented
155C2×C4×Q8C2318yes—
156C2×C4×Q8C2318yes—
157C2×C4×Q8C2314yes—
158C2×C4×Q8C2314yes—
159C2×C4×D4C2×C4116yes—
160C2×C4×D4C2318yes—
161C2×C4×D4C2312yes—
162C2×C4×D4C2312yes—
163C2×C4×D4C2312yes—
164C2×C4×D4C2312yes—
165C2×#117—48no—
166C2×#117—48no—
167C2×#117C2×C4116yescomplemented
168C2×#117C2×C4132yescomplemented
169C2×#117C2312yes—
170C2×#117C2312yes—
171C2×#117C2312yes—
172C2×#117C2312yes—
173C2×#117C2314yes—
174C2×#117C2318yes—
175C2×#117C2314yes—
176C2×#117C2314yes—
177C2×#117C2314yes—
178C2×#117C2318yes—
179C2×#117C2314yes—
180C2×#117C2314yes—
181C2×#117C2314yes—
182C2×#117C2314yes—
183C2×#117C2314yes—
184C2×#117C2314yes—
185C2×#117C2314yes—
186C2×#117C2314yes—
187C22×C4⋊C4C2×C4116yescomplemented
188C22×C4⋊C4C2314yes—
189C22×C4⋊C4C2318yes—
190C22×C4⋊C4C2314yes—
191C22×C4⋊C4C2312yes—
192C22×C4⋊C4C2312yes—
193C22×C4⋊C4C2311yescharacteristic
194C22×C4⋊C4C2311yescharacteristic
195C22×C4⋊C4C2311yescharacteristic
196C22×C4⋊C4C2314yes—
197C22×C4⋊C4C2312yes—
198C22×C4⋊C4C2311yescharacteristic
199C22×C4⋊C4C2312yes—
200C22×C4⋊C4C2314yes—
201C22×C4⋊C4C2312yes—
202C22×C4⋊C4C2312yes—
203C22×C22⋊C4C2314yes—
204C22×C22⋊C4C2314yes—
205C22×C22⋊C4C2312yes—
206C22×C22⋊C4C2311yescharacteristic
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2311yescharacteristic
209C22×C22⋊C4C2312yes—
210C22×C42C2314yes—
211C22×C42C2314yes—
212C22×C42C2312yes—
213C22×C42C2312yes—
214C22×C42C2311yescharacteristic
215#391C2318yes—
216#391C2318yes—
217#390C2318yes—
218#389C2318yes—
219#389C2318yes—
220#389C2318yes—
221#389C23116yes—
222#389C2318yes—
223#389C2318yes—
224#389C23116yes—
225#389C2318yes—
226#389C2318yes—
227#389C2318yes—
228#389C23116yes—
229#389C23116yes—
230#389C23116yes—
231#389C23116yes—
232#389C23116yes—
233#389C23116yes—
234#389C2318yes—
235#388C23116yes—
236#388C23116yes—
237#388C2318yes—
238#388C2318yes—
239#388C23116yes—
240#388C23116yes—
241#388C23116yes—
242#388C23116yes—
243#388C2318yes—
244#388C2318yes—
245#387C23116yes—
246#387C23116yes—
247#387C23116yes—
248#387C23116yes—
249#387C23116yes—
250#387C23116yes—
251#387C23116yes—
252#387C23116yes—
253#387C23116yes—
254#387C23116yes—
255#387C2318yes—
256#387C23116yes—
257#387C23116yes—
258#387C2318yes—
259#386C2318yes—
260#386C2318yes—
261#385C23116yes—
262#385C23116yes—
263#385C2318yes—
264#385C23116yes—
265#385C23116yes—
266#385C2318yes—
267#384C2318yes—
268#384C2318yes—
269#384C2314yes—
270#383C2318yes—
271#383C2318yes—
272#382C2314yes—
273#382C2318yes—
274#382C2318yes—
275#382C2318yes—
276#382C2318yes—
277#381C2318yes—
278#381C2314yes—
279#381C2318yes—
280#381C2314yes—
281#380C2314yes—
282#380C2314yes—
283#380C2314yes—
284#380C2314yes—
285#380C2318yes—
286#380C2318yes—
287#380C2318yes—
288#380C2314yes—
289#380C2318yes—
290#380C2318yes—
291#380C2314yes—
292#380C2314yes—
293#380C2314yes—
294#380C2314yes—
295#380C2314yes—
296#379C2314yes—
297#379C2314yes—
298C4×C4⋊C4C23116yes—
299C4×C4⋊C4C2318yes—
300C4×C4⋊C4C2318yes—
301C4×C4⋊C4C23116yes—
302C4×C4⋊C4C2318yes—
303C4×C4⋊C4C2318yes—
304C4×C4⋊C4C2318yes—
305C4×C4⋊C4C2318yes—
306C4×C4⋊C4C2314yes—
307C4×C4⋊C4C2318yes—
308C4×C4⋊C4C2318yes—
309C4×C4⋊C4C23116yes—
310C4×C4⋊C4C2318yes—
311C4×C4⋊C4C2318yes—
312C4×C4⋊C4C23116yes—
313C4×C4⋊C4C2318yes—
314C4×C4⋊C4C2314yes—
315C4×C4⋊C4C2314yes—
316C4×C4⋊C4C2314yes—
317C4×C22⋊C4C2318yes—
318C4×C22⋊C4C2314yes—
319C4×C22⋊C4C2318yes—
320C4×C22⋊C4C23116yes—
321C4×C22⋊C4C2318yes—
322C4×C22⋊C4C23116yes—
323C4×C22⋊C4C2318yes—
324C4×C22⋊C4C2314yes—
325C4×C22⋊C4C2318yes—
326C4×C22⋊C4C2314yes—
327C4×C22⋊C4C2314yes—
328C4×C22⋊C4C2314yes—
329C4×C22⋊C4C2314yes—
330#376C2314yes—
331#376C2318yes—
332#376C2318yes—
333C2×#95C2318yes—
334C43C2314yes—
335C25C2411yescharacteristic
336C25C2411yescharacteristic
337C22×Q8—24no—
338C22×Q8—24no—
339C22×Q8C22×C418yes—
340C22×Q8C2414yes—
341C22×D4—44no—
342C22×D4C22×C418yes—
343C22×D4C2412yes—
344C22×D4C2412yes—
345C23×C4—24no—
346C23×C4—24no—
347C23×C4—24no—
348C23×C4—24no—
349C23×C4—48no—
350C23×C4C22×C418yes—
351C23×C4C22×C418yes—
352C23×C4C22×C4116yes—
353C23×C4C2412yes—
354C23×C4C2411yescharacteristic
355C23×C4C2411yescharacteristic
356C23×C4C2414yes—
357C23×C4C2412yes—
358C23×C4C2412yes—
359C23×C4C2412yes—
360C23×C4C2412yes—
361C23×C4C2418yes—
362C23×C4C2418yes—
363C23×C4C2412yes—
364C23×C4C2411yescharacteristic
365C23×C4C2412yes—
366C23×C4C2412yes—
367C23×C4C2411yescharacteristic
368C23×C4C2414yes—
369C23×C4C2411yescharacteristic
370#126C22×C4164yes—
371#126C22×C4164yes—
372#125C22×C4164yes—
373#125C22×C4164yes—
374#125C22×C4132yes—
375#125C22×C4132yes—
376#123C22×C4164yes—
377#123C22×C4164yes—
378C22⋊Q8C22×C4132yes—
379C22⋊Q8C22×C4132yes—
380C22⋊Q8C22×C4132yes—
381C22⋊Q8C22×C4132yes—
382C4×Q8—416no—
383C4×Q8—416no—
384C4×Q8C22×C4132yes—
385C4×Q8C22×C4132yes—
386C4×D4—416no—
387C4×D4C22×C4116yes—
388C4×D4C22×C4116yes—
389C4×D4C22×C4116yes—
390C4×D4C22×C4116yes—
391#117—28no—
392#117—28no—
393#117—28no—
394#117—28no—
395#117—48no—
396#117—48no—
397#117—48no—
398#117—48no—
399#117—416no—
400#117—416no—
401#117—48no—
402#117—48no—
403#117C22×C4132yes—
404#117C22×C4132yes—
405#117C22×C4132yes—
406#117C22×C4132yes—
407#117C22×C4132yes—
408#117C22×C4132yes—
409C2×C4⋊C4—48no—
410C2×C4⋊C4—48no—
411C2×C4⋊C4—416no—
412C2×C4⋊C4C22×C418yes—
413C2×C4⋊C4C22×C418yes—
414C2×C4⋊C4C22×C4116yes—
415C2×C4⋊C4C22×C4132yes—
416C2×C4⋊C4C22×C4132yes—
417C2×C4⋊C4C22×C4116yes—
418C2×C4⋊C4C22×C418yes—
419C2×C4⋊C4C22×C4116yes—
420C2×C4⋊C4C22×C418yes—
421C2×C4⋊C4C22×C4116yes—
422C2×C4⋊C4C22×C4116yes—
423C2×C4⋊C4C22×C4116yes—
424C2×C4⋊C4C2414yes—
425C2×C4⋊C4C2414yes—
426C2×C4⋊C4C2414yes—
427C2×C4⋊C4C2414yes—
428C2×C4⋊C4C2418yes—
429C2×C4⋊C4C2418yes—
430C2×C4⋊C4C2418yes—
431C2×C4⋊C4C2418yes—
432C2×C4⋊C4C24116yes—
433C2×C4⋊C4C24116yes—
434C2×C4⋊C4C2418yes—
435C2×C4⋊C4C2418yes—
436C2×C4⋊C4C2418yes—
437C2×C4⋊C4C2418yes—
438C2×C4⋊C4C24116yes—
439C2×C4⋊C4C2414yes—
440C2×C4⋊C4C2414yes—
441C2×C4⋊C4C2418yes—
442C2×C4⋊C4C2414yes—
443C2×C4⋊C4C2414yes—
444C2×C4⋊C4C2414yes—
445C2×C4⋊C4C2414yes—
446C2×C4⋊C4C2414yes—
447C2×C4⋊C4C2412yes—
448C2×C4⋊C4C2412yes—
449C2×C4⋊C4C2418yes—
450C2×C4⋊C4C2418yes—
451C2×C4⋊C4C2418yes—
452C2×C22⋊C4—48no—
453C2×C22⋊C4—48no—
454C2×C22⋊C4C22×C418yes—
455C2×C22⋊C4C22×C4116yes—
456C2×C22⋊C4C22×C4116yes—
457C2×C22⋊C4C22×C418yes—
458C2×C22⋊C4C22×C4116yes—
459C2×C22⋊C4C2414yes—
460C2×C22⋊C4C2414yes—
461C2×C22⋊C4C2414yes—
462C2×C22⋊C4C2418yes—
463C2×C22⋊C4C2414yes—
464C2×C22⋊C4C2418yes—
465C2×C22⋊C4C2418yes—
466C2×C22⋊C4C2418yes—
467C2×C22⋊C4C2418yes—
468C2×C22⋊C4C2418yes—
469C2×C22⋊C4C2411yescharacteristic
470C2×C22⋊C4C2411yescharacteristic
471C2×C22⋊C4C2411yescharacteristic
472C2×C22⋊C4C2411yescharacteristic
473C2×C22⋊C4C2414yes—
474C2×C22⋊C4C2414yes—
475C2×C22⋊C4C2418yes—
476C2×C22⋊C4C2412yes—
477C2×C22⋊C4C2412yes—
478C2×C22⋊C4C2418yes—
479C2×C42—48no—
480C2×C42—48no—
481C2×C42C22×C4116yes—
482C2×C42C22×C4116yes—
483C2×C42C22×C418yes—
484C2×C42C2414yes—
485C2×C42C2414yes—
486C2×C42C2414yes—
487C2×C42C2414yes—
488C2×C42C2418yes—
489C2×C42C2418yes—
490C2×C42C24116yes—
491C2×C42C24116yes—
492C2×C42C2418yes—
493C2×C42C2418yes—
494C2×C42C24116yes—
495C2×C42C2414yes—
496C2×C42C2414yes—
497C2×C42C2414yes—
498C2×C42C2414yes—
499C2×C42C2412yes—
500C2×C42C2412yes—
501#95C2418yes—
502#95C2418yes—
503#95C24116yes—
504#95C2418yes—
505#95C2418yes—
506#95C24116yes—
507#95C2418yes—
508#95C2418yes—
509#95C2418yes—
510#95C2418yes—
511#95C2418yes—
512#95C2418yes—
513#95C24116yes—
514#95C2418yes—
515#95C24116yes—
516#95C24116yes—
517#95C24116yes—
518#95C2418yes—
519C24—22no—
520C24—22no—
521C24—24no—
522C24—22no—
523C24—22no—
524C24—42no—
525C24—42no—
526C24—42no—
527C24C23×C414yes—
528C24C23×C414yes—
529C24C2511yescharacteristic
530C24C2512yes—
531C24C2511yescharacteristic
532C24C2511yescharacteristic
533C2×Q8—232no—
534C2×Q8—28no—
535C2×Q8—28no—
536C2×Q8C23×C4116yes—
537C2×D4—28no—
538C2×D4—44no—
539C2×D4—416no—
540C2×D4C23×C418yes—
541C2×D4C23×C418yes—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—24no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—24no—
548C22×C4—216no—
549C22×C4—232no—
550C22×C4—232no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—24no—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—24no—
558C22×C4—24no—
559C22×C4—216no—
560C22×C4—432no—
561C22×C4—44no—
562C22×C4—48no—
563C22×C4—44no—
564C22×C4—42no—
565C22×C4—44no—
566C22×C4—42no—
567C22×C4—48no—
568C22×C4—48no—
569C22×C4—48no—
570C22×C4—48no—
571C22×C4—48no—
572C22×C4C23×C414yes—
573C22×C4C23×C418yes—
574C22×C4C23×C414yes—
575C22×C4C23×C4116yes—
576C22×C4C23×C418yes—
577C22×C4C23×C418yes—
578C22×C4C23×C418yes—
579C22×C4C23×C418yes—
580C22×C4C23×C414yes—
581C22×C4C23×C418yes—
582C22×C4C23×C418yes—
583C22×C4C23×C414yes—
584C22×C4C23×C418yes—
585C22×C4C23×C4116yes—
586C22×C4C23×C414yes—
587C22×C4H(5,𝔽2)14yes—
588C22×C42−1+414yes—
589C22×C4C2518yes—
590C22×C4C2518yes—
591C22×C4C2518yes—
592C22×C4C2518yes—
593C22×C4C2511yescharacteristic
594C22×C4C2511yescharacteristic
595C22×C4C2514yes—
596C22×C4C2511yescharacteristic
597C22×C4C2514yes—
598C22×C4C2512yes—
599C22×C4C2512yes—
600C22×C4C2511yescharacteristic
601C22×C4C2514yes—
602C22×C4C2514yes—
603C22×C4C2512yes—
604C4⋊C4—28no—
605C4⋊C4—28no—
606C4⋊C4—28no—
607C4⋊C4—28no—
608C4⋊C4—416no—
609C4⋊C4—48no—
610C4⋊C4—48no—
611C4⋊C4—48no—
612C4⋊C4—48no—
613C4⋊C4—416no—
614C4⋊C4—48no—
615C4⋊C4—48no—
616C4⋊C4—48no—
617C4⋊C4—416no—
618C4⋊C4—48no—
619C4⋊C4C23×C4116yes—
620C4⋊C4C23×C4116yes—
621C4⋊C4C23×C4132yes—
622C4⋊C4C23×C4116yes—
623C4⋊C4C23×C4116yes—
624C4⋊C4C23×C4116yes—
625C4⋊C4C23×C4116yes—
626C4⋊C4C23×C4116yes—
627C4⋊C4C23×C418yes—
628C4⋊C4C23×C418yes—
629C4⋊C4C23×C4132yes—
630C4⋊C4C23×C4132yes—
631C4⋊C4C23×C4132yes—
632C22⋊C4—28no—
633C22⋊C4—28no—
634C22⋊C4—28no—
635C22⋊C4—28no—
636C22⋊C4—216no—
637C22⋊C4—48no—
638C22⋊C4—48no—
639C22⋊C4—48no—
640C22⋊C4—48no—
641C22⋊C4—48no—
642C22⋊C4C23×C414yes—
643C22⋊C4C23×C414yes—
644C22⋊C4C23×C414yes—
645C22⋊C4C23×C414yes—
646C22⋊C4C23×C4116yes—
647C22⋊C4C23×C4116yes—
648C22⋊C4C23×C4132yes—
649C22⋊C4C23×C418yes—
650C22⋊C4C23×C418yes—
651C22⋊C4C23×C4132yes—
652C42—28no—
653C42—28no—
654C42—28no—
655C42—28no—
656C42—48no—
657C42—48no—
658C42—48no—
659C42—416no—
660C42—416no—
661C42—416no—
662C42—48no—
663C42C23×C4116yes—
664C42C23×C4116yes—
665C42C23×C4116yes—
666C42C23×C4116yes—
667C42C23×C418yes—
668C42C23×C418yes—
669C23—21no—
670C23—21no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—21no—
675C23—22no—
676C23—21no—
677C23—22no—
678C23—24no—
679C23—22no—
680C23—22no—
681C23—24no—
682C23—28no—
683C23—28no—
684C23—28no—
685C23—44no—
686C23—44no—
687C23—44no—
688C23—48no—
689C23—48no—
690C23—84no—
691C23—84no—
692C23C24×C414yes—
693C23C24×C412yes—
694C23C24×C412yes—
695C23C24×C412yes—
696C23C2×H(5,𝔽2)12yes—
697C23C2×2−1+412yes—
698C23#58514yes—
699C23C2611yescharacteristic
700Q8—232no—
701D4—216no—
702D4—48no—
703C2×C4—21no—
704C2×C4—22no—
705C2×C4—24no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—22no—
709C2×C4—21no—
710C2×C4—24no—
711C2×C4—28no—
712C2×C4—24no—
713C2×C4—28no—
714C2×C4—22no—
715C2×C4—28no—
716C2×C4—22no—
717C2×C4—28no—
718C2×C4—28no—
719C2×C4—216no—
720C2×C4—232no—
721C2×C4—216no—
722C2×C4—216no—
723C2×C4—216no—
724C2×C4—216no—
725C2×C4—28no—
726C2×C4—28no—
727C2×C4—28no—
728C2×C4—28no—
729C2×C4—28no—
730C2×C4—28no—
731C2×C4—28no—
732C2×C4—28no—
733C2×C4—28no—
734C2×C4—28no—
735C2×C4—28no—
736C2×C4—28no—
737C2×C4—48no—
738C2×C4—48no—
739C2×C4—416no—
740C2×C4—44no—
741C2×C4—48no—
742C2×C4—44no—
743C2×C4—816no—
744C2×C4—816no—
745C2×C4#520116yes—
746C2×C4C24×C412yes—
747C2×C4C24×C412yes—
748C2×C4C24×C412yes—
749C2×C4C24×C412yes—
750C2×C4C24×C418yes—
751C2×C4C24×C418yes—
752C2×C4C24×C418yes—
753C2×C4C24×C414yes—
754C2×C4C24×C414yes—
755C2×C4C24×C418yes—
756C2×C4C24×C414yes—
757C2×C4C2×H(5,𝔽2)14yes—
758C2×C4C2×2−1+414yes—
759C22—22no—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—24no—
764C22—24no—
765C22—24no—
766C22—24no—
767C22—22no—
768C22—24no—
769C22—22no—
770C22—24no—
771C22—22no—
772C22—24no—
773C22—416no—
774C22—44no—
775C22—42no—
776C22—42no—
777C22—44no—
778C22—88no—
779C22C2×#52014yes—
780C22#342814yes—
781C22C25×C411yescharacteristic
782C22C22×H(5,𝔽2)11yescharacteristic
783C22C22×2−1+411yescharacteristic
784C22C2×#58512yes—
785C222−1+612yes—
786C4—22no—
787C4—24no—
788C4—22no—
789C4—28no—
790C4—28no—
791C4—28no—
792C4—24no—
793C4—22no—
794C4—28no—
795C4—22no—
796C4—48no—
797C4—48no—
798C4—48no—
799C4—48no—
800C4C2×#52018yes—
801C2—24no—
802C2—24no—
803C2—42no—
804C2—44no—
805C2C22×#52011yescharacteristic
806C2C2×#342811yescharacteristic
807C2#6265311yescharacteristic
808C2#6292712yes—
809C2#6292812yes—
subgroupG/H
center, Frattini, socle, cosocleC23C26
commutatorC22C25×C4
prime radicalC23×D4C23
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34482C2semidirect
3. #34465C2semidirect
4. #34462C2semidirect
5. #34381C2semidirect
6. #34378C2semidirect
8. #34314C2semidirect
9. #34217C2semidirect
10. #34203C2semidirect
11. #34203C2semidirect
12. #34182C2semidirect
13. #34180C2semidirect
14. #34179C2semidirect
15. #34178C2semidirect
17. #34059C2semidirect
18. #34052C2semidirect
19. C2×#2316C2semidirect
20. C2×#552C4semidirect
39. #2383C22semidirect
40. #2382C22semidirect
42. #2373C22semidirect
43. #2370C22semidirect
44. #2370C22semidirect
45. #2370C22semidirect
46. #2362C22semidirect
47. #2362C22semidirect
48. #2360C22semidirect
49. #2360C22semidirect
54. #2351C22semidirect
55. Q8×C4⋊C4C22semidirect
57. #2347C22semidirect
58. #2347C22semidirect
59. #2346C22semidirect
60. #2346C22semidirect
63. #2345C22semidirect
67. #2344C22semidirect
68. #2343C22semidirect
69. #2343C22semidirect
75. #2336C22semidirect
77. #2334C22semidirect
78. #2334C22semidirect
79. #2330C22semidirect
80. #2330C22semidirect
81. #2323C22semidirect
82. #2323C22semidirect
84. #2320C22semidirect
85. #2317C22semidirect
86. #2317C22semidirect
95. #2316C22semidirect
97. #2314C22semidirect
98. #2314C22semidirect
103. C4×#125C22semidirect
104. C4×C22⋊Q8C22semidirect
105. C4×C22⋊Q8C22semidirect
106. #2296C22semidirect
107. #2295C22semidirect
109. C2×#389C22semidirect
123. #2274C22semidirect
131. #552C2×C4semidirect
132. #552C2×C4semidirect
133. #552C2×C4semidirect
134. #552C2×C4semidirect
135. C2×#126C2×C4semidirect
138. C2×#125C2×C4semidirect
139. C2×#125C2×C4semidirect
147. C2×C22⋊Q8C2×C4semidirect
148. C2×C22⋊Q8C2×C4semidirect
154. C2×C4×Q8C2×C4semidirect
167. C2×#117C2×C4semidirect
168. C2×#117C2×C4semidirect
187. C22×C4⋊C4C2×C4semidirect

Maximal subgroups

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

subgroupindex
C22×#5522
#344822
#344652
#344622
#343812
#343782
#343762
#343142
#342172
#342032
#341822
#341802
#341792
#341782
D4×#1172
#340592
#340522
C2×#23162