Finite Group Databasebeta

← #7625874

Subgroups — #7625874

Order 512.

7302 conjugacy classes of subgroups.

The subgroup lattice has 789 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#552C211yesmaximal, characteristic
2#34318C218yesmaximal, complemented
3#34304C218yesmaximal, complemented
4#34300C218yesmaximal, complemented
5#34247C214yesmaximal, complemented
6#34239C214yesmaximal, complemented
7#34238C214yesmaximal
8#34217C212yesmaximal, complemented
9#34203C212yesmaximal, complemented
10#34203C212yesmaximal, complemented
11#34187C211yesmaximal, characteristic, complemented
12#34179C211yesmaximal, characteristic, complemented
13#34178C211yesmaximal, characteristic, complemented
14C4×#552C218yesmaximal, complemented
15D4×#117C212yesmaximal
16#34109C214yesmaximal, complemented
17C4×#519C211yesmaximal, characteristic, complemented
18#33996C211yesmaximal, characteristic, complemented
19C2×#2274C211yesmaximal, characteristic, complemented
20C2×#552C4132yescomplemented
21C2×#552C2214yes—
22C2×#552C2214yes—
23C2×#552C2214yes—
24C2×#552C2214yes—
25C22×#126C2212yes—
26C22×#125C2211yescharacteristic
27C22×#125C2212yes—
28C22×#123C2212yes—
29C22×C22⋊Q8C2211yescharacteristic
30C22×C22⋊Q8C2211yescharacteristic
31C2×#519C2212yes—
32C22×C4×Q8C2211yescharacteristic
33C22×C4×D4C2211yescharacteristic
34C22×#117C2212yes—
35C22×#117C2212yes—
36C22×#117C2212yes—
37C22×#117C2211yescharacteristic
38C23×C4⋊C4C2211yescharacteristic
39#2374C22116yes—
40#2373C22116yescomplemented
41#2373C22116yescomplemented
42#2371C22116yescomplemented
43#2370C22116yescomplemented
44#2370C2218yescomplemented
45#2370C2218yescomplemented
46#2362C2218yescomplemented
47#2362C2218yescomplemented
48#2360C2218yescomplemented
49#2360C2218yescomplemented
50#2359C22116yes—
51#2356C2218yescomplemented
52#2355C2218yescomplemented
53#2354C2214yes—
54#2352C2214yes—
55#2352C2214yes—
56D4×C4⋊C4C2214yes—
57#2347C2218yescomplemented
58#2347C2218yescomplemented
59#2346C2218yescomplemented
60#2346C2218yescomplemented
61#2345C2218yes—
62#2345C2218yes—
63#2345C2218yescomplemented
64#2344C2218yes—
65#2344C2214yes—
66#2344C2218yes—
67#2344C2218yescomplemented
68#2343C2218yescomplemented
69#2343C2218yescomplemented
70#2342C2214yes—
71#2342C2218yes—
72#2342C2214yes—
73#2342C2218yes—
74D4×C22⋊C4C2214yes—
75#2336C22116yescomplemented
76#2335C22116yes—
77#2334C22116yescomplemented
78#2330C2218yescomplemented
79#2323C2218yescomplemented
80#2323C2218yescomplemented
81#2316C2212yes—
82#2316C2212yes—
83#2313C2214yes—
84#2313C2214yes—
85#2312C2214yes—
86#2310C2212yes—
87C4×#125C2218yescomplemented
88C4×#125C22116yescomplemented
89C4×#126C22116yescomplemented
90C4×C22⋊Q8C2218yescomplemented
91C4×C22⋊Q8C2218yescomplemented
92C4×#123C22116yes—
93#2298C2218yescomplemented
94#2298C2218yescomplemented
95#2296C2218yescomplemented
96#2293C2214yes—
97#2290C2214yes—
98#2290C2214yes—
99#2285C2212yes—
100#2283C2214yes—
101#2283C2214yes—
102#2280C2214yes—
103#2280C2212yes—
104#2280C2212yes—
105#2276C2218yescomplemented
106#2274C2211yescharacteristic
107#2274C2211yescharacteristic
108#2274C2211yescharacteristic
109#2274C2212yes—
110#2274C2212yes—
111#2274C2214yes—
112#2274C2214yes—
113#2274C2211yescharacteristic
114#2274C2218yescomplemented
115#2274C2218yescomplemented
116#2273C2214yes—
117C42×Q8C2218yescomplemented
118C42×D4C2214yes—
119C4×#117C2214yes—
120C4×#117C2214yes—
121C4×#117C2212yes—
122C4×#117C2218yescomplemented
123C4×#117C2218yescomplemented
124C2×C4×C4⋊C4C2218yescomplemented
125C2×C4×C22⋊C4C2214yes—
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×#125C2318yes—
142C2×#125C2314yes—
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—216no—
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—216no—
166C2×#117—216no—
167C2×#117C2×C4116yescomplemented
168C2×#117C2×C4132yescomplemented
169C2×#117C2312yes—
170C2×#117C2312yes—
171C2×#117C2312yes—
172C2×#117C2314yes—
173C2×#117C2314yes—
174C2×#117C2318yes—
175C2×#117C2314yes—
176C2×#117C2314yes—
177C2×#117C2314yes—
178C2×#117C2314yes—
179C2×#117C2318yes—
180C2×#117C2314yes—
181C2×#117C2314yes—
182C2×#117C2314yes—
183C2×#117C2314yes—
184C2×#117C2314yes—
185C2×#117C2314yes—
186C2×#117C2312yes—
187C22×C4⋊C4C2×C4116yescomplemented
188C22×C4⋊C4C2314yes—
189C22×C4⋊C4C2314yes—
190C22×C4⋊C4C2312yes—
191C22×C4⋊C4C2312yes—
192C22×C4⋊C4C2311yescharacteristic
193C22×C4⋊C4C2311yescharacteristic
194C22×C4⋊C4C2312yes—
195C22×C4⋊C4C2311yescharacteristic
196C22×C4⋊C4C2312yes—
197C22×C4⋊C4C2314yes—
198C22×C4⋊C4C2312yes—
199C22×C4⋊C4C2312yes—
200C22×C4⋊C4C2314yes—
201C22×C4⋊C4C2311yescharacteristic
202C22×C22⋊C4C2314yes—
203C22×C22⋊C4C2314yes—
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2311yescharacteristic
206C22×C22⋊C4C2312yes—
207C22×C22⋊C4C2311yescharacteristic
208C22×C22⋊C4C2312yes—
209C22×C42C2314yes—
210C22×C42C2314yes—
211C22×C42C2318yes—
212C22×C42C2312yes—
213C22×C42C2312yes—
214C22×C42C2311yescharacteristic
215#391C2318yes—
216#391C2318yes—
217#390C2318yes—
218#389C2318yes—
219#389C2318yes—
220#389C23116yes—
221#389C23116yes—
222#389C2318yes—
223#389C2318yes—
224#389C23116yes—
225#389C23116yes—
226#389C2318yes—
227#388C2318yes—
228#388C23116yes—
229#388C23116yes—
230#388C23116yes—
231#388C23116yes—
232#388C23116yes—
233#388C23116yes—
234#388C2318yes—
235#388C2318yes—
236#388C2318yes—
237#387C23116yes—
238#387C23116yes—
239#387C23116yes—
240#387C2318yes—
241#387C23116yes—
242#387C23116yes—
243#387C23116yes—
244#387C23116yes—
245#387C23116yes—
246#387C23116yes—
247#387C23116yes—
248#387C23116yes—
249#387C23116yes—
250#387C2318yes—
251#386C2318yes—
252#386C2318yes—
253#385C2318yes—
254#385C23116yes—
255#385C2318yes—
256#385C23116yes—
257#384C2314yes—
258#383C2318yes—
259#383C2318yes—
260#382C2318yes—
261#382C2314yes—
262#382C2318yes—
263#381C2318yes—
264#381C2314yes—
265#381C2314yes—
266#381C2318yes—
267#380C2318yes—
268#380C2314yes—
269#380C2318yes—
270#380C2314yes—
271#380C2314yes—
272#380C2318yes—
273#380C2314yes—
274#380C2314yes—
275#380C2314yes—
276#379C2314yes—
277#379C2314yes—
278C4×C4⋊C4C23116yes—
279C4×C4⋊C4C23116yes—
280C4×C4⋊C4C23116yes—
281C4×C4⋊C4C2318yes—
282C4×C4⋊C4C23116yes—
283C4×C4⋊C4C2318yes—
284C4×C4⋊C4C2318yes—
285C4×C4⋊C4C23116yes—
286C4×C4⋊C4C23116yes—
287C4×C4⋊C4C2318yes—
288C4×C4⋊C4C2318yes—
289C4×C4⋊C4C2318yes—
290C4×C4⋊C4C2318yes—
291C4×C4⋊C4C2318yes—
292C4×C4⋊C4C2318yes—
293C4×C4⋊C4C2318yes—
294C4×C4⋊C4C2318yes—
295C4×C4⋊C4C2314yes—
296C4×C4⋊C4C2314yes—
297C4×C4⋊C4C2314yes—
298C4×C4⋊C4C2318yes—
299C4×C4⋊C4C2314yes—
300C4×C4⋊C4C23116yes—
301C4×C4⋊C4C2318yes—
302C4×C4⋊C4C2318yes—
303C4×C4⋊C4C23116yes—
304C4×C4⋊C4C2318yes—
305C4×C22⋊C4C2318yes—
306C4×C22⋊C4C23116yes—
307C4×C22⋊C4C23116yes—
308C4×C22⋊C4C2314yes—
309C4×C22⋊C4C2314yes—
310C4×C22⋊C4C2314yes—
311C4×C22⋊C4C2318yes—
312C4×C22⋊C4C2314yes—
313C4×C22⋊C4C2314yes—
314C4×C22⋊C4C2318yes—
315C4×C22⋊C4C23116yes—
316C4×C22⋊C4C2318yes—
317C4×C22⋊C4C2318yes—
318C4×C22⋊C4C2314yes—
319C4×C22⋊C4C2314yes—
320C4×C22⋊C4C2318yes—
321C4×C22⋊C4C2314yes—
322C4×C22⋊C4C2318yes—
323C4×C22⋊C4C2314yes—
324C4×C22⋊C4C23116yes—
325C4×C22⋊C4C2314yes—
326#376C2314yes—
327#376C2318yes—
328#376C2318yes—
329#376C2318yes—
330#376C2318yes—
331C2×#95C2318yes—
332C43C2318yes—
333C43C2318yes—
334C43C2314yes—
335C25C2411yescharacteristic
336C25C2411yescharacteristic
337C22×Q8—28no—
338C22×Q8C22×C418yes—
339C22×Q8C2414yes—
340C22×D4—44no—
341C22×D4C22×C418yes—
342C22×D4C2412yes—
343C22×D4C2412yes—
344C23×C4—28no—
345C23×C4—28no—
346C23×C4—48no—
347C23×C4C22×C418yes—
348C23×C4C22×C418yes—
349C23×C4C22×C4116yes—
350C23×C4C2418yes—
351C23×C4C2412yes—
352C23×C4C2411yescharacteristic
353C23×C4C2411yescharacteristic
354C23×C4C2412yes—
355C23×C4C2412yes—
356C23×C4C2412yes—
357C23×C4C2414yes—
358C23×C4C2412yes—
359C23×C4C2418yes—
360C23×C4C2412yes—
361C23×C4C2411yescharacteristic
362C23×C4C2412yes—
363C23×C4C2412yes—
364C23×C4C2411yescharacteristic
365C23×C4C2414yes—
366C23×C4C2411yescharacteristic
367#126C22×C4164yes—
368#126C22×C4164yes—
369#125C22×C4164yes—
370#125C22×C4164yes—
371#125C22×C4132yes—
372#125C22×C4132yes—
373#123C22×C4164yes—
374#123C22×C4164yes—
375C22⋊Q8C22×C4132yes—
376C22⋊Q8C22×C4132yes—
377C22⋊Q8C22×C4132yes—
378C22⋊Q8C22×C4132yes—
379C4×Q8—232no—
380C4×Q8—232no—
381C4×Q8C22×C4132yes—
382C4×Q8C22×C4132yes—
383C4×D4—416no—
384C4×D4C22×C4116yes—
385C4×D4C22×C4116yes—
386C4×D4C22×C4116yes—
387C4×D4C22×C4116yes—
388#117—28no—
389#117—28no—
390#117—28no—
391#117—216no—
392#117—216no—
393#117—216no—
394#117—216no—
395#117—232no—
396#117—216no—
397#117—216no—
398#117—416no—
399#117C22×C4132yes—
400#117C22×C4132yes—
401#117C22×C4132yes—
402#117C22×C4132yes—
403#117C22×C4132yes—
404#117C22×C4132yes—
405#117#41116yes—
406C2×C4⋊C4—216no—
407C2×C4⋊C4—216no—
408C2×C4⋊C4C22×C418yes—
409C2×C4⋊C4C22×C418yes—
410C2×C4⋊C4C22×C4116yes—
411C2×C4⋊C4C22×C4132yes—
412C2×C4⋊C4C22×C4132yes—
413C2×C4⋊C4C22×C4116yes—
414C2×C4⋊C4C22×C418yes—
415C2×C4⋊C4C22×C4116yes—
416C2×C4⋊C4C22×C418yes—
417C2×C4⋊C4C22×C4116yes—
418C2×C4⋊C4C22×C4116yes—
419C2×C4⋊C4C22×C4116yes—
420C2×C4⋊C4C2414yes—
421C2×C4⋊C4C2414yes—
422C2×C4⋊C4C2418yes—
423C2×C4⋊C4C2418yes—
424C2×C4⋊C4C2414yes—
425C2×C4⋊C4C24116yes—
426C2×C4⋊C4C24116yes—
427C2×C4⋊C4C2418yes—
428C2×C4⋊C4C2418yes—
429C2×C4⋊C4C24116yes—
430C2×C4⋊C4C2414yes—
431C2×C4⋊C4C2414yes—
432C2×C4⋊C4C2418yes—
433C2×C4⋊C4C2414yes—
434C2×C4⋊C4C2414yes—
435C2×C4⋊C4C2414yes—
436C2×C4⋊C4C2414yes—
437C2×C4⋊C4C2414yes—
438C2×C4⋊C4C2412yes—
439C2×C4⋊C4C2412yes—
440C2×C4⋊C4C2418yes—
441C2×C4⋊C4C2418yes—
442C2×C4⋊C4C2418yes—
443C2×C4⋊C4C2414yes—
444C2×C22⋊C4—216no—
445C2×C22⋊C4—216no—
446C2×C22⋊C4C22×C418yes—
447C2×C22⋊C4C22×C4116yes—
448C2×C22⋊C4C22×C4116yes—
449C2×C22⋊C4C22×C418yes—
450C2×C22⋊C4C22×C4116yes—
451C2×C22⋊C4C2414yes—
452C2×C22⋊C4C2414yes—
453C2×C22⋊C4C2418yes—
454C2×C22⋊C4C2418yes—
455C2×C22⋊C4C2414yes—
456C2×C22⋊C4C2418yes—
457C2×C22⋊C4C2418yes—
458C2×C22⋊C4C2418yes—
459C2×C22⋊C4C2418yes—
460C2×C22⋊C4C2411yescharacteristic
461C2×C22⋊C4C2411yescharacteristic
462C2×C22⋊C4C2411yescharacteristic
463C2×C22⋊C4C2411yescharacteristic
464C2×C22⋊C4C2414yes—
465C2×C22⋊C4C2414yes—
466C2×C22⋊C4C2418yes—
467C2×C22⋊C4C2412yes—
468C2×C22⋊C4C2412yes—
469C2×C22⋊C4C2418yes—
470C2×C22⋊C4C2414yes—
471C2×C42—216no—
472C2×C42—216no—
473C2×C42—416no—
474C2×C42C22×C4116yes—
475C2×C42C22×C4116yes—
476C2×C42C22×C418yes—
477C2×C42C2418yes—
478C2×C42C2414yes—
479C2×C42C2414yes—
480C2×C42C2418yes—
481C2×C42C2414yes—
482C2×C42C24116yes—
483C2×C42C2418yes—
484C2×C42C2418yes—
485C2×C42C2418yes—
486C2×C42C2418yes—
487C2×C42C2418yes—
488C2×C42C24116yes—
489C2×C42C2418yes—
490C2×C42C24116yes—
491C2×C42C2414yes—
492C2×C42C2414yes—
493C2×C42C2414yes—
494C2×C42C2414yes—
495C2×C42C2412yes—
496C2×C42C2412yes—
497C2×C42C2414yes—
498#95C2418yes—
499#95C2418yes—
500#95C24116yes—
501#95C2418yes—
502#95C2418yes—
503#95C2418yes—
504#95C2418yes—
505#95C24116yes—
506#95C2418yes—
507#95C2418yes—
508#95C24116yes—
509#95C24116yes—
510#95C2418yes—
511#95C24116yes—
512#95C2418yes—
513#95C2418yes—
514#95C24116yes—
515#95C2418yes—
516C24—24no—
517C24—24no—
518C24—24no—
519C24—42no—
520C24—42no—
521C24—42no—
522C24C23×C414yes—
523C24C23×C414yes—
524C24C2511yescharacteristic
525C24C2512yes—
526C24C2511yescharacteristic
527C24C2511yescharacteristic
528C2×Q8—232no—
529C2×Q8—28no—
530C2×Q8—28no—
531C2×Q8C23×C4116yes—
532C2×D4—28no—
533C2×D4—44no—
534C2×D4—416no—
535C2×D4C23×C418yes—
536C2×D4C23×C418yes—
537C22×C4—24no—
538C22×C4—24no—
539C22×C4—28no—
540C22×C4—216no—
541C22×C4—232no—
542C22×C4—232no—
543C22×C4—24no—
544C22×C4—24no—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—24no—
549C22×C4—24no—
550C22×C4—24no—
551C22×C4—216no—
552C22×C4—216no—
553C22×C4—216no—
554C22×C4—432no—
555C22×C4—44no—
556C22×C4—48no—
557C22×C4—44no—
558C22×C4—42no—
559C22×C4—48no—
560C22×C4—44no—
561C22×C4—42no—
562C22×C4—48no—
563C22×C4—48no—
564C22×C4C23×C414yes—
565C22×C4C23×C418yes—
566C22×C4C23×C414yes—
567C22×C4C23×C4116yes—
568C22×C4C23×C418yes—
569C22×C4C23×C418yes—
570C22×C4C23×C418yes—
571C22×C4C23×C418yes—
572C22×C4C23×C414yes—
573C22×C4C23×C418yes—
574C22×C4C23×C418yes—
575C22×C4C23×C414yes—
576C22×C4C23×C418yes—
577C22×C4C23×C4116yes—
578C22×C4C23×C414yes—
579C22×C4C2×#4118yes—
580C22×C4C2518yes—
581C22×C4C2518yes—
582C22×C4C2518yes—
583C22×C4C2511yescharacteristic
584C22×C4C2511yescharacteristic
585C22×C4C2514yes—
586C22×C4C2514yes—
587C22×C4C2511yescharacteristic
588C22×C4C2514yes—
589C22×C4C2512yes—
590C22×C4C2512yes—
591C22×C4C2511yescharacteristic
592C22×C4C2514yes—
593C22×C4C2518yes—
594C22×C4C2512yes—
595C4⋊C4—216no—
596C4⋊C4—216no—
597C4⋊C4—28no—
598C4⋊C4—28no—
599C4⋊C4—232no—
600C4⋊C4—28no—
601C4⋊C4—416no—
602C4⋊C4—48no—
603C4⋊C4—416no—
604C4⋊C4—48no—
605C4⋊C4C23×C4116yes—
606C4⋊C4C23×C4116yes—
607C4⋊C4C23×C4132yes—
608C4⋊C4C23×C4116yes—
609C4⋊C4C23×C4116yes—
610C4⋊C4C23×C4116yes—
611C4⋊C4C23×C4116yes—
612C4⋊C4C23×C4116yes—
613C4⋊C4C23×C418yes—
614C4⋊C4C23×C418yes—
615C4⋊C4C23×C4132yes—
616C4⋊C4C23×C4132yes—
617C4⋊C4C23×C4132yes—
618C4⋊C4C2×#41116yes—
619C22⋊C4—28no—
620C22⋊C4—28no—
621C22⋊C4—28no—
622C22⋊C4—216no—
623C22⋊C4—216no—
624C22⋊C4—216no—
625C22⋊C4—48no—
626C22⋊C4—48no—
627C22⋊C4—48no—
628C22⋊C4C23×C414yes—
629C22⋊C4C23×C414yes—
630C22⋊C4C23×C414yes—
631C22⋊C4C23×C414yes—
632C22⋊C4C23×C4116yes—
633C22⋊C4C23×C4116yes—
634C22⋊C4C23×C4132yes—
635C22⋊C4C23×C418yes—
636C22⋊C4C23×C418yes—
637C22⋊C4C23×C4132yes—
638C22⋊C4C2×#41116yes—
639C42—216no—
640C42—216no—
641C42—28no—
642C42—28no—
643C42—232no—
644C42—28no—
645C42—48no—
646C42—416no—
647C42—48no—
648C42—48no—
649C42—416no—
650C42—48no—
651C42—48no—
652C42—48no—
653C42C23×C4116yes—
654C42C23×C4116yes—
655C42C23×C4116yes—
656C42C23×C4116yes—
657C42C23×C418yes—
658C42C23×C418yes—
659C42C2×#41116yes—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—24no—
668C23—22no—
669C23—22no—
670C23—24no—
671C23—28no—
672C23—28no—
673C23—28no—
674C23—44no—
675C23—44no—
676C23—44no—
677C23—416no—
678C23—88no—
679C23C24×C414yes—
680C23C24×C412yes—
681C23C24×C412yes—
682C23C24×C412yes—
683C23C22×#4114yes—
684C23#58514yes—
685C23C2611yescharacteristic
686Q8—232no—
687D4—216no—
688D4—48no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—28no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—28no—
695C2×C4—28no—
696C2×C4—28no—
697C2×C4—24no—
698C2×C4—22no—
699C2×C4—28no—
700C2×C4—28no—
701C2×C4—22no—
702C2×C4—28no—
703C2×C4—28no—
704C2×C4—216no—
705C2×C4—232no—
706C2×C4—216no—
707C2×C4—216no—
708C2×C4—216no—
709C2×C4—216no—
710C2×C4—28no—
711C2×C4—28no—
712C2×C4—28no—
713C2×C4—28no—
714C2×C4—28no—
715C2×C4—28no—
716C2×C4—28no—
717C2×C4—28no—
718C2×C4—28no—
719C2×C4—48no—
720C2×C4—48no—
721C2×C4—416no—
722C2×C4—44no—
723C2×C4—48no—
724C2×C4—44no—
725C2×C4—432no—
726C2×C4—816no—
727C2×C4C4×#41116yes—
728C2×C4C24×C412yes—
729C2×C4C24×C412yes—
730C2×C4C24×C412yes—
731C2×C4C24×C412yes—
732C2×C4C24×C418yes—
733C2×C4C24×C418yes—
734C2×C4C24×C418yes—
735C2×C4C24×C414yes—
736C2×C4C24×C414yes—
737C2×C4C24×C418yes—
738C2×C4C24×C414yes—
739C2×C4C22×#41116yes—
740C2×C4C22×#4114yes—
741C2×C4C22×#4114yes—
742C22—28no—
743C22—28no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—24no—
750C22—22no—
751C22—24no—
752C22—22no—
753C22—24no—
754C22—416no—
755C22—44no—
756C22—44no—
757C22—44no—
758C22—88no—
759C22C2×C4×#4114yes—
760C22#342814yes—
761C22C25×C411yescharacteristic
762C22C23×#4112yes—
763C22C2×#58512yes—
764C222−1+612yes—
765C4—216no—
766C4—22no—
767C4—24no—
768C4—22no—
769C4—28no—
770C4—28no—
771C4—28no—
772C4—24no—
773C4—22no—
774C4—28no—
775C4—22no—
776C4—48no—
777C4—48no—
778C4—48no—
779C4C2×C4×#4118yes—
780C2—24no—
781C2—24no—
782C2—42no—
783C2—44no—
784C2C22×C4×#4111yescharacteristic
785C2C2×#342811yescharacteristic
786C2#6265311yescharacteristic
787C2#6299314yes—
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. #34318C2semidirect
3. #34304C2semidirect
4. #34300C2semidirect
5. #34247C2semidirect
6. #34239C2semidirect
8. #34217C2semidirect
9. #34203C2semidirect
10. #34203C2semidirect
11. #34187C2semidirect
12. #34179C2semidirect
13. #34178C2semidirect
14. C4×#552C2semidirect
16. #34109C2semidirect
17. C4×#519C2semidirect
18. #33996C2semidirect
19. C2×#2274C2semidirect
20. C2×#552C4semidirect
40. #2373C22semidirect
41. #2373C22semidirect
42. #2371C22semidirect
43. #2370C22semidirect
44. #2370C22semidirect
45. #2370C22semidirect
46. #2362C22semidirect
47. #2362C22semidirect
48. #2360C22semidirect
49. #2360C22semidirect
51. #2356C22semidirect
52. #2355C22semidirect
57. #2347C22semidirect
58. #2347C22semidirect
59. #2346C22semidirect
60. #2346C22semidirect
63. #2345C22semidirect
67. #2344C22semidirect
68. #2343C22semidirect
69. #2343C22semidirect
75. #2336C22semidirect
77. #2334C22semidirect
78. #2330C22semidirect
79. #2323C22semidirect
80. #2323C22semidirect
87. C4×#125C22semidirect
88. C4×#125C22semidirect
89. C4×#126C22semidirect
90. C4×C22⋊Q8C22semidirect
91. C4×C22⋊Q8C22semidirect
93. #2298C22semidirect
94. #2298C22semidirect
95. #2296C22semidirect
105. #2276C22semidirect
114. #2274C22semidirect
115. #2274C22semidirect
117. C42×Q8C22semidirect
122. C4×#117C22semidirect
123. C4×#117C22semidirect
124. C2×C4×C4⋊C4C22semidirect
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
#343182
#343042
#343002
#342472
#342392
#342382
#342172
#342032
#341872
#341792
#341782
C4×#5522
D4×#1172
#341092
C4×#5192
#339962
C2×#22742