Finite Group Databasebeta

← #11634182

Subgroups — #11634182

Order 768.

2238 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5730C211yesmaximal, characteristic, complemented
2C2×#5728C211yesmaximal, characteristic, complemented
3C3×#2369C211yesmaximal, characteristic, complemented
4#76656C214yesmaximal, complemented
5#76623C214yesmaximal, complemented
6#76221C212yesmaximal, complemented
7#76212C212yesmaximal, complemented
8#76016C212yesmaximal, complemented
9#76000C212yesmaximal, complemented
10#73800C211yesmaximal, characteristic, complemented
11#73800C212yesmaximal, complemented
12#73773C212yesmaximal, complemented
13C4×#897C211yesmaximal, characteristic, complemented
14C4×#895C211yesmaximal, characteristic
15#73717C212yesmaximal, complemented
16#73711C211yesmaximal, characteristic, complemented
17#73649C212yesmaximal
18#59052—31nomaximal, Sylow
19C2×C3×C4⋊Q8C2211yescharacteristic
20C2×#946C2214yes—
21C2×#946C2212yes—
22C2×Q8×Dic3C2212yes—
23#5730—28no—
24#5728—28no—
25C2×#897C2211yescharacteristic
26C2×#897C2212yes—
27C2×#897C2212yes—
28C2×#897C2212yes—
29C2×#897C2212yes—
30C2×#895C2211yescharacteristic
31C2×#893C2212yes—
32C2×#892C2212yes—
33C2×D3×C4⋊C4C2212yes—
34C2×#890C2212yes—
35C2×#890C2212yes—
36C2×#887C2212yes—
37C2×C4×D12C2211yescharacteristic
38C2×C4×D12C2212yes—
39C2×C42×D3C2211yescharacteristic
40C2×#869C2211yescharacteristic
41C2×#869C2212yes—
42C2×C4×Dic6C2211yescharacteristic
43C3×#391C2214yes—
44C3×#389C2212yes—
45C3×#389C2212yes—
46C3×C4×C4⋊C4C2211yescharacteristic
47C3×C4×C4⋊C4C2211yescharacteristic
48C3×C4×C4⋊C4C2212yes—
49C3×C4×C4⋊C4C2212yes—
50#4994C2214yes—
51#4994C2214yes—
52#4988C2211yescharacteristic
53#4987C2211yescharacteristic
54#4987C2211yescharacteristic
55#4987C2214yes—
56#4984C2211yescharacteristic
57#4984C2211yescharacteristic
58#4984C2214yes—
59#4984C2212yes—
60#4984C2212yes—
61#4973C2211yescharacteristic
62#4939C2214yes—
63#4939C2212yes—
64C4×(C2×D3)⋊C4C2212yes—
65C4×(C2×D3)⋊C4C2212yes—
66C4×(C2×D3)⋊C4C2214yes—
67#4935C2214yes—
68#4935C2212yes—
69C4×C4⋊Dic3C2212yes—
70#4929C2212yes—
71#4928C2214yes—
72#4677C2214yes—
73#4677C2214yes—
74#4677C2214yes—
75#4670C2212yes—
76#4670C2214yes—
77#4668C2212yes—
78#4668C2214yes—
79#4665C2212yes—
80#4665C2214yes—
81#4661C2214yes—
82#4661C2214yes—
83#4661C2214yes—
84#4653C2212yes—
85#4653C2214yes—
86C2×#554—31no—
87C2×#533—31no—
88#2732—34no—
89#2552—32no—
90#2546—31no—
91#2542—31no—
92#2542—32no—
93#2454—32no—
94#2441—32no—
95#2429—32no—
96#2423—34no—
97#2417—32no—
98#2369D311yescharacteristic, complemented
99#2363—32no—
100#2360—32no—
101C4×C22⋊Q8—31no—
102C4×#121—31no—
103C22×C3×Q8C2312yes—
104C22×D12C2311yescharacteristic
105C22×D12C2312yes—
106C22×C4×D3C2312yes—
107C22×C4×D3C2311yescharacteristic
108C22×C4×D3C2311yescharacteristic
109C22×C4×D3C2311yescharacteristic
110C22×C4×D3C2314yes—
111C22×Dic6C2312yes—
112C22×Dic6C2311yescharacteristic
113C3×C4⋊Q8D418yescomplemented
114C2×C3×C4⋊C4C2311yescharacteristic
115C2×C3×C4⋊C4C2311yescharacteristic
116C2×C3×C4⋊C4C2314yes—
117C2×C3×C4⋊C4C2312yes—
118C2×C3×C4⋊C4C2312yes—
119C2×C3×C4⋊C4C2311yescharacteristic
120C2×C3×C4⋊C4C2311yescharacteristic
121C2×C3×C42C2312yes—
122C2×C3×C42C2312yes—
123C2×C3×C42C2314yes—
124C2×C3×C42C2311yescharacteristic
125#946—28no—
126#946—216no—
127Q8×Dic3—28no—
128C2×(C2×D3)⋊C4C2312yes—
129C2×(C2×D3)⋊C4C2314yes—
130C2×(C2×D3)⋊C4C2312yes—
131C2×(C2×D3)⋊C4C2314yes—
132C2×(C2×D3)⋊C4C2314yes—
133C2×(C2×D3)⋊C4C2312yes—
134C2×(C2×D3)⋊C4C2312yes—
135C2×(C2×D3)⋊C4C2314yes—
136C2×(C2×D3)⋊C4C2312yes—
137C2×(C2×D3)⋊C4C2312yes—
138C2×(C2×D3)⋊C4C2312yes—
139C2×C4⋊Dic3C2314yes—
140C2×C4⋊Dic3C2312yes—
141C2×C4⋊Dic3C2312yes—
142C2×C4⋊Dic3C2314yes—
143C2×C4⋊Dic3C2314yes—
144C2×C4⋊Dic3C2311yescharacteristic
145C2×C4⋊Dic3C2311yescharacteristic
146C2×C4⋊Dic3C2312yes—
147C2×C4⋊Dic3C2312yes—
148C2×C4⋊Dic3C2314yes—
149C2×C4⋊Dic3C2314yes—
150C2×C4⋊Dic3C2314yes—
151C2×C4⋊Dic3C2312yes—
152C2×Dic3⋊C4C2312yes—
153C2×Dic3⋊C4C2314yes—
154C2×Dic3⋊C4C2314yes—
155C2×C4×Dic3C2311yescharacteristic
156C2×C4×Dic3C2314yes—
157C2×C4×Dic3C2311yescharacteristic
158C2×C4×Dic3C2312yes—
159C2×C4×Dic3C2311yescharacteristic
160#897—28no—
161#897—28no—
162#897—24no—
163#897—28no—
164#897—44no—
165#895Q818yescomplemented
166#893—28no—
167#892—28no—
168D3×C4⋊C4—28no—
169#890—28no—
170#890—28no—
171#887—28no—
172C4×D12—24no—
173C4×D12—44no—
174C42×D3—24no—
175#869—24no—
176#869—44no—
177C4×Dic6—24no—
178C3×#95C2314yes—
179C3×#95C2312yes—
180C3×#95C2314yes—
181C3×#95C2312yes—
182C3⋊#95C2312yes—
183C3⋊#95C2312yes—
184C3⋊#95C2312yes—
185C3⋊#95C2314yes—
186C3⋊#95C2312yes—
187C3⋊#95C2312yes—
188C3⋊#95C2314yes—
189C3⋊#95C2312yes—
190#554—68no—
191#533—68no—
192C2×C4⋊Q8—31no—
193C2×C4⋊Q8—32no—
194C2×C4⋊Q8C2×D311yescharacteristic
195C2×#125—32no—
196C2×#125—32no—
197C2×C22⋊Q8—32no—
198C2×C22⋊Q8—34no—
199C2×C22⋊Q8—32no—
200C2×C22⋊Q8—32no—
201C2×C22⋊Q8—32no—
202C2×C22⋊Q8—31no—
203C2×C22⋊Q8—32no—
204C2×#121—31no—
205C2×C4×Q8—32no—
206C2×C4×Q8—32no—
207C2×C4×Q8—31no—
208C2×C4×D4—32no—
209C2×C4×D4—31no—
210C2×C4×D4—32no—
211C2×#117—32no—
212C22×C4⋊C4—32no—
213C22×C42—31no—
214#399—34no—
215#399—34no—
216#399—34no—
217#398—34no—
218#398—34no—
219#398—34no—
220#396—34no—
221#396—34no—
222#391—31no—
223#391—32no—
224#391C2×D314yes—
225#390—31no—
226#390—32no—
227#390—34no—
228#389—31no—
229#389—32no—
230#389—34no—
231#389—32no—
232#389—31no—
233#389—34no—
234#389C2×D312yes—
235#389C2×D312yes—
236#388—34no—
237#388—32no—
238#387—34no—
239#387—32no—
240#386—34no—
241#386—32no—
242#385—34no—
243#385—32no—
244#384—34no—
245#384—32no—
246#380—31no—
247#380—34no—
248#380—31no—
249C4×C4⋊C4—32no—
250C4×C4⋊C4C2×D312yes—
251C4×C4⋊C4C2×D312yes—
252C4×C4⋊C4C2×D311yescharacteristic
253C4×C4⋊C4C2×D311yescharacteristic
254C4×C22⋊C4—34no—
255C4×C22⋊C4—32no—
256C4×C22⋊C4—32no—
257C23×D3C2411yescharacteristic
258C23×D3C2412yes—
259C2×C3×Q8—42no—
260C2×C3×Q8—42no—
261C2×C3×Q8C2×D418yes—
262C22×C3×C4C2412yes—
263C22×C3×C4C2412yes—
264C22×C3×C4C2411yescharacteristic
265C22×C3×C4C2414yes—
266C22×C3×C4C2412yes—
267C22×C3×C4C2412yes—
268C22×C3×C4C2411yescharacteristic
269C22×C3×C4C2411yescharacteristic
270C22×Dic3C2412yes—
271C22×Dic3C2411yescharacteristic
272C22×Dic3C2411yescharacteristic
273C22×Dic3C2414yes—
274C22×Dic3C2412yes—
275C22×Dic3C2412yes—
276C22×Dic3C2411yescharacteristic
277C2×D12—22no—
278C2×D12—22no—
279C2×D12—42no—
280C2×D12—42no—
281C2×D12C2×Q814yes—
282C2×D12C2×Q818yes—
283C2×C4×D3—22no—
284C2×C4×D3—22no—
285C2×C4×D3—22no—
286C2×C4×D3—22no—
287C2×C4×D3—24no—
288C2×C4×D3—24no—
289C2×C4×D3—22no—
290C2×C4×D3—22no—
291C2×C4×D3—24no—
292C2×C4×D3—28no—
293C2×C4×D3—41no—
294C2×C4×D3—41no—
295C2×C4×D3—44no—
296C2×C4×D3—44no—
297C2×C4×D3C2×Q814yes—
298C2×Dic6—22no—
299C2×Dic6—24no—
300C2×Dic6—24no—
301C2×Dic6—22no—
302C2×Dic6—22no—
303C2×Dic6—24no—
304C3×C4⋊C4—22no—
305C3×C4⋊C4—22no—
306C3×C4⋊C4—44no—
307C3×C4⋊C4C2×D418yes—
308C3×C4⋊C4C2×D418yes—
309C3×C4⋊C4C2×Q814yes—
310C3×C4⋊C4#4114yes—
311C3×C42—24no—
312C3×C42—24no—
313C3×C42—44no—
314C3×C42C2×D414yes—
315(C2×D3)⋊C4—24no—
316(C2×D3)⋊C4—28no—
317(C2×D3)⋊C4—28no—
318(C2×D3)⋊C4—24no—
319(C2×D3)⋊C4—28no—
320(C2×D3)⋊C4—42no—
321(C2×D3)⋊C4—42no—
322(C2×D3)⋊C4—44no—
323(C2×D3)⋊C4—42no—
324(C2×D3)⋊C4—42no—
325(C2×D3)⋊C4C2×Q818yes—
326C4⋊Dic3—22no—
327C4⋊Dic3—24no—
328C4⋊Dic3—24no—
329C4⋊Dic3—22no—
330C4⋊Dic3—28no—
331C4⋊Dic3—28no—
332C4⋊Dic3—28no—
333C4⋊Dic3—24no—
334C4⋊Dic3—44no—
335C4⋊Dic3—44no—
336C4⋊Dic3—42no—
337C4⋊Dic3—44no—
338C4⋊Dic3—42no—
339Dic3⋊C4—24no—
340Dic3⋊C4—28no—
341Dic3⋊C4—28no—
342C4×Dic3—24no—
343C4×Dic3—22no—
344C4×Dic3—22no—
345C4×Dic3—22no—
346C4×Dic3—28no—
347C22×Q8—31no—
348C22×Q8—32no—
349C22×Q8C22×D312yes—
350C22×D4—31no—
351C22×D4—32no—
352C23×C4—31no—
353C23×C4—32no—
354C23×C4—31no—
355C23×C4—34no—
356C23×C4—31no—
357C4⋊Q8—64no—
358C4⋊Q8—124no—
359C4⋊Q8D1218yescomplemented
360#125—68no—
361#125—68no—
362C22⋊Q8—68no—
363C22⋊Q8—616no—
364C22⋊Q8—68no—
365C22⋊Q8—68no—
366C22⋊Q8—68no—
367C22⋊Q8—64no—
368C22⋊Q8—124no—
369#121—38no—
370C4×Q8—68no—
371C4×Q8—68no—
372C4×Q8—64no—
373C4×D4—68no—
374C4×D4—64no—
375C4×D4—124no—
376#117—68no—
377C2×C4⋊C4—31no—
378C2×C4⋊C4—34no—
379C2×C4⋊C4—32no—
380C2×C4⋊C4—31no—
381C2×C4⋊C4—32no—
382C2×C4⋊C4—34no—
383C2×C4⋊C4—34no—
384C2×C4⋊C4—32no—
385C2×C4⋊C4—34no—
386C2×C4⋊C4—32no—
387C2×C4⋊C4—34no—
388C2×C4⋊C4—32no—
389C2×C4⋊C4—34no—
390C2×C4⋊C4—34no—
391C2×C4⋊C4—34no—
392C2×C4⋊C4—32no—
393C2×C4⋊C4—68no—
394C2×C4⋊C4C22×D311yescharacteristic
395C2×C4⋊C4C22×D311yescharacteristic
396C2×C4⋊C4C22×D314yes—
397C2×C4⋊C4C22×D312yes—
398C2×C4⋊C4C22×D312yes—
399C2×C4⋊C4C22×D311yescharacteristic
400C2×C4⋊C4C22×D311yescharacteristic
401C2×C22⋊C4—32no—
402C2×C22⋊C4—34no—
403C2×C22⋊C4—32no—
404C2×C22⋊C4—34no—
405C2×C22⋊C4—34no—
406C2×C22⋊C4—32no—
407C2×C22⋊C4—32no—
408C2×C22⋊C4—32no—
409C2×C22⋊C4—34no—
410C2×C22⋊C4—32no—
411C2×C22⋊C4—32no—
412C2×C42—34no—
413C2×C42—32no—
414C2×C42—31no—
415C2×C42—31no—
416C2×C42—31no—
417C2×C42—64no—
418C2×C42C22×D312yes—
419C2×C42C22×D312yes—
420C2×C42C22×D314yes—
421C2×C42C22×D311yescharacteristic
422#95—32no—
423#95—32no—
424#95—32no—
425#95—34no—
426#95—32no—
427#95—32no—
428#95—32no—
429#95—34no—
430#95C22×D314yes—
431#95C22×D312yes—
432#95C22×D314yes—
433#95C22×D312yes—
434C23×C3C2511yescharacteristic
435C22×D3—21no—
436C22×D3—22no—
437C22×D3—21no—
438C22×D3—22no—
439C22×D3—22no—
440C22×D3—21no—
441C22×D3—21no—
442C22×D3—22no—
443C22×D3—21no—
444C22×D3—22no—
445C22×D3—22no—
446C22×D3—21no—
447C22×D3C22×Q814yes—
448C22×D3C22×Q812yes—
449C3×Q8—48no—
450C2×C3×C4—22no—
451C2×C3×C4—22no—
452C2×C3×C4—22no—
453C2×C3×C4—22no—
454C2×C3×C4—24no—
455C2×C3×C4—24no—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
458C2×C3×C4—22no—
459C2×C3×C4—22no—
460C2×C3×C4—22no—
461C2×C3×C4—22no—
462C2×C3×C4—22no—
463C2×C3×C4—22no—
464C2×C3×C4C22×D412yes—
465C2×C3×C4C22×D418yes—
466C2×C3×C4C22×D412yes—
467C2×C3×C4C22×D412yes—
468C2×C3×C4C22×Q814yes—
469C2×C3×C4C22×Q812yes—
470C2×C3×C4C2×#4114yes—
471C2×C3×C4C2×#4112yes—
472C2×C3×C4H(5,𝔽2)12yes—
473C2×C3×C42−1+412yes—
474C2×Dic3—21no—
475C2×Dic3—21no—
476C2×Dic3—21no—
477C2×Dic3—21no—
478C2×Dic3—22no—
479C2×Dic3—24no—
480C2×Dic3—22no—
481C2×Dic3—22no—
482C2×Dic3—21no—
483C2×Dic3—22no—
484C2×Dic3—24no—
485C2×Dic3—22no—
486C2×Dic3—22no—
487C2×Dic3—24no—
488C2×Dic3—22no—
489C2×Dic3—21no—
490C2×Dic3—21no—
491C2×Dic3—22no—
492C2×Dic3—21no—
493C2×Dic3—22no—
494C2×Dic3C22×Q812yes—
495D12—28no—
496D12—48no—
497C4×D3—28no—
498C4×D3—44no—
499C4×D3—44no—
500C4×D3—48no—
501C4×D3—88no—
502Dic6—44no—
503Dic6—48no—
504C24—32no—
505C24—31no—
506C2×Q8—42no—
507C2×Q8—42no—
508C2×Q8—62no—
509C2×Q8—64no—
510C2×Q8—62no—
511C2×Q8—64no—
512C2×Q8—64no—
513C2×Q8—62no—
514C2×Q8C2×D1218yes—
515C2×D4—34no—
516C2×D4—38no—
517C2×D4—62no—
518C2×D4—62no—
519C2×D4—122no—
520C2×D4—122no—
521C22×C4—31no—
522C22×C4—34no—
523C22×C4—32no—
524C22×C4—31no—
525C22×C4—31no—
526C22×C4—32no—
527C22×C4—34no—
528C22×C4—32no—
529C22×C4—62no—
530C22×C4—62no—
531C22×C4—62no—
532C22×C4—62no—
533C22×C4—64no—
534C22×C4—64no—
535C22×C4—62no—
536C22×C4—62no—
537C22×C4—64no—
538C22×C4—68no—
539C22×C4—121no—
540C22×C4—121no—
541C22×C4—124no—
542C22×C4—124no—
543C22×C4C23×D312yes—
544C22×C4C23×D312yes—
545C22×C4C23×D311yescharacteristic
546C22×C4C23×D314yes—
547C22×C4C23×D312yes—
548C22×C4C23×D312yes—
549C22×C4C23×D311yescharacteristic
550C22×C4C23×D311yescharacteristic
551C4⋊C4—22no—
552C4⋊C4—22no—
553C4⋊C4—44no—
554C4⋊C4—62no—
555C4⋊C4—68no—
556C4⋊C4—64no—
557C4⋊C4—62no—
558C4⋊C4—64no—
559C4⋊C4—68no—
560C4⋊C4—68no—
561C4⋊C4—64no—
562C4⋊C4—68no—
563C4⋊C4—64no—
564C4⋊C4—68no—
565C4⋊C4—122no—
566C4⋊C4—124no—
567C4⋊C4—124no—
568C4⋊C4—124no—
569C4⋊C4—122no—
570C4⋊C4C2×D1218yes—
571C4⋊C4C2×D1218yes—
572C4⋊C4D3×Q814yes—
573C4⋊C4#23914yes—
574C22⋊C4—38no—
575C22⋊C4—68no—
576C22⋊C4—68no—
577C22⋊C4—64no—
578C22⋊C4—68no—
579C22⋊C4—64no—
580C22⋊C4—122no—
581C22⋊C4—122no—
582C22⋊C4—124no—
583C22⋊C4—122no—
584C22⋊C4—122no—
585C42—24no—
586C42—24no—
587C42—44no—
588C42—62no—
589C42—62no—
590C42—62no—
591C42—68no—
592C42—64no—
593C42C2×D1214yes—
594C22×C3C23×D411yescharacteristic
595C22×C3C23×Q811yescharacteristic
596C22×C3C22×#4111yescharacteristic
597C22×C3C2×H(5,𝔽2)11yescharacteristic
598C22×C3C2×2−1+411yescharacteristic
599C22×C3#58511yescharacteristic
600C22×C3#58511yescharacteristic
601C2×D3—22no—
602C2×D3—24no—
603C2×D3—22no—
604C2×D3—24no—
605C2×D3—22no—
606C2×D3—24no—
607C2×D3—41no—
608C2×D3—42no—
609C2×D3—41no—
610C2×D3—42no—
611C2×D3—41no—
612C2×D3—42no—
613C2×D3—42no—
614C2×D3—41no—
615C3×C4—22no—
616C3×C4—28no—
617C3×C4—24no—
618C3×C4—24no—
619C3×C4—42no—
620C3×C4—42no—
621C3×C4D4×Q814yes—
622C3×C4#55014yes—
623Dic3—22no—
624Dic3—44no—
625Dic3—42no—
626Dic3—41no—
627Dic3—42no—
628Dic3—41no—
629Dic3—42no—
630C23—34no—
631C23—32no—
632C23—61no—
633C23—62no—
634C23—62no—
635C23—61no—
636C23—62no—
637C23—61no—
638C23—61no—
639C23—62no—
640C23—61no—
641C23—62no—
642C23—62no—
643C23—61no—
644C23C24×D311yescharacteristic
645Q8—48no—
646Q8—124no—
647Q8—128no—
648D4—68no—
649D4—128no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—24no—
655C2×C4—24no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—32no—
665C2×C4—61no—
666C2×C4—61no—
667C2×C4—68no—
668C2×C4—61no—
669C2×C4—61no—
670C2×C4—62no—
671C2×C4—64no—
672C2×C4—62no—
673C2×C4—62no—
674C2×C4—62no—
675C2×C4—64no—
676C2×C4—61no—
677C2×C4—62no—
678C2×C4—61no—
679C2×C4—62no—
680C2×C4—64no—
681C2×C4—62no—
682C2×C4—61no—
683C2×C4—62no—
684C2×C4—61no—
685C2×C4—62no—
686C2×C4—124no—
687C2×C4—124no—
688C2×C4—128no—
689C2×C4—248no—
690C2×C4C22×D1212yes—
691C2×C4C22×D1218yes—
692C2×C4C22×D1212yes—
693C2×C4C22×D1212yes—
694C2×C4C2×D3×Q814yes—
695C2×C4C2×D3×Q812yes—
696C2×C4C2×#23914yes—
697C2×C4C2×#23912yes—
698C2×C4#100912yes—
699C2×C4#101012yes—
700C2×C3C2×D4×Q811yescharacteristic
701C2×C3C2×#55011yescharacteristic
702C2×C3Q8×#4111yescharacteristic
703C2×C3#348511yescharacteristic
704C2×C3#350111yescharacteristic
705C2×C3#351511yescharacteristic
706C2×C3#354711yescharacteristic
707D3—42no—
708D3—44no—
709C22—62no—
710C22—64no—
711C22—62no—
712C22—64no—
713C22—64no—
714C22—62no—
715C22—121no—
716C22—122no—
717C22—121no—
718C22—122no—
719C22—121no—
720C22—122no—
721C22—122no—
722C22—121no—
723C22C23×D1211yescharacteristic
724C22C22×D3×Q811yescharacteristic
725C22C22×#23911yescharacteristic
726C22C2×#100911yescharacteristic
727C22C2×#101011yescharacteristic
728C22#596611yescharacteristic
729C22#596611yescharacteristic
730C4—22no—
731C4—28no—
732C4—24no—
733C4—24no—
734C4—42no—
735C4—42no—
736C4—62no—
737C4—121no—
738C4—122no—
739C4—122no—
740C4—124no—
741C4—121no—
742C4—122no—
743C4Q8×D1214yes—
744C4#557714yes—
745C3#5905211yescharacteristic, complemented, Sylow
746C2—122no—
747C2—124no—
748C2C2×#557711yescharacteristic
749C2C2×Q8×D1211yescharacteristic
750C2#8585811yescharacteristic
751C2#8693011yescharacteristic
752C2#8694811yescharacteristic
753C2#8697711yescharacteristic
754C2Q8×#23911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2369C2
prime radicalC2×#895C22
hypercenter#2369D3
hypocenterC3#59052
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2369

Complements

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

NH ≅ G/Ntype
1. C2×#5730C2semidirect
2. C2×#5728C2semidirect
3. C3×#2369C2semidirect
4. #76656C2semidirect
5. #76623C2semidirect
6. #76221C2semidirect
7. #76212C2semidirect
8. #76016C2semidirect
9. #76000C2semidirect
10. #73800C2semidirect
11. #73800C2semidirect
12. #73773C2semidirect
13. C4×#897C2semidirect
15. #73717C2semidirect
16. #73711C2semidirect
98. #2369D3semidirect
113. C3×C4⋊Q8D4semidirect
165. #895Q8semidirect
359. C4⋊Q8D12semidirect
745. C3#59052semidirect

Maximal subgroups

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

subgroupindex
C2×#57302
C2×#57282
C3×#23692
#766562
#766232
#762212
#762122
#760162
#760002
#738002
#737732
C4×#8972
C4×#8952
#737172
#737112
#736492
#590523