Finite Group Databasebeta

← #11634189

Subgroups — #11634189

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×#5728C211yesmaximal, characteristic, complemented
2C2×#5579C211yesmaximal, characteristic, complemented
3C3×#2546C211yesmaximal, characteristic, complemented
4#83259C211yesmaximal, characteristic, complemented
5#83259C212yesmaximal, complemented
6#83254C212yesmaximal, complemented
7C4×#946C211yesmaximal, characteristic, complemented
8#77986C214yesmaximal, complemented
9#77743C214yesmaximal, complemented
10#76621C212yesmaximal, complemented
11#76615C212yesmaximal, complemented
12#76224C212yesmaximal, complemented
13#76065C212yesmaximal, complemented
14#76015C212yesmaximal, complemented
15#75985C212yesmaximal
16C4×#895C211yesmaximal, characteristic
17#73656C211yesmaximal, characteristic, complemented
18#59052—31nomaximal, Sylow
19C2×C3×C4⋊Q8C2211yescharacteristic
20C2×C3×C4⋊Q8C2212yes—
21C2×C3×C4×Q8C2211yescharacteristic
22C2×#946C2212yes—
23C2×#946C2211yescharacteristic
24C2×#946C2212yes—
25C2×#946C2212yes—
26C2×#946C2212yes—
27C2×Q8×Dic3C2212yes—
28#5728—28no—
29#5579—28no—
30C2×#897C2212yes—
31C2×#896C2214yes—
32C2×#895C2211yescharacteristic
33C2×#892C2212yes—
34C2×D3×C4⋊C4C2212yes—
35C2×#890C2212yes—
36C2×#887C2212yes—
37C2×C4×D12C2211yescharacteristic
38C2×C4×D12C2212yes—
39C2×C4×D12C2212yes—
40C2×C42×D3C2211yescharacteristic
41C2×#870C2212yes—
42C2×#869C2211yescharacteristic
43C3×#398C2214yes—
44C3×#391C2212yes—
45C3×#389C2212yes—
46C3×#389C2212yes—
47C3×C4×C4⋊C4C2211yescharacteristic
48#5229C2211yescharacteristic
49#4994C2214yes—
50#4993C2214yes—
51#4993C2214yes—
52#4993C2214yes—
53#4990C2214yes—
54#4989C2212yes—
55#4988C2211yescharacteristic
56#4988C2214yes—
57#4988C2212yes—
58#4987C2211yescharacteristic
59#4987C2211yescharacteristic
60#4984C2211yescharacteristic
61#4982C2214yes—
62#4978C2212yes—
63#4976C2214yes—
64#4975C2214yes—
65#4975C2212yes—
66Dic3×C4⋊C4C2212yes—
67#4972C2211yescharacteristic
68#4972C2212yes—
69C4×(C2×D3)⋊C4C2212yes—
70C4×(C2×D3)⋊C4C2212yes—
71C4×C4⋊Dic3C2211yescharacteristic
72C4×C4⋊Dic3C2212yes—
73C4×Dic3⋊C4C2212yes—
74#4928C2212yes—
75#4676C2214yes—
76#4670C2212yes—
77#4668C2214yes—
78#4667C2214yes—
79#4666C2214yes—
80#4665C2212yes—
81#4665C2214yes—
82#4657C2214yes—
83#4652C2214yes—
84#4647C2214yes—
85#4646C2214yes—
86C2×#554—31no—
87C2×#533—31no—
88#2732—34no—
89#2552—32no—
90#2546D311yescharacteristic, complemented
91#2542—31no—
92#2542—32no—
93#2454—32no—
94#2441—32no—
95#2429—32no—
96#2423—34no—
97#2417—32no—
98#2369—31no—
99#2363—32no—
100#2360—32no—
101C4×C22⋊Q8—31no—
102C4×#121—31no—
103C22×C3×Q8C2311yescharacteristic
104C22×C3×Q8C2312yes—
105C22×D12C2311yescharacteristic
106C22×D12C2312yes—
107C22×C4×D3C2312yes—
108C22×C4×D3C2311yescharacteristic
109C22×C4×D3C2311yescharacteristic
110C22×C4×D3C2311yescharacteristic
111C22×C4×D3C2314yes—
112C22×Dic6C2312yes—
113C3×C4⋊Q8—24no—
114C3×C4⋊Q8—44no—
115C3×C4×Q8—24no—
116C2×C3×C4⋊C4C2311yescharacteristic
117C2×C3×C4⋊C4C2311yescharacteristic
118C2×C3×C4⋊C4C2312yes—
119C2×C3×C4⋊C4C2312yes—
120C2×C3×C4⋊C4C2312yes—
121C2×C3×C4⋊C4C2314yes—
122C2×C3×C4⋊C4C2314yes—
123C2×C3×C4⋊C4C2311yescharacteristic
124C2×C3×C42C2312yes—
125C2×C3×C42C2312yes—
126C2×C3×C42C2311yescharacteristic
127#946—28no—
128#946—28no—
129#946—24no—
130#946—28no—
131#946—44no—
132Q8×Dic3—28no—
133C2×(C2×D3)⋊C4C2312yes—
134C2×(C2×D3)⋊C4C2314yes—
135C2×(C2×D3)⋊C4C2314yes—
136C2×(C2×D3)⋊C4C2312yes—
137C2×(C2×D3)⋊C4C2314yes—
138C2×(C2×D3)⋊C4C2312yes—
139C2×(C2×D3)⋊C4C2314yes—
140C2×(C2×D3)⋊C4C2312yes—
141C2×(C2×D3)⋊C4C2312yes—
142C2×(C2×D3)⋊C4C2312yes—
143C2×(C2×D3)⋊C4C2312yes—
144C2×C4⋊Dic3C2314yes—
145C2×C4⋊Dic3C2311yescharacteristic
146C2×C4⋊Dic3C2311yescharacteristic
147C2×C4⋊Dic3C2312yes—
148C2×C4⋊Dic3C2312yes—
149C2×C4⋊Dic3C2312yes—
150C2×C4⋊Dic3C2311yescharacteristic
151C2×Dic3⋊C4C2314yes—
152C2×Dic3⋊C4C2314yes—
153C2×Dic3⋊C4C2314yes—
154C2×Dic3⋊C4C2312yes—
155C2×Dic3⋊C4C2314yes—
156C2×Dic3⋊C4C2314yes—
157C2×Dic3⋊C4C2312yes—
158C2×Dic3⋊C4C2314yes—
159C2×C4×Dic3C2314yes—
160C2×C4×Dic3C2311yescharacteristic
161C2×C4×Dic3C2311yescharacteristic
162C2×C4×Dic3C2312yes—
163C2×C4×Dic3C2311yescharacteristic
164C2×C4×Dic3C2314yes—
165#897—28no—
166#896—216no—
167#895Q818yescomplemented
168#892—28no—
169D3×C4⋊C4—28no—
170#890—28no—
171#887—28no—
172C4×D12—24no—
173C4×D12—28no—
174C4×D12—44no—
175C42×D3—24no—
176#870—28no—
177#869D418yescomplemented
178C3×#95C2312yes—
179C3×#95C2314yes—
180C3×#95C2314yes—
181C3⋊#95C2312yes—
182C3⋊#95C2314yes—
183C3⋊#95C2314yes—
184C3⋊#95C2312yes—
185C3⋊#95C2312yes—
186C3⋊#95C2312yes—
187C3⋊#95C2312yes—
188C3⋊#95C2312yes—
189C3⋊#95C2312yes—
190#554—68no—
191#533—68no—
192C2×C4⋊Q8—31no—
193C2×C4⋊Q8C2×D311yescharacteristic
194C2×C4⋊Q8C2×D312yes—
195C2×#125—32no—
196C2×#125—32no—
197C2×C22⋊Q8—32no—
198C2×C22⋊Q8—32no—
199C2×C22⋊Q8—32no—
200C2×C22⋊Q8—31no—
201C2×C22⋊Q8—32no—
202C2×C22⋊Q8—32no—
203C2×C22⋊Q8—34no—
204C2×#121—31no—
205C2×C4×Q8—32no—
206C2×C4×Q8—32no—
207C2×C4×Q8C2×D311yescharacteristic
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#398C2×D314yes—
220#396—34no—
221#396—34no—
222#391—31no—
223#391—34no—
224#391C2×D312yes—
225#390—32no—
226#390—34no—
227#390—31no—
228#389—31no—
229#389—32no—
230#389—34no—
231#389—31no—
232#389—32no—
233#389—34no—
234#389C2×D312yes—
235#389C2×D312yes—
236#388—34no—
237#388—32no—
238#387—32no—
239#387—34no—
240#386—34no—
241#386—32no—
242#385—32no—
243#385—34no—
244#384—34no—
245#384—32no—
246#380—31no—
247#380—31no—
248#380—34no—
249C4×C4⋊C4—32no—
250C4×C4⋊C4—32no—
251C4×C4⋊C4—31no—
252C4×C4⋊C4—32no—
253C4×C4⋊C4C2×D311yescharacteristic
254C4×C22⋊C4—32no—
255C4×C22⋊C4—32no—
256C4×C22⋊C4—34no—
257C23×D3C2411yescharacteristic
258C23×D3C2412yes—
259C2×C3×Q8—24no—
260C2×C3×Q8—22no—
261C2×C3×Q8—22no—
262C2×C3×Q8—24no—
263C2×C3×Q8—24no—
264C2×C3×Q8—22no—
265C22×C3×C4C2412yes—
266C22×C3×C4C2412yes—
267C22×C3×C4C2412yes—
268C22×C3×C4C2414yes—
269C22×C3×C4C2411yescharacteristic
270C22×C3×C4C2412yes—
271C22×C3×C4C2411yescharacteristic
272C22×C3×C4C2411yescharacteristic
273C22×Dic3C2412yes—
274C22×Dic3C2411yescharacteristic
275C22×Dic3C2411yescharacteristic
276C22×Dic3C2412yes—
277C22×Dic3C2414yes—
278C22×Dic3C2411yescharacteristic
279C22×Dic3C2412yes—
280C2×D12—22no—
281C2×D12—22no—
282C2×D12—42no—
283C2×D12—42no—
284C2×D12C2×Q814yes—
285C2×D12C2×Q818yes—
286C2×C4×D3—22no—
287C2×C4×D3—22no—
288C2×C4×D3—22no—
289C2×C4×D3—22no—
290C2×C4×D3—24no—
291C2×C4×D3—24no—
292C2×C4×D3—22no—
293C2×C4×D3—22no—
294C2×C4×D3—24no—
295C2×C4×D3—28no—
296C2×C4×D3—41no—
297C2×C4×D3—41no—
298C2×C4×D3—44no—
299C2×C4×D3—44no—
300C2×C4×D3C2×Q814yes—
301C2×Dic6—42no—
302C2×Dic6—42no—
303C2×Dic6C2×D418yes—
304C3×C4⋊C4—24no—
305C3×C4⋊C4—24no—
306C3×C4⋊C4—22no—
307C3×C4⋊C4—24no—
308C3×C4⋊C4—22no—
309C3×C4⋊C4—44no—
310C3×C4⋊C4—44no—
311C3×C4⋊C4C2×Q814yes—
312C3×C42—24no—
313C3×C42—24no—
314C3×C42C2×D414yes—
315(C2×D3)⋊C4—24no—
316(C2×D3)⋊C4—28no—
317(C2×D3)⋊C4—28no—
318(C2×D3)⋊C4—28no—
319(C2×D3)⋊C4—24no—
320(C2×D3)⋊C4—42no—
321(C2×D3)⋊C4—42no—
322(C2×D3)⋊C4—42no—
323(C2×D3)⋊C4—42no—
324(C2×D3)⋊C4—44no—
325(C2×D3)⋊C4C2×Q818yes—
326C4⋊Dic3—22no—
327C4⋊Dic3—22no—
328C4⋊Dic3—28no—
329C4⋊Dic3—42no—
330C4⋊Dic3C2×D418yes—
331C4⋊Dic3C2×D418yes—
332C4⋊Dic3#4114yes—
333Dic3⋊C4—28no—
334Dic3⋊C4—28no—
335Dic3⋊C4—28no—
336Dic3⋊C4—28no—
337Dic3⋊C4—24no—
338Dic3⋊C4—42no—
339Dic3⋊C4—44no—
340Dic3⋊C4—44no—
341C4×Dic3—22no—
342C4×Dic3—22no—
343C4×Dic3—22no—
344C4×Dic3—24no—
345C4×Dic3—28no—
346C4×Dic3—44no—
347C22×Q8—32no—
348C22×Q8C22×D312yes—
349C22×Q8C22×D311yescharacteristic
350C22×D4—31no—
351C22×D4—32no—
352C23×C4—31no—
353C23×C4—32no—
354C23×C4—31no—
355C23×C4—34no—
356C23×C4—31no—
357C4⋊Q8—24no—
358C4⋊Q8—38no—
359C4⋊Q8—44no—
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—24no—
371C4×Q8—68no—
372C4×Q8—68no—
373C4×D4—68no—
374C4×D4—64no—
375C4×D4—124no—
376#117—68no—
377C2×C4⋊C4—32no—
378C2×C4⋊C4—32no—
379C2×C4⋊C4—31no—
380C2×C4⋊C4—34no—
381C2×C4⋊C4—31no—
382C2×C4⋊C4—34no—
383C2×C4⋊C4—34no—
384C2×C4⋊C4—34no—
385C2×C4⋊C4—31no—
386C2×C4⋊C4—32no—
387C2×C4⋊C4—34no—
388C2×C4⋊C4—32no—
389C2×C4⋊C4—34no—
390C2×C4⋊C4—32no—
391C2×C4⋊C4—34no—
392C2×C4⋊C4—68no—
393C2×C4⋊C4C22×D311yescharacteristic
394C2×C4⋊C4C22×D312yes—
395C2×C4⋊C4C22×D312yes—
396C2×C4⋊C4C22×D312yes—
397C2×C4⋊C4C22×D311yescharacteristic
398C2×C4⋊C4C22×D314yes—
399C2×C4⋊C4C22×D314yes—
400C2×C4⋊C4C22×D311yescharacteristic
401C2×C22⋊C4—32no—
402C2×C22⋊C4—34no—
403C2×C22⋊C4—32no—
404C2×C22⋊C4—34no—
405C2×C22⋊C4—32no—
406C2×C22⋊C4—34no—
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—31no—
414C2×C42—31no—
415C2×C42—31no—
416C2×C42—32no—
417C2×C42—34no—
418C2×C42—64no—
419C2×C42C22×D312yes—
420C2×C42C22×D312yes—
421C2×C42C22×D311yescharacteristic
422#95—32no—
423#95—32no—
424#95—32no—
425#95—32no—
426#95—32no—
427#95—34no—
428#95—32no—
429#95—32no—
430#95—34no—
431#95C22×D314yes—
432#95C22×D312yes—
433#95C22×D314yes—
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—
450C3×Q8—44no—
451C2×C3×C4—22no—
452C2×C3×C4—22no—
453C2×C3×C4—21no—
454C2×C3×C4—21no—
455C2×C3×C4—24no—
456C2×C3×C4—22no—
457C2×C3×C4—22no—
458C2×C3×C4—22no—
459C2×C3×C4—24no—
460C2×C3×C4—24no—
461C2×C3×C4—22no—
462C2×C3×C4—22no—
463C2×C3×C4—22no—
464C2×C3×C4—22no—
465C2×C3×C4—22no—
466C2×C3×C4—22no—
467C2×C3×C4C22×D412yes—
468C2×C3×C4C22×D412yes—
469C2×C3×C4C22×D412yes—
470C2×C3×C4C22×Q814yes—
471C2×C3×C4C22×Q812yes—
472C2×C3×C4C2×#4112yes—
473C2×C3×C4H(5,𝔽2)12yes—
474C2×C3×C42−1+412yes—
475C2×Dic3—21no—
476C2×Dic3—22no—
477C2×Dic3—21no—
478C2×Dic3—22no—
479C2×Dic3—24no—
480C2×Dic3—24no—
481C2×Dic3—21no—
482C2×Dic3—21no—
483C2×Dic3—22no—
484C2×Dic3—21no—
485C2×Dic3—22no—
486C2×Dic3—22no—
487C2×Dic3—22no—
488C2×Dic3—21no—
489C2×Dic3—22no—
490C2×Dic3—22no—
491C2×Dic3—21no—
492C2×Dic3—21no—
493C2×Dic3C22×D418yes—
494C2×Dic3C22×Q812yes—
495C2×Dic3C2×#4114yes—
496D12—28no—
497D12—48no—
498C4×D3—28no—
499C4×D3—44no—
500C4×D3—44no—
501C4×D3—48no—
502C4×D3—88no—
503Dic6—48no—
504C24—32no—
505C24—31no—
506C2×Q8—22no—
507C2×Q8—24no—
508C2×Q8—24no—
509C2×Q8—22no—
510C2×Q8—24no—
511C2×Q8—22no—
512C2×Q8—38no—
513C2×Q8—122no—
514C2×Q8—122no—
515C2×D4—34no—
516C2×D4—38no—
517C2×D4—62no—
518C2×D4—62no—
519C2×D4—122no—
520C2×D4—122no—
521C22×C4—31no—
522C22×C4—32no—
523C22×C4—34no—
524C22×C4—34no—
525C22×C4—32no—
526C22×C4—31no—
527C22×C4—31no—
528C22×C4—32no—
529C22×C4—68no—
530C22×C4—62no—
531C22×C4—62no—
532C22×C4—62no—
533C22×C4—62no—
534C22×C4—64no—
535C22×C4—62no—
536C22×C4—64no—
537C22×C4—64no—
538C22×C4—62no—
539C22×C4—121no—
540C22×C4—121no—
541C22×C4—124no—
542C22×C4—124no—
543C22×C4C23×D312yes—
544C22×C4C23×D312yes—
545C22×C4C23×D312yes—
546C22×C4C23×D314yes—
547C22×C4C23×D311yescharacteristic
548C22×C4C23×D312yes—
549C22×C4C23×D311yescharacteristic
550C22×C4C23×D311yescharacteristic
551C4⋊C4—22no—
552C4⋊C4—24no—
553C4⋊C4—24no—
554C4⋊C4—24no—
555C4⋊C4—22no—
556C4⋊C4—38no—
557C4⋊C4—38no—
558C4⋊C4—34no—
559C4⋊C4—44no—
560C4⋊C4—44no—
561C4⋊C4—68no—
562C4⋊C4—68no—
563C4⋊C4—68no—
564C4⋊C4—68no—
565C4⋊C4—64no—
566C4⋊C4—68no—
567C4⋊C4—62no—
568C4⋊C4—62no—
569C4⋊C4—122no—
570C4⋊C4—124no—
571C4⋊C4—124no—
572C4⋊C4—122no—
573C4⋊C4D3×Q814yes—
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—68no—
588C42—62no—
589C42—62no—
590C42—62no—
591C42—64no—
592C42—124no—
593C42D3×D414yes—
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—24no—
617C3×C4—44no—
618C3×C4—42no—
619C3×C4—42no—
620C3×C4—42no—
621C3×C4D4×Q814yes—
622C3×C4#55014yes—
623Dic3—22no—
624Dic3—28no—
625Dic3—24no—
626Dic3—41no—
627Dic3—42no—
628Dic3—41no—
629Dic3—42no—
630C23—34no—
631C23—32no—
632C23—61no—
633C23—62no—
634C23—62no—
635C23—61no—
636C23—61no—
637C23—62no—
638C23—62no—
639C23—61no—
640C23—61no—
641C23—62no—
642C23—62no—
643C23—61no—
644C23C24×D311yescharacteristic
645Q8—44no—
646Q8—48no—
647Q8—128no—
648D4—68no—
649D4—128no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—24no—
657C2×C4—22no—
658C2×C4—24no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—24no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—38no—
667C2×C4—32no—
668C2×C4—34no—
669C2×C4—61no—
670C2×C4—62no—
671C2×C4—61no—
672C2×C4—62no—
673C2×C4—64no—
674C2×C4—64no—
675C2×C4—68no—
676C2×C4—61no—
677C2×C4—61no—
678C2×C4—62no—
679C2×C4—62no—
680C2×C4—61no—
681C2×C4—62no—
682C2×C4—62no—
683C2×C4—61no—
684C2×C4—62no—
685C2×C4—61no—
686C2×C4—62no—
687C2×C4—61no—
688C2×C4—124no—
689C2×C4—124no—
690C2×C4—128no—
691C2×C4—248no—
692C2×C4C2×D3×D412yes—
693C2×C4C2×D3×D412yes—
694C2×C4C2×D3×D412yes—
695C2×C4#100412yes—
696C2×C4C2×D3×Q814yes—
697C2×C4C2×D3×Q812yes—
698C2×C4#100712yes—
699C2×C4D3×#4112yes—
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—64no—
712C22—62no—
713C22—62no—
714C22—64no—
715C22—121no—
716C22—122no—
717C22—121no—
718C22—122no—
719C22—122no—
720C22—121no—
721C22—121no—
722C22—122no—
723C22C22×D3×D411yescharacteristic
724C22C2×#100411yescharacteristic
725C22C22×D3×Q811yescharacteristic
726C22C2×#100711yescharacteristic
727C22C2×D3×#4111yescharacteristic
728C22#596811yescharacteristic
729C22#596811yescharacteristic
730C4—22no—
731C4—24no—
732C4—42no—
733C4—42no—
734C4—44no—
735C4—42no—
736C4—68no—
737C4—62no—
738C4—64no—
739C4—121no—
740C4—121no—
741C4—122no—
742C4—122no—
743C4#559914yes—
744C4#572714yes—
745C3#5905211yescharacteristic, complemented, Sylow
746C2—122no—
747C2—124no—
748C2C2×#559911yescharacteristic
749C2C2×#572711yescharacteristic
750C2#8635411yescharacteristic
751C2#8676111yescharacteristic
752C2#8676311yescharacteristic
753C2#8701511yescharacteristic
754C2#8702111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2546C2
prime radicalC2×#895C22
hypercenter#2546D3
hypocenterC3#59052
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2546

Complements

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

NH ≅ G/Ntype
1. C2×#5728C2semidirect
2. C2×#5579C2semidirect
3. C3×#2546C2semidirect
4. #83259C2semidirect
5. #83259C2semidirect
6. #83254C2semidirect
7. C4×#946C2semidirect
8. #77986C2semidirect
9. #77743C2semidirect
10. #76621C2semidirect
11. #76615C2semidirect
12. #76224C2semidirect
13. #76065C2semidirect
14. #76015C2semidirect
17. #73656C2semidirect
90. #2546D3semidirect
167. #895Q8semidirect
177. #869D4semidirect
745. C3#59052semidirect

Maximal subgroups

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

subgroupindex
C2×#57282
C2×#55792
C3×#25462
#832592
#832542
C4×#9462
#779862
#777432
#766212
#766152
#762242
#760652
#760152
#759852
C4×#8952
#736562
#590523