Finite Group Databasebeta

← #11634188

Subgroups — #11634188

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×#5579C211yesmaximal, characteristic, complemented
2C2×#5470C211yesmaximal, characteristic, complemented
3C3×C4×C22⋊Q8C211yesmaximal, characteristic, complemented
4#82780C212yesmaximal, complemented
5#82475C211yesmaximal, characteristic, complemented
6C4×#930C211yesmaximal, characteristic
7#76625C212yesmaximal, complemented
8#76205C212yesmaximal, complemented
9#74982C214yesmaximal, complemented
10#74541C214yesmaximal, complemented
11#73888C212yesmaximal, complemented
12#73800C211yesmaximal, characteristic, complemented
13#73716C212yesmaximal, complemented
14#73677C212yesmaximal, complemented
15#73656C211yesmaximal, characteristic, complemented
16#73494C212yesmaximal, complemented
17#73469C212yesmaximal
18#59052—31nomaximal, Sylow
19C2×C3×C22⋊Q8C2211yescharacteristic
20C2×C3×C4×Q8C2211yescharacteristic
21C22×C3×C42C2211yescharacteristic
22C2×#946C2212yes—
23C2×#944C2212yes—
24C2×#930C2211yescharacteristic
25C2×C4×#67C2212yes—
26C2×#926C2212yes—
27C2×#924C2212yes—
28C2×#924C2212yes—
29#5579—28no—
30C2×#897C2212yes—
31C2×#897C2212yes—
32C2×#896C2214yes—
33C2×D3×C4⋊C4C2212yes—
34C2×C4×D12C2211yescharacteristic
35C2×C4×D12C2212yes—
36#5470—28no—
37C2×#870C2212yes—
38C2×#870C2212yes—
39C2×#869C2211yescharacteristic
40C2×#869C2211yescharacteristic
41C2×C4×Dic6C2212yes—
42C2×C4×Dic6C2212yes—
43C3×#391C2211yescharacteristic
44C3×#389C2211yescharacteristic
45C3×#387C2212yes—
46C3×#385C2212yes—
47C3×#380C2211yescharacteristic
48C3×C4×C4⋊C4C2211yescharacteristic
49C3×C4×C4⋊C4C2212yes—
50C3×C4×C22⋊C4C2212yes—
51#5213C2212yes—
52#5212C2211yescharacteristic
53#4993C2214yes—
54#4989C2214yes—
55#4981C2214yes—
56#4975C2214yes—
57Dic3×C4⋊C4C2212yes—
58#4973C2212yes—
59#4972C2214yes—
60#4972C2212yes—
61#4957C2214yes—
62#4956C2214yes—
63#4949C2214yes—
64#4948C2214yes—
65#4940C2212yes—
66#4939C2212yes—
67#4939C2211yescharacteristic
68C4×(C2×D3)⋊C4C2212yes—
69#4935C2212yes—
70C4×C4⋊Dic3C2211yescharacteristic
71C4×C4⋊Dic3C2212yes—
72#4928C2212yes—
73#4928C2212yes—
74#4928C2212yes—
75#4928C2211yescharacteristic
76#4677C2214yes—
77#4676C2214yes—
78#4669C2214yes—
79#4667C2214yes—
80#4666C2214yes—
81#4657C2214yes—
82#4657C2214yes—
83#4654C2214yes—
84#4647C2214yes—
85#4646C2214yes—
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#2369—31no—
99#2363—32no—
100#2360—32no—
101C4×C22⋊Q8D311yescharacteristic, complemented
102C4×#121—31no—
103C22×C3×Q8C2311yescharacteristic
104C23×C3×C4C2311yescharacteristic
105C23×C3×C4C2311yescharacteristic
106C23×C3×C4C2311yescharacteristic
107C22×#67C2312yes—
108C22×D12C2311yescharacteristic
109C22×C4×D3C2312yes—
110C22×C4×D3C2314yes—
111C22×Dic6C2312yes—
112C22×Dic6C2312yes—
113C3×C22⋊Q8—24no—
114C3×C4×Q8—24no—
115C2×C3×C4⋊C4C2311yescharacteristic
116C2×C3×C4⋊C4C2311yescharacteristic
117C2×C3×C4⋊C4C2312yes—
118C2×C3×C4⋊C4C2312yes—
119C2×C3×C4⋊C4C2312yes—
120C2×C3×C4⋊C4C2311yescharacteristic
121C2×C3×C22⋊C4C2312yes—
122C2×C3×C22⋊C4C2312yes—
123C2×C3×C42—24no—
124C2×C3×C42C2312yes—
125C2×C3×C42C2312yes—
126C2×C3×C42C2311yescharacteristic
127C2×C3×C42C2311yescharacteristic
128C2×C3×C42C2311yescharacteristic
129C2×C3×C42C2311yescharacteristic
130C2×#217C2314yes—
131C2×#217C2312yes—
132#946—28no—
133#944—44no—
134#930Q818yescomplemented
135C4×#67—44no—
136C2×(C2×D3)⋊C4C2314yes—
137C2×(C2×D3)⋊C4C2314yes—
138C2×(C2×D3)⋊C4C2312yes—
139C2×(C2×D3)⋊C4C2312yes—
140C2×(C2×D3)⋊C4C2314yes—
141C2×(C2×D3)⋊C4C2312yes—
142C2×(C2×D3)⋊C4C2312yes—
143#926—28no—
144C2×C4⋊Dic3C2314yes—
145C2×C4⋊Dic3C2311yescharacteristic
146C2×C4⋊Dic3C2312yes—
147C2×C4⋊Dic3C2311yescharacteristic
148C2×C4⋊Dic3C2312yes—
149C2×C4⋊Dic3C2314yes—
150C2×C4⋊Dic3C2312yes—
151C2×C4⋊Dic3C2312yes—
152C2×C4⋊Dic3C2311yescharacteristic
153#924—28no—
154#924—28no—
155C2×Dic3⋊C4C2314yes—
156C2×Dic3⋊C4C2314yes—
157C2×Dic3⋊C4C2314yes—
158C2×Dic3⋊C4C2314yes—
159C2×Dic3⋊C4C2314yes—
160C2×Dic3⋊C4C2314yes—
161C2×Dic3⋊C4C2312yes—
162C2×Dic3⋊C4C2314yes—
163C2×C4×Dic3C2314yes—
164C2×C4×Dic3C2312yes—
165C2×C4×Dic3C2314yes—
166#897—28no—
167#897—44no—
168#896—216no—
169D3×C4⋊C4—28no—
170C4×D12—24no—
171C4×D12—28no—
172#870—28no—
173#870—28no—
174#869—24no—
175#869D418yescomplemented
176C4×Dic6—28no—
177C4×Dic6—28no—
178C3×#95C2312yes—
179C3×#95C2312yes—
180C3×#95C2312yes—
181C3×#95C2312yes—
182C3×#95C2312yes—
183C3⋊#95C2312yes—
184C3⋊#95C2314yes—
185C3⋊#95C2314yes—
186C3⋊#95C2312yes—
187C3⋊#95C2314yes—
188C3⋊#95C2312yes—
189C3⋊#95C2314yes—
190#554—68no—
191#533—68no—
192C2×C4⋊Q8—32no—
193C2×C4⋊Q8—31no—
194C2×C4⋊Q8—31no—
195C2×#125—32no—
196C2×#125—32no—
197C2×C22⋊Q8—32no—
198C2×C22⋊Q8—32no—
199C2×C22⋊Q8—32no—
200C2×C22⋊Q8—32no—
201C2×C22⋊Q8—34no—
202C2×C22⋊Q8—32no—
203C2×C22⋊Q8C2×D311yescharacteristic
204C2×#121—31no—
205C2×C4×Q8—32no—
206C2×C4×Q8—32no—
207C2×C4×Q8C2×D311yescharacteristic
208C2×C4×D4—32no—
209C2×C4×D4—32no—
210C2×C4×D4—31no—
211C2×#117—32no—
212C22×C4⋊C4—32no—
213C22×C42C2×D311yescharacteristic
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—32no—
223#391—34no—
224#391C2×D311yescharacteristic
225#390—34no—
226#390—32no—
227#390—31no—
228#389—34no—
229#389—32no—
230#389—32no—
231#389—32no—
232#389—32no—
233#389—31no—
234#389—34no—
235#389C2×D311yescharacteristic
236#388—32no—
237#388—34no—
238#387—34no—
239#387C2×D312yes—
240#386—32no—
241#386—34no—
242#385—34no—
243#385C2×D312yes—
244#384—34no—
245#384—32no—
246#380—31no—
247#380—34no—
248#380C2×D311yescharacteristic
249C4×C4⋊C4—32no—
250C4×C4⋊C4—32no—
251C4×C4⋊C4—31no—
252C4×C4⋊C4C2×D311yescharacteristic
253C4×C4⋊C4C2×D312yes—
254C4×C22⋊C4—32no—
255C4×C22⋊C4—34no—
256C4×C22⋊C4C2×D312yes—
257C24×C3C2411yescharacteristic
258C23×D3C2412yes—
259C2×C3×Q8—22no—
260C2×C3×Q8—22no—
261C2×C3×Q8—22no—
262C22×C3×C4—22no—
263C22×C3×C4—22no—
264C22×C3×C4—22no—
265C22×C3×C4—22no—
266C22×C3×C4—22no—
267C22×C3×C4—22no—
268C22×C3×C4—41no—
269C22×C3×C4—41no—
270C22×C3×C4C2×Q814yes—
271C22×C3×C4C2412yes—
272C22×C3×C4C2412yes—
273C22×C3×C4C2411yescharacteristic
274C22×C3×C4C2411yescharacteristic
275C22×C3×C4C2412yes—
276C22×C3×C4C2411yescharacteristic
277C22×C3×C4C2411yescharacteristic
278C22×C3×C4C2412yes—
279C22×C3×C4C2411yescharacteristic
280C22×C3×C4C2411yescharacteristic
281C2×#67—42no—
282C2×#67—42no—
283C2×#67C2×Q818yes—
284C22×Dic3C2412yes—
285C22×Dic3C2414yes—
286C22×Dic3C2412yes—
287C22×Dic3C2414yes—
288C22×Dic3C2412yes—
289C2×D12—22no—
290C2×D12—22no—
291C2×D12C2×Q814yes—
292C2×C4×D3—24no—
293C2×C4×D3—24no—
294C2×C4×D3—24no—
295C2×C4×D3—28no—
296C2×C4×D3—44no—
297C2×C4×D3—44no—
298C2×Dic6—24no—
299C2×Dic6—24no—
300C2×Dic6—24no—
301C2×Dic6—42no—
302C2×Dic6—42no—
303C2×Dic6C2×D418yes—
304C3×C4⋊C4—22no—
305C3×C4⋊C4—24no—
306C3×C4⋊C4—24no—
307C3×C4⋊C4—22no—
308C3×C4⋊C4—42no—
309C3×C4⋊C4#4114yes—
310C3×C22⋊C4—24no—
311C3×C22⋊C4—42no—
312C3×C42—22no—
313C3×C42—22no—
314C3×C42—22no—
315C3×C42—24no—
316C3×C42—24no—
317C3×C42C2×D414yes—
318#217—28no—
319#217—42no—
320(C2×D3)⋊C4—24no—
321(C2×D3)⋊C4—28no—
322(C2×D3)⋊C4—28no—
323(C2×D3)⋊C4—44no—
324(C2×D3)⋊C4—42no—
325(C2×D3)⋊C4—42no—
326(C2×D3)⋊C4C2×Q818yes—
327C4⋊Dic3—24no—
328C4⋊Dic3—24no—
329C4⋊Dic3—22no—
330C4⋊Dic3—28no—
331C4⋊Dic3—22no—
332C4⋊Dic3—44no—
333C4⋊Dic3C2×D418yes—
334C4⋊Dic3C2×D418yes—
335C4⋊Dic3C2×Q814yes—
336Dic3⋊C4—28no—
337Dic3⋊C4—28no—
338Dic3⋊C4—28no—
339Dic3⋊C4—28no—
340Dic3⋊C4—44no—
341Dic3⋊C4—42no—
342Dic3⋊C4—44no—
343Dic3⋊C4—44no—
344C4×Dic3—24no—
345C4×Dic3—28no—
346C4×Dic3—44no—
347C22×Q8—32no—
348C22×Q8—32no—
349C22×Q8C22×D311yescharacteristic
350C22×D4—32no—
351C22×D4—31no—
352C23×C4—32no—
353C23×C4—34no—
354C23×C4C22×D311yescharacteristic
355C23×C4C22×D311yescharacteristic
356C23×C4C22×D311yescharacteristic
357C4⋊Q8—38no—
358C4⋊Q8—64no—
359C4⋊Q8—124no—
360#125—68no—
361#125—68no—
362C22⋊Q8—24no—
363C22⋊Q8—616no—
364C22⋊Q8—68no—
365C22⋊Q8—68no—
366C22⋊Q8—68no—
367C22⋊Q8—68no—
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—32no—
382C2×C4⋊C4—31no—
383C2×C4⋊C4—34no—
384C2×C4⋊C4—34no—
385C2×C4⋊C4—32no—
386C2×C4⋊C4—34no—
387C2×C4⋊C4—34no—
388C2×C4⋊C4—31no—
389C2×C4⋊C4—32no—
390C2×C4⋊C4—34no—
391C2×C4⋊C4—34no—
392C2×C4⋊C4—34no—
393C2×C4⋊C4—34no—
394C2×C4⋊C4—68no—
395C2×C4⋊C4C22×D311yescharacteristic
396C2×C4⋊C4C22×D312yes—
397C2×C4⋊C4C22×D311yescharacteristic
398C2×C4⋊C4C22×D312yes—
399C2×C4⋊C4C22×D312yes—
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—34no—
409C2×C22⋊C4—32no—
410C2×C22⋊C4C22×D312yes—
411C2×C22⋊C4C22×D312yes—
412C2×C42—24no—
413C2×C42—34no—
414C2×C42—32no—
415C2×C42—34no—
416C2×C42C22×D312yes—
417C2×C42C22×D311yescharacteristic
418C2×C42C22×D311yescharacteristic
419C2×C42C22×D311yescharacteristic
420C2×C42C22×D312yes—
421C2×C42C22×D311yescharacteristic
422#95—32no—
423#95—32no—
424#95—34no—
425#95—34no—
426#95—34no—
427#95—32no—
428#95—34no—
429#95C22×D312yes—
430#95C22×D312yes—
431#95C22×D312yes—
432#95C22×D312yes—
433#95C22×D312yes—
434C23×C3—21no—
435C23×C3—21no—
436C23×C3—21no—
437C23×C3—21no—
438C23×C3—21no—
439C23×C3—21no—
440C23×C3C22×Q812yes—
441C23×C3C2511yescharacteristic
442C22×D3—22no—
443C22×D3—22no—
444C22×D3—22no—
445C22×D3—22no—
446C22×D3—22no—
447C22×D3—22no—
448C22×D3C22×Q814yes—
449C3×Q8—44no—
450C2×C3×C4—21no—
451C2×C3×C4—22no—
452C2×C3×C4—21no—
453C2×C3×C4—22no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—28no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—22no—
460C2×C3×C4—22no—
461C2×C3×C4—22no—
462C2×C3×C4—21no—
463C2×C3×C4—22no—
464C2×C3×C4—21no—
465C2×C3×C4—22no—
466C2×C3×C4—22no—
467C2×C3×C4—22no—
468C2×C3×C4—21no—
469C2×C3×C4—22no—
470C2×C3×C4—21no—
471C2×C3×C4—22no—
472C2×C3×C4—44no—
473C2×C3×C4—44no—
474C2×C3×C4C22×D412yes—
475C2×C3×C4C22×D412yes—
476C2×C3×C4C22×D412yes—
477C2×C3×C4C22×Q812yes—
478C2×C3×C4C22×Q812yes—
479C2×C3×C4C2×#4114yes—
480C2×C3×C4C2×#4112yes—
481C2×C3×C4H(5,𝔽2)12yes—
482C2×C3×C42−1+412yes—
483#67—48no—
484C2×Dic3—22no—
485C2×Dic3—22no—
486C2×Dic3—24no—
487C2×Dic3—24no—
488C2×Dic3—24no—
489C2×Dic3—22no—
490C2×Dic3—22no—
491C2×Dic3—24no—
492C2×Dic3—22no—
493C2×Dic3—24no—
494C2×Dic3—22no—
495C2×Dic3—22no—
496C2×Dic3—22no—
497C2×Dic3C22×D418yes—
498C2×Dic3C22×Q814yes—
499D12—28no—
500C4×D3—48no—
501C4×D3—88no—
502Dic6—48no—
503Dic6—48no—
504C24—32no—
505C24C23×D311yescharacteristic
506C2×Q8—22no—
507C2×Q8—22no—
508C2×Q8—22no—
509C2×Q8—38no—
510C2×Q8—64no—
511C2×Q8—64no—
512C2×Q8—64no—
513C2×Q8—122no—
514C2×Q8—122no—
515C2×D4—38no—
516C2×D4—34no—
517C2×D4—62no—
518C2×D4—62no—
519C2×D4—122no—
520C2×D4—122no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—32no—
528C22×C4—34no—
529C22×C4—32no—
530C22×C4—34no—
531C22×C4—32no—
532C22×C4—41no—
533C22×C4—41no—
534C22×C4—68no—
535C22×C4—64no—
536C22×C4—64no—
537C22×C4—64no—
538C22×C4—124no—
539C22×C4—124no—
540C22×C4D3×Q814yes—
541C22×C4C23×D312yes—
542C22×C4C23×D312yes—
543C22×C4C23×D311yescharacteristic
544C22×C4C23×D311yescharacteristic
545C22×C4C23×D312yes—
546C22×C4C23×D312yes—
547C22×C4C23×D311yescharacteristic
548C22×C4C23×D311yescharacteristic
549C22×C4C23×D311yescharacteristic
550C22×C4C23×D311yescharacteristic
551C4⋊C4—24no—
552C4⋊C4—22no—
553C4⋊C4—24no—
554C4⋊C4—22no—
555C4⋊C4—38no—
556C4⋊C4—38no—
557C4⋊C4—34no—
558C4⋊C4—42no—
559C4⋊C4—68no—
560C4⋊C4—68no—
561C4⋊C4—68no—
562C4⋊C4—68no—
563C4⋊C4—68no—
564C4⋊C4—64no—
565C4⋊C4—62no—
566C4⋊C4—64no—
567C4⋊C4—62no—
568C4⋊C4—122no—
569C4⋊C4—124no—
570C4⋊C4—124no—
571C4⋊C4—124no—
572C4⋊C4—124no—
573C4⋊C4#23514yes—
574C22⋊C4—24no—
575C22⋊C4—38no—
576C22⋊C4—42no—
577C22⋊C4—68no—
578C22⋊C4—68no—
579C22⋊C4—68no—
580C22⋊C4—64no—
581C22⋊C4—122no—
582C22⋊C4—124no—
583C22⋊C4—122no—
584C22⋊C4—122no—
585C42—22no—
586C42—22no—
587C42—22no—
588C42—24no—
589C42—24no—
590C42—68no—
591C42—64no—
592C42—124no—
593C42D3×D414yes—
594C22×C3—22no—
595C22×C3—22no—
596C22×C3—22no—
597C22×C3—41no—
598C22×C3—41no—
599C22×C3—41no—
600C22×C3—41no—
601C22×C3C23×D411yescharacteristic
602C22×C3C23×Q811yescharacteristic
603C22×C3C22×#4111yescharacteristic
604C22×C3C2×H(5,𝔽2)11yescharacteristic
605C22×C3C2×2−1+411yescharacteristic
606C22×C3#58511yescharacteristic
607C22×C3#58511yescharacteristic
608C2×D3—24no—
609C2×D3—24no—
610C2×D3—24no—
611C2×D3—42no—
612C2×D3—42no—
613C2×D3—42no—
614C2×D3—42no—
615C3×C4—22no—
616C3×C4—22no—
617C3×C4—24no—
618C3×C4—41no—
619C3×C4—42no—
620C3×C4—42no—
621C3×C4—41no—
622C3×C4—42no—
623C3×C4D4×Q814yes—
624C3×C4#55014yes—
625Dic3—28no—
626Dic3—24no—
627Dic3—44no—
628Dic3—42no—
629Dic3—42no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—34no—
637C23—62no—
638C23—62no—
639C23—62no—
640C23—62no—
641C23—62no—
642C23—62no—
643C23C2×D3×Q812yes—
644C23C24×D311yescharacteristic
645Q8—44no—
646Q8—128no—
647Q8—128no—
648D4—68no—
649D4—128no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—28no—
657C2×C4—22no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—21no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—22no—
672C2×C4—38no—
673C2×C4—34no—
674C2×C4—44no—
675C2×C4—44no—
676C2×C4—62no—
677C2×C4—62no—
678C2×C4—64no—
679C2×C4—64no—
680C2×C4—64no—
681C2×C4—62no—
682C2×C4—64no—
683C2×C4—62no—
684C2×C4—62no—
685C2×C4—62no—
686C2×C4—64no—
687C2×C4—62no—
688C2×C4—62no—
689C2×C4—128no—
690C2×C4—248no—
691C2×C4C2×#23514yes—
692C2×C4C2×#23512yes—
693C2×C4C2×D3×D412yes—
694C2×C4C2×D3×D412yes—
695C2×C4C2×D3×D412yes—
696C2×C4C2×D3×Q812yes—
697C2×C4C2×D3×Q812yes—
698C2×C4#100912yes—
699C2×C4#101012yes—
700C2×C3—42no—
701C2×C3C2×D4×Q811yescharacteristic
702C2×C3C2×#55011yescharacteristic
703C2×C3Q8×#4111yescharacteristic
704C2×C3#348511yescharacteristic
705C2×C3#350111yescharacteristic
706C2×C3#351511yescharacteristic
707C2×C3#354711yescharacteristic
708D3—44no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—64no—
717C22—64no—
718C22—64no—
719C22—122no—
720C22—122no—
721C22—122no—
722C22—122no—
723C22C22×#23511yescharacteristic
724C22C22×D3×D411yescharacteristic
725C22C22×D3×Q811yescharacteristic
726C22C2×#100911yescharacteristic
727C22C2×#101011yescharacteristic
728C22#596411yescharacteristic
729C22#596411yescharacteristic
730C4—22no—
731C4—24no—
732C4—22no—
733C4—41no—
734C4—42no—
735C4—42no—
736C4—41no—
737C4—42no—
738C4—64no—
739C4—68no—
740C4—122no—
741C4—122no—
742C4—124no—
743C4#555314yes—
744C4#563214yes—
745C3#5905211yescharacteristic, complemented, Sylow
746C2—42no—
747C2—124no—
748C2C2×#555311yescharacteristic
749C2Q8×#23511yescharacteristic
750C2#8583111yescharacteristic
751C2C2×#563211yescharacteristic
752C2#8604011yescharacteristic
753C2#8617511yescharacteristic
754C2#8628011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×C4×C22⋊Q8C2
prime radicalC2×#930C22
hypercenterC4×C22⋊Q8D3
hypocenterC3#59052
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ C4×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#5579C2semidirect
2. C2×#5470C2semidirect
3. C3×C4×C22⋊Q8C2semidirect
4. #82780C2semidirect
5. #82475C2semidirect
7. #76625C2semidirect
8. #76205C2semidirect
9. #74982C2semidirect
10. #74541C2semidirect
11. #73888C2semidirect
12. #73800C2semidirect
13. #73716C2semidirect
14. #73677C2semidirect
15. #73656C2semidirect
16. #73494C2semidirect
101. C4×C22⋊Q8D3semidirect
134. #930Q8semidirect
175. #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×#55792
C2×#54702
C3×C4×C22⋊Q82
#827802
#824752
C4×#9302
#766252
#762052
#749822
#745412
#738882
#738002
#737162
#736772
#736562
#734942
#734692
#590523