Finite Group Databasebeta

← #11633858

Subgroups — #11633858

Order 768.

2374 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×D12C211yesmaximal, characteristic, complemented
2C2×#5470C211yesmaximal, characteristic, complemented
3C3×C4×C22⋊Q8C211yesmaximal, characteristic, complemented
4#82751C212yesmaximal, complemented
5#82478C211yesmaximal, characteristic, complemented
6C4×#930C211yesmaximal, characteristic
7#76614C212yesmaximal, complemented
8#76216C212yesmaximal, complemented
9#74999C214yesmaximal, complemented
10#74516C214yesmaximal, complemented
11#73936C212yesmaximal, complemented
12#73807C211yesmaximal, characteristic, complemented
13#73713C212yesmaximal, complemented
14#73677C212yesmaximal, complemented
15#73650C211yesmaximal, characteristic, complemented
16#73492C212yesmaximal, complemented
17#73469C212yesmaximal
18#59036—31nomaximal, Sylow
19C22×D3×Q8C2212yes—
20C2×C3×C22⋊Q8C2211yescharacteristic
21C2×C3×C4×Q8C2211yescharacteristic
22C22×C3×C42C2211yescharacteristic
23C2×#930C2211yescharacteristic
24C2×C4×#67C2212yes—
25C2×#926C2212yes—
26C2×#924C2212yes—
27C2×#924C2212yes—
28Q8×D12—28no—
29C2×#897C2214yes—
30C2×#897C2212yes—
31C2×#887C2212yes—
32C2×C4×D12C2211yescharacteristic
33C2×C4×D12C2212yes—
34#5470—28no—
35C2×#870C2212yes—
36C2×#869C2212yes—
37C2×#869C2211yescharacteristic
38C2×#869C2211yescharacteristic
39C2×C4×Dic6C2212yes—
40C2×C4×Dic6C2212yes—
41C3×#391C2211yescharacteristic
42C3×#389C2211yescharacteristic
43C3×#387C2212yes—
44C3×#385C2212yes—
45C3×#380C2211yescharacteristic
46C3×C4×C4⋊C4C2211yescharacteristic
47C3×C4×C4⋊C4C2212yes—
48C3×C4×C22⋊C4C2212yes—
49#5229C2212yes—
50#5213C2212yes—
51#5212C2211yescharacteristic
52#4993C2214yes—
53#4989C2214yes—
54#4987C2212yes—
55#4987C2212yes—
56#4982C2214yes—
57#4979C2214yes—
58#4979C2214yes—
59#4975C2212yes—
60#4973C2212yes—
61#4957C2214yes—
62#4956C2214yes—
63#4948C2214yes—
64#4947C2214yes—
65#4940C2212yes—
66#4939C2212yes—
67#4939C2211yescharacteristic
68C4×(C2×D3)⋊C4C2212yes—
69#4936C2212yes—
70C4×C4⋊Dic3C2211yescharacteristic
71C4×C4⋊Dic3C2212yes—
72#4928C2212yes—
73#4928C2212yes—
74#4928C2212yes—
75#4928C2211yescharacteristic
76#4676C2214yes—
77#4673C2214yes—
78#4669C2214yes—
79#4667C2214yes—
80#4666C2214yes—
81#4655C2214yes—
82#4653C2214yes—
83#4647C2214yes—
84#4646C2214yes—
85#4646C2214yes—
86C2×D4×Q8—31no—
87C2×#533—31no—
88#2692—34no—
89#2567—31no—
90#2563—31no—
91#2550—32no—
92#2538—32no—
93#2465—34no—
94#2454—32no—
95#2439—32no—
96#2423—32no—
97#2409—32no—
98#2365—31no—
99#2363—32no—
100Q8×C22⋊C4—32no—
101C4×C22⋊Q8D311yescharacteristic, complemented
102C4×#121—31no—
103C22×C3×Q8C2311yescharacteristic
104C23×C3×C4C2311yescharacteristic
105C23×C3×C4C2311yescharacteristic
106C23×C3×C4C2311yescharacteristic
107C22×#67C2312yes—
108C2×D3×Q8—28no—
109C2×D3×Q8—28no—
110C2×D3×Q8—44no—
111C22×D12C2311yescharacteristic
112C22×C4×D3C2312yes—
113C22×C4×D3C2314yes—
114C22×Dic6C2314yes—
115C22×Dic6C2312yes—
116C22×Dic6C2312yes—
117C3×C22⋊Q8—24no—
118C3×C4×Q8—24no—
119C2×C3×C4⋊C4C2311yescharacteristic
120C2×C3×C4⋊C4C2311yescharacteristic
121C2×C3×C4⋊C4C2312yes—
122C2×C3×C4⋊C4C2312yes—
123C2×C3×C4⋊C4C2311yescharacteristic
124C2×C3×C4⋊C4C2312yes—
125C2×C3×C22⋊C4C2312yes—
126C2×C3×C22⋊C4C2312yes—
127C2×C3×C42—24no—
128C2×C3×C42C2312yes—
129C2×C3×C42C2312yes—
130C2×C3×C42C2311yescharacteristic
131C2×C3×C42C2311yescharacteristic
132C2×C3×C42C2311yescharacteristic
133C2×C3×C42C2311yescharacteristic
134C2×#217C2314yes—
135C2×#217C2312yes—
136#930Q818yescomplemented
137C4×#67—44no—
138C2×(C2×D3)⋊C4C2314yes—
139C2×(C2×D3)⋊C4C2312yes—
140C2×(C2×D3)⋊C4C2314yes—
141C2×(C2×D3)⋊C4C2312yes—
142C2×(C2×D3)⋊C4C2314yes—
143C2×(C2×D3)⋊C4C2312yes—
144C2×(C2×D3)⋊C4C2312yes—
145#926—28no—
146C2×C4⋊Dic3C2314yes—
147C2×C4⋊Dic3C2311yescharacteristic
148C2×C4⋊Dic3C2312yes—
149C2×C4⋊Dic3C2311yescharacteristic
150C2×C4⋊Dic3C2312yes—
151C2×C4⋊Dic3C2312yes—
152C2×C4⋊Dic3C2312yes—
153C2×C4⋊Dic3C2311yescharacteristic
154#924—28no—
155#924—28no—
156C2×Dic3⋊C4C2314yes—
157C2×Dic3⋊C4C2314yes—
158C2×Dic3⋊C4C2314yes—
159C2×Dic3⋊C4C2312yes—
160C2×Dic3⋊C4C2314yes—
161C2×Dic3⋊C4C2314yes—
162C2×C4×Dic3C2314yes—
163C2×C4×Dic3C2312yes—
164C2×C4×Dic3C2314yes—
165#897—28no—
166#897—216no—
167#887—44no—
168C4×D12—24no—
169C4×D12—28no—
170#870—28no—
171#869—24no—
172#869—28no—
173#869D418yescomplemented
174C4×Dic6—28no—
175C4×Dic6—28no—
176C3×#95C2312yes—
177C3×#95C2312yes—
178C3×#95C2312yes—
179C3×#95C2312yes—
180C3×#95C2312yes—
181C3⋊#95C2314yes—
182C3⋊#95C2312yes—
183C3⋊#95C2312yes—
184C3⋊#95C2314yes—
185C3⋊#95C2314yes—
186C3⋊#95C2312yes—
187C3⋊#95C2314yes—
188C3⋊#95C2314yes—
189C3⋊#95C2314yes—
190C23×Q8—32no—
191D4×Q8—68no—
192#533—68no—
193C2×C4⋊Q8—31no—
194C2×C4⋊Q8—31no—
195C2×C4⋊Q8—32no—
196C2×#125—32no—
197C2×C22⋊Q8—32no—
198C2×C22⋊Q8—32no—
199C2×C22⋊Q8—32no—
200C2×C22⋊Q8—34no—
201C2×C22⋊Q8C2×D311yescharacteristic
202C2×#121—31no—
203C2×C4×Q8—32no—
204C2×C4×Q8—32no—
205C2×C4×Q8—32no—
206C2×C4×Q8C2×D311yescharacteristic
207C2×C4×D4—32no—
208C2×C4×D4—31no—
209C2×C4×D4—32no—
210C2×#117—32no—
211C22×C42C2×D311yescharacteristic
212#399—34no—
213#398—34no—
214#396—34no—
215#396—34no—
216#395—34no—
217#395—34no—
218#393—34no—
219#393—34no—
220#391—32no—
221#391—32no—
222#391—34no—
223#391—34no—
224#391C2×D311yescharacteristic
225#390—34no—
226#390—32no—
227#390—31no—
228#389—32no—
229#389—32no—
230#389—32no—
231#389—31no—
232#389—34no—
233#389C2×D311yescharacteristic
234#388—32no—
235#388—34no—
236#387—34no—
237#387—34no—
238#387C2×D312yes—
239#386—32no—
240#386—34no—
241#385—34no—
242#385C2×D312yes—
243#384—32no—
244#382—32no—
245#380—31no—
246#380—32no—
247#380—32no—
248#380—34no—
249#380C2×D311yescharacteristic
250C4×C4⋊C4—31no—
251C4×C4⋊C4—32no—
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#4114yes—
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×Q814yescomplemented
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×Q818yescomplemented
284C22×Dic3C2412yes—
285C22×Dic3C2412yes—
286C22×Dic3C2414yes—
287C22×Dic3C2414yes—
288C22×Dic3C2412yes—
289D3×Q8—432no—
290C2×D12—22no—
291C2×D12—22no—
292C2×D12C2×Q814yes—
293C2×C4×D3—24no—
294C2×C4×D3—28no—
295C2×C4×D3—24no—
296C2×C4×D3—24no—
297C2×C4×D3—28no—
298C2×C4×D3—44no—
299C2×Dic6—24no—
300C2×Dic6—24no—
301C2×Dic6—24no—
302C2×Dic6—28no—
303C2×Dic6—28no—
304C2×Dic6—42no—
305C2×Dic6—42no—
306C2×Dic6—44no—
307C2×Dic6C2×D418yes—
308C3×C4⋊C4—24no—
309C3×C4⋊C4—22no—
310C3×C4⋊C4—22no—
311C3×C4⋊C4—24no—
312C3×C4⋊C4—22no—
313C3×C4⋊C4—42no—
314C3×C22⋊C4—24no—
315C3×C22⋊C4—42no—
316C3×C42—22no—
317C3×C42—22no—
318C3×C42—24no—
319C3×C42—22no—
320C3×C42—24no—
321C3×C42C2×D414yes—
322#217—28no—
323#217—42no—
324(C2×D3)⋊C4—24no—
325(C2×D3)⋊C4—28no—
326(C2×D3)⋊C4—42no—
327(C2×D3)⋊C4—44no—
328(C2×D3)⋊C4—44no—
329(C2×D3)⋊C4—42no—
330(C2×D3)⋊C4C2×Q818yescomplemented
331C4⋊Dic3—24no—
332C4⋊Dic3—22no—
333C4⋊Dic3—24no—
334C4⋊Dic3—22no—
335C4⋊Dic3—28no—
336C4⋊Dic3C2×D418yes—
337C4⋊Dic3C2×D418yes—
338C4⋊Dic3C2×Q814yescomplemented
339Dic3⋊C4—28no—
340Dic3⋊C4—28no—
341Dic3⋊C4—44no—
342Dic3⋊C4—44no—
343Dic3⋊C4—44no—
344Dic3⋊C4—42no—
345C4×Dic3—24no—
346C4×Dic3—28no—
347C4×Dic3—44no—
348C22×Q8—32no—
349C22×Q8—34no—
350C22×Q8—32no—
351C22×Q8—68no—
352C22×Q8—68no—
353C22×Q8—124no—
354C22×Q8C22×D311yescharacteristic
355C22×D4—32no—
356C22×D4—31no—
357C23×C4—32no—
358C23×C4—34no—
359C23×C4C22×D311yescharacteristic
360C23×C4C22×D311yescharacteristic
361C23×C4C22×D311yescharacteristic
362C4⋊Q8—38no—
363C4⋊Q8—68no—
364C4⋊Q8—64no—
365#125—68no—
366C22⋊Q8—24no—
367C22⋊Q8—616no—
368C22⋊Q8—68no—
369C22⋊Q8—68no—
370C22⋊Q8—68no—
371#121—38no—
372C4×Q8—24no—
373C4×Q8—68no—
374C4×Q8—68no—
375C4×Q8—124no—
376C4×D4—68no—
377C4×D4—64no—
378C4×D4—124no—
379#117—68no—
380C2×C4⋊C4—32no—
381C2×C4⋊C4—32no—
382C2×C4⋊C4—31no—
383C2×C4⋊C4—32no—
384C2×C4⋊C4—31no—
385C2×C4⋊C4—34no—
386C2×C4⋊C4—34no—
387C2×C4⋊C4—32no—
388C2×C4⋊C4—34no—
389C2×C4⋊C4—31no—
390C2×C4⋊C4—32no—
391C2×C4⋊C4—34no—
392C2×C4⋊C4—34no—
393C2×C4⋊C4—34no—
394C2×C4⋊C4C22×D311yescharacteristic
395C2×C4⋊C4C22×D311yescharacteristic
396C2×C4⋊C4C22×D312yes—
397C2×C4⋊C4C22×D311yescharacteristic
398C2×C4⋊C4C22×D312yes—
399C2×C4⋊C4C22×D312yes—
400C2×C22⋊C4—32no—
401C2×C22⋊C4—34no—
402C2×C22⋊C4—32no—
403C2×C22⋊C4—34no—
404C2×C22⋊C4—32no—
405C2×C22⋊C4—32no—
406C2×C22⋊C4—32no—
407C2×C22⋊C4—34no—
408C2×C22⋊C4—34no—
409C2×C22⋊C4C22×D312yes—
410C2×C22⋊C4C22×D312yes—
411C2×C42—24no—
412C2×C42—34no—
413C2×C42—32no—
414C2×C42—34no—
415C2×C42C22×D312yes—
416C2×C42C22×D311yescharacteristic
417C2×C42C22×D311yescharacteristic
418C2×C42C22×D311yescharacteristic
419C2×C42C22×D312yes—
420C2×C42C22×D311yescharacteristic
421#95—32no—
422#95—34no—
423#95—32no—
424#95—32no—
425#95—34no—
426#95—34no—
427#95—34no—
428#95—34no—
429#95—34no—
430#95C22×D312yes—
431#95C22×D312yes—
432#95C22×D312yes—
433#95C22×D312yes—
434#95C22×D312yes—
435C23×C3—21no—
436C23×C3—21no—
437C23×C3—21no—
438C23×C3—21no—
439C23×C3—21no—
440C23×C3—21no—
441C23×C3C22×Q812yes—
442C23×C3C2511yescharacteristic
443C22×D3—22no—
444C22×D3—22no—
445C22×D3—22no—
446C22×D3—22no—
447C22×D3—22no—
448C22×D3—22no—
449C22×D3C22×Q814yes—
450C3×Q8—28no—
451C2×C3×C4—21no—
452C2×C3×C4—22no—
453C2×C3×C4—22no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—21no—
457C2×C3×C4—28no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
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—22no—
469C2×C3×C4—22no—
470C2×C3×C4—22no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—44no—
474C2×C3×C4—44no—
475C2×C3×C4C22×D412yes—
476C2×C3×C4C22×D412yes—
477C2×C3×C4C22×D412yes—
478C2×C3×C4C22×Q812yes—
479C2×C3×C4C22×Q812yes—
480C2×C3×C4C2×#4114yes—
481C2×C3×C4C2×#4112yes—
482C2×C3×C4H(5,𝔽2)12yes—
483C2×C3×C42−1+412yes—
484#67—48no—
485C2×Dic3—24no—
486C2×Dic3—22no—
487C2×Dic3—24no—
488C2×Dic3—22no—
489C2×Dic3—24no—
490C2×Dic3—22no—
491C2×Dic3—22no—
492C2×Dic3—22no—
493C2×Dic3—22no—
494C2×Dic3—22no—
495C2×Dic3—22no—
496C2×Dic3—24no—
497C2×Dic3—24no—
498C2×Dic3C22×D418yes—
499C2×Dic3C22×Q814yes—
500D12—28no—
501C4×D3—416no—
502C4×D3—48no—
503Dic6—216no—
504Dic6—416no—
505Dic6—48no—
506C24—32no—
507C24C23×D311yescharacteristic
508C2×Q8—22no—
509C2×Q8—22no—
510C2×Q8—38no—
511C2×Q8—68no—
512C2×Q8—64no—
513C2×Q8—68no—
514C2×Q8—64no—
515C2×Q8—64no—
516C2×Q8—124no—
517C2×Q8—122no—
518C2×Q8—122no—
519C2×Q8—1232no—
520C2×Q8#23514yes—
521C2×D4—38no—
522C2×D4—34no—
523C2×D4—62no—
524C2×D4—62no—
525C2×D4—122no—
526C2×D4—122no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—32no—
534C22×C4—34no—
535C22×C4—32no—
536C22×C4—32no—
537C22×C4—34no—
538C22×C4—41no—
539C22×C4—41no—
540C22×C4—68no—
541C22×C4—68no—
542C22×C4—64no—
543C22×C4—64no—
544C22×C4—64no—
545C22×C4—124no—
546C22×C4D3×Q814yescomplemented
547C22×C4C23×D312yes—
548C22×C4C23×D312yes—
549C22×C4C23×D311yescharacteristic
550C22×C4C23×D311yescharacteristic
551C22×C4C23×D312yes—
552C22×C4C23×D312yes—
553C22×C4C23×D311yescharacteristic
554C22×C4C23×D311yescharacteristic
555C22×C4C23×D311yescharacteristic
556C22×C4C23×D311yescharacteristic
557C4⋊C4—22no—
558C4⋊C4—24no—
559C4⋊C4—24no—
560C4⋊C4—22no—
561C4⋊C4—22no—
562C4⋊C4—38no—
563C4⋊C4—38no—
564C4⋊C4—34no—
565C4⋊C4—42no—
566C4⋊C4—68no—
567C4⋊C4—68no—
568C4⋊C4—68no—
569C4⋊C4—64no—
570C4⋊C4—62no—
571C4⋊C4—64no—
572C4⋊C4—62no—
573C4⋊C4—122no—
574C4⋊C4—124no—
575C4⋊C4—124no—
576C4⋊C4—124no—
577C22⋊C4—24no—
578C22⋊C4—38no—
579C22⋊C4—42no—
580C22⋊C4—68no—
581C22⋊C4—68no—
582C22⋊C4—64no—
583C22⋊C4—122no—
584C22⋊C4—124no—
585C22⋊C4—124no—
586C22⋊C4—122no—
587C22⋊C4—122no—
588C42—22no—
589C42—22no—
590C42—22no—
591C42—24no—
592C42—24no—
593C42—68no—
594C42—64no—
595C42—124no—
596C42D3×D414yes—
597C22×C3—22no—
598C22×C3—22no—
599C22×C3—22no—
600C22×C3—41no—
601C22×C3—41no—
602C22×C3—41no—
603C22×C3—41no—
604C22×C3C23×D411yescharacteristic
605C22×C3C23×Q811yescharacteristic
606C22×C3C22×#4111yescharacteristic
607C22×C3C2×H(5,𝔽2)11yescharacteristic
608C22×C3C2×2−1+411yescharacteristic
609C22×C3#58511yescharacteristic
610C22×C3#58511yescharacteristic
611C2×D3—24no—
612C2×D3—24no—
613C2×D3—24no—
614C2×D3—42no—
615C2×D3—42no—
616C2×D3—42no—
617C2×D3—42no—
618C3×C4—24no—
619C3×C4—22no—
620C3×C4—22no—
621C3×C4—41no—
622C3×C4—42no—
623C3×C4—41no—
624C3×C4—42no—
625C3×C4—42no—
626C3×C4#54614yes—
627C3×C4D4×Q814yes—
628Dic3—28no—
629Dic3—24no—
630Dic3—42no—
631Dic3—44no—
632Dic3—42no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—34no—
640C23—62no—
641C23—62no—
642C23—62no—
643C23—62no—
644C23—62no—
645C23—62no—
646C23C2×D3×Q812yes—
647C23C24×D311yescharacteristic
648Q8—28no—
649Q8—616no—
650Q8—1216no—
651Q8—128no—
652D4—68no—
653D4—128no—
654C2×C4—21no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—28no—
661C2×C4—22no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—21no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—22no—
676C2×C4—38no—
677C2×C4—34no—
678C2×C4—44no—
679C2×C4—44no—
680C2×C4—64no—
681C2×C4—62no—
682C2×C4—64no—
683C2×C4—62no—
684C2×C4—62no—
685C2×C4—64no—
686C2×C4—62no—
687C2×C4—62no—
688C2×C4—62no—
689C2×C4—62no—
690C2×C4—62no—
691C2×C4—64no—
692C2×C4—64no—
693C2×C4—1216no—
694C2×C4—128no—
695C2×C4C2×#23514yes—
696C2×C4C2×#23512yes—
697C2×C4C2×D3×D412yes—
698C2×C4C2×D3×D412yes—
699C2×C4C2×D3×D412yes—
700C2×C4C2×D3×Q812yes—
701C2×C4C2×D3×Q812yes—
702C2×C4#100912yes—
703C2×C4#101012yes—
704C2×C3—42no—
705C2×C3C2×#54611yescharacteristic
706C2×C3C2×D4×Q811yescharacteristic
707C2×C3Q8×#4111yescharacteristic
708C2×C3#348711yescharacteristic
709C2×C3#350111yescharacteristic
710C2×C3#351811yescharacteristic
711C2×C3#354711yescharacteristic
712D3—44no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—64no—
721C22—64no—
722C22—64no—
723C22—122no—
724C22—122no—
725C22—122no—
726C22—122no—
727C22C22×#23511yescharacteristic
728C22C22×D3×D411yescharacteristic
729C22C22×D3×Q811yescharacteristic
730C22C2×#100911yescharacteristic
731C22C2×#101011yescharacteristic
732C22#596411yescharacteristic
733C22#596411yescharacteristic
734C4—22no—
735C4—24no—
736C4—22no—
737C4—41no—
738C4—42no—
739C4—41no—
740C4—42no—
741C4—42no—
742C4—64no—
743C4—68no—
744C4—124no—
745C4—122no—
746C4—122no—
747C4#555014yes—
748C4#563214yes—
749C3#5903611yescharacteristic, complemented, Sylow
750C2—42no—
751C2—124no—
752C2C2×#555011yescharacteristic
753C2Q8×#23511yescharacteristic
754C2#8583211yescharacteristic
755C2C2×#563211yescharacteristic
756C2#8602311yescharacteristic
757C2#8617511yescharacteristic
758C2#8628011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×C4×C22⋊Q8C2
prime radicalC2×#930C22
hypercenterC4×C22⋊Q8D3
hypocenterC3#59036
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×Q8×D12C2semidirect
2. C2×#5470C2semidirect
3. C3×C4×C22⋊Q8C2semidirect
4. #82751C2semidirect
5. #82478C2semidirect
7. #76614C2semidirect
8. #76216C2semidirect
9. #74999C2semidirect
10. #74516C2semidirect
11. #73936C2semidirect
12. #73807C2semidirect
13. #73713C2semidirect
14. #73677C2semidirect
15. #73650C2semidirect
16. #73492C2semidirect
101. C4×C22⋊Q8D3semidirect
136. #930Q8semidirect
173. #869D4semidirect
270. C22×C3×C4C2×Q8semidirect
283. C2×#67C2×Q8semidirect
330. (C2×D3)⋊C4C2×Q8semidirect
338. C4⋊Dic3C2×Q8semidirect
546. C22×C4D3×Q8semidirect
749. C3#59036semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×D122
C2×#54702
C3×C4×C22⋊Q82
#827512
#824782
C4×#9302
#766142
#762162
#749992
#745162
#739362
#738072
#737132
#736772
#736502
#734922
#734692
#590363