Finite Group Databasebeta

← #11635866

Subgroups — #11635866

Order 768.

3082 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×C4⋊Q8C211yesmaximal, characteristic, complemented
2C2×#5677C212yesmaximal, complemented
3C2×#5555C211yesmaximal, characteristic, complemented
4C3×#2547C211yesmaximal, characteristic, complemented
5#83259C211yesmaximal, characteristic, complemented
6#82959C212yesmaximal, complemented
7C4×#938C211yesmaximal, characteristic, complemented
8#77673C214yesmaximal, complemented
9#77567C214yesmaximal, complemented
10#76625C212yesmaximal, complemented
11#76619C212yesmaximal, complemented
12#74010C212yesmaximal, complemented
13#73915C212yesmaximal, complemented
14#73899C212yesmaximal, complemented
15#73887C212yesmaximal, complemented
16C4×#895C211yesmaximal, characteristic, complemented
17#73651C211yesmaximal, characteristic, complemented
18#59125—31nomaximal, Sylow
19C22×D3×Q8C2212yes—
20C22×#237C2212yes—
21C2×C3×C4⋊Q8C2211yescharacteristic
22C2×C3×#124C2212yes—
23C2×C3×C4×D4C2211yescharacteristic
24C2×#946C2212yes—
25C2×#946C2212yes—
26C2×#944C2212yes—
27C2×#938C2211yescharacteristic
28C2×#930C2212yes—
29C2×C4×#67C2212yes—
30C22×C4⋊Dic3C2212yes—
31D3×C4⋊Q8—28no—
32#5677—216no—
33#5555—28no—
34C2×#897C2212yes—
35C2×#895C2211yescharacteristic
36C2×D3×C4⋊C4C2212yes—
37C2×D3×C4⋊C4C2212yes—
38C2×#888C2212yes—
39C2×#888C2212yes—
40C2×#886C2214yes—
41C2×#885C2214yes—
42C2×#884C2214yes—
43C2×#67⋊C4C2214yes—
44C2×#878C2214yes—
45C2×C4×D12C2212yes—
46C2×C4×D12C2211yescharacteristic
47C2×C42×D3C2211yescharacteristic
48C2×#869C2211yescharacteristic
49C2×C4×Dic6C2212yes—
50C3×#397C2214yes—
51C3×#391C2212yes—
52C3×#380C2212yes—
53C3×#380C2212yes—
54C3×C4×C4⋊C4C2211yescharacteristic
55#5221C2211yescharacteristic
56C4×#217C2212yes—
57#4993C2214yes—
58#4988C2211yescharacteristic
59#4988C2212yes—
60#4987C2211yescharacteristic
61#4987C2211yescharacteristic
62#4984C2211yescharacteristic
63#4975C2212yes—
64Dic3×C4⋊C4C2212yes—
65#4972C2211yescharacteristic
66#4972C2212yes—
67#4959C2214yes—
68#4959C2214yes—
69#4956C2212yes—
70#4946C2214yes—
71#4946C2214yes—
72#4944C2212yes—
73C4×(C2×D3)⋊C4C2212yes—
74C4×C4⋊Dic3C2211yescharacteristic
75#4929C2212yes—
76#4676C2214yes—
77#4673C2214yes—
78#4670C2212yes—
79#4669C2214yes—
80#4668C2214yes—
81#4665C2212yes—
82#4665C2214yes—
83#4657C2214yes—
84#4656C2214yes—
85#4654C2214yes—
86#4647C2214yes—
87C2×#548—32no—
88C2×#547—31no—
89C22×C4⋊Q8—31no—
90#2674—34no—
91#2547D311yescharacteristic, complemented
92#2542—31no—
93#2491—32no—
94#2443—34no—
95#2440—32no—
96#2432—32no—
97#2429—32no—
98#2416—32no—
99#2409—32no—
100#2365—31no—
101D4×C4⋊C4—32no—
102C4×#121—31no—
103C4×#121—31no—
104C22×C3×Q8C2312yes—
105C22×C3×D4C2311yescharacteristic
106C23×C3×C4C2312yes—
107C22×#67C2314yes—
108C22×#67C2312yes—
109C23×Dic3C2314yes—
110C2×D3×Q8—28no—
111C2×D3×Q8—28no—
112C2×D3×Q8—44no—
113C2×#237—28no—
114C2×#237—28no—
115C2×#237—44no—
116C22×D12C2312yes—
117C22×D12C2311yescharacteristic
118C22×C4×D3C2311yescharacteristic
119C22×C4×D3C2312yes—
120C22×C4×D3C2314yes—
121C22×C4×D3C2311yescharacteristic
122C22×C4×D3C2311yescharacteristic
123C22×Dic6C2314yes—
124C22×Dic6C2312yes—
125C3×C4⋊Q8—24no—
126C3×#124—28no—
127C3×C4×D4—24no—
128C2×C3×C4⋊C4C2311yescharacteristic
129C2×C3×C4⋊C4C2311yescharacteristic
130C2×C3×C4⋊C4C2311yescharacteristic
131C2×C3×C4⋊C4C2312yes—
132C2×C3×C4⋊C4C2312yes—
133C2×C3×C22⋊C4C2312yes—
134C2×C3×C22⋊C4C2314yes—
135C2×C3×C22⋊C4C2314yes—
136C2×C3×C42C2312yes—
137C2×C3×C42C2311yescharacteristic
138C2×#217C2312yes—
139C2×#217C2312yes—
140C2×#217C2312yes—
141#946—28no—
142#946—44no—
143#944—28no—
144#938D418yescomplemented
145#930—28no—
146C4×#67—28no—
147C2×(C2×D3)⋊C4C2312yes—
148C2×(C2×D3)⋊C4C2312yes—
149C2×(C2×D3)⋊C4C2312yes—
150C2×(C2×D3)⋊C4C2314yes—
151C2×(C2×D3)⋊C4C2312yes—
152C2×(C2×D3)⋊C4C2314yes—
153C2×(C2×D3)⋊C4C2312yes—
154C2×(C2×D3)⋊C4C2312yes—
155C2×(C2×D3)⋊C4C2314yes—
156C2×C4⋊Dic3—28no—
157C2×C4⋊Dic3C2314yes—
158C2×C4⋊Dic3C2312yes—
159C2×C4⋊Dic3C2311yescharacteristic
160C2×C4⋊Dic3C2311yescharacteristic
161C2×C4⋊Dic3C2312yes—
162C2×C4⋊Dic3C2311yescharacteristic
163C2×C4⋊Dic3C2312yes—
164C2×Dic3⋊C4C2312yes—
165C2×Dic3⋊C4C2314yes—
166C2×Dic3⋊C4C2314yes—
167C2×Dic3⋊C4C2314yes—
168C2×Dic3⋊C4C2314yes—
169C2×Dic3⋊C4C2314yes—
170C2×C4×Dic3C2314yes—
171C2×C4×Dic3C2311yescharacteristic
172C2×C4×Dic3C2312yes—
173C2×C4×Dic3C2311yescharacteristic
174C2×C4×Dic3C2311yescharacteristic
175#897—28no—
176#895—24no—
177D3×C4⋊C4—28no—
178D3×C4⋊C4—28no—
179#888—28no—
180#888—28no—
181#886—216no—
182#885—216no—
183#884—216no—
184#67⋊C4—216no—
185#878—216no—
186C4×D12—28no—
187C4×D12—24no—
188C42×D3—24no—
189#869D418yescomplemented
190C4×Dic6—28no—
191C3×#95C2314yes—
192C3×#95C2312yes—
193C3×#95C2314yes—
194C3⋊#95C2312yes—
195C3⋊#95C2312yes—
196C3⋊#95C2314yes—
197C3⋊#95C2314yes—
198C3⋊#95C2312yes—
199C3⋊#95C2312yes—
200C3⋊#95C2312yes—
201C22×#41—32no—
202C23×Q8—32no—
203#548—616no—
204#547—68no—
205C2×C4⋊Q8—32no—
206C2×C4⋊Q8—32no—
207C2×C4⋊Q8—32no—
208C2×C4⋊Q8—31no—
209C2×C4⋊Q8—68no—
210C2×C4⋊Q8C2×D311yescharacteristic
211C2×#124—34no—
212C2×#124C2×D312yes—
213C2×#123—34no—
214C2×C22⋊Q8—32no—
215C2×C22⋊Q8—32no—
216C2×C22⋊Q8—32no—
217C2×C22⋊Q8—34no—
218C2×#121—31no—
219C2×#121—32no—
220C2×#121—31no—
221C2×#121—34no—
222C2×C4×Q8—32no—
223C2×C4×D4—32no—
224C2×C4×D4—34no—
225C2×C4×D4—32no—
226C2×C4×D4—31no—
227C2×C4×D4C2×D311yescharacteristic
228C22×C4⋊C4—32no—
229C22×C4⋊C4—32no—
230C22×C4⋊C4—32no—
231C22×C42—31no—
232#399—34no—
233#398—34no—
234#397C2×D314yes—
235#396—34no—
236#395—34no—
237#394—34no—
238#394—34no—
239#393—34no—
240#391—32no—
241#391C2×D312yes—
242#390—31no—
243#390—32no—
244#390—31no—
245#389—32no—
246#389—31no—
247#389—31no—
248#389—34no—
249#388—32no—
250#388—34no—
251#388—32no—
252#387—34no—
253#386—32no—
254#386—34no—
255#386—32no—
256#385—34no—
257#385—34no—
258#385—34no—
259#384—32no—
260#380—31no—
261#380—31no—
262#380C2×D312yes—
263#380C2×D312yes—
264C4×C4⋊C4—32no—
265C4×C4⋊C4—31no—
266C4×C4⋊C4C2×D311yescharacteristic
267C4×C22⋊C4—32no—
268C4×C22⋊C4—32no—
269C24×C3C2412yes—
270C23×D3C2412yes—
271C23×D3C2411yescharacteristic
272C2×C3×Q8—24no—
273C2×C3×Q8—24no—
274C2×C3×Q8—24no—
275C2×C3×D4—22no—
276C2×C3×D4—22no—
277C2×C3×D4C2×D414yes—
278C22×C3×C4—24no—
279C22×C3×C4—24no—
280C22×C3×C4—24no—
281C22×C3×C4C2412yes—
282C22×C3×C4C2412yes—
283C22×C3×C4C2412yes—
284C22×C3×C4C2414yes—
285C22×C3×C4C2411yescharacteristic
286C22×C3×C4C2411yescharacteristic
287C22×C3×C4C2411yescharacteristic
288C2×#67—24no—
289C2×#67—24no—
290C2×#67—28no—
291C2×#67—28no—
292C2×#67—44no—
293C2×#67C2×D418yes—
294C22×Dic3—28no—
295C22×Dic3—28no—
296C22×Dic3—44no—
297C22×Dic3C2412yes—
298C22×Dic3C2412yes—
299C22×Dic3C2412yes—
300C22×Dic3C2411yescharacteristic
301C22×Dic3C2414yes—
302C22×Dic3C2411yescharacteristic
303C22×Dic3C2411yescharacteristic
304D3×Q8—432no—
305#237—432no—
306C2×D12—24no—
307C2×D12—24no—
308C2×D12—24no—
309C2×D12—22no—
310C2×D12—22no—
311C2×D12—22no—
312C2×C4×D3—22no—
313C2×C4×D3—22no—
314C2×C4×D3—22no—
315C2×C4×D3—22no—
316C2×C4×D3—22no—
317C2×C4×D3—22no—
318C2×C4×D3—22no—
319C2×C4×D3—28no—
320C2×C4×D3—24no—
321C2×C4×D3—24no—
322C2×C4×D3—24no—
323C2×C4×D3—28no—
324C2×C4×D3—44no—
325C2×C4×D3C2×D414yes—
326C2×C4×D3#4114yescomplemented
327C2×Dic6—24no—
328C2×Dic6—24no—
329C2×Dic6—28no—
330C2×Dic6—28no—
331C2×Dic6—44no—
332C2×Dic6C2×D418yes—
333C3×C4⋊C4—24no—
334C3×C4⋊C4—24no—
335C3×C4⋊C4—22no—
336C3×C4⋊C4—22no—
337C3×C4⋊C4—22no—
338C3×C22⋊C4—28no—
339C3×C22⋊C4—28no—
340C3×C22⋊C4—24no—
341C3×C42—24no—
342C3×C42C2×D414yes—
343#217—24no—
344#217—24no—
345#217C2×D418yes—
346(C2×D3)⋊C4—24no—
347(C2×D3)⋊C4—24no—
348(C2×D3)⋊C4—24no—
349(C2×D3)⋊C4—24no—
350(C2×D3)⋊C4—28no—
351(C2×D3)⋊C4—28no—
352(C2×D3)⋊C4—24no—
353(C2×D3)⋊C4—24no—
354(C2×D3)⋊C4—44no—
355C4⋊Dic3—22no—
356C4⋊Dic3—22no—
357C4⋊Dic3—24no—
358C4⋊Dic3—28no—
359C4⋊Dic3C2×D414yes—
360C4⋊Dic3C2×D418yes—
361C4⋊Dic3C2×D418yes—
362Dic3⋊C4—28no—
363Dic3⋊C4—28no—
364Dic3⋊C4—28no—
365Dic3⋊C4—28no—
366Dic3⋊C4—24no—
367Dic3⋊C4—44no—
368C4×Dic3—22no—
369C4×Dic3—22no—
370C4×Dic3—22no—
371C4×Dic3—24no—
372C4×Dic3—28no—
373C2×#41—68no—
374C2×#41—68no—
375C2×#41—124no—
376C22×Q8—32no—
377C22×Q8—34no—
378C22×Q8—68no—
379C22×Q8—68no—
380C22×Q8—124no—
381C22×Q8C22×D312yes—
382C22×D4—32no—
383C22×D4—34no—
384C22×D4—32no—
385C22×D4—31no—
386C22×D4C22×D311yescharacteristic
387C23×C4—31no—
388C23×C4—31no—
389C23×C4—34no—
390C23×C4—31no—
391C23×C4—32no—
392C23×C4—34no—
393C23×C4C22×D312yes—
394C4⋊Q8—24no—
395C4⋊Q8—38no—
396C4⋊Q8—68no—
397C4⋊Q8—68no—
398C4⋊Q8—68no—
399#124—28no—
400#124—616no—
401#123—616no—
402C22⋊Q8—616no—
403C22⋊Q8—68no—
404C22⋊Q8—68no—
405C22⋊Q8—124no—
406#121—38no—
407#121—616no—
408#121—64no—
409#121—68no—
410C4×Q8—68no—
411C4×D4—24no—
412C4×D4—68no—
413C4×D4—616no—
414C4×D4—68no—
415C4×D4—64no—
416C2×C4⋊C4—32no—
417C2×C4⋊C4—32no—
418C2×C4⋊C4—31no—
419C2×C4⋊C4—31no—
420C2×C4⋊C4—34no—
421C2×C4⋊C4—34no—
422C2×C4⋊C4—34no—
423C2×C4⋊C4—34no—
424C2×C4⋊C4—32no—
425C2×C4⋊C4—32no—
426C2×C4⋊C4—34no—
427C2×C4⋊C4—31no—
428C2×C4⋊C4—34no—
429C2×C4⋊C4—68no—
430C2×C4⋊C4—68no—
431C2×C4⋊C4—68no—
432C2×C4⋊C4C22×D312yes—
433C2×C4⋊C4C22×D312yes—
434C2×C4⋊C4C22×D311yescharacteristic
435C2×C4⋊C4C22×D311yescharacteristic
436C2×C4⋊C4C22×D311yescharacteristic
437C2×C22⋊C4—32no—
438C2×C22⋊C4—32no—
439C2×C22⋊C4—32no—
440C2×C22⋊C4—32no—
441C2×C22⋊C4—32no—
442C2×C22⋊C4—32no—
443C2×C22⋊C4—32no—
444C2×C22⋊C4—34no—
445C2×C22⋊C4—34no—
446C2×C22⋊C4—32no—
447C2×C22⋊C4—32no—
448C2×C22⋊C4—34no—
449C2×C22⋊C4C22×D314yes—
450C2×C22⋊C4C22×D312yes—
451C2×C22⋊C4C22×D314yes—
452C2×C42—34no—
453C2×C42—32no—
454C2×C42—31no—
455C2×C42—31no—
456C2×C42—31no—
457C2×C42—64no—
458C2×C42C22×D312yes—
459C2×C42C22×D311yescharacteristic
460#95—32no—
461#95—32no—
462#95—32no—
463#95—32no—
464#95—34no—
465#95—32no—
466#95—34no—
467#95C22×D312yes—
468#95C22×D314yes—
469#95C22×D314yes—
470C23×C3—22no—
471C23×C3—22no—
472C23×C3—22no—
473C23×C3—22no—
474C23×C3—22no—
475C23×C3—22no—
476C23×C3C22×D414yes—
477C23×C3C2511yescharacteristic
478C22×D3—21no—
479C22×D3—21no—
480C22×D3—21no—
481C22×D3—21no—
482C22×D3—22no—
483C22×D3—22no—
484C22×D3—22no—
485C22×D3—22no—
486C22×D3—22no—
487C22×D3—22no—
488C22×D3—22no—
489C22×D3C22×D412yes—
490C22×D3C2×#4112yes—
491C22×D32−1+412yes—
492C3×Q8—48no—
493C3×D4—28no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—22no—
497C2×C3×C4—22no—
498C2×C3×C4—24no—
499C2×C3×C4—24no—
500C2×C3×C4—22no—
501C2×C3×C4—22no—
502C2×C3×C4—22no—
503C2×C3×C4—24no—
504C2×C3×C4—22no—
505C2×C3×C4—22no—
506C2×C3×C4—22no—
507C2×C3×C4—22no—
508C2×C3×C4—48no—
509C2×C3×C4C22×D412yes—
510C2×C3×C4C22×D412yes—
511C2×C3×C4C22×D412yes—
512C2×C3×C4C22×D412yes—
513C2×C3×C4C2×#4112yes—
514C2×C3×C4H(5,𝔽2)12yes—
515C2×C3×C42−1+412yes—
516#67—216no—
517#67—416no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—24no—
522C2×Dic3—22no—
523C2×Dic3—24no—
524C2×Dic3—21no—
525C2×Dic3—21no—
526C2×Dic3—21no—
527C2×Dic3—22no—
528C2×Dic3—22no—
529C2×Dic3—22no—
530C2×Dic3—22no—
531C2×Dic3—22no—
532C2×Dic3—22no—
533C2×Dic3—22no—
534C2×Dic3—416no—
535C2×Dic3C22×D414yes—
536C2×Dic3C22×D418yes—
537C2×Dic3C22×D412yes—
538C2×Dic3C2×#4112yes—
539C2×Dic32−1+412yes—
540D12—48no—
541D12—44no—
542C4×D3—28no—
543C4×D3—28no—
544C4×D3—28no—
545C4×D3—416no—
546C4×D3—48no—
547Dic6—216no—
548Dic6—416no—
549C24—31no—
550C24—32no—
551C24C23×D312yes—
552#41—1232no—
553C2×Q8—24no—
554C2×Q8—24no—
555C2×Q8—24no—
556C2×Q8—38no—
557C2×Q8—68no—
558C2×Q8—68no—
559C2×Q8—64no—
560C2×Q8—64no—
561C2×Q8—124no—
562C2×Q8—1232no—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—38no—
566C2×D4—64no—
567C2×D4—64no—
568C2×D4—64no—
569C2×D4—68no—
570C2×D4—64no—
571C2×D4—64no—
572C2×D4—68no—
573C2×D4—62no—
574C2×D4—62no—
575C2×D4—62no—
576C2×D4—124no—
577C2×D4D3×D414yes—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—24no—
581C22×C4—31no—
582C22×C4—32no—
583C22×C4—31no—
584C22×C4—31no—
585C22×C4—34no—
586C22×C4—34no—
587C22×C4—34no—
588C22×C4—32no—
589C22×C4—32no—
590C22×C4—62no—
591C22×C4—68no—
592C22×C4—62no—
593C22×C4—68no—
594C22×C4—68no—
595C22×C4—62no—
596C22×C4—62no—
597C22×C4—62no—
598C22×C4—62no—
599C22×C4—62no—
600C22×C4—68no—
601C22×C4—64no—
602C22×C4—64no—
603C22×C4—64no—
604C22×C4—124no—
605C22×C4—124no—
606C22×C4C23×D312yes—
607C22×C4C23×D312yes—
608C22×C4C23×D312yes—
609C22×C4C23×D314yes—
610C22×C4C23×D311yescharacteristic
611C22×C4C23×D311yescharacteristic
612C22×C4C23×D311yescharacteristic
613C4⋊C4—24no—
614C4⋊C4—24no—
615C4⋊C4—22no—
616C4⋊C4—22no—
617C4⋊C4—22no—
618C4⋊C4—38no—
619C4⋊C4—38no—
620C4⋊C4—34no—
621C4⋊C4—68no—
622C4⋊C4—68no—
623C4⋊C4—68no—
624C4⋊C4—68no—
625C4⋊C4—64no—
626C4⋊C4—64no—
627C4⋊C4—68no—
628C4⋊C4—62no—
629C4⋊C4—62no—
630C4⋊C4—124no—
631C22⋊C4—28no—
632C22⋊C4—28no—
633C22⋊C4—24no—
634C22⋊C4—38no—
635C22⋊C4—64no—
636C22⋊C4—68no—
637C22⋊C4—68no—
638C22⋊C4—64no—
639C22⋊C4—64no—
640C22⋊C4—64no—
641C22⋊C4—64no—
642C22⋊C4—64no—
643C22⋊C4—64no—
644C22⋊C4—64no—
645C22⋊C4—124no—
646C42—24no—
647C42—68no—
648C42—62no—
649C42—62no—
650C42—62no—
651C42—64no—
652C42D3×D414yes—
653C22×C3—24no—
654C22×C3—24no—
655C22×C3—24no—
656C22×C3—42no—
657C22×C3—42no—
658C22×C3—42no—
659C22×C3—42no—
660C22×C3C23×D411yescharacteristic
661C22×C3C23×D411yescharacteristic
662C22×C3C22×#4111yescharacteristic
663C22×C3C2×H(5,𝔽2)11yescharacteristic
664C22×C3C2×2−1+411yescharacteristic
665C22×C3C2×2−1+411yescharacteristic
666C22×C3C2×2−1+411yescharacteristic
667C2×D3—22no—
668C2×D3—22no—
669C2×D3—22no—
670C2×D3—22no—
671C2×D3—22no—
672C2×D3—22no—
673C2×D3—42no—
674C2×D3—42no—
675C2×D3—42no—
676C2×D3—42no—
677C2×D3—42no—
678C2×D3—42no—
679C2×D3—42no—
680C2×D3#54714yescomplemented
681C3×C4—22no—
682C3×C4—44no—
683C3×C4—42no—
684C3×C4—42no—
685C3×C4—42no—
686C3×C4D4214yes—
687C3×C4#54814yescomplemented
688Dic3—28no—
689Dic3—22no—
690Dic3—24no—
691Dic3—22no—
692Dic3—22no—
693Dic3—42no—
694Dic3—42no—
695C23—22no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—32no—
702C23—32no—
703C23—32no—
704C23—61no—
705C23—61no—
706C23—61no—
707C23—61no—
708C23—62no—
709C23—62no—
710C23—62no—
711C23—62no—
712C23—62no—
713C23—62no—
714C23—62no—
715C23C2×D3×D414yes—
716C23C24×D311yescharacteristic
717Q8—48no—
718Q8—616no—
719Q8—1216no—
720D4—28no—
721D4—616no—
722D4—128no—
723D4—1216no—
724D4—124no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—24no—
730C2×C4—22no—
731C2×C4—24no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—24no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—34no—
740C2×C4—32no—
741C2×C4—38no—
742C2×C4—32no—
743C2×C4—32no—
744C2×C4—48no—
745C2×C4—68no—
746C2×C4—61no—
747C2×C4—61no—
748C2×C4—61no—
749C2×C4—64no—
750C2×C4—62no—
751C2×C4—61no—
752C2×C4—64no—
753C2×C4—61no—
754C2×C4—61no—
755C2×C4—62no—
756C2×C4—68no—
757C2×C4—68no—
758C2×C4—62no—
759C2×C4—62no—
760C2×C4—62no—
761C2×C4—62no—
762C2×C4—62no—
763C2×C4—62no—
764C2×C4—1216no—
765C2×C4—1216no—
766C2×C4—128no—
767C2×C4C2×D3×D412yes—
768C2×C4C2×D3×D412yes—
769C2×C4C2×D3×D412yes—
770C2×C4C2×D3×D412yes—
771C2×C4D3×#4112yes—
772C2×C4#100912yes—
773C2×C4#101012yes—
774C2×C3—44no—
775C2×C3C2×D4211yescharacteristic
776C2×C3C2×#54711yescharacteristic
777C2×C3C2×#54811yescharacteristic
778C2×C3#348611yescharacteristic
779C2×C3#349911yescharacteristic
780C2×C3#351111yescharacteristic
781C2×C3#355211yescharacteristic
782D3—24no—
783D3—82no—
784C22—24no—
785C22—24no—
786C22—24no—
787C22—34no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—62no—
793C22—62no—
794C22—62no—
795C22—62no—
796C22—62no—
797C22—62no—
798C22—122no—
799C22—122no—
800C22—122no—
801C22—122no—
802C22—122no—
803C22—122no—
804C22—122no—
805C22C22×D3×D411yescharacteristic
806C22C22×D3×D411yescharacteristic
807C22C2×D3×#4111yescharacteristic
808C22C2×#100911yescharacteristic
809C22C2×#101011yescharacteristic
810C22D3×2−1+411yescharacteristic
811C22D3×2−1+411yescharacteristic
812C4—22no—
813C4—42no—
814C4—42no—
815C4—42no—
816C4—44no—
817C4—62no—
818C4—62no—
819C4—64no—
820C4—62no—
821C4—68no—
822C4—122no—
823C4—122no—
824C4#560914yes—
825C4#567714yescomplemented
826C3#5912511yescharacteristic, complemented, Sylow
827C2—44no—
828C2—64no—
829C2—242no—
830C2C2×#560911yescharacteristic
831C2C2×#567711yescharacteristic
832C2#8635511yescharacteristic
833C2#8667911yescharacteristic
834C2D3×#54711yescharacteristic
835C2#8698511yescharacteristic
836C2#8701011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2547C2
hypercenter#2547D3
hypocenterC3#59125
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2547

Complements

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

NH ≅ G/Ntype
1. C2×D3×C4⋊Q8C2semidirect
2. C2×#5677C2semidirect
3. C2×#5555C2semidirect
4. C3×#2547C2semidirect
5. #83259C2semidirect
6. #82959C2semidirect
7. C4×#938C2semidirect
8. #77673C2semidirect
9. #77567C2semidirect
10. #76625C2semidirect
11. #76619C2semidirect
12. #74010C2semidirect
13. #73915C2semidirect
14. #73899C2semidirect
15. #73887C2semidirect
16. C4×#895C2semidirect
17. #73651C2semidirect
91. #2547D3semidirect
144. #938D4semidirect
189. #869D4semidirect
326. C2×C4×D3#41semidirect
680. C2×D3#547semidirect
687. C3×C4#548semidirect
825. C4#5677semidirect
826. C3#59125semidirect

Maximal subgroups

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

subgroupindex
C2×D3×C4⋊Q82
C2×#56772
C2×#55552
C3×#25472
#832592
#829592
C4×#9382
#776732
#775672
#766252
#766192
#740102
#739152
#738992
#738872
C4×#8952
#736512
#591253