Finite Group Databasebeta

← #11635865

Subgroups — #11635865

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×#5598C212yesmaximal, complemented
2C2×#5555C211yesmaximal, characteristic, complemented
3C22×#869C211yesmaximal, characteristic, complemented
4C3×C4×#121C211yesmaximal, characteristic, complemented
5#82382C211yesmaximal, characteristic, complemented
6#82352C212yesmaximal, complemented
7D4×C4⋊Dic3C212yesmaximal, complemented
8C4×#930C211yesmaximal, characteristic, complemented
9#76445C212yesmaximal, complemented
10#76221C212yesmaximal, complemented
11#75666C214yesmaximal, complemented
12#74703C214yesmaximal, complemented
13#74017C212yesmaximal, complemented
14#73800C211yesmaximal, characteristic, complemented
15#73650C211yesmaximal, characteristic, complemented
16#73507C212yesmaximal, complemented
17#73493C212yesmaximal, complemented
18#59125—31nomaximal, Sylow
19C22×#237C2212yes—
20C23×Dic6C2212yes—
21C2×C3×#121C2211yescharacteristic
22C2×C3×C4×D4C2212yes—
23C2×C3×C4×D4C2211yescharacteristic
24C22×C3×C42C2211yescharacteristic
25C2×#939C2214yes—
26C2×#936C2212yes—
27C2×D4×Dic3C2214yes—
28C2×#930C2212yes—
29C2×#930C2211yescharacteristic
30C2×C4×#67C2212yes—
31C22×C4⋊Dic3C2212yes—
32C22×C4⋊Dic3C2212yes—
33C22×C4⋊Dic3C2212yes—
34#5598—216no—
35#5555—28no—
36C2×#897C2212yes—
37C2×#897C2212yes—
38C2×#897C2212yes—
39C2×#887C2212yes—
40C2×#886C2214yes—
41C2×#885C2214yes—
42C2×#878C2214yes—
43C2×C4×D12C2211yescharacteristic
44C2×#869—28no—
45C2×#869C2212yes—
46C2×#869C2211yescharacteristic
47C2×#869C2212yes—
48C2×#869C2212yes—
49C2×#869C2211yescharacteristic
50C3×#390C2211yescharacteristic
51C3×#389C2211yescharacteristic
52C3×#388C2212yes—
53C3×#386C2212yes—
54C3×#380C2211yescharacteristic
55C3×C4×C4⋊C4C2211yescharacteristic
56C3×C4×C22⋊C4C2212yes—
57#5213C2212yes—
58#5212C2212yes—
59#5212C2212yes—
60#5212C2211yescharacteristic
61#4994C2214yes—
62#4984C2214yes—
63#4973C2212yes—
64#4973C2212yes—
65#4961C2214yes—
66#4961C2214yes—
67#4958C2214yes—
68#4953C2214yes—
69#4950C2214yes—
70#4950C2214yes—
71#4950C2214yes—
72#4940C2212yes—
73#4939C2211yescharacteristic
74#4939C2212yes—
75C4×(C2×D3)⋊C4C2212yes—
76#4935C2212yes—
77C4×C4⋊Dic3C2212yes—
78C4×C4⋊Dic3C2211yescharacteristic
79#4928C2211yescharacteristic
80#4928C2212yes—
81#4677C2214yes—
82#4673C2214yes—
83#4670C2214yes—
84#4661C2214yes—
85#4656C2214yes—
86#4653C2214yes—
87C2×#548—32no—
88C2×#547—31no—
89C22×C4⋊Q8—31no—
90#2674—34no—
91#2547—31no—
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×#121D311yescharacteristic, complemented
104C22×C3×D4C2311yescharacteristic
105C22×C3×D4C2312yes—
106C23×C3×C4C2312yes—
107C23×C3×C4C2311yescharacteristic
108C23×C3×C4C2311yescharacteristic
109C23×C3×C4C2311yescharacteristic
110C22×#67C2312yes—
111C22×#67C2314yes—
112C23×Dic3C2314yes—
113C23×Dic3C2314yes—
114C2×#237—28no—
115C2×#237—28no—
116C2×#237—44no—
117C22×D12C2311yescharacteristic
118C22×C4×D3C2312yes—
119C22×Dic6—28no—
120C22×Dic6—28no—
121C22×Dic6—44no—
122C22×Dic6C2312yes—
123C22×Dic6C2314yes—
124C22×Dic6C2312yes—
125C3×#121D418yescomplemented
126C3×C4×D4—28no—
127C3×C4×D4—24no—
128C2×C3×C4⋊C4C2311yescharacteristic
129C2×C3×C4⋊C4C2311yescharacteristic
130C2×C3×C4⋊C4C2312yes—
131C2×C3×C4⋊C4C2311yescharacteristic
132C2×C3×C22⋊C4C2312yes—
133C2×C3×C22⋊C4C2312yes—
134C2×C3×C22⋊C4C2312yes—
135C2×C3×C22⋊C4C2312yes—
136C2×C3×C22⋊C4C2312yes—
137C2×C3×C42—24no—
138C2×C3×C42C2312yes—
139C2×C3×C42C2311yescharacteristic
140C2×C3×C42C2311yescharacteristic
141C2×C3×C42C2311yescharacteristic
142C2×C3×C42C2311yescharacteristic
143C2×#217C2312yes—
144C2×#217C2314yes—
145C2×#217C2314yes—
146#939—216no—
147#936—28no—
148D4×Dic3—216no—
149#930—24no—
150#930—28no—
151C4×#67—28no—
152C2×(C2×D3)⋊C4C2312yes—
153C2×(C2×D3)⋊C4C2314yes—
154C2×(C2×D3)⋊C4C2314yes—
155C2×(C2×D3)⋊C4C2312yes—
156C2×(C2×D3)⋊C4C2312yes—
157C2×(C2×D3)⋊C4C2312yes—
158C2×(C2×D3)⋊C4C2314yes—
159C2×C4⋊Dic3—28no—
160C2×C4⋊Dic3—28no—
161C2×C4⋊Dic3—28no—
162C2×C4⋊Dic3C2314yes—
163C2×C4⋊Dic3C2314yes—
164C2×C4⋊Dic3C2314yes—
165C2×C4⋊Dic3C2311yescharacteristic
166C2×C4⋊Dic3C2311yescharacteristic
167C2×C4⋊Dic3C2312yes—
168C2×C4⋊Dic3C2311yescharacteristic
169C2×C4⋊Dic3C2312yes—
170C2×C4⋊Dic3C2314yes—
171C2×C4⋊Dic3C2314yes—
172C2×C4⋊Dic3C2312yes—
173C2×C4⋊Dic3C2312yes—
174C2×Dic3⋊C4C2314yes—
175C2×Dic3⋊C4C2312yes—
176C2×C4×Dic3C2314yes—
177C2×C4×Dic3C2312yes—
178#897—28no—
179#897—28no—
180#897—44no—
181#887—28no—
182#886—216no—
183#885—216no—
184#878—216no—
185C4×D12—24no—
186#869—28no—
187#869—24no—
188#869—28no—
189#869—28no—
190#869D418yescomplemented
191C3×#95C2312yes—
192C3×#95C2312yes—
193C3×#95C2312yes—
194C3⋊#95C2312yes—
195C3⋊#95C2314yes—
196C3⋊#95C2314yes—
197C3⋊#95C2314yes—
198C3⋊#95C2312yes—
199C3⋊#95C2314yes—
200C3⋊#95C2312yes—
201C22×#41—32no—
202C23×Q8—32no—
203#548—616no—
204#547—68no—
205C2×C4⋊Q8—31no—
206C2×C4⋊Q8—32no—
207C2×C4⋊Q8—32no—
208C2×C4⋊Q8—32no—
209C2×C4⋊Q8—31no—
210C2×C4⋊Q8—68no—
211C2×#124—32no—
212C2×#124—34no—
213C2×#123—34no—
214C2×C22⋊Q8—32no—
215C2×C22⋊Q8—32no—
216C2×C22⋊Q8—32no—
217C2×C22⋊Q8—34no—
218C2×#121—34no—
219C2×#121—31no—
220C2×#121—32no—
221C2×#121C2×D311yescharacteristic
222C2×C4×Q8—32no—
223C2×C4×D4—34no—
224C2×C4×D4—32no—
225C2×C4×D4—31no—
226C2×C4×D4C2×D312yes—
227C2×C4×D4C2×D311yescharacteristic
228C22×C4⋊C4—32no—
229C22×C4⋊C4—32no—
230C22×C4⋊C4—32no—
231C22×C42C2×D311yescharacteristic
232#399—34no—
233#398—34no—
234#397—34no—
235#396—34no—
236#395—34no—
237#394—34no—
238#394—34no—
239#393—34no—
240#391—32no—
241#391—32no—
242#390—32no—
243#390—31no—
244#390C2×D311yescharacteristic
245#389—34no—
246#389—32no—
247#389—31no—
248#389C2×D311yescharacteristic
249#388—32no—
250#388—34no—
251#388C2×D312yes—
252#387—34no—
253#386—32no—
254#386—34no—
255#386C2×D312yes—
256#385—34no—
257#385—34no—
258#385—34no—
259#384—32no—
260#380—31no—
261#380—32no—
262#380—32no—
263#380C2×D311yescharacteristic
264C4×C4⋊C4—32no—
265C4×C4⋊C4—31no—
266C4×C4⋊C4C2×D311yescharacteristic
267C4×C22⋊C4—32no—
268C4×C22⋊C4C2×D312yes—
269C24×C3C2412yes—
270C24×C3C2411yescharacteristic
271C23×D3C2412yes—
272C2×C3×D4—24no—
273C2×C3×D4—24no—
274C2×C3×D4—22no—
275C2×C3×D4—22no—
276C2×C3×D4C2×D418yes—
277C2×C3×D4C2×D414yes—
278C22×C3×C4—22no—
279C22×C3×C4—22no—
280C22×C3×C4—22no—
281C22×C3×C4—22no—
282C22×C3×C4—22no—
283C22×C3×C4—22no—
284C22×C3×C4—22no—
285C22×C3×C4—24no—
286C22×C3×C4—24no—
287C22×C3×C4—24no—
288C22×C3×C4C2×D414yes—
289C22×C3×C4#4114yescomplemented
290C22×C3×C4C2412yes—
291C22×C3×C4C2412yes—
292C22×C3×C4C2411yescharacteristic
293C22×C3×C4C2412yes—
294C22×C3×C4C2411yescharacteristic
295C22×C3×C4C2411yescharacteristic
296C22×C3×C4C2411yescharacteristic
297C22×C3×C4C2411yescharacteristic
298C22×C3×C4C2411yescharacteristic
299C2×#67—28no—
300C2×#67—24no—
301C2×#67—24no—
302C2×#67—24no—
303C2×#67—28no—
304C2×#67—44no—
305C22×Dic3—28no—
306C22×Dic3—28no—
307C22×Dic3—28no—
308C22×Dic3—28no—
309C22×Dic3—44no—
310C22×Dic3—44no—
311C22×Dic3C2412yes—
312C22×Dic3C2412yes—
313C22×Dic3C2412yes—
314C22×Dic3C2414yes—
315C22×Dic3C2414yes—
316#237—432no—
317C2×D12—22no—
318C2×D12—22no—
319C2×D12—22no—
320C2×C4×D3—24no—
321C2×C4×D3—24no—
322C2×C4×D3—24no—
323C2×Dic6—24no—
324C2×Dic6—24no—
325C2×Dic6—24no—
326C2×Dic6—28no—
327C2×Dic6—24no—
328C2×Dic6—24no—
329C2×Dic6—28no—
330C2×Dic6—432no—
331C2×Dic6—44no—
332C2×Dic6C2×D418yes—
333C3×C4⋊C4—22no—
334C3×C4⋊C4—24no—
335C3×C4⋊C4—22no—
336C3×C4⋊C4C2×D414yes—
337C3×C22⋊C4—24no—
338C3×C22⋊C4—24no—
339C3×C22⋊C4—24no—
340C3×C22⋊C4—24no—
341C3×C22⋊C4C2×D418yes—
342C3×C42—22no—
343C3×C42—22no—
344C3×C42—22no—
345C3×C42—24no—
346C3×C42C2×D414yes—
347#217—28no—
348#217—28no—
349#217—24no—
350(C2×D3)⋊C4—24no—
351(C2×D3)⋊C4—24no—
352(C2×D3)⋊C4—28no—
353(C2×D3)⋊C4—24no—
354(C2×D3)⋊C4—24no—
355(C2×D3)⋊C4—28no—
356(C2×D3)⋊C4—44no—
357C4⋊Dic3—24no—
358C4⋊Dic3—24no—
359C4⋊Dic3—22no—
360C4⋊Dic3—28no—
361C4⋊Dic3—22no—
362C4⋊Dic3—22no—
363C4⋊Dic3—28no—
364C4⋊Dic3—28no—
365C4⋊Dic3—28no—
366C4⋊Dic3—44no—
367C4⋊Dic3C2×D418yes—
368C4⋊Dic3C2×D418yes—
369Dic3⋊C4—24no—
370Dic3⋊C4—28no—
371C4×Dic3—28no—
372C4×Dic3—24no—
373C2×#41—68no—
374C2×#41—68no—
375C2×#41—124no—
376C22×Q8—32no—
377C22×Q8—32no—
378C22×Q8—34no—
379C22×Q8—68no—
380C22×Q8—68no—
381C22×Q8—124no—
382C22×D4—32no—
383C22×D4—34no—
384C22×D4—31no—
385C22×D4C22×D312yes—
386C22×D4C22×D311yescharacteristic
387C23×C4—34no—
388C23×C4—34no—
389C23×C4—32no—
390C23×C4C22×D311yescharacteristic
391C23×C4C22×D312yes—
392C23×C4C22×D311yescharacteristic
393C23×C4C22×D311yescharacteristic
394C4⋊Q8—38no—
395C4⋊Q8—68no—
396C4⋊Q8—68no—
397C4⋊Q8—68no—
398C4⋊Q8—64no—
399#124—68no—
400#124—616no—
401#123—616no—
402C22⋊Q8—68no—
403C22⋊Q8—68no—
404C22⋊Q8—616no—
405C22⋊Q8—124no—
406#121—68no—
407#121—616no—
408#121—64no—
409#121D1218yescomplemented
410C4×Q8—68no—
411C4×D4—28no—
412C4×D4—24no—
413C4×D4—616no—
414C4×D4—68no—
415C4×D4—64no—
416C2×C4⋊C4—32no—
417C2×C4⋊C4—32no—
418C2×C4⋊C4—31no—
419C2×C4⋊C4—34no—
420C2×C4⋊C4—32no—
421C2×C4⋊C4—34no—
422C2×C4⋊C4—34no—
423C2×C4⋊C4—32no—
424C2×C4⋊C4—34no—
425C2×C4⋊C4—32no—
426C2×C4⋊C4—34no—
427C2×C4⋊C4—31no—
428C2×C4⋊C4—31no—
429C2×C4⋊C4—34no—
430C2×C4⋊C4—68no—
431C2×C4⋊C4—68no—
432C2×C4⋊C4—68no—
433C2×C4⋊C4C22×D311yescharacteristic
434C2×C4⋊C4C22×D312yes—
435C2×C4⋊C4C22×D311yescharacteristic
436C2×C4⋊C4C22×D311yescharacteristic
437C2×C22⋊C4—32no—
438C2×C22⋊C4—34no—
439C2×C22⋊C4—34no—
440C2×C22⋊C4—32no—
441C2×C22⋊C4—32no—
442C2×C22⋊C4—34no—
443C2×C22⋊C4—34no—
444C2×C22⋊C4—32no—
445C2×C22⋊C4—32no—
446C2×C22⋊C4—34no—
447C2×C22⋊C4C22×D312yes—
448C2×C22⋊C4C22×D312yes—
449C2×C22⋊C4C22×D312yes—
450C2×C22⋊C4C22×D312yes—
451C2×C22⋊C4C22×D312yes—
452C2×C42—24no—
453C2×C42—32no—
454C2×C42—34no—
455C2×C42C22×D312yes—
456C2×C42C22×D311yescharacteristic
457C2×C42C22×D311yescharacteristic
458C2×C42C22×D311yescharacteristic
459C2×C42C22×D311yescharacteristic
460#95—32no—
461#95—32no—
462#95—34no—
463#95—32no—
464#95—34no—
465#95—34no—
466#95—34no—
467#95C22×D312yes—
468#95C22×D312yes—
469#95C22×D312yes—
470C23×C3—21no—
471C23×C3—21no—
472C23×C3—21no—
473C23×C3—21no—
474C23×C3—22no—
475C23×C3—22no—
476C23×C3—22no—
477C23×C3—22no—
478C23×C3—22no—
479C23×C3—22no—
480C23×C3C22×D414yes—
481C23×C3C22×D412yes—
482C23×C3C2×#4112yes—
483C23×C32−1+412yes—
484C23×C3C2511yescharacteristic
485C22×D3—22no—
486C22×D3—22no—
487C22×D3—22no—
488C22×D3—22no—
489C22×D3—22no—
490C22×D3—22no—
491C22×D3—22no—
492C3×D4—216no—
493C3×D4—28no—
494C2×C3×C4—28no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—22no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—22no—
505C2×C3×C4—28no—
506C2×C3×C4—28no—
507C2×C3×C4—22no—
508C2×C3×C4—22no—
509C2×C3×C4—22no—
510C2×C3×C4—22no—
511C2×C3×C4—22no—
512C2×C3×C4—22no—
513C2×C3×C4—48no—
514C2×C3×C4C22×D414yes—
515C2×C3×C4C22×D412yes—
516C2×C3×C4C22×D412yes—
517C2×C3×C4C22×D412yes—
518C2×C3×C4C22×D412yes—
519C2×C3×C4C22×D412yes—
520C2×C3×C4C2×#4112yes—
521C2×C3×C4C2×#4112yes—
522C2×C3×C4H(5,𝔽2)12yes—
523C2×C3×C42−1+412yes—
524C2×C3×C42−1+412yes—
525#67—416no—
526#67—48no—
527C2×Dic3—24no—
528C2×Dic3—24no—
529C2×Dic3—22no—
530C2×Dic3—22no—
531C2×Dic3—22no—
532C2×Dic3—24no—
533C2×Dic3—22no—
534C2×Dic3—24no—
535C2×Dic3—22no—
536C2×Dic3—22no—
537C2×Dic3—24no—
538C2×Dic3—22no—
539C2×Dic3—22no—
540C2×Dic3—22no—
541C2×Dic3—416no—
542C2×Dic3—416no—
543C2×Dic3C22×D418yes—
544D12—44no—
545C4×D3—48no—
546Dic6—216no—
547Dic6—416no—
548Dic6—48no—
549C24—32no—
550C24C23×D312yes—
551C24C23×D311yescharacteristic
552#41—1232no—
553C2×Q8—38no—
554C2×Q8—68no—
555C2×Q8—64no—
556C2×Q8—68no—
557C2×Q8—64no—
558C2×Q8—64no—
559C2×Q8—64no—
560C2×Q8—64no—
561C2×Q8—124no—
562C2×Q8—1232no—
563C2×D4—24no—
564C2×D4—24no—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—68no—
568C2×D4—64no—
569C2×D4—68no—
570C2×D4—64no—
571C2×D4—64no—
572C2×D4—62no—
573C2×D4—62no—
574C2×D4—62no—
575C2×D4—124no—
576C2×D4C2×D1218yes—
577C2×D4C2×D1214yes—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—24no—
586C22×C4—24no—
587C22×C4—24no—
588C22×C4—34no—
589C22×C4—32no—
590C22×C4—32no—
591C22×C4—34no—
592C22×C4—32no—
593C22×C4—68no—
594C22×C4—68no—
595C22×C4—68no—
596C22×C4—68no—
597C22×C4—64no—
598C22×C4—64no—
599C22×C4—64no—
600C22×C4—124no—
601C22×C4—124no—
602C22×C4C2×D1214yes—
603C22×C4#23714yescomplemented
604C22×C4C23×D312yes—
605C22×C4C23×D312yes—
606C22×C4C23×D312yes—
607C22×C4C23×D311yescharacteristic
608C22×C4C23×D311yescharacteristic
609C22×C4C23×D311yescharacteristic
610C22×C4C23×D311yescharacteristic
611C22×C4C23×D311yescharacteristic
612C22×C4C23×D311yescharacteristic
613C4⋊C4—22no—
614C4⋊C4—24no—
615C4⋊C4—22no—
616C4⋊C4—38no—
617C4⋊C4—38no—
618C4⋊C4—68no—
619C4⋊C4—68no—
620C4⋊C4—68no—
621C4⋊C4—64no—
622C4⋊C4—68no—
623C4⋊C4—68no—
624C4⋊C4—62no—
625C4⋊C4—64no—
626C4⋊C4—64no—
627C4⋊C4—62no—
628C4⋊C4—62no—
629C4⋊C4—124no—
630C4⋊C4C2×D1214yes—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—24no—
634C22⋊C4—24no—
635C22⋊C4—68no—
636C22⋊C4—64no—
637C22⋊C4—68no—
638C22⋊C4—68no—
639C22⋊C4—64no—
640C22⋊C4—68no—
641C22⋊C4—64no—
642C22⋊C4—64no—
643C22⋊C4—64no—
644C22⋊C4—124no—
645C22⋊C4C2×D1218yes—
646C42—22no—
647C42—22no—
648C42—22no—
649C42—24no—
650C42—68no—
651C42—64no—
652C42D3×D414yes—
653C22×C3—22no—
654C22×C3—22no—
655C22×C3—22no—
656C22×C3—22no—
657C22×C3—22no—
658C22×C3—22no—
659C22×C3—24no—
660C22×C3—24no—
661C22×C3—24no—
662C22×C3—42no—
663C22×C3—42no—
664C22×C3—42no—
665C22×C3—42no—
666C22×C3#54714yescomplemented
667C22×C3C23×D411yescharacteristic
668C22×C3C23×D411yescharacteristic
669C22×C3C22×#4111yescharacteristic
670C22×C3C2×H(5,𝔽2)11yescharacteristic
671C22×C3C2×2−1+411yescharacteristic
672C22×C3C2×2−1+411yescharacteristic
673C22×C3C2×2−1+411yescharacteristic
674C2×D3—42no—
675C2×D3—42no—
676C2×D3—42no—
677C2×D3—42no—
678C2×D3—42no—
679C2×D3—42no—
680C2×D3—42no—
681C3×C4—22no—
682C3×C4—24no—
683C3×C4—22no—
684C3×C4—22no—
685C3×C4—22no—
686C3×C4—42no—
687C3×C4—42no—
688C3×C4D4214yes—
689C3×C4#54814yescomplemented
690Dic3—28no—
691Dic3—44no—
692Dic3—42no—
693Dic3—42no—
694Dic3—42no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—62no—
706C23—62no—
707C23—62no—
708C23—62no—
709C23—62no—
710C23—62no—
711C23—62no—
712C23C22×D1214yes—
713C23C22×D1212yes—
714C23C2×#23712yes—
715C23#101012yes—
716C23C24×D311yescharacteristic
717Q8—616no—
718Q8—1216no—
719Q8—128no—
720D4—216no—
721D4—28no—
722D4—1216no—
723D4—128no—
724D4—124no—
725C2×C4—28no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—22no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—22no—
736C2×C4—28no—
737C2×C4—28no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—38no—
745C2×C4—48no—
746C2×C4—64no—
747C2×C4—64no—
748C2×C4—62no—
749C2×C4—62no—
750C2×C4—64no—
751C2×C4—62no—
752C2×C4—62no—
753C2×C4—64no—
754C2×C4—62no—
755C2×C4—64no—
756C2×C4—62no—
757C2×C4—62no—
758C2×C4—62no—
759C2×C4—62no—
760C2×C4—1216no—
761C2×C4—1216no—
762C2×C4—128no—
763C2×C4C22×D1214yes—
764C2×C4C22×D1212yes—
765C2×C4C22×D1212yes—
766C2×C4C2×D3×D412yes—
767C2×C4C2×D3×D412yes—
768C2×C4C2×D3×D412yes—
769C2×C4C2×#23712yes—
770C2×C4C2×#23712yes—
771C2×C4#100912yes—
772C2×C4#101012yes—
773C2×C4#101012yes—
774C2×C3—24no—
775C2×C3—44no—
776C2×C3C2×D4211yescharacteristic
777C2×C3C2×#54711yescharacteristic
778C2×C3C2×#54811yescharacteristic
779C2×C3#348611yescharacteristic
780C2×C3#349911yescharacteristic
781C2×C3#351111yescharacteristic
782C2×C3#355211yescharacteristic
783D3—82no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—22no—
789C22—22no—
790C22—24no—
791C22—24no—
792C22—24no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—122no—
798C22—122no—
799C22—122no—
800C22—122no—
801C22—122no—
802C22—122no—
803C22—122no—
804C22#555514yescomplemented
805C22C23×D1211yescharacteristic
806C22C22×D3×D411yescharacteristic
807C22C22×#23711yescharacteristic
808C22C2×#100911yescharacteristic
809C22C2×#101011yescharacteristic
810C22C2×#101011yescharacteristic
811C22C2×#101011yescharacteristic
812C4—22no—
813C4—22no—
814C4—22no—
815C4—22no—
816C4—24no—
817C4—42no—
818C4—42no—
819C4—68no—
820C4—122no—
821C4—124no—
822C4—122no—
823C4—122no—
824C4D4×D1214yes—
825C4#559814yescomplemented
826C3#5912511yescharacteristic, complemented, Sylow
827C2—24no—
828C2—44no—
829C2—242no—
830C2C2×#555511yescharacteristic
831C2C2×D4×D1211yescharacteristic
832C2#8582711yescharacteristic
833C2C2×#559811yescharacteristic
834C2#8602211yescharacteristic
835C2#8613411yescharacteristic
836C2#8622511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×C4×#121C2
hypercenterC4×#121D3
hypocenterC3#59125
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
1. C2×#5598C2semidirect
2. C2×#5555C2semidirect
3. C22×#869C2semidirect
4. C3×C4×#121C2semidirect
5. #82382C2semidirect
6. #82352C2semidirect
7. D4×C4⋊Dic3C2semidirect
8. C4×#930C2semidirect
9. #76445C2semidirect
10. #76221C2semidirect
11. #75666C2semidirect
12. #74703C2semidirect
13. #74017C2semidirect
14. #73800C2semidirect
15. #73650C2semidirect
16. #73507C2semidirect
17. #73493C2semidirect
103. C4×#121D3semidirect
125. C3×#121D4semidirect
190. #869D4semidirect
289. C22×C3×C4#41semidirect
409. #121D12semidirect
603. C22×C4#237semidirect
666. C22×C3#547semidirect
689. C3×C4#548semidirect
804. C22#5555semidirect
825. C4#5598semidirect
826. C3#59125semidirect

Maximal subgroups

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

subgroupindex
C2×#55982
C2×#55552
C22×#8692
C3×C4×#1212
#823822
#823522
D4×C4⋊Dic32
C4×#9302
#764452
#762212
#756662
#747032
#740172
#738002
#736502
#735072
#734932
#591253