Finite Group Databasebeta

← #10957276

Subgroups — #10957276

Order 768.

3276 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5553C211yesmaximal, characteristic
2C2×#5504C212yesmaximal, complemented
3C3×D4×C4⋊C4C211yesmaximal, characteristic, complemented
4#82343C212yesmaximal, complemented
5C4×#940C212yesmaximal, complemented
6#82319C211yesmaximal, characteristic, complemented
7#82163C212yesmaximal, complemented
8#76202C212yesmaximal, complemented
9#75961C212yesmaximal, complemented
10#74397C214yesmaximal, complemented
11#74385C214yesmaximal, complemented
12#74323C211yesmaximal, characteristic, complemented
13#74319C211yesmaximal, characteristic, complemented
14#73877C212yesmaximal, complemented
15#73872C212yesmaximal, complemented
16#73653C211yesmaximal, characteristic, complemented
17C4×#887C211yesmaximal, characteristic, complemented
18#34313—31nomaximal, Sylow
19C22×#235C2212yes—
20C2×C3×C4×D4C2212yes—
21C2×C3×C4×D4C2211yescharacteristic
22C22×C3×C4⋊C4C2212yes—
23C2×#940C2212yes—
24C2×#930C2212yes—
25C2×C4×#67C2214yes—
26C2×C4×#67C2214yes—
27C2×C4×#67C2214yes—
28C2×#926C2212yes—
29#5553C4116yescomplemented
30#5504—216no—
31C2×#893C2212yes—
32C2×#893C2212yes—
33C2×#893C2212yes—
34C2×#893C2212yes—
35C2×#893C2212yes—
36C2×#892C2214yes—
37C2×D3×C4⋊C4C2214yes—
38C2×#887C2212yes—
39C2×#887C2211yescharacteristic
40C2×#887C2211yescharacteristic
41C2×#884C2214yes—
42C2×#874C2211yescharacteristic
43C2×C4×D12C2212yes—
44C2×C4×Dic6C2211yescharacteristic
45C3×#389C2212yes—
46C3×#385C2214yes—
47C3×#384C2211yescharacteristic
48C3×#380C2212yes—
49C3×C4×C4⋊C4C2211yescharacteristic
50#5221C2211yescharacteristic
51#5221C2211yescharacteristic
52#5213C2214yes—
53C4×#217C2212yes—
54#4990C2214yes—
55#4989C2214yes—
56#4988C2212yes—
57#4988C2212yes—
58#4988C2212yes—
59#4988C2212yes—
60#4984C2211yescharacteristic
61#4984C2211yescharacteristic
62#4976C2214yes—
63#4975C2212yes—
64Dic3×C4⋊C4C2212yes—
65Dic3×C4⋊C4C2211yescharacteristic
66Dic3×C4⋊C4C2211yescharacteristic
67#4972C2212yes—
68#4957C2214yes—
69#4957C2214yes—
70#4957C2214yes—
71#4956C2214yes—
72#4951C2212yes—
73#4951C2212yes—
74#4939C2212yes—
75C4×C4⋊Dic3C2211yescharacteristic
76C4×Dic3⋊C4C2212yes—
77C42×Dic3C2211yescharacteristic
78C42×Dic3C2212yes—
79#4670C2214yes—
80#4668C2214yes—
81#4667C2214yes—
82#4666C2214yes—
83#4665C2214yes—
84#4649C2212yes—
85#4649C2212yes—
86C2×#550—31no—
87C2×#520—32no—
88#2366—31no—
89#2366—32no—
90#2361—34no—
91#2361—32no—
92Q8×C4⋊C4—31no—
93D4×C4⋊C4—32no—
94D4×C4⋊C4D311yescharacteristic, complemented
95#2341—32no—
96#2324—34no—
97#2324—32no—
98C4×#127—31no—
99C4×#127—32no—
100#2293—32no—
101#2293—31no—
102C42×Q8—31no—
103C22×C3×D4C2311yescharacteristic
104C23×C3×C4C2312yes—
105C23×C3×C4C2314yes—
106C22×#67C2314yes—
107C22×#67C2314yes—
108C2×#235—28no—
109C2×#235—28no—
110C2×#235C2×C4116yescomplemented
111C22×D12C2312yes—
112C22×D12C2312yes—
113C22×D12C2312yes—
114C22×C4×D3C2314yes—
115C22×C4×D3C2314yes—
116C22×C4×D3C2314yes—
117C22×Dic6C2311yescharacteristic
118C3×C4×D4—44no—
119C3×C4×D4C2×C418yescomplemented
120C2×C3×C4⋊C4—28no—
121C2×C3×C4⋊C4C2312yes—
122C2×C3×C4⋊C4C2312yes—
123C2×C3×C4⋊C4C2311yescharacteristic
124C2×C3×C4⋊C4C2314yes—
125C2×C3×C4⋊C4C2312yes—
126C2×C3×C4⋊C4C2311yescharacteristic
127C2×C3×C4⋊C4C2311yescharacteristic
128C2×C3×C22⋊C4C2314yes—
129C2×C3×C22⋊C4C2312yes—
130C2×C3×C42C2312yes—
131C2×C3×C42C2311yescharacteristic
132C2×#217C2312yes—
133C2×#217C2312yes—
134C2×#217C2312yes—
135C2×#217C2312yes—
136#940C2×C4116yescomplemented
137#930C2×C4116yescomplemented
138C4×#67—216no—
139C4×#67—216no—
140C4×#67—48no—
141C2×(C2×D3)⋊C4C2314yes—
142C2×(C2×D3)⋊C4C2314yes—
143C2×(C2×D3)⋊C4C2314yes—
144C2×(C2×D3)⋊C4C2314yes—
145C2×(C2×D3)⋊C4C2314yes—
146C2×(C2×D3)⋊C4C2314yes—
147C2×(C2×D3)⋊C4C2314yes—
148#926—28no—
149C2×C4⋊Dic3C2312yes—
150C2×C4⋊Dic3C2312yes—
151C2×C4⋊Dic3C2311yescharacteristic
152C2×C4⋊Dic3C2311yescharacteristic
153C2×C4⋊Dic3C2311yescharacteristic
154C2×Dic3⋊C4C2312yes—
155C2×Dic3⋊C4C2314yes—
156C2×Dic3⋊C4C2314yes—
157C2×Dic3⋊C4C2312yes—
158C2×Dic3⋊C4C2312yes—
159C2×C4×Dic3C2311yescharacteristic
160C2×C4×Dic3C2312yes—
161C2×C4×Dic3C2312yes—
162C2×C4×Dic3C2314yes—
163C2×C4×Dic3C2311yescharacteristic
164C2×C4×Dic3C2311yescharacteristic
165C2×C4×Dic3C2311yescharacteristic
166C2×C4×Dic3C2312yes—
167C2×C4×Dic3C2311yescharacteristic
168C2×C4×Dic3C2312yes—
169C2×C4×Dic3C2312yes—
170C2×C4×Dic3C2312yes—
171C2×C4×Dic3C2311yescharacteristic
172#893—28no—
173#893—28no—
174#893—44no—
175#893—44no—
176#893C2×C4116yescomplemented
177#892—216no—
178D3×C4⋊C4—216no—
179#887—28no—
180#887—24no—
181#887D418yescomplemented
182#884C2×C4132yescomplemented
183#874C2×C418yescomplemented
184C4×D12—44no—
185C4×Dic6C2×C418yescomplemented
186C3×#95C2312yes—
187C3×#95C2314yes—
188C3⋊#95C2312yes—
189C3⋊#95C2312yes—
190C3⋊#95C2312yes—
191C3⋊#95C2312yes—
192C3⋊#95C2312yes—
193C3⋊#95C2314yes—
194C22×#41—32no—
195#550—316no—
196C2×#127—32no—
197C2×#127—31no—
198C2×#121—32no—
199C2×#121—34no—
200#520—616no—
201C2×C4×Q8—31no—
202C2×C4×Q8—31no—
203C2×C4×Q8—32no—
204C2×C4×Q8—31no—
205C2×C4×D4—34no—
206C2×C4×D4—34no—
207C2×C4×D4—34no—
208C2×C4×D4—32no—
209C2×C4×D4—32no—
210C2×C4×D4—32no—
211C2×C4×D4—32no—
212C2×C4×D4—32no—
213C2×C4×D4—32no—
214C2×C4×D4C2×D312yes—
215C2×C4×D4C2×D311yescharacteristic
216C2×#117—32no—
217C2×#117—34no—
218C22×C4⋊C4—34no—
219C22×C4⋊C4C2×D312yes—
220#390—31no—
221#390—31no—
222#390—32no—
223#390—32no—
224#390—32no—
225#390—32no—
226#390—34no—
227#390—34no—
228#390—34no—
229#390—32no—
230#389—32no—
231#389—34no—
232#389—31no—
233#389—31no—
234#389C2×D312yes—
235#388—34no—
236#388—32no—
237#388—32no—
238#388—34no—
239#386—34no—
240#386—34no—
241#386—34no—
242#385—34no—
243#385—34no—
244#385C2×D314yes—
245#384—32no—
246#384C2×D311yescharacteristic
247#380—34no—
248#380C2×D312yes—
249C4×C4⋊C4—31no—
250C4×C4⋊C4—32no—
251C4×C4⋊C4—31no—
252C4×C4⋊C4—32no—
253C4×C4⋊C4—31no—
254C4×C4⋊C4—32no—
255C4×C4⋊C4—32no—
256C4×C4⋊C4C2×D311yescharacteristic
257C4×C22⋊C4—32no—
258C4×C22⋊C4—34no—
259C43—32no—
260C43—31no—
261C24×C3C2412yes—
262C23×D3C2414yes—
263C2×C3×D4—22no—
264C2×C3×D4—22no—
265C2×C3×D4C22×C414yes—
266C22×C3×C4—24no—
267C22×C3×C4—24no—
268C22×C3×C4—28no—
269C22×C3×C4—44no—
270C22×C3×C4—44no—
271C22×C3×C4C22×C418yes—
272C22×C3×C4C2412yes—
273C22×C3×C4C2414yes—
274C22×C3×C4C2411yescharacteristic
275C22×C3×C4C2412yes—
276C22×C3×C4C2412yes—
277C22×C3×C4C2411yescharacteristic
278C22×C3×C4C2411yescharacteristic
279C2×#67—28no—
280C2×#67—28no—
281C2×#67—44no—
282C2×#67—44no—
283C2×#67C22×C4116yes—
284C2×#67C22×C4116yes—
285C22×Dic3C2411yescharacteristic
286C22×Dic3C2412yes—
287C22×Dic3C2412yes—
288C22×Dic3C2412yes—
289C22×Dic3C2411yescharacteristic
290C22×Dic3C2411yescharacteristic
291C22×Dic3C2411yescharacteristic
292C22×Dic3C2412yes—
293#235—264no—
294C2×D12—24no—
295C2×D12—24no—
296C2×D12—24no—
297C2×D12—24no—
298C2×D12—42no—
299C2×D12—42no—
300C2×D12C22×C418yes—
301C2×D12C22×C418yes—
302C2×D12C22×C418yes—
303C2×C4×D3—28no—
304C2×C4×D3—28no—
305C2×C4×D3—28no—
306C2×C4×D3—28no—
307C2×C4×D3—44no—
308C2×C4×D3—44no—
309C2×C4×D3—44no—
310C2×C4×D3—44no—
311C2×C4×D3C22×C4116yes—
312C2×Dic6C22×C414yes—
313C2×Dic6C2×D414yes—
314C2×Dic6#4114yes—
315C3×C4⋊C4—24no—
316C3×C4⋊C4—28no—
317C3×C4⋊C4—22no—
318C3×C4⋊C4—24no—
319C3×C4⋊C4—42no—
320C3×C4⋊C4C22×C414yes—
321C3×C4⋊C4C2×D414yes—
322C3×C22⋊C4—44no—
323C3×C22⋊C4C22×C418yes—
324C3×C42—24no—
325C3×C42C22×C414yes—
326#217—24no—
327#217—24no—
328#217—24no—
329#217—42no—
330(C2×D3)⋊C4—28no—
331(C2×D3)⋊C4—28no—
332(C2×D3)⋊C4—28no—
333(C2×D3)⋊C4—44no—
334(C2×D3)⋊C4—44no—
335(C2×D3)⋊C4—44no—
336(C2×D3)⋊C4C22×C4116yes—
337C4⋊Dic3—22no—
338C4⋊Dic3—22no—
339C4⋊Dic3—24no—
340C4⋊Dic3—24no—
341C4⋊Dic3C22×C414yes—
342Dic3⋊C4—28no—
343Dic3⋊C4—24no—
344Dic3⋊C4—44no—
345Dic3⋊C4C22×C418yes—
346Dic3⋊C4C2×D418yes—
347C4×Dic3—24no—
348C4×Dic3—22no—
349C4×Dic3—22no—
350C4×Dic3—22no—
351C4×Dic3—28no—
352C4×Dic3—24no—
353C4×Dic3—22no—
354C4×Dic3—24no—
355C4×Dic3—42no—
356C4×Dic3—41no—
357C4×Dic3C22×C418yes—
358C4×Dic3C2×D418yes—
359C4×Dic3C2×D414yes—
360C2×#41—316no—
361C2×#41—68no—
362C2×#41—68no—
363C22×Q8—31no—
364C22×D4—34no—
365C22×D4—34no—
366C22×D4—32no—
367C22×D4—32no—
368C22×D4—32no—
369C22×D4C22×D311yescharacteristic
370C23×C4—34no—
371C23×C4—34no—
372C23×C4—34no—
373C23×C4C22×D312yes—
374C23×C4C22×D314yes—
375#127—316no—
376#127—38no—
377#121—316no—
378#121—332no—
379C4×Q8—38no—
380C4×Q8—38no—
381C4×Q8—68no—
382C4×Q8—64no—
383C4×D4—316no—
384C4×D4—44no—
385C4×D4—68no—
386C4×D4—616no—
387C4×D4—616no—
388C4×D4—68no—
389C4×D4—124no—
390C4×D4—124no—
391C4×D4—128no—
392C4×D4—124no—
393C4×D4C4×D318yescomplemented
394#117—616no—
395#117—68no—
396C2×C4⋊C4—28no—
397C2×C4⋊C4—32no—
398C2×C4⋊C4—32no—
399C2×C4⋊C4—31no—
400C2×C4⋊C4—32no—
401C2×C4⋊C4—34no—
402C2×C4⋊C4—32no—
403C2×C4⋊C4—31no—
404C2×C4⋊C4—32no—
405C2×C4⋊C4—31no—
406C2×C4⋊C4—34no—
407C2×C4⋊C4—616no—
408C2×C4⋊C4C22×D314yes—
409C2×C4⋊C4C22×D312yes—
410C2×C4⋊C4C22×D312yes—
411C2×C4⋊C4C22×D311yescharacteristic
412C2×C4⋊C4C22×D312yes—
413C2×C4⋊C4C22×D311yescharacteristic
414C2×C4⋊C4C22×D311yescharacteristic
415C2×C22⋊C4—34no—
416C2×C22⋊C4—32no—
417C2×C22⋊C4—32no—
418C2×C22⋊C4—32no—
419C2×C22⋊C4—34no—
420C2×C22⋊C4—34no—
421C2×C22⋊C4—34no—
422C2×C22⋊C4—32no—
423C2×C22⋊C4—34no—
424C2×C22⋊C4—34no—
425C2×C22⋊C4—34no—
426C2×C22⋊C4C22×D314yes—
427C2×C22⋊C4C22×D312yes—
428C2×C42—32no—
429C2×C42—31no—
430C2×C42—32no—
431C2×C42—34no—
432C2×C42—32no—
433C2×C42—32no—
434C2×C42—31no—
435C2×C42—31no—
436C2×C42—32no—
437C2×C42—31no—
438C2×C42—31no—
439C2×C42—32no—
440C2×C42—31no—
441C2×C42C22×D312yes—
442C2×C42C22×D311yescharacteristic
443#95—32no—
444#95—32no—
445#95—32no—
446#95—32no—
447#95—34no—
448#95—32no—
449#95C22×D314yes—
450#95C22×D312yes—
451C23×C3—22no—
452C23×C3—22no—
453C23×C3—22no—
454C23×C3—22no—
455C23×C3—22no—
456C23×C3—22no—
457C23×C3C23×C414yes—
458C23×C3C2511yescharacteristic
459C22×D3—24no—
460C22×D3—24no—
461C22×D3—24no—
462C22×D3—24no—
463C22×D3—24no—
464C22×D3—24no—
465C22×D3C23×C418yes—
466C3×D4—28no—
467C2×C3×C4—22no—
468C2×C3×C4—22no—
469C2×C3×C4—21no—
470C2×C3×C4—22no—
471C2×C3×C4—22no—
472C2×C3×C4—21no—
473C2×C3×C4—216no—
474C2×C3×C4—24no—
475C2×C3×C4—22no—
476C2×C3×C4—24no—
477C2×C3×C4—22no—
478C2×C3×C4—24no—
479C2×C3×C4—22no—
480C2×C3×C4—88no—
481C2×C3×C4C23×C412yes—
482C2×C3×C4C23×C414yes—
483C2×C3×C4C23×C412yes—
484C2×C3×C4C23×C412yes—
485C2×C3×C4C22×D414yes—
486C2×C3×C4C22×D412yes—
487C2×C3×C4C2×#4112yes—
488C2×C3×C4H(5,𝔽2)12yes—
489C2×C3×C42−1+412yes—
490#67—232no—
491#67—416no—
492C2×Dic3—21no—
493C2×Dic3—22no—
494C2×Dic3—21no—
495C2×Dic3—21no—
496C2×Dic3—21no—
497C2×Dic3—21no—
498C2×Dic3—21no—
499C2×Dic3—22no—
500C2×Dic3—22no—
501C2×Dic3—22no—
502C2×Dic3—21no—
503C2×Dic3—21no—
504C2×Dic3—22no—
505C2×Dic3—22no—
506C2×Dic3—22no—
507C2×Dic3—21no—
508C2×Dic3—22no—
509C2×Dic3C23×C414yes—
510C2×Dic3C23×C414yes—
511C2×Dic3C22×D412yes—
512C2×Dic3C22×D412yes—
513C2×Dic3C22×D414yes—
514C2×Dic3C2×#4114yes—
515C2×Dic3H(5,𝔽2)12yes—
516D12—216no—
517D12—216no—
518D12—48no—
519C4×D3—232no—
520C4×D3—88no—
521C4×D3—88no—
522Dic6C4×D4116yescomplemented
523C24—34no—
524C24C23×D312yes—
525#41—664no—
526C2×Q8—34no—
527C2×Q8—34no—
528C2×Q8—34no—
529C2×D4—22no—
530C2×D4—22no—
531C2×D4—316no—
532C2×D4—316no—
533C2×D4—38no—
534C2×D4—38no—
535C2×D4—38no—
536C2×D4—68no—
537C2×D4—68no—
538C2×D4—64no—
539C2×D4—64no—
540C2×D4—64no—
541C2×D4—64no—
542C2×D4—122no—
543C2×D4—122no—
544C2×D4—124no—
545C2×D4—124no—
546C2×D4C2×C4×D314yes—
547C22×C4—24no—
548C22×C4—24no—
549C22×C4—28no—
550C22×C4—32no—
551C22×C4—32no—
552C22×C4—31no—
553C22×C4—31no—
554C22×C4—31no—
555C22×C4—316no—
556C22×C4—32no—
557C22×C4—31no—
558C22×C4—32no—
559C22×C4—44no—
560C22×C4—44no—
561C22×C4—68no—
562C22×C4—68no—
563C22×C4—68no—
564C22×C4—68no—
565C22×C4—124no—
566C22×C4—124no—
567C22×C4—124no—
568C22×C4—124no—
569C22×C4C2×C4×D318yes—
570C22×C4C23×D312yes—
571C22×C4C23×D314yes—
572C22×C4C23×D311yescharacteristic
573C22×C4C23×D312yes—
574C22×C4C23×D312yes—
575C22×C4C23×D311yescharacteristic
576C22×C4C23×D311yescharacteristic
577C4⋊C4—28no—
578C4⋊C4—24no—
579C4⋊C4—24no—
580C4⋊C4—22no—
581C4⋊C4—38no—
582C4⋊C4—34no—
583C4⋊C4—38no—
584C4⋊C4—42no—
585C4⋊C4—64no—
586C4⋊C4—68no—
587C4⋊C4—64no—
588C4⋊C4—64no—
589C4⋊C4—62no—
590C4⋊C4—62no—
591C4⋊C4—124no—
592C4⋊C4C2×C4×D314yes—
593C4⋊C4D3×D414yes—
594C22⋊C4—316no—
595C22⋊C4—44no—
596C22⋊C4—68no—
597C22⋊C4—68no—
598C22⋊C4—64no—
599C22⋊C4—64no—
600C22⋊C4—64no—
601C22⋊C4—68no—
602C22⋊C4—124no—
603C22⋊C4—124no—
604C22⋊C4—124no—
605C22⋊C4—122no—
606C22⋊C4C2×C4×D318yes—
607C42—24no—
608C42—38no—
609C42—38no—
610C42—34no—
611C42—68no—
612C42—62no—
613C42—64no—
614C42—64no—
615C42—64no—
616C42—62no—
617C42—62no—
618C42—62no—
619C42—121no—
620C42—122no—
621C42C2×C4×D314yes—
622C22×C3—24no—
623C22×C3—24no—
624C22×C3—24no—
625C22×C3—42no—
626C22×C3—42no—
627C22×C3—42no—
628C22×C3—42no—
629C22×C3C24×C411yescharacteristic
630C22×C3C23×D411yescharacteristic
631C22×C3C22×#4111yescharacteristic
632C22×C3C2×H(5,𝔽2)11yescharacteristic
633C22×C3C2×H(5,𝔽2)11yescharacteristic
634C22×C3C2×2−1+411yescharacteristic
635C22×C3#58511yescharacteristic
636C2×D3—28no—
637C2×D3—28no—
638C2×D3—28no—
639C2×D3—44no—
640C2×D3—44no—
641C2×D3—44no—
642C2×D3—44no—
643C3×C4—24no—
644C3×C4—22no—
645C3×C4—24no—
646C3×C4—44no—
647C3×C4—42no—
648C3×C4C2×C4×D414yes—
649C3×C4#52014yescomplemented
650Dic3—24no—
651Dic3—22no—
652Dic3—22no—
653Dic3—22no—
654Dic3—42no—
655Dic3—42no—
656Dic3—41no—
657Dic3C2×C4×D418yes—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—38no—
665C23—64no—
666C23—64no—
667C23—64no—
668C23—64no—
669C23—64no—
670C23—64no—
671C23C22×C4×D314yes—
672C23C24×D311yescharacteristic
673Q8—316no—
674D4—28no—
675D4—632no—
676D4—616no—
677D4—616no—
678D4—128no—
679D4—1216no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—21no—
684C2×C4—22no—
685C2×C4—21no—
686C2×C4—216no—
687C2×C4—24no—
688C2×C4—22no—
689C2×C4—24no—
690C2×C4—22no—
691C2×C4—24no—
692C2×C4—22no—
693C2×C4—34no—
694C2×C4—34no—
695C2×C4—34no—
696C2×C4—34no—
697C2×C4—32no—
698C2×C4—32no—
699C2×C4—32no—
700C2×C4—632no—
701C2×C4—61no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—62no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—62no—
709C2×C4—62no—
710C2×C4—62no—
711C2×C4—61no—
712C2×C4—62no—
713C2×C4—62no—
714C2×C4—61no—
715C2×C4—62no—
716C2×C4—61no—
717C2×C4—62no—
718C2×C4—88no—
719C2×C4—248no—
720C2×C4—248no—
721C2×C4C22×C4×D312yes—
722C2×C4C22×C4×D314yes—
723C2×C4C22×C4×D312yes—
724C2×C4C22×C4×D312yes—
725C2×C4C2×D3×D414yes—
726C2×C4C2×D3×D412yes—
727C2×C4#100412yes—
728C2×C4#100712yes—
729C2×C4D3×#4112yes—
730C2×C3—44no—
731C2×C3C22×C4×D411yescharacteristic
732C2×C3C2×#52011yescharacteristic
733C2×C3C4×H(5,𝔽2)11yescharacteristic
734C2×C3#349711yescharacteristic
735C2×C3#349811yescharacteristic
736C2×C3#351711yescharacteristic
737C2×C3#352211yescharacteristic
738D3—48no—
739C22—24no—
740C22—24no—
741C22—24no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—68no—
747C22—68no—
748C22—68no—
749C22—124no—
750C22—124no—
751C22—124no—
752C22—124no—
753C22C23×C4×D311yescharacteristic
754C22C22×D3×D411yescharacteristic
755C22C2×#100411yescharacteristic
756C22C2×#100711yescharacteristic
757C22C2×D3×#4111yescharacteristic
758C22D3×H(5,𝔽2)11yescharacteristic
759C22#596811yescharacteristic
760C4—24no—
761C4—24no—
762C4—22no—
763C4—38no—
764C4—44no—
765C4—42no—
766C4—62no—
767C4—64no—
768C4—62no—
769C4—62no—
770C4—122no—
771C4—121no—
772C4—122no—
773C4#550414yescomplemented
774C4C4×D3×D414yes—
775C3#3431311yescharacteristic, complemented, Sylow
776C2—44no—
777C2—128no—
778C2C2×#550411yescharacteristic
779C2C2×C4×D3×D411yescharacteristic
780C2#8588611yescharacteristic
781C2#8660811yescharacteristic
782C2#8668411yescharacteristic
783C2#8676011yescharacteristic
784C2#8693611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutatorC22×C3C24×C4
FittingC3×D4×C4⋊C4C2
socle, cosocleC23×C3C25
prime radicalC2×#5553C2
hypercenterD4×C4⋊C4D3
hypocenterC3#34313
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ D4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#5504C2semidirect
3. C3×D4×C4⋊C4C2semidirect
4. #82343C2semidirect
5. C4×#940C2semidirect
6. #82319C2semidirect
7. #82163C2semidirect
8. #76202C2semidirect
9. #75961C2semidirect
10. #74397C2semidirect
11. #74385C2semidirect
12. #74323C2semidirect
13. #74319C2semidirect
14. #73877C2semidirect
15. #73872C2semidirect
16. #73653C2semidirect
17. C4×#887C2semidirect
29. #5553C4semidirect
94. D4×C4⋊C4D3semidirect
110. C2×#235C2×C4semidirect
119. C3×C4×D4C2×C4semidirect
136. #940C2×C4semidirect
137. #930C2×C4semidirect
176. #893C2×C4semidirect
181. #887D4semidirect
182. #884C2×C4semidirect
183. #874C2×C4semidirect
185. C4×Dic6C2×C4semidirect
393. C4×D4C4×D3semidirect
522. Dic6C4×D4semidirect
649. C3×C4#520semidirect
773. C4#5504semidirect
775. C3#34313semidirect

Maximal subgroups

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

subgroupindex
C2×#55532
C2×#55042
C3×D4×C4⋊C42
#823432
C4×#9402
#823192
#821632
#762022
#759612
#743972
#743852
#743232
#743192
#738772
#738722
#736532
C4×#8872
#343133