Finite Group Databasebeta

← #11900135

Subgroups — #11900135

Order 1152.

3245 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3796C211yesmaximal, characteristic
2C3⋊D3×#117C211yesmaximal, characteristic, complemented
3C3×#5521C211yesmaximal, characteristic, complemented
4C3×#5516C211yesmaximal, characteristic, complemented
5#10594982C211yesmaximal, characteristic, complemented
6#10594969C211yesmaximal, characteristic, complemented
7#10594818C211yesmaximal, characteristic, complemented
8#10594361C214yesmaximal, complemented
9#10594360C214yesmaximal, complemented
10#10594182C214yesmaximal, complemented
11D3×#877C214yesmaximal, complemented
12#10593889C214yesmaximal, complemented
13C4×#3796C214yesmaximal, complemented
14#85872—31nomaximal
15#85856—31nomaximal
16C22×C4×C3⋊D3C2211yescharacteristic
17C22×C3×D12C2211yescharacteristic
18C22×C3×Dic6C2211yescharacteristic
19C22×#626C2212yes—
20C22×D3×Dic3C2212yes—
21C2×#3796C4116yescomplemented
22C2×#3796C2212yes—
23C2×#3796C2212yes—
24C2×#3796C2212yes—
25C2×#3796C2212yes—
26C32×#117C2211yescharacteristic
27#64135C2211yescharacteristic
28#64101C2212yescomplemented
29C4⋊C4×C3⋊D3C2212yescomplemented
30C22⋊C4×C3⋊D3C2212yes—
31#64086C2212yes—
32#64081C2212yescomplemented
33C42×C3⋊D3C2212yescomplemented
34C3×#926C2211yescharacteristic
35C3×#926C2211yescharacteristic
36C3×#893C2214yescomplemented
37C3×#887C2214yescomplemented
38C3×D3×C22⋊C4C2214yes—
39C3×#877C2214yes—
40C3×C4×D12C2214yescomplemented
41C3×C4×Dic6C2214yescomplemented
42#63974C2212yes—
43D3×#217C2214yes—
44#63957C2212yes—
45#63955C2214yes—
46#63904C2218yescomplemented
47C4×#626C2218yescomplemented
48#63900C2212yescomplemented
49#63898C2214yescomplemented
50Dic3×D12C2214yescomplemented
51C4×#624C2212yescomplemented
52#63881C2218yescomplemented
53#63880C2218yescomplemented
54#63878C2218yescomplemented
55#63877C2218yescomplemented
56D3×Dic3⋊C4C2218yescomplemented
57C4×D3×Dic3C2218yescomplemented
58#63874C2212yescomplemented
59#63849C2212yescomplemented
60#63843C2214yescomplemented
61Dic3×Dic6C2214yescomplemented
62C22×#239—31no—
63C22×#237—31no—
64C3×#519—31no—
65C3×#518—31no—
66#5812—31no—
67#5798—31no—
68#5574—34no—
69#5574—34no—
70C4×#239—34no—
71C4×#239—34no—
72#5546—34no—
73#5546—34no—
74C4×#237—34no—
75C4×#237—34no—
76#5521—31no—
77#5521—34no—
78#5521D311yescharacteristic, complemented
79D3×#117—31no—
80D3×#117—31no—
81D3×#117—31no—
82D3×#117—31no—
83D3×#117—34no—
84D3×#117—61no—
85#5516—31no—
86#5516D311yescharacteristic, complemented
87#5486—34no—
88C2×#877—34no—
89C23×C3⋊D3C2311yescharacteristic
90C23×C3×D3C2312yes—
91C22×C32×C4C2311yescharacteristic
92C22×C3⋊Dic3C2311yescharacteristic
93C2×C4×C3⋊D3C2×C418yescomplemented
94C2×C4×C3⋊D3C2314yes—
95C2×C4×C3⋊D3C2311yescharacteristic
96C2×C4×C3⋊D3C2311yescharacteristic
97C2×C4×C3⋊D3C2311yescharacteristic
98C2×C4×C3⋊D3C2311yescharacteristic
99C22×C3×Dic3C2312yes—
100C2×C3×D12C2×C418yescomplemented
101C2×C3×D12C2312yes—
102C2×C3×D12C2312yes—
103C2×C3×C4×D3C2318yes—
104C2×C3×Dic6C2×C418yescomplemented
105C2×C3×Dic6C2312yes—
106C2×C3×Dic6C2312yes—
107C2×#626C2×C4116yescomplemented
108C2×#626C2314yes—
109C2×#626C2314yes—
110C2×#624C2314yes—
111C2×D3×Dic3C2×C4116yescomplemented
112C2×D3×Dic3C2318yes—
113C2×D3×Dic3C2314yes—
114C2×D3×Dic3C2314yes—
115#3796C2×C4116yescomplemented
116#3796C2×C4116yescomplemented
117#3796C2×C4116yescomplemented
118#3796C2×C4116yescomplemented
119C32×C4⋊C4C2312yes—
120C32×C22⋊C4C2312yes—
121C32×C42C2312yes—
122#3757C2312yes—
123#3752C2314yes—
124C4⋊(C3⋊Dic3)C2312yes—
125#3750C2314yes—
126C4×C3⋊Dic3C2312yes—
127C4×C3⋊Dic3C2314yes—
128C3×#217C2312yes—
129C3×#217C2312yes—
130C3×(C2×D3)⋊C4C2318yes—
131C3×C4⋊Dic3C2312yes—
132C3×C4⋊Dic3C2312yes—
133C3×Dic3⋊C4C2318yes—
134C3×C4×Dic3C2318yes—
135C3×C4×Dic3C2312yes—
136C3×C4×Dic3C2312yes—
137#3724C2314yes—
138Dic3⋊Dic3C2318yes—
139#3722C2314yes—
140(C2×D3)⋊Dic3C2318yes—
141Dic32C2318yes—
142Dic32C2314yes—
143#3428—91noSylow
144C22×C3×Q8—31no—
145C22×C3×D4—31no—
146C22×#67—32no—
147C23×Dic3—32no—
148C2×#239—316no—
149C2×#239—32no—
150C2×#239—32no—
151C2×#239—32no—
152C2×#239—32no—
153C2×#237—316no—
154C2×#237—32no—
155C2×#237—32no—
156C2×#237—32no—
157C2×#237—32no—
158C22×D12—32no—
159C22×D12C2×D311yescharacteristic
160C22×C4×D3—32no—
161C22×C4×D3—31no—
162C22×C4×D3—31no—
163C22×C4×D3—61no—
164C22×Dic6C2×D311yescharacteristic
165C3×C4×Q8—34no—
166C3×C4×Q8—34no—
167C3×C4×D4—34no—
168C3×C4×D4—34no—
169C3×#117—21no—
170C3×#117—31no—
171C3×#117—31no—
172C3×#117—34no—
173C3×#117C2×D311yescharacteristic
174C3×#117C2×D311yescharacteristic
175C2×C3×C22⋊C4—34no—
176C2×#217—34no—
177Q8×Dic3—34no—
178Q8×Dic3—34no—
179D4×Dic3—34no—
180D4×Dic3—34no—
181C4×#67—38no—
182C4×#67—38no—
183#926—31no—
184#926—31no—
185#926—34no—
186#926—61no—
187#926C2×D311yescharacteristic
188#926C2×D311yescharacteristic
189C2×Dic3⋊C4—38no—
190C2×C4×Dic3—38no—
191#893—34no—
192#893—38no—
193#893—38no—
194#893C2×D314yescomplemented
195#892—32no—
196#892—32no—
197#892—38no—
198#892—32no—
199#892—32no—
200#892—62no—
201D3×C4⋊C4—38no—
202D3×C4⋊C4—32no—
203D3×C4⋊C4—32no—
204D3×C4⋊C4—32no—
205D3×C4⋊C4—32no—
206D3×C4⋊C4—62no—
207#887—34no—
208#887C2×D314yescomplemented
209#67⋊C4—38no—
210#67⋊C4—38no—
211D3×C22⋊C4—34no—
212D3×C22⋊C4—32no—
213D3×C22⋊C4—32no—
214D3×C22⋊C4—32no—
215D3×C22⋊C4—32no—
216D3×C22⋊C4—62no—
217D3×C22⋊C4C2×D314yes—
218#877—34no—
219#877—32no—
220#877—32no—
221#877—32no—
222#877—32no—
223#877—38no—
224#877—38no—
225#877—62no—
226#877C2×D314yes—
227C4×D12—34no—
228C4×D12—38no—
229C4×D12—38no—
230C4×D12C2×D314yescomplemented
231#872—32no—
232#872—32no—
233#872—38no—
234#872—32no—
235#872—32no—
236#872—62no—
237C42×D3—38no—
238C42×D3—32no—
239C42×D3—32no—
240C42×D3—32no—
241C42×D3—32no—
242C42×D3—62no—
243C4×Dic6—34no—
244C4×Dic6C2×D314yescomplemented
245C23×C32C2411yescharacteristic
246C22×C3⋊D3—42no—
247C22×C3⋊D3C22×C414yes—
248C22×C3⋊D3C2411yescharacteristic
249C22×C3⋊D3C2411yescharacteristic
250C22×C3×D3—44no—
251C22×C3×D3C22×C418yes—
252C22×C3×D3C2414yes—
253C2×C32×C4C22×C414yes—
254C2×C32×C4C2414yes—
255C2×C32×C4C2411yescharacteristic
256C2×C32×C4C2411yescharacteristic
257C2×C3⋊Dic3C22×C414yes—
258C2×C3⋊Dic3C2414yes—
259C2×C3⋊Dic3C2411yescharacteristic
260C2×C3⋊Dic3C2411yescharacteristic
261C4×C3⋊D3—44no—
262C4×C3⋊D3C22×C414yes—
263C4×C3⋊D3C22×C414yes—
264C4×C3⋊D3C22×C414yes—
265C4×C3⋊D3C22×C414yes—
266C2×C3×Dic3C22×C418yes—
267C2×C3×Dic3C2414yes—
268C2×C3×Dic3C2414yes—
269C2×C3×Dic3C2414yes—
270C3×D12C22×C418yes—
271C3×D12C22×C418yes—
272C3×C4×D3—48no—
273C3×Dic6C22×C418yes—
274C3×Dic6C22×C418yes—
275#626C22×C4116yes—
276#626C22×C4116yes—
277#624—44no—
278D3×Dic3—48no—
279D3×Dic3C22×C4116yes—
280D3×Dic3C22×C4116yes—
281C22×#41—91no—
282#520—94no—
283#520—94no—
284#519—31no—
285#519—91no—
286#518—31no—
287#518—94no—
288#518—91no—
289C4×#41—94no—
290C4×#41—94no—
291C2×#117—94no—
292C2×#117—91no—
293C2×#117—91no—
294C24×C3—32no—
295C23×D3—31no—
296C23×D3—31no—
297C23×D3—61no—
298C23×D3C22×D312yes—
299C2×C3×Q8—38no—
300C2×C3×Q8—32no—
301C2×C3×Q8—32no—
302C2×C3×D4—38no—
303C2×C3×D4—32no—
304C2×C3×D4—32no—
305C22×C3×C4—21no—
306C22×C3×C4—32no—
307C22×C3×C4—38no—
308C22×C3×C4C22×D311yescharacteristic
309C22×C3×C4C22×D311yescharacteristic
310C2×#67—316no—
311C2×#67—34no—
312C2×#67—34no—
313C22×Dic3—31no—
314C22×Dic3—31no—
315C22×Dic3—316no—
316C22×Dic3—34no—
317C22×Dic3—34no—
318C22×Dic3—38no—
319C22×Dic3—61no—
320C22×Dic3C22×D312yes—
321#239—316no—
322#239—316no—
323#239—316no—
324#239—316no—
325#237—316no—
326#237—316no—
327#237—316no—
328#237—316no—
329C2×D12—316no—
330C2×D12—34no—
331C2×D12—34no—
332C2×D12C4×D318yescomplemented
333C2×D12C22×D312yes—
334C2×D12C22×D312yes—
335C2×C4×D3—316no—
336C2×C4×D3—34no—
337C2×C4×D3—34no—
338C2×C4×D3—38no—
339C2×C4×D3—38no—
340C2×C4×D3—31no—
341C2×C4×D3—31no—
342C2×C4×D3—31no—
343C2×C4×D3—31no—
344C2×C4×D3—31no—
345C2×C4×D3—31no—
346C2×C4×D3—31no—
347C2×C4×D3—31no—
348C2×C4×D3—38no—
349C2×C4×D3—34no—
350C2×C4×D3—34no—
351C2×C4×D3—34no—
352C2×C4×D3—34no—
353C2×C4×D3—61no—
354C2×C4×D3—61no—
355C2×C4×D3—61no—
356C2×C4×D3—61no—
357C2×C4×D3—68no—
358C2×C4×D3—64no—
359C2×C4×D3C22×D318yes—
360C2×Dic6C4×D318yescomplemented
361C2×Dic6C22×D312yes—
362C2×Dic6C22×D312yes—
363C3×C4⋊C4—22no—
364C3×C4⋊C4—32no—
365C3×C4⋊C4—38no—
366C3×C4⋊C4—32no—
367C3×C4⋊C4C22×D312yes—
368C3×C4⋊C4C22×D312yes—
369C3×C22⋊C4—22no—
370C3×C22⋊C4—32no—
371C3×C22⋊C4—32no—
372C3×C22⋊C4—38no—
373C3×C22⋊C4C22×D312yes—
374C3×C22⋊C4C22×D312yes—
375C3×C42—22no—
376C3×C42—32no—
377C3×C42—38no—
378C3×C42—32no—
379C3×C42C22×D312yes—
380C3×C42C22×D312yes—
381#217—32no—
382#217—32no—
383#217—38no—
384#217—62no—
385#217C22×D312yes—
386#217C22×D312yes—
387(C2×D3)⋊C4—38no—
388(C2×D3)⋊C4—34no—
389(C2×D3)⋊C4—34no—
390(C2×D3)⋊C4—34no—
391(C2×D3)⋊C4—34no—
392(C2×D3)⋊C4—64no—
393(C2×D3)⋊C4C22×D318yes—
394C4⋊Dic3—32no—
395C4⋊Dic3—32no—
396C4⋊Dic3—38no—
397C4⋊Dic3—62no—
398C4⋊Dic3C22×D312yes—
399C4⋊Dic3C22×D312yes—
400Dic3⋊C4—34no—
401Dic3⋊C4—34no—
402Dic3⋊C4—38no—
403Dic3⋊C4—34no—
404Dic3⋊C4—34no—
405Dic3⋊C4—64no—
406Dic3⋊C4C22×D318yes—
407C4×Dic3—34no—
408C4×Dic3—32no—
409C4×Dic3—32no—
410C4×Dic3—34no—
411C4×Dic3—38no—
412C4×Dic3—34no—
413C4×Dic3—38no—
414C4×Dic3—34no—
415C4×Dic3—62no—
416C4×Dic3—64no—
417C4×Dic3C22×D318yes—
418C4×Dic3C22×D312yes—
419C4×Dic3C22×D312yes—
420C22×C32—22no—
421C22×C32C23×C412yes—
422C22×C32C2511yescharacteristic
423C2×C3⋊D3—22no—
424C2×C3⋊D3—22no—
425C2×C3⋊D3—44no—
426C2×C3⋊D3C23×C412yes—
427C2×C3⋊D3C23×C412yes—
428C2×C3×D3—28no—
429C2×C3×D3—48no—
430C2×C3×D3C23×C418yes—
431C32×C4—24no—
432C32×C4C23×C412yes—
433C32×C4C23×C412yes—
434C3⋊Dic3—24no—
435C3⋊Dic3C23×C412yes—
436C3⋊Dic3C23×C412yes—
437C3×Dic3—24no—
438C3×Dic3—24no—
439C3×Dic3C23×C418yes—
440C2×#41—92no—
441C2×#41—92no—
442C2×#41—92no—
443C2×#41—92no—
444C2×#41—916no—
445C22×Q8—31no—
446C22×D4—31no—
447C22×D4—92no—
448C23×C4—92no—
449C23×C4—91no—
450C4×Q8—34no—
451C4×Q8—34no—
452C4×Q8—94no—
453C4×Q8—94no—
454C4×D4—34no—
455C4×D4—34no—
456C4×D4—98no—
457C4×D4—98no—
458C4×D4—94no—
459C4×D4—98no—
460C4×D4—98no—
461C4×D4—94no—
462#117—31no—
463#117—31no—
464#117—34no—
465#117—92no—
466#117—98no—
467#117—92no—
468#117—98no—
469#117—94no—
470#117—92no—
471#117—91no—
472#117—92no—
473#117—92no—
474#117—92no—
475#117D3211yescharacteristic
476C2×C4⋊C4—92no—
477C2×C4⋊C4—98no—
478C2×C4⋊C4—92no—
479C2×C22⋊C4—34no—
480C2×C22⋊C4—92no—
481C2×C22⋊C4—94no—
482C2×C22⋊C4—92no—
483C2×C42—92no—
484C2×C42—98no—
485C2×C42—92no—
486C23×C3—21no—
487C23×C3—34no—
488C23×C3—38no—
489C23×C3—124no—
490C23×C3C23×D311yescharacteristic
491C23×C3C23×D311yescharacteristic
492C22×D3—31no—
493C22×D3—31no—
494C22×D3—31no—
495C22×D3—31no—
496C22×D3—34no—
497C22×D3—34no—
498C22×D3—44no—
499C22×D3—61no—
500C22×D3—64no—
501C22×D3—61no—
502C22×D3—122no—
503C22×D3—122no—
504C22×D3—124no—
505C22×D3C2×C4×D318yes—
506C22×D3C23×D314yes—
507C3×Q8—38no—
508C3×Q8—38no—
509C3×D4—38no—
510C3×D4—38no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—24no—
514C2×C3×C4—24no—
515C2×C3×C4—38no—
516C2×C3×C4—34no—
517C2×C3×C4—34no—
518C2×C3×C4—34no—
519C2×C3×C4—128no—
520C2×C3×C4C2×C4×D314yes—
521C2×C3×C4C2×C4×D314yes—
522C2×C3×C4C23×D314yes—
523C2×C3×C4C23×D314yes—
524C2×C3×C4C23×D311yescharacteristic
525C2×C3×C4C23×D311yescharacteristic
526C2×C3×C4C23×D311yescharacteristic
527C2×C3×C4C23×D311yescharacteristic
528#67—316no—
529#67—316no—
530C2×Dic3—34no—
531C2×Dic3—34no—
532C2×Dic3—31no—
533C2×Dic3—31no—
534C2×Dic3—31no—
535C2×Dic3—31no—
536C2×Dic3—316no—
537C2×Dic3—316no—
538C2×Dic3—34no—
539C2×Dic3—34no—
540C2×Dic3—64no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—64no—
544C2×Dic3—128no—
545C2×Dic3C2×C4×D318yes—
546C2×Dic3C23×D314yes—
547C2×Dic3C23×D314yes—
548C2×Dic3C23×D314yes—
549D12—316no—
550D12—316no—
551D12C2×C4×D318yes—
552D12C2×C4×D318yes—
553C4×D3—316no—
554C4×D3—316no—
555C4×D3—34no—
556C4×D3—34no—
557C4×D3—34no—
558C4×D3—34no—
559C4×D3—34no—
560C4×D3—34no—
561C4×D3—34no—
562C4×D3—34no—
563C4×D3—48no—
564C4×D3—64no—
565C4×D3—64no—
566C4×D3—64no—
567C4×D3—64no—
568C4×D3—124no—
569C4×D3—124no—
570C4×D3—124no—
571C4×D3—124no—
572C4×D3—128no—
573C4×D3—128no—
574Dic6C2×C4×D318yes—
575Dic6C2×C4×D318yes—
576C2×C32—22no—
577C2×C32C24×C411yescharacteristic
578C2×C32#58512yes—
579C3⋊D3—22no—
580C3⋊D3—22no—
581C3×D3—28no—
582C24—32no—
583C24—91no—
584#41—916no—
585#41—916no—
586#41—916no—
587#41—916no—
588C2×Q8—32no—
589C2×Q8—32no—
590C2×Q8—38no—
591C2×D4—32no—
592C2×D4—32no—
593C2×D4—38no—
594C2×D4—94no—
595C2×D4—94no—
596C2×D4—916no—
597C22×C4—32no—
598C22×C4—38no—
599C22×C4—94no—
600C22×C4—94no—
601C22×C4—94no—
602C22×C4—916no—
603C22×C4—98no—
604C22×C4—91no—
605C22×C4—91no—
606C22×C4—91no—
607C22×C4—91no—
608C22×C4—91no—
609C22×C4—98no—
610C22×C4—94no—
611C22×C4C2×D3211yescharacteristic
612C4⋊C4—32no—
613C4⋊C4—38no—
614C4⋊C4—32no—
615C4⋊C4—94no—
616C4⋊C4—98no—
617C4⋊C4—94no—
618C4⋊C4—92no—
619C4⋊C4C2×D3212yes—
620C22⋊C4—32no—
621C22⋊C4—32no—
622C22⋊C4—38no—
623C22⋊C4—94no—
624C22⋊C4—98no—
625C22⋊C4—92no—
626C22⋊C4—94no—
627C22⋊C4C2×D3212yes—
628C42—32no—
629C42—38no—
630C42—32no—
631C42—94no—
632C42—98no—
633C42—94no—
634C42—92no—
635C42C2×D3212yes—
636C22×C3—22no—
637C22×C3—22no—
638C22×C3—22no—
639C22×C3—21no—
640C22×C3—38no—
641C22×C3—42no—
642C22×C3—68no—
643C22×C3—128no—
644C22×C3C22×C4×D312yes—
645C22×C3C22×C4×D312yes—
646C22×C3C24×D311yescharacteristic
647C22×C3C24×D311yescharacteristic
648C2×D3—28no—
649C2×D3—32no—
650C2×D3—32no—
651C2×D3—32no—
652C2×D3—32no—
653C2×D3—48no—
654C2×D3—62no—
655C2×D3—62no—
656C2×D3—64no—
657C2×D3—62no—
658C2×D3—62no—
659C2×D3—62no—
660C2×D3—62no—
661C2×D3—122no—
662C2×D3—124no—
663C2×D3—124no—
664C2×D3—128no—
665C2×D3C22×C4×D318yes—
666C3×C4—24no—
667C3×C4—24no—
668C3×C4—22no—
669C3×C4—22no—
670C3×C4—38no—
671C3×C4—44no—
672C3×C4—64no—
673C3×C4—64no—
674C3×C4C22×C4×D312yes—
675C3×C4C22×C4×D312yes—
676C3×C4C22×C4×D312yes—
677C3×C4C22×C4×D312yes—
678Dic3—24no—
679Dic3—24no—
680Dic3—32no—
681Dic3—32no—
682Dic3—32no—
683Dic3—32no—
684Dic3—62no—
685Dic3—62no—
686Dic3—64no—
687Dic3—64no—
688Dic3—124no—
689Dic3C22×C4×D318yes—
690C32#342811yescharacteristic, complemented, Sylow
691C23—34no—
692C23—38no—
693C23—91no—
694C23—91no—
695C23—94no—
696C23—124no—
697C23—362no—
698C23C22×D3211yescharacteristic
699Q8—38no—
700Q8—38no—
701D4—38no—
702D4—38no—
703D4—916no—
704D4—916no—
705C2×C4—38no—
706C2×C4—34no—
707C2×C4—34no—
708C2×C4—34no—
709C2×C4—916no—
710C2×C4—916no—
711C2×C4—94no—
712C2×C4—91no—
713C2×C4—91no—
714C2×C4—94no—
715C2×C4—94no—
716C2×C4—94no—
717C2×C4—94no—
718C2×C4—94no—
719C2×C4—128no—
720C2×C4—364no—
721C2×C4—364no—
722C2×C4—368no—
723C2×C4C4×D3214yes—
724C2×C4C22×D3214yes—
725C2×C4C22×D3211yescharacteristic
726C2×C4C22×D3211yescharacteristic
727C2×C3—22no—
728C2×C3—22no—
729C2×C3—21no—
730C2×C3—22no—
731C2×C3—42no—
732C2×C3—68no—
733C2×C3C23×C4×D311yescharacteristic
734C2×C3C23×C4×D311yescharacteristic
735C2×C3#596612yes—
736C2×C3#596812yes—
737D3—28no—
738D3—64no—
739D3—62no—
740D3—62no—
741D3—62no—
742D3—62no—
743D3—122no—
744C22—22no—
745C22—38no—
746C22—68no—
747C22—92no—
748C22—92no—
749C22—128no—
750C22—182no—
751C22—182no—
752C22—364no—
753C22C2×C4×D3212yes—
754C22C23×D3211yescharacteristic
755C4—24no—
756C4—38no—
757C4—64no—
758C4—64no—
759C4—92no—
760C4—92no—
761C4—184no—
762C4C2×C4×D3212yes—
763C4C2×C4×D3212yes—
764C3—21no—
765C3#8585611yescharacteristic, complemented
766C3#8587211yescharacteristic, complemented
767C2—22no—
768C2—68no—
769C2—182no—
770C2—182no—
771C2C22×C4×D3211yescharacteristic
772C2#1059669812yes—
subgroupG/H
center, FrattiniC22C23×D32
commutatorC2×C32C24×C4
FittingC32×#117C22
socle, cosocleC22×C32C25
prime radicalC22×#3796C2
hypercenter#117D32
hypocenterC32#3428
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
2. C3⋊D3×#117C2semidirect
3. C3×#5521C2semidirect
4. C3×#5516C2semidirect
5. #10594982C2semidirect
6. #10594969C2semidirect
7. #10594818C2semidirect
8. #10594361C2semidirect
9. #10594360C2semidirect
10. #10594182C2semidirect
11. D3×#877C2semidirect
12. #10593889C2semidirect
13. C4×#3796C2semidirect
21. C2×#3796C4semidirect
28. #64101C22semidirect
29. C4⋊C4×C3⋊D3C22semidirect
32. #64081C22semidirect
33. C42×C3⋊D3C22semidirect
36. C3×#893C22semidirect
37. C3×#887C22semidirect
40. C3×C4×D12C22semidirect
41. C3×C4×Dic6C22semidirect
46. #63904C22semidirect
47. C4×#626C22semidirect
48. #63900C22semidirect
49. #63898C22semidirect
50. Dic3×D12C22semidirect
51. C4×#624C22semidirect
52. #63881C22semidirect
53. #63880C22semidirect
54. #63878C22semidirect
55. #63877C22semidirect
56. D3×Dic3⋊C4C22semidirect
57. C4×D3×Dic3C22semidirect
58. #63874C22semidirect
59. #63849C22semidirect
60. #63843C22semidirect
61. Dic3×Dic6C22semidirect
78. #5521D3semidirect
86. #5516D3semidirect
93. C2×C4×C3⋊D3C2×C4semidirect
100. C2×C3×D12C2×C4semidirect
104. C2×C3×Dic6C2×C4semidirect
107. C2×#626C2×C4semidirect
111. C2×D3×Dic3C2×C4semidirect
115. #3796C2×C4semidirect
116. #3796C2×C4semidirect
117. #3796C2×C4semidirect
118. #3796C2×C4semidirect
194. #893C2×D3semidirect
208. #887C2×D3semidirect
230. C4×D12C2×D3semidirect
244. C4×Dic6C2×D3semidirect
332. C2×D12C4×D3semidirect
360. C2×Dic6C4×D3semidirect
690. C32#3428semidirect
765. C3#85856semidirect
766. C3#85872semidirect

Maximal subgroups

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

subgroupindex
C22×#37962
C3⋊D3×#1172
C3×#55212
C3×#55162
#105949822
#105949692
#105948182
#105943612
#105943602
#105941822
D3×#8772
#105938892
C4×#37962
#858723
#858563