Finite Group Databasebeta

← #11872313

Subgroups — #11872313

Order 1152.

840 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5535C211yesmaximal, characteristic, complemented
2C3×#5523C211yesmaximal, characteristic, complemented
3#10592699C211yesmaximal, characteristic, complemented
4#10591161C211yesmaximal, characteristic, complemented
5#10591161C211yesmaximal, characteristic, complemented
6#10591091C211yesmaximal, characteristic, complemented
7#10591089C211yesmaximal, characteristic, complemented
8#10590364C211yesmaximal, characteristic, complemented
9#10590358C211yesmaximal, characteristic, complemented
10C4×#3715C211yesmaximal, characteristic, complemented
11#10590347C211yesmaximal, characteristic, complemented
12#10590344C211yesmaximal, characteristic, complemented
13C4×#3713C211yesmaximal, characteristic, complemented
14#10590286C211yesmaximal, characteristic, complemented
15#10590270C211yesmaximal, characteristic, complemented
16#83434—31nomaximal
17#82568—31nomaximal
18C2×C3×#235C2211yescharacteristic
19C32×#117C2211yescharacteristic
20C3×#930C2211yescharacteristic
21C3×#930C2211yescharacteristic
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C3×#894—21no—
24C3×#894—21no—
25C3×#892—21no—
26C3×D3×C4⋊C4—21no—
27C3×#884—21no—
28C3×#884—21no—
29C3×#67⋊C4—21no—
30C3×#67⋊C4—21no—
31C3×#874C2211yescharacteristic
32C3×C4×D12C2211yescharacteristic
33C3×C4×D12C2211yescharacteristic
34C3×C4×D12C2211yescharacteristic
35C3×C4×D12C2211yescharacteristic
36C3×#870C2211yescharacteristic
37C3×C4×Dic6C2211yescharacteristic
38C3×C4×Dic6C2211yescharacteristic
39C2×#3715C2211yescharacteristic
40C2×#3715C2211yescharacteristic
41C2×#3713C2211yescharacteristic
42C2×#3713C2211yescharacteristic
43#63657C2211yescharacteristic
44#63657C2211yescharacteristic
45C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
46C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
47#63630C2211yescharacteristic
48C4×C3⋊(C3⋊C8)C2211yescharacteristic
49#63576C2211yescharacteristic
50#63576C2211yescharacteristic
51#63574C2211yescharacteristic
52#63574C2211yescharacteristic
53#63565C2211yescharacteristic
54#63565C2211yescharacteristic
55#63562C2211yescharacteristic
56#63562C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59#63562C2211yescharacteristic
60#63562C2211yescharacteristic
61C3×#540—31no—
62C3×#520—31no—
63#5535D311yescharacteristic, complemented
64#5523D311yescharacteristic, complemented
65#5238—31no—
66#5238—31no—
67#5075—31no—
68#5072—31no—
69#5066—31no—
70#5063—31no—
71#5037—31no—
72#5037—31no—
73#5034—31no—
74#5033—31no—
75#5027—31no—
76#5026—31no—
77C4×#215—31no—
78#5022—31no—
79#5018—31no—
80C4×#214—31no—
81#5015—31no—
82#5014—31no—
83#5014—31no—
84C4×#213—31no—
85C4×#213—31no—
86#5009—31no—
87#5000—31no—
88#5000—31no—
89#5000—61no—
90#4968—31no—
91#4967—31no—
92C22×C32×C4C2311yescharacteristic
93C2×C3×#67—21no—
94C2×C3×#67—21no—
95C2×C3×#67—21no—
96C22×C3×Dic3—21no—
97C3×#235—22no—
98C3×#235—22no—
99C2×C3×D12—21no—
100C2×C3×D12—21no—
101C2×C3×D12C2311yescharacteristic
102C2×C3×D12C2311yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3—21no—
109C2×C3×Dic6C2311yescharacteristic
110C32×C4⋊C4D411yescharacteristic
111C32×C4⋊C4D411yescharacteristic
112C32×C22⋊C4D411yescharacteristic
113C32×C22⋊C4D411yescharacteristic
114C32×C42C2311yescharacteristic
115C32×C42C2311yescharacteristic
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4—21no—
134C3×Dic3⋊C4—21no—
135C3×C4×Dic3—21no—
136C3×C4×Dic3—21no—
137#3715—22no—
138#3715—22no—
139#3713—22no—
140#3713—22no—
141#3119—91noSylow
142C2×C3×#41—31no—
143C2×#235C2×D311yescharacteristic
144C3×#127—31no—
145C3×#125—31no—
146C3×#123—61no—
147C3×#123—61no—
148C3×#121—31no—
149C3×#121—31no—
150C3×#121—61no—
151C3×#121—61no—
152C3×C4×Q8—31no—
153C3×C4×Q8—31no—
154C3×C4×D4—31no—
155C3×C4×D4—31no—
156C3×C4×D4—31no—
157C3×C4×D4—31no—
158C3×C4×D4—61no—
159C3×C4×D4—61no—
160C3×#117—21no—
161C3×#117—61no—
162C3×#117C2×D311yescharacteristic
163C3×#117C2×D311yescharacteristic
164C2×C3×C4⋊C4—31no—
165C2×C3×C4⋊C4—61no—
166C2×#215—31no—
167C2×#215—31no—
168C2×#214—31no—
169C2×#214—31no—
170C2×#213—31no—
171C2×#213—31no—
172C2×#213—31no—
173C2×#213—31no—
174#930C2×D311yescharacteristic
175#930C2×D311yescharacteristic
176C2×C4⋊Dic3C2×D311yescharacteristic
177#894—21no—
178#894—21no—
179#892—21no—
180D3×C4⋊C4—21no—
181#884—21no—
182#884—21no—
183#67⋊C4—21no—
184#67⋊C4—21no—
185#874C2×D311yescharacteristic
186C4×D12C2×D311yescharacteristic
187C4×D12C2×D311yescharacteristic
188C4×D12C2×D311yescharacteristic
189C4×D12C2×D311yescharacteristic
190#870C2×D311yescharacteristic
191C4×Dic6C2×D311yescharacteristic
192C4×Dic6C2×D311yescharacteristic
193#835—31no—
194#835—31no—
195#832—31no—
196#832—31no—
197#832—31no—
198#832—31no—
199#832—31no—
200#832—31no—
201#830—31no—
202#830—31no—
203#830—31no—
204#830—31no—
205#830—61no—
206#830—61no—
207#810—31no—
208#810—31no—
209#809—31no—
210#809—31no—
211#809—31no—
212#809—31no—
213#809—31no—
214#809—31no—
215#808—31no—
216#808—31no—
217#808—31no—
218#808—31no—
219#807—31no—
220#807—31no—
221#807—31no—
222#807—31no—
223C4⋊(C3⋊C8)—31no—
224C4⋊(C3⋊C8)—31no—
225C4⋊(C3⋊C8)—31no—
226C4⋊(C3⋊C8)—31no—
227C4⋊(C3⋊C8)—61no—
228C4⋊(C3⋊C8)—61no—
229#803—31no—
230#803—31no—
231#803—61no—
232C4×C3⋊C8—31no—
233C4×C3⋊C8—31no—
234C4×C3⋊C8—61no—
235C23×C32C2×D411yescharacteristic
236C22×C3×D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3—21no—
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4C2×D411yescharacteristic
242C2×C32×C4C2×D411yescharacteristic
243C2×C32×C4C2×D411yescharacteristic
244C2×C32×C4C2×D411yescharacteristic
245C2×C32×C4C2×D411yescharacteristic
246C2×C32×C4C2411yescharacteristic
247C3×#67—24no—
248C3×#67—81no—
249C3×#67—81no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—81no—
256C3×D12—21no—
257C3×D12—21no—
258C3×D12—21no—
259C3×D12—21no—
260C3×D12—21no—
261C3×D12—81no—
262C3×D12—81no—
263C3×D12#4112yes—
264C3×C4×D3—24no—
265C3×C4×D3—81no—
266C3×C4×D3—81no—
267C3×C4×D3—81no—
268C3×C4×D3—81no—
269C3×Dic6—21no—
270C3×Dic6#4112yes—
271C3⋊(C3⋊C8)—21no—
272C3⋊(C3⋊C8)—21no—
273C3⋊(C3⋊C8)—21no—
274C3⋊(C3⋊C8)—21no—
275#540—31no—
276#520—31no—
277#481—91no—
278#480—91no—
279#479—91no—
280#478—91no—
281#460—91no—
282#459—91no—
283#449—91no—
284#449—91no—
285#442—91no—
286#440—91no—
287C4×SD16—91no—
288C4×D8—91no—
289#433—91no—
290C3×#41—62no—
291C3×#41—62no—
292C2×C3×Q8—31no—
293C2×C3×D4—31no—
294C2×C3×D4—31no—
295C2×C3×D4—31no—
296C2×C3×D4—61no—
297C2×C3×D4—61no—
298C2×C3×D4—61no—
299C2×C3×D4—61no—
300C2×C3×D4—61no—
301C22×C3×C4—21no—
302C22×C3×C4—61no—
303C22×C3×C4—61no—
304C22×C3×C4—61no—
305C22×C3×C4—61no—
306C22×C3×C4—61no—
307C22×C3×C4—61no—
308C22×C3×C4C22×D311yescharacteristic
309C22×C3×C4C22×D311yescharacteristic
310C2×#67—21no—
311C2×#67—21no—
312C2×#67—21no—
313C22×Dic3—21no—
314#235—22no—
315#235—22no—
316C2×D12—21no—
317C2×D12—21no—
318C2×D12C22×D311yescharacteristic
319C2×D12C22×D311yescharacteristic
320C2×D12C22×D311yescharacteristic
321C2×C4×D3—21no—
322C2×C4×D3—21no—
323C2×C4×D3—21no—
324C2×C4×D3—21no—
325C2×C4×D3—21no—
326C2×Dic6C22×D311yescharacteristic
327C3×C4⋊C4—21no—
328C3×C4⋊C4—21no—
329C3×C4⋊C4—31no—
330C3×C4⋊C4—31no—
331C3×C4⋊C4—31no—
332C3×C4⋊C4—31no—
333C3×C4⋊C4—61no—
334C3×C4⋊C4—61no—
335C3×C4⋊C4—61no—
336C3×C4⋊C4—61no—
337C3×C4⋊C4—61no—
338C3×C4⋊C4#6711yescharacteristic
339C3×C4⋊C4#6711yescharacteristic
340C3×C4⋊C4#6711yescharacteristic
341C3×C4⋊C4#6711yescharacteristic
342C3×C22⋊C4—21no—
343C3×C22⋊C4—21no—
344C3×C22⋊C4—61no—
345C3×C22⋊C4—61no—
346C3×C22⋊C4—61no—
347C3×C22⋊C4—61no—
348C3×C22⋊C4—61no—
349C3×C22⋊C4—61no—
350C3×C22⋊C4#6711yescharacteristic
351C3×C22⋊C4#6711yescharacteristic
352C3×C22⋊C4#6711yescharacteristic
353C3×C22⋊C4#6711yescharacteristic
354C3×C42—21no—
355C3×C42—21no—
356C3×C42—61no—
357C3×C42—61no—
358C3×C42C22×D311yescharacteristic
359C3×C42C22×D311yescharacteristic
360C3×C42C22×D311yescharacteristic
361C3×C42C22×D311yescharacteristic
362#215—62no—
363#215—62no—
364#214—62no—
365#214—62no—
366#213—62no—
367#213—62no—
368#213—62no—
369#213—62no—
370(C2×D3)⋊C4—21no—
371(C2×D3)⋊C4—21no—
372(C2×D3)⋊C4—21no—
373(C2×D3)⋊C4—21no—
374(C2×D3)⋊C4—21no—
375(C2×D3)⋊C4—21no—
376C4⋊Dic3—21no—
377C4⋊Dic3C22×D311yescharacteristic
378C4⋊Dic3C22×D311yescharacteristic
379C4⋊Dic3C22×D311yescharacteristic
380C4⋊Dic3C22×D311yescharacteristic
381Dic3⋊C4—21no—
382Dic3⋊C4—21no—
383Dic3⋊C4—21no—
384Dic3⋊C4—21no—
385C4×Dic3—21no—
386C4×Dic3—21no—
387C2×C3⋊C8—31no—
388C2×C3⋊C8—31no—
389C2×C3⋊C8—31no—
390C2×C3⋊C8—31no—
391C2×C3⋊C8—31no—
392C2×C3⋊C8—31no—
393C2×C3⋊C8—31no—
394C2×C3⋊C8—31no—
395C2×C3⋊C8—61no—
396C2×C3⋊C8—61no—
397C2×C3⋊C8—61no—
398C2×C3⋊C8—61no—
399C22×C32—21no—
400C22×C32—21no—
401C22×C32—21no—
402C22×C32C22×D411yescharacteristic
403C2×C3×D3—22no—
404C2×C3×D3—41no—
405C2×C3×D3—41no—
406C2×C3×D3—41no—
407C2×C3×D3—41no—
408C2×C3×D3—41no—
409C2×C3×D3—41no—
410C2×C3×D3—41no—
411C2×C3×D3—41no—
412C32×C4—21no—
413C32×C4—21no—
414C32×C4—21no—
415C32×C4—21no—
416C32×C4—21no—
417C32×C4C2×#4111yescharacteristic
418C32×C4C2×#4111yescharacteristic
419C3×Dic3—22no—
420C3×Dic3—41no—
421C3×Dic3—41no—
422C3×Dic3—41no—
423C3×Dic3—41no—
424C2×#41—31no—
425C2×SD16—91no—
426C2×SD16—91no—
427C2×D8—91no—
428C2×D8—91no—
429#127—31no—
430#125—31no—
431#123—61no—
432#123—61no—
433#121—31no—
434#121—31no—
435#121—61no—
436#121—61no—
437C4×Q8—31no—
438C4×Q8—31no—
439C4×D4—31no—
440C4×D4—31no—
441C4×D4—31no—
442C4×D4—31no—
443C4×D4—61no—
444C4×D4—61no—
445#117—61no—
446#117D3211yescharacteristic
447C2×C4⋊C4—31no—
448C2×C4⋊C4—61no—
449#107—91no—
450#107—91no—
451#106—91no—
452#106—91no—
453C4⋊C8—91no—
454C4⋊C8—91no—
455#103—91no—
456#103—91no—
457#102—91no—
458#102—91no—
459#102—91no—
460#102—91no—
461#102—91no—
462#102—91no—
463C22⋊C8—91no—
464C22⋊C8—91no—
465#97—91no—
466C4×C8—91no—
467C23×C3—21no—
468C23×C3—61no—
469C23×C3—61no—
470C23×C3—61no—
471C23×C3C2×#6711yescharacteristic
472C23×C3C2×#6711yescharacteristic
473C22×D3—21no—
474C22×D3—21no—
475C22×D3—21no—
476C3×Q8—32no—
477C3×Q8—61no—
478C3×D4—32no—
479C3×D4—64no—
480C3×D4—61no—
481C3×D4—61no—
482C3×D4—61no—
483C3×D4—61no—
484C3×D4—61no—
485C3×D4—241no—
486C3×D4—241no—
487C3×D4—241no—
488C3×D4—241no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—41no—
500C2×C3×C4—41no—
501C2×C3×C4—64no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—241no—
508C2×C3×C4—241no—
509C2×C3×C4—241no—
510C2×C3×C4—241no—
511C2×C3×C4—241no—
512C2×C3×C4C2×#6711yescharacteristic
513C2×C3×C4C2×#6711yescharacteristic
514C2×C3×C4C2×#6711yescharacteristic
515C2×C3×C4C2×#6711yescharacteristic
516C2×C3×C4C2×#6711yescharacteristic
517C2×C3×C4C2×#6711yescharacteristic
518C2×C3×C4C2×#6711yescharacteristic
519C2×C3×C4C2×#6711yescharacteristic
520C2×C3×C4C2×#6711yescharacteristic
521C2×C3×C4C2×#6711yescharacteristic
522C2×C3×C4C23×D311yescharacteristic
523C2×C3×C4C23×D311yescharacteristic
524#67—24no—
525#67—81no—
526#67—81no—
527C2×Dic3—21no—
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—81no—
533D12—21no—
534D12—21no—
535D12—21no—
536D12—21no—
537D12—21no—
538D12—81no—
539D12—81no—
540D12#23512yes—
541C4×D3—24no—
542C4×D3—81no—
543C4×D3—81no—
544C4×D3—81no—
545C4×D3—81no—
546Dic6—21no—
547Dic6#23512yes—
548C3⋊C8—61no—
549C3⋊C8—61no—
550C3⋊C8—61no—
551C3⋊C8—61no—
552C3⋊C8—61no—
553C3⋊C8—61no—
554C3⋊C8—61no—
555C3⋊C8—61no—
556C3⋊C8—121no—
557C3⋊C8—121no—
558C3⋊C8—121no—
559C3⋊C8—121no—
560C2×C32—41no—
561C2×C32#52511yescharacteristic
562C2×C32#57611yescharacteristic
563C2×C32#57711yescharacteristic
564C3×D3—42no—
565C3×D3—81no—
566C3×D3—81no—
567#41—62no—
568#41—62no—
569C2×Q8—31no—
570C2×D4—31no—
571C2×D4—31no—
572C2×D4—31no—
573C2×D4—61no—
574C2×D4—61no—
575C2×D4—61no—
576C2×D4—61no—
577C2×D4—61no—
578C22×C4—61no—
579C22×C4—61no—
580C22×C4—61no—
581C22×C4—61no—
582C22×C4—61no—
583C22×C4—61no—
584C22×C4C2×D3211yescharacteristic
585SD16—182no—
586SD16—182no—
587D8—182no—
588D8—182no—
589C2×C8—91no—
590C2×C8—91no—
591C2×C8—91no—
592C2×C8—91no—
593C4⋊C4—31no—
594C4⋊C4—31no—
595C4⋊C4—31no—
596C4⋊C4—31no—
597C4⋊C4—61no—
598C4⋊C4—61no—
599C4⋊C4—61no—
600C4⋊C4—61no—
601C4⋊C4—61no—
602C4⋊C4#62511yescharacteristic
603C4⋊C4#62511yescharacteristic
604C22⋊C4—61no—
605C22⋊C4—61no—
606C22⋊C4—61no—
607C22⋊C4—61no—
608C22⋊C4—61no—
609C22⋊C4—61no—
610C22⋊C4#62511yescharacteristic
611C22⋊C4#62511yescharacteristic
612C42—61no—
613C42—61no—
614C42C2×D3211yescharacteristic
615C42C2×D3211yescharacteristic
616C22×C3—21no—
617C22×C3—21no—
618C22×C3—21no—
619C22×C3—21no—
620C22×C3—21no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—41no—
624C22×C3—41no—
625C22×C3—41no—
626C22×C3—62no—
627C22×C3—121no—
628C22×C3—121no—
629C22×C3—121no—
630C22×C3—121no—
631C22×C3—121no—
632C22×C3—121no—
633C22×C3—121no—
634C22×C3—121no—
635C22×C3C22×#6711yescharacteristic
636C22×C3C22×#6711yescharacteristic
637C2×D3—22no—
638C2×D3—41no—
639C2×D3—41no—
640C2×D3—41no—
641C2×D3—41no—
642C2×D3—41no—
643C2×D3—41no—
644C2×D3—41no—
645C2×D3—41no—
646C3×C4—21no—
647C3×C4—21no—
648C3×C4—21no—
649C3×C4—21no—
650C3×C4—21no—
651C3×C4—21no—
652C3×C4—21no—
653C3×C4—21no—
654C3×C4—21no—
655C3×C4—21no—
656C3×C4—21no—
657C3×C4—21no—
658C3×C4—41no—
659C3×C4—41no—
660C3×C4—41no—
661C3×C4—41no—
662C3×C4—41no—
663C3×C4—62no—
664C3×C4—121no—
665C3×C4—121no—
666C3×C4—121no—
667C3×C4—121no—
668C3×C4C2×#23511yescharacteristic
669C3×C4C2×#23511yescharacteristic
670C3×C4D3×#4111yescharacteristic
671C3×C4D3×#4111yescharacteristic
672Dic3—22no—
673Dic3—41no—
674Dic3—41no—
675Dic3—41no—
676Dic3—41no—
677C32#311911yescharacteristic, complemented, Sylow
678C23—61no—
679C23—61no—
680C23—61no—
681C23C2×#62511yescharacteristic
682Q8—32no—
683Q8—61no—
684D4—32no—
685D4—64no—
686D4—61no—
687D4—61no—
688D4—61no—
689D4—61no—
690D4—61no—
691D4—241no—
692D4—241no—
693D4—241no—
694D4—241no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—64no—
698C2×C4—61no—
699C2×C4—61no—
700C2×C4—61no—
701C2×C4—61no—
702C2×C4—61no—
703C2×C4—241no—
704C2×C4—241no—
705C2×C4—241no—
706C2×C4—241no—
707C2×C4—241no—
708C2×C4C2×#62511yescharacteristic
709C2×C4C2×#62511yescharacteristic
710C2×C4C2×#62511yescharacteristic
711C2×C4C2×#62511yescharacteristic
712C2×C4C2×#62511yescharacteristic
713C2×C4C22×D3211yescharacteristic
714C8—181no—
715C8—181no—
716C8—181no—
717C8—181no—
718C2×C3—21no—
719C2×C3—21no—
720C2×C3—21no—
721C2×C3—41no—
722C2×C3—41no—
723C2×C3—81no—
724C2×C3—122no—
725C2×C3—241no—
726C2×C3—241no—
727C2×C3#579111yescharacteristic
728C2×C3#582811yescharacteristic
729C2×C3#583511yescharacteristic
730C2×C3#583511yescharacteristic
731C2×C3#583611yescharacteristic
732C2×C3#583711yescharacteristic
733D3—42no—
734D3—81no—
735D3—81no—
736C22—21no—
737C22—21no—
738C22—21no—
739C22—62no—
740C22—121no—
741C22—121no—
742C22—121no—
743C22—121no—
744C22—121no—
745C22—121no—
746C22—121no—
747C22—121no—
748C22C22×#62511yescharacteristic
749C4—21no—
750C4—21no—
751C4—21no—
752C4—21no—
753C4—21no—
754C4—62no—
755C4—121no—
756C4—121no—
757C4—121no—
758C4—121no—
759C4D3×#23511yescharacteristic
760C4D3×#23511yescharacteristic
761C3—21no—
762C3#8256811yescharacteristic, complemented
763C3#8343411yescharacteristic, complemented
764C2—41no—
765C2—122no—
766C2—241no—
767C2—241no—
768C2#1059502211yescharacteristic
769C2#1059544411yescharacteristic
770C2#1059544611yescharacteristic
subgroupG/H
centerC22C22×#625
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
hypercenter#117D32
hypocenterC32#3119
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C3×#5535C2semidirect
2. C3×#5523C2semidirect
3. #10592699C2semidirect
4. #10591161C2semidirect
5. #10591161C2semidirect
6. #10591091C2semidirect
7. #10591089C2semidirect
8. #10590364C2semidirect
9. #10590358C2semidirect
10. C4×#3715C2semidirect
11. #10590347C2semidirect
12. #10590344C2semidirect
13. C4×#3713C2semidirect
14. #10590286C2semidirect
15. #10590270C2semidirect
63. #5535D3semidirect
64. #5523D3semidirect
677. C32#3119semidirect
762. C3#82568semidirect
763. C3#83434semidirect

Maximal subgroups

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

subgroupindex
C3×#55352
C3×#55232
#105926992
#105911612
#105910912
#105910892
#105903642
#105903582
C4×#37152
#105903472
#105903442
C4×#37132
#105902862
#105902702
#834343
#825683