Finite Group Databasebeta

← #10812199

Subgroups — #10812199

Order 768.

1060 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
1#84027C211yesmaximal, characteristic
2C2×#5207C211yesmaximal, characteristic
3C2×#4720C211yesmaximal, characteristic, complemented
4C3×#1779C211yesmaximal, characteristic
5#69951C211yesmaximal, characteristic, complemented
6#69951C211yesmaximal, characteristic, complemented
7#69949C211yesmaximal, characteristic, complemented
8#69949C211yesmaximal, characteristic, complemented
9#69915C211yesmaximal, characteristic, complemented
10#69914C211yesmaximal, characteristic, complemented
11#69913C211yesmaximal, characteristic, complemented
12#69912C211yesmaximal, characteristic, complemented
13#69911C211yesmaximal, characteristic, complemented
14#69909C211yesmaximal, characteristic, complemented
15#69907C211yesmaximal, characteristic, complemented
16#22559—31nomaximal, Sylow
17C24×C3×C4C2211yescharacteristic
18C2×#926C2211yescharacteristic
19C2×#926C2211yescharacteristic
20C22×#208C2211yescharacteristic
21C22×#208C2211yescharacteristic
22C2×C3×C22⋊C8C2211yescharacteristic
23C2×C3×C22⋊C8C2211yescharacteristic
24C2×C3×C22⋊C8C2211yescharacteristic
25C2×C3×C22⋊C8C2211yescharacteristic
26C2×C3×C22⋊C8C2211yescharacteristic
27C2×C3×C22⋊C8C2211yescharacteristic
28#5247C411yescharacteristic
29#5247C411yescharacteristic
30#5212C411yescharacteristic
31#5212C411yescharacteristic
32#5212C411yescharacteristic
33#5212C411yescharacteristic
34#5211C411yescharacteristic
35#5211C411yescharacteristic
36C4×#217C2211yescharacteristic
37C4×#217C2211yescharacteristic
38C4×#217C2211yescharacteristic
39C4×#217C2211yescharacteristic
40#5207—24no—
41C2×#830C2211yescharacteristic
42C2×#830C2211yescharacteristic
43C2×#830C2211yescharacteristic
44C2×#830C2211yescharacteristic
45C2×#815C2211yescharacteristic, complemented
46C2×#815C2211yescharacteristic, complemented
47C2×Dic3⋊C8C2211yescharacteristic, complemented
48C2×Dic3⋊C8C2211yescharacteristic, complemented
49C2×Dic3⋊C8C2211yescharacteristic, complemented
50C2×Dic3⋊C8C2211yescharacteristic, complemented
51C2×C8×Dic3C2211yescharacteristic, complemented
52C2×C8×Dic3C2211yescharacteristic, complemented
53#4720—24no—
54#4550C2211yescharacteristic, complemented
55#4550C2211yescharacteristic, complemented
56#4550C2211yescharacteristic, complemented
57#4550C2211yescharacteristic, complemented
58#4550C2211yescharacteristic, complemented
59#4550C2211yescharacteristic, complemented
60#4550C2211yescharacteristic, complemented
61#4550C2211yescharacteristic, complemented
62C2×#433—31no—
63C2×#407—31no—
64#2280—31no—
65#1924—31no—
66#1924—31no—
67#1923—31no—
68#1923—31no—
69#1851—31no—
70#1851—31no—
71#1818—31no—
72#1798—31no—
73#1779D311yescharacteristic
74#1753—31no—
75#1753—31no—
76#1750—31no—
77C25×C3C2×C411yescharacteristic
78C23×C3×C4—22no—
79C23×C3×C4—22no—
80C23×C3×C4—22no—
81C23×C3×C4—22no—
82C23×C3×C4—41no—
83C23×C3×C4—41no—
84C23×C3×C4C2×C411yescharacteristic
85C23×C3×C4C2×C411yescharacteristic
86C23×C3×C4C2×C411yescharacteristic
87C23×C3×C4C2311yescharacteristic
88C23×C3×C4C2311yescharacteristic
89C23×C3×C4C2311yescharacteristic
90C22×C3×C8C2311yescharacteristic
91C22×C3×C8C2311yescharacteristic
92C22×C3×C8C2311yescharacteristic
93C22×C3×C8C2311yescharacteristic
94C2×#217C2×C411yescharacteristic
95C2×#217C2×C411yescharacteristic
96C2×#217C2×C411yescharacteristic
97C2×#217C2×C411yescharacteristic
98C2×#217C2×C411yescharacteristic
99C2×#217C2×C411yescharacteristic
100C2×#217C2×C411yescharacteristic
101C2×#217C2×C411yescharacteristic
102C2×#217C2×C411yescharacteristic
103C2×#217C2×C411yescharacteristic
104C2×#217C2×C411yescharacteristic
105C2×#217C2×C411yescharacteristic
106#926—22no—
107#926—22no—
108#926—41no—
109#926—41no—
110C2×C4⋊Dic3C2×C411yescharacteristic
111C2×C4⋊Dic3C2×C411yescharacteristic
112C2×C4⋊Dic3C2×C411yescharacteristic
113C2×C4⋊Dic3C2×C411yescharacteristic
114C2×C4×Dic3C2311yescharacteristic
115C2×C4×Dic3C2311yescharacteristic
116C2×C4×Dic3C2311yescharacteristic
117C2×C4×Dic3C2311yescharacteristic
118C2×#208—22no—
119C2×#208—22no—
120C2×#208—22no—
121C2×#208—22no—
122C2×#208—41no—
123C2×#208—41no—
124C22×C3⋊C8C2311yescharacteristic
125C22×C3⋊C8C2311yescharacteristic
126C22×C3⋊C8C2311yescharacteristic
127C22×C3⋊C8C2311yescharacteristic
128C3×C22⋊C8—22no—
129C3×C22⋊C8—22no—
130C3×C22⋊C8—22no—
131C3×C22⋊C8—22no—
132C3×C22⋊C8—41no—
133C3×C22⋊C8—41no—
134C3⋊#95C2×C411yescharacteristic
135C3⋊#95C2×C411yescharacteristic
136C3⋊#95C2×C411yescharacteristic
137C3⋊#95C2×C411yescharacteristic
138C3⋊#95C2×C411yescharacteristic
139C3⋊#95C2×C411yescharacteristic
140C3⋊#95C2×C411yescharacteristic
141C3⋊#95C2×C411yescharacteristic
142#830—22no—
143#830—22no—
144#830—22no—
145#830D414yes—
146#815—22no—
147#815—41no—
148Dic3⋊C8—22no—
149Dic3⋊C8—22no—
150Dic3⋊C8—41no—
151Dic3⋊C8—41no—
152C8×Dic3—22no—
153C8×Dic3—41no—
154C24×C4C2×D311yescharacteristic
155C22×M16—31no—
156C22×M16—31no—
157C2×#117—31no—
158C2×#117—31no—
159#433—64no—
160C2×C4⋊C8—31no—
161C2×C4⋊C8—31no—
162C2×C4⋊C8—31no—
163C2×C4⋊C8—31no—
164#407—64no—
165C2×C22⋊C8—31no—
166C2×C22⋊C8—31no—
167C2×C22⋊C8—31no—
168C2×C22⋊C8—31no—
169C2×C22⋊C8C2×D311yescharacteristic
170C2×C22⋊C8C2×D311yescharacteristic
171C2×C22⋊C8C2×D311yescharacteristic
172C2×C22⋊C8C2×D311yescharacteristic
173C2×C22⋊C8C2×D311yescharacteristic
174C2×C22⋊C8C2×D311yescharacteristic
175C2×#97—31no—
176C2×#97—31no—
177C2×C4×C8—31no—
178C2×C4×C8—31no—
179#381—31no—
180#381—31no—
181#380—31no—
182#380—31no—
183#380—31no—
184#380—31no—
185#379—31no—
186#379—31no—
187C4×C22⋊C4—31no—
188C4×C22⋊C4—31no—
189C4×C22⋊C4—31no—
190C4×C22⋊C4—31no—
191#336—31no—
192#336—31no—
193#336—31no—
194#336—31no—
195#336—31no—
196#336—31no—
197#336—31no—
198#336—31no—
199C24×C3—22no—
200C24×C3—22no—
201C24×C3—22no—
202C24×C3—41no—
203C24×C3—41no—
204C24×C3—41no—
205C24×C3—41no—
206C24×C3C22×C411yescharacteristic
207C24×C3C22×C411yescharacteristic
208C24×C3C22×C411yescharacteristic
209C22×C3×C4—21no—
210C22×C3×C4—21no—
211C22×C3×C4—21no—
212C22×C3×C4—21no—
213C22×C3×C4—21no—
214C22×C3×C4—21no—
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4—22no—
218C22×C3×C4—22no—
219C22×C3×C4—22no—
220C22×C3×C4—22no—
221C22×C3×C4—22no—
222C22×C3×C4—22no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—41no—
230C22×C3×C4—41no—
231C22×C3×C4—41no—
232C22×C3×C4—44no—
233C22×C3×C4—44no—
234C22×C3×C4—44no—
235C22×C3×C4—44no—
236C22×C3×C4C22×C411yescharacteristic
237C22×C3×C4C22×C411yescharacteristic
238C22×C3×C4C22×C411yescharacteristic
239C22×C3×C4C2×D412yes—
240C22×C3×C4#4112yes—
241C22×C3×C4#4112yes—
242C22×C3×C4#4112yes—
243C22×C3×C4C2411yescharacteristic
244C22×Dic3C22×C411yescharacteristic
245C22×Dic3C22×C411yescharacteristic
246C22×Dic3C22×C411yescharacteristic
247C22×Dic3C22×C411yescharacteristic
248C22×Dic3C22×C411yescharacteristic
249C22×Dic3C22×C411yescharacteristic
250C22×Dic3C22×C411yescharacteristic
251C22×Dic3C22×C411yescharacteristic
252C2×C3×C8—21no—
253C2×C3×C8—21no—
254C2×C3×C8—21no—
255C2×C3×C8—21no—
256C2×C3×C8—21no—
257C2×C3×C8—21no—
258C2×C3×C8—21no—
259C2×C3×C8—21no—
260C2×C3×C8—21no—
261C2×C3×C8—21no—
262C2×C3×C8—21no—
263C2×C3×C8—21no—
264#217—22no—
265#217—22no—
266#217—22no—
267#217—22no—
268#217—41no—
269#217—41no—
270#217—41no—
271#217—41no—
272#217—41no—
273#217—41no—
274#217—41no—
275#217—41no—
276C4⋊Dic3—22no—
277C4⋊Dic3—22no—
278C4⋊Dic3—41no—
279C4⋊Dic3—41no—
280C4×Dic3—21no—
281C4×Dic3—21no—
282C4×Dic3—21no—
283C4×Dic3—21no—
284C4×Dic3—21no—
285C4×Dic3—21no—
286C4×Dic3—21no—
287C4×Dic3—21no—
288#208—44no—
289#208—44no—
290C2×C3⋊C8—21no—
291C2×C3⋊C8—21no—
292C2×C3⋊C8—21no—
293C2×C3⋊C8—21no—
294C2×C3⋊C8—21no—
295C2×C3⋊C8—21no—
296C2×C3⋊C8—21no—
297C2×C3⋊C8—21no—
298C2×C3⋊C8—21no—
299C2×C3⋊C8—21no—
300C2×C3⋊C8C2×D412yes—
301C2×C3⋊C8C2×D412yes—
302C25C4×D311yescharacteristic
303C23×C4—22no—
304C23×C4—22no—
305C23×C4—22no—
306C23×C4—22no—
307C23×C4—41no—
308C23×C4—41no—
309C23×C4C4×D311yescharacteristic
310C23×C4C4×D311yescharacteristic
311C23×C4C4×D311yescharacteristic
312C23×C4C22×D311yescharacteristic
313C23×C4C22×D311yescharacteristic
314C23×C4C22×D311yescharacteristic
315C2×M16—62no—
316C2×M16—62no—
317C2×M16—62no—
318C2×M16—62no—
319C2×M16—121no—
320C2×M16—121no—
321C22×C8—31no—
322C22×C8—31no—
323C22×C8—31no—
324C22×C8—31no—
325C22×C8C22×D311yescharacteristic
326C22×C8C22×D311yescharacteristic
327C22×C8C22×D311yescharacteristic
328C22×C8C22×D311yescharacteristic
329#117—62no—
330#117—62no—
331#117—121no—
332#117—121no—
333C2×C4⋊C4—31no—
334C2×C4⋊C4—31no—
335C2×C4⋊C4—31no—
336C2×C4⋊C4—31no—
337C2×C22⋊C4—31no—
338C2×C22⋊C4—31no—
339C2×C22⋊C4—31no—
340C2×C22⋊C4—31no—
341C2×C22⋊C4—31no—
342C2×C22⋊C4—31no—
343C2×C22⋊C4—31no—
344C2×C22⋊C4—31no—
345C2×C22⋊C4—31no—
346C2×C22⋊C4—31no—
347C2×C22⋊C4—31no—
348C2×C22⋊C4—31no—
349C2×C42—31no—
350C2×C42—31no—
351C2×C42—31no—
352C2×C42—31no—
353C4⋊C8—62no—
354C4⋊C8—62no—
355C4⋊C8—121no—
356C4⋊C8—121no—
357C22⋊C8—22no—
358C22⋊C8—22no—
359C22⋊C8—22no—
360C22⋊C8—22no—
361C22⋊C8—34no—
362C22⋊C8—41no—
363C22⋊C8—41no—
364C22⋊C8—62no—
365C22⋊C8—62no—
366C22⋊C8—62no—
367#97—62no—
368#97—121no—
369C4×C8—62no—
370C4×C8—121no—
371#95—31no—
372#95—31no—
373#95—31no—
374#95—31no—
375#95—31no—
376#95—31no—
377#95—31no—
378#95—31no—
379C23×C3—21no—
380C23×C3—21no—
381C23×C3—21no—
382C23×C3—21no—
383C23×C3—21no—
384C23×C3—21no—
385C23×C3—21no—
386C23×C3—21no—
387C23×C3—21no—
388C23×C3—21no—
389C23×C3—21no—
390C23×C3—21no—
391C23×C3—21no—
392C23×C3—21no—
393C23×C3—21no—
394C23×C3—21no—
395C23×C3—21no—
396C23×C3—21no—
397C23×C3—44no—
398C23×C3—44no—
399C23×C3—44no—
400C23×C3—44no—
401C23×C3—44no—
402C23×C3—44no—
403C23×C3—44no—
404C23×C3#11712yes—
405C23×C3C4×D412yes—
406C23×C3#13112yes—
407C23×C3C23×C411yescharacteristic
408C2×C3×C4—21no—
409C2×C3×C4—21no—
410C2×C3×C4—21no—
411C2×C3×C4—21no—
412C2×C3×C4—22no—
413C2×C3×C4—22no—
414C2×C3×C4—22no—
415C2×C3×C4—22no—
416C2×C3×C4—22no—
417C2×C3×C4—22no—
418C2×C3×C4—22no—
419C2×C3×C4—22no—
420C2×C3×C4—21no—
421C2×C3×C4—21no—
422C2×C3×C4—21no—
423C2×C3×C4—44no—
424C2×C3×C4—44no—
425C2×C3×C4—44no—
426C2×C3×C4—41no—
427C2×C3×C4—41no—
428C2×C3×C4—41no—
429C2×C3×C4—41no—
430C2×C3×C4#11712yes—
431C2×C3×C4C4×D412yes—
432C2×C3×C4C22×D411yescharacteristic
433C2×C3×C4C2×#4111yescharacteristic
434C2×C3×C4C2×#4111yescharacteristic
435C2×C3×C4C2×#4111yescharacteristic
436C2×C3×C4H(5,𝔽2)11yescharacteristic
437C2×C3×C4H(5,𝔽2)11yescharacteristic
438C2×Dic3—21no—
439C2×Dic3—21no—
440C2×Dic3—21no—
441C2×Dic3—21no—
442C2×Dic3—21no—
443C2×Dic3—21no—
444C2×Dic3—21no—
445C2×Dic3—21no—
446C2×Dic3—21no—
447C2×Dic3—21no—
448C2×Dic3—21no—
449C2×Dic3—21no—
450C2×Dic3—21no—
451C2×Dic3—21no—
452C2×Dic3—21no—
453C2×Dic3—21no—
454C2×Dic3—21no—
455C2×Dic3—21no—
456C2×Dic3—21no—
457C2×Dic3—21no—
458C2×Dic3—21no—
459C2×Dic3—21no—
460C2×Dic3—21no—
461C2×Dic3—21no—
462C3×C8—41no—
463C3×C8—41no—
464C3×C8—41no—
465C3×C8—41no—
466C3⋊C8—22no—
467C3⋊C8—22no—
468C3⋊C8—41no—
469C3⋊C8—41no—
470C24—22no—
471C24—22no—
472C24—22no—
473C24—41no—
474C24—41no—
475C24—41no—
476C24—41no—
477C24C2×C4×D311yescharacteristic
478C24C2×C4×D311yescharacteristic
479C24C2×C4×D311yescharacteristic
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—31no—
501C22×C4—31no—
502C22×C4—31no—
503C22×C4—31no—
504C22×C4—31no—
505C22×C4—31no—
506C22×C4—31no—
507C22×C4—31no—
508C22×C4—41no—
509C22×C4—41no—
510C22×C4—41no—
511C22×C4—44no—
512C22×C4—44no—
513C22×C4—44no—
514C22×C4—44no—
515C22×C4C2×C4×D311yescharacteristic
516C22×C4C2×C4×D311yescharacteristic
517C22×C4C2×C4×D311yescharacteristic
518C22×C4D3×D412yes—
519C22×C4#23712yes—
520C22×C4#23712yes—
521C22×C4#23712yes—
522C22×C4C23×D311yescharacteristic
523M16—124no—
524M16—124no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—32no—
538C2×C8—32no—
539C2×C8—61no—
540C2×C8—61no—
541C2×C8—61no—
542C2×C8—61no—
543C2×C8—61no—
544C2×C8—61no—
545C2×C8—61no—
546C2×C8—61no—
547C2×C8—61no—
548C2×C8—61no—
549C4⋊C4—62no—
550C4⋊C4—62no—
551C4⋊C4—121no—
552C4⋊C4—121no—
553C22⋊C4—62no—
554C22⋊C4—62no—
555C22⋊C4—62no—
556C22⋊C4—62no—
557C22⋊C4—121no—
558C22⋊C4—121no—
559C22⋊C4—121no—
560C22⋊C4—121no—
561C22⋊C4—121no—
562C22⋊C4—121no—
563C22⋊C4—121no—
564C22⋊C4—121no—
565C42—61no—
566C42—61no—
567C42—61no—
568C42—61no—
569C42—61no—
570C42—61no—
571C42—61no—
572C42—61no—
573C22×C3—22no—
574C22×C3—22no—
575C22×C3—22no—
576C22×C3—22no—
577C22×C3—22no—
578C22×C3—22no—
579C22×C3—22no—
580C22×C3—22no—
581C22×C3—22no—
582C22×C3—416no—
583C22×C3—41no—
584C22×C3—41no—
585C22×C3—41no—
586C22×C3—41no—
587C22×C3—41no—
588C22×C3—41no—
589C22×C3—41no—
590C22×C3—41no—
591C22×C3—41no—
592C22×C3—41no—
593C22×C3—41no—
594C22×C3—41no—
595C22×C3C2×#11711yescharacteristic
596C22×C3C2×C4×D411yescharacteristic
597C22×C3#51811yescharacteristic
598C22×C3C2×#13111yescharacteristic
599C22×C3#56811yescharacteristic
600C22×C3#56811yescharacteristic
601C22×C3#56811yescharacteristic
602C3×C4—22no—
603C3×C4—22no—
604C3×C4—41no—
605C3×C4#54611yescharacteristic
606C3×C4#54611yescharacteristic
607C3×C4#55111yescharacteristic
608C3×C4#55111yescharacteristic
609Dic3—41no—
610Dic3—41no—
611Dic3—41no—
612Dic3—41no—
613Dic3—41no—
614Dic3—41no—
615Dic3—41no—
616Dic3—41no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—44no—
636C23—44no—
637C23—44no—
638C23—44no—
639C23—44no—
640C23—44no—
641C23—44no—
642C23#87712yes—
643C23#67⋊C412yes—
644C23#90112yes—
645C23C22×C4×D311yescharacteristic
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—44no—
662C2×C4—44no—
663C2×C4—44no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—61no—
669C2×C4—61no—
670C2×C4—61no—
671C2×C4—61no—
672C2×C4—61no—
673C2×C4—61no—
674C2×C4—61no—
675C2×C4—61no—
676C2×C4—61no—
677C2×C4—61no—
678C2×C4—61no—
679C2×C4—61no—
680C2×C4—61no—
681C2×C4—61no—
682C2×C4—61no—
683C2×C4—61no—
684C2×C4—61no—
685C2×C4—61no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—61no—
692C2×C4#87712yes—
693C2×C4#67⋊C412yes—
694C2×C4C2×D3×D411yescharacteristic
695C2×C4C2×#23711yescharacteristic
696C2×C4C2×#23711yescharacteristic
697C2×C4C2×#23711yescharacteristic
698C2×C4#100411yescharacteristic
699C2×C4#100411yescharacteristic
700C8—41no—
701C8—41no—
702C8—41no—
703C8—41no—
704C8—62no—
705C8—62no—
706C8—121no—
707C8—121no—
708C2×C3—42no—
709C2×C3—42no—
710C2×C3—42no—
711C2×C3#234211yescharacteristic
712C2×C3#292111yescharacteristic
713C2×C3#292411yescharacteristic
714C2×C3#293011yescharacteristic
715C2×C3#293311yescharacteristic
716C2×C3#297611yescharacteristic
717C2×C3#297811yescharacteristic
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—416no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22C2×#87711yescharacteristic
741C22C2×#67⋊C411yescharacteristic
742C22#548611yescharacteristic
743C22C2×#90111yescharacteristic
744C22#574511yescharacteristic
745C22#574511yescharacteristic
746C22#574511yescharacteristic
747C4—22no—
748C4—22no—
749C4—41no—
750C4—121no—
751C4—121no—
752C4—121no—
753C4—121no—
754C4—121no—
755C4—121no—
756C4—121no—
757C4—121no—
758C4#558711yescharacteristic
759C4#558711yescharacteristic
760C4#559111yescharacteristic
761C4#559111yescharacteristic
762C3#2255911yescharacteristic, complemented, Sylow
763C2—42no—
764C2—42no—
765C2—42no—
766C2#7382211yescharacteristic
767C2#7858411yescharacteristic
768C2#7859611yescharacteristic
769C2#7860411yescharacteristic
770C2#7862011yescharacteristic
771C2#7862711yescharacteristic
772C2#7863611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D3
commutator, socleC23×C3C23×C4
FittingC3×#1779C2
prime radicalC25×C3C2×C4
cosocleC22×C3×C4C24
hypercenter#1779D3
hypocenterC3#22559
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C22×C4 ◁ #1779

Complements

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

NH ≅ G/Ntype
3. C2×#4720C2semidirect
5. #69951C2semidirect
6. #69951C2semidirect
7. #69949C2semidirect
8. #69949C2semidirect
9. #69915C2semidirect
10. #69914C2semidirect
11. #69913C2semidirect
12. #69912C2semidirect
13. #69911C2semidirect
14. #69909C2semidirect
15. #69907C2semidirect
45. C2×#815C22semidirect
46. C2×#815C22semidirect
47. C2×Dic3⋊C8C22semidirect
48. C2×Dic3⋊C8C22semidirect
49. C2×Dic3⋊C8C22semidirect
50. C2×Dic3⋊C8C22semidirect
51. C2×C8×Dic3C22semidirect
52. C2×C8×Dic3C22semidirect
54. #4550C22semidirect
55. #4550C22semidirect
56. #4550C22semidirect
57. #4550C22semidirect
58. #4550C22semidirect
59. #4550C22semidirect
60. #4550C22semidirect
61. #4550C22semidirect
762. C3#22559semidirect

Maximal subgroups

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

subgroupindex
#840272
C2×#52072
C2×#47202
C3×#17792
#699512
#699492
#699152
#699142
#699132
#699122
#699112
#699092
#699072
#225593