Finite Group Databasebeta

← #10725789

Subgroups — #10725789

Order 768.

1550 conjugacy classes of subgroups.

The subgroup lattice has 1116 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5222C211yesmaximal, characteristic
2C3×#1438C211yesmaximal, characteristic
3#72131C211yesmaximal, characteristic
4#71549C211yesmaximal, characteristic, complemented
5#71549C211yesmaximal, characteristic, complemented
6#71545C211yesmaximal, characteristic, complemented
7#71545C211yesmaximal, characteristic, complemented
8#71545C211yesmaximal, characteristic, complemented
9#71545C211yesmaximal, characteristic, complemented
10#71545C211yesmaximal, characteristic, complemented
11#71545C211yesmaximal, characteristic, complemented
12#69421C211yesmaximal, characteristic, complemented
13#69406C211yesmaximal, characteristic, complemented
14#69403C211yesmaximal, characteristic, complemented
15#69402C211yesmaximal, characteristic, complemented
16#14617—31nomaximal, Sylow
17C23×C3×D4C2211yescharacteristic
18C22×C3×C22⋊C4C2211yescharacteristic
19C22×C3×C22⋊C4C2211yescharacteristic
20C22×C3×C22⋊C4C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×#217C2211yescharacteristic
23C22×#217C2211yescharacteristic
24C22×#217C2211yescharacteristic
25C22×#217C2211yescharacteristic
26C22×#217C2211yescharacteristic
27C22×#217C2211yescharacteristic
28C22×#217C2211yescharacteristic
29C22×#217C2211yescharacteristic
30C22×Dic3⋊C4C2211yescharacteristic
31C22×C4×Dic3C2211yescharacteristic
32C22×C4×Dic3C2211yescharacteristic
33C22×C4×Dic3C2211yescharacteristic
34C2×C3×#95C2211yescharacteristic
35C2×C3×#95C2211yescharacteristic
36#5222C418yescomplemented
37C2×C3⋊#95C2211yescharacteristic
38C2×C3⋊#95C2211yescharacteristic
39C2×C3⋊#95C2211yescharacteristic
40C2×C3⋊#95C2211yescharacteristic
41C2×C3⋊#95C2211yescharacteristic
42C2×C3⋊#95C2211yescharacteristic
43C2×C3⋊#95C2211yescharacteristic
44C2×C3⋊#95C2211yescharacteristic
45C2×C3⋊#95C2211yescharacteristic
46C2×C3⋊#95C2211yescharacteristic
47C2×C3⋊#95C2211yescharacteristic
48C2×C3⋊#95C2211yescharacteristic
49C2×C3⋊#95C2211yescharacteristic
50C2×C3⋊#95C2211yescharacteristic
51C2×C3⋊#95C2211yescharacteristic
52C2×C3⋊#95C2211yescharacteristic
53C2×#394—31no—
54#1445—31no—
55#1440—31no—
56#1440—31no—
57#1438—31no—
58#1438D311yescharacteristic
59#1437—31no—
60#1437—31no—
61#1437—31no—
62#1437—31no—
63#1437—31no—
64#1437—31no—
65#1436—31no—
66#1434—31no—
67#1434—31no—
68C25×C3C2311yescharacteristic
69C25×C3C2311yescharacteristic
70C22×C3×D4—41no—
71C22×C3×D4—41no—
72C22×C3×D4—41no—
73C22×C3×D4—41no—
74C22×C3×D4—41no—
75C22×C3×D4—41no—
76C22×C3×D4C2×C414yes—
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C23×Dic3C2311yescharacteristic
83C23×Dic3C2311yescharacteristic
84C23×Dic3C2311yescharacteristic
85C23×Dic3C2311yescharacteristic
86C23×Dic3C2311yescharacteristic
87C23×Dic3C2311yescharacteristic
88C23×Dic3C2311yescharacteristic
89C23×Dic3C2311yescharacteristic
90C2×C3×C22⋊C4—22no—
91C2×C3×C22⋊C4—22no—
92C2×C3×C22⋊C4—22no—
93C2×C3×C22⋊C4—22no—
94C2×C3×C22⋊C4—22no—
95C2×C3×C22⋊C4—22no—
96C2×C3×C22⋊C4—41no—
97C2×C3×C22⋊C4—41no—
98C2×C3×C22⋊C4—41no—
99C2×C3×C22⋊C4—41no—
100C2×C3×C22⋊C4—41no—
101C2×C3×C22⋊C4—41no—
102C2×#217—22no—
103C2×#217—22no—
104C2×#217—22no—
105C2×#217—22no—
106C2×#217—22no—
107C2×#217—22no—
108C2×#217—41no—
109C2×#217—41no—
110C2×#217—41no—
111C2×#217—41no—
112C2×#217—41no—
113C2×#217—41no—
114C2×#217—41no—
115C2×#217—41no—
116C2×#217—41no—
117C2×#217—41no—
118C2×#217—41no—
119C2×#217—41no—
120C2×#217—41no—
121C2×#217—41no—
122C2×#217C2×C414yes—
123C2×#217C2×C414yes—
124C2×#217C2×C414yes—
125C2×#217C2×C414yes—
126C2×Dic3⋊C4—41no—
127C2×Dic3⋊C4—41no—
128C2×Dic3⋊C4C2×C414yes—
129C2×C4×Dic3—22no—
130C2×C4×Dic3—22no—
131C2×C4×Dic3—41no—
132C2×C4×Dic3—41no—
133C2×C4×Dic3—41no—
134C2×C4×Dic3—41no—
135C2×C4×Dic3—41no—
136C2×C4×Dic3—41no—
137C2×C4×Dic3—41no—
138C3×#95—41no—
139C3×#95—41no—
140C3⋊#95—22no—
141C3⋊#95—22no—
142C3⋊#95—22no—
143C3⋊#95—22no—
144C3⋊#95—41no—
145C3⋊#95—41no—
146C3⋊#95—41no—
147C3⋊#95—41no—
148C3⋊#95—41no—
149C3⋊#95—41no—
150C3⋊#95—41no—
151C3⋊#95—41no—
152C3⋊#95—41no—
153C3⋊#95—41no—
154C3⋊#95—41no—
155C3⋊#95C2×C414yes—
156C23×D4C2×D311yescharacteristic
157C22×C4⋊C4—31no—
158C22×C22⋊C4—31no—
159C22×C22⋊C4—31no—
160C22×C22⋊C4—31no—
161C22×C22⋊C4—31no—
162C22×C22⋊C4—31no—
163C22×C22⋊C4—31no—
164C22×C22⋊C4—31no—
165C22×C22⋊C4—31no—
166C22×C22⋊C4C2×D311yescharacteristic
167C22×C22⋊C4C2×D311yescharacteristic
168C22×C22⋊C4C2×D311yescharacteristic
169C22×C22⋊C4C2×D311yescharacteristic
170C22×C42—31no—
171C22×C42—31no—
172C22×C42—31no—
173#394—38no—
174C2×#95—31no—
175C2×#95—31no—
176C2×#95—31no—
177C2×#95—31no—
178C2×#95—31no—
179C2×#95—31no—
180C2×#95—31no—
181C2×#95—31no—
182C2×#95—31no—
183C2×#95—31no—
184C2×#95—31no—
185C2×#95—31no—
186C2×#95—31no—
187C2×#95—31no—
188C2×#95—31no—
189C2×#95—31no—
190C2×#95C2×D311yescharacteristic
191C2×#95C2×D311yescharacteristic
192C24×C3—21no—
193C24×C3—21no—
194C24×C3—21no—
195C24×C3—21no—
196C24×C3—21no—
197C24×C3—21no—
198C24×C3—21no—
199C24×C3—21no—
200C24×C3—21no—
201C24×C3—21no—
202C24×C3—21no—
203C24×C3—21no—
204C24×C3—21no—
205C24×C3—21no—
206C24×C3—21no—
207C24×C3—21no—
208C24×C3—21no—
209C24×C3—21no—
210C24×C3—21no—
211C24×C3—21no—
212C24×C3—21no—
213C24×C3—21no—
214C24×C3—21no—
215C24×C3—21no—
216C24×C3—21no—
217C24×C3—21no—
218C24×C3—21no—
219C24×C3—21no—
220C24×C3C22×C412yes—
221C24×C3C22×C412yes—
222C24×C3C2411yescharacteristic
223C2×C3×D4—44no—
224C2×C3×D4—44no—
225C2×C3×D4—44no—
226C2×C3×D4—44no—
227C2×C3×D4—44no—
228C2×C3×D4—44no—
229C2×C3×D4—44no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4C22×C412yes—
262C22×C3×C4#4112yes—
263C22×C3×C4#4112yes—
264C22×C3×C4#4112yes—
265C22×Dic3—21no—
266C22×Dic3—21no—
267C22×Dic3—21no—
268C22×Dic3—21no—
269C22×Dic3—21no—
270C22×Dic3—21no—
271C22×Dic3—21no—
272C22×Dic3—21no—
273C22×Dic3—21no—
274C22×Dic3—21no—
275C22×Dic3—21no—
276C22×Dic3—21no—
277C22×Dic3—21no—
278C22×Dic3—21no—
279C22×Dic3—21no—
280C22×Dic3—21no—
281C22×Dic3—21no—
282C22×Dic3—21no—
283C22×Dic3—21no—
284C22×Dic3—21no—
285C22×Dic3—21no—
286C22×Dic3—21no—
287C22×Dic3—21no—
288C22×Dic3—21no—
289C22×Dic3—21no—
290C22×Dic3—21no—
291C22×Dic3—21no—
292C22×Dic3—21no—
293C22×Dic3—21no—
294C22×Dic3—21no—
295C22×Dic3—21no—
296C22×Dic3—21no—
297C22×Dic3—21no—
298C22×Dic3—21no—
299C22×Dic3—21no—
300C22×Dic3—21no—
301C22×Dic3—21no—
302C22×Dic3—21no—
303C22×Dic3—21no—
304C22×Dic3—21no—
305C22×Dic3—21no—
306C22×Dic3—21no—
307C22×Dic3—21no—
308C22×Dic3—21no—
309C22×Dic3—21no—
310C22×Dic3—21no—
311C22×Dic3—21no—
312C22×Dic3—21no—
313C22×Dic3—21no—
314C22×Dic3C22×C412yes—
315C22×Dic3C22×C412yes—
316C22×Dic3C22×C412yes—
317C22×Dic3C22×C412yes—
318C22×Dic3#4112yes—
319C22×Dic3#4112yes—
320C22×Dic3#4112yes—
321C3×C22⋊C4—44no—
322C3×C22⋊C4—44no—
323C3×C22⋊C4—44no—
324C3×C22⋊C4—44no—
325#217—44no—
326#217—44no—
327#217—44no—
328#217—44no—
329#217—44no—
330#217—44no—
331#217—44no—
332#217—44no—
333Dic3⋊C4—44no—
334C4×Dic3—44no—
335C4×Dic3—44no—
336C4×Dic3—44no—
337C25C22×D311yescharacteristic
338C25C22×D311yescharacteristic
339C22×D4—41no—
340C22×D4—41no—
341C22×D4—41no—
342C22×D4—41no—
343C22×D4—41no—
344C22×D4—41no—
345C22×D4C4×D314yes—
346C23×C4—31no—
347C23×C4—31no—
348C23×C4—31no—
349C23×C4—31no—
350C23×C4—31no—
351C23×C4—31no—
352C23×C4—31no—
353C23×C4—31no—
354C23×C4C22×D311yescharacteristic
355C23×C4C22×D311yescharacteristic
356C23×C4C22×D311yescharacteristic
357C23×C4C22×D311yescharacteristic
358C23×C4C22×D311yescharacteristic
359C2×C4⋊C4—34no—
360C2×C4⋊C4—121no—
361C2×C4⋊C4—121no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—34no—
369C2×C22⋊C4—34no—
370C2×C22⋊C4—34no—
371C2×C22⋊C4—34no—
372C2×C22⋊C4—41no—
373C2×C22⋊C4—41no—
374C2×C22⋊C4—41no—
375C2×C22⋊C4—41no—
376C2×C22⋊C4—41no—
377C2×C22⋊C4—41no—
378C2×C22⋊C4—62no—
379C2×C22⋊C4—62no—
380C2×C22⋊C4—62no—
381C2×C22⋊C4—62no—
382C2×C22⋊C4—62no—
383C2×C22⋊C4—62no—
384C2×C22⋊C4—121no—
385C2×C22⋊C4—121no—
386C2×C22⋊C4—121no—
387C2×C22⋊C4—121no—
388C2×C22⋊C4—121no—
389C2×C22⋊C4—121no—
390C2×C22⋊C4—121no—
391C2×C22⋊C4—121no—
392C2×C22⋊C4—121no—
393C2×C22⋊C4—121no—
394C2×C22⋊C4—121no—
395C2×C22⋊C4—121no—
396C2×C22⋊C4—121no—
397C2×C22⋊C4—121no—
398C2×C42—62no—
399C2×C42—62no—
400C2×C42—121no—
401C2×C42—121no—
402C2×C42—121no—
403C2×C42—121no—
404C2×C42—121no—
405C2×C42—121no—
406C2×C42—121no—
407#95—34no—
408#95—41no—
409#95—41no—
410#95—62no—
411#95—62no—
412#95—62no—
413#95—62no—
414#95—121no—
415#95—121no—
416#95—121no—
417#95—121no—
418#95—121no—
419#95—121no—
420#95—121no—
421#95—121no—
422#95—121no—
423#95—121no—
424#95—121no—
425C23×C3—22no—
426C23×C3—22no—
427C23×C3—22no—
428C23×C3—22no—
429C23×C3—22no—
430C23×C3—22no—
431C23×C3—22no—
432C23×C3—22no—
433C23×C3—22no—
434C23×C3—22no—
435C23×C3—22no—
436C23×C3—22no—
437C23×C3—22no—
438C23×C3—22no—
439C23×C3—41no—
440C23×C3—41no—
441C23×C3—41no—
442C23×C3—41no—
443C23×C3—41no—
444C23×C3—41no—
445C23×C3—41no—
446C23×C3—41no—
447C23×C3—41no—
448C23×C3—41no—
449C23×C3—41no—
450C23×C3—41no—
451C23×C3—41no—
452C23×C3—41no—
453C23×C3—41no—
454C23×C3—41no—
455C23×C3—41no—
456C23×C3—41no—
457C23×C3—41no—
458C23×C3—41no—
459C23×C3—41no—
460C23×C3—41no—
461C23×C3—41no—
462C23×C3—41no—
463C23×C3—41no—
464C23×C3—41no—
465C23×C3—41no—
466C23×C3—41no—
467C23×C3—41no—
468C23×C3—41no—
469C23×C3—41no—
470C23×C3—41no—
471C23×C3—41no—
472C23×C3—41no—
473C23×C3—41no—
474C23×C3—41no—
475C23×C3—41no—
476C23×C3—41no—
477C23×C3—41no—
478C23×C3—41no—
479C23×C3—41no—
480C23×C3—41no—
481C23×C3—41no—
482C23×C3—41no—
483C23×C3—41no—
484C23×C3—41no—
485C23×C3—41no—
486C23×C3—41no—
487C23×C3—41no—
488C23×C3—41no—
489C23×C3—41no—
490C23×C3—41no—
491C23×C3—41no—
492C23×C3—41no—
493C23×C3—41no—
494C23×C3—41no—
495C23×C3C23×C411yescharacteristic
496C23×C3C2×#4111yescharacteristic
497C23×C3C2×#4111yescharacteristic
498C23×C3C2×#4111yescharacteristic
499C23×C3C2×#4111yescharacteristic
500C23×C3C2×#4111yescharacteristic
501C23×C3C2×#4111yescharacteristic
502C23×C3H(5,𝔽2)11yescharacteristic
503C23×C3H(5,𝔽2)11yescharacteristic
504C23×C3H(5,𝔽2)11yescharacteristic
505C23×C3H(5,𝔽2)11yescharacteristic
506C23×C3H(5,𝔽2)11yescharacteristic
507C23×C3H(5,𝔽2)11yescharacteristic
508C23×C3H(5,𝔽2)11yescharacteristic
509C23×C3H(5,𝔽2)11yescharacteristic
510C3×D4—416no—
511C2×C3×C4—22no—
512C2×C3×C4—22no—
513C2×C3×C4—22no—
514C2×C3×C4—22no—
515C2×C3×C4—22no—
516C2×C3×C4—22no—
517C2×C3×C4—22no—
518C2×C3×C4—22no—
519C2×C3×C4—22no—
520C2×C3×C4—22no—
521C2×C3×C4—22no—
522C2×C3×C4—22no—
523C2×C3×C4—41no—
524C2×C3×C4—41no—
525C2×C3×C4—41no—
526C2×C3×C4—41no—
527C2×C3×C4—41no—
528C2×C3×C4—41no—
529C2×C3×C4—41no—
530C2×C3×C4—41no—
531C2×C3×C4—41no—
532C2×C3×C4—41no—
533C2×C3×C4—41no—
534C2×C3×C4—41no—
535C2×C3×C4—41no—
536C2×C3×C4—41no—
537C2×C3×C4—41no—
538C2×C3×C4—41no—
539C2×C3×C4—41no—
540C2×C3×C4—41no—
541C2×C3×C4—41no—
542C2×C3×C4—41no—
543C2×C3×C4—41no—
544C2×C3×C4—41no—
545C2×C3×C4—41no—
546C2×Dic3—22no—
547C2×Dic3—22no—
548C2×Dic3—22no—
549C2×Dic3—22no—
550C2×Dic3—22no—
551C2×Dic3—22no—
552C2×Dic3—22no—
553C2×Dic3—22no—
554C2×Dic3—22no—
555C2×Dic3—22no—
556C2×Dic3—22no—
557C2×Dic3—22no—
558C2×Dic3—22no—
559C2×Dic3—22no—
560C2×Dic3—22no—
561C2×Dic3—22no—
562C2×Dic3—22no—
563C2×Dic3—22no—
564C2×Dic3—22no—
565C2×Dic3—22no—
566C2×Dic3—22no—
567C2×Dic3—41no—
568C2×Dic3—41no—
569C2×Dic3—41no—
570C2×Dic3—41no—
571C2×Dic3—41no—
572C2×Dic3—41no—
573C2×Dic3—41no—
574C2×Dic3—41no—
575C2×Dic3—41no—
576C2×Dic3—41no—
577C2×Dic3—41no—
578C2×Dic3—41no—
579C2×Dic3—41no—
580C2×Dic3—41no—
581C2×Dic3—41no—
582C2×Dic3—41no—
583C2×Dic3—41no—
584C2×Dic3—41no—
585C2×Dic3—41no—
586C2×Dic3—41no—
587C2×Dic3—41no—
588C2×Dic3—41no—
589C2×Dic3—41no—
590C2×Dic3—41no—
591C2×Dic3—41no—
592C2×Dic3—41no—
593C2×Dic3—41no—
594C2×Dic3—41no—
595C2×Dic3—41no—
596C2×Dic3—41no—
597C2×Dic3—41no—
598C2×Dic3—41no—
599C2×Dic3—41no—
600C2×Dic3—41no—
601C2×Dic3—41no—
602C24—21no—
603C24—21no—
604C24—21no—
605C24—21no—
606C24—21no—
607C24—21no—
608C24—21no—
609C24—21no—
610C24—21no—
611C24—21no—
612C24—21no—
613C24—21no—
614C24—21no—
615C24—21no—
616C24—21no—
617C24—21no—
618C24—21no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24—21no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24C2×C4×D312yes—
631C24C2×C4×D312yes—
632C24C23×D311yescharacteristic
633C2×D4—44no—
634C2×D4—44no—
635C2×D4—44no—
636C2×D4—44no—
637C2×D4—44no—
638C2×D4—44no—
639C2×D4—44no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—32no—
672C22×C4—32no—
673C22×C4—32no—
674C22×C4—32no—
675C22×C4—32no—
676C22×C4—32no—
677C22×C4—32no—
678C22×C4—61no—
679C22×C4—61no—
680C22×C4—61no—
681C22×C4—61no—
682C22×C4—61no—
683C22×C4—61no—
684C22×C4—61no—
685C22×C4—61no—
686C22×C4—61no—
687C22×C4—61no—
688C22×C4—61no—
689C22×C4—61no—
690C22×C4—61no—
691C22×C4—61no—
692C22×C4—61no—
693C22×C4—61no—
694C22×C4—61no—
695C22×C4—61no—
696C22×C4—61no—
697C22×C4—61no—
698C22×C4—61no—
699C22×C4—61no—
700C22×C4—61no—
701C22×C4—61no—
702C22×C4—61no—
703C22×C4—61no—
704C22×C4—61no—
705C22×C4—61no—
706C22×C4—61no—
707C22×C4—61no—
708C22×C4—61no—
709C22×C4—61no—
710C22×C4—61no—
711C22×C4—61no—
712C22×C4—61no—
713C22×C4—61no—
714C22×C4—61no—
715C22×C4—61no—
716C22×C4—61no—
717C22×C4—61no—
718C22×C4—61no—
719C22×C4—61no—
720C22×C4—61no—
721C22×C4—61no—
722C22×C4—61no—
723C22×C4—61no—
724C22×C4—61no—
725C22×C4—61no—
726C22×C4—61no—
727C22×C4C2×C4×D312yes—
728C22×C4#23712yes—
729C22×C4#23712yes—
730C22×C4#23712yes—
731C4⋊C4—124no—
732C22⋊C4—44no—
733C22⋊C4—44no—
734C22⋊C4—44no—
735C22⋊C4—44no—
736C22⋊C4—124no—
737C22⋊C4—124no—
738C22⋊C4—124no—
739C22⋊C4—124no—
740C22⋊C4—124no—
741C22⋊C4—124no—
742C22⋊C4—124no—
743C22⋊C4—124no—
744C42—124no—
745C42—124no—
746C42—124no—
747C22×C3—42no—
748C22×C3—42no—
749C22×C3—42no—
750C22×C3—42no—
751C22×C3—42no—
752C22×C3—42no—
753C22×C3—42no—
754C22×C3—42no—
755C22×C3—42no—
756C22×C3—42no—
757C22×C3—42no—
758C22×C3—42no—
759C22×C3—42no—
760C22×C3—42no—
761C22×C3—81no—
762C22×C3—81no—
763C22×C3—81no—
764C22×C3—81no—
765C22×C3—81no—
766C22×C3—81no—
767C22×C3—81no—
768C22×C3—81no—
769C22×C3—81no—
770C22×C3—81no—
771C22×C3—81no—
772C22×C3—81no—
773C22×C3—81no—
774C22×C3—81no—
775C22×C3—81no—
776C22×C3—81no—
777C22×C3C4×#4111yescharacteristic
778C22×C3C4×#4111yescharacteristic
779C22×C3C4×#4111yescharacteristic
780C22×C3#51811yescharacteristic
781C22×C3#51811yescharacteristic
782C22×C3#51811yescharacteristic
783C22×C3#51811yescharacteristic
784C22×C3#53811yescharacteristic
785C22×C3#53811yescharacteristic
786C22×C3#53811yescharacteristic
787C22×C3#53811yescharacteristic
788C22×C3#53811yescharacteristic
789C22×C3#53811yescharacteristic
790C22×C3#54011yescharacteristic
791C22×C3#54011yescharacteristic
792C22×C3#54011yescharacteristic
793C22×C3#54011yescharacteristic
794C22×C3#54011yescharacteristic
795C22×C3#54011yescharacteristic
796C22×C3#55111yescharacteristic
797C22×C3#55111yescharacteristic
798C22×C3#55111yescharacteristic
799C22×C3#55111yescharacteristic
800C22×C3#55311yescharacteristic
801C22×C3#55311yescharacteristic
802C22×C3#55311yescharacteristic
803C22×C3#55311yescharacteristic
804C22×C3#55511yescharacteristic
805C22×C3#55511yescharacteristic
806C22×C3#55911yescharacteristic
807C22×C3#55911yescharacteristic
808C22×C3#56011yescharacteristic
809C22×C3#56011yescharacteristic
810C22×C3#56011yescharacteristic
811C22×C3H(3,𝔽4)11yescharacteristic
812C3×C4—42no—
813C3×C4—42no—
814C3×C4—42no—
815C3×C4—42no—
816C3×C4—81no—
817Dic3—42no—
818Dic3—42no—
819Dic3—42no—
820Dic3—42no—
821Dic3—42no—
822Dic3—42no—
823Dic3—42no—
824Dic3—81no—
825C23—22no—
826C23—22no—
827C23—22no—
828C23—22no—
829C23—22no—
830C23—22no—
831C23—22no—
832C23—22no—
833C23—22no—
834C23—22no—
835C23—22no—
836C23—22no—
837C23—22no—
838C23—22no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23—41no—
843C23—41no—
844C23—41no—
845C23—41no—
846C23—41no—
847C23—41no—
848C23—41no—
849C23—41no—
850C23—41no—
851C23—41no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—41no—
870C23—41no—
871C23—41no—
872C23—41no—
873C23—41no—
874C23—41no—
875C23—41no—
876C23—41no—
877C23—41no—
878C23—41no—
879C23—41no—
880C23—41no—
881C23—41no—
882C23—41no—
883C23—41no—
884C23—41no—
885C23—41no—
886C23—41no—
887C23—41no—
888C23—41no—
889C23—41no—
890C23—41no—
891C23—41no—
892C23—41no—
893C23—41no—
894C23—41no—
895C23C22×C4×D311yescharacteristic
896C23C2×#23711yescharacteristic
897C23C2×#23711yescharacteristic
898C23C2×#23711yescharacteristic
899C23#100411yescharacteristic
900C23#100411yescharacteristic
901C23#100411yescharacteristic
902C23#100411yescharacteristic
903C23#100411yescharacteristic
904C23#100411yescharacteristic
905C23#100411yescharacteristic
906C23D3×#4111yescharacteristic
907C23D3×#4111yescharacteristic
908C23D3×#4111yescharacteristic
909C23#100911yescharacteristic
910D4—416no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—62no—
947C2×C4—62no—
948C2×C4—62no—
949C2×C4—62no—
950C2×C4—62no—
951C2×C4—62no—
952C2×C4—62no—
953C2×C4—62no—
954C2×C4—62no—
955C2×C4—62no—
956C2×C4—62no—
957C2×C4—62no—
958C2×C4—62no—
959C2×C4—62no—
960C2×C4—62no—
961C2×C4—62no—
962C2×C4—62no—
963C2×C4—62no—
964C2×C4—62no—
965C2×C4—62no—
966C2×C4—62no—
967C2×C4—121no—
968C2×C4—121no—
969C2×C4—121no—
970C2×C4—121no—
971C2×C4—121no—
972C2×C4—121no—
973C2×C4—121no—
974C2×C4—121no—
975C2×C4—121no—
976C2×C4—121no—
977C2×C4—121no—
978C2×C4—121no—
979C2×C4—121no—
980C2×C4—121no—
981C2×C4—121no—
982C2×C4—121no—
983C2×C4—121no—
984C2×C4—121no—
985C2×C4—121no—
986C2×C4—121no—
987C2×C4—121no—
988C2×C4—121no—
989C2×C4—121no—
990C2×C4—121no—
991C2×C4—121no—
992C2×C4—121no—
993C2×C4—121no—
994C2×C4—121no—
995C2×C4—121no—
996C2×C4—121no—
997C2×C4—121no—
998C2×C4—121no—
999C2×C4—121no—
1000C2×C4—121no—
1001C2×C4—121no—
1002C2×C3—82no—
1003C2×C3—82no—
1004C2×C3#233311yescharacteristic
1005C2×C3#233311yescharacteristic
1006C2×C3#233311yescharacteristic
1007C2×C3#237211yescharacteristic
1008C2×C3#237411yescharacteristic
1009C2×C3#237411yescharacteristic
1010C2×C3#237511yescharacteristic
1011C2×C3#275211yescharacteristic
1012C2×C3#275211yescharacteristic
1013C2×C3#275311yescharacteristic
1014C2×C3#275311yescharacteristic
1015C2×C3#275611yescharacteristic
1016C2×C3#275611yescharacteristic
1017C2×C3#280311yescharacteristic
1018C2×C3#280311yescharacteristic
1019C22—42no—
1020C22—42no—
1021C22—42no—
1022C22—42no—
1023C22—42no—
1024C22—42no—
1025C22—42no—
1026C22—42no—
1027C22—42no—
1028C22—42no—
1029C22—42no—
1030C22—42no—
1031C22—42no—
1032C22—42no—
1033C22—81no—
1034C22—81no—
1035C22—81no—
1036C22—81no—
1037C22—81no—
1038C22—81no—
1039C22—81no—
1040C22—81no—
1041C22—81no—
1042C22—81no—
1043C22—81no—
1044C22—81no—
1045C22—81no—
1046C22—81no—
1047C22—81no—
1048C22—81no—
1049C22#548611yescharacteristic
1050C22#548611yescharacteristic
1051C22#548611yescharacteristic
1052C22C4×#23711yescharacteristic
1053C22C4×#23711yescharacteristic
1054C22C4×#23711yescharacteristic
1055C22#554511yescharacteristic
1056C22#558711yescharacteristic
1057C22#558711yescharacteristic
1058C22#559311yescharacteristic
1059C22#559311yescharacteristic
1060C22#559411yescharacteristic
1061C22#559511yescharacteristic
1062C22#559511yescharacteristic
1063C22#559511yescharacteristic
1064C22#560111yescharacteristic
1065C22#560111yescharacteristic
1066C22#561311yescharacteristic
1067C22#561411yescharacteristic
1068C22#561411yescharacteristic
1069C22#561511yescharacteristic
1070C22#561511yescharacteristic
1071C22#561611yescharacteristic
1072C22#561611yescharacteristic
1073C22#561711yescharacteristic
1074C22#561911yescharacteristic
1075C22#561911yescharacteristic
1076C22#565711yescharacteristic
1077C22#565911yescharacteristic
1078C22#566311yescharacteristic
1079C22#566411yescharacteristic
1080C22#567811yescharacteristic
1081C22#567911yescharacteristic
1082C22#571311yescharacteristic
1083C22#571911yescharacteristic
1084C4—42no—
1085C4—42no—
1086C4—42no—
1087C4—42no—
1088C4—81no—
1089C4—122no—
1090C4—122no—
1091C4—122no—
1092C4—122no—
1093C4—122no—
1094C4—122no—
1095C4—122no—
1096C4—241no—
1097C3#1461711yescharacteristic, complemented, Sylow
1098C2—82no—
1099C2—82no—
1100C2#7385111yescharacteristic
1101C2#7466811yescharacteristic
1102C2#7466911yescharacteristic
1103C2#7468011yescharacteristic
1104C2#7468111yescharacteristic
1105C2#7629911yescharacteristic
1106C2#7630811yescharacteristic
1107C2#7673411yescharacteristic
1108C2#7673511yescharacteristic
1109C2#7673611yescharacteristic
1110C2#7674011yescharacteristic
1111C2#7705711yescharacteristic
1112C2#7706111yescharacteristic
1113C2#7708011yescharacteristic
1114C2#7715511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC3×#1438C2
socle, cosocleC24×C3C24
prime radicalC23×C3×D4C22
hypercenter#1438D3
hypocenterC3#14617
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
4. #71549C2semidirect
5. #71549C2semidirect
6. #71545C2semidirect
7. #71545C2semidirect
8. #71545C2semidirect
9. #71545C2semidirect
10. #71545C2semidirect
11. #71545C2semidirect
12. #69421C2semidirect
13. #69406C2semidirect
14. #69403C2semidirect
15. #69402C2semidirect
36. #5222C4semidirect
1097. C3#14617semidirect

Maximal subgroups

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

subgroupindex
C2×#52222
C3×#14382
#721312
#715492
#715452
#694212
#694062
#694032
#694022
#146173