Finite Group Databasebeta

← #10732159

Subgroups — #10732159

Order 768.

1530 conjugacy classes of subgroups.

The subgroup lattice has 922 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4982C211yesmaximal, characteristic
2C2×#4979C211yesmaximal, characteristic
3C2×#4657C211yesmaximal, characteristic
4C2×#4656C211yesmaximal, characteristic
5C2×#4646C211yesmaximal, characteristic
6C2×#4647C211yesmaximal, characteristic
7C3×C4⋊#95C211yesmaximal, characteristic
8#71568C211yesmaximal, characteristic
9#71568C211yesmaximal, characteristic
10#71535C211yesmaximal, characteristic
11C4×C3⋊#95C211yesmaximal, characteristic
12#69420C211yesmaximal, characteristic
13#69420C211yesmaximal, characteristic
14Dic3⋊#95C211yesmaximal, characteristic
15Dic3⋊#95C211yesmaximal, characteristic
16#15173—31nomaximal, Sylow
17C23×Dic6C2211yescharacteristic
18C22×C3×C4⋊C4C2211yescharacteristic
19C22×C3×C4⋊C4C2211yescharacteristic
20C22×C3×C42C2211yescharacteristic
21C22×C4⋊Dic3C2211yescharacteristic
22C22×C4⋊Dic3C2211yescharacteristic
23C22×C4⋊Dic3C2211yescharacteristic
24C22×Dic3⋊C4C2211yescharacteristic
25C22×Dic3⋊C4C2211yescharacteristic
26C22×Dic3⋊C4C2211yescharacteristic
27C22×Dic3⋊C4C2211yescharacteristic
28C22×Dic3⋊C4C2211yescharacteristic
29C22×Dic3⋊C4C2211yescharacteristic
30C22×Dic3⋊C4C2211yescharacteristic
31C22×Dic3⋊C4C2211yescharacteristic
32C22×C4×Dic3C2211yescharacteristic
33C22×C4×Dic3C2211yescharacteristic
34C2×C3×#95C2211yescharacteristic
35C2×C3×#95C2211yescharacteristic
36C2×C3×#95C2211yescharacteristic
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
52#4982—24no—
53#4979—24no—
54#4657—24no—
55#4656—24no—
56#4647—24no—
57#4646—24no—
58C2×#398—31no—
59C2×#398—31no—
60C2×#395—31no—
61C2×#395—31no—
62C2×#391—31no—
63C2×#389—31no—
64#1444—31no—
65#1444—31no—
66#1444—31no—
67#1444—31no—
68C4⋊#95—31no—
69C4⋊#95—31no—
70C4⋊#95—31no—
71C4⋊#95D311yescharacteristic
72C4×#95—31no—
73C23×C3×C4C2311yescharacteristic
74C23×C3×C4C2311yescharacteristic
75C23×C3×C4C2311yescharacteristic
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C23×Dic3C2311yescharacteristic
81C23×Dic3C2311yescharacteristic
82C23×Dic3C2311yescharacteristic
83C23×Dic3C2311yescharacteristic
84C23×Dic3C2311yescharacteristic
85C23×Dic3C2311yescharacteristic
86C23×Dic3C2311yescharacteristic
87C23×Dic3C2311yescharacteristic
88C22×Dic6—22no—
89C22×Dic6—22no—
90C22×Dic6—22no—
91C22×Dic6—22no—
92C22×Dic6—22no—
93C22×Dic6—41no—
94C22×Dic6—41no—
95C2×C3×C4⋊C4—22no—
96C2×C3×C4⋊C4—22no—
97C2×C3×C4⋊C4—22no—
98C2×C3×C4⋊C4—22no—
99C2×C3×C4⋊C4—41no—
100C2×C3×C4⋊C4—41no—
101C2×C3×C42—41no—
102C2×C3×C42—41no—
103C2×C3×C42Q814yescomplemented
104C2×C4⋊Dic3—22no—
105C2×C4⋊Dic3—22no—
106C2×C4⋊Dic3—22no—
107C2×C4⋊Dic3—22no—
108C2×C4⋊Dic3—22no—
109C2×C4⋊Dic3—22no—
110C2×C4⋊Dic3—22no—
111C2×C4⋊Dic3—41no—
112C2×C4⋊Dic3—41no—
113C2×Dic3⋊C4—22no—
114C2×Dic3⋊C4—22no—
115C2×Dic3⋊C4—22no—
116C2×Dic3⋊C4—22no—
117C2×Dic3⋊C4—22no—
118C2×Dic3⋊C4—22no—
119C2×Dic3⋊C4—22no—
120C2×Dic3⋊C4—22no—
121C2×Dic3⋊C4—22no—
122C2×Dic3⋊C4—22no—
123C2×Dic3⋊C4—22no—
124C2×Dic3⋊C4—22no—
125C2×Dic3⋊C4—22no—
126C2×Dic3⋊C4—22no—
127C2×Dic3⋊C4—22no—
128C2×Dic3⋊C4—22no—
129C2×Dic3⋊C4—22no—
130C2×Dic3⋊C4—22no—
131C2×Dic3⋊C4—41no—
132C2×Dic3⋊C4—41no—
133C2×Dic3⋊C4—41no—
134C2×Dic3⋊C4—41no—
135C2×Dic3⋊C4—41no—
136C2×Dic3⋊C4—41no—
137C2×C4×Dic3—41no—
138C2×C4×Dic3—41no—
139C2×C4×Dic3—41no—
140C2×C4×Dic3—41no—
141C2×C4×Dic3D414yes—
142C2×C4×Dic3Q814yescomplemented
143C3×#95—22no—
144C3×#95—22no—
145C3×#95—22no—
146C3×#95—22no—
147C3⋊#95—22no—
148C3⋊#95—22no—
149C3⋊#95—22no—
150C3⋊#95—22no—
151C3⋊#95—22no—
152C3⋊#95—22no—
153C3⋊#95—22no—
154C3⋊#95—22no—
155C3⋊#95—22no—
156C3⋊#95—22no—
157C3⋊#95D414yes—
158C3⋊#95D414yes—
159C3⋊#95Q814yescomplemented
160C3⋊#95Q814yescomplemented
161C23×Q8—31no—
162C22×C4⋊C4—31no—
163C22×C4⋊C4—31no—
164C22×C4⋊C4—31no—
165C22×C4⋊C4—31no—
166C22×C4⋊C4—31no—
167C22×C4⋊C4—31no—
168C22×C4⋊C4—31no—
169C22×C4⋊C4—31no—
170C22×C4⋊C4—31no—
171C22×C4⋊C4—31no—
172C22×C4⋊C4—31no—
173C22×C4⋊C4C2×D311yescharacteristic
174C22×C4⋊C4C2×D311yescharacteristic
175C22×C42—31no—
176C22×C42—31no—
177C22×C42C2×D311yescharacteristic
178#398—64no—
179#398—64no—
180#395—64no—
181#395—64no—
182#391—64no—
183#389—64no—
184C2×#95—31no—
185C2×#95—31no—
186C2×#95—31no—
187C2×#95—31no—
188C2×#95—31no—
189C2×#95—31no—
190C2×#95—31no—
191C2×#95—31no—
192C2×#95—31no—
193C2×#95—31no—
194C2×#95—31no—
195C2×#95—31no—
196C2×#95—31no—
197C2×#95—31no—
198C2×#95C2×D311yescharacteristic
199C2×#95C2×D311yescharacteristic
200C2×#95C2×D311yescharacteristic
201C2×#95C2×D311yescharacteristic
202C24×C3C2411yescharacteristic
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—21no—
207C22×C3×C4—21no—
208C22×C3×C4—21no—
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—21no—
218C22×C3×C4—21no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
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—21no—
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×C4C2×D412yes—
242C22×C3×C4C2×D412yes—
243C22×C3×C4C2×D412yes—
244C22×C3×C4C2×Q812yes—
245C22×C3×C4C2×Q812yes—
246C22×C3×C4C2×Q812yes—
247C22×C3×C4C2×Q812yes—
248C22×C3×C4C2×Q812yes—
249C22×C3×C4C2×Q812yes—
250C22×C3×C4#4112yes—
251C22×C3×C4#4112yes—
252C22×Dic3—21no—
253C22×Dic3—21no—
254C22×Dic3—21no—
255C22×Dic3—21no—
256C22×Dic3—21no—
257C22×Dic3—21no—
258C22×Dic3—21no—
259C22×Dic3—21no—
260C22×Dic3—21no—
261C22×Dic3—21no—
262C22×Dic3—21no—
263C22×Dic3—21no—
264C22×Dic3—21no—
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×Dic3C2×D412yes—
295C22×Dic3C2×D412yes—
296C22×Dic3C2×D412yes—
297C22×Dic3C2×D412yes—
298C22×Dic3C2×D412yes—
299C22×Dic3C2×D412yes—
300C22×Dic3C2×Q812yes—
301C22×Dic3C2×Q812yes—
302C22×Dic3C2×Q812yes—
303C22×Dic3C2×Q812yes—
304C22×Dic3C2×Q812yes—
305C22×Dic3C2×Q812yes—
306C22×Dic3#4112yes—
307C22×Dic3#4112yes—
308C2×Dic6—28no—
309C2×Dic6—44no—
310C2×Dic6—44no—
311C2×Dic6—44no—
312C2×Dic6—44no—
313C2×Dic6—44no—
314C2×Dic6—44no—
315C3×C4⋊C4—44no—
316C3×C4⋊C4—44no—
317C3×C42—44no—
318C4⋊Dic3—44no—
319C4⋊Dic3—44no—
320C4⋊Dic3—44no—
321Dic3⋊C4—28no—
322Dic3⋊C4—44no—
323Dic3⋊C4—44no—
324Dic3⋊C4—44no—
325Dic3⋊C4—44no—
326Dic3⋊C4—44no—
327Dic3⋊C4—44no—
328Dic3⋊C4—44no—
329C4×Dic3—44no—
330C4×Dic3—44no—
331C22×Q8—62no—
332C22×Q8—62no—
333C22×Q8—62no—
334C22×Q8—62no—
335C22×Q8—62no—
336C22×Q8—121no—
337C22×Q8—121no—
338C23×C4—31no—
339C23×C4—31no—
340C23×C4—31no—
341C23×C4—31no—
342C23×C4—31no—
343C23×C4—31no—
344C23×C4—31no—
345C23×C4—31no—
346C23×C4C22×D311yescharacteristic
347C23×C4C22×D311yescharacteristic
348C23×C4C22×D311yescharacteristic
349C23×C4C22×D311yescharacteristic
350C23×C4C22×D311yescharacteristic
351C23×C4C22×D311yescharacteristic
352C23×C4C22×D311yescharacteristic
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—41no—
358C2×C4⋊C4—41no—
359C2×C4⋊C4—62no—
360C2×C4⋊C4—62no—
361C2×C4⋊C4—62no—
362C2×C4⋊C4—62no—
363C2×C4⋊C4—62no—
364C2×C4⋊C4—62no—
365C2×C4⋊C4—62no—
366C2×C4⋊C4—62no—
367C2×C4⋊C4—62no—
368C2×C4⋊C4—62no—
369C2×C4⋊C4—62no—
370C2×C4⋊C4—62no—
371C2×C4⋊C4—62no—
372C2×C4⋊C4—62no—
373C2×C4⋊C4—62no—
374C2×C4⋊C4—62no—
375C2×C4⋊C4—62no—
376C2×C4⋊C4—62no—
377C2×C4⋊C4—62no—
378C2×C4⋊C4—62no—
379C2×C4⋊C4—62no—
380C2×C4⋊C4—62no—
381C2×C4⋊C4—62no—
382C2×C4⋊C4—62no—
383C2×C4⋊C4—62no—
384C2×C4⋊C4—121no—
385C2×C4⋊C4—121no—
386C2×C4⋊C4—121no—
387C2×C4⋊C4—121no—
388C2×C4⋊C4—121no—
389C2×C4⋊C4—121no—
390C2×C4⋊C4—121no—
391C2×C4⋊C4—121no—
392C2×C42—34no—
393C2×C42—34no—
394C2×C42—41no—
395C2×C42—41no—
396C2×C42—121no—
397C2×C42—121no—
398C2×C42—121no—
399C2×C42—121no—
400C2×C42Dic614yescomplemented
401#95—22no—
402#95—22no—
403#95—22no—
404#95—22no—
405#95—34no—
406#95—34no—
407#95—34no—
408#95—34no—
409#95—62no—
410#95—62no—
411#95—62no—
412#95—62no—
413#95—62no—
414#95—62no—
415#95—62no—
416#95—62no—
417#95—62no—
418#95—62no—
419C23×C3C22×D411yescharacteristic
420C23×C3C22×D411yescharacteristic
421C23×C3C22×D411yescharacteristic
422C23×C3C22×Q811yescharacteristic
423C23×C3C22×Q811yescharacteristic
424C23×C3C22×Q811yescharacteristic
425C23×C3C22×Q811yescharacteristic
426C23×C3C2×#4111yescharacteristic
427C23×C3C2×#4111yescharacteristic
428C23×C3C2×#4111yescharacteristic
429C23×C3C2×#4111yescharacteristic
430C23×C3H(5,𝔽2)11yescharacteristic
431C23×C3H(5,𝔽2)11yescharacteristic
432C23×C3H(5,𝔽2)11yescharacteristic
433C23×C32−1+411yescharacteristic
434C2×C3×C4—22no—
435C2×C3×C4—22no—
436C2×C3×C4—22no—
437C2×C3×C4—22no—
438C2×C3×C4—22no—
439C2×C3×C4—22no—
440C2×C3×C4—22no—
441C2×C3×C4—22no—
442C2×C3×C4—22no—
443C2×C3×C4—22no—
444C2×C3×C4—22no—
445C2×C3×C4—22no—
446C2×C3×C4—22no—
447C2×C3×C4—22no—
448C2×C3×C4—22no—
449C2×C3×C4—22no—
450C2×C3×C4—22no—
451C2×C3×C4—22no—
452C2×C3×C4—22no—
453C2×C3×C4—22no—
454C2×C3×C4—22no—
455C2×C3×C4—22no—
456C2×C3×C4—22no—
457C2×C3×C4—22no—
458C2×C3×C4—41no—
459C2×C3×C4—41no—
460C2×C3×C4—41no—
461C2×C3×C4—41no—
462C2×C3×C4—41no—
463C2×C3×C4—41no—
464C2×C3×C4—41no—
465C2×C3×C4—41no—
466C2×C3×C4—41no—
467C2×C3×C4—41no—
468C2×C3×C4—41no—
469C2×C3×C4—41no—
470C2×C3×C4—41no—
471C2×C3×C4—41no—
472C2×C3×C4—41no—
473C2×C3×C4—41no—
474C2×C3×C4—41no—
475C2×C3×C4—41no—
476C2×C3×C4—41no—
477C2×C3×C4—41no—
478C2×C3×C4—41no—
479C2×C3×C4—41no—
480C2×C3×C4C4⋊Q814yes—
481C2×C3×C4C4⋊Q814yes—
482C2×C3×C4C4⋊Q814yes—
483C2×Dic3—22no—
484C2×Dic3—22no—
485C2×Dic3—22no—
486C2×Dic3—22no—
487C2×Dic3—22no—
488C2×Dic3—22no—
489C2×Dic3—22no—
490C2×Dic3—22no—
491C2×Dic3—22no—
492C2×Dic3—22no—
493C2×Dic3—22no—
494C2×Dic3—22no—
495C2×Dic3—22no—
496C2×Dic3—22no—
497C2×Dic3—22no—
498C2×Dic3—22no—
499C2×Dic3—22no—
500C2×Dic3—22no—
501C2×Dic3—22no—
502C2×Dic3—22no—
503C2×Dic3—22no—
504C2×Dic3—22no—
505C2×Dic3—22no—
506C2×Dic3—22no—
507C2×Dic3—22no—
508C2×Dic3—22no—
509C2×Dic3—22no—
510C2×Dic3—22no—
511C2×Dic3—22no—
512C2×Dic3—22no—
513C2×Dic3—41no—
514C2×Dic3—41no—
515C2×Dic3—41no—
516C2×Dic3—41no—
517C2×Dic3—41no—
518C2×Dic3—41no—
519C2×Dic3—41no—
520C2×Dic3—41no—
521C2×Dic3—41no—
522C2×Dic3—41no—
523C2×Dic3—41no—
524C2×Dic3—41no—
525C2×Dic3—41no—
526C2×Dic3—41no—
527C2×Dic3—41no—
528C2×Dic3—41no—
529C2×Dic3—41no—
530C2×Dic3—41no—
531C2×Dic3—41no—
532C2×Dic3—41no—
533C2×Dic3—41no—
534C2×Dic3—41no—
535C2×Dic3#12714yes—
536C2×Dic3C4⋊Q814yes—
537C2×Dic3C4⋊Q814yes—
538C2×Dic3C4⋊Q814yes—
539Dic6—416no—
540C24C23×D311yescharacteristic
541C2×Q8—68no—
542C2×Q8—124no—
543C2×Q8—124no—
544C2×Q8—124no—
545C2×Q8—124no—
546C2×Q8—124no—
547C2×Q8—124no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—32no—
587C22×C4—32no—
588C22×C4—32no—
589C22×C4—32no—
590C22×C4—32no—
591C22×C4—32no—
592C22×C4—32no—
593C22×C4—32no—
594C22×C4—32no—
595C22×C4—32no—
596C22×C4—32no—
597C22×C4—32no—
598C22×C4—32no—
599C22×C4—32no—
600C22×C4—61no—
601C22×C4—61no—
602C22×C4—61no—
603C22×C4—61no—
604C22×C4—61no—
605C22×C4—61no—
606C22×C4—61no—
607C22×C4—61no—
608C22×C4—61no—
609C22×C4—61no—
610C22×C4—61no—
611C22×C4—61no—
612C22×C4—61no—
613C22×C4—61no—
614C22×C4—61no—
615C22×C4—61no—
616C22×C4—61no—
617C22×C4—61no—
618C22×C4—61no—
619C22×C4—61no—
620C22×C4—61no—
621C22×C4—61no—
622C22×C4—61no—
623C22×C4—61no—
624C22×C4—61no—
625C22×C4—61no—
626C22×C4—61no—
627C22×C4—61no—
628C22×C4—61no—
629C22×C4—61no—
630C22×C4—61no—
631C22×C4—61no—
632C22×C4—61no—
633C22×C4—61no—
634C22×C4—61no—
635C22×C4—61no—
636C22×C4—61no—
637C22×C4—61no—
638C22×C4—61no—
639C22×C4—61no—
640C22×C4—61no—
641C22×C4—61no—
642C22×C4C2×Dic612yes—
643C22×C4C2×Dic612yes—
644C22×C4C2×Dic612yes—
645C22×C4#23512yes—
646C22×C4#23512yes—
647C22×C4D3×D412yes—
648C22×C4D3×D412yes—
649C22×C4D3×D412yes—
650C22×C4D3×Q812yes—
651C22×C4D3×Q812yes—
652C22×C4D3×Q812yes—
653C4⋊C4—44no—
654C4⋊C4—44no—
655C4⋊C4—68no—
656C4⋊C4—124no—
657C4⋊C4—124no—
658C4⋊C4—124no—
659C4⋊C4—124no—
660C4⋊C4—124no—
661C4⋊C4—124no—
662C4⋊C4—124no—
663C4⋊C4—124no—
664C4⋊C4—124no—
665C4⋊C4—124no—
666C42—44no—
667C42—124no—
668C42—124no—
669C22×C3#52511yescharacteristic
670C22×C3#52511yescharacteristic
671C22×C3C2×#12711yescharacteristic
672C22×C3C2×C4⋊Q811yescharacteristic
673C22×C3C2×C4⋊Q811yescharacteristic
674C22×C3C2×C4⋊Q811yescharacteristic
675C22×C3C2×C4⋊Q811yescharacteristic
676C22×C3C2×C4⋊Q811yescharacteristic
677C22×C3C2×C4⋊Q811yescharacteristic
678C22×C3#53311yescharacteristic
679C22×C3#53311yescharacteristic
680C22×C3#53311yescharacteristic
681C22×C3#53311yescharacteristic
682C22×C3#53411yescharacteristic
683C22×C3#53711yescharacteristic
684C22×C3#54311yescharacteristic
685C22×C3#54311yescharacteristic
686C22×C3#54411yescharacteristic
687C22×C3#54411yescharacteristic
688C22×C3#54611yescharacteristic
689C22×C3#54611yescharacteristic
690C22×C3#54611yescharacteristic
691C22×C3#54611yescharacteristic
692C22×C3#54611yescharacteristic
693C22×C3#54611yescharacteristic
694C22×C3#54811yescharacteristic
695C22×C3#54811yescharacteristic
696C22×C3#55411yescharacteristic
697C22×C3#55411yescharacteristic
698C22×C3#55411yescharacteristic
699C22×C3#55411yescharacteristic
700C22×C3#55411yescharacteristic
701C22×C3#55411yescharacteristic
702C22×C3#55711yescharacteristic
703C22×C3#55711yescharacteristic
704C3×C4—24no—
705C3×C4—24no—
706C3×C4—24no—
707C3×C4—42no—
708C3×C4—42no—
709C3×C4—81no—
710C3×C4—81no—
711Dic3—24no—
712Dic3—24no—
713Dic3—24no—
714Dic3—24no—
715Dic3—42no—
716Dic3—42no—
717Dic3—81no—
718Dic3—81no—
719C23C22×Dic611yescharacteristic
720C23C2×#23511yescharacteristic
721C23C2×#23511yescharacteristic
722C23C2×D3×D411yescharacteristic
723C23C2×D3×D411yescharacteristic
724C23C2×D3×D411yescharacteristic
725C23#100411yescharacteristic
726C23#100411yescharacteristic
727C23C2×D3×Q811yescharacteristic
728C23C2×D3×Q811yescharacteristic
729C23C2×D3×Q811yescharacteristic
730C23D3×#4111yescharacteristic
731C23D3×#4111yescharacteristic
732C23#100911yescharacteristic
733C23#101011yescharacteristic
734Q8—1216no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—34no—
760C2×C4—34no—
761C2×C4—34no—
762C2×C4—34no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—62no—
786C2×C4—62no—
787C2×C4—62no—
788C2×C4—62no—
789C2×C4—62no—
790C2×C4—62no—
791C2×C4—62no—
792C2×C4—62no—
793C2×C4—62no—
794C2×C4—62no—
795C2×C4—62no—
796C2×C4—62no—
797C2×C4—62no—
798C2×C4—62no—
799C2×C4—62no—
800C2×C4—62no—
801C2×C4—62no—
802C2×C4—62no—
803C2×C4—62no—
804C2×C4—62no—
805C2×C4—62no—
806C2×C4—62no—
807C2×C4—62no—
808C2×C4—62no—
809C2×C4—62no—
810C2×C4—62no—
811C2×C4—62no—
812C2×C4—62no—
813C2×C4—62no—
814C2×C4—62no—
815C2×C4—121no—
816C2×C4—121no—
817C2×C4—121no—
818C2×C4—121no—
819C2×C4—121no—
820C2×C4—121no—
821C2×C4—121no—
822C2×C4—121no—
823C2×C4—121no—
824C2×C4—121no—
825C2×C4—121no—
826C2×C4—121no—
827C2×C4—121no—
828C2×C4—121no—
829C2×C4—121no—
830C2×C4—121no—
831C2×C4—121no—
832C2×C4—121no—
833C2×C4—121no—
834C2×C4—121no—
835C2×C4—121no—
836C2×C4—121no—
837C2×C4#88814yes—
838C2×C4#88814yes—
839C2×C4#88814yes—
840C2×C3#239911yescharacteristic
841C2×C3#253911yescharacteristic
842C2×C3#254011yescharacteristic
843C2×C3#254911yescharacteristic
844C2×C3#254911yescharacteristic
845C2×C3#254911yescharacteristic
846C2×C3#254911yescharacteristic
847C2×C3#255011yescharacteristic
848C2×C3#255011yescharacteristic
849C2×C3#255011yescharacteristic
850C2×C3#255011yescharacteristic
851C2×C3#258311yescharacteristic
852C2×C3#258411yescharacteristic
853C2×C3#265911yescharacteristic
854C2×C3#286811yescharacteristic
855C22#547011yescharacteristic
856C22#548311yescharacteristic
857C22#549011yescharacteristic
858C22#549011yescharacteristic
859C22C2×#88811yescharacteristic
860C22C2×#88811yescharacteristic
861C22C2×#88811yescharacteristic
862C22#551111yescharacteristic
863C22#551111yescharacteristic
864C22#551711yescharacteristic
865C22#551911yescharacteristic
866C22#554711yescharacteristic
867C22#554711yescharacteristic
868C22#555011yescharacteristic
869C22#555211yescharacteristic
870C22#556711yescharacteristic
871C22#557811yescharacteristic
872C22#557811yescharacteristic
873C22#557911yescharacteristic
874C22#559711yescharacteristic
875C22#560511yescharacteristic
876C22#561011yescharacteristic
877C22#561011yescharacteristic
878C22#562311yescharacteristic
879C22#563411yescharacteristic
880C22#563611yescharacteristic
881C22#563611yescharacteristic
882C22#567611yescharacteristic
883C22#567711yescharacteristic
884C22#568511yescharacteristic
885C22#569011yescharacteristic
886C22D3×#12711yescharacteristic
887C22D3×C4⋊Q811yescharacteristic
888C22D3×C4⋊Q811yescharacteristic
889C22D3×C4⋊Q811yescharacteristic
890C4—24no—
891C4—24no—
892C4—24no—
893C4—42no—
894C4—42no—
895C4—64no—
896C4—64no—
897C4—64no—
898C4—64no—
899C4—81no—
900C4—81no—
901C4—122no—
902C4—122no—
903C4—241no—
904C4—241no—
905C3#1517311yescharacteristic, complemented, Sylow
906C2#7335711yescharacteristic
907C2#7366911yescharacteristic
908C2#7371311yescharacteristic
909C2#7393811yescharacteristic
910C2#7395711yescharacteristic
911C2#7418011yescharacteristic
912C2#7435611yescharacteristic
913C2#7606311yescharacteristic
914C2#7608011yescharacteristic
915C2#7624411yescharacteristic
916C2#7624711yescharacteristic
917C2#7634711yescharacteristic
918C2#7645411yescharacteristic
919C2#7653711yescharacteristic
920C2#7663711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, prime radical, cosocleC24×C3C24
FittingC3×C4⋊#95C2
hypercenterC4⋊#95D3
hypocenterC3#15173
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
103. C2×C3×C42Q8semidirect
142. C2×C4×Dic3Q8semidirect
159. C3⋊#95Q8semidirect
160. C3⋊#95Q8semidirect
400. C2×C42Dic6semidirect
905. C3#15173semidirect

Maximal subgroups

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

subgroupindex
C2×#49822
C2×#49792
C2×#46572
C2×#46562
C2×#46462
C2×#46472
C3×C4⋊#952
#715682
#715352
C4×C3⋊#952
#694202
Dic3⋊#952
#151733