Finite Group Databasebeta

← #10723116

Subgroups — #10723116

Order 768.

1750 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#380C211yesmaximal, characteristic
2C2×#5210C211yesmaximal, characteristic
3C2×#5212C211yesmaximal, characteristic
4C2×#4976C211yesmaximal, characteristic, complemented
5C2×#4945C211yesmaximal, characteristic
6C2×#4944C211yesmaximal, characteristic
7C2×#4647C211yesmaximal, characteristic, complemented
8#71568C211yesmaximal, characteristic, complemented
9#71566C211yesmaximal, characteristic, complemented
10#71564C211yesmaximal, characteristic, complemented
11#71547C211yesmaximal, characteristic
12#71547C211yesmaximal, characteristic
13#69420C211yesmaximal, characteristic, complemented
14#69410C211yesmaximal, characteristic, complemented
15#69407C211yesmaximal, characteristic, complemented
16#14402—31nomaximal, Sylow
17C24×C3×C4C2211yescharacteristic
18C22×C3×C4⋊C4C2211yescharacteristic
19C22×C3×C4⋊C4C2211yescharacteristic
20C22×C3×C22⋊C4C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×#217C2211yescharacteristic
23C22×#217C2211yescharacteristic
24C22×#217C2211yescharacteristic
25C22×#217C2211yescharacteristic
26C22×C4⋊Dic3C2211yescharacteristic
27C22×C4⋊Dic3C2211yescharacteristic
28C22×Dic3⋊C4C2211yescharacteristic
29C22×Dic3⋊C4C2211yescharacteristic
30C22×Dic3⋊C4C2211yescharacteristic
31C22×Dic3⋊C4C2211yescharacteristic
32C22×Dic3⋊C4C2211yescharacteristic
33C22×Dic3⋊C4C2211yescharacteristic
34C22×C4×Dic3C2211yescharacteristic
35C22×C4×Dic3C2211yescharacteristic
36C3×#380—24no—
37C2×C3×#95C2211yescharacteristic
38C2×C3×#95C2211yescharacteristic
39#5212—24no—
40#5210C418yescomplemented
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×C3⋊#95C2211yescharacteristic
54C2×C3⋊#95C2211yescharacteristic
55#4976—24no—
56#4945—24no—
57#4944—24no—
58#4647—24no—
59C2×#389—31no—
60C2×#389—31no—
61C2×#388—31no—
62C2×#388—31no—
63C2×#385—31no—
64C2×#380—31no—
65C2×#380D311yescharacteristic
66#1444—31no—
67#1444—31no—
68#1441—31no—
69#1441—31no—
70#1439—31no—
71#1439—31no—
72#1436—31no—
73#1436—31no—
74C25×C3C2311yescharacteristic
75C23×C3×C4—22no—
76C23×C3×C4—22no—
77C23×C3×C4—22no—
78C23×C3×C4—22no—
79C23×C3×C4—41no—
80C23×C3×C4—41no—
81C23×C3×C4C2×C414yes—
82C23×C3×C4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C23×C3×C4C2311yescharacteristic
87C23×C3×C4C2311yescharacteristic
88C23×Dic3C2311yescharacteristic
89C23×Dic3C2311yescharacteristic
90C23×Dic3C2311yescharacteristic
91C23×Dic3C2311yescharacteristic
92C23×Dic3C2311yescharacteristic
93C23×Dic3C2311yescharacteristic
94C23×Dic3C2311yescharacteristic
95C23×Dic3C2311yescharacteristic
96C2×C3×C4⋊C4—22no—
97C2×C3×C4⋊C4—22no—
98C2×C3×C4⋊C4—22no—
99C2×C3×C4⋊C4—22no—
100C2×C3×C4⋊C4—41no—
101C2×C3×C4⋊C4—41no—
102C2×C3×C22⋊C4—22no—
103C2×C3×C22⋊C4—22no—
104C2×C3×C22⋊C4—22no—
105C2×C3×C22⋊C4—22no—
106C2×C3×C22⋊C4—41no—
107C2×C3×C22⋊C4—41no—
108C2×#217—22no—
109C2×#217—22no—
110C2×#217—22no—
111C2×#217—22no—
112C2×#217—41no—
113C2×#217—41no—
114C2×#217—41no—
115C2×#217—41no—
116C2×#217C2×C414yes—
117C2×#217C2×C414yes—
118C2×#217D414yes—
119C2×#217Q814yes—
120C2×C4⋊Dic3—22no—
121C2×C4⋊Dic3—22no—
122C2×C4⋊Dic3—22no—
123C2×C4⋊Dic3—22no—
124C2×C4⋊Dic3—41no—
125C2×C4⋊Dic3—41no—
126C2×Dic3⋊C4—22no—
127C2×Dic3⋊C4—22no—
128C2×Dic3⋊C4—22no—
129C2×Dic3⋊C4—22no—
130C2×Dic3⋊C4—22no—
131C2×Dic3⋊C4—22no—
132C2×Dic3⋊C4—22no—
133C2×Dic3⋊C4—22no—
134C2×Dic3⋊C4—22no—
135C2×Dic3⋊C4—22no—
136C2×Dic3⋊C4—41no—
137C2×Dic3⋊C4—41no—
138C2×Dic3⋊C4—41no—
139C2×Dic3⋊C4—41no—
140C2×Dic3⋊C4—41no—
141C2×Dic3⋊C4—41no—
142C2×Dic3⋊C4C2×C414yes—
143C2×Dic3⋊C4C2×C414yes—
144C2×C4×Dic3—22no—
145C2×C4×Dic3—22no—
146C2×C4×Dic3—22no—
147C2×C4×Dic3—22no—
148C2×C4×Dic3—41no—
149C2×C4×Dic3—41no—
150C3×#95—22no—
151C3×#95D414yes—
152C3⋊#95—22no—
153C3⋊#95—22no—
154C3⋊#95—22no—
155C3⋊#95—22no—
156C3⋊#95—22no—
157C3⋊#95—22no—
158C3⋊#95—22no—
159C3⋊#95—41no—
160C3⋊#95—41no—
161C3⋊#95—41no—
162C3⋊#95—41no—
163C3⋊#95C2×C414yes—
164C3⋊#95C2×C414yes—
165C3⋊#95D414yes—
166C24×C4C2×D311yescharacteristic
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⋊C4—31no—
174C22×C4⋊C4—31no—
175C22×C4⋊C4C2×D311yescharacteristic
176C22×C4⋊C4C2×D311yescharacteristic
177C22×C22⋊C4—31no—
178C22×C22⋊C4—31no—
179C22×C22⋊C4—31no—
180C22×C22⋊C4—31no—
181C22×C22⋊C4C2×D311yescharacteristic
182C22×C22⋊C4C2×D311yescharacteristic
183C22×C42—31no—
184C22×C42—31no—
185#389—64no—
186#389—64no—
187#388—64no—
188#388—64no—
189#385—38no—
190#380—24no—
191#380—64no—
192C2×#95—31no—
193C2×#95—31no—
194C2×#95—31no—
195C2×#95—31no—
196C2×#95—31no—
197C2×#95—31no—
198C2×#95—31no—
199C2×#95—31no—
200C2×#95—31no—
201C2×#95—31no—
202C2×#95—31no—
203C2×#95—31no—
204C2×#95—31no—
205C2×#95—31no—
206C2×#95C2×D311yescharacteristic
207C2×#95C2×D311yescharacteristic
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×C3C2×D412yes—
222C24×C3C2×Q812yes—
223C24×C3C2411yescharacteristic
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×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—28no—
245C22×C3×C4—28no—
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—44no—
261C22×C3×C4—44no—
262C22×C3×C4—44no—
263C22×C3×C4—44no—
264C22×C3×C4—44no—
265C22×C3×C4C22×C412yes—
266C22×C3×C4C22×C412yes—
267C22×C3×C4C2×D412yes—
268C22×C3×C4C2×D412yes—
269C22×C3×C4C2×D412yes—
270C22×C3×C4C2×D412yes—
271C22×C3×C4#4112yes—
272C22×C3×C4#4112yes—
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×Dic3—21no—
315C22×Dic3—21no—
316C22×Dic3—21no—
317C22×Dic3—21no—
318C22×Dic3—21no—
319C22×Dic3C22×C412yes—
320C22×Dic3C22×C412yes—
321C22×Dic3C22×C412yes—
322C22×Dic3C22×C412yes—
323C22×Dic3C2×D412yes—
324C22×Dic3C2×D412yes—
325C22×Dic3C2×D412yes—
326C22×Dic3C2×D412yes—
327C22×Dic3C2×Q812yes—
328C22×Dic3C2×Q812yes—
329C3×C4⋊C4—44no—
330C3×C4⋊C4—44no—
331C3×C22⋊C4—44no—
332C3×C22⋊C4—44no—
333#217—44no—
334#217—44no—
335#217—44no—
336#217C4⋊C4116yescomplemented
337C4⋊Dic3—44no—
338C4⋊Dic3—44no—
339Dic3⋊C4—28no—
340Dic3⋊C4—28no—
341Dic3⋊C4—44no—
342Dic3⋊C4—44no—
343Dic3⋊C4—44no—
344Dic3⋊C4—44no—
345C4×Dic3—44no—
346C4×Dic3—44no—
347C25C22×D311yescharacteristic
348C23×C4—22no—
349C23×C4—22no—
350C23×C4—22no—
351C23×C4—22no—
352C23×C4—31no—
353C23×C4—31no—
354C23×C4—31no—
355C23×C4—31no—
356C23×C4—31no—
357C23×C4—31no—
358C23×C4—31no—
359C23×C4—31no—
360C23×C4—41no—
361C23×C4—41no—
362C23×C4C4×D314yes—
363C23×C4C22×D311yescharacteristic
364C23×C4C22×D311yescharacteristic
365C23×C4C22×D311yescharacteristic
366C23×C4C22×D311yescharacteristic
367C23×C4C22×D311yescharacteristic
368C23×C4C22×D311yescharacteristic
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—34no—
374C2×C4⋊C4—34no—
375C2×C4⋊C4—41no—
376C2×C4⋊C4—41no—
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—62no—
385C2×C4⋊C4—62no—
386C2×C4⋊C4—62no—
387C2×C4⋊C4—62no—
388C2×C4⋊C4—62no—
389C2×C4⋊C4—62no—
390C2×C4⋊C4—62no—
391C2×C4⋊C4—121no—
392C2×C4⋊C4—121no—
393C2×C4⋊C4—121no—
394C2×C4⋊C4—121no—
395C2×C4⋊C4—121no—
396C2×C4⋊C4—121no—
397C2×C4⋊C4—121no—
398C2×C4⋊C4—121no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—34no—
404C2×C22⋊C4—34no—
405C2×C22⋊C4—34no—
406C2×C22⋊C4—34no—
407C2×C22⋊C4—41no—
408C2×C22⋊C4—41no—
409C2×C22⋊C4—62no—
410C2×C22⋊C4—62no—
411C2×C22⋊C4—62no—
412C2×C22⋊C4—62no—
413C2×C22⋊C4—121no—
414C2×C22⋊C4—121no—
415C2×C22⋊C4—121no—
416C2×C22⋊C4—121no—
417C2×C42—62no—
418C2×C42—62no—
419C2×C42—62no—
420C2×C42—62no—
421C2×C42—121no—
422C2×C42—121no—
423#95—22no—
424#95—34no—
425#95—34no—
426#95—34no—
427#95—62no—
428#95—62no—
429#95—62no—
430#95—62no—
431#95—62no—
432#95—62no—
433#95—62no—
434#95—121no—
435#95—121no—
436#95—121no—
437#95—121no—
438#95#6714yes—
439C23×C3—22no—
440C23×C3—22no—
441C23×C3—22no—
442C23×C3—22no—
443C23×C3—22no—
444C23×C3—22no—
445C23×C3—22no—
446C23×C3—22no—
447C23×C3—22no—
448C23×C3—22no—
449C23×C3—22no—
450C23×C3—22no—
451C23×C3—22no—
452C23×C3—22no—
453C23×C3—22no—
454C23×C3—22no—
455C23×C3—22no—
456C23×C3—22no—
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×C3C2×C4⋊C414yes—
474C23×C3C23×C411yescharacteristic
475C23×C3C22×D411yescharacteristic
476C23×C3C22×D411yescharacteristic
477C23×C3C22×D411yescharacteristic
478C23×C3C22×Q811yescharacteristic
479C23×C3C2×#4111yescharacteristic
480C23×C3C2×#4111yescharacteristic
481C23×C3H(5,𝔽2)11yescharacteristic
482C23×C3H(5,𝔽2)11yescharacteristic
483C23×C3H(5,𝔽2)11yescharacteristic
484C23×C3H(5,𝔽2)11yescharacteristic
485C23×C32−1+411yescharacteristic
486C23×C32−1+411yescharacteristic
487C23×C32−1+411yescharacteristic
488C23×C32−1+411yescharacteristic
489C2×C3×C4—22no—
490C2×C3×C4—22no—
491C2×C3×C4—22no—
492C2×C3×C4—22no—
493C2×C3×C4—22no—
494C2×C3×C4—22no—
495C2×C3×C4—22no—
496C2×C3×C4—22no—
497C2×C3×C4—22no—
498C2×C3×C4—22no—
499C2×C3×C4—22no—
500C2×C3×C4—22no—
501C2×C3×C4—22no—
502C2×C3×C4—22no—
503C2×C3×C4—22no—
504C2×C3×C4—22no—
505C2×C3×C4—22no—
506C2×C3×C4—22no—
507C2×C3×C4—416no—
508C2×C3×C4—41no—
509C2×C3×C4—41no—
510C2×C3×C4—41no—
511C2×C3×C4—41no—
512C2×C3×C4—41no—
513C2×C3×C4—41no—
514C2×C3×C4—41no—
515C2×C3×C4—41no—
516C2×C3×C4—41no—
517C2×C3×C4—41no—
518C2×C3×C4—41no—
519C2×C3×C4—41no—
520C2×C3×C4—41no—
521C2×C3×C4—41no—
522C2×C3×C4—41no—
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×C4C4×D414yes—
531C2×C3×C4C4×D414yes—
532C2×Dic3—22no—
533C2×Dic3—22no—
534C2×Dic3—22no—
535C2×Dic3—22no—
536C2×Dic3—22no—
537C2×Dic3—22no—
538C2×Dic3—22no—
539C2×Dic3—22no—
540C2×Dic3—22no—
541C2×Dic3—22no—
542C2×Dic3—22no—
543C2×Dic3—22no—
544C2×Dic3—22no—
545C2×Dic3—22no—
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—41no—
557C2×Dic3—41no—
558C2×Dic3—41no—
559C2×Dic3—41no—
560C2×Dic3—41no—
561C2×Dic3—41no—
562C2×Dic3—41no—
563C2×Dic3—41no—
564C2×Dic3—41no—
565C2×Dic3—41no—
566C2×Dic3—41no—
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×Dic3C2×C4⋊C414yes—
587C2×Dic3C2×C4⋊C414yes—
588C24—21no—
589C24—21no—
590C24—21no—
591C24—21no—
592C24—21no—
593C24—21no—
594C24—21no—
595C24—21no—
596C24—21no—
597C24—21no—
598C24—21no—
599C24—21no—
600C24C2×C4×D312yes—
601C24D3×D412yes—
602C24D3×Q812yes—
603C24C23×D311yescharacteristic
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—28no—
625C22×C4—28no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—32no—
641C22×C4—32no—
642C22×C4—32no—
643C22×C4—32no—
644C22×C4—32no—
645C22×C4—32no—
646C22×C4—32no—
647C22×C4—32no—
648C22×C4—32no—
649C22×C4—32no—
650C22×C4—44no—
651C22×C4—44no—
652C22×C4—44no—
653C22×C4—44no—
654C22×C4—44no—
655C22×C4—61no—
656C22×C4—61no—
657C22×C4—61no—
658C22×C4—61no—
659C22×C4—61no—
660C22×C4—61no—
661C22×C4—61no—
662C22×C4—61no—
663C22×C4—61no—
664C22×C4—61no—
665C22×C4—61no—
666C22×C4—61no—
667C22×C4—61no—
668C22×C4—61no—
669C22×C4—61no—
670C22×C4—61no—
671C22×C4—61no—
672C22×C4—61no—
673C22×C4—61no—
674C22×C4—61no—
675C22×C4—61no—
676C22×C4—61no—
677C22×C4—61no—
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×C4C2×C4×D312yes—
702C22×C4C2×C4×D312yes—
703C22×C4#23512yes—
704C22×C4D3×D412yes—
705C22×C4#23712yes—
706C22×C4C2×#6712yes—
707C22×C4C2×#6712yes—
708C22×C4C2×#6712yes—
709C4⋊C4—44no—
710C4⋊C4—44no—
711C4⋊C4—68no—
712C4⋊C4—68no—
713C4⋊C4—124no—
714C4⋊C4—124no—
715C4⋊C4—124no—
716C4⋊C4—124no—
717C4⋊C4—124no—
718C4⋊C4—124no—
719C22⋊C4—316no—
720C22⋊C4—44no—
721C22⋊C4—44no—
722C22⋊C4—124no—
723C22⋊C4—124no—
724C22⋊C4—124no—
725C42—124no—
726C42—124no—
727C22×C3—24no—
728C22×C3—24no—
729C22×C3—24no—
730C22×C3—42no—
731C22×C3—42no—
732C22×C3—42no—
733C22×C3—42no—
734C22×C3—42no—
735C22×C3—42no—
736C22×C3—42no—
737C22×C3—42no—
738C22×C3—42no—
739C22×C3—42no—
740C22×C3—42no—
741C22×C3—42no—
742C22×C3C22×C4⋊C411yescharacteristic
743C22×C3C2×C4×D411yescharacteristic
744C22×C3C2×C4×D411yescharacteristic
745C22×C3#51811yescharacteristic
746C22×C3#51911yescharacteristic
747C22×C3#52011yescharacteristic
748C22×C3#52011yescharacteristic
749C22×C3#53611yescharacteristic
750C22×C3#53611yescharacteristic
751C22×C3#53711yescharacteristic
752C22×C3#53711yescharacteristic
753C22×C3#53711yescharacteristic
754C22×C3#53711yescharacteristic
755C22×C3#54111yescharacteristic
756C22×C3#54111yescharacteristic
757C22×C3#54211yescharacteristic
758C22×C3#54211yescharacteristic
759C22×C3#54411yescharacteristic
760C22×C3#54411yescharacteristic
761C22×C3D4211yescharacteristic
762C22×C3D4211yescharacteristic
763C22×C3D4211yescharacteristic
764C22×C3#54611yescharacteristic
765C22×C3#54611yescharacteristic
766C22×C3#54711yescharacteristic
767C22×C3#54711yescharacteristic
768C22×C3D4×Q811yescharacteristic
769C22×C3D4×Q811yescharacteristic
770C22×C3#55111yescharacteristic
771C22×C3#55411yescharacteristic
772C22×C3#55411yescharacteristic
773C22×C3#56011yescharacteristic
774C22×C3#56211yescharacteristic
775C22×C3#56211yescharacteristic
776C22×C3#56311yescharacteristic
777C3×C4—24no—
778C3×C4—24no—
779C3×C4—42no—
780C3×C4—42no—
781C3×C4—81no—
782C3×C4—81no—
783Dic3—24no—
784Dic3—24no—
785Dic3—42no—
786Dic3—42no—
787Dic3—42no—
788Dic3—42no—
789Dic3—81no—
790Dic3—81no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23D3×C4⋊C414yes—
826C23C22×C4×D311yescharacteristic
827C23C2×#23511yescharacteristic
828C23C2×D3×D411yescharacteristic
829C23C2×D3×D411yescharacteristic
830C23C2×#23711yescharacteristic
831C23#100411yescharacteristic
832C23#100411yescharacteristic
833C23#100411yescharacteristic
834C23C2×D3×Q811yescharacteristic
835C23#100711yescharacteristic
836C23#100911yescharacteristic
837C23#101011yescharacteristic
838C23#101011yescharacteristic
839C23#101011yescharacteristic
840C23C22×#6711yescharacteristic
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—34no—
860C2×C4—34no—
861C2×C4—416no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—62no—
885C2×C4—62no—
886C2×C4—62no—
887C2×C4—62no—
888C2×C4—62no—
889C2×C4—62no—
890C2×C4—62no—
891C2×C4—62no—
892C2×C4—62no—
893C2×C4—62no—
894C2×C4—62no—
895C2×C4—62no—
896C2×C4—62no—
897C2×C4—62no—
898C2×C4—62no—
899C2×C4—62no—
900C2×C4—62no—
901C2×C4—62no—
902C2×C4—62no—
903C2×C4—62no—
904C2×C4—62no—
905C2×C4—62no—
906C2×C4—62no—
907C2×C4—62no—
908C2×C4—121no—
909C2×C4—121no—
910C2×C4—121no—
911C2×C4—121no—
912C2×C4—121no—
913C2×C4—121no—
914C2×C4—121no—
915C2×C4—121no—
916C2×C4—121no—
917C2×C4—121no—
918C2×C4—121no—
919C2×C4—121no—
920C2×C4—121no—
921C2×C4—121no—
922C2×C4—121no—
923C2×C4—121no—
924C2×C4—121no—
925C2×C4—121no—
926C2×C4—121no—
927C2×C4—121no—
928C2×C4—121no—
929C2×C4—121no—
930C2×C4—121no—
931C2×C4—121no—
932C2×C4—121no—
933C2×C4—121no—
934C2×C4—121no—
935C2×C4—121no—
936C2×C4—121no—
937C2×C4—121no—
938C2×C4#67⋊C414yes—
939C2×C4C4×#6714yes—
940C2×C3—44no—
941C2×C3#231611yescharacteristic
942C2×C3#232311yescharacteristic
943C2×C3#232311yescharacteristic
944C2×C3D4×C4⋊C411yescharacteristic
945C2×C3D4×C4⋊C411yescharacteristic
946C2×C3#235811yescharacteristic
947C2×C3#237611yescharacteristic
948C2×C3#267211yescharacteristic
949C2×C3#267211yescharacteristic
950C2×C3#267511yescharacteristic
951C2×C3#267711yescharacteristic
952C2×C3#270411yescharacteristic
953C2×C3#270411yescharacteristic
954C2×C3#272211yescharacteristic
955C2×C3#274211yescharacteristic
956C22—24no—
957C22—24no—
958C22—24no—
959C22—42no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—42no—
968C22—42no—
969C22—42no—
970C22—42no—
971C22C2×#67⋊C411yescharacteristic
972C22#548611yescharacteristic
973C22#549011yescharacteristic
974C22#549511yescharacteristic
975C22C2×D3×C4⋊C411yescharacteristic
976C22#550411yescharacteristic
977C22#550711yescharacteristic
978C22#551111yescharacteristic
979C22#551611yescharacteristic
980C22#551811yescharacteristic
981C22#552311yescharacteristic
982C22#553411yescharacteristic
983C22#559711yescharacteristic
984C22#559711yescharacteristic
985C22#560311yescharacteristic
986C22#560811yescharacteristic
987C22#560911yescharacteristic
988C22#561111yescharacteristic
989C22#562011yescharacteristic
990C22#562111yescharacteristic
991C22#562311yescharacteristic
992C22#562311yescharacteristic
993C22#562511yescharacteristic
994C22#562811yescharacteristic
995C22#563211yescharacteristic
996C22#563511yescharacteristic
997C22#564611yescharacteristic
998C22#564711yescharacteristic
999C22C2×C4×#6711yescharacteristic
1000C22D4×#6711yescharacteristic
1001C22D4×#6711yescharacteristic
1002C22#580611yescharacteristic
1003C22Q8×#6711yescharacteristic
1004C22#582511yescharacteristic
1005C22#583311yescharacteristic
1006C4—24no—
1007C4—24no—
1008C4—42no—
1009C4—42no—
1010C4—64no—
1011C4—64no—
1012C4—81no—
1013C4—81no—
1014C4—122no—
1015C4—122no—
1016C4—122no—
1017C4—122no—
1018C4—241no—
1019C4—241no—
1020C3#1440211yescharacteristic, complemented, Sylow
1021C2—44no—
1022C2#7386911yescharacteristic
1023C2#7387111yescharacteristic
1024C2#7396711yescharacteristic
1025C2#7397211yescharacteristic
1026C2#7397911yescharacteristic
1027C2#7401011yescharacteristic
1028C2#7401311yescharacteristic
1029C2#7403611yescharacteristic
1030C2#8209911yescharacteristic
1031C2C4⋊C4×#6711yescharacteristic
1032C2#8223511yescharacteristic
1033C2#8268211yescharacteristic
1034C2#8271811yescharacteristic
1035C2#8279111yescharacteristic
1036C2#8280211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC2×C3×#380C2
socle, cosocleC24×C3C24
prime radicalC25×C3C23
hypercenterC2×#380D3
hypocenterC3#14402
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
4. C2×#4976C2semidirect
7. C2×#4647C2semidirect
8. #71568C2semidirect
9. #71566C2semidirect
10. #71564C2semidirect
13. #69420C2semidirect
14. #69410C2semidirect
15. #69407C2semidirect
40. #5210C4semidirect
336. #217C4⋊C4semidirect
1020. C3#14402semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#3802
C2×#52102
C2×#52122
C2×#49762
C2×#49452
C2×#49442
C2×#46472
#715682
#715662
#715642
#715472
#694202
#694102
#694072
#144023