Finite Group Databasebeta

← #10719422

Subgroups — #10719422

Order 768.

1962 conjugacy classes of subgroups.

The subgroup lattice has 1158 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×C22⋊C4C211yesmaximal, characteristic, complemented
2C2×#5213C211yesmaximal, characteristic
3C2×#4957C211yesmaximal, characteristic
4C2×#4940C211yesmaximal, characteristic, complemented
5C2×#4932C211yesmaximal, characteristic, complemented
6#72127C211yesmaximal, characteristic, complemented
7#71550C211yesmaximal, characteristic
8#71547C211yesmaximal, characteristic, complemented
9#71545C211yesmaximal, characteristic, complemented
10#71537C211yesmaximal, characteristic, complemented
11#71536C211yesmaximal, characteristic, complemented
12#69429C211yesmaximal, characteristic, complemented
13#69409C211yesmaximal, characteristic, complemented
14#69408C211yesmaximal, characteristic, complemented
15#69403C211yesmaximal, characteristic, complemented
16#14082—31nomaximal, Sylow
17C24×C3×C4C2211yescharacteristic
18C23×#67C2211yescharacteristic
19C22×C3×C22⋊C4C2211yescharacteristic
20C22×C3×C22⋊C4C2211yescharacteristic
21C22×C3×C42C2211yescharacteristic
22C22×C3×C42C2211yescharacteristic
23C22×#217C2211yescharacteristic
24C22×#217C2211yescharacteristic
25C22×#217C2211yescharacteristic
26C22×(C2×D3)⋊C4C2211yescharacteristic
27C22×(C2×D3)⋊C4C2211yescharacteristic
28C22×(C2×D3)⋊C4C2211yescharacteristic
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×(C2×D3)⋊C4C2211yescharacteristic
31C22×(C2×D3)⋊C4C2211yescharacteristic
32C22×Dic3⋊C4C2211yescharacteristic
33C22×Dic3⋊C4C2211yescharacteristic
34C22×C4×Dic3C2211yescharacteristic
35C22×C4×Dic3C2211yescharacteristic
36C3×C4×C22⋊C4—24no—
37C2×C3×#95C2211yescharacteristic
38C2×C3×#95C2211yescharacteristic
39#5213—24no—
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×C3⋊#95C2211yescharacteristic
54#4957C418yescomplemented
55#4940—24no—
56#4932—24no—
57C2×#390—31no—
58C2×#388—31no—
59C2×#386—31no—
60C2×C4×C22⋊C4D311yescharacteristic, complemented
61C2×#376—31no—
62#1441—31no—
63#1440—31no—
64#1439—31no—
65#1438—31no—
66#1437—31no—
67#1437—31no—
68#1437—31no—
69#1436—31no—
70#1434—31no—
71C22⋊#95—31no—
72C25×C3C2311yescharacteristic
73C24×D3C2311yescharacteristic
74C23×C3×C4—22no—
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×C4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C23×C3×C4C2311yescharacteristic
87C22×#67—22no—
88C22×#67—22no—
89C22×#67—22no—
90C22×#67—22no—
91C22×#67—41no—
92C22×#67—41no—
93C22×#67C2×C414yes—
94C23×Dic3C2311yescharacteristic
95C23×Dic3C2311yescharacteristic
96C23×Dic3C2311yescharacteristic
97C23×Dic3C2311yescharacteristic
98C23×Dic3C2311yescharacteristic
99C23×Dic3C2311yescharacteristic
100C23×Dic3C2311yescharacteristic
101C2×C3×C22⋊C4—22no—
102C2×C3×C22⋊C4—22no—
103C2×C3×C22⋊C4—22no—
104C2×C3×C22⋊C4—22no—
105C2×C3×C22⋊C4—22no—
106C2×C3×C22⋊C4C2×C414yes—
107C2×C3×C42—22no—
108C2×C3×C42—22no—
109C2×C3×C42—22no—
110C2×C3×C42—41no—
111C2×C3×C42—41no—
112C2×C3×C42D414yescomplemented
113C2×#217—22no—
114C2×#217—22no—
115C2×#217—22no—
116C2×#217—22no—
117C2×#217—41no—
118C2×#217—41no—
119C2×#217—41no—
120C2×#217—41no—
121C2×#217C2×C414yes—
122C2×(C2×D3)⋊C4—22no—
123C2×(C2×D3)⋊C4—22no—
124C2×(C2×D3)⋊C4—22no—
125C2×(C2×D3)⋊C4—22no—
126C2×(C2×D3)⋊C4—22no—
127C2×(C2×D3)⋊C4—22no—
128C2×(C2×D3)⋊C4—22no—
129C2×(C2×D3)⋊C4—22no—
130C2×(C2×D3)⋊C4—22no—
131C2×(C2×D3)⋊C4—22no—
132C2×(C2×D3)⋊C4—41no—
133C2×(C2×D3)⋊C4—41no—
134C2×(C2×D3)⋊C4—41no—
135C2×(C2×D3)⋊C4—41no—
136C2×(C2×D3)⋊C4—41no—
137C2×(C2×D3)⋊C4—41no—
138C2×(C2×D3)⋊C4C2×C414yescomplemented
139C2×(C2×D3)⋊C4C2×C414yescomplemented
140C2×Dic3⋊C4—22no—
141C2×Dic3⋊C4—41no—
142C2×Dic3⋊C4—41no—
143C2×Dic3⋊C4—41no—
144C2×Dic3⋊C4—41no—
145C2×Dic3⋊C4C2×C414yescomplemented
146C2×C4×Dic3—22no—
147C2×C4×Dic3—22no—
148C2×C4×Dic3—22no—
149C2×C4×Dic3—22no—
150C2×C4×Dic3—22no—
151C2×C4×Dic3C2×C414yescomplemented
152C3×#95—22no—
153C3×#95—22no—
154C3⋊#95—22no—
155C3⋊#95—22no—
156C3⋊#95—22no—
157C3⋊#95—22no—
158C3⋊#95—22no—
159C3⋊#95—22no—
160C3⋊#95—22no—
161C3⋊#95—22no—
162C3⋊#95—22no—
163C3⋊#95—41no—
164C3⋊#95—41no—
165C3⋊#95—41no—
166C3⋊#95—41no—
167C3⋊#95D414yes—
168C23×D4—31no—
169C24×C4C2×D311yescharacteristic
170C22×C4⋊C4—31no—
171C22×C4⋊C4—31no—
172C22×C22⋊C4—31no—
173C22×C22⋊C4—31no—
174C22×C22⋊C4—31no—
175C22×C22⋊C4—31no—
176C22×C22⋊C4—31no—
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—
185C22×C42C2×D311yescharacteristic
186C22×C42C2×D311yescharacteristic
187#390—38no—
188#388—64no—
189#386—64no—
190C4×C22⋊C4—24no—
191#376—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×C3#4112yes—
222C24×C3#4112yes—
223C24×C3C2411yescharacteristic
224C23×D3—21no—
225C23×D3—21no—
226C23×D3—21no—
227C23×D3—21no—
228C23×D3—21no—
229C23×D3—21no—
230C23×D3—21no—
231C23×D3—21no—
232C23×D3—21no—
233C23×D3—21no—
234C23×D3—21no—
235C23×D3—21no—
236C23×D3—21no—
237C23×D3—21no—
238C23×D3C22×C412yes—
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—28no—
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×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—21no—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—44no—
273C22×C3×C4—44no—
274C22×C3×C4—44no—
275C22×C3×C4—44no—
276C22×C3×C4—44no—
277C22×C3×C4—44no—
278C22×C3×C4C22×C412yes—
279C22×C3×C4C22×C412yes—
280C22×C3×C4C2×D412yes—
281C22×C3×C4C2×D412yes—
282C22×C3×C4C2×D412yes—
283C22×C3×C4C2×D412yes—
284C22×C3×C4#4112yes—
285C22×C3×C4#4112yes—
286C22×C3×C4#4112yes—
287C22×C3×C4#4112yes—
288C2×#67—28no—
289C2×#67—28no—
290C2×#67—44no—
291C2×#67—44no—
292C2×#67—44no—
293C2×#67—44no—
294C2×#67—44no—
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×Dic3—21no—
320C22×Dic3—21no—
321C22×Dic3—21no—
322C22×Dic3—21no—
323C22×Dic3—21no—
324C22×Dic3—21no—
325C22×Dic3—21no—
326C22×Dic3—21no—
327C22×Dic3—21no—
328C22×Dic3—21no—
329C22×Dic3—21no—
330C22×Dic3—21no—
331C22×Dic3—21no—
332C22×Dic3—21no—
333C22×Dic3—21no—
334C22×Dic3—21no—
335C22×Dic3—21no—
336C22×Dic3—21no—
337C22×Dic3C22×C412yes—
338C22×Dic3C22×C412yes—
339C22×Dic3C22×C412yes—
340C22×Dic3C2×D412yes—
341C22×Dic3C2×D412yes—
342C22×Dic3#4112yes—
343C22×Dic3#4112yes—
344C3×C22⋊C4—28no—
345C3×C22⋊C4—28no—
346C3×C42—28no—
347C3×C42—44no—
348#217—44no—
349#217—44no—
350#217—44no—
351(C2×D3)⋊C4—28no—
352(C2×D3)⋊C4—44no—
353(C2×D3)⋊C4—44no—
354(C2×D3)⋊C4—44no—
355(C2×D3)⋊C4—44no—
356(C2×D3)⋊C4—44no—
357Dic3⋊C4—44no—
358Dic3⋊C4—44no—
359C4×Dic3—28no—
360C4×Dic3—28no—
361C25—31no—
362C25C22×D311yescharacteristic
363C22×D4—34no—
364C22×D4—62no—
365C22×D4—62no—
366C22×D4—62no—
367C22×D4—62no—
368C22×D4—121no—
369C22×D4—121no—
370C23×C4—22no—
371C23×C4—22no—
372C23×C4—22no—
373C23×C4—22no—
374C23×C4—22no—
375C23×C4—31no—
376C23×C4—31no—
377C23×C4—31no—
378C23×C4—31no—
379C23×C4—31no—
380C23×C4—31no—
381C23×C4—31no—
382C23×C4—41no—
383C23×C4—41no—
384C23×C4C22×D311yescharacteristic
385C23×C4C22×D311yescharacteristic
386C23×C4C22×D311yescharacteristic
387C23×C4C22×D311yescharacteristic
388C23×C4C22×D311yescharacteristic
389C23×C4C22×D311yescharacteristic
390C2×C4⋊C4—34no—
391C2×C4⋊C4—62no—
392C2×C4⋊C4—121no—
393C2×C4⋊C4—121no—
394C2×C4⋊C4—121no—
395C2×C4⋊C4—121no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—34no—
402C2×C22⋊C4—34no—
403C2×C22⋊C4—34no—
404C2×C22⋊C4—62no—
405C2×C22⋊C4—62no—
406C2×C22⋊C4—62no—
407C2×C22⋊C4—62no—
408C2×C22⋊C4—62no—
409C2×C22⋊C4—62no—
410C2×C22⋊C4—62no—
411C2×C22⋊C4—62no—
412C2×C22⋊C4—62no—
413C2×C22⋊C4—62no—
414C2×C22⋊C4—62no—
415C2×C22⋊C4—62no—
416C2×C22⋊C4—62no—
417C2×C22⋊C4—62no—
418C2×C22⋊C4—121no—
419C2×C22⋊C4—121no—
420C2×C22⋊C4—121no—
421C2×C22⋊C4—121no—
422C2×C22⋊C4—121no—
423C2×C22⋊C4—121no—
424C2×C22⋊C4—121no—
425C2×C22⋊C4—121no—
426C2×C22⋊C4—121no—
427C2×C22⋊C4—121no—
428C2×C22⋊C4C4×D314yes—
429C2×C42—22no—
430C2×C42—22no—
431C2×C42—22no—
432C2×C42—34no—
433C2×C42—41no—
434C2×C42—41no—
435C2×C42—62no—
436C2×C42—62no—
437C2×C42—62no—
438C2×C42—62no—
439C2×C42—62no—
440C2×C42#6714yescomplemented
441#95—22no—
442#95—22no—
443#95—34no—
444#95—62no—
445#95—62no—
446#95—62no—
447#95—62no—
448#95—62no—
449#95—62no—
450#95—62no—
451#95—62no—
452#95—62no—
453#95—121no—
454#95—121no—
455#95—121no—
456#95—121no—
457C23×C3—22no—
458C23×C3—22no—
459C23×C3—22no—
460C23×C3—22no—
461C23×C3—22no—
462C23×C3—22no—
463C23×C3—22no—
464C23×C3—22no—
465C23×C3—22no—
466C23×C3—22no—
467C23×C3—22no—
468C23×C3—22no—
469C23×C3—22no—
470C23×C3—22no—
471C23×C3—22no—
472C23×C3—22no—
473C23×C3—22no—
474C23×C3—22no—
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#11714yes—
492C23×C3C23×C411yescharacteristic
493C23×C3C22×D411yescharacteristic
494C23×C3C22×D411yescharacteristic
495C23×C3C2×#4111yescharacteristic
496C23×C3C2×#4111yescharacteristic
497C23×C3C2×#4111yescharacteristic
498C23×C3C2×#4111yescharacteristic
499C23×C3C2×#4111yescharacteristic
500C23×C3C2×#4111yescharacteristic
501C23×C3C2×#4111yescharacteristic
502C23×C3C2×#4111yescharacteristic
503C23×C3H(5,𝔽2)11yescharacteristic
504C23×C3H(5,𝔽2)11yescharacteristic
505C23×C3H(5,𝔽2)11yescharacteristic
506C23×C3H(5,𝔽2)11yescharacteristic
507C22×D3—22no—
508C22×D3—22no—
509C22×D3—22no—
510C22×D3—22no—
511C22×D3—22no—
512C22×D3—22no—
513C22×D3—22no—
514C22×D3—41no—
515C22×D3—41no—
516C22×D3—41no—
517C22×D3—41no—
518C22×D3—41no—
519C22×D3—41no—
520C22×D3—41no—
521C22×D3—41no—
522C22×D3—41no—
523C22×D3—41no—
524C22×D3—41no—
525C22×D3—41no—
526C22×D3—41no—
527C22×D3—41no—
528C22×D3—41no—
529C22×D3—41no—
530C22×D3—41no—
531C22×D3—41no—
532C22×D3—41no—
533C22×D3—41no—
534C22×D3—41no—
535C22×D3—41no—
536C22×D3—41no—
537C22×D3—41no—
538C22×D3—41no—
539C22×D3—41no—
540C22×D3—41no—
541C22×D3—41no—
542C2×C3×C4—22no—
543C2×C3×C4—22no—
544C2×C3×C4—22no—
545C2×C3×C4—22no—
546C2×C3×C4—22no—
547C2×C3×C4—22no—
548C2×C3×C4—22no—
549C2×C3×C4—22no—
550C2×C3×C4—22no—
551C2×C3×C4—22no—
552C2×C3×C4—22no—
553C2×C3×C4—22no—
554C2×C3×C4—22no—
555C2×C3×C4—22no—
556C2×C3×C4—22no—
557C2×C3×C4—22no—
558C2×C3×C4—22no—
559C2×C3×C4—22no—
560C2×C3×C4—22no—
561C2×C3×C4—22no—
562C2×C3×C4—22no—
563C2×C3×C4—22no—
564C2×C3×C4—22no—
565C2×C3×C4—22no—
566C2×C3×C4—416no—
567C2×C3×C4—41no—
568C2×C3×C4—41no—
569C2×C3×C4—41no—
570C2×C3×C4—41no—
571C2×C3×C4—41no—
572C2×C3×C4—41no—
573C2×C3×C4—41no—
574C2×C3×C4—41no—
575C2×C3×C4—41no—
576C2×C3×C4—41no—
577C2×C3×C4—41no—
578C2×C3×C4—41no—
579C2×C3×C4—41no—
580C2×C3×C4—41no—
581C2×C3×C4—41no—
582C2×C3×C4—41no—
583C2×C3×C4C4×D414yes—
584C2×C3×C4#12114yes—
585#67—416no—
586C2×Dic3—22no—
587C2×Dic3—22no—
588C2×Dic3—22no—
589C2×Dic3—22no—
590C2×Dic3—22no—
591C2×Dic3—22no—
592C2×Dic3—22no—
593C2×Dic3—22no—
594C2×Dic3—22no—
595C2×Dic3—22no—
596C2×Dic3—22no—
597C2×Dic3—22no—
598C2×Dic3—22no—
599C2×Dic3—22no—
600C2×Dic3—22no—
601C2×Dic3—22no—
602C2×Dic3—22no—
603C2×Dic3—22no—
604C2×Dic3—41no—
605C2×Dic3—41no—
606C2×Dic3—41no—
607C2×Dic3—41no—
608C2×Dic3—41no—
609C2×Dic3—41no—
610C2×Dic3—41no—
611C2×Dic3—41no—
612C2×Dic3—41no—
613C2×Dic3—41no—
614C2×Dic3—41no—
615C2×Dic3—41no—
616C2×Dic3—41no—
617C2×Dic3—41no—
618C2×Dic3—41no—
619C2×Dic3—41no—
620C2×Dic3—41no—
621C2×Dic3—41no—
622C2×Dic3—41no—
623C2×Dic3—41no—
624C2×Dic3—41no—
625C2×Dic3—41no—
626C2×Dic3—41no—
627C2×Dic3—41no—
628C2×Dic3—41no—
629C2×Dic3—41no—
630C2×Dic3—41no—
631C2×Dic3—41no—
632C2×Dic3—41no—
633C2×Dic3—41no—
634C2×Dic3C4×D414yes—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—32no—
648C24—61no—
649C24—61no—
650C24—61no—
651C24—61no—
652C24—61no—
653C24—61no—
654C24—61no—
655C24—61no—
656C24—61no—
657C24—61no—
658C24—61no—
659C24—61no—
660C24—61no—
661C24—61no—
662C24C2×C4×D312yes—
663C24#23512yes—
664C24#23512yes—
665C24C23×D311yescharacteristic
666C2×D4—68no—
667C2×D4—68no—
668C2×D4—124no—
669C2×D4—124no—
670C2×D4—124no—
671C2×D4—124no—
672C2×D4—124no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—28no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—32no—
707C22×C4—32no—
708C22×C4—32no—
709C22×C4—32no—
710C22×C4—32no—
711C22×C4—32no—
712C22×C4—32no—
713C22×C4—44no—
714C22×C4—44no—
715C22×C4—44no—
716C22×C4—44no—
717C22×C4—44no—
718C22×C4—44no—
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×C4—61no—
728C22×C4—61no—
729C22×C4—61no—
730C22×C4—61no—
731C22×C4—61no—
732C22×C4—61no—
733C22×C4—61no—
734C22×C4—61no—
735C22×C4—61no—
736C22×C4—61no—
737C22×C4—61no—
738C22×C4—61no—
739C22×C4—61no—
740C22×C4—61no—
741C22×C4—61no—
742C22×C4—61no—
743C22×C4—61no—
744C22×C4—61no—
745C22×C4—61no—
746C22×C4—61no—
747C22×C4—61no—
748C22×C4—61no—
749C22×C4—61no—
750C22×C4—61no—
751C22×C4—61no—
752C22×C4—61no—
753C22×C4—61no—
754C22×C4—61no—
755C22×C4—61no—
756C22×C4—61no—
757C22×C4—61no—
758C22×C4—61no—
759C22×C4—61no—
760C22×C4—61no—
761C22×C4C2×C4×D312yes—
762C22×C4C2×C4×D312yes—
763C22×C4#23512yes—
764C22×C4#23512yes—
765C22×C4#23512yes—
766C22×C4D3×D412yes—
767C22×C4#23712yes—
768C22×C4C2×#6712yes—
769C22×C4C2×#6712yes—
770C22×C4C2×#6712yes—
771C4⋊C4—124no—
772C4⋊C4—124no—
773C22⋊C4—28no—
774C22⋊C4—28no—
775C22⋊C4—68no—
776C22⋊C4—124no—
777C22⋊C4—124no—
778C22⋊C4—124no—
779C22⋊C4—124no—
780C22⋊C4—124no—
781C22⋊C4—124no—
782C22⋊C4—124no—
783C22⋊C4—124no—
784C42—28no—
785C42—44no—
786C42—68no—
787C42—68no—
788C22×C3—24no—
789C22×C3—24no—
790C22×C3—24no—
791C22×C3—42no—
792C22×C3—42no—
793C22×C3—42no—
794C22×C3—42no—
795C22×C3—42no—
796C22×C3—42no—
797C22×C3—42no—
798C22×C3—42no—
799C22×C3—42no—
800C22×C3—42no—
801C22×C3—42no—
802C22×C3—42no—
803C22×C3C2×#11711yescharacteristic
804C22×C3C2×C4×D411yescharacteristic
805C22×C3C2×C4×D411yescharacteristic
806C22×C3C4×#4111yescharacteristic
807C22×C3C4×#4111yescharacteristic
808C22×C3#51811yescharacteristic
809C22×C3#51811yescharacteristic
810C22×C3C2×#12111yescharacteristic
811C22×C3#52511yescharacteristic
812C22×C3#52511yescharacteristic
813C22×C3#52511yescharacteristic
814C22×C3#52911yescharacteristic
815C22×C3#52911yescharacteristic
816C22×C3#52911yescharacteristic
817C22×C3#53211yescharacteristic
818C22×C3#53511yescharacteristic
819C22×C3#53511yescharacteristic
820C22×C3#54011yescharacteristic
821C22×C3#54011yescharacteristic
822C22×C3#54611yescharacteristic
823C22×C3#54611yescharacteristic
824C22×C3#54611yescharacteristic
825C22×C3#55011yescharacteristic
826C22×C3#55111yescharacteristic
827C22×C3#55111yescharacteristic
828C22×C3#55111yescharacteristic
829C22×C3#55111yescharacteristic
830C22×C3#55111yescharacteristic
831C22×C3#55111yescharacteristic
832C22×C3#55311yescharacteristic
833C22×C3#55311yescharacteristic
834C22×C3#55311yescharacteristic
835C22×C3#55511yescharacteristic
836C22×C3#55511yescharacteristic
837C22×C3#55511yescharacteristic
838C2×D3—42no—
839C2×D3—42no—
840C2×D3—42no—
841C2×D3—42no—
842C2×D3—42no—
843C2×D3—42no—
844C2×D3—42no—
845C2×D3—81no—
846C2×D3—81no—
847C2×D3—81no—
848C2×D3—81no—
849C2×D3—81no—
850C2×D3—81no—
851C2×D3—81no—
852C2×D3—81no—
853C3×C4—24no—
854C3×C4—24no—
855C3×C4—42no—
856C3×C4—42no—
857C3×C4—42no—
858C3×C4—42no—
859Dic3—24no—
860Dic3—42no—
861Dic3—42no—
862Dic3—42no—
863Dic3—42no—
864Dic3—81no—
865Dic3—81no—
866C23—22no—
867C23—22no—
868C23—22no—
869C23—22no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—22no—
874C23—22no—
875C23—22no—
876C23—22no—
877C23—22no—
878C23—22no—
879C23—22no—
880C23—22no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—41no—
885C23—41no—
886C23—41no—
887C23—41no—
888C23—41no—
889C23—41no—
890C23—41no—
891C23—41no—
892C23—41no—
893C23—41no—
894C23—41no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—62no—
901C23—62no—
902C23—62no—
903C23—62no—
904C23—62no—
905C23—62no—
906C23—62no—
907C23—121no—
908C23—121no—
909C23—121no—
910C23—121no—
911C23—121no—
912C23—121no—
913C23—121no—
914C23—121no—
915C23—121no—
916C23—121no—
917C23—121no—
918C23—121no—
919C23—121no—
920C23—121no—
921C23—121no—
922C23—121no—
923C23—121no—
924C23—121no—
925C23—121no—
926C23—121no—
927C23—121no—
928C23—121no—
929C23—121no—
930C23—121no—
931C23—121no—
932C23—121no—
933C23—121no—
934C23—121no—
935C23#87214yes—
936C23C22×C4×D311yescharacteristic
937C23C2×#23511yescharacteristic
938C23C2×#23511yescharacteristic
939C23C2×#23511yescharacteristic
940C23C2×#23511yescharacteristic
941C23C2×#23511yescharacteristic
942C23C2×D3×D411yescharacteristic
943C23C2×#23711yescharacteristic
944C23#100411yescharacteristic
945C23#100411yescharacteristic
946C23D3×#4111yescharacteristic
947C23D3×#4111yescharacteristic
948C23#100911yescharacteristic
949C23#100911yescharacteristic
950C23C22×#6711yescharacteristic
951D4—1216no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—34no—
977C2×C4—416no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—62no—
995C2×C4—62no—
996C2×C4—62no—
997C2×C4—62no—
998C2×C4—62no—
999C2×C4—62no—
1000C2×C4—62no—
1001C2×C4—62no—
1002C2×C4—62no—
1003C2×C4—62no—
1004C2×C4—62no—
1005C2×C4—62no—
1006C2×C4—62no—
1007C2×C4—62no—
1008C2×C4—62no—
1009C2×C4—62no—
1010C2×C4—62no—
1011C2×C4—62no—
1012C2×C4—121no—
1013C2×C4—121no—
1014C2×C4—121no—
1015C2×C4—121no—
1016C2×C4—121no—
1017C2×C4—121no—
1018C2×C4—121no—
1019C2×C4—121no—
1020C2×C4—121no—
1021C2×C4—121no—
1022C2×C4—121no—
1023C2×C4—121no—
1024C2×C4—121no—
1025C2×C4—121no—
1026C2×C4—121no—
1027C2×C4—121no—
1028C2×C4—121no—
1029C2×C4—121no—
1030C2×C4—121no—
1031C2×C4—121no—
1032C2×C4—121no—
1033C2×C4—121no—
1034C2×C4—121no—
1035C2×C4—121no—
1036C2×C4—121no—
1037C2×C4—121no—
1038C2×C4—121no—
1039C2×C4—121no—
1040C2×C4—121no—
1041C2×C4—121no—
1042C2×C4C4×#6714yes—
1043C2×C4#93914yes—
1044C2×C3—44no—
1045C2×C3#229011yescharacteristic
1046C2×C3C4×#12111yescharacteristic
1047C2×C3#232811yescharacteristic
1048C2×C3#234211yescharacteristic
1049C2×C3#235311yescharacteristic
1050C2×C3#236311yescharacteristic
1051C2×C3#237211yescharacteristic
1052C2×C3#241111yescharacteristic
1053C2×C3#241411yescharacteristic
1054C2×C3#247111yescharacteristic
1055C2×C3#247611yescharacteristic
1056C2×C3#252611yescharacteristic
1057C2×C3#253111yescharacteristic
1058C2×C3#260311yescharacteristic
1059C2×C3#261011yescharacteristic
1060D3—82no—
1061C22—24no—
1062C22—24no—
1063C22—24no—
1064C22—42no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22—42no—
1070C22—42no—
1071C22—42no—
1072C22—42no—
1073C22—42no—
1074C22—42no—
1075C22—42no—
1076C22—122no—
1077C22—122no—
1078C22—122no—
1079C22—122no—
1080C22—122no—
1081C22—122no—
1082C22—122no—
1083C22—241no—
1084C22—241no—
1085C22—241no—
1086C22—241no—
1087C22—241no—
1088C22—241no—
1089C22—241no—
1090C22—241no—
1091C22C2×#87211yescharacteristic
1092C22C4×#23511yescharacteristic
1093C22#547911yescharacteristic
1094C22#547911yescharacteristic
1095C22#549011yescharacteristic
1096C22#549011yescharacteristic
1097C22#549511yescharacteristic
1098C22#549511yescharacteristic
1099C22#552711yescharacteristic
1100C22#552711yescharacteristic
1101C22#553211yescharacteristic
1102C22#553211yescharacteristic
1103C22C4×#23711yescharacteristic
1104C22#553811yescharacteristic
1105C22#554011yescharacteristic
1106C22#554011yescharacteristic
1107C22C4×D3×D411yescharacteristic
1108C22#554511yescharacteristic
1109C22#554511yescharacteristic
1110C22#554711yescharacteristic
1111C22#555011yescharacteristic
1112C22#555311yescharacteristic
1113C22#555611yescharacteristic
1114C22#555611yescharacteristic
1115C22#556211yescharacteristic
1116C22#556211yescharacteristic
1117C22#556311yescharacteristic
1118C22#556511yescharacteristic
1119C22C2×C4×#6711yescharacteristic
1120C22#579111yescharacteristic
1121C22#579111yescharacteristic
1122C22C2×#93911yescharacteristic
1123C22#580511yescharacteristic
1124C22#583011yescharacteristic
1125C22#583211yescharacteristic
1126C4—24no—
1127C4—24no—
1128C4—42no—
1129C4—42no—
1130C4—42no—
1131C4—42no—
1132C4—64no—
1133C4—122no—
1134C4—122no—
1135C4—122no—
1136C4—122no—
1137C4—241no—
1138C4—241no—
1139C3#1408211yescharacteristic, complemented, Sylow
1140C2—44no—
1141C2—242no—
1142C2#7346211yescharacteristic
1143C2#7347011yescharacteristic
1144C2#7347511yescharacteristic
1145C2#7350011yescharacteristic
1146C2#7353011yescharacteristic
1147C2#7353311yescharacteristic
1148C2#7357411yescharacteristic
1149C2#7359511yescharacteristic
1150C2#8206511yescharacteristic
1151C2#8210611yescharacteristic
1152C2#8226011yescharacteristic
1153C2C4×#93911yescharacteristic
1154C2#8232911yescharacteristic
1155C2#8235011yescharacteristic
1156C2#8239011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC2×C3×C4×C22⋊C4C2
socle, cosocleC24×C3C24
prime radicalC23×#67C22
hypercenterC2×C4×C22⋊C4D3
hypocenterC3#14082
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×C4×C22⋊C4C2semidirect
4. C2×#4940C2semidirect
5. C2×#4932C2semidirect
6. #72127C2semidirect
8. #71547C2semidirect
9. #71545C2semidirect
10. #71537C2semidirect
11. #71536C2semidirect
12. #69429C2semidirect
13. #69409C2semidirect
14. #69408C2semidirect
15. #69403C2semidirect
54. #4957C4semidirect
60. C2×C4×C22⋊C4D3semidirect
112. C2×C3×C42D4semidirect
138. C2×(C2×D3)⋊C4C2×C4semidirect
139. C2×(C2×D3)⋊C4C2×C4semidirect
145. C2×Dic3⋊C4C2×C4semidirect
151. C2×C4×Dic3C2×C4semidirect
440. C2×C42#67semidirect
1139. C3#14082semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×C22⋊C42
C2×#52132
C2×#49572
C2×#49402
C2×#49322
#721272
#715502
#715472
#715452
#715372
#715362
#694292
#694092
#694082
#694032
#140823