Finite Group Databasebeta

← #10742726

Subgroups — #10742726

Order 768.

2462 conjugacy classes of subgroups.

The subgroup lattice has 1228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C22⋊Q8C211yesmaximal, characteristic, complemented
2C22×#946C211yesmaximal, characteristic, complemented
3C2×#5213C211yesmaximal, characteristic
4C2×#5210C211yesmaximal, characteristic, complemented
5C2×#4989C211yesmaximal, characteristic, complemented
6C2×#4956C211yesmaximal, characteristic
7#72134C211yesmaximal, characteristic, complemented
8#71570C211yesmaximal, characteristic, complemented
9#71570C211yesmaximal, characteristic, complemented
10#71568C211yesmaximal, characteristic, complemented
11#71566C211yesmaximal, characteristic, complemented
12#71565C211yesmaximal, characteristic, complemented
13#71550C211yesmaximal, characteristic
14#71547C211yesmaximal, characteristic, complemented
15#71546C211yesmaximal, characteristic, complemented
16#15951—31nomaximal, Sylow
17C23×C3×Q8C2211yescharacteristic
18C24×C3×C4C2211yescharacteristic
19C23×#67C2211yescharacteristic
20C23×C4×D3C2211yescharacteristic
21C2×C3×C22⋊Q8—24no—
22C2×C3×C22⋊Q8—24no—
23C2×C3×C22⋊Q8—24no—
24C22×C3×C4⋊C4C2211yescharacteristic
25C22×C3×C4⋊C4C2211yescharacteristic
26C22×C3×C4⋊C4C2211yescharacteristic
27C22×C3×C22⋊C4C2211yescharacteristic
28C22×C3×C22⋊C4C2211yescharacteristic
29C22×#217C2211yescharacteristic
30C22×#217C2211yescharacteristic
31C22×#217C2211yescharacteristic
32C2×#946—24no—
33C2×#946—24no—
34C2×#946—24no—
35C22×(C2×D3)⋊C4C2211yescharacteristic
36C22×(C2×D3)⋊C4C2211yescharacteristic
37C22×(C2×D3)⋊C4C2211yescharacteristic
38C22×(C2×D3)⋊C4C2211yescharacteristic
39C22×(C2×D3)⋊C4C2211yescharacteristic
40C22×C4⋊Dic3C2211yescharacteristic
41C22×Dic3⋊C4C2211yescharacteristic
42C22×Dic3⋊C4C2211yescharacteristic
43C22×Dic3⋊C4C2211yescharacteristic
44#5213—24no—
45#5210—24no—
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
55C2×C3⋊#95C2211yescharacteristic
56C2×C3⋊#95C2211yescharacteristic
57C2×C3⋊#95C2211yescharacteristic
58C2×C3⋊#95C2211yescharacteristic
59C2×C3⋊#95C2211yescharacteristic
60#4989—24no—
61#4956—24no—
62C22×C22⋊Q8—31no—
63C22×C22⋊Q8D311yescharacteristic, complemented
64C2×#386—31no—
65C2×#386—31no—
66C2×#385—31no—
67C2×#385—31no—
68#1446—31no—
69#1444—31no—
70#1441—31no—
71#1441—31no—
72#1439—31no—
73#1439—31no—
74#1439—31no—
75#1439—31no—
76#1438—31no—
77C25×C3C2311yescharacteristic
78C24×D3C2311yescharacteristic
79C22×C3×Q8—22no—
80C22×C3×Q8—22no—
81C22×C3×Q8—22no—
82C22×C3×Q8—22no—
83C22×C3×Q8—41no—
84C22×C3×Q8—41no—
85C22×C3×Q8D414yescomplemented
86C23×C3×C4—22no—
87C23×C3×C4—22no—
88C23×C3×C4—22no—
89C23×C3×C4—22no—
90C23×C3×C4—22no—
91C23×C3×C4—41no—
92C23×C3×C4—41no—
93C23×C3×C4C2311yescharacteristic
94C23×C3×C4C2311yescharacteristic
95C23×C3×C4C2311yescharacteristic
96C23×C3×C4C2311yescharacteristic
97C23×C3×C4C2311yescharacteristic
98C23×C3×C4C2311yescharacteristic
99C22×#67—22no—
100C22×#67—22no—
101C22×#67—22no—
102C22×#67—22no—
103C22×#67—41no—
104C22×#67—41no—
105C22×#67Q814yescomplemented
106C23×Dic3C2311yescharacteristic
107C23×Dic3C2311yescharacteristic
108C23×Dic3C2311yescharacteristic
109C23×Dic3C2311yescharacteristic
110C23×Dic3C2311yescharacteristic
111C23×Dic3C2311yescharacteristic
112C23×Dic3C2311yescharacteristic
113C22×C4×D3—22no—
114C22×C4×D3—22no—
115C22×C4×D3—22no—
116C22×C4×D3—22no—
117C22×C4×D3—22no—
118C22×C4×D3—41no—
119C22×C4×D3—41no—
120C3×C22⋊Q8—232no—
121C2×C3×C4⋊C4—22no—
122C2×C3×C4⋊C4—22no—
123C2×C3×C4⋊C4—22no—
124C2×C3×C4⋊C4—22no—
125C2×C3×C4⋊C4—22no—
126C2×C3×C4⋊C4—22no—
127C2×C3×C4⋊C4—22no—
128C2×C3×C4⋊C4—22no—
129C2×C3×C4⋊C4D414yescomplemented
130C2×C3×C22⋊C4—22no—
131C2×C3×C22⋊C4—22no—
132C2×C3×C22⋊C4—22no—
133C2×C3×C22⋊C4—22no—
134C2×C3×C22⋊C4—22no—
135C2×C3×C22⋊C4D414yes—
136C2×#217—22no—
137C2×#217—22no—
138C2×#217—22no—
139C2×#217—22no—
140C2×#217—22no—
141C2×#217—22no—
142C2×#217—22no—
143C2×#217—41no—
144C2×#217—41no—
145#946—232no—
146C2×(C2×D3)⋊C4—22no—
147C2×(C2×D3)⋊C4—22no—
148C2×(C2×D3)⋊C4—22no—
149C2×(C2×D3)⋊C4—22no—
150C2×(C2×D3)⋊C4—22no—
151C2×(C2×D3)⋊C4—22no—
152C2×(C2×D3)⋊C4—22no—
153C2×(C2×D3)⋊C4—22no—
154C2×(C2×D3)⋊C4—22no—
155C2×(C2×D3)⋊C4—22no—
156C2×(C2×D3)⋊C4—22no—
157C2×(C2×D3)⋊C4—22no—
158C2×(C2×D3)⋊C4—41no—
159C2×(C2×D3)⋊C4—41no—
160C2×(C2×D3)⋊C4D414yes—
161C2×C4⋊Dic3—22no—
162C2×C4⋊Dic3—22no—
163C2×C4⋊Dic3—22no—
164C2×Dic3⋊C4—22no—
165C2×Dic3⋊C4—22no—
166C2×Dic3⋊C4—22no—
167C2×Dic3⋊C4—22no—
168C2×Dic3⋊C4—22no—
169C2×Dic3⋊C4—22no—
170C2×Dic3⋊C4—22no—
171C2×Dic3⋊C4—41no—
172C2×Dic3⋊C4D414yescomplemented
173C3⋊#95—22no—
174C3⋊#95—22no—
175C3⋊#95—22no—
176C3⋊#95—22no—
177C3⋊#95—22no—
178C3⋊#95—22no—
179C3⋊#95—22no—
180C3⋊#95—22no—
181C3⋊#95—22no—
182C3⋊#95—41no—
183C3⋊#95—41no—
184C3⋊#95—41no—
185C3⋊#95—41no—
186C3⋊#95—41no—
187C23×Q8C2×D311yescharacteristic
188C23×D4—31no—
189C24×C4—31no—
190C24×C4C2×D311yescharacteristic
191C2×C22⋊Q8—24no—
192C2×C22⋊Q8—24no—
193C2×C22⋊Q8—24no—
194C2×C22⋊Q8—64no—
195C2×C22⋊Q8—64no—
196C2×C22⋊Q8—64no—
197C22×C4⋊C4—31no—
198C22×C4⋊C4—31no—
199C22×C4⋊C4—31no—
200C22×C4⋊C4—31no—
201C22×C4⋊C4C2×D311yescharacteristic
202C22×C4⋊C4C2×D311yescharacteristic
203C22×C4⋊C4C2×D311yescharacteristic
204C22×C22⋊C4—31no—
205C22×C22⋊C4—31no—
206C22×C22⋊C4—31no—
207C22×C22⋊C4—31no—
208C22×C22⋊C4—31no—
209C22×C22⋊C4—31no—
210C22×C22⋊C4—31no—
211C22×C22⋊C4—31no—
212C22×C22⋊C4C2×D311yescharacteristic
213C22×C22⋊C4C2×D311yescharacteristic
214#386—64no—
215#386—64no—
216#385—64no—
217#385—64no—
218C2×#95—31no—
219C2×#95—31no—
220C2×#95—31no—
221C2×#95—31no—
222C2×#95—31no—
223C2×#95—31no—
224C2×#95—31no—
225C2×#95—31no—
226C2×#95—31no—
227C2×#95—31no—
228C2×#95—31no—
229C2×#95—31no—
230C2×#95—31no—
231C2×#95—31no—
232C24×C3—21no—
233C24×C3—21no—
234C24×C3—21no—
235C24×C3—21no—
236C24×C3—21no—
237C24×C3—21no—
238C24×C3—21no—
239C24×C3—21no—
240C24×C3—21no—
241C24×C3—21no—
242C24×C3—21no—
243C24×C3—21no—
244C24×C3C2×D412yes—
245C24×C3C2×Q812yes—
246C24×C3#4112yes—
247C24×C3C2411yescharacteristic
248C23×D3—21no—
249C23×D3—21no—
250C23×D3—21no—
251C23×D3—21no—
252C23×D3—21no—
253C23×D3—21no—
254C23×D3—21no—
255C23×D3—21no—
256C23×D3—21no—
257C23×D3—21no—
258C23×D3—21no—
259C23×D3—21no—
260C23×D3C2×D412yes—
261C23×D3C2×Q812yes—
262C23×D3#4112yes—
263C2×C3×Q8—28no—
264C2×C3×Q8—28no—
265C2×C3×Q8—44no—
266C2×C3×Q8—44no—
267C2×C3×Q8—44no—
268C2×C3×Q8—44no—
269C2×C3×Q8—44no—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—21no—
273C22×C3×C4—21no—
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—28no—
279C22×C3×C4—21no—
280C22×C3×C4—21no—
281C22×C3×C4—21no—
282C22×C3×C4—21no—
283C22×C3×C4—21no—
284C22×C3×C4—21no—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4—21no—
299C22×C3×C4—21no—
300C22×C3×C4—21no—
301C22×C3×C4—21no—
302C22×C3×C4—21no—
303C22×C3×C4—44no—
304C22×C3×C4—44no—
305C22×C3×C4—44no—
306C22×C3×C4—44no—
307C22×C3×C4—44no—
308C22×C3×C4—44no—
309C22×C3×C4C2×D412yes—
310C22×C3×C4C2×D412yes—
311C22×C3×C4C2×D412yes—
312C22×C3×C4C2×D412yes—
313C22×C3×C4C2×D412yes—
314C22×C3×C4C2×D412yes—
315C22×C3×C4C2×D412yes—
316C22×C3×C4C2×D412yes—
317C22×C3×C4C2×D412yes—
318C22×C3×C4C2×D412yes—
319C2×#67—28no—
320C2×#67—28no—
321C2×#67—44no—
322C2×#67—44no—
323C2×#67—44no—
324C2×#67—44no—
325C2×#67—44no—
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×Dic3—21no—
338C22×Dic3—21no—
339C22×Dic3—21no—
340C22×Dic3—21no—
341C22×Dic3—21no—
342C22×Dic3—21no—
343C22×Dic3—21no—
344C22×Dic3—21no—
345C22×Dic3—21no—
346C22×Dic3—21no—
347C22×Dic3—21no—
348C22×Dic3—21no—
349C22×Dic3—21no—
350C22×Dic3—21no—
351C22×Dic3—21no—
352C22×Dic3—21no—
353C22×Dic3—21no—
354C22×Dic3—21no—
355C22×Dic3—21no—
356C22×Dic3—21no—
357C22×Dic3—21no—
358C22×Dic3—21no—
359C22×Dic3—21no—
360C22×Dic3—21no—
361C22×Dic3—21no—
362C22×Dic3—21no—
363C22×Dic3—21no—
364C22×Dic3—21no—
365C22×Dic3—21no—
366C22×Dic3—21no—
367C22×Dic3—21no—
368C22×Dic3—21no—
369C22×Dic3—21no—
370C22×Dic3C2×D412yes—
371C22×Dic3C2×D412yes—
372C22×Dic3C2×D412yes—
373C22×Dic3C2×Q812yes—
374C22×Dic3#4112yes—
375C2×C4×D3—28no—
376C2×C4×D3—44no—
377C2×C4×D3—44no—
378C2×C4×D3—44no—
379C2×C4×D3—44no—
380C2×C4×D3—44no—
381C2×C4×D3—44no—
382C3×C4⋊C4—28no—
383C3×C4⋊C4—28no—
384C3×C4⋊C4—28no—
385C3×C22⋊C4—28no—
386C3×C22⋊C4—28no—
387#217—28no—
388#217—44no—
389#217—44no—
390(C2×D3)⋊C4—28no—
391(C2×D3)⋊C4—28no—
392(C2×D3)⋊C4—28no—
393(C2×D3)⋊C4—44no—
394(C2×D3)⋊C4—44no—
395C4⋊Dic3—28no—
396Dic3⋊C4—28no—
397Dic3⋊C4—28no—
398Dic3⋊C4—44no—
399C25—31no—
400C25C22×D311yescharacteristic
401C22×Q8—22no—
402C22×Q8—22no—
403C22×Q8—22no—
404C22×Q8—22no—
405C22×Q8—41no—
406C22×Q8—41no—
407C22×Q8#6714yescomplemented
408C22×D4—34no—
409C22×D4—62no—
410C22×D4—62no—
411C22×D4—62no—
412C22×D4—62no—
413C22×D4—121no—
414C22×D4—121no—
415C23×C4—22no—
416C23×C4—22no—
417C23×C4—22no—
418C23×C4—22no—
419C23×C4—22no—
420C23×C4—31no—
421C23×C4—31no—
422C23×C4—31no—
423C23×C4—31no—
424C23×C4—31no—
425C23×C4—31no—
426C23×C4—31no—
427C23×C4—41no—
428C23×C4—41no—
429C23×C4—62no—
430C23×C4—62no—
431C23×C4—62no—
432C23×C4—62no—
433C23×C4—62no—
434C23×C4—121no—
435C23×C4—121no—
436C23×C4C22×D311yescharacteristic
437C23×C4C22×D311yescharacteristic
438C23×C4C22×D311yescharacteristic
439C23×C4C22×D311yescharacteristic
440C23×C4C22×D311yescharacteristic
441C23×C4C22×D311yescharacteristic
442C22⋊Q8—232no—
443C22⋊Q8—632no—
444C2×C4⋊C4—22no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—22no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—22no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—34no—
453C2×C4⋊C4—62no—
454C2×C4⋊C4—62no—
455C2×C4⋊C4—62no—
456C2×C4⋊C4—62no—
457C2×C4⋊C4—62no—
458C2×C4⋊C4—62no—
459C2×C4⋊C4—62no—
460C2×C4⋊C4—62no—
461C2×C4⋊C4—62no—
462C2×C4⋊C4—62no—
463C2×C4⋊C4—121no—
464C2×C4⋊C4#6714yescomplemented
465C2×C22⋊C4—22no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—22no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—34no—
471C2×C22⋊C4—62no—
472C2×C22⋊C4—62no—
473C2×C22⋊C4—62no—
474C2×C22⋊C4—62no—
475C2×C22⋊C4—62no—
476C2×C22⋊C4—62no—
477C2×C22⋊C4—62no—
478C2×C22⋊C4—62no—
479C2×C22⋊C4—62no—
480C2×C22⋊C4—62no—
481C2×C22⋊C4—62no—
482C2×C22⋊C4—62no—
483C2×C22⋊C4—62no—
484C2×C22⋊C4—62no—
485C2×C22⋊C4—62no—
486C2×C22⋊C4—62no—
487C2×C22⋊C4—62no—
488C2×C22⋊C4—62no—
489C2×C22⋊C4—62no—
490C2×C22⋊C4—121no—
491C2×C22⋊C4—121no—
492C2×C22⋊C4—121no—
493C2×C22⋊C4—121no—
494C2×C22⋊C4#6714yes—
495#95—62no—
496#95—62no—
497#95—62no—
498#95—62no—
499#95—62no—
500#95—62no—
501#95—62no—
502#95—62no—
503#95—62no—
504#95—121no—
505#95—121no—
506#95—121no—
507#95—121no—
508#95—121no—
509C23×C3—22no—
510C23×C3—22no—
511C23×C3—22no—
512C23×C3—22no—
513C23×C3—22no—
514C23×C3—22no—
515C23×C3—22no—
516C23×C3—22no—
517C23×C3—22no—
518C23×C3—22no—
519C23×C3—22no—
520C23×C3—22no—
521C23×C3—22no—
522C23×C3—22no—
523C23×C3—22no—
524C23×C3—22no—
525C23×C3—22no—
526C23×C3—22no—
527C23×C3—41no—
528C23×C3—41no—
529C23×C3—41no—
530C23×C3—41no—
531C23×C3—41no—
532C23×C3—41no—
533C23×C3—41no—
534C23×C3—41no—
535C23×C3—41no—
536C23×C3—41no—
537C23×C3—41no—
538C23×C3—41no—
539C23×C3—41no—
540C23×C3—41no—
541C23×C3—41no—
542C23×C3—41no—
543C23×C3C22⋊Q814yescomplemented
544C23×C3C22×D411yescharacteristic
545C23×C3C22×D411yescharacteristic
546C23×C3C22×D411yescharacteristic
547C23×C3C22×D411yescharacteristic
548C23×C3C22×D411yescharacteristic
549C23×C3C22×Q811yescharacteristic
550C23×C3C2×#4111yescharacteristic
551C23×C3C2×#4111yescharacteristic
552C23×C3C2×#4111yescharacteristic
553C23×C3H(5,𝔽2)11yescharacteristic
554C23×C3H(5,𝔽2)11yescharacteristic
555C23×C3H(5,𝔽2)11yescharacteristic
556C23×C32−1+411yescharacteristic
557C23×C32−1+411yescharacteristic
558C23×C32−1+411yescharacteristic
559C22×D3—22no—
560C22×D3—22no—
561C22×D3—22no—
562C22×D3—22no—
563C22×D3—22no—
564C22×D3—22no—
565C22×D3—22no—
566C22×D3—22no—
567C22×D3—22no—
568C22×D3—22no—
569C22×D3—22no—
570C22×D3—22no—
571C22×D3—22no—
572C22×D3—22no—
573C22×D3—22no—
574C22×D3—22no—
575C22×D3—22no—
576C22×D3—22no—
577C22×D3—41no—
578C22×D3—41no—
579C22×D3—41no—
580C22×D3—41no—
581C22×D3—41no—
582C22×D3—41no—
583C22×D3—41no—
584C22×D3—41no—
585C22×D3—41no—
586C22×D3—41no—
587C22×D3—41no—
588C22×D3—41no—
589C22×D3—41no—
590C22×D3—41no—
591C22×D3—41no—
592C22×D3—41no—
593C22×D3C22⋊Q814yescomplemented
594C3×Q8—416no—
595C2×C3×C4—22no—
596C2×C3×C4—22no—
597C2×C3×C4—22no—
598C2×C3×C4—22no—
599C2×C3×C4—22no—
600C2×C3×C4—22no—
601C2×C3×C4—22no—
602C2×C3×C4—22no—
603C2×C3×C4—22no—
604C2×C3×C4—22no—
605C2×C3×C4—22no—
606C2×C3×C4—22no—
607C2×C3×C4—22no—
608C2×C3×C4—22no—
609C2×C3×C4—22no—
610C2×C3×C4—22no—
611C2×C3×C4—22no—
612C2×C3×C4—22no—
613C2×C3×C4—22no—
614C2×C3×C4—22no—
615C2×C3×C4—22no—
616C2×C3×C4—22no—
617C2×C3×C4—22no—
618C2×C3×C4—22no—
619C2×C3×C4—416no—
620C2×C3×C4—41no—
621C2×C3×C4—41no—
622C2×C3×C4—41no—
623C2×C3×C4—41no—
624C2×C3×C4—41no—
625C2×C3×C4—41no—
626C2×C3×C4—41no—
627C2×C3×C4—41no—
628C2×C3×C4—41no—
629C2×C3×C4—41no—
630C2×C3×C4—41no—
631C2×C3×C4—41no—
632C2×C3×C4—41no—
633C2×C3×C4—41no—
634C2×C3×C4—41no—
635C2×C3×C4—41no—
636C2×C3×C4#12014yes—
637C2×C3×C4#12014yes—
638#67—416no—
639C2×Dic3—22no—
640C2×Dic3—22no—
641C2×Dic3—22no—
642C2×Dic3—22no—
643C2×Dic3—22no—
644C2×Dic3—22no—
645C2×Dic3—22no—
646C2×Dic3—22no—
647C2×Dic3—22no—
648C2×Dic3—22no—
649C2×Dic3—22no—
650C2×Dic3—22no—
651C2×Dic3—22no—
652C2×Dic3—22no—
653C2×Dic3—22no—
654C2×Dic3—41no—
655C2×Dic3—41no—
656C2×Dic3—41no—
657C2×Dic3—41no—
658C2×Dic3—41no—
659C2×Dic3—41no—
660C2×Dic3—41no—
661C2×Dic3—41no—
662C2×Dic3—41no—
663C2×Dic3—41no—
664C2×Dic3—41no—
665C2×Dic3—41no—
666C2×Dic3—41no—
667C2×Dic3—41no—
668C2×Dic3—41no—
669C2×Dic3—41no—
670C2×Dic3—41no—
671C2×Dic3—41no—
672C2×Dic3—41no—
673C2×Dic3—41no—
674C2×Dic3—41no—
675C2×Dic3—41no—
676C2×Dic3—41no—
677C2×Dic3—41no—
678C2×Dic3—41no—
679C2×Dic3—41no—
680C2×Dic3—41no—
681C2×Dic3—41no—
682C2×Dic3—41no—
683C2×Dic3—41no—
684C2×Dic3—41no—
685C2×Dic3—41no—
686C2×Dic3—41no—
687C2×Dic3—41no—
688C4×D3—416no—
689C24—21no—
690C24—21no—
691C24—21no—
692C24—21no—
693C24—21no—
694C24—21no—
695C24—21no—
696C24—21no—
697C24—21no—
698C24—21no—
699C24—21no—
700C24—21no—
701C24—32no—
702C24—32no—
703C24—32no—
704C24—61no—
705C24—61no—
706C24—61no—
707C24—61no—
708C24—61no—
709C24—61no—
710C24—61no—
711C24—61no—
712C24—61no—
713C24—61no—
714C24—61no—
715C24—61no—
716C24D3×Q812yes—
717C24#23912yes—
718C24C2×#6712yes—
719C24C23×D311yescharacteristic
720C2×Q8—28no—
721C2×Q8—28no—
722C2×Q8—44no—
723C2×Q8—44no—
724C2×Q8—44no—
725C2×Q8—44no—
726C2×Q8—44no—
727C2×D4—68no—
728C2×D4—68no—
729C2×D4—124no—
730C2×D4—124no—
731C2×D4—124no—
732C2×D4—124no—
733C2×D4—124no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—28no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—32no—
768C22×C4—32no—
769C22×C4—32no—
770C22×C4—32no—
771C22×C4—32no—
772C22×C4—44no—
773C22×C4—44no—
774C22×C4—44no—
775C22×C4—44no—
776C22×C4—44no—
777C22×C4—44no—
778C22×C4—68no—
779C22×C4—61no—
780C22×C4—61no—
781C22×C4—61no—
782C22×C4—61no—
783C22×C4—61no—
784C22×C4—61no—
785C22×C4—61no—
786C22×C4—61no—
787C22×C4—61no—
788C22×C4—61no—
789C22×C4—61no—
790C22×C4—61no—
791C22×C4—61no—
792C22×C4—61no—
793C22×C4—61no—
794C22×C4—61no—
795C22×C4—61no—
796C22×C4—61no—
797C22×C4—61no—
798C22×C4—61no—
799C22×C4—61no—
800C22×C4—61no—
801C22×C4—61no—
802C22×C4—61no—
803C22×C4—61no—
804C22×C4—61no—
805C22×C4—61no—
806C22×C4—61no—
807C22×C4—61no—
808C22×C4—61no—
809C22×C4—61no—
810C22×C4—61no—
811C22×C4—61no—
812C22×C4—61no—
813C22×C4—61no—
814C22×C4—61no—
815C22×C4—61no—
816C22×C4—61no—
817C22×C4—61no—
818C22×C4—61no—
819C22×C4—61no—
820C22×C4—61no—
821C22×C4—61no—
822C22×C4—61no—
823C22×C4—124no—
824C22×C4—124no—
825C22×C4—124no—
826C22×C4—124no—
827C22×C4—124no—
828C22×C4—124no—
829C22×C4D3×D412yes—
830C22×C4D3×D412yes—
831C22×C4C2×#6712yes—
832C22×C4C2×#6712yes—
833C22×C4C2×#6712yes—
834C22×C4C2×#6712yes—
835C22×C4C2×#6712yes—
836C22×C4C2×#6712yes—
837C22×C4C2×#6712yes—
838C22×C4C2×#6712yes—
839C4⋊C4—28no—
840C4⋊C4—28no—
841C4⋊C4—28no—
842C4⋊C4—68no—
843C4⋊C4—68no—
844C4⋊C4—68no—
845C4⋊C4—124no—
846C22⋊C4—28no—
847C22⋊C4—28no—
848C22⋊C4—68no—
849C22⋊C4—68no—
850C22⋊C4—68no—
851C22⋊C4—68no—
852C22⋊C4—124no—
853C22⋊C4—124no—
854C22⋊C4—124no—
855C22⋊C4—124no—
856C22×C3—24no—
857C22×C3—24no—
858C22×C3—24no—
859C22×C3—42no—
860C22×C3—42no—
861C22×C3—42no—
862C22×C3—42no—
863C22×C3—42no—
864C22×C3—42no—
865C22×C3—42no—
866C22×C3—42no—
867C22×C3—42no—
868C22×C3—42no—
869C22×C3—42no—
870C22×C3—42no—
871C22×C3C2×#12011yescharacteristic
872C22×C3C2×#12011yescharacteristic
873C22×C3C2×C22⋊Q811yescharacteristic
874C22×C3C2×C22⋊Q811yescharacteristic
875C22×C3#52511yescharacteristic
876C22×C3#52511yescharacteristic
877C22×C3#53411yescharacteristic
878C22×C3#53611yescharacteristic
879C22×C3#53611yescharacteristic
880C22×C3#53711yescharacteristic
881C22×C3#53711yescharacteristic
882C22×C3#53911yescharacteristic
883C22×C3#53911yescharacteristic
884C22×C3#53911yescharacteristic
885C22×C3#54311yescharacteristic
886C22×C3D4211yescharacteristic
887C22×C3D4211yescharacteristic
888C22×C3D4211yescharacteristic
889C22×C3D4211yescharacteristic
890C22×C3#54611yescharacteristic
891C22×C3#54611yescharacteristic
892C22×C3#54711yescharacteristic
893C22×C3#54711yescharacteristic
894C22×C3#54811yescharacteristic
895C22×C3#54811yescharacteristic
896C22×C3#54811yescharacteristic
897C22×C3#54811yescharacteristic
898C22×C3D4×Q811yescharacteristic
899C22×C3D4×Q811yescharacteristic
900C22×C3D4×Q811yescharacteristic
901C22×C3#55011yescharacteristic
902C22×C3#55111yescharacteristic
903C22×C3#55411yescharacteristic
904C22×C3#56211yescharacteristic
905C22×C3#56311yescharacteristic
906C2×D3—24no—
907C2×D3—24no—
908C2×D3—24no—
909C2×D3—42no—
910C2×D3—42no—
911C2×D3—42no—
912C2×D3—42no—
913C2×D3—42no—
914C2×D3—42no—
915C2×D3—42no—
916C2×D3—42no—
917C2×D3—42no—
918C2×D3—42no—
919C2×D3—42no—
920C2×D3—42no—
921C3×C4—24no—
922C3×C4—24no—
923C3×C4—42no—
924C3×C4—42no—
925C3×C4—42no—
926C3×C4—42no—
927Dic3—42no—
928Dic3—42no—
929Dic3—42no—
930Dic3—42no—
931Dic3—42no—
932Dic3—81no—
933Dic3—81no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—34no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—62no—
970C23—62no—
971C23—62no—
972C23—62no—
973C23—62no—
974C23—62no—
975C23—62no—
976C23—62no—
977C23—62no—
978C23—62no—
979C23—62no—
980C23—62no—
981C23—62no—
982C23—62no—
983C23—62no—
984C23—62no—
985C23—62no—
986C23—62no—
987C23—121no—
988C23—121no—
989C23—121no—
990C23—121no—
991C23—121no—
992C23—121no—
993C23—121no—
994C23—121no—
995C23—121no—
996C23—121no—
997C23—121no—
998C23—121no—
999C23—121no—
1000C23—121no—
1001C23—121no—
1002C23—121no—
1003C23#94614yescomplemented
1004C23C2×D3×D411yescharacteristic
1005C23C2×D3×D411yescharacteristic
1006C23#100411yescharacteristic
1007C23#100411yescharacteristic
1008C23C2×D3×Q811yescharacteristic
1009C23C2×#23911yescharacteristic
1010C23#100711yescharacteristic
1011C23#100711yescharacteristic
1012C23D3×#4111yescharacteristic
1013C23D3×#4111yescharacteristic
1014C23#100911yescharacteristic
1015C23#101011yescharacteristic
1016C23C22×#6711yescharacteristic
1017C23C22×#6711yescharacteristic
1018C23C22×#6711yescharacteristic
1019Q8—416no—
1020D4—1216no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—416no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—62no—
1063C2×C4—62no—
1064C2×C4—62no—
1065C2×C4—62no—
1066C2×C4—62no—
1067C2×C4—62no—
1068C2×C4—62no—
1069C2×C4—62no—
1070C2×C4—62no—
1071C2×C4—62no—
1072C2×C4—62no—
1073C2×C4—62no—
1074C2×C4—62no—
1075C2×C4—62no—
1076C2×C4—62no—
1077C2×C4—1216no—
1078C2×C4—121no—
1079C2×C4—121no—
1080C2×C4—121no—
1081C2×C4—121no—
1082C2×C4—121no—
1083C2×C4—121no—
1084C2×C4—121no—
1085C2×C4—121no—
1086C2×C4—121no—
1087C2×C4—121no—
1088C2×C4—121no—
1089C2×C4—121no—
1090C2×C4—121no—
1091C2×C4—121no—
1092C2×C4—121no—
1093C2×C4—121no—
1094C2×C4—121no—
1095C2×C4—121no—
1096C2×C4—121no—
1097C2×C4—121no—
1098C2×C4—121no—
1099C2×C4—121no—
1100C2×C4—121no—
1101C2×C4—121no—
1102C2×C4—121no—
1103C2×C4—121no—
1104C2×C4—121no—
1105C2×C4—121no—
1106C2×C4—121no—
1107C2×C4—121no—
1108C2×C4—121no—
1109C2×C4—121no—
1110C2×C4—121no—
1111C2×C4—121no—
1112C2×C4#93714yes—
1113C2×C4#95314yes—
1114C2×C3—44no—
1115C2×C3#240311yescharacteristic
1116C2×C3#240711yescharacteristic
1117C2×C3#240711yescharacteristic
1118C2×C3#240911yescharacteristic
1119C2×C3#240911yescharacteristic
1120C2×C3#243711yescharacteristic
1121C2×C3#244911yescharacteristic
1122C2×C3#244911yescharacteristic
1123C2×C3#246311yescharacteristic
1124C2×C3#268011yescharacteristic
1125C2×C3#268111yescharacteristic
1126C2×C3#268111yescharacteristic
1127C2×C3#268311yescharacteristic
1128C2×C3#272811yescharacteristic
1129C2×C3#273211yescharacteristic
1130D3—44no—
1131C22—24no—
1132C22—24no—
1133C22—24no—
1134C22—42no—
1135C22—42no—
1136C22—42no—
1137C22—42no—
1138C22—42no—
1139C22—42no—
1140C22—42no—
1141C22—42no—
1142C22—42no—
1143C22—42no—
1144C22—42no—
1145C22—42no—
1146C22—64no—
1147C22—64no—
1148C22—64no—
1149C22—122no—
1150C22—122no—
1151C22—122no—
1152C22—122no—
1153C22—122no—
1154C22—122no—
1155C22—122no—
1156C22—122no—
1157C22—122no—
1158C22—122no—
1159C22—122no—
1160C22—122no—
1161C22D3×C22⋊Q811yescharacteristic
1162C22#562711yescharacteristic
1163C22#562811yescharacteristic
1164C22#562911yescharacteristic
1165C22#563011yescharacteristic
1166C22#563111yescharacteristic
1167C22#563211yescharacteristic
1168C22#563311yescharacteristic
1169C22#563411yescharacteristic
1170C22#563611yescharacteristic
1171C22#563711yescharacteristic
1172C22#563811yescharacteristic
1173C22#563811yescharacteristic
1174C22#564511yescharacteristic
1175C22#564611yescharacteristic
1176C22#564711yescharacteristic
1177C22C2×#93711yescharacteristic
1178C22D4×#6711yescharacteristic
1179C22D4×#6711yescharacteristic
1180C22D4×#6711yescharacteristic
1181C22D4×#6711yescharacteristic
1182C22#580411yescharacteristic
1183C22C2×#94611yescharacteristic
1184C22Q8×#6711yescharacteristic
1185C22Q8×#6711yescharacteristic
1186C22#581611yescharacteristic
1187C22#581711yescharacteristic
1188C22#581711yescharacteristic
1189C22#582411yescharacteristic
1190C22#582811yescharacteristic
1191C22#582911yescharacteristic
1192C22#583111yescharacteristic
1193C22#583311yescharacteristic
1194C22#583411yescharacteristic
1195C22C2×#95311yescharacteristic
1196C4—24no—
1197C4—24no—
1198C4—42no—
1199C4—42no—
1200C4—42no—
1201C4—42no—
1202C4—122no—
1203C4—122no—
1204C4—122no—
1205C4—122no—
1206C4—122no—
1207C4—241no—
1208C4—241no—
1209C3#1595111yescharacteristic, complemented, Sylow
1210C2—44no—
1211C2—124no—
1212C2#8275111yescharacteristic
1213C2#8276411yescharacteristic
1214C2#8279211yescharacteristic
1215C2#8279311yescharacteristic
1216C2#8280711yescharacteristic
1217C2#8281211yescharacteristic
1218C2#8281611yescharacteristic
1219C2#8281711yescharacteristic
1220C2#8281811yescharacteristic
1221C2#8282811yescharacteristic
1222C2#8282911yescharacteristic
1223C2#8283111yescharacteristic
1224C2#8405211yescharacteristic
1225C2#8406811yescharacteristic
1226C2#8409711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC22×C3×C22⋊Q8C2
prime radicalC23×#67C22
hypercenterC22×C22⋊Q8D3
hypocenterC3#15951
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×C3×C22⋊Q8C2semidirect
2. C22×#946C2semidirect
4. C2×#5210C2semidirect
5. C2×#4989C2semidirect
7. #72134C2semidirect
8. #71570C2semidirect
9. #71570C2semidirect
10. #71568C2semidirect
11. #71566C2semidirect
12. #71565C2semidirect
14. #71547C2semidirect
15. #71546C2semidirect
63. C22×C22⋊Q8D3semidirect
85. C22×C3×Q8D4semidirect
105. C22×#67Q8semidirect
129. C2×C3×C4⋊C4D4semidirect
172. C2×Dic3⋊C4D4semidirect
407. C22×Q8#67semidirect
464. C2×C4⋊C4#67semidirect
543. C23×C3C22⋊Q8semidirect
593. C22×D3C22⋊Q8semidirect
1003. C23#946semidirect
1209. C3#15951semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C22⋊Q82
C22×#9462
C2×#52132
C2×#52102
C2×#49892
C2×#49562
#721342
#715702
#715682
#715662
#715652
#715502
#715472
#715462
#159513