Finite Group Databasebeta

← #10733103

Subgroups — #10733103

Order 768.

1926 conjugacy classes of subgroups.

The subgroup lattice has 1064 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C22⋊Q8C211yesmaximal, characteristic
2C2×#5230C211yesmaximal, characteristic, complemented
3C2×#5229C211yesmaximal, characteristic, complemented
4C2×#5210C211yesmaximal, characteristic
5C2×#4976C211yesmaximal, characteristic, complemented
6C2×#4948C211yesmaximal, characteristic
7#72127C211yesmaximal, characteristic
8#71568C211yesmaximal, characteristic, complemented
9#71568C211yesmaximal, characteristic, complemented
10#71566C211yesmaximal, characteristic, complemented
11#71566C211yesmaximal, characteristic, complemented
12#71565C211yesmaximal, characteristic, complemented
13#71547C211yesmaximal, characteristic
14#71547C211yesmaximal, characteristic
15#71545C211yesmaximal, characteristic
16#15276—31nomaximal, Sylow
17C23×C3×Q8C2211yescharacteristic
18C24×C3×C4C2211yescharacteristic
19C2×C3×C22⋊Q8—24no—
20C2×C3×C22⋊Q8—24no—
21C2×C3×C22⋊Q8—24no—
22C22×C3×C4⋊C4C2211yescharacteristic
23C22×C3×C4⋊C4C2211yescharacteristic
24C22×C3×C4⋊C4C2211yescharacteristic
25C22×C3×C22⋊C4C2211yescharacteristic
26C22×C3×C22⋊C4C2211yescharacteristic
27C22×#217C2211yescharacteristic
28C22×#217C2211yescharacteristic
29C22×#217C2211yescharacteristic
30C22×#217C2211yescharacteristic
31C22×C4⋊Dic3C2211yescharacteristic
32C22×Dic3⋊C4C2211yescharacteristic
33C22×Dic3⋊C4C2211yescharacteristic
34C22×Dic3⋊C4C2211yescharacteristic
35C22×Dic3⋊C4C2211yescharacteristic
36C22×Dic3⋊C4C2211yescharacteristic
37C22×Dic3⋊C4C2211yescharacteristic
38C22×C4×Dic3C2211yescharacteristic
39#5230—24no—
40#5229—24no—
41#5210—24no—
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
55C2×C3⋊#95C2211yescharacteristic
56C2×C3⋊#95C2211yescharacteristic
57C2×C3⋊#95C2211yescharacteristic
58#4976—24no—
59#4948—24no—
60C22×C22⋊Q8D311yescharacteristic
61C2×#396—31no—
62C2×#395—31no—
63C2×#391—31no—
64C2×#389—31no—
65C2×#385—31no—
66#1444—31no—
67#1444—31no—
68#1441—31no—
69#1441—31no—
70#1441—31no—
71#1439—31no—
72#1439—31no—
73#1437—31no—
74C22⋊#95—31no—
75C25×C3C2311yescharacteristic
76C22×C3×Q8—22no—
77C22×C3×Q8—22no—
78C22×C3×Q8—22no—
79C22×C3×Q8—22no—
80C22×C3×Q8—41no—
81C22×C3×Q8—41no—
82C22×C3×Q8D414yes—
83C23×C3×C4—22no—
84C23×C3×C4—22no—
85C23×C3×C4—22no—
86C23×C3×C4—22no—
87C23×C3×C4—22no—
88C23×C3×C4—41no—
89C23×C3×C4—41no—
90C23×C3×C4C2311yescharacteristic
91C23×C3×C4C2311yescharacteristic
92C23×C3×C4C2311yescharacteristic
93C23×C3×C4C2311yescharacteristic
94C23×C3×C4C2311yescharacteristic
95C23×C3×C4C2311yescharacteristic
96C23×Dic3C2311yescharacteristic
97C23×Dic3C2311yescharacteristic
98C23×Dic3C2311yescharacteristic
99C23×Dic3C2311yescharacteristic
100C23×Dic3C2311yescharacteristic
101C23×Dic3C2311yescharacteristic
102C23×Dic3C2311yescharacteristic
103C23×Dic3C2311yescharacteristic
104C3×C22⋊Q8—232no—
105C2×C3×C4⋊C4—22no—
106C2×C3×C4⋊C4—22no—
107C2×C3×C4⋊C4—22no—
108C2×C3×C4⋊C4—22no—
109C2×C3×C4⋊C4—22no—
110C2×C3×C4⋊C4—22no—
111C2×C3×C4⋊C4—22no—
112C2×C3×C4⋊C4—22no—
113C2×C3×C4⋊C4D414yes—
114C2×C3×C22⋊C4—22no—
115C2×C3×C22⋊C4—22no—
116C2×C3×C22⋊C4—22no—
117C2×C3×C22⋊C4—22no—
118C2×C3×C22⋊C4—22no—
119C2×C3×C22⋊C4D414yes—
120C2×#217—22no—
121C2×#217—22no—
122C2×#217—22no—
123C2×#217—22no—
124C2×#217—22no—
125C2×#217—22no—
126C2×#217—41no—
127C2×#217—41no—
128C2×#217—41no—
129C2×#217—41no—
130C2×#217Q814yescomplemented
131C2×#217Q814yescomplemented
132C2×C4⋊Dic3—22no—
133C2×C4⋊Dic3—22no—
134C2×C4⋊Dic3—41no—
135C2×Dic3⋊C4—22no—
136C2×Dic3⋊C4—22no—
137C2×Dic3⋊C4—22no—
138C2×Dic3⋊C4—22no—
139C2×Dic3⋊C4—22no—
140C2×Dic3⋊C4—22no—
141C2×Dic3⋊C4—22no—
142C2×Dic3⋊C4—22no—
143C2×Dic3⋊C4—22no—
144C2×Dic3⋊C4—22no—
145C2×Dic3⋊C4—22no—
146C2×Dic3⋊C4—22no—
147C2×Dic3⋊C4—22no—
148C2×Dic3⋊C4—22no—
149C2×Dic3⋊C4—41no—
150C2×Dic3⋊C4—41no—
151C2×Dic3⋊C4—41no—
152C2×Dic3⋊C4—41no—
153C2×C4×Dic3—22no—
154C2×C4×Dic3—22no—
155C2×C4×Dic3—41no—
156C3⋊#95—22no—
157C3⋊#95—22no—
158C3⋊#95—22no—
159C3⋊#95—22no—
160C3⋊#95—22no—
161C3⋊#95—22no—
162C3⋊#95—22no—
163C3⋊#95—22no—
164C3⋊#95—22no—
165C3⋊#95—22no—
166C3⋊#95—22no—
167C3⋊#95—41no—
168C3⋊#95—41no—
169C3⋊#95—41no—
170C3⋊#95—41no—
171C3⋊#95D414yes—
172C23×Q8C2×D311yescharacteristic
173C24×C4C2×D311yescharacteristic
174C2×C22⋊Q8—24no—
175C2×C22⋊Q8—24no—
176C2×C22⋊Q8—24no—
177C22×C4⋊C4—31no—
178C22×C4⋊C4—31no—
179C22×C4⋊C4—31no—
180C22×C4⋊C4—31no—
181C22×C4⋊C4—31no—
182C22×C4⋊C4—31no—
183C22×C4⋊C4—31no—
184C22×C4⋊C4C2×D311yescharacteristic
185C22×C4⋊C4C2×D311yescharacteristic
186C22×C4⋊C4C2×D311yescharacteristic
187C22×C22⋊C4—31no—
188C22×C22⋊C4—31no—
189C22×C22⋊C4—31no—
190C22×C22⋊C4—31no—
191C22×C22⋊C4C2×D311yescharacteristic
192C22×C22⋊C4C2×D311yescharacteristic
193C22×C42—31no—
194#396—64no—
195#395—64no—
196#391—64no—
197#389—64no—
198#385—64no—
199C2×#95—31no—
200C2×#95—31no—
201C2×#95—31no—
202C2×#95—31no—
203C2×#95—31no—
204C2×#95—31no—
205C2×#95—31no—
206C2×#95—31no—
207C2×#95—31no—
208C2×#95—31no—
209C2×#95—31no—
210C2×#95—31no—
211C2×#95—31no—
212C2×#95—31no—
213C2×#95—31no—
214C2×#95—31no—
215C24×C3—21no—
216C24×C3—21no—
217C24×C3—21no—
218C24×C3—21no—
219C24×C3—21no—
220C24×C3—21no—
221C24×C3—21no—
222C24×C3—21no—
223C24×C3—21no—
224C24×C3—21no—
225C24×C3—21no—
226C24×C3—21no—
227C24×C3C2×D412yes—
228C24×C3C2×Q812yes—
229C24×C3C2×Q812yes—
230C24×C3C2411yescharacteristic
231C2×C3×Q8—28no—
232C2×C3×Q8—28no—
233C2×C3×Q8—44no—
234C2×C3×Q8—44no—
235C2×C3×Q8—44no—
236C2×C3×Q8—44no—
237C2×C3×Q8—44no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—28no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×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—44no—
272C22×C3×C4—44no—
273C22×C3×C4—44no—
274C22×C3×C4—44no—
275C22×C3×C4—44no—
276C22×C3×C4—44no—
277C22×C3×C4C2×D412yes—
278C22×C3×C4C2×D412yes—
279C22×C3×C4C2×D412yes—
280C22×C3×C4C2×D412yes—
281C22×C3×C4C2×D412yes—
282C22×C3×C4C2×D412yes—
283C22×C3×C4C2×D412yes—
284C22×C3×C4C2×D412yes—
285C22×C3×C4C2×D412yes—
286C22×C3×C4#4112yes—
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×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×Dic3C2×D412yes—
336C22×Dic3C2×D412yes—
337C22×Dic3C2×Q812yes—
338C22×Dic3C2×Q812yes—
339C22×Dic3C2×Q812yes—
340C22×Dic3C2×Q812yes—
341C22×Dic3#4112yes—
342C22×Dic3#4112yes—
343C3×C4⋊C4—28no—
344C3×C4⋊C4—28no—
345C3×C4⋊C4—28no—
346C3×C22⋊C4—28no—
347C3×C22⋊C4—28no—
348#217—28no—
349#217—44no—
350#217—44no—
351#217—44no—
352C4⋊Dic3—44no—
353Dic3⋊C4—28no—
354Dic3⋊C4—44no—
355Dic3⋊C4—44no—
356Dic3⋊C4—44no—
357Dic3⋊C4—44no—
358Dic3⋊C4—44no—
359C4×Dic3—44no—
360C25C22×D311yescharacteristic
361C22×Q8—22no—
362C22×Q8—22no—
363C22×Q8—22no—
364C22×Q8—22no—
365C22×Q8—41no—
366C22×Q8—41no—
367C22×Q8#6714yes—
368C23×C4—22no—
369C23×C4—22no—
370C23×C4—22no—
371C23×C4—22no—
372C23×C4—22no—
373C23×C4—31no—
374C23×C4—31no—
375C23×C4—31no—
376C23×C4—31no—
377C23×C4—31no—
378C23×C4—31no—
379C23×C4—31no—
380C23×C4—31no—
381C23×C4—41no—
382C23×C4—41no—
383C23×C4C22×D311yescharacteristic
384C23×C4C22×D311yescharacteristic
385C23×C4C22×D311yescharacteristic
386C23×C4C22×D311yescharacteristic
387C23×C4C22×D311yescharacteristic
388C23×C4C22×D311yescharacteristic
389C22⋊Q8—232no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—62no—
399C2×C4⋊C4—62no—
400C2×C4⋊C4—62no—
401C2×C4⋊C4—62no—
402C2×C4⋊C4—62no—
403C2×C4⋊C4—62no—
404C2×C4⋊C4—62no—
405C2×C4⋊C4—62no—
406C2×C4⋊C4—62no—
407C2×C4⋊C4—62no—
408C2×C4⋊C4—62no—
409C2×C4⋊C4—62no—
410C2×C4⋊C4—62no—
411C2×C4⋊C4—62no—
412C2×C4⋊C4—62no—
413C2×C4⋊C4—62no—
414C2×C4⋊C4—121no—
415C2×C4⋊C4—121no—
416C2×C4⋊C4—121no—
417C2×C4⋊C4—121no—
418C2×C4⋊C4—121no—
419C2×C4⋊C4#6714yes—
420C2×C22⋊C4—22no—
421C2×C22⋊C4—22no—
422C2×C22⋊C4—22no—
423C2×C22⋊C4—22no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—34no—
426C2×C22⋊C4—34no—
427C2×C22⋊C4—62no—
428C2×C22⋊C4—62no—
429C2×C22⋊C4—62no—
430C2×C22⋊C4—62no—
431C2×C22⋊C4—62no—
432C2×C22⋊C4—62no—
433C2×C22⋊C4—121no—
434C2×C22⋊C4—121no—
435C2×C22⋊C4—121no—
436C2×C22⋊C4—121no—
437C2×C22⋊C4#6714yes—
438C2×C42—62no—
439C2×C42—62no—
440C2×C42—121no—
441#95—34no—
442#95—62no—
443#95—62no—
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×C3C4⋊Q814yes—
492C23×C3C22×D411yescharacteristic
493C23×C3C22×D411yescharacteristic
494C23×C3C22×D411yescharacteristic
495C23×C3C22×D411yescharacteristic
496C23×C3C22×Q811yescharacteristic
497C23×C3C22×Q811yescharacteristic
498C23×C3C2×#4111yescharacteristic
499C23×C3C2×#4111yescharacteristic
500C23×C3C2×#4111yescharacteristic
501C23×C3H(5,𝔽2)11yescharacteristic
502C23×C3H(5,𝔽2)11yescharacteristic
503C23×C3H(5,𝔽2)11yescharacteristic
504C23×C32−1+411yescharacteristic
505C23×C32−1+411yescharacteristic
506C23×C32−1+411yescharacteristic
507C3×Q8—416no—
508C2×C3×C4—22no—
509C2×C3×C4—22no—
510C2×C3×C4—22no—
511C2×C3×C4—22no—
512C2×C3×C4—22no—
513C2×C3×C4—22no—
514C2×C3×C4—22no—
515C2×C3×C4—22no—
516C2×C3×C4—22no—
517C2×C3×C4—22no—
518C2×C3×C4—22no—
519C2×C3×C4—22no—
520C2×C3×C4—22no—
521C2×C3×C4—22no—
522C2×C3×C4—22no—
523C2×C3×C4—22no—
524C2×C3×C4—22no—
525C2×C3×C4—22no—
526C2×C3×C4—22no—
527C2×C3×C4—22no—
528C2×C3×C4—22no—
529C2×C3×C4—22no—
530C2×C3×C4—22no—
531C2×C3×C4—22no—
532C2×C3×C4—416no—
533C2×C3×C4—41no—
534C2×C3×C4—41no—
535C2×C3×C4—41no—
536C2×C3×C4—41no—
537C2×C3×C4—41no—
538C2×C3×C4—41no—
539C2×C3×C4—41no—
540C2×C3×C4—41no—
541C2×C3×C4—41no—
542C2×C3×C4—41no—
543C2×C3×C4—41no—
544C2×C3×C4—41no—
545C2×C3×C4—41no—
546C2×C3×C4—41no—
547C2×C3×C4—41no—
548C2×C3×C4—41no—
549C2×C3×C4#12014yes—
550C2×C3×C4#12114yes—
551C2×Dic3—22no—
552C2×Dic3—22no—
553C2×Dic3—22no—
554C2×Dic3—22no—
555C2×Dic3—22no—
556C2×Dic3—22no—
557C2×Dic3—22no—
558C2×Dic3—22no—
559C2×Dic3—22no—
560C2×Dic3—22no—
561C2×Dic3—22no—
562C2×Dic3—22no—
563C2×Dic3—22no—
564C2×Dic3—22no—
565C2×Dic3—22no—
566C2×Dic3—22no—
567C2×Dic3—22no—
568C2×Dic3—22no—
569C2×Dic3—22no—
570C2×Dic3—22no—
571C2×Dic3—22no—
572C2×Dic3—41no—
573C2×Dic3—41no—
574C2×Dic3—41no—
575C2×Dic3—41no—
576C2×Dic3—41no—
577C2×Dic3—41no—
578C2×Dic3—41no—
579C2×Dic3—41no—
580C2×Dic3—41no—
581C2×Dic3—41no—
582C2×Dic3—41no—
583C2×Dic3—41no—
584C2×Dic3—41no—
585C2×Dic3—41no—
586C2×Dic3—41no—
587C2×Dic3—41no—
588C2×Dic3—41no—
589C2×Dic3—41no—
590C2×Dic3—41no—
591C2×Dic3—41no—
592C2×Dic3—41no—
593C2×Dic3—41no—
594C2×Dic3—41no—
595C2×Dic3—41no—
596C2×Dic3—41no—
597C2×Dic3—41no—
598C2×Dic3—41no—
599C2×Dic3—41no—
600C2×Dic3—41no—
601C2×Dic3—41no—
602C2×Dic3—41no—
603C2×Dic3—41no—
604C2×Dic3—41no—
605C2×Dic3—41no—
606C2×Dic3C22⋊Q814yescomplemented
607C24—21no—
608C24—21no—
609C24—21no—
610C24—21no—
611C24—21no—
612C24—21no—
613C24—21no—
614C24—21no—
615C24—21no—
616C24—21no—
617C24—21no—
618C24—21no—
619C24D3×Q812yes—
620C24D3×Q812yes—
621C24C2×#6712yes—
622C24C23×D311yescharacteristic
623C2×Q8—28no—
624C2×Q8—28no—
625C2×Q8—44no—
626C2×Q8—44no—
627C2×Q8—44no—
628C2×Q8—44no—
629C2×Q8—44no—
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—28no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—32no—
664C22×C4—32no—
665C22×C4—32no—
666C22×C4—32no—
667C22×C4—32no—
668C22×C4—32no—
669C22×C4—32no—
670C22×C4—32no—
671C22×C4—44no—
672C22×C4—44no—
673C22×C4—44no—
674C22×C4—44no—
675C22×C4—44no—
676C22×C4—44no—
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×C4—61no—
702C22×C4—61no—
703C22×C4—61no—
704C22×C4—61no—
705C22×C4—61no—
706C22×C4—61no—
707C22×C4—61no—
708C22×C4—61no—
709C22×C4—61no—
710C22×C4—61no—
711C22×C4—61no—
712C22×C4—61no—
713C22×C4—61no—
714C22×C4—61no—
715C22×C4—61no—
716C22×C4—61no—
717C22×C4—61no—
718C22×C4—61no—
719C22×C4—61no—
720C22×C4—61no—
721C22×C4—61no—
722C22×C4—61no—
723C22×C4—61no—
724C22×C4—61no—
725C22×C4D3×D412yes—
726C22×C4#23712yes—
727C22×C4C2×#6712yes—
728C22×C4C2×#6712yes—
729C22×C4C2×#6712yes—
730C22×C4C2×#6712yes—
731C22×C4C2×#6712yes—
732C22×C4C2×#6712yes—
733C22×C4C2×#6712yes—
734C22×C4C2×#6712yes—
735C4⋊C4—28no—
736C4⋊C4—28no—
737C4⋊C4—28no—
738C4⋊C4—68no—
739C4⋊C4—124no—
740C4⋊C4—124no—
741C4⋊C4—124no—
742C4⋊C4—124no—
743C4⋊C4—124no—
744C4⋊C4—124no—
745C22⋊C4—28no—
746C22⋊C4—28no—
747C22⋊C4—68no—
748C22⋊C4—124no—
749C22⋊C4—124no—
750C22⋊C4—124no—
751C42—124no—
752C22×C3—24no—
753C22×C3—24no—
754C22×C3—24no—
755C22×C3—42no—
756C22×C3—42no—
757C22×C3—42no—
758C22×C3—42no—
759C22×C3—42no—
760C22×C3—42no—
761C22×C3—42no—
762C22×C3—42no—
763C22×C3—42no—
764C22×C3—42no—
765C22×C3—42no—
766C22×C3—42no—
767C22×C3C2×#12011yescharacteristic
768C22×C3C2×#12111yescharacteristic
769C22×C3C2×C22⋊Q811yescharacteristic
770C22×C3#52511yescharacteristic
771C22×C3C2×C4⋊Q811yescharacteristic
772C22×C3#53311yescharacteristic
773C22×C3#53411yescharacteristic
774C22×C3#53611yescharacteristic
775C22×C3#53711yescharacteristic
776C22×C3#53711yescharacteristic
777C22×C3#53911yescharacteristic
778C22×C3#54111yescharacteristic
779C22×C3#54211yescharacteristic
780C22×C3#54311yescharacteristic
781C22×C3#54411yescharacteristic
782C22×C3D4211yescharacteristic
783C22×C3D4211yescharacteristic
784C22×C3#54611yescharacteristic
785C22×C3#54611yescharacteristic
786C22×C3#54611yescharacteristic
787C22×C3#54711yescharacteristic
788C22×C3#54711yescharacteristic
789C22×C3#54811yescharacteristic
790C22×C3D4×Q811yescharacteristic
791C22×C3D4×Q811yescharacteristic
792C22×C3D4×Q811yescharacteristic
793C22×C3D4×Q811yescharacteristic
794C22×C3D4×Q811yescharacteristic
795C22×C3#55011yescharacteristic
796C22×C3#55411yescharacteristic
797C22×C3#55411yescharacteristic
798C22×C3#55411yescharacteristic
799C22×C3#55611yescharacteristic
800C22×C3#56211yescharacteristic
801C22×C3#56311yescharacteristic
802C3×C4—24no—
803C3×C4—24no—
804C3×C4—42no—
805C3×C4—42no—
806C3×C4—42no—
807C3×C4—42no—
808Dic3—24no—
809Dic3—42no—
810Dic3—42no—
811Dic3—42no—
812Dic3—42no—
813Dic3—42no—
814Dic3—81no—
815Dic3—81no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—22no—
827C23—22no—
828C23—22no—
829C23—22no—
830C23—22no—
831C23—22no—
832C23—22no—
833C23—22no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23—41no—
843C23—41no—
844C23—41no—
845C23—41no—
846C23—41no—
847C23—41no—
848C23—41no—
849C23—41no—
850C23#94414yes—
851C23C2×D3×D411yescharacteristic
852C23C2×#23711yescharacteristic
853C23#100411yescharacteristic
854C23#100411yescharacteristic
855C23C2×D3×Q811yescharacteristic
856C23C2×D3×Q811yescharacteristic
857C23#100711yescharacteristic
858C23#100711yescharacteristic
859C23D3×#4111yescharacteristic
860C23D3×#4111yescharacteristic
861C23#100911yescharacteristic
862C23#101011yescharacteristic
863C23C22×#6711yescharacteristic
864C23C22×#6711yescharacteristic
865C23C22×#6711yescharacteristic
866Q8—416no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—34no—
892C2×C4—416no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—62no—
910C2×C4—62no—
911C2×C4—62no—
912C2×C4—62no—
913C2×C4—62no—
914C2×C4—62no—
915C2×C4—62no—
916C2×C4—62no—
917C2×C4—62no—
918C2×C4—62no—
919C2×C4—62no—
920C2×C4—62no—
921C2×C4—62no—
922C2×C4—62no—
923C2×C4—62no—
924C2×C4—62no—
925C2×C4—62no—
926C2×C4—62no—
927C2×C4—62no—
928C2×C4—62no—
929C2×C4—62no—
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—121no—
939C2×C4—121no—
940C2×C4—121no—
941C2×C4—121no—
942C2×C4—121no—
943C2×C4—121no—
944C2×C4—121no—
945C2×C4—121no—
946C2×C4—121no—
947C2×C4—121no—
948C2×C4—121no—
949C2×C4—121no—
950C2×C4—121no—
951C2×C4—121no—
952C2×C4—121no—
953C2×C4—121no—
954C2×C4—121no—
955C2×C4—121no—
956C2×C4—121no—
957C2×C4—121no—
958C2×C4—121no—
959C2×C4—121no—
960C2×C4—121no—
961C2×C4—121no—
962C2×C4—121no—
963C2×C4—121no—
964C2×C4#93914yes—
965C2×C4#95314yes—
966C2×C3—44no—
967C2×C3#240711yescharacteristic
968C2×C3#241011yescharacteristic
969C2×C3#242911yescharacteristic
970C2×C3#243411yescharacteristic
971C2×C3#244011yescharacteristic
972C2×C3#244911yescharacteristic
973C2×C3#246511yescharacteristic
974C2×C3#253811yescharacteristic
975C2×C3#254911yescharacteristic
976C2×C3#267211yescharacteristic
977C2×C3#268311yescharacteristic
978C2×C3#268911yescharacteristic
979C2×C3#270411yescharacteristic
980C2×C3#272911yescharacteristic
981C2×C3#273211yescharacteristic
982C22—24no—
983C22—24no—
984C22—24no—
985C22—42no—
986C22—42no—
987C22—42no—
988C22—42no—
989C22—42no—
990C22—42no—
991C22—42no—
992C22—42no—
993C22—42no—
994C22—42no—
995C22—42no—
996C22—42no—
997C22#562211yescharacteristic
998C22#562311yescharacteristic
999C22#562511yescharacteristic
1000C22D3×C22⋊Q811yescharacteristic
1001C22#562911yescharacteristic
1002C22#563111yescharacteristic
1003C22#563211yescharacteristic
1004C22#563411yescharacteristic
1005C22#563511yescharacteristic
1006C22#563611yescharacteristic
1007C22#563611yescharacteristic
1008C22#563811yescharacteristic
1009C22#564011yescharacteristic
1010C22#564111yescharacteristic
1011C22#564611yescharacteristic
1012C22#564711yescharacteristic
1013C22D4×#6711yescharacteristic
1014C22D4×#6711yescharacteristic
1015C22C2×#93911yescharacteristic
1016C22#580411yescharacteristic
1017C22#580611yescharacteristic
1018C22#580611yescharacteristic
1019C22C2×#94411yescharacteristic
1020C22Q8×#6711yescharacteristic
1021C22Q8×#6711yescharacteristic
1022C22Q8×#6711yescharacteristic
1023C22Q8×#6711yescharacteristic
1024C22#581611yescharacteristic
1025C22#582411yescharacteristic
1026C22#582811yescharacteristic
1027C22#582911yescharacteristic
1028C22#583111yescharacteristic
1029C22#583311yescharacteristic
1030C22#583411yescharacteristic
1031C22C2×#95311yescharacteristic
1032C4—24no—
1033C4—24no—
1034C4—42no—
1035C4—42no—
1036C4—42no—
1037C4—42no—
1038C4—64no—
1039C4—122no—
1040C4—122no—
1041C4—122no—
1042C4—122no—
1043C4—122no—
1044C4—241no—
1045C4—241no—
1046C3#1527611yescharacteristic, complemented, Sylow
1047C2—44no—
1048C2#8275811yescharacteristic
1049C2#8276311yescharacteristic
1050C2#8276811yescharacteristic
1051C2#8277811yescharacteristic
1052C2#8278111yescharacteristic
1053C2#8279311yescharacteristic
1054C2#8279511yescharacteristic
1055C2#8280211yescharacteristic
1056C2#8280511yescharacteristic
1057C2#8280711yescharacteristic
1058C2#8281711yescharacteristic
1059C2#8282611yescharacteristic
1060C2#8404811yescharacteristic
1061C2#8406511yescharacteristic
1062C2#8409711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC22×C3×C22⋊Q8C2
prime radicalC25×C3C23
hypercenterC22×C22⋊Q8D3
hypocenterC3#15276
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×#5230C2semidirect
3. C2×#5229C2semidirect
5. C2×#4976C2semidirect
8. #71568C2semidirect
9. #71568C2semidirect
10. #71566C2semidirect
11. #71566C2semidirect
12. #71565C2semidirect
130. C2×#217Q8semidirect
131. C2×#217Q8semidirect
606. C2×Dic3C22⋊Q8semidirect
1046. C3#15276semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C22⋊Q82
C2×#52302
C2×#52292
C2×#52102
C2×#49762
C2×#49482
#721272
#715682
#715662
#715652
#715472
#715452
#152763