Finite Group Databasebeta

← #10733695

Subgroups — #10733695

Order 768.

1722 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C4⋊Q8C211yesmaximal, characteristic
2C2×#5230C211yesmaximal, characteristic
3C2×#5230C211yesmaximal, characteristic
4C2×#5229C211yesmaximal, characteristic
5C2×#4982C211yesmaximal, characteristic
6C2×#4976C211yesmaximal, characteristic
7#72134C211yesmaximal, characteristic
8#71568C211yesmaximal, characteristic
9#71568C211yesmaximal, characteristic
10#71567C211yesmaximal, characteristic
11#71566C211yesmaximal, characteristic
12#71565C211yesmaximal, characteristic
13#71564C211yesmaximal, characteristic
14#71536C211yesmaximal, characteristic
15#71536C211yesmaximal, characteristic
16#15318—31nomaximal, Sylow
17C23×C3×Q8C2211yescharacteristic
18C23×C3×Q8C2211yescharacteristic
19C2×C3×C4⋊Q8—24no—
20C2×C3×C4⋊Q8—24no—
21C2×C3×C4⋊Q8—24no—
22C22×C3×C4⋊C4C2211yescharacteristic
23C22×C3×C4⋊C4C2211yescharacteristic
24C22×C3×C4⋊C4C2211yescharacteristic
25C22×C3×C4⋊C4C2211yescharacteristic
26C22×C3×C42C2211yescharacteristic
27C22×C4⋊Dic3C2211yescharacteristic
28C22×Dic3⋊C4C2211yescharacteristic
29C22×Dic3⋊C4C2211yescharacteristic
30C22×Dic3⋊C4C2211yescharacteristic
31C22×Dic3⋊C4C2211yescharacteristic
32C22×Dic3⋊C4C2211yescharacteristic
33C22×Dic3⋊C4C2211yescharacteristic
34C22×C4×Dic3C2211yescharacteristic
35#5230—24no—
36#5230—24no—
37#5229—24no—
38C2×C3⋊#95C2211yescharacteristic
39C2×C3⋊#95C2211yescharacteristic
40C2×C3⋊#95C2211yescharacteristic
41C2×C3⋊#95C2211yescharacteristic
42C2×C3⋊#95C2211yescharacteristic
43C2×C3⋊#95C2211yescharacteristic
44C2×C3⋊#95C2211yescharacteristic
45C2×C3⋊#95C2211yescharacteristic
46C2×C3⋊#95C2211yescharacteristic
47C2×C3⋊#95C2211yescharacteristic
48C2×C3⋊#95C2211yescharacteristic
49C2×C3⋊#95C2211yescharacteristic
50C2×C3⋊#95C2211yescharacteristic
51C2×C3⋊#95C2211yescharacteristic
52C2×C3⋊#95C2211yescharacteristic
53C2×C3⋊#95C2211yescharacteristic
54C2×C3⋊#95C2211yescharacteristic
55C2×C3⋊#95C2211yescharacteristic
56C2×C3⋊#95C2211yescharacteristic
57C2×C3⋊#95C2211yescharacteristic
58#4982—24no—
59#4976—24no—
60C22×C4⋊Q8D311yescharacteristic
61C2×#398—31no—
62C2×#395—31no—
63C2×#395—31no—
64C2×#391—31no—
65C2×#389—31no—
66#1446—31no—
67#1444—31no—
68#1444—31no—
69#1442—31no—
70#1441—31no—
71#1441—31no—
72#1436—31no—
73#1436—31no—
74#1436—31no—
75C22×C3×Q8—22no—
76C22×C3×Q8—22no—
77C22×C3×Q8—22no—
78C22×C3×Q8—22no—
79C22×C3×Q8—22no—
80C22×C3×Q8—22no—
81C22×C3×Q8—22no—
82C22×C3×Q8—22no—
83C22×C3×Q8—22no—
84C22×C3×Q8—41no—
85C22×C3×Q8—41no—
86C22×C3×Q8—41no—
87C22×C3×Q8—41no—
88C22×C3×Q8D414yes—
89C23×C3×C4C2311yescharacteristic
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×C4⋊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⋊C4—22no—
114C2×C3×C4⋊C4—22no—
115C2×C3×C4⋊C4D414yes—
116C2×C3×C4⋊C4D414yes—
117C2×C3×C42—22no—
118C2×C3×C42—22no—
119C2×C3×C42—22no—
120C2×C4⋊Dic3—22no—
121C2×C4⋊Dic3—22no—
122C2×C4⋊Dic3—41no—
123C2×Dic3⋊C4—22no—
124C2×Dic3⋊C4—22no—
125C2×Dic3⋊C4—22no—
126C2×Dic3⋊C4—22no—
127C2×Dic3⋊C4—22no—
128C2×Dic3⋊C4—22no—
129C2×Dic3⋊C4—22no—
130C2×Dic3⋊C4—22no—
131C2×Dic3⋊C4—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⋊C4Q814yescomplemented
141C2×C4×Dic3—22no—
142C2×C4×Dic3—22no—
143C2×C4×Dic3—41no—
144C3⋊#95—22no—
145C3⋊#95—22no—
146C3⋊#95—22no—
147C3⋊#95—22no—
148C3⋊#95—22no—
149C3⋊#95—22no—
150C3⋊#95—22no—
151C3⋊#95—22no—
152C3⋊#95—22no—
153C3⋊#95—22no—
154C3⋊#95—22no—
155C3⋊#95—22no—
156C3⋊#95—22no—
157C3⋊#95—22no—
158C3⋊#95—22no—
159C3⋊#95—41no—
160C3⋊#95—41no—
161C3⋊#95D414yes—
162C3⋊#95Q814yescomplemented
163C3⋊#95Q814yescomplemented
164C23×Q8C2×D311yescharacteristic
165C23×Q8C2×D311yescharacteristic
166C2×C4⋊Q8—24no—
167C2×C4⋊Q8—24no—
168C2×C4⋊Q8—24no—
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⋊C4—31no—
176C22×C4⋊C4C2×D311yescharacteristic
177C22×C4⋊C4C2×D311yescharacteristic
178C22×C4⋊C4C2×D311yescharacteristic
179C22×C4⋊C4C2×D311yescharacteristic
180C22×C42—31no—
181C22×C42C2×D311yescharacteristic
182#398—64no—
183#395—64no—
184#395—64no—
185#391—64no—
186#389—64no—
187C2×#95—31no—
188C2×#95—31no—
189C2×#95—31no—
190C2×#95—31no—
191C2×#95—31no—
192C2×#95—31no—
193C2×#95—31no—
194C2×#95—31no—
195C2×#95—31no—
196C2×#95—31no—
197C2×#95—31no—
198C2×#95—31no—
199C2×#95—31no—
200C2×#95—31no—
201C2×#95—31no—
202C2×#95—31no—
203C2×#95—31no—
204C2×#95—31no—
205C2×#95—31no—
206C2×#95—31no—
207C24×C3C2411yescharacteristic
208C2×C3×Q8—28no—
209C2×C3×Q8—28no—
210C2×C3×Q8—28no—
211C2×C3×Q8—44no—
212C2×C3×Q8—44no—
213C2×C3×Q8—44no—
214C2×C3×Q8—44no—
215C2×C3×Q8—44no—
216C2×C3×Q8—44no—
217C2×C3×Q8—44no—
218C2×C3×Q8—44no—
219C2×C3×Q8—44no—
220C2×C3×Q8—44no—
221C2×C3×Q8—44no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×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—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×C4C2×D412yes—
257C22×C3×C4C2×D412yes—
258C22×C3×C4C2×D412yes—
259C22×C3×C4C2×D412yes—
260C22×C3×C4C2×D412yes—
261C22×C3×C4C2×D412yes—
262C22×C3×C4C2×D412yes—
263C22×C3×C4C2×D412yes—
264C22×C3×C4C2×D412yes—
265C22×C3×C4C2×D412yes—
266C22×C3×C4C2×Q812yes—
267C22×C3×C4C2×Q812yes—
268C22×C3×C4C2×Q812yes—
269C22×C3×C4#4112yes—
270C22×C3×C4#4112yes—
271C22×Dic3—21no—
272C22×Dic3—21no—
273C22×Dic3—21no—
274C22×Dic3—21no—
275C22×Dic3—21no—
276C22×Dic3—21no—
277C22×Dic3—21no—
278C22×Dic3—21no—
279C22×Dic3—21no—
280C22×Dic3—21no—
281C22×Dic3—21no—
282C22×Dic3—21no—
283C22×Dic3—21no—
284C22×Dic3—21no—
285C22×Dic3—21no—
286C22×Dic3—21no—
287C22×Dic3—21no—
288C22×Dic3—21no—
289C22×Dic3—21no—
290C22×Dic3—21no—
291C22×Dic3—21no—
292C22×Dic3—21no—
293C22×Dic3—21no—
294C22×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×Dic3C2×D412yes—
320C22×Dic3C2×D412yes—
321C22×Dic3C2×Q812yes—
322C22×Dic3C2×Q812yes—
323C22×Dic3C2×Q812yes—
324C22×Dic3C2×Q812yes—
325C22×Dic3C2×Q812yes—
326C22×Dic3C2×Q812yes—
327C3×C4⋊C4—28no—
328C3×C4⋊C4—28no—
329C3×C4⋊C4—28no—
330C3×C4⋊C4—28no—
331C3×C42—28no—
332C4⋊Dic3—44no—
333Dic3⋊C4—28no—
334Dic3⋊C4—44no—
335Dic3⋊C4—44no—
336Dic3⋊C4—44no—
337Dic3⋊C4—44no—
338Dic3⋊C4—44no—
339C4×Dic3—44no—
340C22×Q8—22no—
341C22×Q8—22no—
342C22×Q8—22no—
343C22×Q8—22no—
344C22×Q8—22no—
345C22×Q8—22no—
346C22×Q8—22no—
347C22×Q8—22no—
348C22×Q8—22no—
349C22×Q8—41no—
350C22×Q8—41no—
351C22×Q8—41no—
352C22×Q8—41no—
353C22×Q8#6714yes—
354C23×C4—31no—
355C23×C4—31no—
356C23×C4—31no—
357C23×C4—31no—
358C23×C4—31no—
359C23×C4—31no—
360C23×C4—31no—
361C23×C4—31no—
362C23×C4C22×D311yescharacteristic
363C23×C4C22×D311yescharacteristic
364C23×C4C22×D311yescharacteristic
365C23×C4C22×D311yescharacteristic
366C23×C4C22×D311yescharacteristic
367C23×C4C22×D311yescharacteristic
368C23×C4C22×D311yescharacteristic
369C4⋊Q8—232no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—34no—
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—62no—
392C2×C4⋊C4—62no—
393C2×C4⋊C4—62no—
394C2×C4⋊C4—62no—
395C2×C4⋊C4—62no—
396C2×C4⋊C4—121no—
397C2×C4⋊C4—121no—
398C2×C4⋊C4—121no—
399C2×C4⋊C4—121no—
400C2×C4⋊C4—121no—
401C2×C4⋊C4#6714yes—
402C2×C4⋊C4#6714yes—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—62no—
407C2×C42—62no—
408C2×C42—121no—
409#95—34no—
410#95—34no—
411#95—34no—
412#95—62no—
413#95—62no—
414#95—62no—
415#95—62no—
416#95—62no—
417#95—62no—
418#95—62no—
419#95—62no—
420#95—62no—
421#95—62no—
422#95—62no—
423#95—62no—
424#95—62no—
425#95—62no—
426#95—62no—
427#95—121no—
428#95—121no—
429C23×C3C22×D411yescharacteristic
430C23×C3C22×D411yescharacteristic
431C23×C3C22×D411yescharacteristic
432C23×C3C22×D411yescharacteristic
433C23×C3C22×Q811yescharacteristic
434C23×C3C22×Q811yescharacteristic
435C23×C3C22×Q811yescharacteristic
436C23×C3C2×#4111yescharacteristic
437C23×C3C2×#4111yescharacteristic
438C23×C3H(5,𝔽2)11yescharacteristic
439C23×C3H(5,𝔽2)11yescharacteristic
440C23×C32−1+411yescharacteristic
441C23×C32−1+411yescharacteristic
442C23×C32−1+411yescharacteristic
443C23×C32−1+411yescharacteristic
444C3×Q8—416no—
445C3×Q8—416no—
446C2×C3×C4—22no—
447C2×C3×C4—22no—
448C2×C3×C4—22no—
449C2×C3×C4—22no—
450C2×C3×C4—22no—
451C2×C3×C4—22no—
452C2×C3×C4—22no—
453C2×C3×C4—22no—
454C2×C3×C4—22no—
455C2×C3×C4—22no—
456C2×C3×C4—22no—
457C2×C3×C4—22no—
458C2×C3×C4—22no—
459C2×C3×C4—22no—
460C2×C3×C4—22no—
461C2×C3×C4—22no—
462C2×C3×C4—22no—
463C2×C3×C4—22no—
464C2×C3×C4—22no—
465C2×C3×C4—22no—
466C2×C3×C4—22no—
467C2×C3×C4—22no—
468C2×C3×C4—22no—
469C2×C3×C4—22no—
470C2×C3×C4—22no—
471C2×C3×C4—22no—
472C2×C3×C4—22no—
473C2×C3×C4—22no—
474C2×C3×C4—22no—
475C2×C3×C4—22no—
476C2×C3×C4—22no—
477C2×C3×C4—22no—
478C2×C3×C4—22no—
479C2×C3×C4—41no—
480C2×C3×C4—41no—
481C2×C3×C4—41no—
482C2×C3×C4—41no—
483C2×C3×C4—41no—
484C2×C3×C4—41no—
485C2×C3×C4—41no—
486C2×C3×C4—41no—
487C2×C3×C4—41no—
488C2×C3×C4—41no—
489C2×C3×C4—41no—
490C2×C3×C4—41no—
491C2×C3×C4#12014yes—
492C2×C3×C4#12114yes—
493C2×C3×C4C22⋊Q814yes—
494C2×C3×C4C4⋊Q814yes—
495C2×Dic3—22no—
496C2×Dic3—22no—
497C2×Dic3—22no—
498C2×Dic3—22no—
499C2×Dic3—22no—
500C2×Dic3—22no—
501C2×Dic3—22no—
502C2×Dic3—22no—
503C2×Dic3—22no—
504C2×Dic3—22no—
505C2×Dic3—22no—
506C2×Dic3—22no—
507C2×Dic3—22no—
508C2×Dic3—22no—
509C2×Dic3—22no—
510C2×Dic3—22no—
511C2×Dic3—22no—
512C2×Dic3—22no—
513C2×Dic3—22no—
514C2×Dic3—22no—
515C2×Dic3—22no—
516C2×Dic3—41no—
517C2×Dic3—41no—
518C2×Dic3—41no—
519C2×Dic3—41no—
520C2×Dic3—41no—
521C2×Dic3—41no—
522C2×Dic3—41no—
523C2×Dic3—41no—
524C2×Dic3—41no—
525C2×Dic3—41no—
526C2×Dic3—41no—
527C2×Dic3—41no—
528C2×Dic3—41no—
529C2×Dic3—41no—
530C2×Dic3—41no—
531C2×Dic3—41no—
532C2×Dic3—41no—
533C2×Dic3—41no—
534C2×Dic3—41no—
535C2×Dic3—41no—
536C2×Dic3—41no—
537C2×Dic3—41no—
538C2×Dic3—41no—
539C2×Dic3—41no—
540C2×Dic3—41no—
541C2×Dic3—41no—
542C2×Dic3—41no—
543C2×Dic3—41no—
544C2×Dic3—41no—
545C2×Dic3—41no—
546C2×Dic3—41no—
547C2×Dic3—41no—
548C2×Dic3—41no—
549C2×Dic3—41no—
550C2×Dic3C4⋊Q814yescomplemented
551C24C23×D311yescharacteristic
552C2×Q8—28no—
553C2×Q8—28no—
554C2×Q8—28no—
555C2×Q8—44no—
556C2×Q8—44no—
557C2×Q8—44no—
558C2×Q8—44no—
559C2×Q8—44no—
560C2×Q8—44no—
561C2×Q8—44no—
562C2×Q8—44no—
563C2×Q8—44no—
564C2×Q8—44no—
565C2×Q8—44no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—32no—
601C22×C4—32no—
602C22×C4—32no—
603C22×C4—32no—
604C22×C4—32no—
605C22×C4—32no—
606C22×C4—32no—
607C22×C4—32no—
608C22×C4—61no—
609C22×C4—61no—
610C22×C4—61no—
611C22×C4—61no—
612C22×C4—61no—
613C22×C4—61no—
614C22×C4—61no—
615C22×C4—61no—
616C22×C4—61no—
617C22×C4—61no—
618C22×C4—61no—
619C22×C4—61no—
620C22×C4—61no—
621C22×C4—61no—
622C22×C4—61no—
623C22×C4—61no—
624C22×C4—61no—
625C22×C4—61no—
626C22×C4—61no—
627C22×C4—61no—
628C22×C4—61no—
629C22×C4—61no—
630C22×C4—61no—
631C22×C4—61no—
632C22×C4—61no—
633C22×C4—61no—
634C22×C4—61no—
635C22×C4—61no—
636C22×C4—61no—
637C22×C4—61no—
638C22×C4—61no—
639C22×C4—61no—
640C22×C4—61no—
641C22×C4—61no—
642C22×C4—61no—
643C22×C4—61no—
644C22×C4—61no—
645C22×C4—61no—
646C22×C4—61no—
647C22×C4—61no—
648C22×C4—61no—
649C22×C4—61no—
650C22×C4—61no—
651C22×C4—61no—
652C22×C4—61no—
653C22×C4—61no—
654C22×C4—61no—
655C22×C4—61no—
656C22×C4D3×D412yes—
657C22×C4#23712yes—
658C22×C4D3×Q812yes—
659C22×C4D3×Q812yes—
660C22×C4D3×Q812yes—
661C22×C4#23912yes—
662C22×C4C2×#6712yes—
663C22×C4C2×#6712yes—
664C22×C4C2×#6712yes—
665C22×C4C2×#6712yes—
666C22×C4C2×#6712yes—
667C22×C4C2×#6712yes—
668C22×C4C2×#6712yes—
669C22×C4C2×#6712yes—
670C22×C4C2×#6712yes—
671C4⋊C4—28no—
672C4⋊C4—28no—
673C4⋊C4—28no—
674C4⋊C4—28no—
675C4⋊C4—68no—
676C4⋊C4—124no—
677C4⋊C4—124no—
678C4⋊C4—124no—
679C4⋊C4—124no—
680C4⋊C4—124no—
681C4⋊C4—124no—
682C42—28no—
683C42—124no—
684C22×C3C2×#12011yescharacteristic
685C22×C3C2×#12111yescharacteristic
686C22×C3C2×C22⋊Q811yescharacteristic
687C22×C3C2×C4⋊Q811yescharacteristic
688C22×C3C2×C4⋊Q811yescharacteristic
689C22×C3#53311yescharacteristic
690C22×C3#53411yescharacteristic
691C22×C3#53611yescharacteristic
692C22×C3#53611yescharacteristic
693C22×C3#53611yescharacteristic
694C22×C3#54111yescharacteristic
695C22×C3#54211yescharacteristic
696C22×C3#54411yescharacteristic
697C22×C3#54411yescharacteristic
698C22×C3#54411yescharacteristic
699C22×C3D4211yescharacteristic
700C22×C3D4211yescharacteristic
701C22×C3#54611yescharacteristic
702C22×C3#54611yescharacteristic
703C22×C3#54711yescharacteristic
704C22×C3#54811yescharacteristic
705C22×C3#54811yescharacteristic
706C22×C3D4×Q811yescharacteristic
707C22×C3D4×Q811yescharacteristic
708C22×C3D4×Q811yescharacteristic
709C22×C3D4×Q811yescharacteristic
710C22×C3D4×Q811yescharacteristic
711C22×C3D4×Q811yescharacteristic
712C22×C3D4×Q811yescharacteristic
713C22×C3#55411yescharacteristic
714C22×C3#55711yescharacteristic
715C22×C3#55711yescharacteristic
716C22×C3Q8211yescharacteristic
717C22×C3#56311yescharacteristic
718C22×C3#56311yescharacteristic
719C3×C4—24no—
720C3×C4—24no—
721C3×C4—24no—
722C3×C4—24no—
723C3×C4—42no—
724C3×C4—42no—
725C3×C4—42no—
726Dic3—24no—
727Dic3—42no—
728Dic3—42no—
729Dic3—42no—
730Dic3—42no—
731Dic3—42no—
732Dic3—81no—
733Dic3—81no—
734C23C2×D3×D411yescharacteristic
735C23C2×#23711yescharacteristic
736C23#100411yescharacteristic
737C23#100411yescharacteristic
738C23C2×D3×Q811yescharacteristic
739C23C2×D3×Q811yescharacteristic
740C23C2×D3×Q811yescharacteristic
741C23C2×#23911yescharacteristic
742C23#100711yescharacteristic
743C23#100711yescharacteristic
744C23#100711yescharacteristic
745C23#100711yescharacteristic
746C23C22×#6711yescharacteristic
747C23C22×#6711yescharacteristic
748C23C22×#6711yescharacteristic
749Q8—416no—
750Q8—416no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—34no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—62no—
798C2×C4—62no—
799C2×C4—62no—
800C2×C4—62no—
801C2×C4—62no—
802C2×C4—62no—
803C2×C4—62no—
804C2×C4—62no—
805C2×C4—62no—
806C2×C4—62no—
807C2×C4—62no—
808C2×C4—62no—
809C2×C4—62no—
810C2×C4—62no—
811C2×C4—62no—
812C2×C4—62no—
813C2×C4—62no—
814C2×C4—62no—
815C2×C4—62no—
816C2×C4—62no—
817C2×C4—62no—
818C2×C4—121no—
819C2×C4—121no—
820C2×C4—121no—
821C2×C4—121no—
822C2×C4—121no—
823C2×C4—121no—
824C2×C4—121no—
825C2×C4—121no—
826C2×C4—121no—
827C2×C4—121no—
828C2×C4—121no—
829C2×C4—121no—
830C2×C4—121no—
831C2×C4—121no—
832C2×C4—121no—
833C2×C4—121no—
834C2×C4—121no—
835C2×C4—121no—
836C2×C4—121no—
837C2×C4—121no—
838C2×C4—121no—
839C2×C4—121no—
840C2×C4—121no—
841C2×C4—121no—
842C2×C4—121no—
843C2×C4—121no—
844C2×C4—121no—
845C2×C4—121no—
846C2×C4—121no—
847C2×C4—121no—
848C2×C4—121no—
849C2×C4—121no—
850C2×C4—121no—
851C2×C4—121no—
852C2×C4#93914yes—
853C2×C4#94414yes—
854C2×C4#94614yes—
855C2×C4#95314yes—
856C2×C3#240911yescharacteristic
857C2×C3#241011yescharacteristic
858C2×C3#242911yescharacteristic
859C2×C3#243411yescharacteristic
860C2×C3#244011yescharacteristic
861C2×C3#245111yescharacteristic
862C2×C3#254611yescharacteristic
863C2×C3#255011yescharacteristic
864C2×C3#255111yescharacteristic
865C2×C3#267411yescharacteristic
866C2×C3#267711yescharacteristic
867C2×C3#271311yescharacteristic
868C2×C3#271311yescharacteristic
869C2×C3#272911yescharacteristic
870C2×C3#273411yescharacteristic
871C22#572111yescharacteristic
872C22#572111yescharacteristic
873C22#572211yescharacteristic
874C22D3×C4⋊Q811yescharacteristic
875C22#572411yescharacteristic
876C22#572611yescharacteristic
877C22#572711yescharacteristic
878C22#572811yescharacteristic
879C22#572911yescharacteristic
880C22#572911yescharacteristic
881C22#572911yescharacteristic
882C22#573011yescharacteristic
883C22#573111yescharacteristic
884C22#573311yescharacteristic
885C22#573511yescharacteristic
886C22#573511yescharacteristic
887C22D4×#6711yescharacteristic
888C22D4×#6711yescharacteristic
889C22C2×#93911yescharacteristic
890C22#580411yescharacteristic
891C22#580611yescharacteristic
892C22#580611yescharacteristic
893C22C2×#94411yescharacteristic
894C22C2×#94611yescharacteristic
895C22Q8×#6711yescharacteristic
896C22Q8×#6711yescharacteristic
897C22Q8×#6711yescharacteristic
898C22Q8×#6711yescharacteristic
899C22Q8×#6711yescharacteristic
900C22Q8×#6711yescharacteristic
901C22#581611yescharacteristic
902C22#581611yescharacteristic
903C22#581711yescharacteristic
904C22#581711yescharacteristic
905C22C2×#95311yescharacteristic
906C4—24no—
907C4—24no—
908C4—24no—
909C4—24no—
910C4—42no—
911C4—42no—
912C4—42no—
913C4—64no—
914C4—122no—
915C4—122no—
916C4—122no—
917C4—122no—
918C4—122no—
919C4—241no—
920C4—241no—
921C3#1531811yescharacteristic, complemented, Sylow
922C2#8323311yescharacteristic
923C2#8323511yescharacteristic
924C2#8323811yescharacteristic
925C2#8324111yescharacteristic
926C2#8324211yescharacteristic
927C2#8324711yescharacteristic
928C2#8324711yescharacteristic
929C2#8325011yescharacteristic
930C2#8325411yescharacteristic
931C2#8326511yescharacteristic
932C2#8326611yescharacteristic
933C2#8326711yescharacteristic
934C2#8404811yescharacteristic
935C2#8406511yescharacteristic
936C2#8406811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, prime radical, cosocleC24×C3C24
FittingC22×C3×C4⋊Q8C2
hypercenterC22×C4⋊Q8D3
hypocenterC3#15318
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22×C4⋊Q8

Complements

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

NH ≅ G/Ntype
140. C2×Dic3⋊C4Q8semidirect
162. C3⋊#95Q8semidirect
163. C3⋊#95Q8semidirect
550. C2×Dic3C4⋊Q8semidirect
921. C3#15318semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C4⋊Q82
C2×#52302
C2×#52292
C2×#49822
C2×#49762
#721342
#715682
#715672
#715662
#715652
#715642
#715362
#153183