Finite Group Databasebeta

← #10733157

Subgroups — #10733157

Order 768.

2142 conjugacy classes of subgroups.

The subgroup lattice has 1200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×#5231C211yesmaximal, characteristic, complemented
3C2×#5229C211yesmaximal, characteristic, complemented
4C2×#5213C211yesmaximal, characteristic
5C2×#4994C211yesmaximal, characteristic, complemented
6C2×#4957C211yesmaximal, characteristic
7#72127C211yesmaximal, characteristic, complemented
8#71570C211yesmaximal, characteristic, complemented
9#71570C211yesmaximal, characteristic, complemented
10#71568C211yesmaximal, characteristic, complemented
11#71566C211yesmaximal, characteristic, complemented
12#71564C211yesmaximal, characteristic, complemented
13#71550C211yesmaximal, characteristic
14#71547C211yesmaximal, characteristic, complemented
15#71546C211yesmaximal, characteristic, complemented
16#15280—31nomaximal, Sylow
17C23×C3×Q8C2211yescharacteristic
18C24×C3×C4C2211yescharacteristic
19C23×#67C2211yescharacteristic
20C2×C3×C22⋊Q8—24no—
21C2×C3×C22⋊Q8—24no—
22C2×C3×C22⋊Q8—24no—
23C22×C3×C4⋊C4C2211yescharacteristic
24C22×C3×C4⋊C4C2211yescharacteristic
25C22×C3×C4⋊C4C2211yescharacteristic
26C22×C3×C22⋊C4C2211yescharacteristic
27C22×C3×C22⋊C4C2211yescharacteristic
28C22×#217C2211yescharacteristic
29C22×#217C2211yescharacteristic
30C22×#217C2211yescharacteristic
31C22×(C2×D3)⋊C4C2211yescharacteristic
32C22×(C2×D3)⋊C4C2211yescharacteristic
33C22×(C2×D3)⋊C4C2211yescharacteristic
34C22×(C2×D3)⋊C4C2211yescharacteristic
35C22×(C2×D3)⋊C4C2211yescharacteristic
36C22×(C2×D3)⋊C4C2211yescharacteristic
37C22×C4⋊Dic3C2211yescharacteristic
38C22×Dic3⋊C4C2211yescharacteristic
39C22×Dic3⋊C4C2211yescharacteristic
40C22×C4×Dic3C2211yescharacteristic
41#5231—24no—
42#5229—24no—
43#5213—24no—
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#4994—24no—
59#4957—24no—
60C22×C22⋊Q8D311yescharacteristic, complemented
61C2×#396—31no—
62C2×#393—31no—
63C2×#391—31no—
64C2×#390—31no—
65C2×#386—31no—
66#1444—31no—
67#1441—31no—
68#1439—31no—
69#1439—31no—
70#1439—31no—
71#1439—31no—
72#1438—31no—
73#1436—31no—
74C22⋊#95—31no—
75C25×C3C2311yescharacteristic
76C24×D3C2311yescharacteristic
77C22×C3×Q8—22no—
78C22×C3×Q8—22no—
79C22×C3×Q8—22no—
80C22×C3×Q8—22no—
81C22×C3×Q8—41no—
82C22×C3×Q8—41no—
83C22×C3×Q8D414yescomplemented
84C23×C3×C4—22no—
85C23×C3×C4—22no—
86C23×C3×C4—22no—
87C23×C3×C4—22no—
88C23×C3×C4—22no—
89C23×C3×C4—41no—
90C23×C3×C4—41no—
91C23×C3×C4C2311yescharacteristic
92C23×C3×C4C2311yescharacteristic
93C23×C3×C4C2311yescharacteristic
94C23×C3×C4C2311yescharacteristic
95C23×C3×C4C2311yescharacteristic
96C23×C3×C4C2311yescharacteristic
97C22×#67—22no—
98C22×#67—22no—
99C22×#67—22no—
100C22×#67—22no—
101C22×#67—41no—
102C22×#67—41no—
103C22×#67Q814yescomplemented
104C23×Dic3C2311yescharacteristic
105C23×Dic3C2311yescharacteristic
106C23×Dic3C2311yescharacteristic
107C23×Dic3C2311yescharacteristic
108C23×Dic3C2311yescharacteristic
109C23×Dic3C2311yescharacteristic
110C23×Dic3C2311yescharacteristic
111C3×C22⋊Q8—232no—
112C2×C3×C4⋊C4—22no—
113C2×C3×C4⋊C4—22no—
114C2×C3×C4⋊C4—22no—
115C2×C3×C4⋊C4—22no—
116C2×C3×C4⋊C4—22no—
117C2×C3×C4⋊C4—22no—
118C2×C3×C4⋊C4—22no—
119C2×C3×C4⋊C4—22no—
120C2×C3×C4⋊C4D414yescomplemented
121C2×C3×C22⋊C4—22no—
122C2×C3×C22⋊C4—22no—
123C2×C3×C22⋊C4—22no—
124C2×C3×C22⋊C4—22no—
125C2×C3×C22⋊C4—22no—
126C2×C3×C22⋊C4D414yes—
127C2×#217—22no—
128C2×#217—22no—
129C2×#217—22no—
130C2×#217—22no—
131C2×#217—22no—
132C2×#217—41no—
133C2×#217—41no—
134C2×#217—41no—
135C2×#217—41no—
136C2×(C2×D3)⋊C4—22no—
137C2×(C2×D3)⋊C4—22no—
138C2×(C2×D3)⋊C4—22no—
139C2×(C2×D3)⋊C4—22no—
140C2×(C2×D3)⋊C4—22no—
141C2×(C2×D3)⋊C4—22no—
142C2×(C2×D3)⋊C4—22no—
143C2×(C2×D3)⋊C4—22no—
144C2×(C2×D3)⋊C4—22no—
145C2×(C2×D3)⋊C4—22no—
146C2×(C2×D3)⋊C4—22no—
147C2×(C2×D3)⋊C4—22no—
148C2×(C2×D3)⋊C4—41no—
149C2×(C2×D3)⋊C4—41no—
150C2×(C2×D3)⋊C4—41no—
151C2×(C2×D3)⋊C4—41no—
152C2×(C2×D3)⋊C4—41no—
153C2×(C2×D3)⋊C4—41no—
154C2×C4⋊Dic3—22no—
155C2×C4⋊Dic3—22no—
156C2×C4⋊Dic3—41no—
157C2×Dic3⋊C4—22no—
158C2×Dic3⋊C4—22no—
159C2×Dic3⋊C4—22no—
160C2×Dic3⋊C4—41no—
161C2×Dic3⋊C4—41no—
162C2×Dic3⋊C4—41no—
163C2×C4×Dic3—22no—
164C2×C4×Dic3—22no—
165C2×C4×Dic3—41no—
166C3⋊#95—22no—
167C3⋊#95—22no—
168C3⋊#95—22no—
169C3⋊#95—22no—
170C3⋊#95—22no—
171C3⋊#95—22no—
172C3⋊#95—22no—
173C3⋊#95—22no—
174C3⋊#95—22no—
175C3⋊#95—22no—
176C3⋊#95—41no—
177C3⋊#95—41no—
178C3⋊#95—41no—
179C3⋊#95D414yes—
180C23×Q8C2×D311yescharacteristic
181C23×D4—31no—
182C24×C4C2×D311yescharacteristic
183C2×C22⋊Q8—24no—
184C2×C22⋊Q8—24no—
185C2×C22⋊Q8—24no—
186C22×C4⋊C4—31no—
187C22×C4⋊C4—31no—
188C22×C4⋊C4—31no—
189C22×C4⋊C4C2×D311yescharacteristic
190C22×C4⋊C4C2×D311yescharacteristic
191C22×C4⋊C4C2×D311yescharacteristic
192C22×C22⋊C4—31no—
193C22×C22⋊C4—31no—
194C22×C22⋊C4—31no—
195C22×C22⋊C4—31no—
196C22×C22⋊C4—31no—
197C22×C22⋊C4—31no—
198C22×C22⋊C4—31no—
199C22×C22⋊C4—31no—
200C22×C22⋊C4—31no—
201C22×C22⋊C4C2×D311yescharacteristic
202C22×C22⋊C4C2×D311yescharacteristic
203C22×C42—31no—
204#396—64no—
205#393—64no—
206#391—64no—
207#390—64no—
208#386—64no—
209C2×#95—31no—
210C2×#95—31no—
211C2×#95—31no—
212C2×#95—31no—
213C2×#95—31no—
214C2×#95—31no—
215C2×#95—31no—
216C2×#95—31no—
217C2×#95—31no—
218C2×#95—31no—
219C2×#95—31no—
220C2×#95—31no—
221C2×#95—31no—
222C2×#95—31no—
223C24×C3—21no—
224C24×C3—21no—
225C24×C3—21no—
226C24×C3—21no—
227C24×C3—21no—
228C24×C3—21no—
229C24×C3—21no—
230C24×C3—21no—
231C24×C3—21no—
232C24×C3—21no—
233C24×C3—21no—
234C24×C3—21no—
235C24×C3C2×D412yes—
236C24×C3C2×Q812yes—
237C24×C3#4112yes—
238C24×C3C2411yescharacteristic
239C23×D3—21no—
240C23×D3—21no—
241C23×D3—21no—
242C23×D3—21no—
243C23×D3—21no—
244C23×D3—21no—
245C23×D3—21no—
246C23×D3—21no—
247C23×D3—21no—
248C23×D3—21no—
249C23×D3—21no—
250C23×D3—21no—
251C23×D3—21no—
252C23×D3—21no—
253C23×D3C2×Q812yes—
254C2×C3×Q8—28no—
255C2×C3×Q8—28no—
256C2×C3×Q8—44no—
257C2×C3×Q8—44no—
258C2×C3×Q8—44no—
259C2×C3×Q8—44no—
260C2×C3×Q8—44no—
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—28no—
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—21no—
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—44no—
295C22×C3×C4—44no—
296C22×C3×C4—44no—
297C22×C3×C4—44no—
298C22×C3×C4—44no—
299C22×C3×C4—44no—
300C22×C3×C4C2×D412yes—
301C22×C3×C4C2×D412yes—
302C22×C3×C4C2×D412yes—
303C22×C3×C4C2×D412yes—
304C22×C3×C4C2×D412yes—
305C22×C3×C4C2×D412yes—
306C22×C3×C4C2×D412yes—
307C22×C3×C4C2×D412yes—
308C22×C3×C4C2×D412yes—
309C22×C3×C4#4112yes—
310C2×#67—28no—
311C2×#67—28no—
312C2×#67—44no—
313C2×#67—44no—
314C2×#67—44no—
315C2×#67—44no—
316C2×#67—44no—
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×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×Dic3C2×D412yes—
362C22×Dic3C2×D412yes—
363C22×Dic3C2×Q812yes—
364C22×Dic3#4112yes—
365C22×Dic3#4112yes—
366C3×C4⋊C4—28no—
367C3×C4⋊C4—28no—
368C3×C4⋊C4—28no—
369C3×C22⋊C4—28no—
370C3×C22⋊C4—28no—
371#217—44no—
372#217—44no—
373#217—44no—
374(C2×D3)⋊C4—44no—
375(C2×D3)⋊C4—44no—
376(C2×D3)⋊C4—44no—
377(C2×D3)⋊C4—44no—
378(C2×D3)⋊C4—44no—
379(C2×D3)⋊C4—44no—
380C4⋊Dic3—44no—
381Dic3⋊C4—44no—
382Dic3⋊C4—44no—
383C4×Dic3—44no—
384C25—31no—
385C25C22×D311yescharacteristic
386C22×Q8—22no—
387C22×Q8—22no—
388C22×Q8—22no—
389C22×Q8—22no—
390C22×Q8—41no—
391C22×Q8—41no—
392C22×Q8#6714yescomplemented
393C22×D4—34no—
394C22×D4—62no—
395C22×D4—62no—
396C22×D4—62no—
397C22×D4—62no—
398C22×D4—121no—
399C22×D4—121no—
400C23×C4—22no—
401C23×C4—22no—
402C23×C4—22no—
403C23×C4—22no—
404C23×C4—22no—
405C23×C4—31no—
406C23×C4—31no—
407C23×C4—31no—
408C23×C4—31no—
409C23×C4—31no—
410C23×C4—31no—
411C23×C4—31no—
412C23×C4—41no—
413C23×C4—41no—
414C23×C4C22×D311yescharacteristic
415C23×C4C22×D311yescharacteristic
416C23×C4C22×D311yescharacteristic
417C23×C4C22×D311yescharacteristic
418C23×C4C22×D311yescharacteristic
419C23×C4C22×D311yescharacteristic
420C22⋊Q8—232no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—62no—
430C2×C4⋊C4—62no—
431C2×C4⋊C4—62no—
432C2×C4⋊C4—62no—
433C2×C4⋊C4—62no—
434C2×C4⋊C4—121no—
435C2×C4⋊C4—121no—
436C2×C4⋊C4—121no—
437C2×C4⋊C4—121no—
438C2×C4⋊C4#6714yescomplemented
439C2×C22⋊C4—22no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—22no—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—22no—
444C2×C22⋊C4—62no—
445C2×C22⋊C4—62no—
446C2×C22⋊C4—62no—
447C2×C22⋊C4—62no—
448C2×C22⋊C4—62no—
449C2×C22⋊C4—62no—
450C2×C22⋊C4—62no—
451C2×C22⋊C4—62no—
452C2×C22⋊C4—62no—
453C2×C22⋊C4—62no—
454C2×C22⋊C4—62no—
455C2×C22⋊C4—62no—
456C2×C22⋊C4—62no—
457C2×C22⋊C4—62no—
458C2×C22⋊C4—62no—
459C2×C22⋊C4—62no—
460C2×C22⋊C4—62no—
461C2×C22⋊C4—121no—
462C2×C22⋊C4—121no—
463C2×C22⋊C4—121no—
464C2×C22⋊C4—121no—
465C2×C22⋊C4—121no—
466C2×C22⋊C4—121no—
467C2×C22⋊C4—121no—
468C2×C22⋊C4—121no—
469C2×C22⋊C4—121no—
470C2×C22⋊C4—121no—
471C2×C22⋊C4#6714yes—
472C2×C42—62no—
473C2×C42—62no—
474C2×C42—121no—
475#95—34no—
476#95—62no—
477#95—62no—
478#95—62no—
479#95—62no—
480#95—62no—
481#95—62no—
482#95—62no—
483#95—62no—
484#95—62no—
485#95—62no—
486#95—121no—
487#95—121no—
488#95—121no—
489C23×C3—22no—
490C23×C3—22no—
491C23×C3—22no—
492C23×C3—22no—
493C23×C3—22no—
494C23×C3—22no—
495C23×C3—22no—
496C23×C3—22no—
497C23×C3—22no—
498C23×C3—22no—
499C23×C3—22no—
500C23×C3—22no—
501C23×C3—22no—
502C23×C3—22no—
503C23×C3—22no—
504C23×C3—22no—
505C23×C3—22no—
506C23×C3—22no—
507C23×C3—41no—
508C23×C3—41no—
509C23×C3—41no—
510C23×C3—41no—
511C23×C3—41no—
512C23×C3—41no—
513C23×C3—41no—
514C23×C3—41no—
515C23×C3—41no—
516C23×C3—41no—
517C23×C3—41no—
518C23×C3—41no—
519C23×C3—41no—
520C23×C3—41no—
521C23×C3—41no—
522C23×C3—41no—
523C23×C3C22⋊Q814yes—
524C23×C3C22×D411yescharacteristic
525C23×C3C22×D411yescharacteristic
526C23×C3C22×D411yescharacteristic
527C23×C3C22×D411yescharacteristic
528C23×C3C22×Q811yescharacteristic
529C23×C3C2×#4111yescharacteristic
530C23×C3C2×#4111yescharacteristic
531C23×C3C2×#4111yescharacteristic
532C23×C3C2×#4111yescharacteristic
533C23×C3H(5,𝔽2)11yescharacteristic
534C23×C3H(5,𝔽2)11yescharacteristic
535C23×C3H(5,𝔽2)11yescharacteristic
536C23×C3H(5,𝔽2)11yescharacteristic
537C23×C32−1+411yescharacteristic
538C23×C32−1+411yescharacteristic
539C22×D3—22no—
540C22×D3—22no—
541C22×D3—22no—
542C22×D3—22no—
543C22×D3—22no—
544C22×D3—22no—
545C22×D3—22no—
546C22×D3—41no—
547C22×D3—41no—
548C22×D3—41no—
549C22×D3—41no—
550C22×D3—41no—
551C22×D3—41no—
552C22×D3—41no—
553C22×D3—41no—
554C22×D3—41no—
555C22×D3—41no—
556C22×D3—41no—
557C22×D3—41no—
558C22×D3—41no—
559C22×D3—41no—
560C22×D3—41no—
561C22×D3—41no—
562C22×D3—41no—
563C22×D3—41no—
564C22×D3—41no—
565C22×D3—41no—
566C22×D3—41no—
567C22×D3—41no—
568C22×D3—41no—
569C22×D3—41no—
570C22×D3—41no—
571C22×D3—41no—
572C22×D3—41no—
573C22×D3—41no—
574C3×Q8—416no—
575C2×C3×C4—22no—
576C2×C3×C4—22no—
577C2×C3×C4—22no—
578C2×C3×C4—22no—
579C2×C3×C4—22no—
580C2×C3×C4—22no—
581C2×C3×C4—22no—
582C2×C3×C4—22no—
583C2×C3×C4—22no—
584C2×C3×C4—22no—
585C2×C3×C4—22no—
586C2×C3×C4—22no—
587C2×C3×C4—22no—
588C2×C3×C4—22no—
589C2×C3×C4—22no—
590C2×C3×C4—22no—
591C2×C3×C4—22no—
592C2×C3×C4—22no—
593C2×C3×C4—22no—
594C2×C3×C4—22no—
595C2×C3×C4—22no—
596C2×C3×C4—22no—
597C2×C3×C4—22no—
598C2×C3×C4—22no—
599C2×C3×C4—416no—
600C2×C3×C4—41no—
601C2×C3×C4—41no—
602C2×C3×C4—41no—
603C2×C3×C4—41no—
604C2×C3×C4—41no—
605C2×C3×C4—41no—
606C2×C3×C4—41no—
607C2×C3×C4—41no—
608C2×C3×C4—41no—
609C2×C3×C4—41no—
610C2×C3×C4—41no—
611C2×C3×C4—41no—
612C2×C3×C4—41no—
613C2×C3×C4—41no—
614C2×C3×C4—41no—
615C2×C3×C4—41no—
616C2×C3×C4#12014yes—
617C2×C3×C4#12114yes—
618#67—416no—
619C2×Dic3—22no—
620C2×Dic3—22no—
621C2×Dic3—22no—
622C2×Dic3—22no—
623C2×Dic3—22no—
624C2×Dic3—22no—
625C2×Dic3—22no—
626C2×Dic3—22no—
627C2×Dic3—22no—
628C2×Dic3—22no—
629C2×Dic3—22no—
630C2×Dic3—22no—
631C2×Dic3—41no—
632C2×Dic3—41no—
633C2×Dic3—41no—
634C2×Dic3—41no—
635C2×Dic3—41no—
636C2×Dic3—41no—
637C2×Dic3—41no—
638C2×Dic3—41no—
639C2×Dic3—41no—
640C2×Dic3—41no—
641C2×Dic3—41no—
642C2×Dic3—41no—
643C2×Dic3—41no—
644C2×Dic3—41no—
645C2×Dic3—41no—
646C2×Dic3—41no—
647C2×Dic3—41no—
648C2×Dic3—41no—
649C2×Dic3—41no—
650C2×Dic3—41no—
651C2×Dic3—41no—
652C2×Dic3—41no—
653C2×Dic3—41no—
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×Dic3C22⋊Q814yescomplemented
668C24—21no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24—21no—
674C24—21no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—32no—
681C24—61no—
682C24—61no—
683C24—61no—
684C24—61no—
685C24—61no—
686C24—61no—
687C24—61no—
688C24—61no—
689C24—61no—
690C24—61no—
691C24—61no—
692C24—61no—
693C24—61no—
694C24—61no—
695C24D3×Q812yes—
696C24#23912yes—
697C24C2×#6712yes—
698C24C23×D311yescharacteristic
699C2×Q8—28no—
700C2×Q8—28no—
701C2×Q8—44no—
702C2×Q8—44no—
703C2×Q8—44no—
704C2×Q8—44no—
705C2×Q8—44no—
706C2×D4—68no—
707C2×D4—68no—
708C2×D4—124no—
709C2×D4—124no—
710C2×D4—124no—
711C2×D4—124no—
712C2×D4—124no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—28no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
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—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—32no—
747C22×C4—32no—
748C22×C4—32no—
749C22×C4—32no—
750C22×C4—32no—
751C22×C4—44no—
752C22×C4—44no—
753C22×C4—44no—
754C22×C4—44no—
755C22×C4—44no—
756C22×C4—44no—
757C22×C4—61no—
758C22×C4—61no—
759C22×C4—61no—
760C22×C4—61no—
761C22×C4—61no—
762C22×C4—61no—
763C22×C4—61no—
764C22×C4—61no—
765C22×C4—61no—
766C22×C4—61no—
767C22×C4—61no—
768C22×C4—61no—
769C22×C4—61no—
770C22×C4—61no—
771C22×C4—61no—
772C22×C4—61no—
773C22×C4—61no—
774C22×C4—61no—
775C22×C4—61no—
776C22×C4—61no—
777C22×C4—61no—
778C22×C4—61no—
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×C4D3×D412yes—
802C22×C4#23712yes—
803C22×C4C2×#6712yes—
804C22×C4C2×#6712yes—
805C22×C4C2×#6712yes—
806C22×C4C2×#6712yes—
807C22×C4C2×#6712yes—
808C22×C4C2×#6712yes—
809C22×C4C2×#6712yes—
810C22×C4C2×#6712yes—
811C4⋊C4—28no—
812C4⋊C4—28no—
813C4⋊C4—28no—
814C4⋊C4—124no—
815C4⋊C4—124no—
816C4⋊C4—124no—
817C22⋊C4—28no—
818C22⋊C4—28no—
819C22⋊C4—124no—
820C22⋊C4—124no—
821C22⋊C4—124no—
822C22⋊C4—124no—
823C22⋊C4—124no—
824C22⋊C4—124no—
825C22⋊C4—124no—
826C22⋊C4—124no—
827C22⋊C4—124no—
828C42—124no—
829C22×C3—24no—
830C22×C3—24no—
831C22×C3—24no—
832C22×C3—42no—
833C22×C3—42no—
834C22×C3—42no—
835C22×C3—42no—
836C22×C3—42no—
837C22×C3—42no—
838C22×C3—42no—
839C22×C3—42no—
840C22×C3—42no—
841C22×C3—42no—
842C22×C3—42no—
843C22×C3—42no—
844C22×C3C2×#12011yescharacteristic
845C22×C3C2×#12111yescharacteristic
846C22×C3C2×C22⋊Q811yescharacteristic
847C22×C3C2×C22⋊Q811yescharacteristic
848C22×C3#52911yescharacteristic
849C22×C3#53211yescharacteristic
850C22×C3#53411yescharacteristic
851C22×C3#53511yescharacteristic
852C22×C3#53611yescharacteristic
853C22×C3#53711yescharacteristic
854C22×C3#53811yescharacteristic
855C22×C3#53911yescharacteristic
856C22×C3#54211yescharacteristic
857C22×C3#54211yescharacteristic
858C22×C3#54311yescharacteristic
859C22×C3D4211yescharacteristic
860C22×C3D4211yescharacteristic
861C22×C3#54611yescharacteristic
862C22×C3#54611yescharacteristic
863C22×C3#54611yescharacteristic
864C22×C3#54611yescharacteristic
865C22×C3#54611yescharacteristic
866C22×C3#54811yescharacteristic
867C22×C3#54811yescharacteristic
868C22×C3#54811yescharacteristic
869C22×C3D4×Q811yescharacteristic
870C22×C3D4×Q811yescharacteristic
871C22×C3#55011yescharacteristic
872C22×C3#55011yescharacteristic
873C22×C3#55111yescharacteristic
874C22×C3#55411yescharacteristic
875C22×C3#55411yescharacteristic
876C22×C3#55611yescharacteristic
877C22×C3#56211yescharacteristic
878C22×C3#56211yescharacteristic
879C2×D3—42no—
880C2×D3—42no—
881C2×D3—42no—
882C2×D3—42no—
883C2×D3—42no—
884C2×D3—42no—
885C2×D3—42no—
886C2×D3—81no—
887C2×D3—81no—
888C2×D3—81no—
889C2×D3—81no—
890C2×D3—81no—
891C2×D3—81no—
892C2×D3—81no—
893C2×D3—81no—
894C3×C4—24no—
895C3×C4—24no—
896C3×C4—42no—
897C3×C4—42no—
898C3×C4—42no—
899C3×C4—42no—
900Dic3—24no—
901Dic3—42no—
902Dic3—42no—
903Dic3—81no—
904Dic3—81no—
905Dic3—81no—
906Dic3—81no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—62no—
942C23—62no—
943C23—62no—
944C23—62no—
945C23—62no—
946C23—62no—
947C23—62no—
948C23—121no—
949C23—121no—
950C23—121no—
951C23—121no—
952C23—121no—
953C23—121no—
954C23—121no—
955C23—121no—
956C23—121no—
957C23—121no—
958C23—121no—
959C23—121no—
960C23—121no—
961C23—121no—
962C23—121no—
963C23—121no—
964C23—121no—
965C23—121no—
966C23—121no—
967C23—121no—
968C23—121no—
969C23—121no—
970C23—121no—
971C23—121no—
972C23—121no—
973C23—121no—
974C23—121no—
975C23—121no—
976C23#94614yes—
977C23C2×D3×D411yescharacteristic
978C23C2×#23711yescharacteristic
979C23#100411yescharacteristic
980C23#100411yescharacteristic
981C23C2×D3×Q811yescharacteristic
982C23C2×#23911yescharacteristic
983C23#100711yescharacteristic
984C23#100711yescharacteristic
985C23D3×#4111yescharacteristic
986C23D3×#4111yescharacteristic
987C23#100911yescharacteristic
988C23#100911yescharacteristic
989C23C22×#6711yescharacteristic
990C23C22×#6711yescharacteristic
991C23C22×#6711yescharacteristic
992Q8—416no—
993D4—1216no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—34no—
1019C2×C4—416no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—62no—
1037C2×C4—62no—
1038C2×C4—62no—
1039C2×C4—62no—
1040C2×C4—62no—
1041C2×C4—62no—
1042C2×C4—62no—
1043C2×C4—62no—
1044C2×C4—62no—
1045C2×C4—62no—
1046C2×C4—62no—
1047C2×C4—62no—
1048C2×C4—121no—
1049C2×C4—121no—
1050C2×C4—121no—
1051C2×C4—121no—
1052C2×C4—121no—
1053C2×C4—121no—
1054C2×C4—121no—
1055C2×C4—121no—
1056C2×C4—121no—
1057C2×C4—121no—
1058C2×C4—121no—
1059C2×C4—121no—
1060C2×C4—121no—
1061C2×C4—121no—
1062C2×C4—121no—
1063C2×C4—121no—
1064C2×C4—121no—
1065C2×C4—121no—
1066C2×C4—121no—
1067C2×C4—121no—
1068C2×C4—121no—
1069C2×C4—121no—
1070C2×C4—121no—
1071C2×C4—121no—
1072C2×C4—121no—
1073C2×C4—121no—
1074C2×C4—121no—
1075C2×C4—121no—
1076C2×C4—121no—
1077C2×C4—121no—
1078C2×C4—121no—
1079C2×C4—121no—
1080C2×C4—121no—
1081C2×C4—121no—
1082C2×C4—121no—
1083C2×C4—121no—
1084C2×C4#93914yes—
1085C2×C4#95314yes—
1086C2×C3—44no—
1087C2×C3#240911yescharacteristic
1088C2×C3#241011yescharacteristic
1089C2×C3#242611yescharacteristic
1090C2×C3#243111yescharacteristic
1091C2×C3#243711yescharacteristic
1092C2×C3#245011yescharacteristic
1093C2×C3#245211yescharacteristic
1094C2×C3#253811yescharacteristic
1095C2×C3#256011yescharacteristic
1096C2×C3#267611yescharacteristic
1097C2×C3#268111yescharacteristic
1098C2×C3#269211yescharacteristic
1099C2×C3#270011yescharacteristic
1100C2×C3#273011yescharacteristic
1101C2×C3#273211yescharacteristic
1102D3—82no—
1103C22—24no—
1104C22—24no—
1105C22—24no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22—122no—
1119C22—122no—
1120C22—122no—
1121C22—122no—
1122C22—122no—
1123C22—122no—
1124C22—122no—
1125C22—241no—
1126C22—241no—
1127C22—241no—
1128C22—241no—
1129C22—241no—
1130C22—241no—
1131C22—241no—
1132C22—241no—
1133C22#562411yescharacteristic
1134C22D3×C22⋊Q811yescharacteristic
1135C22#562911yescharacteristic
1136C22#563011yescharacteristic
1137C22#563311yescharacteristic
1138C22#563411yescharacteristic
1139C22#563511yescharacteristic
1140C22#563611yescharacteristic
1141C22#563711yescharacteristic
1142C22#563811yescharacteristic
1143C22#564011yescharacteristic
1144C22#564111yescharacteristic
1145C22#564311yescharacteristic
1146C22#564411yescharacteristic
1147C22#564711yescharacteristic
1148C22#564711yescharacteristic
1149C22D4×#6711yescharacteristic
1150C22D4×#6711yescharacteristic
1151C22C2×#93911yescharacteristic
1152C22#580411yescharacteristic
1153C22#580611yescharacteristic
1154C22#580611yescharacteristic
1155C22C2×#94611yescharacteristic
1156C22Q8×#6711yescharacteristic
1157C22Q8×#6711yescharacteristic
1158C22#581611yescharacteristic
1159C22#581711yescharacteristic
1160C22#581711yescharacteristic
1161C22#582911yescharacteristic
1162C22#582911yescharacteristic
1163C22#583011yescharacteristic
1164C22#583211yescharacteristic
1165C22#583411yescharacteristic
1166C22#583411yescharacteristic
1167C22C2×#95311yescharacteristic
1168C4—24no—
1169C4—24no—
1170C4—42no—
1171C4—42no—
1172C4—42no—
1173C4—42no—
1174C4—64no—
1175C4—122no—
1176C4—122no—
1177C4—241no—
1178C4—241no—
1179C4—241no—
1180C4—241no—
1181C3#1528011yescharacteristic, complemented, Sylow
1182C2—44no—
1183C2—242no—
1184C2#8275511yescharacteristic
1185C2#8276511yescharacteristic
1186C2#8276611yescharacteristic
1187C2#8277811yescharacteristic
1188C2#8278311yescharacteristic
1189C2#8279211yescharacteristic
1190C2#8279711yescharacteristic
1191C2#8280011yescharacteristic
1192C2#8280611yescharacteristic
1193C2#8280711yescharacteristic
1194C2#8281611yescharacteristic
1195C2#8282711yescharacteristic
1196C2#8404811yescharacteristic
1197C2#8406811yescharacteristic
1198C2#8409211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC22×C3×C22⋊Q8C2
prime radicalC23×#67C22
hypercenterC22×C22⋊Q8D3
hypocenterC3#15280
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. C2×#5231C2semidirect
3. C2×#5229C2semidirect
5. C2×#4994C2semidirect
7. #72127C2semidirect
8. #71570C2semidirect
9. #71570C2semidirect
10. #71568C2semidirect
11. #71566C2semidirect
12. #71564C2semidirect
14. #71547C2semidirect
15. #71546C2semidirect
60. C22×C22⋊Q8D3semidirect
83. C22×C3×Q8D4semidirect
103. C22×#67Q8semidirect
120. C2×C3×C4⋊C4D4semidirect
392. C22×Q8#67semidirect
438. C2×C4⋊C4#67semidirect
667. C2×Dic3C22⋊Q8semidirect
1181. C3#15280semidirect

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×#52312
C2×#52292
C2×#52132
C2×#49942
C2×#49572
#721272
#715702
#715682
#715662
#715642
#715502
#715472
#715462
#152803