Finite Group Databasebeta

← #30609302

Subgroups — #30609302

Order 15616.

1910 conjugacy classes of subgroups.

The subgroup lattice has 1290 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×(C2×#6923)⋊Q8C211yesmaximal, characteristic, complemented
2C2×#16840713C211yesmaximal, characteristic, complemented
3C2×#16840711C211yesmaximal, characteristic, complemented
4C2×#16840704C211yesmaximal, characteristic
5#21461009C211yesmaximal, characteristic, complemented
6#21461004C211yesmaximal, characteristic, complemented
7#21461004C211yesmaximal, characteristic, complemented
8#21461004C211yesmaximal, characteristic, complemented
9#21461002C211yesmaximal, characteristic
10#21461002C211yesmaximal, characteristic
11#21461000C211yesmaximal, characteristic
12#21461000C211yesmaximal, characteristic
13#21460998C211yesmaximal, characteristic, complemented
14#21460993C211yesmaximal, characteristic
15C2×C22⋊Q8×D61C211yesmaximal, characteristic
16C22×C4⋊#6923C2211yescharacteristic
17C22×C4⋊#6923C2211yescharacteristic
18C22×C4⋊#6923C2211yescharacteristic
19C22×C4⋊#6923C2211yescharacteristic
20C22×C22⋊#6923C2211yescharacteristic
21C22×C22⋊#6923C2211yescharacteristic
22C22×C22⋊#6923C2211yescharacteristic
23C22×C22⋊#6923C2211yescharacteristic
24C22×C4×#6923C2211yescharacteristic
25C22×C4×#6923C2211yescharacteristic
26(C2×#6923)⋊Q8—24no—
27#16840713—24no—
28#16840711—24no—
29#16840704—24no—
30C2×(C2×#6923)⋊C4C2211yescharacteristic
31C2×(C2×#6923)⋊C4C2211yescharacteristic
32C2×(C2×#6923)⋊C4C2211yescharacteristic
33C2×(C2×#6923)⋊C4C2211yescharacteristic
34C2×(C2×#6923)⋊C4C2211yescharacteristic
35C2×(C2×#6923)⋊C4C2211yescharacteristic
36C2×(C2×#6923)⋊C4C2211yescharacteristic
37C2×(C2×#6923)⋊C4C2211yescharacteristic
38C2×(C2×#6923)⋊C4C2211yescharacteristic
39C2×(C2×#6923)⋊C4C2211yescharacteristic
40C2×(C2×#6923)⋊C4C2211yescharacteristic
41C2×(C2×#6923)⋊C4C2211yescharacteristic
42C2×(C2×#6923)⋊C4C2211yescharacteristic
43C2×(C2×#6923)⋊C4C2211yescharacteristic
44C2×(C2×#6923)⋊C4C2211yescharacteristic
45C2×(C2×#6923)⋊C4C2211yescharacteristic
46C2×(C2×#6923)⋊C4C2211yescharacteristic
47C2×(C2×#6923)⋊C4C2211yescharacteristic
48C22×Q8×D61C2211yescharacteristic
49C23×C4×D61C2211yescharacteristic
50C2×#14519757C411yescharacteristic, complemented
51C2×#14519756C411yescharacteristic, complemented
52C2×#14519755C411yescharacteristic, complemented
53C2×#14519755C411yescharacteristic, complemented
54C2×#14519754C411yescharacteristic, complemented
55C2×#14519754C411yescharacteristic, complemented
56C2×#14519753C411yescharacteristic, complemented
57C22⋊Q8×D61—24no—
58C22⋊Q8×D61—24no—
59C2×C4⋊C4×D61C2211yescharacteristic
60C2×C4⋊C4×D61C2211yescharacteristic
61C2×C4⋊C4×D61C2211yescharacteristic
62C2×C22⋊C4×D61C2211yescharacteristic
63C2×C22⋊C4×D61C2211yescharacteristic
64C2×C22⋊Q8×C61C411yescharacteristic, complemented
65C23×#6923C2311yescharacteristic
66C23×#6923C2311yescharacteristic
67C23×#6923C2311yescharacteristic
68C23×#6923C2311yescharacteristic
69C23×#6923C2311yescharacteristic
70C23×#6923C2311yescharacteristic
71C23×#6923C2311yescharacteristic
72C23×#6923C2311yescharacteristic
73C2×C4⋊#6923—22no—
74C2×C4⋊#6923—22no—
75C2×C4⋊#6923—22no—
76C2×C4⋊#6923—22no—
77C2×C4⋊#6923—22no—
78C2×C4⋊#6923—22no—
79C2×C4⋊#6923—22no—
80C2×C4⋊#6923—41no—
81C2×C4⋊#6923—41no—
82C2×C4⋊#6923—41no—
83C2×C4⋊#6923—41no—
84C2×C4⋊#6923—41no—
85C2×C22⋊#6923—22no—
86C2×C22⋊#6923—22no—
87C2×C22⋊#6923—22no—
88C2×C22⋊#6923—22no—
89C2×C22⋊#6923—22no—
90C2×C22⋊#6923—41no—
91C2×C22⋊#6923—41no—
92C2×C22⋊#6923—41no—
93C2×C22⋊#6923—41no—
94C2×C22⋊#6923—41no—
95C2×C22⋊#6923—41no—
96C2×C22⋊#6923Q814yescomplemented
97C2×C4×#6923—22no—
98C2×C4×#6923—22no—
99C2×C4×#6923—22no—
100C2×C4×#6923—41no—
101C2×C4×#6923—41no—
102C2×C4×#6923—41no—
103(C2×#6923)⋊C4—22no—
104(C2×#6923)⋊C4—22no—
105(C2×#6923)⋊C4—22no—
106(C2×#6923)⋊C4—22no—
107(C2×#6923)⋊C4—22no—
108(C2×#6923)⋊C4—22no—
109(C2×#6923)⋊C4—22no—
110(C2×#6923)⋊C4—22no—
111(C2×#6923)⋊C4—22no—
112(C2×#6923)⋊C4—22no—
113(C2×#6923)⋊C4—22no—
114(C2×#6923)⋊C4—41no—
115(C2×#6923)⋊C4—41no—
116(C2×#6923)⋊C4—41no—
117(C2×#6923)⋊C4—41no—
118(C2×#6923)⋊C4—41no—
119(C2×#6923)⋊C4—41no—
120(C2×#6923)⋊C4D414yes—
121C24×D61C2311yescharacteristic
122C22×Dic122C2×C411yescharacteristic
123C22×Dic122C2×C411yescharacteristic
124C22×Dic122C2×C411yescharacteristic
125C2×Q8×D61—22no—
126C2×Q8×D61—22no—
127C2×Q8×D61—22no—
128C2×Q8×D61—22no—
129C2×Q8×D61—41no—
130C2×Q8×D61—41no—
131C23×Dic61C2×C411yescharacteristic
132C22×C4×D61—22no—
133C22×C4×D61—22no—
134C22×C4×D61—22no—
135C22×C4×D61—22no—
136C22×C4×D61—41no—
137C22×C4×D61—41no—
138C22×C4×D61C2×C411yescharacteristic
139C22×C4×D61C2×C411yescharacteristic
140C22×C4×D61C2311yescharacteristic
141C22×C4×D61C2311yescharacteristic
142C22×C4×D61C2311yescharacteristic
143C22×C4×D61C2311yescharacteristic
144C22×C4×D61C2311yescharacteristic
145C22×C4×D61C2311yescharacteristic
146#14519757—24no—
147#14519756—24no—
148#14519755—24no—
149#14519755—24no—
150#14519754—24no—
151#14519754—24no—
152#14519753—24no—
153C2×C4⋊Dic61C2×C411yescharacteristic
154C2×C4⋊Dic61C2×C411yescharacteristic
155C2×C4⋊Dic61C2×C411yescharacteristic
156C2×#11758196C2×C411yescharacteristic
157C2×#11758196C2×C411yescharacteristic
158C2×#11758196C2×C411yescharacteristic
159C2×#11758196C2×C411yescharacteristic
160C2×#11758196C2×C411yescharacteristic
161C2×#11758196C2×C411yescharacteristic
162C4⋊C4×D61—22no—
163C4⋊C4×D61—22no—
164C4⋊C4×D61—22no—
165C4⋊C4×D61—22no—
166C4⋊C4×D61D414yes—
167C4⋊C4×D61D414yes—
168C2×C22⋊Dic61C2×C411yescharacteristic
169C2×C22⋊Dic61C2×C411yescharacteristic
170C2×#11758198C2×C411yescharacteristic
171C2×#11758198C2×C411yescharacteristic
172C2×#11758198C2×C411yescharacteristic
173C2×#11758198C2×C411yescharacteristic
174C22⋊C4×D61—22no—
175C22⋊C4×D61—22no—
176C22⋊C4×D61—22no—
177C22⋊C4×D61—22no—
178C22×Q8×C61C2×C411yescharacteristic
179C23×C4×C61C2×C411yescharacteristic
180C22⋊Q8×C61—24no—
181C2×C4⋊C4×C61C2×C411yescharacteristic
182C2×C4⋊C4×C61C2×C411yescharacteristic
183C2×C4⋊C4×C61C2×C411yescharacteristic
184C2×C22⋊C4×C61C2×C411yescharacteristic
185C2×C22⋊C4×C61C2×C411yescharacteristic
186C24×C61C22×C411yescharacteristic
187C23×D61—21no—
188C23×D61—21no—
189C23×D61—21no—
190C23×D61—21no—
191C23×D61—21no—
192C23×D61—21no—
193C23×D61—21no—
194C23×D61—21no—
195C23×D61—21no—
196C23×D61—21no—
197C23×D61—21no—
198C23×D61—21no—
199C23×D61C22×C411yescharacteristic
200C23×D61C2×Q812yes—
201C23×D61#4112yes—
202C23×D61C2411yescharacteristic
203C22×#6923—21no—
204C22×#6923—21no—
205C22×#6923—21no—
206C22×#6923—21no—
207C22×#6923—21no—
208C22×#6923—21no—
209C22×#6923—21no—
210C22×#6923—21no—
211C22×#6923—21no—
212C22×#6923—21no—
213C22×#6923—21no—
214C22×#6923—21no—
215C22×#6923—21no—
216C22×#6923—21no—
217C22×#6923—21no—
218C22×#6923—21no—
219C22×#6923—21no—
220C22×#6923—21no—
221C22×#6923—21no—
222C22×#6923—21no—
223C22×#6923—21no—
224C22×#6923—21no—
225C22×#6923—21no—
226C22×#6923—21no—
227C22×#6923—21no—
228C22×#6923—21no—
229C22×#6923—21no—
230C22×#6923—21no—
231C22×#6923—21no—
232C22×#6923—21no—
233C22×#6923—21no—
234C22×#6923—21no—
235C22×#6923—21no—
236C22×#6923—21no—
237C22×#6923—21no—
238C22×#6923—21no—
239C22×#6923—21no—
240C22×#6923—21no—
241C22×#6923—21no—
242C22×#6923—21no—
243C22×#6923—21no—
244C22×#6923—21no—
245C22×#6923—21no—
246C22×#6923—21no—
247C22×#6923—21no—
248C22×#6923—21no—
249C22×#6923—21no—
250C22×#6923—21no—
251C22×#6923—21no—
252C22×#6923—21no—
253C22×#6923—21no—
254C22×#6923—21no—
255C22×#6923C2×D412yes—
256C22×#6923C2×D412yes—
257C22×#6923C2×Q812yes—
258C22×#6923C2×Q812yes—
259C2×Q8×C61—22no—
260C2×Q8×C61—22no—
261C2×Q8×C61—41no—
262C22×C4×C61—22no—
263C22×C4×C61—22no—
264C22×C4×C61—41no—
265C22×C4×C61C22×C411yescharacteristic
266C22×C4×C61C22×C411yescharacteristic
267C22×C4×C61C22×C411yescharacteristic
268C22×C4×C61C22×C411yescharacteristic
269C22×C4×C61C22×C411yescharacteristic
270C22×C4×C61C22×C411yescharacteristic
271C22×Dic61—22no—
272C22×Dic61—22no—
273C22×Dic61—41no—
274C22×Dic61C22×C411yescharacteristic
275C22×Dic61C22×C411yescharacteristic
276C22×Dic61C22×C411yescharacteristic
277C22×Dic61C22×C411yescharacteristic
278C22×Dic61C22×C411yescharacteristic
279C22×Dic61C22×C411yescharacteristic
280Q8×D61—44no—
281Q8×D61—44no—
282Q8×D61—44no—
283Q8×D61—44no—
284C2×C4×D61—21no—
285C2×C4×D61—21no—
286C2×C4×D61—21no—
287C2×C4×D61—21no—
288C2×C4×D61—21no—
289C2×C4×D61—21no—
290C2×C4×D61—21no—
291C2×C4×D61—21no—
292C2×C4×D61—21no—
293C2×C4×D61—21no—
294C2×C4×D61—21no—
295C2×C4×D61—21no—
296C2×C4×D61—21no—
297C2×C4×D61—21no—
298C2×C4×D61—21no—
299C2×C4×D61—21no—
300C2×C4×D61—21no—
301C2×C4×D61—21no—
302C2×C4×D61—21no—
303C2×C4×D61—21no—
304C2×C4×D61—21no—
305C2×C4×D61—21no—
306C2×C4×D61—21no—
307C2×C4×D61—21no—
308C2×C4×D61—21no—
309C2×C4×D61—21no—
310C2×C4×D61—21no—
311C2×C4×D61—21no—
312C2×C4×D61—22no—
313C2×C4×D61—22no—
314C2×C4×D61—22no—
315C2×C4×D61—22no—
316C2×C4×D61—44no—
317C2×C4×D61—44no—
318C2×C4×D61—44no—
319C2×C4×D61—44no—
320C2×C4×D61—41no—
321C2×C4×D61—41no—
322C2×C4×D61C2×D412yes—
323C2×C4×D61C2×D412yes—
324C2×C4×D61C2×D412yes—
325C2×C4×D61C2×D412yes—
326C2×C4×D61C2×D412yes—
327C2×C4×D61C2×D412yes—
328C2×C4×D61C2×D412yes—
329C2×C4×D61#4112yes—
330C2×Dic122—22no—
331C2×Dic122—22no—
332C2×Dic122—22no—
333C2×Dic122—22no—
334C2×Dic122—22no—
335C2×Dic122—22no—
336C2×Dic122—41no—
337C2×Dic122—41no—
338C2×Dic122—41no—
339C22⋊#6923—44no—
340C22⋊#6923—44no—
341C22⋊#6923—44no—
342C22⋊#6923—44no—
343C4⋊#6923—44no—
344C4⋊#6923—44no—
345C4⋊#6923—44no—
346C4⋊#6923—44no—
347C4×#6923—44no—
348C4×#6923—44no—
349C4⋊C4×C61—22no—
350C4⋊C4×C61—22no—
351C4⋊C4×C61C22⋊C414yescomplemented
352C22⋊C4×C61—22no—
353C22⋊C4×C61—22no—
354C22⋊Dic61—22no—
355C22⋊Dic61—22no—
356#11758198—22no—
357#11758198—22no—
358#11758198—22no—
359#11758198—22no—
360C4⋊Dic61—22no—
361C4⋊Dic61—22no—
362C4⋊Dic61C22⋊C414yescomplemented
363#11758196—22no—
364#11758196—22no—
365#11758196—22no—
366#11758196—22no—
367#11758196C22⋊C414yescomplemented
368#11758196C22⋊C414yescomplemented
369C23×C61—21no—
370C23×C61—21no—
371C23×C61—21no—
372C23×C61—21no—
373C23×C61—21no—
374C23×C61—21no—
375C23×C61C4×Q812yes—
376C23×C61C23×C411yescharacteristic
377C22×D61—21no—
378C22×D61—21no—
379C22×D61—21no—
380C22×D61—21no—
381C22×D61—21no—
382C22×D61—21no—
383C22×D61—22no—
384C22×D61—22no—
385C22×D61—22no—
386C22×D61—22no—
387C22×D61—22no—
388C22×D61—22no—
389C22×D61—22no—
390C22×D61—22no—
391C22×D61—22no—
392C22×D61—22no—
393C22×D61—22no—
394C22×D61—22no—
395C22×D61—41no—
396C22×D61—41no—
397C22×D61—41no—
398C22×D61—41no—
399C22×D61—41no—
400C22×D61—41no—
401C22×D61—41no—
402C22×D61—41no—
403C22×D61—41no—
404C22×D61—41no—
405C22×D61—41no—
406C22×D61—41no—
407C22×D61—41no—
408C22×D61—41no—
409C22×D61—41no—
410C22×D61—41no—
411C22×D61C4×Q812yes—
412C22×D61C22×D411yescharacteristic
413C22×D61C22×D411yescharacteristic
414C22×D61C22×D411yescharacteristic
415C22×D61C22×Q811yescharacteristic
416C22×D61C2×#4111yescharacteristic
417C22×D61C2×#4111yescharacteristic
418C22×D61H(5,𝔽2)11yescharacteristic
419C22×D61H(5,𝔽2)11yescharacteristic
420C22×D61H(5,𝔽2)11yescharacteristic
421C22×D61H(5,𝔽2)11yescharacteristic
422C22×D612−1+411yescharacteristic
423C22×D612−1+411yescharacteristic
424C22×D612−1+411yescharacteristic
425C22×D612−1+411yescharacteristic
426C2×#6923—22no—
427C2×#6923—22no—
428C2×#6923—22no—
429C2×#6923—22no—
430C2×#6923—22no—
431C2×#6923—22no—
432C2×#6923—22no—
433C2×#6923—22no—
434C2×#6923—22no—
435C2×#6923—22no—
436C2×#6923—22no—
437C2×#6923—22no—
438C2×#6923—41no—
439C2×#6923—41no—
440C2×#6923—41no—
441C2×#6923—41no—
442C2×#6923—41no—
443C2×#6923—41no—
444C2×#6923—41no—
445C2×#6923—41no—
446C2×#6923—41no—
447C2×#6923—41no—
448C2×#6923—41no—
449C2×#6923—41no—
450C2×#6923—41no—
451C2×#6923—41no—
452C2×#6923—41no—
453C2×#6923—41no—
454C2×#6923—41no—
455C2×#6923—41no—
456C2×#6923—41no—
457C2×#6923—41no—
458C2×#6923—41no—
459C2×#6923—41no—
460C2×#6923—41no—
461C2×#6923—41no—
462C2×#6923—41no—
463C2×#6923—41no—
464C2×#6923—41no—
465C2×#6923—41no—
466C2×#6923—41no—
467C2×#6923—41no—
468C2×#6923—41no—
469C2×#6923—41no—
470C2×#6923—41no—
471C2×#6923—41no—
472C2×#6923—41no—
473C2×#6923—41no—
474C2×#6923—41no—
475C2×#6923—41no—
476C2×#6923—41no—
477C2×#6923—41no—
478C2×#6923—41no—
479C2×#6923—41no—
480C2×#6923—41no—
481C2×#6923—41no—
482Q8×C61—44no—
483C2×C4×C61—21no—
484C2×C4×C61—21no—
485C2×C4×C61—21no—
486C2×C4×C61—21no—
487C2×C4×C61—21no—
488C2×C4×C61—21no—
489C2×C4×C61—21no—
490C2×C4×C61—21no—
491C2×C4×C61—21no—
492C2×C4×C61—21no—
493C2×C4×C61—21no—
494C2×C4×C61—21no—
495C2×C4×C61—21no—
496C2×C4×C61—21no—
497C2×C4×C61—44no—
498C2×C4×C61C2×C22⋊C412yes—
499C2×C4×C61C2×C22⋊C412yes—
500C2×C4×C61C2×C22⋊C412yes—
501C2×C4×C61C4×D412yes—
502C2×Dic61—21no—
503C2×Dic61—21no—
504C2×Dic61—21no—
505C2×Dic61—21no—
506C2×Dic61—21no—
507C2×Dic61—21no—
508C2×Dic61—21no—
509C2×Dic61—21no—
510C2×Dic61—21no—
511C2×Dic61—21no—
512C2×Dic61—21no—
513C2×Dic61—21no—
514C2×Dic61—21no—
515C2×Dic61—21no—
516C2×Dic61—44no—
517C2×Dic61C2×C22⋊C412yes—
518C2×Dic61C2×C22⋊C412yes—
519C2×Dic61C2×C22⋊C412yes—
520C2×Dic61C4×D412yes—
521C4×D61—22no—
522C4×D61—22no—
523C4×D61—22no—
524C4×D61—22no—
525C4×D61—22no—
526C4×D61—22no—
527C4×D61—22no—
528C4×D61—22no—
529C4×D61—22no—
530C4×D61—22no—
531C4×D61—22no—
532C4×D61—22no—
533C4×D61—22no—
534C4×D61—22no—
535C4×D61—22no—
536C4×D61—22no—
537C4×D61—44no—
538C4×D61—44no—
539C4×D61—41no—
540C4×D61—41no—
541C4×D61—41no—
542C4×D61—41no—
543C4×D61—41no—
544C4×D61—41no—
545C4×D61—41no—
546C4×D61—41no—
547Dic122—44no—
548Dic122—44no—
549Dic122—44no—
550#14362—611nomaximal, Sylow
551C22×C61—22no—
552C22×C61—22no—
553C22×C61—22no—
554C22×C61—41no—
555C22×C61—41no—
556C22×C61—41no—
557C22×C61—41no—
558C22×C61C22×C22⋊C411yescharacteristic
559C22×C61C2×C4×D411yescharacteristic
560C22×C61C2×C4×Q811yescharacteristic
561C22×C61#51811yescharacteristic
562C22×C61#51911yescharacteristic
563C22×C61#52011yescharacteristic
564C22×C61#52011yescharacteristic
565C2×D61—22no—
566C2×D61—22no—
567C2×D61—22no—
568C2×D61—41no—
569C2×D61—41no—
570C2×D61—41no—
571C2×D61—41no—
572C2×D61—42no—
573C2×D61—42no—
574C2×D61—42no—
575C2×D61—42no—
576C2×D61—42no—
577C2×D61—42no—
578C2×D61—42no—
579C2×D61—42no—
580C2×D61#53511yescharacteristic
581C2×D61#53611yescharacteristic
582C2×D61#53611yescharacteristic
583C2×D61#53711yescharacteristic
584C2×D61#53711yescharacteristic
585C2×D61#53711yescharacteristic
586C2×D61#53811yescharacteristic
587C2×D61#53911yescharacteristic
588C2×D61#54111yescharacteristic
589C2×D61#54211yescharacteristic
590C2×D61#54311yescharacteristic
591C2×D61#54411yescharacteristic
592C2×D61D4211yescharacteristic
593C2×D61D4211yescharacteristic
594C2×D61#54611yescharacteristic
595C2×D61#54611yescharacteristic
596C2×D61#54611yescharacteristic
597C2×D61#54811yescharacteristic
598C2×D61#54811yescharacteristic
599C2×D61D4×Q811yescharacteristic
600C2×D61D4×Q811yescharacteristic
601C2×D61D4×Q811yescharacteristic
602C2×D61#55211yescharacteristic
603C2×D61#55411yescharacteristic
604C2×D61#56211yescharacteristic
605C2×D61#56211yescharacteristic
606C2×D61#56311yescharacteristic
607C2×D61#56311yescharacteristic
608#6923—42no—
609#6923—42no—
610#6923—42no—
611#6923—42no—
612#6923—81no—
613#6923—81no—
614#6923—81no—
615#6923—81no—
616C4×C61—22no—
617C4×C61—22no—
618C4×C61—22no—
619C4×C61—22no—
620C4×C61—41no—
621C4×C61—41no—
622Dic61—22no—
623Dic61—22no—
624Dic61—22no—
625Dic61—22no—
626Dic61—41no—
627Dic61—41no—
628C22×C22⋊Q8—611no—
629C2×#391—611no—
630C2×#389—611no—
631C2×#387—611no—
632C2×#380—611no—
633#1446—611no—
634#1441—611no—
635#1441—611no—
636#1441—611no—
637#1439—611no—
638#1439—611no—
639#1437—611no—
640#1437—611no—
641#1436—611no—
642C22⋊#95—611no—
643C2×C61—42no—
644C2×C61#231111yescharacteristic
645C2×C61#232311yescharacteristic
646C2×C61#232911yescharacteristic
647C2×C61D4×C22⋊C411yescharacteristic
648C2×C61Q8×C22⋊C411yescharacteristic
649C2×C61#236011yescharacteristic
650C2×C61#237811yescharacteristic
651D61—42no—
652D61#267611yescharacteristic
653D61#267711yescharacteristic
654D61#268111yescharacteristic
655D61#268311yescharacteristic
656D61#269011yescharacteristic
657D61#269211yescharacteristic
658D61#270211yescharacteristic
659D61#270411yescharacteristic
660C23×Q8—611no—
661C24×C4—611no—
662C2×C22⋊Q8—611no—
663C2×C22⋊Q8—611no—
664C2×C22⋊Q8—611no—
665C2×C22⋊Q8—611no—
666C2×C22⋊Q8—611no—
667C2×C22⋊Q8—611no—
668C2×C22⋊Q8—611no—
669C2×C22⋊Q8—1224no—
670C2×C22⋊Q8—1224no—
671C2×C22⋊Q8#692311yescharacteristic, complemented
672C22×C4⋊C4—611no—
673C22×C4⋊C4—611no—
674C22×C4⋊C4—611no—
675C22×C4⋊C4—611no—
676C22×C4⋊C4—611no—
677C22×C4⋊C4—611no—
678C22×C4⋊C4—611no—
679C22×C22⋊C4—611no—
680C22×C22⋊C4—611no—
681C22×C22⋊C4—611no—
682C22×C22⋊C4—611no—
683C22×C22⋊C4—611no—
684C22×C22⋊C4—611no—
685C22×C42—611no—
686C22×C42—611no—
687#391—1224no—
688#389—1224no—
689#387—1224no—
690#380—1224no—
691C2×#95—611no—
692C2×#95—611no—
693C2×#95—611no—
694C2×#95—611no—
695C2×#95—611no—
696C2×#95—611no—
697C2×#95—611no—
698C2×#95—611no—
699C2×#95—611no—
700C2×#95—611no—
701C2×#95—611no—
702C2×#95—611no—
703C2×#95—611no—
704C2×#95—611no—
705C2×#95—611no—
706C2×#95—611no—
707C2×#95—611no—
708C2×#95—611no—
709C61#1436211yescharacteristic, complemented, Sylow
710C25—611no—
711C22×Q8—611no—
712C22×Q8—611no—
713C22×Q8—611no—
714C22×Q8—1222no—
715C22×Q8—1222no—
716C22×Q8—1222no—
717C22×Q8—1222no—
718C22×Q8—2441no—
719C22×Q8—2441no—
720C22×Q8C2×#692311yescharacteristic
721C23×C4—611no—
722C23×C4—611no—
723C23×C4—611no—
724C23×C4—611no—
725C23×C4—611no—
726C23×C4—611no—
727C23×C4—611no—
728C23×C4—611no—
729C23×C4—611no—
730C23×C4—611no—
731C23×C4—611no—
732C23×C4—611no—
733C23×C4—611no—
734C23×C4—611no—
735C23×C4—611no—
736C23×C4—611no—
737C23×C4—611no—
738C23×C4—1222no—
739C23×C4—1222no—
740C23×C4—1222no—
741C23×C4—1222no—
742C23×C4—2441no—
743C23×C4—2441no—
744C23×C4C2×#692311yescharacteristic
745C22⋊Q8—24no—
746C22⋊Q8—1224no—
747C22⋊Q8—1224no—
748C22⋊Q8—1224no—
749C22⋊Q8—1224no—
750C22⋊Q8—1224no—
751C22⋊Q8—1224no—
752C22⋊Q8—1224no—
753C2×C4⋊C4—611no—
754C2×C4⋊C4—611no—
755C2×C4⋊C4—611no—
756C2×C4⋊C4—614no—
757C2×C4⋊C4—614no—
758C2×C4⋊C4—611no—
759C2×C4⋊C4—611no—
760C2×C4⋊C4—611no—
761C2×C4⋊C4—611no—
762C2×C4⋊C4—611no—
763C2×C4⋊C4—611no—
764C2×C4⋊C4—1222no—
765C2×C4⋊C4—1222no—
766C2×C4⋊C4—1222no—
767C2×C4⋊C4—1222no—
768C2×C4⋊C4—1222no—
769C2×C4⋊C4—1222no—
770C2×C4⋊C4—1222no—
771C2×C4⋊C4—1222no—
772C2×C4⋊C4—1222no—
773C2×C4⋊C4—1222no—
774C2×C4⋊C4—1222no—
775C2×C4⋊C4—2441no—
776C2×C4⋊C4—2441no—
777C2×C4⋊C4—2441no—
778C2×C4⋊C4—2441no—
779C2×C4⋊C4—2441no—
780C2×C4⋊C4C2×#692311yescharacteristic
781C2×C4⋊C4C2×#692311yescharacteristic
782C2×C4⋊C4C2×#692311yescharacteristic
783C2×C22⋊C4—611no—
784C2×C22⋊C4—611no—
785C2×C22⋊C4—611no—
786C2×C22⋊C4—611no—
787C2×C22⋊C4—611no—
788C2×C22⋊C4—611no—
789C2×C22⋊C4—614no—
790C2×C22⋊C4—1222no—
791C2×C22⋊C4—1222no—
792C2×C22⋊C4—1222no—
793C2×C22⋊C4—1222no—
794C2×C22⋊C4—1222no—
795C2×C22⋊C4—1222no—
796C2×C22⋊C4—1222no—
797C2×C22⋊C4—1222no—
798C2×C22⋊C4—1222no—
799C2×C22⋊C4—2441no—
800C2×C22⋊C4—2441no—
801C2×C22⋊C4—2441no—
802C2×C22⋊C4—2441no—
803C2×C22⋊C4—2441no—
804C2×C22⋊C4—2441no—
805C2×C22⋊C4C2×#692311yescharacteristic
806C2×C22⋊C4C2×#692311yescharacteristic
807C2×C42—1222no—
808C2×C42—1222no—
809C2×C42—1222no—
810C2×C42—2441no—
811C2×C42—2441no—
812C2×C42—2441no—
813#95—614no—
814#95—1222no—
815#95—1222no—
816#95—1222no—
817#95—1222no—
818#95—1222no—
819#95—1222no—
820#95—1222no—
821#95—1222no—
822#95—1222no—
823#95—1222no—
824#95—1222no—
825#95—2441no—
826#95—2441no—
827#95—2441no—
828#95—2441no—
829#95—2441no—
830#95—2441no—
831C24—611no—
832C24—612no—
833C24—612no—
834C24—611no—
835C24—1221no—
836C24—1221no—
837C24—1221no—
838C24—1221no—
839C24—1221no—
840C24—1221no—
841C24—1221no—
842C24—1221no—
843C24—1221no—
844C24—1221no—
845C24—1221no—
846C24—1221no—
847C24C22×#692311yescharacteristic
848C2×Q8—22no—
849C2×Q8—22no—
850C2×Q8—41no—
851C2×Q8—1222no—
852C2×Q8—1222no—
853C2×Q8—1222no—
854C2×Q8—1222no—
855C2×Q8—1222no—
856C2×Q8—1222no—
857C2×Q8—2441no—
858C2×Q8—2441no—
859C2×Q8—2441no—
860C2×Q8—2444no—
861C2×Q8—2444no—
862C2×Q8—2444no—
863C2×Q8—2444no—
864C22×C4—22no—
865C22×C4—22no—
866C22×C4—41no—
867C22×C4—611no—
868C22×C4—611no—
869C22×C4—611no—
870C22×C4—611no—
871C22×C4—612no—
872C22×C4—612no—
873C22×C4—612no—
874C22×C4—612no—
875C22×C4—612no—
876C22×C4—612no—
877C22×C4—612no—
878C22×C4—612no—
879C22×C4—612no—
880C22×C4—612no—
881C22×C4—612no—
882C22×C4—612no—
883C22×C4—611no—
884C22×C4—611no—
885C22×C4—1222no—
886C22×C4—1222no—
887C22×C4—1221no—
888C22×C4—1221no—
889C22×C4—1221no—
890C22×C4—1221no—
891C22×C4—1221no—
892C22×C4—1221no—
893C22×C4—1221no—
894C22×C4—1221no—
895C22×C4—1221no—
896C22×C4—1221no—
897C22×C4—1221no—
898C22×C4—1221no—
899C22×C4—1221no—
900C22×C4—1221no—
901C22×C4—1221no—
902C22×C4—1221no—
903C22×C4—1221no—
904C22×C4—1221no—
905C22×C4—1221no—
906C22×C4—1221no—
907C22×C4—1221no—
908C22×C4—1221no—
909C22×C4—1221no—
910C22×C4—1221no—
911C22×C4—1221no—
912C22×C4—1221no—
913C22×C4—1221no—
914C22×C4—1221no—
915C22×C4—1222no—
916C22×C4—1222no—
917C22×C4—1221no—
918C22×C4—1221no—
919C22×C4—1221no—
920C22×C4—1221no—
921C22×C4—1221no—
922C22×C4—1221no—
923C22×C4—1221no—
924C22×C4—1221no—
925C22×C4—1221no—
926C22×C4—1221no—
927C22×C4—1221no—
928C22×C4—1221no—
929C22×C4—1221no—
930C22×C4—1221no—
931C22×C4—1221no—
932C22×C4—1221no—
933C22×C4—1221no—
934C22×C4—1221no—
935C22×C4—1221no—
936C22×C4—1221no—
937C22×C4—1221no—
938C22×C4—1221no—
939C22×C4—1221no—
940C22×C4—1221no—
941C22×C4—1222no—
942C22×C4—1222no—
943C22×C4—1221no—
944C22×C4—1221no—
945C22×C4—1221no—
946C22×C4—1221no—
947C22×C4—1221no—
948C22×C4—1221no—
949C22×C4—1221no—
950C22×C4—1221no—
951C22×C4—1221no—
952C22×C4—1221no—
953C22×C4—1221no—
954C22×C4—1221no—
955C22×C4—1221no—
956C22×C4—1221no—
957C22×C4—1221no—
958C22×C4—1221no—
959C22×C4—1221no—
960C22×C4—1221no—
961C22×C4—1221no—
962C22×C4—1221no—
963C22×C4—1221no—
964C22×C4—1221no—
965C22×C4—1221no—
966C22×C4—1221no—
967C22×C4—1221no—
968C22×C4—1221no—
969C22×C4—1221no—
970C22×C4—1221no—
971C22×C4—2441no—
972C22×C4—2441no—
973C22×C4—2444no—
974C22×C4—2444no—
975C22×C4—2444no—
976C22×C4—2444no—
977C22×C4—2441no—
978C22×C4C22×#692311yescharacteristic
979C22×C4C22×#692311yescharacteristic
980C22×C4C22×#692311yescharacteristic
981C22×C4C22×#692311yescharacteristic
982C22×C4C22×#692311yescharacteristic
983C22×C4C22×#692311yescharacteristic
984C4⋊C4—22no—
985C4⋊C4—22no—
986C4⋊C4—614no—
987C4⋊C4—614no—
988C4⋊C4—614no—
989C4⋊C4—1222no—
990C4⋊C4—1222no—
991C4⋊C4—1222no—
992C4⋊C4—1222no—
993C4⋊C4—1222no—
994C4⋊C4—1222no—
995C4⋊C4—2444no—
996C4⋊C4—2444no—
997C4⋊C4—2444no—
998C4⋊C4—2444no—
999C4⋊C4C22⋊#692314yescomplemented
1000C22⋊C4—22no—
1001C22⋊C4—22no—
1002C22⋊C4—1222no—
1003C22⋊C4—1222no—
1004C22⋊C4—1222no—
1005C22⋊C4—1222no—
1006C22⋊C4—1222no—
1007C22⋊C4—1222no—
1008C22⋊C4—2444no—
1009C22⋊C4—2444no—
1010C22⋊C4—2444no—
1011C22⋊C4—2444no—
1012C42—2444no—
1013C42—2444no—
1014C23—21no—
1015C23—21no—
1016C23—21no—
1017C23—21no—
1018C23—21no—
1019C23—21no—
1020C23—611no—
1021C23—611no—
1022C23—611no—
1023C23—611no—
1024C23—611no—
1025C23—611no—
1026C23—611no—
1027C23—611no—
1028C23—611no—
1029C23—611no—
1030C23—611no—
1031C23—611no—
1032C23—611no—
1033C23—611no—
1034C23—612no—
1035C23—1222no—
1036C23—1222no—
1037C23—1222no—
1038C23—1222no—
1039C23—1222no—
1040C23—1222no—
1041C23—1222no—
1042C23—1222no—
1043C23—1222no—
1044C23—1222no—
1045C23—1222no—
1046C23—1222no—
1047C23—1221no—
1048C23—1221no—
1049C23—1221no—
1050C23—1221no—
1051C23—1221no—
1052C23—1221no—
1053C23—2441no—
1054C23—2441no—
1055C23—2441no—
1056C23—2441no—
1057C23—2441no—
1058C23—2441no—
1059C23—2441no—
1060C23—2441no—
1061C23—2441no—
1062C23—2441no—
1063C23—2441no—
1064C23—2441no—
1065C23—2441no—
1066C23—2441no—
1067C23—2441no—
1068C23—2441no—
1069C23Q8×#692312yes—
1070C23C23×#692311yescharacteristic
1071Q8—44no—
1072Q8—2444no—
1073Q8—2444no—
1074Q8—2444no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—44no—
1090C2×C4—612no—
1091C2×C4—612no—
1092C2×C4—612no—
1093C2×C4—612no—
1094C2×C4—1222no—
1095C2×C4—1222no—
1096C2×C4—1222no—
1097C2×C4—1222no—
1098C2×C4—1222no—
1099C2×C4—1222no—
1100C2×C4—1222no—
1101C2×C4—1222no—
1102C2×C4—1222no—
1103C2×C4—1222no—
1104C2×C4—1222no—
1105C2×C4—1222no—
1106C2×C4—1222no—
1107C2×C4—1222no—
1108C2×C4—1222no—
1109C2×C4—1222no—
1110C2×C4—1221no—
1111C2×C4—1221no—
1112C2×C4—1221no—
1113C2×C4—1221no—
1114C2×C4—1221no—
1115C2×C4—1221no—
1116C2×C4—1221no—
1117C2×C4—1221no—
1118C2×C4—1222no—
1119C2×C4—1222no—
1120C2×C4—1222no—
1121C2×C4—1222no—
1122C2×C4—1222no—
1123C2×C4—1222no—
1124C2×C4—1222no—
1125C2×C4—1222no—
1126C2×C4—1222no—
1127C2×C4—1222no—
1128C2×C4—1222no—
1129C2×C4—1222no—
1130C2×C4—1221no—
1131C2×C4—1221no—
1132C2×C4—1221no—
1133C2×C4—1221no—
1134C2×C4—1221no—
1135C2×C4—1221no—
1136C2×C4—2444no—
1137C2×C4—2444no—
1138C2×C4—2441no—
1139C2×C4—2441no—
1140C2×C4—2441no—
1141C2×C4—2441no—
1142C2×C4—2441no—
1143C2×C4—2441no—
1144C2×C4—2441no—
1145C2×C4—2441no—
1146C2×C4—2444no—
1147C2×C4—2441no—
1148C2×C4—2441no—
1149C2×C4—2441no—
1150C2×C4—2441no—
1151C2×C4—2441no—
1152C2×C4—2441no—
1153C2×C4—2441no—
1154C2×C4—2441no—
1155C2×C4—2441no—
1156C2×C4—2441no—
1157C2×C4—2441no—
1158C2×C4—2441no—
1159C2×C4—2441no—
1160C2×C4—2441no—
1161C2×C4—2441no—
1162C2×C4—2441no—
1163C2×C4—2441no—
1164C2×C4—2441no—
1165C2×C4—2441no—
1166C2×C4—2441no—
1167C2×C4—2441no—
1168C2×C4—2441no—
1169C2×C4—2441no—
1170C2×C4—2441no—
1171C2×C4—2441no—
1172C2×C4—2441no—
1173C2×C4—2441no—
1174C2×C4—2441no—
1175C2×C4—2441no—
1176C2×C4—2441no—
1177C2×C4—2441no—
1178C2×C4—2441no—
1179C2×C4—2441no—
1180C2×C4—2441no—
1181C2×C4—2441no—
1182C2×C4—2441no—
1183C2×C4—2441no—
1184C2×C4—2441no—
1185C2×C4—2441no—
1186C2×C4—2441no—
1187C2×C4—2441no—
1188C2×C4—2441no—
1189C2×C4—2441no—
1190C2×C4—2441no—
1191C2×C4C2×C22⋊#692312yes—
1192C2×C4C2×C22⋊#692312yes—
1193C2×C4C2×C22⋊#692312yes—
1194C2×C4D4×#692312yes—
1195C22—22no—
1196C22—22no—
1197C22—22no—
1198C22—41no—
1199C22—41no—
1200C22—41no—
1201C22—41no—
1202C22—611no—
1203C22—611no—
1204C22—611no—
1205C22—611no—
1206C22—611no—
1207C22—611no—
1208C22—611no—
1209C22—611no—
1210C22—611no—
1211C22—611no—
1212C22—611no—
1213C22—611no—
1214C22—611no—
1215C22—611no—
1216C22—611no—
1217C22—611no—
1218C22—611no—
1219C22—611no—
1220C22—611no—
1221C22—611no—
1222C22—611no—
1223C22—611no—
1224C22—611no—
1225C22—611no—
1226C22—611no—
1227C22—611no—
1228C22—611no—
1229C22—611no—
1230C22—1222no—
1231C22—1222no—
1232C22—1222no—
1233C22—2442no—
1234C22—2442no—
1235C22—2442no—
1236C22—2442no—
1237C22—2442no—
1238C22—2442no—
1239C22—2442no—
1240C22—2442no—
1241C22—2441no—
1242C22—2441no—
1243C22—2441no—
1244C22—2441no—
1245C22C22×C22⋊#692311yescharacteristic
1246C22C2×D4×#692311yescharacteristic
1247C22C2×Q8×#692311yescharacteristic
1248C22#1684082911yescharacteristic
1249C22#1684083011yescharacteristic
1250C22#1684083111yescharacteristic
1251C22#1684083111yescharacteristic
1252C4—22no—
1253C4—22no—
1254C4—22no—
1255C4—22no—
1256C4—41no—
1257C4—41no—
1258C4—1222no—
1259C4—1222no—
1260C4—1222no—
1261C4—1222no—
1262C4—4881no—
1263C4—4881no—
1264C4—4881no—
1265C4—4881no—
1266C4—2442no—
1267C4—2442no—
1268C4—2442no—
1269C4—2442no—
1270C4—2441no—
1271C4—2441no—
1272C2—42no—
1273C2—611no—
1274C2—611no—
1275C2—611no—
1276C2—611no—
1277C2—611no—
1278C2—611no—
1279C2—611no—
1280C2—611no—
1281C2—2442no—
1282C2#2146229411yescharacteristic
1283C2#2146230611yescharacteristic
1284C2#2146231211yescharacteristic
1285C2D4×C22⋊#692311yescharacteristic
1286C2Q8×C22⋊#692311yescharacteristic
1287C2#2146234311yescharacteristic
1288C2#2146236111yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC2×C22⋊Q8×C61C4
prime radicalC24×D61C23
cosocleC23×D61C24
hypercenterC2×C22⋊Q8#6923
hypocenterC61#14362
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×(C2×#6923)⋊Q8C2semidirect
2. C2×#16840713C2semidirect
3. C2×#16840711C2semidirect
5. #21461009C2semidirect
6. #21461004C2semidirect
7. #21461004C2semidirect
8. #21461004C2semidirect
13. #21460998C2semidirect
50. C2×#14519757C4semidirect
51. C2×#14519756C4semidirect
52. C2×#14519755C4semidirect
53. C2×#14519755C4semidirect
54. C2×#14519754C4semidirect
55. C2×#14519754C4semidirect
56. C2×#14519753C4semidirect
64. C2×C22⋊Q8×C61C4semidirect
96. C2×C22⋊#6923Q8semidirect
351. C4⋊C4×C61C22⋊C4semidirect
362. C4⋊Dic61C22⋊C4semidirect
367. #11758196C22⋊C4semidirect
368. #11758196C22⋊C4semidirect
671. C2×C22⋊Q8#6923semidirect
709. C61#14362semidirect
999. C4⋊C4C22⋊#6923semidirect

Maximal subgroups

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

subgroupindex
C2×(C2×#6923)⋊Q82
C2×#168407132
C2×#168407112
C2×#168407042
#214610092
#214610042
#214610022
#214610002
#214609982
#214609932
C2×C22⋊Q8×D612
#1436261