Finite Group Databasebeta

← #29695698

Subgroups — #29695698

Order 15616.

1494 conjugacy classes of subgroups.

The subgroup lattice has 1244 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#11758194C211yesmaximal, characteristic, complemented
2C2×#16839779C211yesmaximal, characteristic, complemented
3C22×#14519704C211yesmaximal, characteristic, complemented
4#21448264C211yesmaximal, characteristic, complemented
5#21446739C211yesmaximal, characteristic, complemented
6#21446652C211yesmaximal, characteristic, complemented
7#21446268C211yesmaximal, characteristic, complemented
8#21446263C211yesmaximal, characteristic, complemented
9#21446122C211yesmaximal, characteristic, complemented
10#21446122C211yesmaximal, characteristic, complemented
11#21445839C211yesmaximal, characteristic, complemented
12#21445763C211yesmaximal, characteristic, complemented
13#21445763C211yesmaximal, characteristic, complemented
14#21445629C211yesmaximal, characteristic, complemented
15D4×#41×C61C211yesmaximal, characteristic
16C22×#11758194C2211yescharacteristic, complemented
17C22×#11758194C2211yescharacteristic, complemented
18C2×#14519736C2211yescharacteristic, complemented
19C22×C4×Dic61C2211yescharacteristic, complemented
20#16839840—21no—
21#16839834—21no—
22#16839834—21no—
23D4×#92418—21no—
24#16839786C2211yescharacteristic, complemented
25#16839779—24no—
26C2×#14519704—24no—
27C2×#14519704C2211yescharacteristic
28C2×#14519704C2211yescharacteristic
29C2×#14519704C2211yescharacteristic
30C2×#14519704C2211yescharacteristic
31C2×#14519704C2211yescharacteristic, complemented
32C2×#14519704C2211yescharacteristic, complemented
33C2×#14519704C2211yescharacteristic, complemented
34C2×#14519704C2211yescharacteristic, complemented
35C2×#14519704C2211yescharacteristic, complemented
36C2×#14519704C2211yescharacteristic, complemented
37C2×#14519704C2211yescharacteristic, complemented
38C2×#14519704C2211yescharacteristic, complemented
39#16839726C2211yescharacteristic, complemented
40#16839726C2211yescharacteristic, complemented
41C4×#11758194C2211yescharacteristic, complemented
42#16839655—21no—
43#16839648—21no—
44#16839642—21no—
45#16839637—21no—
46C4×C4⋊Dic61C2211yescharacteristic, complemented
47C4×C22⋊Dic61C2211yescharacteristic, complemented
48C4×C22⋊Dic61C2211yescharacteristic, complemented
49#16839608C2211yescharacteristic, complemented
50#16839521C2211yescharacteristic, complemented
51#16839521C2211yescharacteristic, complemented
52#16839521C2211yescharacteristic, complemented
53#16839521C2211yescharacteristic, complemented
54C22×#41×C61C2211yescharacteristic
55C22×#41×C61C2211yescharacteristic
56C61×#550C411yescharacteristic, complemented
57D4×Q8×C61C411yescharacteristic, complemented
58C61×#548C411yescharacteristic, complemented
59C61×#548C411yescharacteristic, complemented
60C61×#547—21no—
61C61×#547C411yescharacteristic, complemented
62C61×#546—21no—
63C61×#546—21no—
64C61×#546C411yescharacteristic, complemented
65C61×#546C411yescharacteristic, complemented
66D42×C61—21no—
67D42×C61C411yescharacteristic, complemented
68C61×#532—21no—
69C61×#532C2211yescharacteristic
70C61×#525—21no—
71C61×#525—21no—
72C61×#525C2211yescharacteristic
73C61×#525C2211yescharacteristic
74C4×#41×C61C2211yescharacteristic
75C2×C4×D4×C61—21no—
76C2×C4×D4×C61C2211yescharacteristic
77C23×Dic61—21no—
78C2×#11758194—21no—
79C2×#11758194—21no—
80C2×#11758194—22no—
81C2×#11758194—22no—
82C2×#11758194—41no—
83C2×#11758194—41no—
84C2×#11758194C2311yescharacteristic
85C2×#11758194C2311yescharacteristic
86C2×#11758194C2311yescharacteristic
87C2×#11758194C2311yescharacteristic
88C22×#92418—21no—
89C22×#92418—21no—
90#14519736—22no—
91#14519736—41no—
92C2×C4⋊Dic61—21no—
93C2×C4⋊Dic61—21no—
94C2×C22⋊Dic61—21no—
95C2×C22⋊Dic61—21no—
96C2×C22⋊Dic61—21no—
97C2×C4×Dic61—22no—
98C2×C4×Dic61—21no—
99C2×C4×Dic61—41no—
100C2×C4×Dic61C2311yescharacteristic
101C2×C4×Dic61C2311yescharacteristic
102C2×C4×Dic61C2311yescharacteristic
103C2×C4×Dic61C2311yescharacteristic
104C4⋊#92418—21no—
105C4⋊#92418—21no—
106#14519704—22no—
107#14519704—22no—
108#14519704—22no—
109#14519704—22no—
110#14519704—22no—
111#14519704—22no—
112#14519704—22no—
113#14519704—41no—
114#14519704—41no—
115#14519704—41no—
116#14519704—41no—
117#14519704D414yescomplemented
118C22⋊#92418—21no—
119C22⋊#92418—21no—
120C22⋊#92418—21no—
121C22⋊#92418—21no—
122#14519688—21no—
123C4×#92418—21no—
124#14519684—21no—
125#14519684—21no—
126#14519684—21no—
127#14519684—21no—
128#14519684—21no—
129C2×#41×C61—21no—
130C2×#41×C61—21no—
131C2×#41×C61—21no—
132C2×#41×C61—21no—
133C2×#41×C61—22no—
134C2×#41×C61—22no—
135C2×#41×C61—22no—
136C2×#41×C61—22no—
137C2×#41×C61—41no—
138C2×#41×C61—41no—
139C2×#41×C61—41no—
140C2×#41×C61—41no—
141C2×#41×C61C2×C411yescharacteristic
142C2×#41×C61C2×C411yescharacteristic
143C2×#41×C61C2×C411yescharacteristic, complemented
144C2×#41×C61C2×C411yescharacteristic, complemented
145C2×#41×C61C2311yescharacteristic
146C2×#41×C61C2311yescharacteristic
147C2×#41×C61C2311yescharacteristic
148C22×Q8×C61C2×C411yescharacteristic
149C22×Q8×C61C2×C411yescharacteristic, complemented
150C22×D4×C61—21no—
151C22×D4×C61—21no—
152C22×D4×C61—21no—
153C22×D4×C61C2×C411yescharacteristic
154C22×D4×C61C2×C411yescharacteristic, complemented
155C22×D4×C61D411yescharacteristic
156C23×C4×C61—21no—
157C23×C4×C61—21no—
158C23×C4×C61C2311yescharacteristic
159C23×C4×C61C2311yescharacteristic
160C4⋊Q8×C61—21no—
161C4⋊Q8×C61C2×C411yescharacteristic, complemented
162#127×C61—21no—
163#127×C61C2×C411yescharacteristic, complemented
164#124×C61—21no—
165#124×C61—21no—
166#124×C61C2×C411yescharacteristic, complemented
167#124×C61C2×C411yescharacteristic, complemented
168#123×C61—21no—
169#123×C61—21no—
170#123×C61—21no—
171#123×C61—21no—
172#123×C61—21no—
173#123×C61—21no—
174C22⋊Q8×C61—21no—
175C22⋊Q8×C61—21no—
176C22⋊Q8×C61—21no—
177C22⋊Q8×C61—21no—
178C22⋊Q8×C61C2×C411yescharacteristic
179C22⋊Q8×C61C2×C411yescharacteristic
180C22⋊Q8×C61C2×C411yescharacteristic, complemented
181C22⋊Q8×C61C2×C411yescharacteristic, complemented
182#121×C61—21no—
183#121×C61—21no—
184#121×C61—21no—
185#121×C61—21no—
186#121×C61—21no—
187#121×C61—21no—
188#121×C61—21no—
189#121×C61—21no—
190#121×C61—21no—
191#121×C61—21no—
192#121×C61C2×C411yescharacteristic
193#121×C61C2×C411yescharacteristic
194#121×C61C2×C411yescharacteristic, complemented
195#121×C61C2×C411yescharacteristic, complemented
196#120×C61—21no—
197#120×C61—21no—
198#120×C61—21no—
199#120×C61—21no—
200#120×C61—21no—
201#120×C61—21no—
202C4×Q8×C61C2×C411yescharacteristic, complemented
203C4×Q8×C61C2×C411yescharacteristic, complemented
204C4×D4×C61—21no—
205C4×D4×C61—21no—
206C4×D4×C61—21no—
207C4×D4×C61—21no—
208C4×D4×C61—21no—
209C4×D4×C61—21no—
210C4×D4×C61—21no—
211C4×D4×C61—21no—
212C4×D4×C61—21no—
213C4×D4×C61—21no—
214C4×D4×C61—21no—
215C4×D4×C61—21no—
216C4×D4×C61C2×C411yescharacteristic
217C4×D4×C61C2×C411yescharacteristic
218C4×D4×C61C2×C411yescharacteristic
219C4×D4×C61C2×C411yescharacteristic
220C4×D4×C61C2×C411yescharacteristic, complemented
221C4×D4×C61C2×C411yescharacteristic, complemented
222C4×D4×C61D411yescharacteristic
223C4×D4×C61D411yescharacteristic
224C4×D4×C61D411yescharacteristic
225C4×D4×C61D411yescharacteristic
226#117×C61—21no—
227#117×C61C2311yescharacteristic
228C2×C4⋊C4×C61—21no—
229C2×C4⋊C4×C61D411yescharacteristic
230C2×C22⋊C4×C61—21no—
231C2×C22⋊C4×C61—21no—
232C2×C22⋊C4×C61D411yescharacteristic
233C2×C22⋊C4×C61D411yescharacteristic
234C2×C42×C61—21no—
235C2×C42×C61C2311yescharacteristic
236C24×C61—21no—
237C24×C61—21no—
238C24×C61C2×D411yescharacteristic
239C24×C61C2×D411yescharacteristic
240#41×C61—21no—
241#41×C61—21no—
242#41×C61—22no—
243#41×C61—22no—
244#41×C61—22no—
245#41×C61—22no—
246#41×C61—21no—
247#41×C61—21no—
248#41×C61—21no—
249#41×C61—21no—
250#41×C61—21no—
251#41×C61—21no—
252#41×C61—21no—
253#41×C61—21no—
254#41×C61—42no—
255#41×C61—42no—
256#41×C61—42no—
257#41×C61—42no—
258#41×C61—41no—
259#41×C61—41no—
260#41×C61—41no—
261#41×C61—41no—
262#41×C61—42no—
263#41×C61—42no—
264#41×C61—42no—
265#41×C61—42no—
266#41×C61C2×D412yes—
267#41×C61#4112yes—
268C2×Q8×C61—21no—
269C2×Q8×C61—21no—
270C2×Q8×C61—22no—
271C2×Q8×C61—22no—
272C2×Q8×C61—41no—
273C2×Q8×C61—41no—
274C2×Q8×C61C22×C411yescharacteristic
275C2×Q8×C61C22×C411yescharacteristic
276C2×Q8×C61C22×C411yescharacteristic
277C2×D4×C61—21no—
278C2×D4×C61—22no—
279C2×D4×C61—22no—
280C2×D4×C61—21no—
281C2×D4×C61—21no—
282C2×D4×C61—21no—
283C2×D4×C61—21no—
284C2×D4×C61—21no—
285C2×D4×C61—21no—
286C2×D4×C61—21no—
287C2×D4×C61—21no—
288C2×D4×C61—21no—
289C2×D4×C61—21no—
290C2×D4×C61—21no—
291C2×D4×C61—21no—
292C2×D4×C61—21no—
293C2×D4×C61—21no—
294C2×D4×C61—41no—
295C2×D4×C61—41no—
296C2×D4×C61—42no—
297C2×D4×C61—42no—
298C2×D4×C61—42no—
299C2×D4×C61—42no—
300C2×D4×C61—42no—
301C2×D4×C61—44no—
302C2×D4×C61C22⋊C411yescharacteristic
303C2×D4×C61C22⋊C411yescharacteristic
304C2×D4×C61C22⋊C411yescharacteristic
305C2×D4×C61C22⋊C411yescharacteristic
306C2×D4×C61C22×C411yescharacteristic
307C2×D4×C61C22×C411yescharacteristic
308C2×D4×C61C22×C411yescharacteristic
309C22×C4×C61—21no—
310C22×C4×C61—21no—
311C22×C4×C61—21no—
312C22×C4×C61—21no—
313C22×C4×C61—21no—
314C22×C4×C61—21no—
315C22×C4×C61—21no—
316C22×C4×C61—21no—
317C22×C4×C61—21no—
318C22×C4×C61—21no—
319C22×C4×C61—21no—
320C22×C4×C61—21no—
321C22×C4×C61—21no—
322C22×C4×C61—21no—
323C22×C4×C61—21no—
324C22×C4×C61—21no—
325C22×C4×C61—21no—
326C22×C4×C61—21no—
327C22×C4×C61—21no—
328C22×C4×C61—42no—
329C22×C4×C61—42no—
330C22×C4×C61—42no—
331C22×C4×C61—42no—
332C22×C4×C61C22×C411yescharacteristic
333C22×C4×C61C22×C411yescharacteristic
334C22×C4×C61C22×C411yescharacteristic
335C22×C4×C61C22×C411yescharacteristic
336C22×C4×C61C2×D411yescharacteristic
337C22×C4×C61C2×D411yescharacteristic
338C22×C4×C61C2×D411yescharacteristic
339C22×C4×C61C2×D411yescharacteristic
340C22×C4×C61C2×D411yescharacteristic
341C22×C4×C61C2×D411yescharacteristic
342C22×C4×C61C2×D411yescharacteristic
343C22×C4×C61C2×D411yescharacteristic
344C22×C4×C61C2411yescharacteristic
345C22×Dic61—21no—
346C22×Dic61—21no—
347C22×Dic61—21no—
348C22×Dic61—21no—
349C22×Dic61—42no—
350C22×Dic61—42no—
351C22×Dic61—42no—
352C4⋊C4×C61—21no—
353C4⋊C4×C61—21no—
354C4⋊C4×C61—21no—
355C4⋊C4×C61—21no—
356C4⋊C4×C61—21no—
357C4⋊C4×C61—21no—
358C4⋊C4×C61—21no—
359C4⋊C4×C61—21no—
360C4⋊C4×C61C22⋊C411yescharacteristic
361C4⋊C4×C61C22⋊C411yescharacteristic
362C4⋊C4×C61C22⋊C411yescharacteristic
363C4⋊C4×C61C22⋊C411yescharacteristic
364C4⋊C4×C61C22×C411yescharacteristic
365C4⋊C4×C61C22×C411yescharacteristic
366C22⋊C4×C61—21no—
367C22⋊C4×C61—21no—
368C22⋊C4×C61—21no—
369C22⋊C4×C61—21no—
370C22⋊C4×C61—21no—
371C22⋊C4×C61—21no—
372C22⋊C4×C61—21no—
373C22⋊C4×C61—21no—
374C22⋊C4×C61—21no—
375C22⋊C4×C61—21no—
376C22⋊C4×C61—21no—
377C22⋊C4×C61—21no—
378C22⋊C4×C61—21no—
379C22⋊C4×C61—21no—
380C22⋊C4×C61—21no—
381C22⋊C4×C61C22⋊C411yescharacteristic
382C22⋊C4×C61C22⋊C411yescharacteristic
383C22⋊C4×C61C22⋊C411yescharacteristic
384C22⋊C4×C61C22⋊C411yescharacteristic
385C22⋊C4×C61C22⋊C411yescharacteristic
386C22⋊C4×C61C22⋊C411yescharacteristic
387C22⋊C4×C61C22⋊C411yescharacteristic
388C22⋊C4×C61C22⋊C411yescharacteristic
389C42×C61—21no—
390C42×C61—21no—
391C42×C61—21no—
392C42×C61C22×C411yescharacteristic
393C42×C61C22×C411yescharacteristic
394C42×C61C2×D411yescharacteristic
395C42×C61C2×D411yescharacteristic
396C22⋊Dic61—42no—
397C22⋊Dic61—42no—
398C22⋊Dic61—42no—
399C4⋊Dic61—42no—
400C4⋊Dic61—42no—
401C4×Dic61—21no—
402C4×Dic61—21no—
403C4×Dic61—21no—
404C4×Dic61—21no—
405C4×Dic61—21no—
406C4×Dic61—21no—
407C4×Dic61—21no—
408C4×Dic61—42no—
409C4×Dic61C2×D412yescomplemented
410#11758194—21no—
411#11758194—21no—
412#11758194—21no—
413#11758194—21no—
414#11758194—21no—
415#11758194—21no—
416#11758194—21no—
417#11758194—42no—
418#11758194—42no—
419#11758194C2×D412yescomplemented
420C2×#92418—21no—
421C2×#92418—21no—
422C2×#92418—21no—
423C2×#92418—21no—
424C2×#92418—42no—
425C2×#92418—42no—
426C23×C61—21no—
427C23×C61—21no—
428C23×C61—21no—
429C23×C61—22no—
430C23×C61—21no—
431C23×C61—21no—
432C23×C61—21no—
433C23×C61—21no—
434C23×C61—41no—
435C23×C61—41no—
436C23×C61—41no—
437C23×C61—42no—
438C23×C61—42no—
439C23×C61—42no—
440C23×C61—42no—
441C23×C61—81no—
442C23×C61—81no—
443C23×C61C2×C22⋊C411yescharacteristic
444C23×C61C2×C22⋊C411yescharacteristic
445C23×C61C2×C22⋊C411yescharacteristic
446C23×C61C2×C22⋊C411yescharacteristic
447C23×C61C22×D411yescharacteristic
448Q8×C61—21no—
449Q8×C61—21no—
450Q8×C61—21no—
451Q8×C61—21no—
452Q8×C61—21no—
453Q8×C61—42no—
454Q8×C61—42no—
455Q8×C61C4×D412yes—
456D4×C61—22no—
457D4×C61—22no—
458D4×C61—22no—
459D4×C61—22no—
460D4×C61—21no—
461D4×C61—21no—
462D4×C61—21no—
463D4×C61—21no—
464D4×C61—21no—
465D4×C61—41no—
466D4×C61—41no—
467D4×C61—42no—
468D4×C61—42no—
469D4×C61—42no—
470D4×C61—42no—
471D4×C61—42no—
472D4×C61—42no—
473D4×C61—42no—
474D4×C61—42no—
475D4×C61—41no—
476D4×C61—41no—
477D4×C61—41no—
478D4×C61—41no—
479D4×C61—42no—
480D4×C61—81no—
481D4×C61—81no—
482D4×C61—81no—
483D4×C61C4×D412yes—
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—21no—
498C2×C4×C61—21no—
499C2×C4×C61—21no—
500C2×C4×C61—21no—
501C2×C4×C61—22no—
502C2×C4×C61—21no—
503C2×C4×C61—21no—
504C2×C4×C61—21no—
505C2×C4×C61—21no—
506C2×C4×C61—22no—
507C2×C4×C61—21no—
508C2×C4×C61—21no—
509C2×C4×C61—21no—
510C2×C4×C61—21no—
511C2×C4×C61—41no—
512C2×C4×C61—41no—
513C2×C4×C61—42no—
514C2×C4×C61—42no—
515C2×C4×C61—42no—
516C2×C4×C61—42no—
517C2×C4×C61—42no—
518C2×C4×C61—42no—
519C2×C4×C61—42no—
520C2×C4×C61—41no—
521C2×C4×C61—41no—
522C2×C4×C61—41no—
523C2×C4×C61—41no—
524C2×C4×C61—81no—
525C2×C4×C61C2×C22⋊C411yescharacteristic
526C2×C4×C61C2×C22⋊C411yescharacteristic
527C2×C4×C61C2×C22⋊C411yescharacteristic
528C2×C4×C61C2×C22⋊C411yescharacteristic
529C2×C4×C61C2×C22⋊C411yescharacteristic
530C2×C4×C61C2×C22⋊C411yescharacteristic
531C2×C4×C61C2×C22⋊C411yescharacteristic
532C2×C4×C61C2×C22⋊C411yescharacteristic
533C2×C4×C61C23×C411yescharacteristic
534C2×C4×C61C22×D411yescharacteristic
535C2×C4×C61C22×D411yescharacteristic
536C2×C4×C61C2×#4111yescharacteristic
537C2×C4×C61H(5,𝔽2)11yescharacteristic
538C2×C4×C61H(5,𝔽2)11yescharacteristic
539C2×Dic61—22no—
540C2×Dic61—22no—
541C2×Dic61—41no—
542C2×Dic61—41no—
543C2×Dic61—41no—
544C2×Dic61—48no—
545C2×Dic61—41no—
546C2×Dic61—41no—
547C2×Dic61—41no—
548C2×Dic61—41no—
549C2×Dic61—41no—
550C2×Dic61—41no—
551C2×Dic61—41no—
552#92418—22no—
553#92418—41no—
554#92418—41no—
555#92418—41no—
556#22434—611nomaximal, Sylow
557C22×C61—21no—
558C22×C61—21no—
559C22×C61—21no—
560C22×C61—21no—
561C22×C61—21no—
562C22×C61—21no—
563C22×C61—21no—
564C22×C61—22no—
565C22×C61—21no—
566C22×C61—21no—
567C22×C61—21no—
568C22×C61—21no—
569C22×C61—21no—
570C22×C61—21no—
571C22×C61—42no—
572C22×C61—42no—
573C22×C61—41no—
574C22×C61—41no—
575C22×C61—41no—
576C22×C61—41no—
577C22×C61—41no—
578C22×C61—41no—
579C22×C61—41no—
580C22×C61—41no—
581C22×C61—81no—
582C22×C61—81no—
583C22×C61—84no—
584C22×C61—84no—
585C22×C61#42112yescomplemented
586C22×C61C22×C22⋊C411yescharacteristic
587C22×C61D4211yescharacteristic
588C22×C61#54611yescharacteristic
589C4×C61—21no—
590C4×C61—21no—
591C4×C61—21no—
592C4×C61—21no—
593C4×C61—22no—
594C4×C61—21no—
595C4×C61—21no—
596C4×C61—21no—
597C4×C61—21no—
598C4×C61—41no—
599C4×C61—41no—
600C4×C61—41no—
601C4×C61—41no—
602C4×C61C2×C4×D411yescharacteristic
603C4×C61#51811yescharacteristic
604C4×C61D4211yescharacteristic
605C4×C61#54611yescharacteristic
606Dic61—42no—
607Dic61—42no—
608Dic61—81no—
609Dic61—81no—
610D4×#41D6111yescharacteristic
611D4×M16—611no—
612C2×#421—611no—
613C22×#104—611no—
614#2290—611no—
615#1980—611no—
616#1963—611no—
617#1897—611no—
618#1896—611no—
619#1871—611no—
620#1871—611no—
621#1806—611no—
622#1789—611no—
623#1789—611no—
624#1759—611no—
625C2×C61—21no—
626C2×C61—21no—
627C2×C61—22no—
628C2×C61—41no—
629C2×C61—41no—
630C2×C61—41no—
631C2×C61—42no—
632C2×C61—81no—
633C2×C61—81no—
634C2×C61D4×C22⋊C411yescharacteristic
635C2×C61C2×#42111yescharacteristic
636C2×C61#290111yescharacteristic
637C22×#41C2×D6111yescharacteristic
638C22×#41C2×D6111yescharacteristic
639C22×M16—611no—
640C22×M16—611no—
641#550Dic6111yescharacteristic, complemented
642D4×Q8Dic6111yescharacteristic, complemented
643#548Dic6111yescharacteristic, complemented
644#548Dic6111yescharacteristic, complemented
645#547—21no—
646#547Dic6111yescharacteristic, complemented
647#546—21no—
648#546—21no—
649#546Dic6111yescharacteristic, complemented
650#546Dic6111yescharacteristic, complemented
651D42—21no—
652D42Dic6111yescharacteristic, complemented
653#532—21no—
654#532C2×D6111yescharacteristic
655#525—21no—
656#525—21no—
657#525C2×D6111yescharacteristic
658#525C2×D6111yescharacteristic
659C4×#41C2×D6111yescharacteristic
660C2×C4×D4—21no—
661C2×C4×D4C2×D6111yescharacteristic
662C2×#117—611no—
663C22×C42—611no—
664#436—1221no—
665#435—1221no—
666#435—1221no—
667C8×D4—1221no—
668#423—611no—
669#421—1224no—
670C2×#104—611no—
671C2×#104—611no—
672C2×#104—611no—
673C2×#104—611no—
674C2×#104—611no—
675C2×#104—611no—
676C2×#104—611no—
677C2×#104—611no—
678C2×#104—611no—
679C2×#104—611no—
680C2×#104—611no—
681C2×#104—611no—
682C2×#104—1224no—
683#407—611no—
684#407—611no—
685C4×M16—611no—
686#388—1221no—
687#387—1221no—
688#386—1221no—
689#385—1221no—
690C4×C4⋊C4—611no—
691C4×C22⋊C4—611no—
692C4×C22⋊C4—611no—
693#376—611no—
694#339—611no—
695#339—611no—
696#339—611no—
697#339—611no—
698C61#2243411yescharacteristic, complemented, Sylow
699C2×#41—21no—
700C2×#41—21no—
701C2×#41—21no—
702C2×#41—21no—
703C2×#41—22no—
704C2×#41—22no—
705C2×#41—22no—
706C2×#41—22no—
707C2×#41—41no—
708C2×#41—41no—
709C2×#41—41no—
710C2×#41—41no—
711C2×#41C2×Dic6111yescharacteristic
712C2×#41C2×Dic6111yescharacteristic
713C2×#41C2×Dic6111yescharacteristic, complemented
714C2×#41C2×Dic6111yescharacteristic, complemented
715C2×#41C22×D6111yescharacteristic
716C2×#41C22×D6111yescharacteristic
717C2×#41C22×D6111yescharacteristic
718C22×Q8C2×Dic6111yescharacteristic
719C22×Q8C2×Dic6111yescharacteristic, complemented
720C22×D4—21no—
721C22×D4—21no—
722C22×D4—21no—
723C22×D4C2×Dic6111yescharacteristic
724C22×D4C2×Dic6111yescharacteristic, complemented
725C22×D4C22⋊D6111yescharacteristic
726C23×C4—21no—
727C23×C4—21no—
728C23×C4—1221no—
729C23×C4C22×D6111yescharacteristic
730C23×C4C22×D6111yescharacteristic
731C2×M16—611no—
732C2×M16—611no—
733C2×M16—611no—
734C2×M16—611no—
735C2×M16—1221no—
736C2×M16—1221no—
737C2×M16—1222no—
738C2×M16—1222no—
739C2×M16—2441no—
740C2×M16—2441no—
741C22×C8—1221no—
742C22×C8—1221no—
743C4⋊Q8—21no—
744C4⋊Q8C2×Dic6111yescharacteristic, complemented
745#127—21no—
746#127C2×Dic6111yescharacteristic, complemented
747#124—21no—
748#124—21no—
749#124C2×Dic6111yescharacteristic, complemented
750#124C2×Dic6111yescharacteristic, complemented
751#123—21no—
752#123—21no—
753#123—21no—
754#123—21no—
755#123—21no—
756#123—21no—
757C22⋊Q8—21no—
758C22⋊Q8—21no—
759C22⋊Q8—21no—
760C22⋊Q8—21no—
761C22⋊Q8C2×Dic6111yescharacteristic
762C22⋊Q8C2×Dic6111yescharacteristic
763C22⋊Q8C2×Dic6111yescharacteristic, complemented
764C22⋊Q8C2×Dic6111yescharacteristic, complemented
765#121—21no—
766#121—21no—
767#121—21no—
768#121—21no—
769#121—21no—
770#121—21no—
771#121—21no—
772#121—21no—
773#121—21no—
774#121—21no—
775#121C2×Dic6111yescharacteristic
776#121C2×Dic6111yescharacteristic
777#121C2×Dic6111yescharacteristic, complemented
778#121C2×Dic6111yescharacteristic, complemented
779#120—21no—
780#120—21no—
781#120—21no—
782#120—21no—
783#120—21no—
784#120—21no—
785C4×Q8C2×Dic6111yescharacteristic, complemented
786C4×Q8C2×Dic6111yescharacteristic, complemented
787C4×D4—21no—
788C4×D4—21no—
789C4×D4—21no—
790C4×D4—21no—
791C4×D4—21no—
792C4×D4—21no—
793C4×D4—21no—
794C4×D4—21no—
795C4×D4—21no—
796C4×D4—21no—
797C4×D4—21no—
798C4×D4—21no—
799C4×D4C2×Dic6111yescharacteristic
800C4×D4C2×Dic6111yescharacteristic
801C4×D4C2×Dic6111yescharacteristic
802C4×D4C2×Dic6111yescharacteristic
803C4×D4C2×Dic6111yescharacteristic, complemented
804C4×D4C2×Dic6111yescharacteristic, complemented
805C4×D4C22⋊D6111yescharacteristic
806C4×D4C22⋊D6111yescharacteristic
807C4×D4C22⋊D6111yescharacteristic
808C4×D4C22⋊D6111yescharacteristic
809#117—21no—
810#117—1222no—
811#117—2441no—
812#117C22×D6111yescharacteristic
813C2×C4⋊C4—21no—
814C2×C4⋊C4—1221no—
815C2×C4⋊C4—1221no—
816C2×C4⋊C4C22⋊D6111yescharacteristic
817C2×C22⋊C4—21no—
818C2×C22⋊C4—21no—
819C2×C22⋊C4—1221no—
820C2×C22⋊C4—1221no—
821C2×C22⋊C4—1221no—
822C2×C22⋊C4C22⋊D6111yescharacteristic
823C2×C22⋊C4C22⋊D6111yescharacteristic
824C2×C42—21no—
825C2×C42—611no—
826C2×C42—611no—
827C2×C42—611no—
828C2×C42—611no—
829C2×C42—1222no—
830C2×C42—1221no—
831C2×C42—2441no—
832C2×C42C22×D6111yescharacteristic
833C4⋊C8—1221no—
834C4⋊C8—1221no—
835#104—614no—
836#104—1222no—
837#104—1222no—
838#104—1222no—
839#104—1222no—
840#104—1222no—
841#104—1222no—
842#104—1222no—
843#104—2441no—
844#104—2441no—
845#104—2441no—
846#104—2441no—
847C22⋊C8—1221no—
848C22⋊C8—1221no—
849C22⋊C8—1221no—
850C22⋊C8—1221no—
851#97—1221no—
852C4×C8—1221no—
853#95—1221no—
854#95—1221no—
855#95—1221no—
856#95—1221no—
857#95—1221no—
858C24—21no—
859C24—21no—
860C24C2×C22⋊D6111yescharacteristic
861C24C2×C22⋊D6111yescharacteristic
862#41—21no—
863#41—21no—
864#41—22no—
865#41—22no—
866#41—22no—
867#41—22no—
868#41—21no—
869#41—21no—
870#41—21no—
871#41—21no—
872#41—21no—
873#41—21no—
874#41—21no—
875#41—21no—
876#41—42no—
877#41—42no—
878#41—42no—
879#41—42no—
880#41—41no—
881#41—41no—
882#41—41no—
883#41—41no—
884#41—42no—
885#41—42no—
886#41—42no—
887#41—42no—
888#41D4×D6112yes—
889#41#1175822412yes—
890C2×Q8—21no—
891C2×Q8—21no—
892C2×Q8—22no—
893C2×Q8—22no—
894C2×Q8—41no—
895C2×Q8—41no—
896C2×Q8C22×Dic6111yescharacteristic
897C2×Q8C22×Dic6111yescharacteristic
898C2×Q8C22×Dic6111yescharacteristic
899C2×D4—21no—
900C2×D4—22no—
901C2×D4—22no—
902C2×D4—21no—
903C2×D4—21no—
904C2×D4—21no—
905C2×D4—21no—
906C2×D4—21no—
907C2×D4—21no—
908C2×D4—21no—
909C2×D4—21no—
910C2×D4—21no—
911C2×D4—21no—
912C2×D4—21no—
913C2×D4—21no—
914C2×D4—21no—
915C2×D4—21no—
916C2×D4—41no—
917C2×D4—41no—
918C2×D4—42no—
919C2×D4—42no—
920C2×D4—42no—
921C2×D4—42no—
922C2×D4—42no—
923C2×D4—44no—
924C2×D4C22⋊Dic6111yescharacteristic
925C2×D4C22⋊Dic6111yescharacteristic
926C2×D4C22⋊Dic6111yescharacteristic
927C2×D4C22⋊Dic6111yescharacteristic
928C2×D4C22×Dic6111yescharacteristic
929C2×D4C22×Dic6111yescharacteristic
930C2×D4C22×Dic6111yescharacteristic
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—42no—
951C22×C4—42no—
952C22×C4—42no—
953C22×C4—42no—
954C22×C4—1221no—
955C22×C4—1221no—
956C22×C4—1221no—
957C22×C4—1221no—
958C22×C4—2442no—
959C22×C4—2442no—
960C22×C4—2442no—
961C22×C4C22×Dic6111yescharacteristic
962C22×C4C22×Dic6111yescharacteristic
963C22×C4C22×Dic6111yescharacteristic
964C22×C4C22×Dic6111yescharacteristic
965C22×C4C2×C22⋊D6111yescharacteristic
966C22×C4C2×C22⋊D6111yescharacteristic
967C22×C4C2×C22⋊D6111yescharacteristic
968C22×C4C2×C22⋊D6111yescharacteristic
969C22×C4C2×C22⋊D6111yescharacteristic
970C22×C4C2×C22⋊D6111yescharacteristic
971C22×C4C2×C22⋊D6111yescharacteristic
972C22×C4C2×C22⋊D6111yescharacteristic
973C22×C4C23×D6111yescharacteristic
974M16—612no—
975M16—1221no—
976M16—1221no—
977M16—1221no—
978M16—1221no—
979M16—1221no—
980M16—1221no—
981M16—1221no—
982M16—2442no—
983M16—2442no—
984C2×C8—1221no—
985C2×C8—1221no—
986C2×C8—1221no—
987C2×C8—1221no—
988C2×C8—2442no—
989C2×C8—2442no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—21no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—2442no—
999C4⋊C4—2442no—
1000C4⋊C4C22⋊Dic6111yescharacteristic
1001C4⋊C4C22⋊Dic6111yescharacteristic
1002C4⋊C4C22⋊Dic6111yescharacteristic
1003C4⋊C4C22⋊Dic6111yescharacteristic
1004C4⋊C4C22×Dic6111yescharacteristic
1005C4⋊C4C22×Dic6111yescharacteristic
1006C22⋊C4—21no—
1007C22⋊C4—21no—
1008C22⋊C4—21no—
1009C22⋊C4—21no—
1010C22⋊C4—21no—
1011C22⋊C4—21no—
1012C22⋊C4—21no—
1013C22⋊C4—21no—
1014C22⋊C4—21no—
1015C22⋊C4—21no—
1016C22⋊C4—21no—
1017C22⋊C4—21no—
1018C22⋊C4—21no—
1019C22⋊C4—21no—
1020C22⋊C4—21no—
1021C22⋊C4—2442no—
1022C22⋊C4—2442no—
1023C22⋊C4—2442no—
1024C22⋊C4C22⋊Dic6111yescharacteristic
1025C22⋊C4C22⋊Dic6111yescharacteristic
1026C22⋊C4C22⋊Dic6111yescharacteristic
1027C22⋊C4C22⋊Dic6111yescharacteristic
1028C22⋊C4C22⋊Dic6111yescharacteristic
1029C22⋊C4C22⋊Dic6111yescharacteristic
1030C22⋊C4C22⋊Dic6111yescharacteristic
1031C22⋊C4C22⋊Dic6111yescharacteristic
1032C42—21no—
1033C42—21no—
1034C42—21no—
1035C42—612no—
1036C42—1221no—
1037C42—1221no—
1038C42—1221no—
1039C42—1221no—
1040C42—1221no—
1041C42—1221no—
1042C42—1221no—
1043C42—2442no—
1044C42C22×Dic6111yescharacteristic
1045C42C22×Dic6111yescharacteristic
1046C42C2×C22⋊D6111yescharacteristic
1047C42C2×C22⋊D6111yescharacteristic
1048C23—21no—
1049C23—22no—
1050C23—21no—
1051C23—21no—
1052C23—21no—
1053C23—21no—
1054C23—21no—
1055C23—21no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—42no—
1060C23—42no—
1061C23—42no—
1062C23—42no—
1063C23—81no—
1064C23—81no—
1065C23C2×C22⋊Dic6111yescharacteristic
1066C23C2×C22⋊Dic6111yescharacteristic
1067C23C2×C22⋊Dic6111yescharacteristic
1068C23C2×C22⋊Dic6111yescharacteristic
1069C23C22×C22⋊D6111yescharacteristic
1070Q8—21no—
1071Q8—21no—
1072Q8—21no—
1073Q8—21no—
1074Q8—21no—
1075Q8—42no—
1076Q8—42no—
1077Q8D4×Dic6112yes—
1078D4—22no—
1079D4—22no—
1080D4—22no—
1081D4—22no—
1082D4—21no—
1083D4—21no—
1084D4—21no—
1085D4—21no—
1086D4—21no—
1087D4—41no—
1088D4—41no—
1089D4—42no—
1090D4—42no—
1091D4—42no—
1092D4—42no—
1093D4—42no—
1094D4—42no—
1095D4—42no—
1096D4—42no—
1097D4—42no—
1098D4—41no—
1099D4—41no—
1100D4—41no—
1101D4—41no—
1102D4—81no—
1103D4—81no—
1104D4—81no—
1105D4D4×Dic6112yes—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—22no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—22no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—42no—
1136C2×C4—42no—
1137C2×C4—42no—
1138C2×C4—42no—
1139C2×C4—42no—
1140C2×C4—42no—
1141C2×C4—42no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—81no—
1147C2×C4—1222no—
1148C2×C4—1222no—
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—2448no—
1159C2×C4—2441no—
1160C2×C4C2×C22⋊Dic6111yescharacteristic
1161C2×C4C2×C22⋊Dic6111yescharacteristic
1162C2×C4C2×C22⋊Dic6111yescharacteristic
1163C2×C4C2×C22⋊Dic6111yescharacteristic
1164C2×C4C2×C22⋊Dic6111yescharacteristic
1165C2×C4C2×C22⋊Dic6111yescharacteristic
1166C2×C4C2×C22⋊Dic6111yescharacteristic
1167C2×C4C2×C22⋊Dic6111yescharacteristic
1168C2×C4C23×Dic6111yescharacteristic
1169C2×C4C2×D4×D6111yescharacteristic
1170C2×C4C22×C22⋊D6111yescharacteristic
1171C2×C4C2×#1175822411yescharacteristic
1172C2×C4#1451982211yescharacteristic
1173C2×C4#1451982211yescharacteristic
1174C8—1222no—
1175C8—2441no—
1176C8—2441no—
1177C8—2441no—
1178C22—21no—
1179C22—21no—
1180C22—21no—
1181C22—21no—
1182C22—21no—
1183C22—21no—
1184C22—21no—
1185C22—21no—
1186C22—21no—
1187C22—21no—
1188C22—21no—
1189C22—21no—
1190C22—21no—
1191C22—22no—
1192C22—42no—
1193C22—42no—
1194C22—41no—
1195C22—41no—
1196C22—41no—
1197C22—41no—
1198C22—41no—
1199C22—41no—
1200C22—41no—
1201C22—41no—
1202C22—81no—
1203C22—81no—
1204C22—84no—
1205C22—84no—
1206C22#1683977912yescomplemented
1207C22C22×C22⋊Dic6111yescharacteristic
1208C22D4×C22⋊D6111yescharacteristic
1209C22#1684040611yescharacteristic
1210C4—21no—
1211C4—21no—
1212C4—21no—
1213C4—21no—
1214C4—21no—
1215C4—21no—
1216C4—21no—
1217C4—21no—
1218C4—22no—
1219C4—41no—
1220C4—41no—
1221C4—41no—
1222C4—41no—
1223C4—4881no—
1224C4—4881no—
1225C4—2442no—
1226C4—2442no—
1227C4C2×D4×Dic6111yescharacteristic
1228C4#1684023711yescharacteristic
1229C4D4×C22⋊D6111yescharacteristic
1230C4#1684040611yescharacteristic
1231C2—21no—
1232C2—21no—
1233C2—22no—
1234C2—41no—
1235C2—41no—
1236C2—41no—
1237C2—42no—
1238C2—81no—
1239C2—81no—
1240C2D4×C22⋊Dic6111yescharacteristic
1241C2C2×#1683977911yescharacteristic
1242C2#2145436611yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
Fitting, prime radicalD4×#41×C61C2
socleC22×C61C22×C22⋊C4
cosocleC22×C4×C61C24
hypercenterD4×#41D61
hypocenterC61#22434
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C4×D4 ◁ D4×#41

Complements

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

NH ≅ G/Ntype
1. D4×#11758194C2semidirect
2. C2×#16839779C2semidirect
3. C22×#14519704C2semidirect
4. #21448264C2semidirect
5. #21446739C2semidirect
6. #21446652C2semidirect
7. #21446268C2semidirect
8. #21446263C2semidirect
9. #21446122C2semidirect
10. #21446122C2semidirect
11. #21445839C2semidirect
12. #21445763C2semidirect
13. #21445763C2semidirect
14. #21445629C2semidirect
16. C22×#11758194C22semidirect
17. C22×#11758194C22semidirect
18. C2×#14519736C22semidirect
19. C22×C4×Dic61C22semidirect
24. #16839786C22semidirect
31. C2×#14519704C22semidirect
32. C2×#14519704C22semidirect
33. C2×#14519704C22semidirect
34. C2×#14519704C22semidirect
35. C2×#14519704C22semidirect
36. C2×#14519704C22semidirect
37. C2×#14519704C22semidirect
38. C2×#14519704C22semidirect
39. #16839726C22semidirect
40. #16839726C22semidirect
41. C4×#11758194C22semidirect
46. C4×C4⋊Dic61C22semidirect
47. C4×C22⋊Dic61C22semidirect
48. C4×C22⋊Dic61C22semidirect
49. #16839608C22semidirect
50. #16839521C22semidirect
51. #16839521C22semidirect
52. #16839521C22semidirect
53. #16839521C22semidirect
56. C61×#550C4semidirect
57. D4×Q8×C61C4semidirect
58. C61×#548C4semidirect
59. C61×#548C4semidirect
61. C61×#547C4semidirect
64. C61×#546C4semidirect
65. C61×#546C4semidirect
67. D42×C61C4semidirect
117. #14519704D4semidirect
143. C2×#41×C61C2×C4semidirect
144. C2×#41×C61C2×C4semidirect
149. C22×Q8×C61C2×C4semidirect
154. C22×D4×C61C2×C4semidirect
161. C4⋊Q8×C61C2×C4semidirect
163. #127×C61C2×C4semidirect
166. #124×C61C2×C4semidirect
167. #124×C61C2×C4semidirect
180. C22⋊Q8×C61C2×C4semidirect
181. C22⋊Q8×C61C2×C4semidirect
194. #121×C61C2×C4semidirect
195. #121×C61C2×C4semidirect
202. C4×Q8×C61C2×C4semidirect
203. C4×Q8×C61C2×C4semidirect
220. C4×D4×C61C2×C4semidirect
221. C4×D4×C61C2×C4semidirect
409. C4×Dic61C2×D4semidirect
419. #11758194C2×D4semidirect
585. C22×C61#421semidirect
641. #550Dic61semidirect
642. D4×Q8Dic61semidirect
643. #548Dic61semidirect
644. #548Dic61semidirect
646. #547Dic61semidirect
649. #546Dic61semidirect
650. #546Dic61semidirect
652. D42Dic61semidirect
698. C61#22434semidirect
713. C2×#41C2×Dic61semidirect
714. C2×#41C2×Dic61semidirect
719. C22×Q8C2×Dic61semidirect
724. C22×D4C2×Dic61semidirect
744. C4⋊Q8C2×Dic61semidirect
746. #127C2×Dic61semidirect
749. #124C2×Dic61semidirect
750. #124C2×Dic61semidirect
763. C22⋊Q8C2×Dic61semidirect
764. C22⋊Q8C2×Dic61semidirect
777. #121C2×Dic61semidirect
778. #121C2×Dic61semidirect
785. C4×Q8C2×Dic61semidirect
786. C4×Q8C2×Dic61semidirect
803. C4×D4C2×Dic61semidirect
804. C4×D4C2×Dic61semidirect
1206. C22#16839779semidirect

Maximal subgroups

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

subgroupindex
D4×#117581942
C2×#168397792
C22×#145197042
#214482642
#214467392
#214466522
#214462682
#214462632
#214461222
#214458392
#214457632
#214456292
D4×#41×C612
#2243461