Finite Group Databasebeta

← #30613397

Subgroups — #30613397

Order 15616.

566 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462728C211yesmaximal, characteristic
2#21462722C211yesmaximal, characteristic
3#21461464C211yesmaximal, characteristic, complemented
4#21461459C211yesmaximal, characteristic, complemented
5#21461445C211yesmaximal, characteristic, complemented
6#21461444C211yesmaximal, characteristic, complemented
7#21461432C211yesmaximal, characteristic, complemented
8#21461430C211yesmaximal, characteristic, complemented
9#21461412C211yesmaximal, characteristic, complemented
10#21461406C211yesmaximal, characteristic, complemented
11#21461390C211yesmaximal, characteristic
12#21461181C211yesmaximal, characteristic
13#21461121C211yesmaximal, characteristic
14#21461040C211yesmaximal, characteristic
15#21455853C211yesmaximal, characteristic
16#16840814—21no—
17#16840813—21no—
18#16840813—21no—
19#16840813C2211yescharacteristic
20#16840813C2211yescharacteristic
21#16840813C2211yescharacteristic
22#16840812C2211yescharacteristic
23#16840811—21no—
24#16840811C2211yescharacteristic
25Q8×#92420C2211yescharacteristic
26Q8×#92420C2211yescharacteristic
27Q8×#92420C2211yescharacteristic
28#16840786—21no—
29#16840786—21no—
30#16840783—21no—
31#16840783C2211yescharacteristic
32#16840779—21no—
33#16840779C2211yescharacteristic
34#16840778C2211yescharacteristic
35#16840778C2211yescharacteristic
36#16840626C2211yescharacteristic
37#16840625C2211yescharacteristic
38#16840624C2211yescharacteristic
39#16840623C2211yescharacteristic
40#16840612C2211yescharacteristic
41#16840612C2211yescharacteristic
42Q8⋊#92420C2211yescharacteristic
43Q8⋊#92420C2211yescharacteristic
44Q8⋊#92420C2211yescharacteristic
45Q8⋊#92420C2211yescharacteristic
46Q8⋊#92420C2211yescharacteristic
47Q8⋊#92420C2211yescharacteristic
48#92420⋊C8C2211yescharacteristic
49#92420⋊C8C2211yescharacteristic
50#16840603C2211yescharacteristic
51C8×#92420C2211yescharacteristic
52#16840314C2211yescharacteristic
53C2×Q8×Dic61C2211yescharacteristic
54#16840098C411yescharacteristic
55#16840095C411yescharacteristic
56#16840055C411yescharacteristic
57#16840055C411yescharacteristic
58#16839970C411yescharacteristic
59#16839970C411yescharacteristic
60#16839918C411yescharacteristic
61Q16×Dic61C2211yescharacteristic
62Q16×Dic61C2211yescharacteristic
63#16839854C2211yescharacteristic
64#16839854C2211yescharacteristic
65#16839812C2211yescharacteristic
66C61×#451C411yescharacteristic
67#14519844—21no—
68#14519844—21no—
69#14519844—21no—
70#14519844—21no—
71#14519844D411yescharacteristic
72#14519844D411yescharacteristic
73C4⋊#92420—21no—
74C4⋊#92420—21no—
75C4⋊#92420—21no—
76C4⋊#92420—21no—
77C4⋊#92420—21no—
78C4⋊#92420C2311yescharacteristic
79C4⋊#92420C2311yescharacteristic
80C4⋊#92420C2311yescharacteristic
81C4⋊#92420C2311yescharacteristic
82C22⋊#92420—21no—
83C22⋊#92420—21no—
84C22⋊#92420—21no—
85C22⋊#92420D411yescharacteristic
86C22⋊#92420D411yescharacteristic
87#14519832—21no—
88#14519832—21no—
89#14519832—21no—
90#14519832—21no—
91#14519832—21no—
92C4×#92420—21no—
93C4×#92420—21no—
94C4×#92420—21no—
95C4×#92420—21no—
96C4×#92420—21no—
97C4×#92420C2311yescharacteristic
98C4×#92420C2311yescharacteristic
99C4×#92420C2311yescharacteristic
100C4×#92420C2311yescharacteristic
101C2×#11758202C2×C411yescharacteristic
102C2×#11758202C2×C411yescharacteristic
103#14519776C2×C411yescharacteristic
104#14519775C2×C411yescharacteristic
105#14519767—21no—
106#14519756C2×C411yescharacteristic
107#14519754—21no—
108Q8×Dic61—21no—
109Q8×Dic61—21no—
110Q8×Dic61C2×C411yescharacteristic
111Q8×Dic61C2×C411yescharacteristic
112Q8×Dic61C2311yescharacteristic
113Q8×Dic61C2311yescharacteristic
114Q8×Dic61C2311yescharacteristic
115#14519742—21no—
116#14519742C2311yescharacteristic
117#14519733—21no—
118C2×C4⋊Dic61—21no—
119C2×C4⋊Dic61C2×C411yescharacteristic
120C2×C4×Dic61—21no—
121C2×C4×Dic61C2311yescharacteristic
122#14519711C2×C411yescharacteristic
123#14519711C2×C411yescharacteristic
124#14519710C2×C411yescharacteristic
125#14519710C2×C411yescharacteristic
126#14519706C2×C411yescharacteristic
127#14519706C2×C411yescharacteristic
128#14519702C2×C411yescharacteristic
129#14519702C2×C411yescharacteristic
130#14519701C2×C411yescharacteristic
131#14519701C2×C411yescharacteristic
132#14519701C2×C411yescharacteristic
133#14519701C2×C411yescharacteristic
134C22⋊#92418C2×C411yescharacteristic
135C8×Dic61C2311yescharacteristic
136C8×Dic61C2311yescharacteristic
137C22×Q8×C61C2×C411yescharacteristic
138C2×Q16×C61C2×C411yescharacteristic
139C2×Q16×C61C2×C411yescharacteristic
140C22⋊Q8×C61C2×C411yescharacteristic
141#103×C61C2×C411yescharacteristic
142#103×C61C2×C411yescharacteristic
143C22⋊C8×C61C2×C411yescharacteristic
144C2×Q8×C61—21no—
145C2×Q8×C61—22no—
146C2×Q8×C61—41no—
147C2×Q8×C61C22×C411yescharacteristic
148C2×Q8×C61C22×C411yescharacteristic
149C2×Q8×C61C22×C411yescharacteristic
150C22×C4×C61—21no—
151C22×C4×C61C22×C411yescharacteristic
152C22×Dic61—21no—
153C22×Dic61C2×D411yescharacteristic
154C22×Dic61#4111yescharacteristic
155C2×Dic122—21no—
156C2×Dic122C22×C411yescharacteristic
157C2×#92420—21no—
158C2×#92420—21no—
159C2×#92420—21no—
160C2×#92420—21no—
161C2×#92420—21no—
162C2×#92420—21no—
163C2×#92420C2×D411yescharacteristic
164C2×#92420C2×D411yescharacteristic
165C2×#92420C2×D411yescharacteristic
166C2×#92420C2×D411yescharacteristic
167Q16×C61—22no—
168Q16×C61—41no—
169C2×C8×C61C22×C411yescharacteristic
170C2×C8×C61C22×C411yescharacteristic
171C4⋊C4×C61—21no—
172C4⋊C4×C61C22×C411yescharacteristic
173C22⋊C4×C61—21no—
174C22⋊Dic61—21no—
175#11758202—22no—
176#11758202—41no—
177C4⋊Dic61—21no—
178C4⋊Dic61—21no—
179C4⋊Dic61—21no—
180C4⋊Dic61—21no—
181C4⋊Dic61—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61C22×C411yescharacteristic
184C4⋊Dic61C22×C411yescharacteristic
185C4⋊Dic61C22×C411yescharacteristic
186#11758196—21no—
187#11758196—21no—
188#11758196—21no—
189#11758196—21no—
190#11758196—21no—
191C4×Dic61—21no—
192C4×Dic61—21no—
193C4×Dic61—21no—
194C4×Dic61—21no—
195C4×Dic61—21no—
196C4×Dic61—21no—
197C4×Dic61C22×C411yescharacteristic
198C4×Dic61C2×D411yescharacteristic
199C4×Dic61#4111yescharacteristic
200C4×Dic61C2411yescharacteristic
201C2×#92418C22×C411yescharacteristic
202C2×#92418C22×C411yescharacteristic
203C23×C61C4×D411yescharacteristic
204Q8×C61—21no—
205Q8×C61—21no—
206Q8×C61—21no—
207Q8×C61—21no—
208Q8×C61—21no—
209Q8×C61—42no—
210Q8×C61#13112yes—
211C2×C4×C61—21no—
212C2×C4×C61—21no—
213C2×C4×C61—21no—
214C2×C4×C61—21no—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—42no—
218C2×C4×C61C4×D411yescharacteristic
219C2×C4×C61C23×C411yescharacteristic
220C2×Dic61—21no—
221C2×Dic61—21no—
222C2×Dic61—21no—
223C2×Dic61—21no—
224C2×Dic61—21no—
225C2×Dic61—21no—
226C2×Dic61—41no—
227C2×Dic61—42no—
228C2×Dic61C4×D411yescharacteristic
229C2×Dic61C4×D411yescharacteristic
230C2×Dic61C22×D411yescharacteristic
231C2×Dic61C2×#4111yescharacteristic
232Dic122—21no—
233Dic122—21no—
234Dic122—42no—
235#92420—21no—
236#92420—21no—
237#92420—21no—
238#92420—21no—
239#92420—41no—
240#92420—41no—
241#92420—41no—
242#92420—41no—
243#92420—41no—
244#92420—41no—
245C8×C61—21no—
246C8×C61—21no—
247#92418—21no—
248#92418—21no—
249#18032—611nomaximal, Sylow
250C22×C61—21no—
251C22×C61—21no—
252C22×C61—21no—
253C22×C61C2×C4×D411yescharacteristic
254C4×C61—21no—
255C4×C61—22no—
256C4×C61—41no—
257C4×C61—41no—
258C4×C61—41no—
259C4×C61C2×#13111yescharacteristic
260C4×C61#56811yescharacteristic
261Dic61—21no—
262Dic61—21no—
263Dic61—21no—
264Dic61—41no—
265Dic61—41no—
266Dic61—41no—
267Dic61—41no—
268Dic61#57811yescharacteristic
269Dic61#57811yescharacteristic
270#3104—611no—
271#2986—611no—
272#2984—611no—
273#1593—611no—
274#1591—611no—
275#1587—611no—
276#1587—611no—
277#1584—611no—
278#1584—611no—
279#1579—611no—
280C8×Q16—611no—
281#1572—611no—
282#1497—611no—
283#1479—611no—
284#1454—611no—
285C2×C61—41no—
286C2×C61#293311yescharacteristic
287C2×C61#295011yescharacteristic
288C2×C61#295511yescharacteristic
289#533—611no—
290C2×C4×Q8—611no—
291#484—611no—
292#484—611no—
293#477—611no—
294#477—611no—
295#462—611no—
296#462—611no—
297#451—611no—
298#451#692311yescharacteristic
299#446—611no—
300#446—611no—
301#446—611no—
302#446—611no—
303#446—1221no—
304#446—1221no—
305#446—1221no—
306C8×Q8—611no—
307C8×Q8—611no—
308C8×Q8—611no—
309C8×Q8—611no—
310C8×Q8—1221no—
311C4×Q16—611no—
312C4×Q16—611no—
313C4×Q16—611no—
314C4×Q16—611no—
315#433—1221no—
316#433—1221no—
317#432—611no—
318#432—1221no—
319#431—611no—
320#431—611no—
321#431—611no—
322#431—611no—
323#431—1221no—
324#335—611no—
325#335—611no—
326#334—611no—
327#334—611no—
328Q8⋊C8—611no—
329Q8⋊C8—611no—
330Q8⋊C8—611no—
331Q8⋊C8—611no—
332Q8⋊C8—611no—
333Q8⋊C8—611no—
334Q8⋊C8—611no—
335Q8⋊C8—611no—
336#322—611no—
337#322—611no—
338#322—611no—
339C82—611no—
340C61#1803211yescharacteristic, complemented, Sylow
341C22×Q8C2×#692311yescharacteristic
342C2×Q16—611no—
343C2×Q16—611no—
344C2×Q16C2×#692311yescharacteristic
345C2×Q16C2×#692311yescharacteristic
346C4⋊Q8—611no—
347C4⋊Q8—611no—
348#125—1221no—
349C22⋊Q8—611no—
350C22⋊Q8—1221no—
351C22⋊Q8C2×#692311yescharacteristic
352C4×Q8—611no—
353C4×Q8—611no—
354C4×Q8—611no—
355C4×Q8—611no—
356C4×Q8—611no—
357C4×Q8—611no—
358C4×Q8—1221no—
359C4×Q8—1221no—
360C4×Q8—1221no—
361#117—1221no—
362C2×C4⋊C4—611no—
363C2×C4⋊C4—1221no—
364C2×C42—611no—
365C2×C42—1221no—
366#107—611no—
367#107—611no—
368#107—611no—
369#107—611no—
370C4⋊C8—611no—
371C4⋊C8—611no—
372C4⋊C8—611no—
373C4⋊C8—611no—
374C4⋊C8—611no—
375C4⋊C8—611no—
376C4⋊C8—611no—
377C4⋊C8—611no—
378C4⋊C8—1221no—
379C4⋊C8—1221no—
380C4⋊C8—1221no—
381C4⋊C8—1221no—
382C4⋊C8—1221no—
383C4⋊C8—1221no—
384C4⋊C8—1221no—
385C4⋊C8—1221no—
386C4⋊C8—1221no—
387#103—611no—
388#103—611no—
389#103—611no—
390#103—611no—
391#103—611no—
392#103—611no—
393#103C2×#692311yescharacteristic
394#103C2×#692311yescharacteristic
395C22⋊C8—611no—
396C22⋊C8—611no—
397C22⋊C8—611no—
398C22⋊C8—1221no—
399C22⋊C8—1221no—
400C22⋊C8—1221no—
401C22⋊C8C2×#692311yescharacteristic
402#97—1221no—
403#97—1221no—
404#97—1221no—
405#97—1221no—
406#97—1221no—
407C4×C8—611no—
408C4×C8—611no—
409C4×C8—611no—
410C4×C8—611no—
411C4×C8—611no—
412C4×C8—611no—
413C4×C8—1221no—
414C4×C8—1221no—
415C4×C8—1221no—
416C4×C8—1221no—
417C4×C8—1221no—
418C2×Q8—21no—
419C2×Q8—22no—
420C2×Q8—41no—
421C2×Q8—611no—
422C2×Q8—1221no—
423C2×Q8C22×#692311yescharacteristic
424C2×Q8C22×#692311yescharacteristic
425C2×Q8C22×#692311yescharacteristic
426C22×C4—21no—
427C22×C4—611no—
428C22×C4—611no—
429C22×C4—1221no—
430C22×C4C22×#692311yescharacteristic
431Q16—22no—
432Q16—41no—
433Q16—1222no—
434Q16—2441no—
435C2×C8—611no—
436C2×C8—611no—
437C2×C8—611no—
438C2×C8—611no—
439C2×C8—611no—
440C2×C8—611no—
441C2×C8—1221no—
442C2×C8—1221no—
443C2×C8—1221no—
444C2×C8—1221no—
445C2×C8—1221no—
446C2×C8—1221no—
447C2×C8C22×#692311yescharacteristic
448C2×C8C22×#692311yescharacteristic
449C4⋊C4—21no—
450C4⋊C4—611no—
451C4⋊C4—611no—
452C4⋊C4—611no—
453C4⋊C4—1221no—
454C4⋊C4—1221no—
455C4⋊C4—1221no—
456C4⋊C4—1221no—
457C4⋊C4—1221no—
458C4⋊C4—1221no—
459C4⋊C4—1221no—
460C4⋊C4—1221no—
461C4⋊C4—1221no—
462C4⋊C4—1221no—
463C4⋊C4—1221no—
464C4⋊C4C22×#692311yescharacteristic
465C22⋊C4—21no—
466C22⋊C4—1221no—
467C42—611no—
468C42—611no—
469C42—611no—
470C42—611no—
471C42—1221no—
472C42—1221no—
473C42—1221no—
474C42—1221no—
475C42—1221no—
476C42—1221no—
477C23D4×#692311yescharacteristic
478Q8—21no—
479Q8—21no—
480Q8—21no—
481Q8—21no—
482Q8—21no—
483Q8—42no—
484Q8—1221no—
485Q8—1221no—
486Q8—2442no—
487Q8#1451986412yes—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—42no—
495C2×C4—611no—
496C2×C4—611no—
497C2×C4—611no—
498C2×C4—611no—
499C2×C4—1221no—
500C2×C4—1221no—
501C2×C4—1221no—
502C2×C4—1221no—
503C2×C4—1221no—
504C2×C4—1221no—
505C2×C4—2441no—
506C2×C4—2442no—
507C2×C4D4×#692311yescharacteristic
508C2×C4C23×#692311yescharacteristic
509C8—21no—
510C8—21no—
511C8—1221no—
512C8—1221no—
513C8—1221no—
514C8—1221no—
515C8—1221no—
516C8—1221no—
517C8—2441no—
518C8—2441no—
519C8—2441no—
520C8—2441no—
521C8—2441no—
522C8—2441no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22C2×D4×#692311yescharacteristic
527C4—21no—
528C4—22no—
529C4—41no—
530C4—41no—
531C4—41no—
532C4—611no—
533C4—611no—
534C4—1221no—
535C4—1221no—
536C4—1221no—
537C4—2441no—
538C4—2441no—
539C4—2441no—
540C4—2441no—
541C4C2×#1451986411yescharacteristic
542C4#1684084011yescharacteristic
543C2—41no—
544C2#2146255111yescharacteristic
545C2#2146258011yescharacteristic
546C2#2146259211yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#451C4
socleC22×C61C2×C4×D4
prime radicalC23×C61C4×D4
cosocleC4×Dic61C24
hypercenter#451#6923
hypocenterC61#18032
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
3. #21461464C2semidirect
4. #21461459C2semidirect
5. #21461445C2semidirect
6. #21461444C2semidirect
7. #21461432C2semidirect
8. #21461430C2semidirect
9. #21461412C2semidirect
10. #21461406C2semidirect
340. C61#18032semidirect

Maximal subgroups

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

subgroupindex
#214627282
#214627222
#214614642
#214614592
#214614452
#214614442
#214614322
#214614302
#214614122
#214614062
#214613902
#214611812
#214611212
#214610402
#214558532
#1803261