Finite Group Databasebeta

← #16829729

Subgroups — #16829729

Order 3712.

418 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271766C211yesmaximal, characteristic, complemented
2#14271638C211yesmaximal, characteristic, complemented
3#14271488C211yesmaximal, characteristic, complemented
4#14271484C211yesmaximal, characteristic, complemented
5#14271465C211yesmaximal, characteristic, complemented
6#14271461C211yesmaximal, characteristic, complemented
7#14271356C211yesmaximal, characteristic, complemented
8#14271356C211yesmaximal, characteristic, complemented
9#14271297C211yesmaximal, characteristic, complemented
10#14271275C211yesmaximal, characteristic, complemented
11#14271272C211yesmaximal, characteristic, complemented
12D8×Dic29C211yesmaximal, characteristic, complemented
13#14271243C211yesmaximal, characteristic, complemented
14#14271221C211yesmaximal, characteristic, complemented
15C29×#447C211yesmaximal, characteristic, complemented
16C22×D4×C29C2211yescharacteristic
17C2×D8×C29C2211yescharacteristic
18C2×D8×C29C2211yescharacteristic
19C29×#121C2211yescharacteristic
20C2×C22⋊Dic29—21no—
21C2×C22⋊Dic29—21no—
22#11745302C2211yescharacteristic, complemented
23#11745301—21no—
24#11745300—21no—
25D4×Dic29—21no—
26D4×Dic29—21no—
27D4×Dic29C2211yescharacteristic
28D4×Dic29C2211yescharacteristic
29D4×Dic29C2211yescharacteristic
30D4×Dic29C2211yescharacteristic
31D4×Dic29C2211yescharacteristic, complemented
32C2×#90782C2211yescharacteristic
33C2×#90782C2211yescharacteristic
34#11745292C2211yescharacteristic
35#11745288C2211yescharacteristic
36#11745288C2211yescharacteristic
37#11745255C2211yescharacteristic, complemented
38#11745252C2211yescharacteristic, complemented
39#11745248—21no—
40#11745245—21no—
41C29×#102C2211yescharacteristic
42C29×#102C2211yescharacteristic
43C29×C22⋊C8C2211yescharacteristic
44#11745180C2211yescharacteristic
45#11745180C2211yescharacteristic
46#11745180C2211yescharacteristic, complemented
47#11745180C2211yescharacteristic, complemented
48C22⋊#6597C2211yescharacteristic
49#11745169C2211yescharacteristic, complemented
50#11745169C2211yescharacteristic, complemented
51#11745166C2211yescharacteristic, complemented
52#11745165C2211yescharacteristic, complemented
53#11745163C2211yescharacteristic, complemented
54#11745162C2211yescharacteristic, complemented
55#11745162C2211yescharacteristic, complemented
56C8×Dic29C2211yescharacteristic, complemented
57#11745156C2211yescharacteristic, complemented
58#11745155C2211yescharacteristic, complemented
59C24×C29—21no—
60C2×D4×C29—22no—
61C2×D4×C29—22no—
62C2×D4×C29—21no—
63C2×D4×C29—21no—
64C2×D4×C29C2311yescharacteristic
65C2×D4×C29C2311yescharacteristic
66C2×D4×C29C2311yescharacteristic
67C22×C4×C29C2311yescharacteristic
68C2×C22⋊D29—21no—
69C2×C22⋊D29—21no—
70C2×C22⋊D29—21no—
71C22×Dic29—21no—
72C22×Dic29—21no—
73C22×Dic29—21no—
74C22×Dic29—21no—
75C22×Dic29—21no—
76C2×D116C2311yescharacteristic
77C2×C4×D29—21no—
78D8×C29—22no—
79D8×C29—22no—
80C2×C8×C29C2311yescharacteristic
81C2×C8×C29C2311yescharacteristic
82C4⋊C4×C29C2311yescharacteristic
83C22⋊C4×C29—21no—
84C22⋊Dic29—21no—
85C22⋊Dic29—21no—
86C22⋊Dic29—21no—
87C22⋊Dic29—21no—
88C22⋊Dic29—21no—
89C22⋊Dic29—21no—
90C22⋊Dic29D411yescharacteristic
91C22⋊Dic29D411yescharacteristic
92#90782—22no—
93#90782—22no—
94#90781—21no—
95#90781—21no—
96C4⋊Dic29—21no—
97C4⋊Dic29D411yescharacteristic
98C4⋊Dic29D411yescharacteristic
99C4⋊Dic29C2311yescharacteristic
100C4⋊Dic29C2311yescharacteristic
101C4⋊Dic29C2311yescharacteristic
102#90779—21no—
103C4×Dic29—21no—
104C4×Dic29C2311yescharacteristic
105C4×Dic29C2311yescharacteristic
106C2×#6597C2311yescharacteristic
107C2×#6597C2311yescharacteristic
108C23×C29—24no—
109C23×C29—21no—
110C23×C29—21no—
111C23×C29—21no—
112C23×C29—81no—
113C23×C29—81no—
114C23×C29C2×D411yescharacteristic
115C22×D29—21no—
116D4×C29—24no—
117D4×C29—21no—
118D4×C29—21no—
119D4×C29—21no—
120D4×C29—21no—
121D4×C29—81no—
122D4×C29#4112yes—
123D4×C29#4112yes—
124C2×C4×C29—21no—
125C2×C4×C29—21no—
126C2×C4×C29—21no—
127C2×C4×C29C2×D411yescharacteristic
128C2×C4×C29C2411yescharacteristic
129C22⋊D29—81no—
130C22⋊D29—81no—
131C22⋊D29—81no—
132C2×Dic29—21no—
133C2×Dic29—21no—
134C2×Dic29—21no—
135C2×Dic29—81no—
136C2×Dic29—81no—
137C2×Dic29—81no—
138C2×Dic29—81no—
139C2×Dic29—81no—
140C2×Dic29C2×D411yescharacteristic
141C2×Dic29C2×D411yescharacteristic
142C2×Dic29C2×D411yescharacteristic
143C2×Dic29C2×D411yescharacteristic
144D116—21no—
145D116—21no—
146C4×D29—81no—
147C8×C29—21no—
148C8×C29—21no—
149#6597—21no—
150#6597—21no—
151#3122—291nomaximal, Sylow
152C22×C29—21no—
153C22×C29—22no—
154C22×C29—22no—
155C22×C29—21no—
156C22×C29—21no—
157C22×C29—41no—
158C22×C29—41no—
159C22×C29—41no—
160C22×C29—41no—
161C22×C29—41no—
162C22×C29—41no—
163C22×C29—41no—
164C22×C29—84no—
165C22×C29C22×D411yescharacteristic
166C2×D29—41no—
167C2×D29—41no—
168C2×D29—41no—
169C4×C29—21no—
170C4×C29—41no—
171C4×C29C2×#4111yescharacteristic
172C4×C29C2×#4111yescharacteristic
173Dic29—21no—
174Dic29—21no—
175Dic29—21no—
176Dic29—21no—
177Dic29—41no—
178Dic29—41no—
179Dic29—41no—
180#540—291no—
181#518—291no—
182#482—291no—
183#482—291no—
184#478—291no—
185#478—291no—
186#459—291no—
187#459—291no—
188#447—291no—
189#447D2911yescharacteristic, complemented
190#442—291no—
191#442—291no—
192C4×D8—291no—
193C4×D8—291no—
194#433—291no—
195C2×C29—41no—
196C2×C29—42no—
197C2×C29—42no—
198C2×C29—81no—
199C2×C29#52511yescharacteristic
200C2×C29#57611yescharacteristic
201C2×C29#57611yescharacteristic
202D29—81no—
203C22×D4C2×D2911yescharacteristic
204C2×D8—291no—
205C2×D8—291no—
206C2×D8C2×D2911yescharacteristic
207C2×D8C2×D2911yescharacteristic
208#127—291no—
209#125—291no—
210#123—581no—
211#123—581no—
212#121—291no—
213#121—581no—
214#121—581no—
215#121C2×D2911yescharacteristic
216C4×D4—291no—
217C4×D4—291no—
218C4×D4—291no—
219C4×D4—291no—
220C4×D4—291no—
221C4×D4—291no—
222C4×D4—581no—
223C4×D4—581no—
224#117—291no—
225#117—291no—
226C2×C22⋊C4—581no—
227C2×C22⋊C4—581no—
228#107—291no—
229#107—291no—
230#106—291no—
231#106—291no—
232C4⋊C8—291no—
233C4⋊C8—291no—
234#102—291no—
235#102—291no—
236#102—291no—
237#102—291no—
238#102—291no—
239#102—291no—
240#102C2×D2911yescharacteristic
241#102C2×D2911yescharacteristic
242C22⋊C8—291no—
243C22⋊C8C2×D2911yescharacteristic
244#97—291no—
245C4×C8—291no—
246C29#312211yescharacteristic, complemented, Sylow
247C24—21no—
248C2×D4—22no—
249C2×D4—22no—
250C2×D4—21no—
251C2×D4—21no—
252C2×D4—291no—
253C2×D4—581no—
254C2×D4—581no—
255C2×D4—581no—
256C2×D4C22×D2911yescharacteristic
257C2×D4C22×D2911yescharacteristic
258C2×D4C22×D2911yescharacteristic
259C22×C4—581no—
260C22×C4—581no—
261C22×C4—581no—
262C22×C4—581no—
263C22×C4—581no—
264C22×C4—581no—
265C22×C4C22×D2911yescharacteristic
266D8—22no—
267D8—22no—
268D8—582no—
269D8—582no—
270C2×C8—291no—
271C2×C8—291no—
272C2×C8C22×D2911yescharacteristic
273C2×C8C22×D2911yescharacteristic
274C4⋊C4—291no—
275C4⋊C4—291no—
276C4⋊C4—291no—
277C4⋊C4—291no—
278C4⋊C4—291no—
279C4⋊C4—581no—
280C4⋊C4—581no—
281C4⋊C4C22×D2911yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—291no—
284C22⋊C4—291no—
285C22⋊C4—581no—
286C22⋊C4—581no—
287C22⋊C4—581no—
288C22⋊C4—581no—
289C22⋊C4—581no—
290C22⋊C4—581no—
291C22⋊C4—581no—
292C22⋊C4—581no—
293C42—291no—
294C42—291no—
295C42—581no—
296C23—24no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—81no—
301C23—81no—
302C23—581no—
303C23D4×D2911yescharacteristic
304D4—24no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—21no—
309D4—81no—
310D4—581no—
311D4—581no—
312D4—2321no—
313D4—2321no—
314D4—2321no—
315D4#9080712yes—
316D4#9080712yes—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—291no—
321C2×C4—291no—
322C2×C4—291no—
323C2×C4—291no—
324C2×C4—581no—
325C2×C4—581no—
326C2×C4—581no—
327C2×C4—2321no—
328C2×C4—2321no—
329C2×C4—2321no—
330C2×C4—2321no—
331C2×C4—2321no—
332C2×C4—2321no—
333C2×C4D4×D2911yescharacteristic
334C2×C4C23×D2911yescharacteristic
335C8—21no—
336C8—21no—
337C8—581no—
338C8—581no—
339C22—21no—
340C22—22no—
341C22—22no—
342C22—21no—
343C22—21no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—84no—
352C22—1161no—
353C22—1161no—
354C22—1161no—
355C22C2×D4×D2911yescharacteristic
356C4—21no—
357C4—41no—
358C4—581no—
359C4—581no—
360C4—581no—
361C4—581no—
362C4—1161no—
363C4—1161no—
364C4—1161no—
365C4C2×#9080711yescharacteristic
366C4C2×#9080711yescharacteristic
367C2—41no—
368C2—42no—
369C2—42no—
370C2—81no—
371C2—2321no—
372C2#1427166911yescharacteristic
373C2#1427196411yescharacteristic
374C2#1427196711yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#447C2
socleC22×C29C22×D4
hypercenter#447D29
hypocenterC29#3122
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #14271766C2semidirect
2. #14271638C2semidirect
3. #14271488C2semidirect
4. #14271484C2semidirect
5. #14271465C2semidirect
6. #14271461C2semidirect
7. #14271356C2semidirect
8. #14271356C2semidirect
9. #14271297C2semidirect
10. #14271275C2semidirect
11. #14271272C2semidirect
12. D8×Dic29C2semidirect
13. #14271243C2semidirect
14. #14271221C2semidirect
15. C29×#447C2semidirect
22. #11745302C22semidirect
31. D4×Dic29C22semidirect
37. #11745255C22semidirect
38. #11745252C22semidirect
46. #11745180C22semidirect
47. #11745180C22semidirect
49. #11745169C22semidirect
50. #11745169C22semidirect
51. #11745166C22semidirect
52. #11745165C22semidirect
53. #11745163C22semidirect
54. #11745162C22semidirect
55. #11745162C22semidirect
56. C8×Dic29C22semidirect
57. #11745156C22semidirect
58. #11745155C22semidirect
189. #447D29semidirect
246. C29#3122semidirect

Maximal subgroups

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

subgroupindex
#142717662
#142716382
#142714882
#142714842
#142714652
#142714612
#142713562
#142712972
#142712752
#142712722
D8×Dic292
#142712432
#142712212
C29×#4472
#312229