Finite Group Databasebeta

← #16831398

Subgroups — #16831398

Order 3712.

398 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271865C211yesmaximal, characteristic, complemented
2#14271824C211yesmaximal, characteristic, complemented
3#14271519C211yesmaximal, characteristic, complemented
4#14271502C211yesmaximal, characteristic, complemented
5#14271482C211yesmaximal, characteristic, complemented
6#14271468C211yesmaximal, characteristic, complemented
7#14271397C211yesmaximal, characteristic, complemented
8#14271389C211yesmaximal, characteristic, complemented
9#14271380C211yesmaximal, characteristic, complemented
10#14271307C211yesmaximal, characteristic, complemented
11SD16×Dic29C211yesmaximal, characteristic, complemented
12#14271226C211yesmaximal, characteristic, complemented
13#14271158C211yesmaximal, characteristic, complemented
14C2×#11745183C211yesmaximal, characteristic, complemented
15C29×#448C211yesmaximal, characteristic, complemented
16C22×Q8×C29C2211yescharacteristic
17C2×#90809C2211yescharacteristic
18C2×SD16×C29C2211yescharacteristic
19C2×SD16×C29C2211yescharacteristic
20C29×#121C2211yescharacteristic
21#11745309—21no—
22#11745309C2211yescharacteristic
23#11745308—21no—
24#11745308C2211yescharacteristic
25Q8×Dic29C2211yescharacteristic
26#11745301—21no—
27#11745300C2211yescharacteristic
28D4×Dic29—21no—
29D4×Dic29C2211yescharacteristic
30C2×#90782C2211yescharacteristic
31#11745292—21no—
32#11745292C2211yescharacteristic
33C4×C22⋊D29—21no—
34C4×C22⋊D29C2211yescharacteristic
35C2×C4⋊Dic29C2211yescharacteristic
36C22×#6597C2211yescharacteristic
37C2×C8×D29C2211yescharacteristic
38#11745254C2211yescharacteristic
39#11745252C2211yescharacteristic
40#11745248—21no—
41#11745241—21no—
42C29×#103C2211yescharacteristic
43C29×#103C2211yescharacteristic
44C29×C22⋊C8C2211yescharacteristic
45#11745183C2211yescharacteristic
46#11745183C2211yescharacteristic
47#11745183C2211yescharacteristic
48#11745183C2211yescharacteristic
49#11745180C2211yescharacteristic
50#11745169C2211yescharacteristic
51#11745169C2211yescharacteristic
52#11745168C2211yescharacteristic
53#11745165C2211yescharacteristic
54#11745165C2211yescharacteristic
55#11745162C2211yescharacteristic
56C8×Dic29C2211yescharacteristic
57#11745157C2211yescharacteristic
58#11745155C2211yescharacteristic
59C2×Q8×C29—21no—
60C2×Q8×C29—22no—
61C2×Q8×C29—41no—
62C2×Q8×C29C2311yescharacteristic
63C2×Q8×C29C2311yescharacteristic
64C2×D4×C29—21no—
65C2×D4×C29C2311yescharacteristic
66C22×C4×C29—21no—
67C22×C4×C29C2311yescharacteristic
68C2×C22⋊D29—21no—
69C2×C22⋊D29—21no—
70C2×C22⋊D29D411yescharacteristic
71C22×Dic29—21no—
72C22×Dic29—21no—
73#90809—22no—
74#90809—41no—
75C2×D116—21no—
76C2×D116C2311yescharacteristic
77C2×C4×D29—21no—
78C2×C4×D29C2311yescharacteristic
79SD16×C29—22no—
80SD16×C29—41no—
81C2×C8×C29C2311yescharacteristic
82C2×C8×C29C2311yescharacteristic
83C4⋊C4×C29C2311yescharacteristic
84C22⋊C4×C29—21no—
85C22⋊Dic29—21no—
86C22⋊Dic29—21no—
87C22⋊Dic29D411yescharacteristic
88#90782—41no—
89#90781—21no—
90#90781—21no—
91#90781—21no—
92#90781—21no—
93#90781—21no—
94#90781D411yescharacteristic
95C4⋊Dic29—21no—
96C4⋊Dic29—21no—
97C4⋊Dic29—21no—
98C4⋊Dic29C2311yescharacteristic
99C4⋊Dic29C2311yescharacteristic
100C4⋊Dic29C2311yescharacteristic
101#90779—21no—
102#90779—21no—
103#90779D411yescharacteristic
104C4×Dic29—21no—
105C4×Dic29—21no—
106C4×Dic29C2311yescharacteristic
107C2×#6597—41no—
108C2×#6597C2311yescharacteristic
109C2×#6597C2311yescharacteristic
110C8×D29—41no—
111C23×C29—21no—
112C23×C29C2×D411yescharacteristic
113C22×D29—21no—
114C22×D29C2×D411yescharacteristic
115Q8×C29—21no—
116Q8×C29—21no—
117Q8×C29—21no—
118Q8×C29—42no—
119Q8×C29#4112yes—
120D4×C29—21no—
121D4×C29—21no—
122D4×C29—42no—
123C2×C4×C29—21no—
124C2×C4×C29—21no—
125C2×C4×C29—21no—
126C2×C4×C29—21no—
127C2×C4×C29—21no—
128C2×C4×C29—42no—
129C2×C4×C29C2×D411yescharacteristic
130C2×C4×C29C2411yescharacteristic
131C22⋊D29—22no—
132C22⋊D29—42no—
133C22⋊D29—81no—
134C2×Dic29—21no—
135C2×Dic29—21no—
136C2×Dic29—21no—
137C2×Dic29—81no—
138C2×Dic29—81no—
139C2×Dic29C2×D411yescharacteristic
140C2×Dic29C2×D411yescharacteristic
141C2×Dic29C2×D411yescharacteristic
142D116—21no—
143D116—21no—
144D116—42no—
145C4×D29—21no—
146C4×D29—21no—
147C4×D29—42no—
148C8×C29—21no—
149C8×C29—21no—
150#6597—21no—
151#6597—21no—
152#3301—291nomaximal, Sylow
153C22×C29—21no—
154C22×C29—21no—
155C22×C29—41no—
156C22×C29—41no—
157C22×C29—41no—
158C22×C29#13512yes—
159C22×C29C22×D411yescharacteristic
160C2×D29—21no—
161C2×D29—21no—
162C2×D29—21no—
163C2×D29—41no—
164C2×D29—41no—
165C2×D29—41no—
166C4×C29—22no—
167C4×C29—21no—
168C4×C29—41no—
169C4×C29—41no—
170C4×C29C2×#4111yescharacteristic
171C4×C29H(5,𝔽2)11yescharacteristic
172Dic29—21no—
173Dic29—21no—
174Dic29—21no—
175Dic29—41no—
176Dic29—41no—
177Dic29—41no—
178#553—291no—
179#548—291no—
180#488—291no—
181#485—291no—
182#481—291no—
183#479—291no—
184#466—291no—
185#465—291no—
186#463—291no—
187#449—291no—
188#448D2911yescharacteristic, complemented
189C4×SD16—291no—
190C8×D4—291no—
191#416—291no—
192C2×#103—291no—
193C2×C29—22no—
194C2×C29—81no—
195C2×C29#54611yescharacteristic
196C2×C29C2×#13511yescharacteristic
197C2×C29#57711yescharacteristic
198D29—41no—
199D29—81no—
200C2×#41—291no—
201C22×Q8C2×D2911yescharacteristic
202C2×SD16C2×D2911yescharacteristic
203C2×SD16C2×D2911yescharacteristic
204C2×D8—291no—
205C22×C8—291no—
206C22×C8—291no—
207#126—581no—
208#125—291no—
209#124—291no—
210#124—581no—
211#123—581no—
212C22⋊Q8—291no—
213C22⋊Q8—581no—
214#121—291no—
215#121—291no—
216#121—581no—
217#121—581no—
218#121C2×D2911yescharacteristic
219C4×Q8—291no—
220C4×D4—291no—
221C4×D4—291no—
222C4×D4—581no—
223C4×D4—581no—
224#117—291no—
225C2×C4⋊C4—291no—
226#107—291no—
227#106—291no—
228#106—291no—
229C4⋊C8—291no—
230#103—291no—
231#103—291no—
232#103—291no—
233#103—291no—
234#103C2×D2911yescharacteristic
235#103C2×D2911yescharacteristic
236#102—291no—
237#102—291no—
238#102—291no—
239#102—291no—
240C22⋊C8—291no—
241C22⋊C8C2×D2911yescharacteristic
242C4×C8—291no—
243C29#330111yescharacteristic, complemented, Sylow
244#41—582no—
245#41—1161no—
246C2×Q8—21no—
247C2×Q8—22no—
248C2×Q8—41no—
249C2×Q8C22×D2911yescharacteristic
250C2×Q8C22×D2911yescharacteristic
251C2×D4—21no—
252C2×D4—291no—
253C2×D4—291no—
254C2×D4—581no—
255C2×D4—581no—
256C2×D4—581no—
257C2×D4C22×D2911yescharacteristic
258C22×C4—21no—
259C22×C4—291no—
260C22×C4—581no—
261C22×C4—581no—
262C22×C4—581no—
263C22×C4C22×D2911yescharacteristic
264SD16—22no—
265SD16—41no—
266D8—1161no—
267C2×C8—291no—
268C2×C8—291no—
269C2×C8—1161no—
270C2×C8—1161no—
271C2×C8C22×D2911yescharacteristic
272C2×C8C22×D2911yescharacteristic
273C4⋊C4—291no—
274C4⋊C4—291no—
275C4⋊C4—291no—
276C4⋊C4—291no—
277C4⋊C4—581no—
278C4⋊C4—581no—
279C4⋊C4—581no—
280C4⋊C4—581no—
281C4⋊C4—581no—
282C4⋊C4C22×D2911yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—291no—
285C22⋊C4—291no—
286C22⋊C4—581no—
287C22⋊C4—581no—
288C22⋊C4—581no—
289C22⋊C4—581no—
290C22⋊C4—581no—
291C22⋊C4—581no—
292C22⋊C4—581no—
293C42—291no—
294C42—581no—
295C42—581no—
296C23—21no—
297C23—291no—
298C23—581no—
299C23D4×D2911yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—21no—
303Q8—42no—
304Q8#9080712yes—
305D4—21no—
306D4—21no—
307D4—42no—
308D4—582no—
309D4—581no—
310D4—581no—
311D4—1162no—
312D4—1162no—
313D4—2321no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—42no—
320C2×C4—291no—
321C2×C4—291no—
322C2×C4—291no—
323C2×C4—581no—
324C2×C4—581no—
325C2×C4—581no—
326C2×C4—581no—
327C2×C4—581no—
328C2×C4—1162no—
329C2×C4—2321no—
330C2×C4—2321no—
331C2×C4D4×D2911yescharacteristic
332C2×C4C23×D2911yescharacteristic
333C8—21no—
334C8—21no—
335C8—581no—
336C8—581no—
337C22—21no—
338C22—21no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—581no—
343C22—581no—
344C22—581no—
345C22—1161no—
346C22—1161no—
347C22—1161no—
348C22#1174527812yes—
349C22C2×D4×D2911yescharacteristic
350C4—21no—
351C4—22no—
352C4—41no—
353C4—41no—
354C4—581no—
355C4—581no—
356C4—581no—
357C4—1161no—
358C4—1161no—
359C4—1161no—
360C4C2×#9080711yescharacteristic
361C4#1174535911yescharacteristic
362C2—22no—
363C2—81no—
364C2—1161no—
365C2—2321no—
366C2#1427180011yescharacteristic
367C2C2×#1174527811yescharacteristic
368C2#1427197211yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#448C2
socleC22×C29C22×D4
hypercenter#448D29
hypocenterC29#3301
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
1. #14271865C2semidirect
2. #14271824C2semidirect
3. #14271519C2semidirect
4. #14271502C2semidirect
5. #14271482C2semidirect
6. #14271468C2semidirect
7. #14271397C2semidirect
8. #14271389C2semidirect
9. #14271380C2semidirect
10. #14271307C2semidirect
11. SD16×Dic29C2semidirect
12. #14271226C2semidirect
13. #14271158C2semidirect
14. C2×#11745183C2semidirect
15. C29×#448C2semidirect
188. #448D29semidirect
243. C29#3301semidirect

Maximal subgroups

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

subgroupindex
#142718652
#142718242
#142715192
#142715022
#142714822
#142714682
#142713972
#142713892
#142713802
#142713072
SD16×Dic292
#142712262
#142711582
C2×#117451832
C29×#4482
#330129