Finite Group Databasebeta

← #16831498

Subgroups — #16831498

Order 3712.

404 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271859C211yesmaximal, characteristic, complemented
2#14271527C211yesmaximal, characteristic, complemented
3#14271484C211yesmaximal, characteristic, complemented
4#14271474C211yesmaximal, characteristic, complemented
5#14271470C211yesmaximal, characteristic, complemented
6#14271414C211yesmaximal, characteristic, complemented
7#14271397C211yesmaximal, characteristic, complemented
8#14271355C211yesmaximal, characteristic, complemented
9#14271308C211yesmaximal, characteristic, complemented
10#14271308C211yesmaximal, characteristic, complemented
11#14271261C211yesmaximal, characteristic, complemented
12#14271235C211yesmaximal, characteristic, complemented
13#14271164C211yesmaximal, characteristic, complemented
14#14271159C211yesmaximal, characteristic, complemented
15C29×#550C211yesmaximal, characteristic, complemented
16C2×#41×C29C2211yescharacteristic
17C2×#41×C29C2211yescharacteristic
18C29×#127—21no—
19C29×#127C2211yescharacteristic
20C29×#121—21no—
21C29×#121—21no—
22C29×#121C2211yescharacteristic
23C29×#121C2211yescharacteristic
24C4×Q8×C29C2211yescharacteristic
25C4×D4×C29—21no—
26C4×D4×C29C2211yescharacteristic
27C2×#90784C2211yescharacteristic
28#11745301—21no—
29C2×#90782C2211yescharacteristic
30C2×#90782C2211yescharacteristic
31#11745292C2211yescharacteristic
32#11745292C2211yescharacteristic
33#11745288C2211yescharacteristic
34C2×C4⋊Dic29C2211yescharacteristic
35C2×#90777C2211yescharacteristic
36C22×#6597C2211yescharacteristic
37#11745260—21no—
38#11745245—21no—
39#11745243—21no—
40C4×D116C2211yescharacteristic
41#11745232C2211yescharacteristic
42#11745183C2211yescharacteristic
43#11745183C2211yescharacteristic
44#11745183C2211yescharacteristic
45#11745180C2211yescharacteristic
46#11745180C2211yescharacteristic
47#11745180C2211yescharacteristic
48#11745180C2211yescharacteristic
49#11745180C2211yescharacteristic
50#11745180C2211yescharacteristic
51C22⋊#6597C2211yescharacteristic
52C22⋊#6597C2211yescharacteristic
53#11745157C2211yescharacteristic
54#11745156C2211yescharacteristic
55#11745155C2211yescharacteristic
56#11745155C2211yescharacteristic
57C4⋊#6597C2211yescharacteristic
58#11745151C2211yescharacteristic
59#41×C29—22no—
60#41×C29—22no—
61#41×C29—41no—
62#41×C29—41no—
63C2×Q8×C29C2311yescharacteristic
64C2×D4×C29—21no—
65C2×D4×C29—21no—
66C2×D4×C29—21no—
67C2×D4×C29—21no—
68C2×D4×C29—21no—
69C2×D4×C29—21no—
70C2×D4×C29D411yescharacteristic
71C2×D4×C29C2311yescharacteristic
72C2×D4×C29C2311yescharacteristic
73C22×C4×C29—21no—
74C22×C4×C29—21no—
75C22×C4×C29C2311yescharacteristic
76C22×C4×C29C2311yescharacteristic
77C2×C22⋊D29—21no—
78C2×C22⋊D29—21no—
79C22×Dic29—21no—
80C2×D116C2311yescharacteristic
81C2×C4×D29—21no—
82C4⋊C4×C29—21no—
83C4⋊C4×C29D411yescharacteristic
84C4⋊C4×C29C2311yescharacteristic
85C22⋊C4×C29—21no—
86C22⋊C4×C29—21no—
87C22⋊C4×C29D411yescharacteristic
88C22⋊C4×C29D411yescharacteristic
89C42×C29—21no—
90C42×C29C2311yescharacteristic
91C22⋊Dic29—21no—
92#90784—22no—
93#90782—41no—
94#90782—41no—
95#90781—21no—
96#90781—21no—
97#90781—21no—
98C4⋊Dic29—21no—
99C4⋊Dic29C2311yescharacteristic
100C4⋊Dic29C2311yescharacteristic
101C4⋊Dic29C2311yescharacteristic
102#90779—21no—
103#90779—21no—
104C4×Dic29—21no—
105#90777—41no—
106C2×#6597—41no—
107C2×#6597C2311yescharacteristic
108C2×#6597C2311yescharacteristic
109C2×#6597C2311yescharacteristic
110C2×#6597C2311yescharacteristic
111C23×C29—21no—
112C23×C29—21no—
113C23×C29C2×D411yescharacteristic
114C23×C29C2×D411yescharacteristic
115C22×D29—21no—
116Q8×C29—21no—
117Q8×C29#4112yes—
118D4×C29—21no—
119D4×C29—21no—
120D4×C29—21no—
121D4×C29—21no—
122D4×C29—41no—
123D4×C29—42no—
124D4×C29—42no—
125D4×C29—42no—
126D4×C29—81no—
127D4×C29—81no—
128D4×C29—81no—
129C2×C4×C29—21no—
130C2×C4×C29—21no—
131C2×C4×C29—21no—
132C2×C4×C29—21no—
133C2×C4×C29—21no—
134C2×C4×C29—21no—
135C2×C4×C29—42no—
136C2×C4×C29—42no—
137C2×C4×C29C2×D411yescharacteristic
138C2×C4×C29C2×D411yescharacteristic
139C2×C4×C29C2×D411yescharacteristic
140C2×C4×C29C2×D411yescharacteristic
141C2×C4×C29C2411yescharacteristic
142C22⋊D29—42no—
143C22⋊D29—81no—
144C2×Dic29—21no—
145C2×Dic29—21no—
146C2×Dic29—21no—
147C2×Dic29—81no—
148D116—21no—
149D116—21no—
150C4×D29—81no—
151#6597—21no—
152#6597—21no—
153#6597—21no—
154#6597—21no—
155#3309—291nomaximal, Sylow
156C22×C29—21no—
157C22×C29—21no—
158C22×C29—21no—
159C22×C29—21no—
160C22×C29—21no—
161C22×C29—21no—
162C22×C29—41no—
163C22×C29—41no—
164C22×C29—41no—
165C22×C29—41no—
166C22×C29—41no—
167C22×C29—41no—
168C22×C29C22×D411yescharacteristic
169C2×D29—41no—
170C2×D29—41no—
171C2×D29—41no—
172C4×C29—21no—
173C4×C29—21no—
174C4×C29—22no—
175C4×C29—21no—
176C4×C29—21no—
177C4×C29—41no—
178C4×C29C2×#4111yescharacteristic
179C4×C29H(5,𝔽2)11yescharacteristic
180Dic29—41no—
181Dic29—41no—
182Dic29—41no—
183#553—291no—
184#550D2911yescharacteristic, complemented
185#490—291no—
186#482—291no—
187#480—291no—
188#479—291no—
189#469—291no—
190#466—291no—
191#459—291no—
192#449—291no—
193#449—291no—
194#440—291no—
195#435—291no—
196#417—291no—
197#416—291no—
198C2×C29—41no—
199C2×C29—41no—
200C2×C29—81no—
201C2×C29—81no—
202C2×C29#54611yescharacteristic
203C2×C29#57511yescharacteristic
204C2×C29#57611yescharacteristic
205D29—81no—
206C2×#41C2×D2911yescharacteristic
207C2×#41C2×D2911yescharacteristic
208C2×SD16—291no—
209C2×D8—291no—
210C2×D8—291no—
211C2×M16—291no—
212C22×C8—291no—
213#127—21no—
214#127C2×D2911yescharacteristic
215#126—581no—
216#125—291no—
217#123—581no—
218#121—21no—
219#121—21no—
220#121—291no—
221#121—291no—
222#121—581no—
223#121C2×D2911yescharacteristic
224#121C2×D2911yescharacteristic
225C4×Q8C2×D2911yescharacteristic
226C4×D4—21no—
227C4×D4—291no—
228C4×D4—581no—
229C4×D4C2×D2911yescharacteristic
230#117—291no—
231C2×C4⋊C4—291no—
232#107—291no—
233#107—291no—
234#106—291no—
235C4⋊C8—291no—
236#103—291no—
237#103—291no—
238#103—291no—
239#102—291no—
240#102—291no—
241#102—291no—
242#102—291no—
243#102—291no—
244#102—291no—
245#102—291no—
246C22⋊C8—291no—
247C22⋊C8—291no—
248#97—291no—
249C29#330911yescharacteristic, complemented, Sylow
250#41—22no—
251#41—22no—
252#41—41no—
253#41—41no—
254C2×Q8C22×D2911yescharacteristic
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—21no—
261C2×D4—291no—
262C2×D4—581no—
263C2×D4—581no—
264C2×D4C22⋊D2911yescharacteristic
265C2×D4C22×D2911yescharacteristic
266C2×D4C22×D2911yescharacteristic
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—581no—
270C22×C4—581no—
271C22×C4C22×D2911yescharacteristic
272C22×C4C22×D2911yescharacteristic
273SD16—582no—
274D8—1161no—
275D8—1161no—
276M16—1161no—
277C2×C8—291no—
278C2×C8—291no—
279C2×C8—291no—
280C2×C8—291no—
281C2×C8—1161no—
282C4⋊C4—21no—
283C4⋊C4—291no—
284C4⋊C4—291no—
285C4⋊C4—291no—
286C4⋊C4—581no—
287C4⋊C4—581no—
288C4⋊C4—581no—
289C4⋊C4C22⋊D2911yescharacteristic
290C4⋊C4C22×D2911yescharacteristic
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—581no—
294C22⋊C4—581no—
295C22⋊C4—581no—
296C22⋊C4—581no—
297C22⋊C4C22⋊D2911yescharacteristic
298C22⋊C4C22⋊D2911yescharacteristic
299C42—21no—
300C42—581no—
301C42C22×D2911yescharacteristic
302C23—21no—
303C23—21no—
304C23—581no—
305C23C2×C22⋊D2911yescharacteristic
306C23C2×C22⋊D2911yescharacteristic
307Q8—21no—
308Q8#9080712yes—
309D4—21no—
310D4—21no—
311D4—21no—
312D4—21no—
313D4—41no—
314D4—42no—
315D4—42no—
316D4—42no—
317D4—81no—
318D4—81no—
319D4—81no—
320D4—581no—
321D4—581no—
322D4—1162no—
323D4—2321no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—581no—
333C2×C4—581no—
334C2×C4—581no—
335C2×C4—2321no—
336C2×C4—2321no—
337C2×C4C2×C22⋊D2911yescharacteristic
338C2×C4C2×C22⋊D2911yescharacteristic
339C2×C4C2×C22⋊D2911yescharacteristic
340C2×C4C2×C22⋊D2911yescharacteristic
341C2×C4C23×D2911yescharacteristic
342C8—581no—
343C8—581no—
344C8—581no—
345C8—581no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—1161no—
359C22—1161no—
360C22—1161no—
361C22C22×C22⋊D2911yescharacteristic
362C4—21no—
363C4—21no—
364C4—22no—
365C4—21no—
366C4—21no—
367C4—41no—
368C4—1161no—
369C4—1161no—
370C4—1161no—
371C4C2×#9080711yescharacteristic
372C4#1174535911yescharacteristic
373C2—41no—
374C2—41no—
375C2—81no—
376C2—81no—
377C2—2321no—
378C2#1427180711yescharacteristic
379C2#1427196111yescharacteristic
380C2#1427196611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#550C2
socleC22×C29C22×D4
hypercenter#550D29
hypocenterC29#3309
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C4×D4 ◁ #550

Complements

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

NH ≅ G/Ntype
1. #14271859C2semidirect
2. #14271527C2semidirect
3. #14271484C2semidirect
4. #14271474C2semidirect
5. #14271470C2semidirect
6. #14271414C2semidirect
7. #14271397C2semidirect
8. #14271355C2semidirect
9. #14271308C2semidirect
10. #14271308C2semidirect
11. #14271261C2semidirect
12. #14271235C2semidirect
13. #14271164C2semidirect
14. #14271159C2semidirect
15. C29×#550C2semidirect
184. #550D29semidirect
249. C29#3309semidirect

Maximal subgroups

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

subgroupindex
#142718592
#142715272
#142714842
#142714742
#142714702
#142714142
#142713972
#142713552
#142713082
#142712612
#142712352
#142711642
#142711592
C29×#5502
#330929