Finite Group Databasebeta

← #16831491

Subgroups — #16831491

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#14271865C211yesmaximal, characteristic, complemented
2#14271832C211yesmaximal, characteristic, complemented
3#14271526C211yesmaximal, characteristic, complemented
4#14271485C211yesmaximal, characteristic, complemented
5#14271477C211yesmaximal, characteristic, complemented
6#14271472C211yesmaximal, characteristic, complemented
7#14271414C211yesmaximal, characteristic, complemented
8#14271396C211yesmaximal, characteristic, complemented
9#14271356C211yesmaximal, characteristic, complemented
10#14271307C211yesmaximal, characteristic, complemented
11#14271264C211yesmaximal, characteristic, complemented
12#14271237C211yesmaximal, characteristic, complemented
13#14271164C211yesmaximal, characteristic, complemented
14#14271158C211yesmaximal, characteristic, complemented
15C29×#449C211yesmaximal, characteristic, complemented
16C2×#41×C29C2211yescharacteristic
17C2×#90809C2211yescharacteristic
18C2×SD16×C29C2211yescharacteristic
19C2×D8×C29C2211yescharacteristic
20C29×#121C2211yescharacteristic
21Q8×Dic29C2211yescharacteristic
22#11745302—21no—
23#11745302C2211yescharacteristic
24#11745301—21no—
25#11745300—21no—
26#11745300C2211yescharacteristic
27#11745300C2211yescharacteristic
28D4×Dic29—21no—
29D4×Dic29C2211yescharacteristic
30C2×#90782C2211yescharacteristic
31#11745292—21no—
32#11745292C2211yescharacteristic
33C4×C22⋊D29—21no—
34C4×C22⋊D29C2211yescharacteristic
35C2×C4⋊Dic29C2211yescharacteristic
36C2×#90777C2211yescharacteristic
37C2×C8×D29C2211yescharacteristic
38#11745254C2211yescharacteristic
39#11745252C2211yescharacteristic
40#11745248—21no—
41#11745241—21no—
42C29×#103C2211yescharacteristic
43C29×#102C2211yescharacteristic
44C29×C22⋊C8C2211yescharacteristic
45#11745183C2211yescharacteristic
46#11745183C2211yescharacteristic
47#11745180C2211yescharacteristic
48#11745180C2211yescharacteristic
49#11745180C2211yescharacteristic
50#11745169C2211yescharacteristic
51#11745169C2211yescharacteristic
52#11745168C2211yescharacteristic
53#11745166C2211yescharacteristic
54#11745166C2211yescharacteristic
55#11745163C2211yescharacteristic
56#11745162C2211yescharacteristic
57#11745157C2211yescharacteristic
58#11745156C2211yescharacteristic
59#41×C29—22no—
60#41×C29—41no—
61C2×Q8×C29C2311yescharacteristic
62C2×D4×C29—21no—
63C2×D4×C29—21no—
64C2×D4×C29C2311yescharacteristic
65C2×D4×C29C2311yescharacteristic
66C22×C4×C29—21no—
67C22×C4×C29C2311yescharacteristic
68C2×C22⋊D29—21no—
69C2×C22⋊D29—21no—
70C2×C22⋊D29—21no—
71C2×C22⋊D29—21no—
72C2×C22⋊D29—21no—
73C2×C22⋊D29D411yescharacteristic
74C22×Dic29—21no—
75C22×Dic29—21no—
76#90809—22no—
77#90809—41no—
78C2×D116—21no—
79C2×D116C2311yescharacteristic
80C2×C4×D29—21no—
81C2×C4×D29C2311yescharacteristic
82SD16×C29—22no—
83D8×C29—41no—
84C2×C8×C29C2311yescharacteristic
85C2×C8×C29C2311yescharacteristic
86C4⋊C4×C29C2311yescharacteristic
87C22⋊C4×C29—21no—
88C22⋊Dic29—21no—
89C22⋊Dic29—21no—
90C22⋊Dic29—21no—
91C22⋊Dic29D411yescharacteristic
92#90782—41no—
93#90781—21no—
94#90781—21no—
95#90781D411yescharacteristic
96C4⋊Dic29—21no—
97C4⋊Dic29—21no—
98C4⋊Dic29—21no—
99C4⋊Dic29C2311yescharacteristic
100C4⋊Dic29C2311yescharacteristic
101C4⋊Dic29C2311yescharacteristic
102#90779—21no—
103#90779D411yescharacteristic
104C4×Dic29—21no—
105C4×Dic29—21no—
106C4×Dic29C2311yescharacteristic
107#90777—41no—
108C2×#6597C2311yescharacteristic
109C2×#6597C2311yescharacteristic
110C8×D29—41no—
111C23×C29—21no—
112C23×C29—21no—
113C23×C29C2×D411yescharacteristic
114C22×D29—21no—
115C22×D29C2×D411yescharacteristic
116Q8×C29—21no—
117Q8×C29#4112yes—
118D4×C29—21no—
119D4×C29—21no—
120D4×C29—21no—
121D4×C29—21no—
122D4×C29—42no—
123D4×C29—42no—
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—41no—
132C22⋊D29—42no—
133C22⋊D29—81no—
134C22⋊D29—81no—
135C22⋊D29—81no—
136C22⋊D29—81no—
137C2×Dic29—21no—
138C2×Dic29—21no—
139C2×Dic29—21no—
140C2×Dic29—81no—
141C2×Dic29—81no—
142C2×Dic29C2×D411yescharacteristic
143C2×Dic29C2×D411yescharacteristic
144C2×Dic29C2×D411yescharacteristic
145D116—21no—
146D116—21no—
147D116—42no—
148C4×D29—21no—
149C4×D29—21no—
150C4×D29—42no—
151C8×C29—21no—
152C8×C29—21no—
153#6597—21no—
154#6597—21no—
155#3309—291nomaximal, Sylow
156C22×C29—21no—
157C22×C29—21no—
158C22×C29—21no—
159C22×C29—41no—
160C22×C29—41no—
161C22×C29—41no—
162C22×C29—41no—
163C22×C29—41no—
164C22×C29—41no—
165C22×C29C22×D411yescharacteristic
166C2×D29—21no—
167C2×D29—21no—
168C2×D29—21no—
169C2×D29—41no—
170C2×D29—41no—
171C2×D29—41no—
172C4×C29—22no—
173C4×C29—21no—
174C4×C29—41no—
175C4×C29C2×#4111yescharacteristic
176C4×C29H(5,𝔽2)11yescharacteristic
177Dic29—21no—
178Dic29—21no—
179Dic29—21no—
180Dic29—41no—
181Dic29—41no—
182Dic29—41no—
183#553—291no—
184#550—291no—
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#449D2911yescharacteristic, complemented
194#440—291no—
195#435—291no—
196#417—291no—
197#416—291no—
198C2×C29—41no—
199C2×C29—81no—
200C2×C29—81no—
201C2×C29#54611yescharacteristic
202C2×C29#57511yescharacteristic
203C2×C29#57611yescharacteristic
204D29—41no—
205D29—81no—
206C2×#41—291no—
207C2×#41C2×D2911yescharacteristic
208C2×SD16C2×D2911yescharacteristic
209C2×D8—291no—
210C2×D8C2×D2911yescharacteristic
211C2×M16—291no—
212C22×C8—291no—
213#127—291no—
214#127—581no—
215#126—581no—
216#125—291no—
217#123—581no—
218#121—291no—
219#121—291no—
220#121—291no—
221#121—581no—
222#121—581no—
223#121—581no—
224#121C2×D2911yescharacteristic
225C4×Q8—291no—
226C4×D4—291no—
227C4×D4—291no—
228C4×D4—581no—
229C4×D4—581no—
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#103C2×D2911yescharacteristic
239#102—291no—
240#102—291no—
241#102—291no—
242#102—291no—
243#102—291no—
244#102—291no—
245#102C2×D2911yescharacteristic
246C22⋊C8—291no—
247C22⋊C8C2×D2911yescharacteristic
248#97—291no—
249C29#330911yescharacteristic, complemented, Sylow
250#41—22no—
251#41—41no—
252#41—582no—
253#41—1161no—
254C2×Q8C22×D2911yescharacteristic
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—291no—
258C2×D4—291no—
259C2×D4—581no—
260C2×D4—581no—
261C2×D4—581no—
262C2×D4—581no—
263C2×D4—581no—
264C2×D4—581no—
265C2×D4C22×D2911yescharacteristic
266C2×D4C22×D2911yescharacteristic
267C22×C4—21no—
268C22×C4—291no—
269C22×C4—581no—
270C22×C4—581no—
271C22×C4—581no—
272C22×C4C22×D2911yescharacteristic
273SD16—22no—
274D8—41no—
275D8—1161no—
276M16—1161no—
277C2×C8—291no—
278C2×C8—291no—
279C2×C8—1161no—
280C2×C8C22×D2911yescharacteristic
281C2×C8C22×D2911yescharacteristic
282C4⋊C4—291no—
283C4⋊C4—291no—
284C4⋊C4—291no—
285C4⋊C4—291no—
286C4⋊C4—581no—
287C4⋊C4—581no—
288C4⋊C4—581no—
289C4⋊C4—581no—
290C4⋊C4C22×D2911yescharacteristic
291C22⋊C4—21no—
292C22⋊C4—291no—
293C22⋊C4—291no—
294C22⋊C4—581no—
295C22⋊C4—581no—
296C22⋊C4—581no—
297C22⋊C4—581no—
298C22⋊C4—581no—
299C42—291no—
300C42—581no—
301C42—581no—
302C23—21no—
303C23—21no—
304C23—291no—
305C23—581no—
306C23D4×D2911yescharacteristic
307Q8—21no—
308Q8#9080712yes—
309D4—21no—
310D4—21no—
311D4—21no—
312D4—21no—
313D4—42no—
314D4—42no—
315D4—581no—
316D4—581no—
317D4—1162no—
318D4—1161no—
319D4—1162no—
320D4—2321no—
321D4—2321no—
322D4—2321no—
323D4—2321no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—42no—
329C2×C4—291no—
330C2×C4—291no—
331C2×C4—291no—
332C2×C4—581no—
333C2×C4—581no—
334C2×C4—581no—
335C2×C4—581no—
336C2×C4—581no—
337C2×C4—1162no—
338C2×C4—2321no—
339C2×C4—2321no—
340C2×C4D4×D2911yescharacteristic
341C2×C4C23×D2911yescharacteristic
342C8—21no—
343C8—21no—
344C8—581no—
345C8—581no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—581no—
356C22—581no—
357C22—581no—
358C22—1161no—
359C22—1161no—
360C22—1161no—
361C22C2×D4×D2911yescharacteristic
362C4—21no—
363C4—22no—
364C4—41no—
365C4—581no—
366C4—581no—
367C4—581no—
368C4—1161no—
369C4—1161no—
370C4—1161no—
371C4C2×#9080711yescharacteristic
372C4#1174535911yescharacteristic
373C2—41no—
374C2—81no—
375C2—81no—
376C2—1161no—
377C2—2321no—
378C2#1427180011yescharacteristic
379C2#1427195911yescharacteristic
380C2#1427196511yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#449C2
socleC22×C29C22×D4
hypercenter#449D29
hypocenterC29#3309
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #14271865C2semidirect
2. #14271832C2semidirect
3. #14271526C2semidirect
4. #14271485C2semidirect
5. #14271477C2semidirect
6. #14271472C2semidirect
7. #14271414C2semidirect
8. #14271396C2semidirect
9. #14271356C2semidirect
10. #14271307C2semidirect
11. #14271264C2semidirect
12. #14271237C2semidirect
13. #14271164C2semidirect
14. #14271158C2semidirect
15. C29×#449C2semidirect
193. #449D29semidirect
249. C29#3309semidirect

Maximal subgroups

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

subgroupindex
#142718652
#142718322
#142715262
#142714852
#142714772
#142714722
#142714142
#142713962
#142713562
#142713072
#142712642
#142712372
#142711642
#142711582
C29×#4492
#330929