Finite Group Databasebeta

← #16831500

Subgroups — #16831500

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#14271834C211yesmaximal, characteristic, complemented
3#14271528C211yesmaximal, characteristic, complemented
4#14271488C211yesmaximal, characteristic, complemented
5#14271477C211yesmaximal, characteristic, complemented
6#14271471C211yesmaximal, characteristic, complemented
7#14271416C211yesmaximal, characteristic, complemented
8#14271399C211yesmaximal, characteristic, complemented
9#14271359C211yesmaximal, characteristic, complemented
10#14271310C211yesmaximal, characteristic, complemented
11#14271310C211yesmaximal, characteristic, complemented
12#14271265C211yesmaximal, characteristic, complemented
13#14271165C211yesmaximal, characteristic, complemented
14#14271160C211yesmaximal, characteristic, complemented
15C29×#435C211yesmaximal, characteristic, complemented
16C2×#90805C2211yescharacteristic
17C2×#90805C2211yescharacteristic
18C2×M16×C29C2211yescharacteristic
19C22×C8×C29C2211yescharacteristic
20C4×D4×C29C2211yescharacteristic
21#11745302—21no—
22#11745301—21no—
23#11745292C2211yescharacteristic
24#11745292C2211yescharacteristic
25#11745292C2211yescharacteristic
26#11745292C2211yescharacteristic
27#11745288C2211yescharacteristic
28C2×C4⋊Dic29C2211yescharacteristic
29C2×D232C2211yescharacteristic
30C2×D232C2211yescharacteristic
31C2×#90773C2211yescharacteristic
32#11745260—21no—
33#11745255—21no—
34#11745246—21no—
35#11745246—21no—
36#11745245—21no—
37#11745243—21no—
38#11745236C2211yescharacteristic
39C4×D116C2211yescharacteristic
40#11745232C2211yescharacteristic
41C4×Dic58C2211yescharacteristic
42C29×C4⋊C8C2211yescharacteristic
43C29×C22⋊C8C2211yescharacteristic
44C29×C22⋊C8C2211yescharacteristic
45C29×#97C2211yescharacteristic
46#11745169C2211yescharacteristic
47#11745169C2211yescharacteristic
48#11745169C2211yescharacteristic
49#11745169C2211yescharacteristic
50#11745169C2211yescharacteristic
51#11745169C2211yescharacteristic
52#11745169C2211yescharacteristic
53#11745166C2211yescharacteristic
54#11745166C2211yescharacteristic
55#11745165C2211yescharacteristic
56#11745164C2211yescharacteristic
57#11745164C2211yescharacteristic
58#11745164C2211yescharacteristic
59C2×D4×C29D411yescharacteristic
60C22×C4×C29C2311yescharacteristic
61C22×C4×C29C2311yescharacteristic
62C2×C22⋊D29—21no—
63C2×C22⋊D29—21no—
64C2×C22⋊D29—21no—
65C2×C22⋊D29—21no—
66C2×C22⋊D29—21no—
67C2×C22⋊D29—21no—
68C22×Dic29—21no—
69#90805—22no—
70#90805—22no—
71#90805—41no—
72#90805—41no—
73C2×D116—21no—
74C2×D116—21no—
75C2×D116C2311yescharacteristic
76C2×D116C2311yescharacteristic
77C2×D116C2311yescharacteristic
78C2×C4×D29—21no—
79C2×C4×D29—21no—
80C2×C4×D29—21no—
81C2×Dic58C2311yescharacteristic
82M16×C29—41no—
83C2×C8×C29—41no—
84C2×C8×C29C2311yescharacteristic
85C2×C8×C29C2311yescharacteristic
86C2×C8×C29C2311yescharacteristic
87C2×C8×C29C2311yescharacteristic
88C4⋊C4×C29D411yescharacteristic
89C22⋊C4×C29D411yescharacteristic
90C22⋊C4×C29D411yescharacteristic
91C42×C29C2311yescharacteristic
92C22⋊Dic29—21no—
93#90781—21no—
94#90781—21no—
95#90781—21no—
96#90781—21no—
97#90781—21no—
98C4⋊Dic29—21no—
99C4⋊Dic29C2311yescharacteristic
100C4⋊Dic29C2311yescharacteristic
101C4⋊Dic29C2311yescharacteristic
102C4⋊Dic29C2311yescharacteristic
103#90779—21no—
104#90779—21no—
105#90779—21no—
106C4×Dic29—21no—
107C4×Dic29—21no—
108D232—41no—
109D232—41no—
110#90773—22no—
111C23×C29C2×D411yescharacteristic
112C23×C29C2×D411yescharacteristic
113C22×D29—21no—
114C22×D29—21no—
115C22×D29—21no—
116D4×C29—41no—
117C2×C4×C29—21no—
118C2×C4×C29—21no—
119C2×C4×C29—21no—
120C2×C4×C29—21no—
121C2×C4×C29C2×D411yescharacteristic
122C2×C4×C29C2×D411yescharacteristic
123C2×C4×C29C2×D411yescharacteristic
124C2×C4×C29C2×D411yescharacteristic
125C2×C4×C29C2411yescharacteristic
126C22⋊D29—42no—
127C22⋊D29—42no—
128C22⋊D29—42no—
129C22⋊D29—81no—
130C22⋊D29—81no—
131C22⋊D29—81no—
132C2×Dic29—21no—
133C2×Dic29—21no—
134C2×Dic29—21no—
135C2×Dic29—21no—
136C2×Dic29—21no—
137C2×Dic29—81no—
138D116—21no—
139D116—21no—
140D116—21no—
141D116—21no—
142D116—21no—
143D116—21no—
144D116—42no—
145D116—81no—
146C4×D29—42no—
147C4×D29—42no—
148C4×D29—81no—
149Dic58—21no—
150Dic58#4112yes—
151C8×C29—21no—
152C8×C29—21no—
153C8×C29—21no—
154C8×C29—21no—
155#3309—291nomaximal, Sylow
156C22×C29—21no—
157C22×C29—21no—
158C22×C29—21no—
159C22×C29—21no—
160C22×C29—21no—
161C22×C29—21no—
162C22×C29C22×D411yescharacteristic
163C2×D29—41no—
164C2×D29—41no—
165C2×D29—41no—
166C2×D29—41no—
167C2×D29—41no—
168C2×D29—41no—
169C2×D29—41no—
170C2×D29—41no—
171C2×D29—41no—
172C4×C29—21no—
173C4×C29—21no—
174C4×C29—21no—
175C4×C29—21no—
176C4×C29C2×#4111yescharacteristic
177C4×C29H(5,𝔽2)11yescharacteristic
178Dic29—22no—
179Dic29—41no—
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#449—291no—
194#440—291no—
195#435D2911yescharacteristic, complemented
196#417—291no—
197#416—291no—
198C2×C29—41no—
199C2×C29—41no—
200C2×C29#54611yescharacteristic
201C2×C29#57511yescharacteristic
202C2×C29#57611yescharacteristic
203D29—81no—
204D29—81no—
205D29—81no—
206C2×#41—291no—
207C2×#41—291no—
208C2×SD16—291no—
209C2×D8—291no—
210C2×D8—291no—
211C2×M16C2×D2911yescharacteristic
212C22×C8C2×D2911yescharacteristic
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—291no—
222#121—581no—
223#121—581no—
224#121—581no—
225C4×Q8—291no—
226C4×D4—291no—
227C4×D4—581no—
228C4×D4—581no—
229C4×D4C2×D2911yescharacteristic
230#117—291no—
231C2×C4⋊C4—291no—
232#107—291no—
233#107—291no—
234#106—291no—
235C4⋊C8C2×D2911yescharacteristic
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⋊C8C2×D2911yescharacteristic
247C22⋊C8C2×D2911yescharacteristic
248#97C2×D2911yescharacteristic
249C29#330911yescharacteristic, complemented, Sylow
250#41—582no—
251#41—582no—
252#41—1161no—
253#41—1161no—
254C2×Q8—291no—
255C2×D4—291no—
256C2×D4—291no—
257C2×D4—291no—
258C2×D4—581no—
259C2×D4—581no—
260C2×D4—581no—
261C2×D4—581no—
262C2×D4—581no—
263C2×D4—581no—
264C2×D4—581no—
265C2×D4—581no—
266C2×D4D11611yescharacteristic
267C22×C4—581no—
268C22×C4—581no—
269C22×C4—581no—
270C22×C4—581no—
271C22×C4C22×D2911yescharacteristic
272C22×C4C22×D2911yescharacteristic
273SD16—582no—
274D8—1161no—
275D8—1161no—
276M16—41no—
277C2×C8—41no—
278C2×C8C22×D2911yescharacteristic
279C2×C8C22×D2911yescharacteristic
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⋊C4D11611yescharacteristic
291C22⋊C4—581no—
292C22⋊C4—581no—
293C22⋊C4—581no—
294C22⋊C4—581no—
295C22⋊C4—581no—
296C22⋊C4—581no—
297C22⋊C4D11611yescharacteristic
298C22⋊C4D11611yescharacteristic
299C42—581no—
300C42—581no—
301C42C22×D2911yescharacteristic
302C23—581no—
303C23—581no—
304C23—581no—
305C23C2×D11611yescharacteristic
306C23C2×D11611yescharacteristic
307Q8—292no—
308Q8—581no—
309D4—41no—
310D4—581no—
311D4—581no—
312D4—581no—
313D4—581no—
314D4—581no—
315D4—581no—
316D4—1162no—
317D4—1162no—
318D4—1162no—
319D4—1162no—
320D4—2321no—
321D4—2321no—
322D4—2321no—
323D4—2321no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—581no—
329C2×C4—581no—
330C2×C4—581no—
331C2×C4—581no—
332C2×C4—581no—
333C2×C4—1162no—
334C2×C4—1162no—
335C2×C4—2321no—
336C2×C4—2321no—
337C2×C4C2×D11611yescharacteristic
338C2×C4C2×D11611yescharacteristic
339C2×C4C2×D11611yescharacteristic
340C2×C4C2×D11611yescharacteristic
341C2×C4C23×D2911yescharacteristic
342C8—21no—
343C8—21no—
344C8—21no—
345C8—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—1161no—
353C22—1161no—
354C22—1161no—
355C22—1161no—
356C22—1161no—
357C22—1161no—
358C22—1161no—
359C22—1161no—
360C22—1161no—
361C22C22×D11611yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—582no—
367C4—1161no—
368C4—1161no—
369C4—1161no—
370C4—1161no—
371C4#1174535911yescharacteristic
372C4#41×D2911yescharacteristic
373C2—41no—
374C2—41no—
375C2—2321no—
376C2—2321no—
377C2—2321no—
378C2#1427180811yescharacteristic
379C2#1427196311yescharacteristic
380C2#1427196811yescharacteristic
subgroupG/H
centerC22C22×D116
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#435C2
socleC22×C29C22×D4
hypercenter#435D29
hypocenterC29#3309
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #14271859C2semidirect
2. #14271834C2semidirect
3. #14271528C2semidirect
4. #14271488C2semidirect
5. #14271477C2semidirect
6. #14271471C2semidirect
7. #14271416C2semidirect
8. #14271399C2semidirect
9. #14271359C2semidirect
10. #14271310C2semidirect
11. #14271310C2semidirect
12. #14271265C2semidirect
13. #14271165C2semidirect
14. #14271160C2semidirect
15. C29×#435C2semidirect
195. #435D29semidirect
249. C29#3309semidirect

Maximal subgroups

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

subgroupindex
#142718592
#142718342
#142715282
#142714882
#142714772
#142714712
#142714162
#142713992
#142713592
#142713102
#142712652
#142711652
#142711602
C29×#4352
#330929