Finite Group Databasebeta

← #16832082

Subgroups — #16832082

Order 3712.

386 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271877C211yesmaximal, characteristic, complemented
2#14271813C211yesmaximal, characteristic, complemented
3#14271560C211yesmaximal, characteristic, complemented
4#14271485C211yesmaximal, characteristic, complemented
5#14271484C211yesmaximal, characteristic, complemented
6#14271480C211yesmaximal, characteristic, complemented
7#14271479C211yesmaximal, characteristic, complemented
8#14271451C211yesmaximal, characteristic, complemented
9#14271441C211yesmaximal, characteristic, complemented
10#14271413C211yesmaximal, characteristic, complemented
11D8×Dic29C211yesmaximal, characteristic, complemented
12#14271239C211yesmaximal, characteristic, complemented
13#14271205C211yesmaximal, characteristic, complemented
14#14271202C211yesmaximal, characteristic, complemented
15C29×#469C211yesmaximal, characteristic, complemented
16C2×#90807—21no—
17C2×D8×C29C2211yescharacteristic
18C2×M16×C29C2211yescharacteristic
19C29×#121C2211yescharacteristic
20C29×#121C2211yescharacteristic
21#11745301—21no—
22#11745300C2211yescharacteristic
23#11745300C2211yescharacteristic
24#11745298—21no—
25#11745297—21no—
26D4×Dic29C2211yescharacteristic
27D4×Dic29C2211yescharacteristic
28C4×C22⋊D29C2211yescharacteristic
29#11745288C2211yescharacteristic
30C2×C4⋊Dic29C2211yescharacteristic
31C2×#90772C2211yescharacteristic
32#11745254C2211yescharacteristic
33C4⋊C4×D29C2211yescharacteristic
34#11745250C2211yescharacteristic
35#11745250C2211yescharacteristic
36#11745247—21no—
37#11745245—21no—
38#11745240—21no—
39#11745239—21no—
40C29×#106C2211yescharacteristic
41C29×#102C2211yescharacteristic
42C29×#102C2211yescharacteristic
43#11745180C2211yescharacteristic
44#11745180C2211yescharacteristic
45#11745180C2211yescharacteristic
46#11745180C2211yescharacteristic
47C22⋊#6597C2211yescharacteristic
48#11745168C2211yescharacteristic
49#11745166C2211yescharacteristic
50#11745166C2211yescharacteristic
51#11745165C2211yescharacteristic
52#11745165C2211yescharacteristic
53#11745162C2211yescharacteristic
54C8×Dic29C2211yescharacteristic
55#11745156C2211yescharacteristic
56#11745156C2211yescharacteristic
57#11745156C2211yescharacteristic
58#11745155C2211yescharacteristic
59C2×D4×C29—21no—
60C2×D4×C29—21no—
61C2×D4×C29C2311yescharacteristic
62C2×D4×C29C2311yescharacteristic
63C22×C4×C29C2311yescharacteristic
64C2×C22⋊D29—21no—
65C2×C22⋊D29—21no—
66C2×C22⋊D29D411yescharacteristic
67C22×Dic29—21no—
68C22×Dic29—21no—
69C22×Dic29—21no—
70#90807—44no—
71C2×C4×D29—21no—
72C2×C4×D29C2311yescharacteristic
73C2×Dic58—21no—
74C2×Dic58—21no—
75D8×C29—22no—
76M16×C29—22no—
77C2×C8×C29C2311yescharacteristic
78C2×C8×C29C2311yescharacteristic
79C4⋊C4×C29C2311yescharacteristic
80C4⋊C4×C29C2311yescharacteristic
81C22⋊C4×C29—21no—
82C22⋊C4×C29—21no—
83C22⋊Dic29—21no—
84C22⋊Dic29—21no—
85C22⋊Dic29—21no—
86C22⋊Dic29—21no—
87C22⋊Dic29—21no—
88C22⋊Dic29D411yescharacteristic
89#90781—21no—
90#90781D411yescharacteristic
91C4⋊Dic29—21no—
92C4⋊Dic29C2311yescharacteristic
93C4⋊Dic29C2311yescharacteristic
94C4⋊Dic29C2311yescharacteristic
95C4⋊Dic29C2311yescharacteristic
96#90779—21no—
97#90779—21no—
98#90779—21no—
99#90779D411yescharacteristic
100C4×Dic29—21no—
101C4×Dic29—21no—
102C4×Dic29C2311yescharacteristic
103C2×#6597C2311yescharacteristic
104C2×#6597C2311yescharacteristic
105#90772—22no—
106C23×C29—21no—
107C23×C29—21no—
108C23×C29C2×D411yescharacteristic
109C22×D29C2×D411yescharacteristic
110D4×C29—21no—
111D4×C29—21no—
112D4×C29—21no—
113D4×C29—21no—
114D4×C29—42no—
115D4×C29—81no—
116C2×C4×C29—21no—
117C2×C4×C29—21no—
118C2×C4×C29—21no—
119C2×C4×C29—21no—
120C2×C4×C29C2×D411yescharacteristic
121C2×C4×C29C2411yescharacteristic
122C22⋊D29—22no—
123C22⋊D29—42no—
124C22⋊D29—81no—
125C2×Dic29—21no—
126C2×Dic29—21no—
127C2×Dic29—21no—
128C2×Dic29—21no—
129C2×Dic29—42no—
130C2×Dic29—42no—
131C2×Dic29—42no—
132C2×Dic29C2×D411yescharacteristic
133C2×Dic29C2×D411yescharacteristic
134C2×Dic29C2×D411yescharacteristic
135C4×D29—21no—
136C4×D29—21no—
137C4×D29—42no—
138Dic58—42no—
139Dic58—81no—
140C8×C29—21no—
141C8×C29#4112yescomplemented
142#6597—21no—
143#6597—21no—
144#3354—291nomaximal, Sylow
145C22×C29—21no—
146C22×C29—21no—
147C22×C29—21no—
148C22×C29—41no—
149C22×C29—41no—
150C22×C29—41no—
151C22×C29—41no—
152C22×C29—41no—
153C22×C29—41no—
154C22×C29C22×D411yescharacteristic
155C2×D29—21no—
156C2×D29—21no—
157C2×D29—21no—
158C4×C29—21no—
159C4×C29—41no—
160C4×C29—41no—
161C4×C29C2×#4111yescharacteristic
162C4×C292−1+411yescharacteristic
163Dic29—21no—
164Dic29—21no—
165Dic29—41no—
166Dic29—41no—
167Dic29—41no—
168Dic29—41no—
169Dic29AGL(1,ℤ/8)12yes—
170#555—291no—
171#547—291no—
172#498—291no—
173#482—291no—
174#482—291no—
175#481—291no—
176#481—291no—
177#476—291no—
178#474—291no—
179#469—291no—
180#469D2911yescharacteristic, complemented
181C4×D8—291no—
182#436—291no—
183#428—291no—
184#428—291no—
185C2×C29—41no—
186C2×C29—81no—
187C2×C29—81no—
188C2×C29#54711yescharacteristic
189C2×C29C2×AGL(1,ℤ/8)11yescharacteristic
190C2×C29#57711yescharacteristic
191D29—41no—
192C2×#41—581no—
193C2×D8C2×D2911yescharacteristic
194C2×M16—291no—
195C2×M16C2×D2911yescharacteristic
196C4⋊Q8—291no—
197C4⋊Q8—291no—
198#124—581no—
199#124—581no—
200#123—581no—
201#123—581no—
202C22⋊Q8—581no—
203#121—291no—
204#121—291no—
205#121—581no—
206#121C2×D2911yescharacteristic
207#121C2×D2911yescharacteristic
208C4×D4—291no—
209C4×D4—291no—
210C4×D4—291no—
211#117—291no—
212#117—291no—
213#117—581no—
214C2×C4⋊C4—291no—
215C2×C4⋊C4—291no—
216#107—291no—
217#107—291no—
218#107—291no—
219#106—291no—
220#106—291no—
221#106—291no—
222#106—291no—
223#106—291no—
224#106C2×D2911yescharacteristic
225C4⋊C8—291no—
226#102—291no—
227#102—291no—
228#102—291no—
229#102—291no—
230#102C2×D2911yescharacteristic
231#102C2×D2911yescharacteristic
232C22⋊C8—291no—
233C22⋊C8—291no—
234C4×C8—291no—
235C29#335411yescharacteristic, complemented, Sylow
236#41—1164no—
237C2×Q8—581no—
238C2×Q8—581no—
239C2×D4—21no—
240C2×D4—21no—
241C2×D4—291no—
242C2×D4—581no—
243C2×D4—581no—
244C2×D4C22×D2911yescharacteristic
245C2×D4C22×D2911yescharacteristic
246C22×C4—291no—
247C22×C4—581no—
248C22×C4—581no—
249C22×C4—581no—
250C22×C4—581no—
251C22×C4C22×D2911yescharacteristic
252D8—22no—
253M16—22no—
254M16—582no—
255C2×C8—291no—
256C2×C8—291no—
257C2×C8C22×D2911yescharacteristic
258C2×C8C22×D2911yescharacteristic
259C4⋊C4—291no—
260C4⋊C4—291no—
261C4⋊C4—291no—
262C4⋊C4—291no—
263C4⋊C4—291no—
264C4⋊C4—581no—
265C4⋊C4—581no—
266C4⋊C4—581no—
267C4⋊C4—581no—
268C4⋊C4C22×D2911yescharacteristic
269C4⋊C4C22×D2911yescharacteristic
270C22⋊C4—21no—
271C22⋊C4—21no—
272C22⋊C4—291no—
273C22⋊C4—291no—
274C22⋊C4—581no—
275C22⋊C4—581no—
276C22⋊C4—581no—
277C22⋊C4—581no—
278C22⋊C4—581no—
279C22⋊C4—581no—
280C42—291no—
281C42—581no—
282C42—581no—
283C23—21no—
284C23—21no—
285C23—291no—
286C23D4×D2911yescharacteristic
287Q8—1162no—
288Q8—2321no—
289D4—21no—
290D4—21no—
291D4—21no—
292D4—21no—
293D4—42no—
294D4—81no—
295D4—582no—
296D4—1162no—
297D4—2321no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—291no—
303C2×C4—291no—
304C2×C4—291no—
305C2×C4—581no—
306C2×C4—581no—
307C2×C4—581no—
308C2×C4—581no—
309C2×C4—581no—
310C2×C4—581no—
311C2×C4—1162no—
312C2×C4—1162no—
313C2×C4—1162no—
314C2×C4—1162no—
315C2×C4D4×D2911yescharacteristic
316C2×C4C23×D2911yescharacteristic
317C8—21no—
318C8—581no—
319C8—581no—
320C8#9080712yescomplemented
321C22—21no—
322C22—21no—
323C22—21no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—581no—
331C22—581no—
332C22—581no—
333C22C2×D4×D2911yescharacteristic
334C4—21no—
335C4—41no—
336C4—41no—
337C4—292no—
338C4—581no—
339C4—581no—
340C4—1161no—
341C4—1161no—
342C4—1161no—
343C4—1161no—
344C4C2×#9080711yescharacteristic
345C4#1174536511yescharacteristic
346C2—41no—
347C2—81no—
348C2—81no—
349C2—1161no—
350C2#1427181311yescharacteristic
351C2AGL(1,ℤ/8)×D2911yescharacteristic
352C2#1427197311yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#469C2
socleC22×C29C22×D4
hypercenter#469D29
hypocenterC29#3354
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #14271877C2semidirect
2. #14271813C2semidirect
3. #14271560C2semidirect
4. #14271485C2semidirect
5. #14271484C2semidirect
6. #14271480C2semidirect
7. #14271479C2semidirect
8. #14271451C2semidirect
9. #14271441C2semidirect
10. #14271413C2semidirect
11. D8×Dic29C2semidirect
12. #14271239C2semidirect
13. #14271205C2semidirect
14. #14271202C2semidirect
15. C29×#469C2semidirect
141. C8×C29#41semidirect
180. #469D29semidirect
235. C29#3354semidirect
320. C8#90807semidirect

Maximal subgroups

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

subgroupindex
#142718772
#142718132
#142715602
#142714852
#142714842
#142714802
#142714792
#142714512
#142714412
#142714132
D8×Dic292
#142712392
#142712052
#142712022
C29×#4692
#335429