Finite Group Databasebeta

← #16831413

Subgroups — #16831413

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#14271877C211yesmaximal, characteristic, complemented
2#14271812C211yesmaximal, characteristic, complemented
3#14271512C211yesmaximal, characteristic, complemented
4#14271505C211yesmaximal, characteristic, complemented
5#14271503C211yesmaximal, characteristic, complemented
6#14271451C211yesmaximal, characteristic, complemented
7#14271390C211yesmaximal, characteristic, complemented
8#14271389C211yesmaximal, characteristic, complemented
9#14271366C211yesmaximal, characteristic, complemented
10#14271305C211yesmaximal, characteristic, complemented
11D8×Dic29C211yesmaximal, characteristic, complemented
12#14271226C211yesmaximal, characteristic, complemented
13#14271159C211yesmaximal, characteristic, complemented
14#14271156C211yesmaximal, characteristic, complemented
15C29×#449C211yesmaximal, characteristic, complemented
16C2×#41×C29C2211yescharacteristic
17C2×#90807C2211yescharacteristic
18C2×SD16×C29C2211yescharacteristic
19C2×D8×C29C2211yescharacteristic
20C29×#121C2211yescharacteristic
21#11745308C2211yescharacteristic
22#11745306C2211yescharacteristic
23#11745301—21no—
24#11745301—21no—
25#11745300C2211yescharacteristic
26#11745298—21no—
27#11745297—21no—
28D4×Dic29C2211yescharacteristic
29D4×Dic29C2211yescharacteristic
30C2×#90783C2211yescharacteristic
31#11745291—21no—
32C4×C22⋊D29C2211yescharacteristic
33#11745288C2211yescharacteristic
34#11745286C2211yescharacteristic
35C2×#90779—21no—
36C22×#6597C2211yescharacteristic
37C2×C8×D29C2211yescharacteristic
38#11745254C2211yescharacteristic
39#11745250C2211yescharacteristic
40#11745247—21no—
41#11745239—21no—
42C29×#103C2211yescharacteristic
43C29×#102C2211yescharacteristic
44C29×C22⋊C8C2211yescharacteristic
45#11745183C2211yescharacteristic
46#11745183C2211yescharacteristic
47#11745180C2211yescharacteristic
48#11745180C2211yescharacteristic
49#11745180C2211yescharacteristic
50#11745168C2211yescharacteristic
51#11745166C2211yescharacteristic
52#11745165C2211yescharacteristic
53#11745164C2211yescharacteristic
54#11745164C2211yescharacteristic
55#11745162C2211yescharacteristic
56C8×Dic29C2211yescharacteristic
57#11745158C2211yescharacteristic
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⋊D29D411yescharacteristic
71C22×Dic29—21no—
72C22×Dic29—21no—
73C22×Dic29—21no—
74#90807—22no—
75#90807—41no—
76C2×C4×D29C2311yescharacteristic
77C2×Dic58—21no—
78C2×Dic58C2311yescharacteristic
79SD16×C29—41no—
80D8×C29—22no—
81C2×C8×C29C2311yescharacteristic
82C2×C8×C29C2311yescharacteristic
83C4⋊C4×C29C2311yescharacteristic
84C22⋊C4×C29—21no—
85C22⋊Dic29—21no—
86C22⋊Dic29—21no—
87C22⋊Dic29—21no—
88C22⋊Dic29—21no—
89C22⋊Dic29—21no—
90C22⋊Dic29D411yescharacteristic
91#90783—41no—
92#90781—21no—
93#90781—21no—
94#90781D411yescharacteristic
95C4⋊Dic29C2311yescharacteristic
96C4⋊Dic29C2311yescharacteristic
97C4⋊Dic29C2311yescharacteristic
98#90779—21no—
99#90779—21no—
100#90779—21no—
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×C29—21no—
113C23×C29C2×D411yescharacteristic
114C22×D29C2×D411yescharacteristic
115Q8×C29—21no—
116Q8×C29—21no—
117D4×C29—21no—
118D4×C29—21no—
119D4×C29—21no—
120D4×C29—42no—
121D4×C29—81no—
122D4×C29#4112yes—
123C2×C4×C29—21no—
124C2×C4×C29—21no—
125C2×C4×C29—21no—
126C2×C4×C29—21no—
127C2×C4×C29—42no—
128C2×C4×C29C2×D411yescharacteristic
129C2×C4×C29C2411yescharacteristic
130C22⋊D29—22no—
131C22⋊D29—42no—
132C22⋊D29—81no—
133C2×Dic29—21no—
134C2×Dic29—21no—
135C2×Dic29—21no—
136C2×Dic29—21no—
137C2×Dic29—42no—
138C2×Dic29—42no—
139C2×Dic29—42no—
140C2×Dic29C2×D411yescharacteristic
141C2×Dic29C2×D411yescharacteristic
142C2×Dic29C2×D411yescharacteristic
143C4×D29—21no—
144C4×D29—21no—
145Dic58—21no—
146Dic58—21no—
147Dic58—81no—
148C8×C29—21no—
149C8×C29—21no—
150#6597—21no—
151#6597—21no—
152#3303—291nomaximal, Sylow
153C22×C29—22no—
154C22×C29—21no—
155C22×C29—21no—
156C22×C29—21no—
157C22×C29—41no—
158C22×C29—41no—
159C22×C29—41no—
160C22×C29—41no—
161C22×C29—41no—
162C22×C29C22×D411yescharacteristic
163C2×D29—21no—
164C2×D29—21no—
165C2×D29—21no—
166C4×C29—21no—
167C4×C29—41no—
168C4×C29—41no—
169C4×C29C2×#4111yescharacteristic
170C4×C29H(5,𝔽2)11yescharacteristic
171Dic29—21no—
172Dic29—21no—
173Dic29—41no—
174Dic29—41no—
175Dic29—41no—
176Dic29—41no—
177Dic29#13512yes—
178#555—291no—
179#547—291no—
180#487—291no—
181#485—291no—
182#485—291no—
183#476—291no—
184#465—291no—
185#465—291no—
186#461—291no—
187#449—291no—
188#449D2911yescharacteristic, complemented
189C4×D8—291no—
190C8×D4—291no—
191#416—291no—
192#416—291no—
193C2×C29—41no—
194C2×C29—42no—
195C2×C29—81no—
196C2×C29#54611yescharacteristic
197C2×C29C2×#13511yescharacteristic
198C2×C29#57711yescharacteristic
199D29—41no—
200C2×#41—291no—
201C2×#41C2×D2911yescharacteristic
202C2×SD16—291no—
203C2×SD16C2×D2911yescharacteristic
204C2×D8C2×D2911yescharacteristic
205C22×C8—291no—
206C22×C8—291no—
207C4⋊Q8—291no—
208C4⋊Q8—291no—
209#124—581no—
210#124—581no—
211#123—581no—
212#123—581no—
213C22⋊Q8—291no—
214C22⋊Q8—291no—
215#121—291no—
216#121—581no—
217#121—581no—
218#121C2×D2911yescharacteristic
219C4×D4—291no—
220C4×D4—291no—
221C4×D4—291no—
222#117—291no—
223#117—291no—
224#117—581no—
225C2×C4⋊C4—581no—
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#103—291no—
235#103C2×D2911yescharacteristic
236#102—291no—
237#102—291no—
238#102—291no—
239#102C2×D2911yescharacteristic
240C22⋊C8—291no—
241C22⋊C8C2×D2911yescharacteristic
242C4×C8—291no—
243C29#330311yescharacteristic, complemented, Sylow
244#41—22no—
245#41—41no—
246#41—582no—
247#41—1161no—
248C2×Q8—291no—
249C2×Q8—581no—
250C2×Q8C22×D2911yescharacteristic
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—291no—
254C2×D4—581no—
255C2×D4—581no—
256C2×D4C22×D2911yescharacteristic
257C2×D4C22×D2911yescharacteristic
258C22×C4—21no—
259C22×C4—291no—
260C22×C4—581no—
261C22×C4—581no—
262C22×C4—581no—
263C22×C4C22×D2911yescharacteristic
264SD16—41no—
265SD16—1161no—
266D8—22no—
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—21no—
298C23—291no—
299C23D4×D2911yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—581no—
303Q8—581no—
304Q8—2321no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—42no—
309D4—81no—
310D4—582no—
311D4—1162no—
312D4—2321no—
313D4#9080712yes—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—42no—
319C2×C4—291no—
320C2×C4—291no—
321C2×C4—291no—
322C2×C4—581no—
323C2×C4—581no—
324C2×C4—581no—
325C2×C4—581no—
326C2×C4—581no—
327C2×C4—581no—
328C2×C4—1162no—
329C2×C4—1162no—
330C2×C4—1162no—
331C2×C4D4×D2911yescharacteristic
332C2×C4C23×D2911yescharacteristic
333C8—21no—
334C8—21no—
335C8—581no—
336C8—581no—
337C22—21no—
338C22—22no—
339C22—21no—
340C22—21no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—581no—
347C22—581no—
348C22—581no—
349C22C2×D4×D2911yescharacteristic
350C4—21no—
351C4—41no—
352C4—41no—
353C4—292no—
354C4—581no—
355C4—581no—
356C4—1161no—
357C4—1161no—
358C4—1161no—
359C4—1161no—
360C4C2×#9080711yescharacteristic
361C4#1174535911yescharacteristic
362C2—41no—
363C2—42no—
364C2—81no—
365C2—1161no—
366C2#1427180011yescharacteristic
367C2#135×D2911yescharacteristic
368C2#1427197311yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#449C2
socleC22×C29C22×D4
hypercenter#449D29
hypocenterC29#3303
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. #14271877C2semidirect
2. #14271812C2semidirect
3. #14271512C2semidirect
4. #14271505C2semidirect
5. #14271503C2semidirect
6. #14271451C2semidirect
7. #14271390C2semidirect
8. #14271389C2semidirect
9. #14271366C2semidirect
10. #14271305C2semidirect
11. D8×Dic29C2semidirect
12. #14271226C2semidirect
13. #14271159C2semidirect
14. #14271156C2semidirect
15. C29×#449C2semidirect
188. #449D29semidirect
243. C29#3303semidirect

Maximal subgroups

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

subgroupindex
#142718772
#142718122
#142715122
#142715052
#142715032
#142714512
#142713902
#142713892
#142713662
#142713052
D8×Dic292
#142712262
#142711592
#142711562
C29×#4492
#330329