Finite Group Databasebeta

← #16829662

Subgroups — #16829662

Order 3712.

386 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271692C211yesmaximal, characteristic
2C4×Q8×D29C211yesmaximal, characteristic, complemented
3#14271497C211yesmaximal, characteristic, complemented
4#14271480C211yesmaximal, characteristic
5#14271471C211yesmaximal, characteristic, complemented
6#14271470C211yesmaximal, characteristic, complemented
7#14271382C211yesmaximal, characteristic, complemented
8#14271317C211yesmaximal, characteristic, complemented
9#14271300C211yesmaximal, characteristic
10#14271270C211yesmaximal, characteristic, complemented
11#14271267C211yesmaximal, characteristic, complemented
12#14271264C211yesmaximal, characteristic, complemented
13#14271260C211yesmaximal, characteristic, complemented
14#14271219C211yesmaximal, characteristic, complemented
15C29×#464C211yesmaximal, characteristic, complemented
16C2×Q8×D29C2211yescharacteristic
17C2×Q16×C29C2211yescharacteristic
18C2×SD16×C29C2211yescharacteristic
19C29×#124C2211yescharacteristic
20C4×Q8×C29C2211yescharacteristic
21#11745308C2211yescharacteristic
22Q8×Dic29C2211yescharacteristic
23Q8×Dic29C2211yescharacteristic
24C2×#90785C2211yescharacteristic
25#11745300C2211yescharacteristic
26D4×Dic29C2211yescharacteristic
27C2×#90783C2211yescharacteristic
28C4⋊C4×D29—21no—
29C4⋊C4×D29C2211yescharacteristic
30#11745249—21no—
31#11745249C2211yescharacteristic
32#11745245—21no—
33#11745243—21no—
34#11745241—21no—
35#11745239—21no—
36C42×D29—21no—
37C42×D29C2211yescharacteristic
38#11745232C2211yescharacteristic
39C4×Dic58—21no—
40C4×Dic58C2211yescharacteristic
41C29×C4⋊C8C2211yescharacteristic
42C29×#103C2211yescharacteristic
43C29×#102C2211yescharacteristic
44#11745183C2211yescharacteristic
45#11745183C2211yescharacteristic
46#11745183C2211yescharacteristic
47#11745180C2211yescharacteristic
48#11745168C2211yescharacteristic
49#11745168C2211yescharacteristic
50#11745166C2211yescharacteristic
51#11745165C2211yescharacteristic
52#11745164C2211yescharacteristic
53#11745164C2211yescharacteristic
54#11745163C2211yescharacteristic
55#11745163C2211yescharacteristic
56#11745156C2211yescharacteristic
57#11745155C2211yescharacteristic
58C4⋊#6597C2211yescharacteristic
59C2×Q8×C29C2311yescharacteristic
60C2×Q8×C29C2311yescharacteristic
61C2×D4×C29C2311yescharacteristic
62C2×C22⋊D29—21no—
63C22×Dic29—21no—
64Q8×D29—22no—
65Q8×D29—22no—
66C2×C4×D29—21no—
67C2×C4×D29—21no—
68C2×C4×D29D411yescharacteristic
69C2×C4×D29D411yescharacteristic
70C2×C4×D29C2311yescharacteristic
71C2×Dic58—21no—
72C2×Dic58C2311yescharacteristic
73Q16×C29—22no—
74SD16×C29—22no—
75C2×C8×C29C2311yescharacteristic
76C2×C8×C29C2311yescharacteristic
77C4⋊C4×C29—21no—
78C4⋊C4×C29C2311yescharacteristic
79C22⋊C4×C29—21no—
80C22⋊C4×C29—21no—
81C42×C29—21no—
82C42×C29C2311yescharacteristic
83C22⋊Dic29—21no—
84C22⋊Dic29—21no—
85#90785—22no—
86#90783—22no—
87#90781—21no—
88C4⋊Dic29—21no—
89C4⋊Dic29—21no—
90C4⋊Dic29C2311yescharacteristic
91C4⋊Dic29C2311yescharacteristic
92C4⋊Dic29C2311yescharacteristic
93#90779—21no—
94#90779—21no—
95#90779—21no—
96#90779—21no—
97#90779—21no—
98#90779—21no—
99C4×Dic29—21no—
100C4×Dic29—21no—
101C4×Dic29—21no—
102C4×Dic29—21no—
103C4×Dic29D411yescharacteristic
104C4×Dic29D411yescharacteristic
105C4×Dic29C2311yescharacteristic
106C2×#6597C2311yescharacteristic
107C2×#6597C2311yescharacteristic
108C23×C29—21no—
109C22×D29C2×D411yescharacteristic
110Q8×C29—21no—
111Q8×C29—21no—
112Q8×C29—21no—
113Q8×C29#4112yes—
114D4×C29—21no—
115D4×C29—21no—
116C2×C4×C29—21no—
117C2×C4×C29—21no—
118C2×C4×C29—21no—
119C2×C4×C29C2×D411yescharacteristic
120C2×C4×C29C2×D411yescharacteristic
121C2×C4×C29C2411yescharacteristic
122C22⋊D29—42no—
123C2×Dic29—21no—
124C2×Dic29—21no—
125C2×Dic29—21no—
126C2×Dic29—21no—
127C2×Dic29—42no—
128C2×Dic29C2×D411yescharacteristic
129C2×Dic29C2×D411yescharacteristic
130C2×Dic29C2×D411yescharacteristic
131C4×D29—24no—
132C4×D29—22no—
133C4×D29—21no—
134C4×D29—21no—
135C4×D29—41no—
136C4×D29—42no—
137Dic58—24no—
138Dic58—21no—
139Dic58#4112yes—
140C8×C29—21no—
141C8×C29—21no—
142#6597—21no—
143#6597—21no—
144#3117—291nomaximal, Sylow
145C22×C29—41no—
146C22×C29—41no—
147C22×C29—41no—
148C22×C29C22×D411yescharacteristic
149C2×D29—21no—
150C2×D29—21no—
151C2×D29#13712yes—
152C4×C29—22no—
153C4×C29—21no—
154C4×C29—21no—
155C4×C29—41no—
156C4×C29—41no—
157C4×C29C2×#4111yescharacteristic
158C4×C29C2×#4111yescharacteristic
159Dic29—21no—
160Dic29—22no—
161Dic29—21no—
162Dic29—21no—
163Dic29—41no—
164Dic29—41no—
165Dic29—41no—
166#529—291no—
167C2×C4×Q8—291no—
168#484—291no—
169#481—291no—
170#479—291no—
171#479—291no—
172#464—291no—
173#464D2911yescharacteristic, complemented
174#451—291no—
175#448—291no—
176#441—291no—
177#441—291no—
178#440—291no—
179#440—291no—
180#432—291no—
181C2×C29—81no—
182C2×C29#52511yescharacteristic
183C2×C29C2×#13711yescharacteristic
184C2×C29#57511yescharacteristic
185D29—22no—
186C22×Q8—291no—
187C2×Q16—291no—
188C2×Q16C2×D2911yescharacteristic
189C2×SD16—291no—
190C2×SD16C2×D2911yescharacteristic
191#126—581no—
192#125—291no—
193#124C2×D2911yescharacteristic
194#123—581no—
195C22⋊Q8—291no—
196#121—291no—
197C4×Q8—291no—
198C4×Q8—291no—
199C4×Q8—291no—
200C4×Q8—291no—
201C4×Q8—581no—
202C4×Q8—581no—
203C4×Q8C2×D2911yescharacteristic
204C4×D4—291no—
205C4×D4—581no—
206#117—581no—
207C2×C4⋊C4—291no—
208C2×C4⋊C4—581no—
209C2×C42—291no—
210C2×C42—581no—
211#107—291no—
212#107—291no—
213#106—291no—
214#106—291no—
215C4⋊C8—291no—
216C4⋊C8C2×D2911yescharacteristic
217#103—291no—
218#103—291no—
219#103—291no—
220#103—291no—
221#103—291no—
222#103C2×D2911yescharacteristic
223#102—291no—
224#102C2×D2911yescharacteristic
225C22⋊C8—291no—
226C22⋊C8—291no—
227#97—291no—
228#97—291no—
229C29#311711yescharacteristic, complemented, Sylow
230C2×Q8—291no—
231C2×Q8—581no—
232C2×Q8—582no—
233C2×Q8—582no—
234C2×Q8C22×D2911yescharacteristic
235C2×Q8C22×D2911yescharacteristic
236C2×D4—581no—
237C2×D4C22×D2911yescharacteristic
238C22×C4—291no—
239C22×C4—291no—
240C22×C4—291no—
241C22×C4—581no—
242C22×C4—581no—
243C22×C4—581no—
244Q16—22no—
245Q16—582no—
246SD16—22no—
247SD16—582no—
248C2×C8—291no—
249C2×C8—291no—
250C2×C8C22×D2911yescharacteristic
251C2×C8C22×D2911yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—291no—
254C4⋊C4—291no—
255C4⋊C4—291no—
256C4⋊C4—581no—
257C4⋊C4—581no—
258C4⋊C4—581no—
259C4⋊C4—581no—
260C4⋊C4—581no—
261C4⋊C4—581no—
262C4⋊C4—581no—
263C4⋊C4—581no—
264C4⋊C4C22×D2911yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—581no—
268C22⋊C4—581no—
269C22⋊C4—581no—
270C42—21no—
271C42—291no—
272C42—291no—
273C42—291no—
274C42—581no—
275C42—581no—
276C42—581no—
277C42—581no—
278C42C22×D2911yescharacteristic
279C23—21no—
280C23—291no—
281Q8—21no—
282Q8—21no—
283Q8—21no—
284Q8—292no—
285Q8—584no—
286Q8—581no—
287Q8#9080712yes—
288D4—21no—
289D4—21no—
290D4—1162no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—291no—
295C2×C4—291no—
296C2×C4—291no—
297C2×C4—582no—
298C2×C4—584no—
299C2×C4—581no—
300C2×C4—581no—
301C2×C4—581no—
302C2×C4—581no—
303C2×C4—581no—
304C2×C4—581no—
305C2×C4—1161no—
306C2×C4—1162no—
307C2×C4—1162no—
308C2×C4D4×D2911yescharacteristic
309C2×C4D4×D2911yescharacteristic
310C2×C4C23×D2911yescharacteristic
311C8—21no—
312C8—21no—
313C8—581no—
314C8—581no—
315C22—41no—
316C22—41no—
317C22—41no—
318C22—292no—
319C22—581no—
320C22—581no—
321C22C2×D4×D2911yescharacteristic
322C4—22no—
323C4—21no—
324C4—21no—
325C4—41no—
326C4—41no—
327C4—581no—
328C4—582no—
329C4—581no—
330C4—581no—
331C4—1161no—
332C4—1161no—
333C4—1161no—
334C4C2×#9080711yescharacteristic
335C4#41×D2911yescharacteristic
336C2—81no—
337C2—582no—
338C2#1427167311yescharacteristic
339C2#137×D2911yescharacteristic
340C2#1427196011yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#464C2
socleC22×C29C22×D4
prime radical#11745300C22
hypercenter#464D29
hypocenterC29#3117
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
2. C4×Q8×D29C2semidirect
3. #14271497C2semidirect
5. #14271471C2semidirect
6. #14271470C2semidirect
7. #14271382C2semidirect
8. #14271317C2semidirect
10. #14271270C2semidirect
11. #14271267C2semidirect
12. #14271264C2semidirect
13. #14271260C2semidirect
14. #14271219C2semidirect
15. C29×#464C2semidirect
173. #464D29semidirect
229. C29#3117semidirect

Maximal subgroups

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

subgroupindex
#142716922
C4×Q8×D292
#142714972
#142714802
#142714712
#142714702
#142713822
#142713172
#142713002
#142712702
#142712672
#142712642
#142712602
#142712192
C29×#4642
#311729