Finite Group Databasebeta

← #16831384

Subgroups — #16831384

Order 3712.

386 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271854C211yesmaximal, characteristic, complemented
2#14271825C211yesmaximal, characteristic
3#14271518C211yesmaximal, characteristic, complemented
4#14271506C211yesmaximal, characteristic, complemented
5#14271478C211yesmaximal, characteristic, complemented
6#14271470C211yesmaximal, characteristic, complemented
7#14271403C211yesmaximal, characteristic, complemented
8#14271395C211yesmaximal, characteristic, complemented
9#14271385C211yesmaximal, characteristic, complemented
10#14271324C211yesmaximal, characteristic, complemented
11#14271317C211yesmaximal, characteristic, complemented
12C8×D116C211yesmaximal, characteristic, complemented
13#14271158C211yesmaximal, characteristic, complemented
14#103×D29C211yesmaximal, characteristic, complemented
15C4×Q16×C29C211yesmaximal, characteristic, complemented
16C2×#90809C2211yescharacteristic
17C2×Q8×D29C2211yescharacteristic
18C2×Q16×C29C2211yescharacteristic
19C4×Q8×C29C2211yescharacteristic
20C4×Q8×C29C2211yescharacteristic
21#11745308C2211yescharacteristic
22#11745308C2211yescharacteristic
23C2×#90785C2211yescharacteristic
24C2×#90784C2211yescharacteristic
25C2×C8×D29C2211yescharacteristic
26C2×C8×D29C2211yescharacteristic
27#11745259—21no—
28#11745259C2211yescharacteristic
29#11745257—21no—
30#11745257C2211yescharacteristic
31#11745256—21no—
32#11745254C2211yescharacteristic
33C4⋊C4×D29C2211yescharacteristic
34#11745251—21no—
35#11745238—21no—
36#11745237—21no—
37#11745237C2211yescharacteristic
38C4×D116—21no—
39C4×D116C2211yescharacteristic
40#11745234—21no—
41#11745232C2211yescharacteristic
42C29×#107C2211yescharacteristic
43C29×#103C2211yescharacteristic
44C29×#103C2211yescharacteristic
45C4×C8×C29C2211yescharacteristic
46#11745183C2211yescharacteristic
47#11745183C2211yescharacteristic
48#11745169C2211yescharacteristic
49#11745169C2211yescharacteristic
50#11745168C2211yescharacteristic
51#11745168C2211yescharacteristic
52#11745164C2211yescharacteristic
53#11745164C2211yescharacteristic
54#11745158C2211yescharacteristic
55#11745157C2211yescharacteristic
56#11745156C2211yescharacteristic
57#11745155C2211yescharacteristic
58C4⋊#6597C2211yescharacteristic
59C2×Q8×C29C2311yescharacteristic
60C2×Q8×C29C2311yescharacteristic
61#90809—22no—
62#90809—41no—
63Q8×D29—22no—
64Q8×D29—41no—
65C2×D116—21no—
66C2×D116—21no—
67C2×D116D411yescharacteristic
68C2×D116C2311yescharacteristic
69C2×C4×D29—21no—
70C2×C4×D29—21no—
71C2×C4×D29—21no—
72C2×C4×D29C2311yescharacteristic
73C2×C4×D29C2311yescharacteristic
74C2×Dic58—21no—
75C2×Dic58C2311yescharacteristic
76Q16×C29—22no—
77C2×C8×C29C2311yescharacteristic
78C2×C8×C29C2311yescharacteristic
79C4⋊C4×C29—21no—
80C4⋊C4×C29—21no—
81C4⋊C4×C29C2311yescharacteristic
82C4⋊C4×C29C2311yescharacteristic
83C42×C29—21no—
84C42×C29—21no—
85C42×C29C2311yescharacteristic
86#90785—41no—
87#90784—41no—
88#90781—21no—
89#90781—21no—
90#90781—21no—
91#90781—21no—
92#90781—21no—
93#90781—21no—
94#90781—21no—
95#90781D411yescharacteristic
96#90781D411yescharacteristic
97C4⋊Dic29—21no—
98C4⋊Dic29D411yescharacteristic
99C4⋊Dic29C2311yescharacteristic
100C4⋊Dic29C2311yescharacteristic
101#90779—21no—
102#90779—21no—
103#90779—21no—
104#90779—21no—
105#90779—21no—
106C4×Dic29—21no—
107C2×#6597C2311yescharacteristic
108C2×#6597C2311yescharacteristic
109C8×D29—41no—
110C8×D29—41no—
111C22×D29—21no—
112C22×D29C2×D411yescharacteristic
113C22×D29C2×D411yescharacteristic
114Q8×C29—21no—
115Q8×C29—21no—
116Q8×C29—21no—
117Q8×C29#4112yes—
118C2×C4×C29—21no—
119C2×C4×C29—21no—
120C2×C4×C29—21no—
121C2×C4×C29—21no—
122C2×C4×C29C2×D411yescharacteristic
123C2×C4×C29C2×D411yescharacteristic
124C2×C4×C29C2411yescharacteristic
125C2×Dic29—21no—
126C2×Dic29—21no—
127C2×Dic29—21no—
128C2×Dic29C2×D411yescharacteristic
129C2×Dic29C2×D411yescharacteristic
130D116—22no—
131D116—21no—
132D116—21no—
133D116—42no—
134D116—42no—
135C4×D29—21no—
136C4×D29—21no—
137C4×D29—21no—
138C4×D29—21no—
139C4×D29—42no—
140C4×D29—42no—
141C4×D29—42no—
142Dic58—21no—
143Dic58—21no—
144Dic58—42no—
145C8×C29—21no—
146C8×C29—21no—
147#6597—21no—
148#6597—21no—
149#3300—291nomaximal, Sylow
150C22×C29C22×D411yescharacteristic
151C2×D29—21no—
152C2×D29—21no—
153C2×D29—21no—
154C2×D29—21no—
155C2×D29—21no—
156C2×D29—41no—
157C2×D29—41no—
158C2×D29—41no—
159C2×D29#13512yes—
160C4×C29—22no—
161C4×C29—21no—
162C4×C29—21no—
163C4×C29—41no—
164C4×C29—41no—
165C4×C29—41no—
166C4×C29C2×#4111yescharacteristic
167C4×C29H(5,𝔽2)11yescharacteristic
168Dic29—21no—
169Dic29—21no—
170Dic29—41no—
171Dic29—41no—
172Dic29—41no—
173#552—291no—
174#548—291no—
175#488—291no—
176#485—291no—
177#480—291no—
178#479—291no—
179#467—291no—
180#465—291no—
181#464—291no—
182#452—291no—
183#451—291no—
184C4×Q16D2911yescharacteristic, complemented
185C8×D4—291no—
186#416—291no—
187C2×#103—291no—
188C2×C29#54611yescharacteristic
189C2×C29C2×#13511yescharacteristic
190C2×C29#57811yescharacteristic
191D29—22no—
192D29—41no—
193D29—81no—
194C2×#41—291no—
195C22×Q8—291no—
196C2×Q16—291no—
197C2×Q16C2×D2911yescharacteristic
198C2×SD16—291no—
199C22×C8—291no—
200C22×C8—291no—
201#126—581no—
202#125—291no—
203#125—581no—
204#124—291no—
205#124—581no—
206#123—581no—
207C22⋊Q8—291no—
208C22⋊Q8—291no—
209C22⋊Q8—291no—
210C22⋊Q8—581no—
211#121—291no—
212#121—581no—
213C4×Q8C2×D2911yescharacteristic
214C4×Q8C2×D2911yescharacteristic
215C4×D4—291no—
216C4×D4—581no—
217#117—291no—
218#117—581no—
219C2×C4⋊C4—291no—
220#107—291no—
221#107C2×D2911yescharacteristic
222#106—291no—
223C4⋊C8—291no—
224#103—291no—
225#103—291no—
226#103—291no—
227#103—291no—
228#103—291no—
229#103C2×D2911yescharacteristic
230#103C2×D2911yescharacteristic
231#102—291no—
232#102—291no—
233#102—291no—
234C22⋊C8—291no—
235C22⋊C8—291no—
236C4×C8C2×D2911yescharacteristic
237C29#330011yescharacteristic, complemented, Sylow
238#41—582no—
239#41—1161no—
240C2×Q8—291no—
241C2×Q8—581no—
242C2×Q8—582no—
243C2×Q8—1161no—
244C2×Q8C22×D2911yescharacteristic
245C2×Q8C22×D2911yescharacteristic
246C2×D4—291no—
247C2×D4—291no—
248C2×D4—581no—
249C2×D4—581no—
250C22×C4—291no—
251C22×C4—291no—
252C22×C4—581no—
253C22×C4—581no—
254C22×C4—581no—
255Q16—22no—
256Q16—1161no—
257SD16—1161no—
258C2×C8—291no—
259C2×C8—291no—
260C2×C8—1161no—
261C2×C8—1161no—
262C2×C8C22×D2911yescharacteristic
263C2×C8C22×D2911yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—291no—
267C4⋊C4—291no—
268C4⋊C4—291no—
269C4⋊C4—581no—
270C4⋊C4—581no—
271C4⋊C4—581no—
272C4⋊C4—581no—
273C4⋊C4—581no—
274C4⋊C4—581no—
275C4⋊C4C22×D2911yescharacteristic
276C4⋊C4C22×D2911yescharacteristic
277C22⋊C4—291no—
278C22⋊C4—291no—
279C22⋊C4—581no—
280C22⋊C4—581no—
281C22⋊C4—581no—
282C22⋊C4—581no—
283C22⋊C4—581no—
284C22⋊C4—581no—
285C22⋊C4—581no—
286C42—21no—
287C42—21no—
288C42—581no—
289C42C22×D2911yescharacteristic
290C23—291no—
291C23—291no—
292C23—581no—
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—581no—
297Q8—581no—
298Q8—1162no—
299Q8#9080512yes—
300D4—582no—
301D4—581no—
302D4—581no—
303D4—1162no—
304D4—1162no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—291no—
310C2×C4—291no—
311C2×C4—581no—
312C2×C4—581no—
313C2×C4—581no—
314C2×C4—581no—
315C2×C4—581no—
316C2×C4—581no—
317C2×C4—581no—
318C2×C4—1162no—
319C2×C4—1162no—
320C2×C4—1162no—
321C2×C4D4×D2911yescharacteristic
322C2×C4D4×D2911yescharacteristic
323C2×C4C23×D2911yescharacteristic
324C8—21no—
325C8—21no—
326C8—581no—
327C8—581no—
328C22—292no—
329C22—581no—
330C22—581no—
331C22—581no—
332C22—581no—
333C22—581no—
334C22—1161no—
335C22—1161no—
336C22—1161no—
337C22C2×D4×D2911yescharacteristic
338C4—22no—
339C4—21no—
340C4—21no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—581no—
345C4—581no—
346C4—1161no—
347C4—1161no—
348C4—1161no—
349C4C2×#9080511yescharacteristic
350C4#1174536411yescharacteristic
351C2—582no—
352C2—1161no—
353C2—2321no—
354C2#1427180911yescharacteristic
355C2#135×D2911yescharacteristic
356C2#1427197611yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC4×Q16×C29C2
socleC22×C29C22×D4
prime radical#14271825C2
hypercenterC4×Q16D29
hypocenterC29#3300
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
1. #14271854C2semidirect
3. #14271518C2semidirect
4. #14271506C2semidirect
5. #14271478C2semidirect
6. #14271470C2semidirect
7. #14271403C2semidirect
8. #14271395C2semidirect
9. #14271385C2semidirect
10. #14271324C2semidirect
11. #14271317C2semidirect
12. C8×D116C2semidirect
13. #14271158C2semidirect
14. #103×D29C2semidirect
15. C4×Q16×C29C2semidirect
184. C4×Q16D29semidirect
237. C29#3300semidirect

Maximal subgroups

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

subgroupindex
#142718542
#142718252
#142715182
#142715062
#142714782
#142714702
#142714032
#142713952
#142713852
#142713242
#142713172
C8×D1162
#142711582
#103×D292
C4×Q16×C292
#330029