Finite Group Databasebeta

← #16833108

Subgroups — #16833108

Order 3712.

1094 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271889C211yesmaximal, characteristic, complemented
2#14271882C213yesmaximal, complemented
3#14271853C213yesmaximal, complemented
4#14271847C213yesmaximal, complemented
5Q8×C22⋊D29C211yesmaximal, characteristic, complemented
6#14271820C211yesmaximal, characteristic, complemented
7#14271813C213yesmaximal, complemented
8#14271715C213yesmaximal, complemented
9#14271694C213yesmaximal, complemented
10#14271692C213yesmaximal, complemented
11#41×Dic29C211yesmaximal, characteristic, complemented
12C4×#90807C213yesmaximal, complemented
13C2×Q8×Dic29C211yesmaximal, characteristic, complemented
14C4×Q8×D29C211yesmaximal, characteristic, complemented
15C29×#548C211yesmaximal, characteristic, complemented
16C2×#41×C29C2211yescharacteristic
17C22×Q8×C29C2211yescharacteristic
18C2×Q8×D29C2211yescharacteristic
19C2×#90807C2213yes—
20C29×#124C2213yes—
21C29×C22⋊Q8C2213yes—
22C29×#121C2213yes—
23C4×Q8×C29C2211yescharacteristic
24C4×D4×C29C2213yes—
25#11745308C2213yes—
26Q8×Dic29C2211yescharacteristic
27Q8×Dic29C2211yescharacteristic
28Q8×Dic29C2213yes—
29Q8×Dic29C2211yescharacteristic
30Q8×Dic29C2213yes—
31#11745306C2213yes—
32#11745300C2213yes—
33#11745298C2213yes—
34#11745297C2216yes—
35D4×Dic29C2213yes—
36D4×Dic29C2213yes—
37D4×Dic29C2213yes—
38C4×C22⋊D29C2213yes—
39C4×C22⋊D29C2213yes—
40#11745288C2213yes—
41C2×C4⋊Dic29C2213yes—
42#11745286C2213yes—
43#11745286C2213yes—
44C2×C4×Dic29C2213yes—
45C2×C4×Dic29C2213yes—
46#11745254C2213yes—
47C4⋊C4×D29C2213yes—
48#11745252C2213yes—
49#11745251C2216yes—
50#11745250C2213yes—
51#11745249C2213yes—
52#11745249C2213yes—
53#11745245C2216yes—
54#11745243C2211yescharacteristic
55#11745243C2213yes—
56#11745241C2216yes—
57#11745241C2216yes—
58#11745240C2216yes—
59#11745239C2213yes—
60#11745239C2213yes—
61#11745239C2216yes—
62C42×D29C2213yes—
63#11745232C2213yes—
64C4×Dic58C2213yes—
65C4×Dic58C2213yes—
66#41×C29—24no—
67C2×Q8×C29—24no—
68C2×Q8×C29C2313yes—
69C2×Q8×C29C2311yescharacteristic
70C2×D4×C29C2313yes—
71C2×D4×C29C2313yes—
72C22×C4×C29C2313yes—
73C22×C4×C29C2313yes—
74C2×C22⋊D29C2313yes—
75C2×C22⋊D29C2311yescharacteristic
76C22×Dic29C2311yescharacteristic
77C22×Dic29C2313yes—
78C22×Dic29C2313yes—
79C22×Dic29C2313yes—
80Q8×D29—24no—
81#90807—212no—
82C2×C4×D29C2313yes—
83C2×C4×D29C2313yes—
84C2×C4×D29C2311yescharacteristic
85C2×Dic58C2313yes—
86C2×Dic58C2313yes—
87C4⋊C4×C29C2313yes—
88C4⋊C4×C29C2313yes—
89C22⋊C4×C29C2311yescharacteristic
90C22⋊C4×C29C2313yes—
91C22⋊C4×C29C2316yes—
92C42×C29C2313yes—
93C22⋊Dic29C2313yes—
94C22⋊Dic29C2316yes—
95C22⋊Dic29C2316yes—
96C22⋊Dic29C2313yes—
97#90781C2311yescharacteristic
98#90781C2313yes—
99C4⋊Dic29C2313yes—
100C4⋊Dic29C2313yes—
101C4⋊Dic29C2313yes—
102C4⋊Dic29C2316yes—
103C4⋊Dic29C2313yes—
104#90779C2313yes—
105#90779C2316yes—
106#90779C2313yes—
107#90779C2316yes—
108#90779C2316yes—
109#90779C2311yescharacteristic
110#90779C2313yes—
111C4×Dic29C2311yescharacteristic
112C4×Dic29C2313yes—
113C4×Dic29C2313yes—
114C4×Dic29C2313yes—
115C4×Dic29C2313yes—
116C4×Dic29C2313yes—
117C4×Dic29C2313yes—
118C4×Dic29C2313yes—
119C4×Dic29C2313yes—
120C23×C29C2413yes—
121C23×C29C2411yescharacteristic
122C22×D29C2411yescharacteristic
123Q8×C29—26no—
124Q8×C29#4114yescomplemented
125D4×C29—26no—
126D4×C29—26no—
127C2×C4×C29—26no—
128C2×C4×C29—26no—
129C2×C4×C29C2411yescharacteristic
130C2×C4×C29C2411yescharacteristic
131C2×C4×C29C2413yes—
132C2×C4×C29C2413yes—
133C2×C4×C29C2413yes—
134C22⋊D29—26no—
135C22⋊D29#4114yescomplemented
136C2×Dic29—26no—
137C2×Dic29—26no—
138C2×Dic29—22no—
139C2×Dic29—26no—
140C2×Dic29C2411yescharacteristic
141C2×Dic29C2413yes—
142C2×Dic29C2413yes—
143C2×Dic29C2413yes—
144C2×Dic29C2413yes—
145C2×Dic29C2411yescharacteristic
146C2×Dic29C2411yescharacteristic
147C4×D29—26no—
148C4×D29—26no—
149C4×D29—22no—
150Dic58—26no—
151Dic58—26no—
152#3482—291nomaximal, Sylow
153C22×C29—21no—
154C22×C29—21no—
155C22×C29—23no—
156C22×C29—23no—
157C22×C29—23no—
158C22×C29C2×#4112yes—
159C22×C29C2511yescharacteristic
160C2×D29—21no—
161C2×D29—21no—
162C2×D29C2×#4112yes—
163C4×C29—23no—
164C4×C29—21no—
165C4×C29—23no—
166C4×C29—21no—
167C4×C29C2×#4116yes—
168Dic29—23no—
169Dic29—23no—
170Dic29—23no—
171Dic29—21no—
172Dic29—23no—
173Dic29C2×#4112yes—
174Dic292−1+412yes—
175#557—291no—
176#556—293no—
177#552—293no—
178#552—293no—
179D4×Q8—291no—
180#548—291no—
181#548D2911yescharacteristic, complemented
182#547—293no—
183#533—293no—
184#529—293no—
185#529—293no—
186C4×#41—291no—
187C4×#41—293no—
188C2×C4×Q8—291no—
189C2×C4×Q8—291no—
190C2×C29—22no—
191C2×C29—43no—
192C2×C29C22×#4111yescharacteristic
193C2×C29C22×#4111yescharacteristic
194C2×C29C2×2−1+411yescharacteristic
195D29—22no—
196C2×#41—293no—
197C2×#41C2×D2911yescharacteristic
198C22×Q8—291no—
199C22×Q8C2×D2911yescharacteristic
200C4⋊Q8—293no—
201C4⋊Q8—293no—
202#126—296no—
203#126—296no—
204#125—293no—
205#125—296no—
206#125—293no—
207#124—293no—
208#124C2×D2913yes—
209#123—296no—
210#123—296no—
211C22⋊Q8—293no—
212C22⋊Q8—293no—
213C22⋊Q8—293no—
214C22⋊Q8—296no—
215C22⋊Q8C2×D2913yes—
216#121—293no—
217#121C2×D2913yes—
218C4×Q8—291no—
219C4×Q8—293no—
220C4×Q8—291no—
221C4×Q8—293no—
222C4×Q8—291no—
223C4×Q8—293no—
224C4×Q8—293no—
225C4×Q8—293no—
226C4×Q8—293no—
227C4×Q8C2×D2911yescharacteristic
228C4×D4—293no—
229C4×D4—293no—
230C4×D4—293no—
231C4×D4—293no—
232C4×D4—293no—
233C4×D4—291no—
234C4×D4—293no—
235C4×D4C2×D2913yes—
236#117—293no—
237#117—293no—
238#117—293no—
239#117—293no—
240#117—296no—
241C2×C4⋊C4—293no—
242C2×C4⋊C4—293no—
243C2×C42—293no—
244C2×C42—293no—
245C2×C42—293no—
246C29#348211yescharacteristic, complemented, Sylow
247#41—24no—
248#41—5812no—
249C2×Q8—24no—
250C2×Q8—293no—
251C2×Q8—293no—
252C2×Q8—584no—
253C2×Q8C22×D2913yes—
254C2×Q8C22×D2911yescharacteristic
255C2×D4—291no—
256C2×D4—293no—
257C2×D4C22×D2913yes—
258C2×D4C22×D2913yes—
259C22×C4—291no—
260C22×C4—293no—
261C22×C4—293no—
262C22×C4—293no—
263C22×C4—291no—
264C22×C4—293no—
265C22×C4—293no—
266C22×C4C22×D2913yes—
267C22×C4C22×D2913yes—
268C4⋊C4—293no—
269C4⋊C4—293no—
270C4⋊C4—296no—
271C4⋊C4—296no—
272C4⋊C4—291no—
273C4⋊C4—293no—
274C4⋊C4—293no—
275C4⋊C4—293no—
276C4⋊C4—293no—
277C4⋊C4—293no—
278C4⋊C4—296no—
279C4⋊C4—296no—
280C4⋊C4C22×D2913yes—
281C4⋊C4C22×D2913yes—
282C22⋊C4—293no—
283C22⋊C4—296no—
284C22⋊C4—293no—
285C22⋊C4—296no—
286C22⋊C4—291no—
287C22⋊C4—293no—
288C22⋊C4C22×D2911yescharacteristic
289C22⋊C4C22×D2913yes—
290C22⋊C4C22×D2916yes—
291C42—291no—
292C42—293no—
293C42—293no—
294C42—293no—
295C42—293no—
296C42—293no—
297C42—293no—
298C42—293no—
299C42—293no—
300C42C22×D2913yes—
301C23—291no—
302C23C23×D2913yes—
303C23C23×D2911yescharacteristic
304Q8—26no—
305Q8—586no—
306Q8—586no—
307Q8#9080714yescomplemented
308D4—26no—
309D4—26no—
310D4—294no—
311D4—586no—
312C2×C4—26no—
313C2×C4—26no—
314C2×C4—291no—
315C2×C4—291no—
316C2×C4—291no—
317C2×C4—293no—
318C2×C4—293no—
319C2×C4—293no—
320C2×C4—293no—
321C2×C4—582no—
322C2×C4—586no—
323C2×C4—586no—
324C2×C4—582no—
325C2×C4—586no—
326C2×C4—586no—
327C2×C4—586no—
328C2×C4C23×D2911yescharacteristic
329C2×C4C23×D2911yescharacteristic
330C2×C4C23×D2913yes—
331C2×C4C23×D2913yes—
332C2×C4C23×D2913yes—
333C22—21no—
334C22—21no—
335C22—23no—
336C22—23no—
337C22—23no—
338C22—292no—
339C22—581no—
340C22—581no—
341C22#41×D2912yes—
342C22C24×D2911yescharacteristic
343C4—23no—
344C4—21no—
345C4—23no—
346C4—21no—
347C4—292no—
348C4—292no—
349C4—583no—
350C4—583no—
351C4—583no—
352C4—581no—
353C4—583no—
354C4C2×#9080716yes—
355C2—22no—
356C2—43no—
357C2—582no—
358C2C2×#41×D2911yescharacteristic
359C2C22×#9080711yescharacteristic
360C22−1+4×D2911yescharacteristic
subgroupG/H
center, FrattiniC22C24×D29
commutator, socle, cosocleC22×C29C25
FittingC29×#548C2
hypercenter#548D29
hypocenterC29#3482
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. #14271889C2semidirect
2. #14271882C2semidirect
3. #14271853C2semidirect
4. #14271847C2semidirect
5. Q8×C22⋊D29C2semidirect
6. #14271820C2semidirect
7. #14271813C2semidirect
8. #14271715C2semidirect
9. #14271694C2semidirect
10. #14271692C2semidirect
11. #41×Dic29C2semidirect
12. C4×#90807C2semidirect
13. C2×Q8×Dic29C2semidirect
14. C4×Q8×D29C2semidirect
15. C29×#548C2semidirect
124. Q8×C29#41semidirect
135. C22⋊D29#41semidirect
181. #548D29semidirect
246. C29#3482semidirect
307. Q8#90807semidirect

Maximal subgroups

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

subgroupindex
#142718892
#142718822
#142718532
#142718472
Q8×C22⋊D292
#142718202
#142718132
#142717152
#142716942
#142716922
#41×Dic292
C4×#908072
C2×Q8×Dic292
C4×Q8×D292
C29×#5482
#348229