Finite Group Databasebeta

← #16833082

Subgroups — #16833082

Order 3712.

1112 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271895C213yesmaximal, complemented
2#14271889C211yesmaximal, characteristic, complemented
3#14271884C213yesmaximal, complemented
4#14271865C213yesmaximal, complemented
5#14271859C213yesmaximal, complemented
6#14271832C211yesmaximal, characteristic, complemented
7#14271824C211yesmaximal, characteristic, complemented
8#14271708C213yesmaximal, complemented
9#14271699C213yesmaximal, complemented
10#14271692C213yesmaximal, complemented
11#41×Dic29C211yesmaximal, characteristic, complemented
12C4×#90809C211yesmaximal, characteristic, complemented
13C4×#90807C213yesmaximal, complemented
14C2×Q8×Dic29C211yesmaximal, characteristic, complemented
15C29×#548C211yesmaximal, characteristic, complemented
16C2×#41×C29C2211yescharacteristic
17C22×Q8×C29C2211yescharacteristic
18C2×#90809C2211yescharacteristic
19C2×#90807C2213yes—
20C29×#124C2213yes—
21C29×C22⋊Q8C2213yes—
22C29×#121C2213yes—
23C4×Q8×C29C2211yescharacteristic
24C4×D4×C29C2213yes—
25#11745309C2213yes—
26#11745308C2213yes—
27Q8×Dic29C2211yescharacteristic
28Q8×Dic29C2211yescharacteristic
29Q8×Dic29C2213yes—
30Q8×Dic29C2211yescharacteristic
31Q8×Dic29C2213yes—
32#11745302C2213yes—
33#11745301C2216yes—
34#11745300C2213yes—
35D4×Dic29C2213yes—
36D4×Dic29C2213yes—
37D4×Dic29C2213yes—
38#11745292C2213yes—
39#11745292C2213yes—
40C4×C22⋊D29C2213yes—
41C4×C22⋊D29C2213yes—
42#11745288C2213yes—
43C2×C4⋊Dic29C2213yes—
44C2×C4×Dic29C2213yes—
45C2×C4×Dic29C2213yes—
46#11745260C2216yes—
47#11745255C2213yes—
48#11745254C2213yes—
49#11745254C2213yes—
50#11745252C2213yes—
51#11745250C2213yes—
52#11745249C2213yes—
53#11745248C2216yes—
54#11745247C2216yes—
55#11745245C2216yes—
56#11745243C2213yes—
57#11745243C2213yes—
58#11745243C2216yes—
59#11745241C2216yes—
60#11745239C2211yescharacteristic
61#11745239C2213yes—
62C4×D116C2213yes—
63C42×D29C2213yes—
64#11745232C2213yes—
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⋊D29C2313yes—
76C2×C22⋊D29C2316yes—
77C22×Dic29C2313yes—
78C22×Dic29C2313yes—
79C22×Dic29C2313yes—
80C22×Dic29C2311yescharacteristic
81#90809—24no—
82#90807—212no—
83C2×D116C2313yes—
84C2×C4×D29C2313yes—
85C2×C4×D29C2313yes—
86C2×C4×D29C2313yes—
87C2×Dic58C2313yes—
88C4⋊C4×C29C2313yes—
89C4⋊C4×C29C2313yes—
90C22⋊C4×C29C2311yescharacteristic
91C22⋊C4×C29C2313yes—
92C22⋊C4×C29C2316yes—
93C42×C29C2313yes—
94C22⋊Dic29C2316yes—
95C22⋊Dic29C2311yescharacteristic
96C22⋊Dic29C2313yes—
97#90781C2313yes—
98#90781C2313yes—
99#90781C2316yes—
100#90781C2316yes—
101C4⋊Dic29C2313yes—
102C4⋊Dic29C2313yes—
103C4⋊Dic29C2316yes—
104C4⋊Dic29C2313yes—
105C4⋊Dic29C2313yes—
106#90779C2311yescharacteristic
107#90779C2313yes—
108#90779C2316yes—
109#90779C2311yescharacteristic
110#90779C2313yes—
111C4×Dic29C2311yescharacteristic
112C4×Dic29C2313yes—
113C4×Dic29C2313yes—
114C4×Dic29C2313yes—
115C4×Dic29C2313yes—
116C4×Dic29C2313yes—
117C4×Dic29C2313yes—
118C4×Dic29C2313yes—
119C4×Dic29C2311yescharacteristic
120C23×C29C2413yes—
121C23×C29C2411yescharacteristic
122C22×D29C2413yes—
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×C29C2413yes—
131C2×C4×C29C2411yescharacteristic
132C2×C4×C29C2413yes—
133C2×C4×C29C2413yes—
134C22⋊D29—26no—
135C22⋊D29—26no—
136C22⋊D29—46no—
137C2×Dic29—26no—
138C2×Dic29—43no—
139C2×Dic29—43no—
140C2×Dic29#4114yescomplemented
141C2×Dic29C2411yescharacteristic
142C2×Dic29C2411yescharacteristic
143C2×Dic29C2413yes—
144C2×Dic29C2413yes—
145C2×Dic29C2413yes—
146C2×Dic29C2411yescharacteristic
147C2×Dic29C2411yescharacteristic
148D116—26no—
149C4×D29—26no—
150C4×D29—26no—
151C4×D29—43no—
152Dic58—26no—
153#3480—291nomaximal, Sylow
154C22×C29—21no—
155C22×C29—21no—
156C22×C29—23no—
157C22×C29—23no—
158C22×C29—23no—
159C22×C29C2×#4112yes—
160C22×C29C2511yescharacteristic
161C2×D29—23no—
162C2×D29—23no—
163C2×D29—23no—
164C4×C29—23no—
165C4×C29—21no—
166C4×C29—23no—
167C4×C29—21no—
168C4×C29C2×#4116yes—
169Dic29—23no—
170Dic29—21no—
171Dic29—23no—
172Dic29—21no—
173Dic29—23no—
174Dic29C2×#4112yes—
175Dic29C2×#4112yes—
176#559—293no—
177#557—291no—
178#556—293no—
179#553—293no—
180#553—293no—
181#550—291no—
182#548—291no—
183#548D2911yescharacteristic, complemented
184#532—293no—
185#529—293no—
186#529—293no—
187C4×#41—291no—
188C4×#41—291no—
189C4×#41—293no—
190C2×C4×Q8—291no—
191C2×C29—22no—
192C2×C29—43no—
193C2×C29C22×#4111yescharacteristic
194C2×C29C22×#4111yescharacteristic
195C2×C29#58511yescharacteristic
196D29—43no—
197C2×#41—291no—
198C2×#41—293no—
199C2×#41C2×D2911yescharacteristic
200C22×Q8C2×D2911yescharacteristic
201C4⋊Q8—293no—
202#127—293no—
203#126—296no—
204#126—296no—
205#125—293no—
206#125—293no—
207#124—293no—
208#124—296no—
209#124C2×D2913yes—
210#123—296no—
211#123—296no—
212C22⋊Q8—293no—
213C22⋊Q8C2×D2913yes—
214#121—293no—
215#121—296no—
216#121—293no—
217#121—293no—
218#121C2×D2913yes—
219C4×Q8—291no—
220C4×Q8—293no—
221C4×Q8—291no—
222C4×Q8—293no—
223C4×Q8—291no—
224C4×Q8—293no—
225C4×Q8—293no—
226C4×Q8C2×D2911yescharacteristic
227C4×D4—293no—
228C4×D4—293no—
229C4×D4—293no—
230C4×D4—293no—
231C4×D4—293no—
232C4×D4—293no—
233C4×D4—293no—
234C4×D4—293no—
235C4×D4—296no—
236C4×D4—293no—
237C4×D4C2×D2913yes—
238#117—293no—
239#117—293no—
240#117—293no—
241#117—291no—
242#117—293no—
243C2×C4⋊C4—293no—
244C2×C42—293no—
245C2×C42—293no—
246C2×C42—293no—
247C29#348011yescharacteristic, complemented, Sylow
248#41—24no—
249#41—5812no—
250#41—584no—
251C2×Q8—24no—
252C2×Q8—293no—
253C2×Q8C22×D2913yes—
254C2×Q8C22×D2911yescharacteristic
255C2×D4—293no—
256C2×D4—293no—
257C2×D4—296no—
258C2×D4—293no—
259C2×D4C22×D2913yes—
260C2×D4C22×D2913yes—
261C22×C4—291no—
262C22×C4—293no—
263C22×C4—293no—
264C22×C4—293no—
265C22×C4—293no—
266C22×C4—293no—
267C22×C4—293no—
268C22×C4C22×D2913yes—
269C22×C4C22×D2913yes—
270C4⋊C4—293no—
271C4⋊C4—293no—
272C4⋊C4—296no—
273C4⋊C4—291no—
274C4⋊C4—291no—
275C4⋊C4—293no—
276C4⋊C4—293no—
277C4⋊C4—293no—
278C4⋊C4—293no—
279C4⋊C4—296no—
280C4⋊C4C22×D2913yes—
281C4⋊C4C22×D2913yes—
282C22⋊C4—291no—
283C22⋊C4—293no—
284C22⋊C4—296no—
285C22⋊C4—293no—
286C22⋊C4—296no—
287C22⋊C4—293no—
288C22⋊C4—296no—
289C22⋊C4C22×D2911yescharacteristic
290C22⋊C4C22×D2913yes—
291C22⋊C4C22×D2916yes—
292C42—291no—
293C42—291no—
294C42—293no—
295C42—293no—
296C42—293no—
297C42—293no—
298C42—293no—
299C42—293no—
300C42—293no—
301C42C22×D2913yes—
302C23—293no—
303C23C23×D2913yes—
304C23C23×D2911yescharacteristic
305Q8—26no—
306Q8—586no—
307Q8#9080714yescomplemented
308D4—26no—
309D4—26no—
310D4—586no—
311D4—586no—
312D4—586no—
313D4—1166no—
314C2×C4—26no—
315C2×C4—26no—
316C2×C4—294no—
317C2×C4—291no—
318C2×C4—291no—
319C2×C4—291no—
320C2×C4—293no—
321C2×C4—291no—
322C2×C4—293no—
323C2×C4—293no—
324C2×C4—586no—
325C2×C4—586no—
326C2×C4—586no—
327C2×C4—1163no—
328C2×C4—1163no—
329C2×C4—1163no—
330C2×C4C23×D2911yescharacteristic
331C2×C4C23×D2913yes—
332C2×C4C23×D2911yescharacteristic
333C2×C4C23×D2913yes—
334C2×C4C23×D2913yes—
335C22—21no—
336C22—21no—
337C22—23no—
338C22—23no—
339C22—23no—
340C22—583no—
341C22—583no—
342C22—583no—
343C22#41×D2912yes—
344C22C24×D2911yescharacteristic
345C4—21no—
346C4—23no—
347C4—21no—
348C4—23no—
349C4—292no—
350C4—292no—
351C4—583no—
352C4—581no—
353C4—583no—
354C4—583no—
355C4—581no—
356C4C2×#9080716yes—
357C2—22no—
358C2—43no—
359C2—1163no—
360C2C2×#41×D2911yescharacteristic
361C2C22×#9080711yescharacteristic
362C2#1427200011yescharacteristic
subgroupG/H
center, FrattiniC22C24×D29
commutator, socle, cosocleC22×C29C25
FittingC29×#548C2
hypercenter#548D29
hypocenterC29#3480
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. #14271895C2semidirect
2. #14271889C2semidirect
3. #14271884C2semidirect
4. #14271865C2semidirect
5. #14271859C2semidirect
6. #14271832C2semidirect
7. #14271824C2semidirect
8. #14271708C2semidirect
9. #14271699C2semidirect
10. #14271692C2semidirect
11. #41×Dic29C2semidirect
12. C4×#90809C2semidirect
13. C4×#90807C2semidirect
14. C2×Q8×Dic29C2semidirect
15. C29×#548C2semidirect
124. Q8×C29#41semidirect
140. C2×Dic29#41semidirect
183. #548D29semidirect
247. C29#3480semidirect
307. Q8#90807semidirect

Maximal subgroups

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

subgroupindex
#142718952
#142718892
#142718842
#142718652
#142718592
#142718322
#142718242
#142717082
#142716992
#142716922
#41×Dic292
C4×#908092
C4×#908072
C2×Q8×Dic292
C29×#5482
#348029