Finite Group Databasebeta

← #16833602

Subgroups — #16833602

Order 3712.

1030 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271895C213yesmaximal, complemented
2#14271892C211yesmaximal, characteristic, complemented
3#14271878C213yesmaximal, complemented
4#14271860C213yesmaximal, complemented
5#14271847C213yesmaximal, complemented
6#14271832C211yesmaximal, characteristic, complemented
7#14271824C211yesmaximal, characteristic, complemented
8#14271782C213yesmaximal, complemented
9#14271766C213yesmaximal, complemented
10#14271699C213yesmaximal, complemented
11#14271693C213yesmaximal, complemented
12#14271645C211yesmaximal, characteristic, complemented
13#14271641C211yesmaximal, characteristic, complemented
14#41×Dic29C211yesmaximal, characteristic, complemented
15C29×#548C211yesmaximal, characteristic, complemented
16C2×#41×C29C2211yescharacteristic
17C22×Q8×C29C2211yescharacteristic
18C2×#90809C2211yescharacteristic
19C29×#124C2213yes—
20C29×C22⋊Q8C2213yes—
21C29×#121C2213yes—
22C4×Q8×C29C2211yescharacteristic
23C4×D4×C29C2213yes—
24#11745309C2213yes—
25#11745308C2213yes—
26Q8×Dic29C2213yes—
27Q8×Dic29C2211yescharacteristic
28Q8×Dic29C2211yescharacteristic
29Q8×Dic29C2213yes—
30Q8×Dic29C2211yescharacteristic
31#11745302C2213yes—
32#11745301C2213yes—
33#11745300C2216yes—
34#11745300C2213yes—
35#11745297C2213yes—
36D4×Dic29C2213yes—
37D4×Dic29C2213yes—
38#11745292C2213yes—
39#11745292C2213yes—
40C4×C22⋊D29C2213yes—
41C4×C22⋊D29C2213yes—
42#11745288C2213yes—
43#11745288C2213yes—
44#11745288C2213yes—
45C2×C4×Dic29C2213yes—
46#11745260C2213yes—
47#11745255C2213yes—
48#11745254C2216yes—
49C4⋊C4×D29C2213yes—
50#11745252C2213yes—
51#11745252C2213yes—
52#11745251C2213yes—
53#11745248C2216yes—
54#11745248C2213yes—
55#11745247C2216yes—
56#11745247C2213yes—
57#11745245C2216yes—
58#11745243C2216yes—
59#11745241C2216yes—
60#11745241C2211yescharacteristic
61#11745240C2213yes—
62C4×D116C2213yes—
63#11745234C2213yes—
64#11745231C2213yes—
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—
79#90809—24no—
80C2×D116C2313yes—
81C2×C4×D29C2313yes—
82C2×C4×D29C2316yes—
83C2×Dic58C2313yes—
84C4⋊C4×C29C2313yes—
85C4⋊C4×C29C2313yes—
86C22⋊C4×C29C2311yescharacteristic
87C22⋊C4×C29C2313yes—
88C22⋊C4×C29C2316yes—
89C42×C29C2313yes—
90C22⋊Dic29C2313yes—
91C22⋊Dic29C2311yescharacteristic
92C22⋊Dic29C2316yes—
93C22⋊Dic29C2311yescharacteristic
94C22⋊Dic29C2313yes—
95#90781C2313yes—
96#90781C2313yes—
97#90781C2316yes—
98#90781C2313yes—
99#90781C2313yes—
100C4⋊Dic29C2313yes—
101C4⋊Dic29C2313yes—
102C4⋊Dic29C2313yes—
103C4⋊Dic29C2313yes—
104C4⋊Dic29C2313yes—
105C4⋊Dic29C2316yes—
106C4⋊Dic29C2311yescharacteristic
107#90779C2311yescharacteristic
108#90779C2313yes—
109#90779C2313yes—
110#90779C2313yes—
111#90779C2313yes—
112#90779C2311yescharacteristic
113C4×Dic29C2311yescharacteristic
114C4×Dic29C2313yes—
115C4×Dic29C2313yes—
116C4×Dic29C2313yes—
117C4×Dic29C2313yes—
118C4×Dic29C2316yes—
119C23×C29C2411yescharacteristic
120C23×C29C2413yes—
121C22×D29C2413yes—
122Q8×C29—26no—
123Q8×C29#4114yes—
124D4×C29—26no—
125D4×C29—43no—
126C2×C4×C29—26no—
127C2×C4×C29—26no—
128C2×C4×C29C2411yescharacteristic
129C2×C4×C29C2413yes—
130C2×C4×C29C2413yes—
131C2×C4×C29C2411yescharacteristic
132C2×C4×C29C2413yes—
133C22⋊D29—43no—
134C22⋊D29—46no—
135C22⋊D29—43no—
136C2×Dic29—43no—
137C2×Dic29—43no—
138C2×Dic29C2411yescharacteristic
139C2×Dic29C2411yescharacteristic
140C2×Dic29C2413yes—
141C2×Dic29C2411yescharacteristic
142C2×Dic29C2413yes—
143C2×Dic29C2413yes—
144C2×Dic29C2411yescharacteristic
145D116—26no—
146C4×D29—26no—
147C4×D29—46no—
148Dic58—43no—
149#3524—291nomaximal, Sylow
150C22×C29—21no—
151C22×C29—23no—
152C22×C29—23no—
153C22×C29—23no—
154C22×C29—21no—
155C22×C29—21no—
156C22×C29C2511yescharacteristic
157C2×D29—23no—
158C2×D29—23no—
159C2×D29—23no—
160C4×C29—21no—
161C4×C29—23no—
162C4×C29—21no—
163C4×C29—23no—
164C4×C29C2×#4116yes—
165Dic29—21no—
166Dic29—23no—
167Dic29—23no—
168Dic29—23no—
169Dic29—21no—
170Dic29—21no—
171Dic29—21no—
172#559—293no—
173#557—291no—
174#555—293no—
175#553—293no—
176#552—293no—
177#550—291no—
178#548—291no—
179#548D2911yescharacteristic, complemented
180#542—293no—
181#540—293no—
182#529—293no—
183#529—293no—
184#520—291no—
185#519—291no—
186C4×#41—291no—
187C2×C29—41no—
188C2×C29—43no—
189C2×C29C22×#4111yescharacteristic
190C2×C29#58511yescharacteristic
191C2×C29#58511yescharacteristic
192D29—43no—
193C2×#41—291no—
194C2×#41C2×D2911yescharacteristic
195C22×Q8C2×D2911yescharacteristic
196C4⋊Q8—293no—
197#127—293no—
198#126—293no—
199#126—291no—
200#126—296no—
201#125—293no—
202#125—293no—
203#125—293no—
204#124—293no—
205#124—293no—
206#124—296no—
207#124C2×D2913yes—
208#123—293no—
209#123—296no—
210#123—293no—
211#123—296no—
212C22⋊Q8—293no—
213C22⋊Q8—293no—
214C22⋊Q8C2×D2913yes—
215#121—293no—
216#121—296no—
217#121—293no—
218#121—293no—
219#121—293no—
220#121C2×D2913yes—
221C4×Q8—291no—
222C4×Q8—291no—
223C4×Q8—293no—
224C4×Q8—291no—
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—296no—
234C4×D4—293no—
235C4×D4C2×D2913yes—
236#117—293no—
237#117—293no—
238#117—293no—
239#117—296no—
240#117—293no—
241C2×C4⋊C4—293no—
242C2×C42—293no—
243C29#352411yescharacteristic, complemented, Sylow
244#41—24no—
245#41—584no—
246C2×Q8—24no—
247C2×Q8—293no—
248C2×Q8C22×D2913yes—
249C2×Q8C22×D2911yescharacteristic
250C2×D4—293no—
251C2×D4—296no—
252C2×D4—293no—
253C2×D4—293no—
254C2×D4C22×D2913yes—
255C2×D4C22×D2913yes—
256C22×C4—293no—
257C22×C4—293no—
258C22×C4—293no—
259C22×C4—296no—
260C22×C4C22×D2913yes—
261C22×C4C22×D2913yes—
262C4⋊C4—293no—
263C4⋊C4—293no—
264C4⋊C4—291no—
265C4⋊C4—293no—
266C4⋊C4—293no—
267C4⋊C4—293no—
268C4⋊C4—293no—
269C4⋊C4—296no—
270C4⋊C4—291no—
271C4⋊C4—293no—
272C4⋊C4—293no—
273C4⋊C4—291no—
274C4⋊C4—293no—
275C4⋊C4C22×D2913yes—
276C4⋊C4C22×D2913yes—
277C22⋊C4—291no—
278C22⋊C4—293no—
279C22⋊C4—296no—
280C22⋊C4—291no—
281C22⋊C4—293no—
282C22⋊C4—293no—
283C22⋊C4—293no—
284C22⋊C4—293no—
285C22⋊C4—296no—
286C22⋊C4—293no—
287C22⋊C4C22×D2916yes—
288C22⋊C4C22×D2911yescharacteristic
289C22⋊C4C22×D2913yes—
290C42—291no—
291C42—293no—
292C42—293no—
293C42—293no—
294C42—296no—
295C42—293no—
296C42C22×D2913yes—
297C23—293no—
298C23C23×D2911yescharacteristic
299C23C23×D2913yes—
300Q8—26no—
301Q8—1163no—
302Q8#9080714yes—
303D4—26no—
304D4—43no—
305D4—586no—
306D4—1163no—
307D4—1166no—
308D4—1163no—
309C2×C4—26no—
310C2×C4—26no—
311C2×C4—291no—
312C2×C4—291no—
313C2×C4—293no—
314C2×C4—293no—
315C2×C4—291no—
316C2×C4—293no—
317C2×C4—291no—
318C2×C4—586no—
319C2×C4—1166no—
320C2×C4—1163no—
321C2×C4—1163no—
322C2×C4C23×D2911yescharacteristic
323C2×C4C23×D2913yes—
324C2×C4C23×D2911yescharacteristic
325C2×C4C23×D2913yes—
326C2×C4C23×D2913yes—
327C22—23no—
328C22—21no—
329C22—21no—
330C22—23no—
331C22—23no—
332C22—21no—
333C22—583no—
334C22—583no—
335C22—583no—
336C22C24×D2911yescharacteristic
337C4—21no—
338C4—21no—
339C4—23no—
340C4—23no—
341C4—581no—
342C4—583no—
343C4—583no—
344C4—581no—
345C4—583no—
346C4—581no—
347C4—581no—
348C4C2×#9080716yes—
349C2—43no—
350C2—41no—
351C2—1163no—
352C2C22×#9080711yescharacteristic
353C2#1427199911yescharacteristic
354C2#1427200011yescharacteristic
subgroupG/H
center, FrattiniC22C24×D29
commutator, socle, cosocleC22×C29C25
FittingC29×#548C2
hypercenter#548D29
hypocenterC29#3524
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. #14271895C2semidirect
2. #14271892C2semidirect
3. #14271878C2semidirect
4. #14271860C2semidirect
5. #14271847C2semidirect
6. #14271832C2semidirect
7. #14271824C2semidirect
8. #14271782C2semidirect
9. #14271766C2semidirect
10. #14271699C2semidirect
11. #14271693C2semidirect
12. #14271645C2semidirect
13. #14271641C2semidirect
14. #41×Dic29C2semidirect
15. C29×#548C2semidirect
179. #548D29semidirect
243. C29#3524semidirect

Maximal subgroups

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

subgroupindex
#142718952
#142718922
#142718782
#142718602
#142718472
#142718322
#142718242
#142717822
#142717662
#142716992
#142716932
#142716452
#142716412
#41×Dic292
C29×#5482
#352429