Finite Group Databasebeta

← #16833603

Subgroups — #16833603

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#14271898C213yesmaximal, complemented
2#14271889C211yesmaximal, characteristic, complemented
3#14271876C213yesmaximal, complemented
4#14271857C213yesmaximal, complemented
5#14271854C213yesmaximal, complemented
6#14271835C211yesmaximal, characteristic, complemented
7#14271824C211yesmaximal, characteristic, complemented
8#14271824C211yesmaximal, characteristic, complemented
9#14271785C213yesmaximal, complemented
10#14271768C213yesmaximal, complemented
11#14271700C213yesmaximal, complemented
12#14271691C213yesmaximal, complemented
13#14271645C211yesmaximal, characteristic, complemented
14C4×#90809C211yesmaximal, characteristic, complemented
15C29×#519C211yesmaximal, characteristic, complemented
16C22×Q8×C29C2211yescharacteristic
17C2×#90809C2211yescharacteristic
18C2×#90809C2211yescharacteristic
19C4×Q8×C29C2213yes—
20C4×Q8×C29C2211yescharacteristic
21C4×Q8×C29C2213yes—
22C4×Q8×C29C2211yescharacteristic
23C29×#117C2213yes—
24C29×#117C2213yes—
25#11745309C2213yes—
26#11745309C2213yes—
27#11745308C2213yes—
28#11745308C2213yes—
29Q8×Dic29C2211yescharacteristic
30Q8×Dic29C2211yescharacteristic
31#11745292C2213yes—
32#11745292C2213yes—
33C4×C22⋊D29C2213yes—
34C4×C22⋊D29C2213yes—
35#11745260C2213yes—
36#11745258C2213yes—
37#11745257C2213yes—
38#11745257C2213yes—
39#11745256C2216yes—
40#11745256C2216yes—
41#11745256C2213yes—
42#11745255C2213yes—
43#11745255C2213yes—
44#11745254C2213yes—
45C4⋊C4×D29C2213yes—
46#11745252C2213yes—
47#11745251C2213yes—
48#11745250C2213yes—
49#11745247C2213yes—
50#11745246C2213yes—
51#11745246C2216yes—
52#11745245C2213yes—
53#11745241C2211yescharacteristic
54#11745238C2216yes—
55#11745237C2216yes—
56#11745236C2213yes—
57C4×D116C2213yes—
58C4×D116C2213yes—
59C4×D116C2213yes—
60C4×D116C2216yes—
61#11745234C2213yes—
62#11745234C2216yes—
63C42×D29C2213yes—
64#11745232C2213yes—
65C4×Dic58C2213yes—
66C2×Q8×C29—24no—
67C2×Q8×C29C2313yes—
68C2×Q8×C29C2311yescharacteristic
69C22×C4×C29C2313yes—
70C2×C22⋊D29C2313yes—
71C2×C22⋊D29C2313yes—
72#90809—24no—
73#90809—24no—
74C2×D116C2313yes—
75C2×D116C2313yes—
76C2×D116C2313yes—
77C2×D116C2316yes—
78C2×C4×D29C2313yes—
79C2×C4×D29C2313yes—
80C2×C4×D29C2313yes—
81C2×C4×D29C2313yes—
82C2×C4×D29C2316yes—
83C2×Dic58C2313yes—
84C4⋊C4×C29C2313yes—
85C4⋊C4×C29C2313yes—
86C4⋊C4×C29C2313yes—
87C4⋊C4×C29C2313yes—
88C22⋊C4×C29C2311yescharacteristic
89C22⋊C4×C29C2313yes—
90C42×C29C2313yes—
91C42×C29C2313yes—
92C42×C29C2316yes—
93C22⋊Dic29C2311yescharacteristic
94C22⋊Dic29C2311yescharacteristic
95#90781C2313yes—
96#90781C2313yes—
97#90781C2316yes—
98#90781C2316yes—
99#90781C2313yes—
100#90781C2313yes—
101#90781C2313yes—
102#90781C2316yes—
103#90781C2313yes—
104C4⋊Dic29C2313yes—
105C4⋊Dic29C2313yes—
106C4⋊Dic29C2313yes—
107C4⋊Dic29C2311yescharacteristic
108#90779C2313yes—
109#90779C2313yes—
110#90779C2311yescharacteristic
111#90779C2313yes—
112#90779C2316yes—
113#90779C2311yescharacteristic
114#90779C2313yes—
115C4×Dic29C2313yes—
116C4×Dic29C2313yes—
117C4×Dic29C2311yescharacteristic
118C4×Dic29C2313yes—
119C23×C29C2411yescharacteristic
120C22×D29C2413yes—
121C22×D29C2413yes—
122Q8×C29—26no—
123Q8×C29#4114yes—
124C2×C4×C29—26no—
125C2×C4×C29C2411yescharacteristic
126C2×C4×C29C2413yes—
127C2×C4×C29C2411yescharacteristic
128C2×C4×C29C2413yes—
129C2×C4×C29C2413yes—
130C2×C4×C29C2413yes—
131C22⋊D29—43no—
132C22⋊D29—43no—
133C2×Dic29C2411yescharacteristic
134C2×Dic29C2411yescharacteristic
135C2×Dic29C2411yescharacteristic
136C2×Dic29C2413yes—
137C2×Dic29C2413yes—
138C2×Dic29C2411yescharacteristic
139D116—26no—
140D116—26no—
141D116—46no—
142D116—43no—
143C4×D29—26no—
144C4×D29—26no—
145C4×D29—43no—
146C4×D29—43no—
147C4×D29—46no—
148Dic58—43no—
149#3524—291nomaximal, Sylow
150C22×C29—21no—
151C22×C29—21no—
152C22×C29—21no—
153C22×C29C2511yescharacteristic
154C2×D29—23no—
155C2×D29—23no—
156C2×D29—23no—
157C2×D29—23no—
158C2×D29—23no—
159C2×D29—23no—
160C4×C29—23no—
161C4×C29—23no—
162C4×C29—21no—
163C4×C29—23no—
164C4×C29—21no—
165C4×C29C2×#4116yes—
166Dic29—21no—
167Dic29—21no—
168Dic29—21no—
169Dic29—23no—
170Dic29—21no—
171Dic29—23no—
172#559—293no—
173#557—291no—
174#555—293no—
175#553—293no—
176#552—293no—
177#550—291no—
178#548—291no—
179#548—291no—
180#542—293no—
181#540—293no—
182#529—293no—
183#529—293no—
184#520—291no—
185#519D2911yescharacteristic, complemented
186C4×#41—291no—
187C2×C29—41no—
188C2×C29C22×#4111yescharacteristic
189C2×C29#58511yescharacteristic
190C2×C29#58511yescharacteristic
191D29—43no—
192D29—43no—
193C2×#41—291no—
194C2×#41—291no—
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—293no—
207#124—296no—
208#123—296no—
209#123—293no—
210#123—296no—
211#123—293no—
212C22⋊Q8—293no—
213C22⋊Q8—293no—
214C22⋊Q8—293no—
215#121—293no—
216#121—293no—
217#121—293no—
218#121—293no—
219#121—293no—
220#121—296no—
221C4×Q8—291no—
222C4×Q8—291no—
223C4×Q8—293no—
224C4×Q8C2×D2911yescharacteristic
225C4×Q8C2×D2913yes—
226C4×Q8C2×D2911yescharacteristic
227C4×Q8C2×D2913yes—
228C4×D4—293no—
229C4×D4—293no—
230C4×D4—293no—
231C4×D4—293no—
232C4×D4—293no—
233C4×D4—293no—
234C4×D4—293no—
235C4×D4—296no—
236#117—293no—
237#117—293no—
238#117—296no—
239#117C2×D2913yes—
240#117C2×D2913yes—
241C2×C4⋊C4—293no—
242C2×C42—293no—
243C29#352411yescharacteristic, complemented, Sylow
244#41—584no—
245#41—584no—
246C2×Q8—24no—
247C2×Q8—293no—
248C2×Q8C22×D2913yes—
249C2×Q8C22×D2911yescharacteristic
250C2×D4—293no—
251C2×D4—293no—
252C2×D4—293no—
253C2×D4—293no—
254C2×D4—296no—
255C2×D4—293no—
256C22×C4—293no—
257C22×C4—293no—
258C22×C4—293no—
259C22×C4—293no—
260C22×C4—296no—
261C22×C4C22×D2913yes—
262C4⋊C4—293no—
263C4⋊C4—293no—
264C4⋊C4—291no—
265C4⋊C4—293no—
266C4⋊C4—293no—
267C4⋊C4—296no—
268C4⋊C4—291no—
269C4⋊C4—293no—
270C4⋊C4—293no—
271C4⋊C4—291no—
272C4⋊C4—293no—
273C4⋊C4C22×D2913yes—
274C4⋊C4C22×D2913yes—
275C4⋊C4C22×D2913yes—
276C4⋊C4C22×D2913yes—
277C22⋊C4—291no—
278C22⋊C4—291no—
279C22⋊C4—293no—
280C22⋊C4—293no—
281C22⋊C4—296no—
282C22⋊C4—293no—
283C22⋊C4—296no—
284C22⋊C4—293no—
285C22⋊C4—293no—
286C22⋊C4—296no—
287C22⋊C4—293no—
288C22⋊C4C22×D2911yescharacteristic
289C22⋊C4C22×D2913yes—
290C42—291no—
291C42—293no—
292C42—293no—
293C42—293no—
294C42C22×D2913yes—
295C42C22×D2916yes—
296C42C22×D2913yes—
297C23—293no—
298C23—293no—
299C23C23×D2911yescharacteristic
300Q8—26no—
301Q8—1163no—
302Q8#9080514yes—
303D4—586no—
304D4—586no—
305D4—1163no—
306D4—1166no—
307D4—1163no—
308D4—1163no—
309C2×C4—26no—
310C2×C4—291no—
311C2×C4—291no—
312C2×C4—291no—
313C2×C4—293no—
314C2×C4—293no—
315C2×C4—291no—
316C2×C4—586no—
317C2×C4—586no—
318C2×C4—1163no—
319C2×C4—1166no—
320C2×C4—1163no—
321C2×C4C23×D2911yescharacteristic
322C2×C4C23×D2913yes—
323C2×C4C23×D2913yes—
324C2×C4C23×D2911yescharacteristic
325C2×C4C23×D2913yes—
326C2×C4C23×D2913yes—
327C22—21no—
328C22—21no—
329C22—21no—
330C22—583no—
331C22—583no—
332C22—583no—
333C22—583no—
334C22—583no—
335C22—583no—
336C22C24×D2911yescharacteristic
337C4—23no—
338C4—21no—
339C4—21no—
340C4—23no—
341C4—23no—
342C4—581no—
343C4—583no—
344C4—583no—
345C4—581no—
346C4—581no—
347C4—581no—
348C4C2×#9080516yes—
349C2—41no—
350C2—1163no—
351C2—1163no—
352C2C22×#9080511yescharacteristic
353C2#1427200011yescharacteristic
354C2#1427200011yescharacteristic
subgroupG/H
center, FrattiniC22C24×D29
commutator, socle, cosocleC22×C29C25
FittingC29×#519C2
hypercenter#519D29
hypocenterC29#3524
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ #519

Complements

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

NH ≅ G/Ntype
1. #14271898C2semidirect
2. #14271889C2semidirect
3. #14271876C2semidirect
4. #14271857C2semidirect
5. #14271854C2semidirect
6. #14271835C2semidirect
7. #14271824C2semidirect
8. #14271824C2semidirect
9. #14271785C2semidirect
10. #14271768C2semidirect
11. #14271700C2semidirect
12. #14271691C2semidirect
13. #14271645C2semidirect
14. C4×#90809C2semidirect
15. C29×#519C2semidirect
185. #519D29semidirect
243. C29#3524semidirect

Maximal subgroups

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

subgroupindex
#142718982
#142718892
#142718762
#142718572
#142718542
#142718352
#142718242
#142717852
#142717682
#142717002
#142716912
#142716452
C4×#908092
C29×#5192
#352429