Finite Group Databasebeta

← #16833601

Subgroups — #16833601

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#14271896C213yesmaximal, complemented
2#14271889C211yesmaximal, characteristic, complemented
3#14271876C213yesmaximal, complemented
4#14271863C213yesmaximal, complemented
5#14271852C213yesmaximal, complemented
6#14271832C211yesmaximal, characteristic, complemented
7#14271825C211yesmaximal, characteristic, complemented
8#14271820C211yesmaximal, characteristic, complemented
9#14271778C213yesmaximal, complemented
10#14271764C213yesmaximal, complemented
11#14271697C213yesmaximal, complemented
12#14271697C213yesmaximal, complemented
13#14271645C211yesmaximal, characteristic, complemented
14#14271639C211yesmaximal, characteristic, complemented
15C4×#41×C29C211yesmaximal, characteristic, complemented
16C2×#41×C29C2211yescharacteristic
17C2×#90809C2211yescharacteristic
18C2×Q8×D29C2211yescharacteristic
19C4×Q8×C29C2211yescharacteristic
20C4×Q8×C29C2211yescharacteristic
21C4×D4×C29C2213yes—
22C4×D4×C29C2213yes—
23C29×#117C2213yes—
24C2×C42×C29C2213yes—
25Q8×Dic29C2211yescharacteristic
26Q8×Dic29C2211yescharacteristic
27#11745302C2213yes—
28#11745300C2213yes—
29#11745300C2213yes—
30#11745298C2213yes—
31#11745292C2213yes—
32#11745292C2213yes—
33#11745291C2216yes—
34#11745291C2213yes—
35#11745291C2213yes—
36C4×C22⋊D29C2213yes—
37C4×C22⋊D29C2213yes—
38C4×C22⋊D29C2216yes—
39#11745286C2213yes—
40#11745286C2213yes—
41#11745259C2213yes—
42#11745257C2213yes—
43#11745255C2213yes—
44#11745254C2213yes—
45C4⋊C4×D29C2213yes—
46#11745252C2213yes—
47#11745250C2213yes—
48#11745249C2213yes—
49#11745247C2216yes—
50#11745246C2216yes—
51#11745245C2216yes—
52#11745241C2216yes—
53#11745238C2211yescharacteristic
54#11745238C2213yes—
55#11745237C2213yes—
56#11745237C2213yes—
57C4×D116C2213yes—
58C4×D116C2213yes—
59#11745234C2213yes—
60#11745234C2213yes—
61#11745234C2216yes—
62#11745232C2213yes—
63#11745232C2213yes—
64C4×Dic58C2213yes—
65C4×Dic58C2213yes—
66#41×C29—24no—
67C2×Q8×C29C2311yescharacteristic
68C2×D4×C29C2313yes—
69C22×C4×C29C2313yes—
70C22×C4×C29C2313yes—
71C22×C4×C29C2313yes—
72C2×C22⋊D29C2313yes—
73C2×C22⋊D29C2316yes—
74C2×C22⋊D29C2313yes—
75#90809—24no—
76Q8×D29—24no—
77C2×D116C2313yes—
78C2×D116C2313yes—
79C2×C4×D29C2313yes—
80C2×C4×D29C2313yes—
81C2×C4×D29C2316yes—
82C2×Dic58C2313yes—
83C2×Dic58C2313yes—
84C4⋊C4×C29C2313yes—
85C4⋊C4×C29C2313yes—
86C22⋊C4×C29C2316yes—
87C42×C29C2311yescharacteristic
88C42×C29C2313yes—
89C42×C29C2313yes—
90C42×C29C2313yes—
91C22⋊Dic29C2313yes—
92C22⋊Dic29C2316yes—
93C22⋊Dic29C2313yes—
94#90781C2311yescharacteristic
95#90781C2313yes—
96#90781C2313yes—
97#90781C2311yescharacteristic
98#90781C2313yes—
99#90781C2316yes—
100#90781C2313yes—
101#90781C2313yes—
102#90781C2311yescharacteristic
103C4⋊Dic29C2313yes—
104C4⋊Dic29C2313yes—
105C4⋊Dic29C2313yes—
106C4⋊Dic29C2313yes—
107#90779C2311yescharacteristic
108#90779C2313yes—
109#90779C2313yes—
110#90779C2311yescharacteristic
111#90779C2313yes—
112#90779C2311yescharacteristic
113#90779C2313yes—
114#90779C2316yes—
115#90779C2313yes—
116C4×Dic29C2313yes—
117C4×Dic29C2313yes—
118C4×Dic29C2316yes—
119C23×C29C2413yes—
120C22×D29C2411yescharacteristic
121C22×D29C2413yes—
122Q8×C29#4114yes—
123D4×C29—26no—
124C2×C4×C29—26no—
125C2×C4×C29—43no—
126C2×C4×C29—43no—
127C2×C4×C29C2413yes—
128C2×C4×C29C2411yescharacteristic
129C2×C4×C29C2411yescharacteristic
130C2×C4×C29C2411yescharacteristic
131C2×C4×C29C2413yes—
132C2×C4×C29C2413yes—
133C22⋊D29—46no—
134C22⋊D29—43no—
135C22⋊D29—43no—
136C2×Dic29C2411yescharacteristic
137C2×Dic29C2413yes—
138C2×Dic29C2411yescharacteristic
139C2×Dic29C2413yes—
140C2×Dic29C2413yes—
141C2×Dic29C2411yescharacteristic
142D116—26no—
143D116—43no—
144C4×D29—26no—
145C4×D29—26no—
146C4×D29—46no—
147Dic58—26no—
148Dic58—43no—
149#3524—291nomaximal, Sylow
150C22×C29—23no—
151C22×C29—23no—
152C22×C29—23no—
153C22×C29C2511yescharacteristic
154C2×D29—21no—
155C2×D29—23no—
156C2×D29—23no—
157C2×D29—21no—
158C2×D29—23no—
159C2×D29—21no—
160C4×C29—21no—
161C4×C29—23no—
162C4×C29—23no—
163C4×C29—21no—
164C4×C29—21no—
165C4×C29C2×#4116yes—
166Dic29—23no—
167Dic29—21no—
168Dic29—21no—
169Dic29—23no—
170Dic29—23no—
171Dic29—21no—
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#519—291no—
186C4×#41D2911yescharacteristic, complemented
187C2×C29—43no—
188C2×C29C22×#4111yescharacteristic
189C2×C29#58511yescharacteristic
190C2×C29#58511yescharacteristic
191D29—41no—
192D29—43no—
193C2×#41—291no—
194C2×#41C2×D2911yescharacteristic
195C22×Q8—291no—
196C4⋊Q8—293no—
197#127—293no—
198#126—296no—
199#126—291no—
200#126—293no—
201#125—293no—
202#125—293no—
203#125—293no—
204#124—293no—
205#124—296no—
206#124—293no—
207#124—293no—
208#123—296no—
209#123—293no—
210#123—293no—
211#123—296no—
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×Q8—293no—
225C4×Q8—293no—
226C4×Q8C2×D2911yescharacteristic
227C4×Q8C2×D2911yescharacteristic
228C4×D4—293no—
229C4×D4—293no—
230C4×D4—296no—
231C4×D4—293no—
232C4×D4—293no—
233C4×D4—293no—
234C4×D4C2×D2913yes—
235C4×D4C2×D2913yes—
236#117—293no—
237#117—293no—
238#117—293no—
239#117—296no—
240#117C2×D2913yes—
241C2×C4⋊C4—293no—
242C2×C42C2×D2913yes—
243C29#352411yescharacteristic, complemented, Sylow
244#41—24no—
245#41—584no—
246C2×Q8—293no—
247C2×Q8—293no—
248C2×Q8—584no—
249C2×Q8C22×D2911yescharacteristic
250C2×D4—293no—
251C2×D4—296no—
252C2×D4—293no—
253C2×D4—293no—
254C2×D4—293no—
255C2×D4C22×D2913yes—
256C22×C4—293no—
257C22×C4—293no—
258C22×C4—296no—
259C22×C4C22×D2913yes—
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—293no—
278C22⋊C4—296no—
279C22⋊C4—293no—
280C22⋊C4—291no—
281C22⋊C4—293no—
282C22⋊C4—293no—
283C22⋊C4—293no—
284C22⋊C4—293no—
285C22⋊C4—296no—
286C22⋊C4—291no—
287C22⋊C4—293no—
288C22⋊C4—291no—
289C22⋊C4C22×D2916yes—
290C42—296no—
291C42—293no—
292C42—293no—
293C42C22×D2911yescharacteristic
294C42C22×D2913yes—
295C42C22×D2913yes—
296C42C22×D2913yes—
297C23—291no—
298C23—293no—
299C23C23×D2913yes—
300Q8—586no—
301Q8—1163no—
302Q8#9080514yes—
303D4—26no—
304D4—586no—
305D4—1163no—
306D4—1163no—
307D4—1163no—
308D4—1166no—
309C2×C4—26no—
310C2×C4—43no—
311C2×C4—43no—
312C2×C4—291no—
313C2×C4—293no—
314C2×C4—291no—
315C2×C4—293no—
316C2×C4—293no—
317C2×C4—291no—
318C2×C4—586no—
319C2×C4—586no—
320C2×C4—1166no—
321C2×C4C23×D2913yes—
322C2×C4C23×D2911yescharacteristic
323C2×C4C23×D2911yescharacteristic
324C2×C4C23×D2911yescharacteristic
325C2×C4C23×D2913yes—
326C2×C4C23×D2913yes—
327C22—23no—
328C22—23no—
329C22—23no—
330C22—581no—
331C22—583no—
332C22—583no—
333C22—581no—
334C22—583no—
335C22—581no—
336C22C24×D2911yescharacteristic
337C4—21no—
338C4—21no—
339C4—21no—
340C4—23no—
341C4—23no—
342C4—581no—
343C4—583no—
344C4—583no—
345C4—581no—
346C4—583no—
347C4—581no—
348C4C2×#9080516yes—
349C2—43no—
350C2—1161no—
351C2—1163no—
352C2C22×#9080511yescharacteristic
353C2#1427199911yescharacteristic
354C2#1427199911yescharacteristic
subgroupG/H
center, FrattiniC22C24×D29
commutator, socle, cosocleC22×C29C25
FittingC4×#41×C29C2
hypercenterC4×#41D29
hypocenterC29#3524
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
1. #14271896C2semidirect
2. #14271889C2semidirect
3. #14271876C2semidirect
4. #14271863C2semidirect
5. #14271852C2semidirect
6. #14271832C2semidirect
7. #14271825C2semidirect
8. #14271820C2semidirect
9. #14271778C2semidirect
10. #14271764C2semidirect
11. #14271697C2semidirect
12. #14271697C2semidirect
13. #14271645C2semidirect
14. #14271639C2semidirect
15. C4×#41×C29C2semidirect
186. C4×#41D29semidirect
243. C29#3524semidirect

Maximal subgroups

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

subgroupindex
#142718962
#142718892
#142718762
#142718632
#142718522
#142718322
#142718252
#142718202
#142717782
#142717642
#142716972
#142716452
#142716392
C4×#41×C292
#352429