Finite Group Databasebeta

← #16833090

Subgroups — #16833090

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#14271896C213yesmaximal, complemented
2#14271889C211yesmaximal, characteristic, complemented
3#14271881C213yesmaximal, complemented
4#14271863C213yesmaximal, complemented
5#14271857C213yesmaximal, complemented
6#14271832C211yesmaximal, characteristic, complemented
7#14271825C211yesmaximal, characteristic, complemented
8#14271820C211yesmaximal, characteristic, complemented
9#14271710C213yesmaximal, complemented
10#14271697C213yesmaximal, complemented
11#14271695C213yesmaximal, complemented
12C4×#90809C211yesmaximal, characteristic, complemented
13C4×#90805C213yesmaximal, complemented
14C4×Q8×D29C211yesmaximal, characteristic, complemented
15C4×#41×C29C211yesmaximal, characteristic, complemented
16C2×#41×C29C2211yescharacteristic
17C2×#90809C2211yescharacteristic
18C2×Q8×D29C2211yescharacteristic
19C2×#90805C2213yes—
20C4×Q8×C29C2211yescharacteristic
21C4×Q8×C29C2211yescharacteristic
22C4×D4×C29C2213yes—
23C4×D4×C29C2213yes—
24C29×#117C2213yes—
25C2×C42×C29C2213yes—
26Q8×Dic29C2211yescharacteristic
27Q8×Dic29C2211yescharacteristic
28#11745302C2213yes—
29#11745300C2213yes—
30#11745300C2213yes—
31#11745298C2213yes—
32#11745292C2213yes—
33#11745291C2216yes—
34C4×C22⋊D29C2213yes—
35C4×C22⋊D29C2213yes—
36C4×C22⋊D29C2213yes—
37C4×C22⋊D29C2213yes—
38C4×C22⋊D29C2216yes—
39#11745288C2213yes—
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#11745238C2216yes—
54#11745237C2213yes—
55C4×D116C2213yes—
56C4×D116C2213yes—
57C4×D116C2213yes—
58#11745234C2211yescharacteristic
59#11745234C2213yes—
60C42×D29C2213yes—
61C42×D29C2213yes—
62#11745232C2213yes—
63C4×Dic58C2213yes—
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⋊D29C2313yes—
74C2×C22⋊D29C2316yes—
75#90809—24no—
76Q8×D29—24no—
77#90805—212no—
78C2×D116C2313yes—
79C2×D116C2313yes—
80C2×C4×D29C2313yes—
81C2×C4×D29C2313yes—
82C2×C4×D29C2313yes—
83C2×C4×D29C2313yes—
84C2×C4×D29C2313yes—
85C2×C4×D29C2311yescharacteristic
86C2×Dic58C2313yes—
87C2×Dic58C2313yes—
88C4⋊C4×C29C2313yes—
89C4⋊C4×C29C2313yes—
90C22⋊C4×C29C2316yes—
91C42×C29C2311yescharacteristic
92C42×C29C2313yes—
93C42×C29C2313yes—
94C42×C29C2313yes—
95C22⋊Dic29C2316yes—
96C22⋊Dic29C2313yes—
97C22⋊Dic29C2313yes—
98#90781C2311yescharacteristic
99#90781C2311yescharacteristic
100#90781C2313yes—
101#90781C2313yes—
102#90781C2316yes—
103#90781C2316yes—
104C4⋊Dic29C2313yes—
105C4⋊Dic29C2313yes—
106C4⋊Dic29C2313yes—
107C4⋊Dic29C2313yes—
108#90779C2313yes—
109#90779C2311yescharacteristic
110#90779C2311yescharacteristic
111#90779C2313yes—
112#90779C2316yes—
113#90779C2316yes—
114C4×Dic29C2311yescharacteristic
115C4×Dic29C2313yes—
116C4×Dic29C2313yes—
117C4×Dic29C2313yes—
118C4×Dic29C2313yes—
119C4×Dic29C2313yes—
120C23×C29C2413yes—
121C22×D29C2413yes—
122C22×D29C2411yescharacteristic
123Q8×C29#4114yescomplemented
124D4×C29—26no—
125C2×C4×C29—26no—
126C2×C4×C29—26no—
127C2×C4×C29—43no—
128C2×C4×C29C2413yes—
129C2×C4×C29C2411yescharacteristic
130C2×C4×C29C2411yescharacteristic
131C2×C4×C29C2413yes—
132C2×C4×C29C2413yes—
133C2×C4×C29C2411yescharacteristic
134C22⋊D29—26no—
135C22⋊D29—26no—
136C22⋊D29—46no—
137C2×Dic29C2411yescharacteristic
138C2×Dic29C2411yescharacteristic
139C2×Dic29C2413yes—
140C2×Dic29C2413yes—
141C2×Dic29C2413yes—
142C2×Dic29C2411yescharacteristic
143D116—26no—
144D116—26no—
145C4×D29—26no—
146C4×D29—26no—
147C4×D29—26no—
148C4×D29—43no—
149C4×D29—43no—
150C4×D29#4114yescomplemented
151Dic58—26no—
152Dic58—26no—
153#3480—291nomaximal, Sylow
154C22×C29—23no—
155C22×C29—23no—
156C22×C29—23no—
157C22×C29C2511yescharacteristic
158C2×D29—21no—
159C2×D29—21no—
160C2×D29—23no—
161C2×D29—23no—
162C2×D29—23no—
163C2×D29C2×#4112yes—
164C4×C29—23no—
165C4×C29—21no—
166C4×C29—23no—
167C4×C29—21no—
168C4×C29C2×#4116yes—
169C4×C29C2×#4112yes—
170Dic29—23no—
171Dic29—23no—
172Dic29—21no—
173Dic29—21no—
174Dic29—23no—
175Dic29C2×#4112yes—
176#559—293no—
177#557—291no—
178#556—293no—
179#553—293no—
180#553—293no—
181#550—291no—
182#548—291no—
183#548—291no—
184#532—293no—
185#529—293no—
186#529—293no—
187C4×#41—291no—
188C4×#41—293no—
189C4×#41D2911yescharacteristic, complemented
190C2×C4×Q8—291no—
191C2×C29—43no—
192C2×C29C22×#4111yescharacteristic
193C2×C29C22×#4111yescharacteristic
194C2×C29#58511yescharacteristic
195D29—22no—
196D29—43no—
197C2×#41—291no—
198C2×#41—293no—
199C2×#41C2×D2911yescharacteristic
200C22×Q8—291no—
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#124—293no—
210#123—296no—
211#123—296no—
212C22⋊Q8—293no—
213C22⋊Q8—293no—
214#121—293no—
215#121—293no—
216#121—293no—
217#121—293no—
218#121—296no—
219C4×Q8—291no—
220C4×Q8—291no—
221C4×Q8—293no—
222C4×Q8—293no—
223C4×Q8—293no—
224C4×Q8—293no—
225C4×Q8C2×D2911yescharacteristic
226C4×Q8C2×D2911yescharacteristic
227C4×D4—293no—
228C4×D4—293no—
229C4×D4—293no—
230C4×D4—293no—
231C4×D4—296no—
232C4×D4—293no—
233C4×D4—293no—
234C4×D4—293no—
235C4×D4—293no—
236C4×D4C2×D2913yes—
237C4×D4C2×D2913yes—
238#117—293no—
239#117—293no—
240#117—291no—
241#117—293no—
242#117C2×D2913yes—
243C2×C4⋊C4—293no—
244C2×C42—293no—
245C2×C42—293no—
246C2×C42C2×D2913yes—
247C29#348011yescharacteristic, complemented, Sylow
248#41—24no—
249#41—5812no—
250#41—584no—
251C2×Q8—293no—
252C2×Q8—293no—
253C2×Q8—584no—
254C2×Q8C22×D2911yescharacteristic
255C2×D4—293no—
256C2×D4—293no—
257C2×D4—296no—
258C2×D4—293no—
259C2×D4—293no—
260C2×D4C22×D2913yes—
261C22×C4—291no—
262C22×C4—293no—
263C22×C4—293no—
264C22×C4—293no—
265C22×C4—293no—
266C22×C4—293no—
267C22×C4C22×D2913yes—
268C22×C4C22×D2913yes—
269C22×C4C22×D2913yes—
270C4⋊C4—293no—
271C4⋊C4—296no—
272C4⋊C4—291no—
273C4⋊C4—291no—
274C4⋊C4—293no—
275C4⋊C4—293no—
276C4⋊C4—293no—
277C4⋊C4—293no—
278C4⋊C4—293no—
279C4⋊C4—296no—
280C4⋊C4C22×D2913yes—
281C4⋊C4C22×D2913yes—
282C22⋊C4—293no—
283C22⋊C4—293no—
284C22⋊C4—296no—
285C22⋊C4—291no—
286C22⋊C4—291no—
287C22⋊C4—293no—
288C22⋊C4—296no—
289C22⋊C4—293no—
290C22⋊C4—296no—
291C22⋊C4C22×D2916yes—
292C42—293no—
293C42—293no—
294C42—293no—
295C42—293no—
296C42—291no—
297C42—293no—
298C42C22×D2913yes—
299C42C22×D2913yes—
300C42C22×D2913yes—
301C42C22×D2911yescharacteristic
302C23—291no—
303C23—293no—
304C23C23×D2913yes—
305Q8—586no—
306Q8—586no—
307Q8#9080514yescomplemented
308D4—26no—
309D4—586no—
310D4—586no—
311D4—586no—
312D4—586no—
313D4—1166no—
314C2×C4—26no—
315C2×C4—26no—
316C2×C4—43no—
317C2×C4—291no—
318C2×C4—294no—
319C2×C4—291no—
320C2×C4—291no—
321C2×C4—293no—
322C2×C4—293no—
323C2×C4—293no—
324C2×C4—586no—
325C2×C4—586no—
326C2×C4—586no—
327C2×C4—1163no—
328C2×C4—1163no—
329C2×C4C23×D2913yes—
330C2×C4C23×D2911yescharacteristic
331C2×C4C23×D2911yescharacteristic
332C2×C4C23×D2913yes—
333C2×C4C23×D2913yes—
334C2×C4C23×D2911yescharacteristic
335C22—23no—
336C22—23no—
337C22—23no—
338C22—292no—
339C22—581no—
340C22—581no—
341C22—583no—
342C22—583no—
343C22—583no—
344C22C24×D2911yescharacteristic
345C4—23no—
346C4—21no—
347C4—21no—
348C4—23no—
349C4—292no—
350C4—583no—
351C4—581no—
352C4—583no—
353C4—581no—
354C4—583no—
355C4C2×#9080516yes—
356C4#41×D2912yes—
357C2—43no—
358C2—582no—
359C2—1163no—
360C2C2×#41×D2911yescharacteristic
361C2C22×#9080511yescharacteristic
362C2#1427199911yescharacteristic
subgroupG/H
centerC2×C4C23×D29
commutator, socle, cosocleC22×C29C25
FrattiniC22C24×D29
FittingC4×#41×C29C2
hypercenterC4×#41D29
hypocenterC29#3480
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C2×C4 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
1. #14271896C2semidirect
2. #14271889C2semidirect
3. #14271881C2semidirect
4. #14271863C2semidirect
5. #14271857C2semidirect
6. #14271832C2semidirect
7. #14271825C2semidirect
8. #14271820C2semidirect
9. #14271710C2semidirect
10. #14271697C2semidirect
11. #14271695C2semidirect
12. C4×#90809C2semidirect
13. C4×#90805C2semidirect
14. C4×Q8×D29C2semidirect
15. C4×#41×C29C2semidirect
123. Q8×C29#41semidirect
150. C4×D29#41semidirect
189. C4×#41D29semidirect
247. C29#3480semidirect
307. Q8#90805semidirect

Maximal subgroups

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

subgroupindex
#142718962
#142718892
#142718812
#142718632
#142718572
#142718322
#142718252
#142718202
#142717102
#142716972
#142716952
C4×#908092
C4×#908052
C4×Q8×D292
C4×#41×C292
#348029