Finite Group Databasebeta

← #16833109

Subgroups — #16833109

Order 3712.

1094 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271889C211yesmaximal, characteristic, complemented
2#14271885C213yesmaximal, complemented
3#14271854C213yesmaximal, complemented
4#14271848C213yesmaximal, complemented
5Q8×C22⋊D29C211yesmaximal, characteristic, complemented
6#14271825C211yesmaximal, characteristic, complemented
7#14271824C211yesmaximal, characteristic, complemented
8#14271814C213yesmaximal, complemented
9#14271717C213yesmaximal, complemented
10#14271700C213yesmaximal, complemented
11#14271697C213yesmaximal, complemented
12C4×#90809C211yesmaximal, characteristic, complemented
13C4×#90805C213yesmaximal, complemented
14C4×Q8×D29C211yesmaximal, characteristic, complemented
15C2×C4×Q8×C29C211yesmaximal, characteristic, complemented
16C22×Q8×C29C2211yescharacteristic
17C2×#90809C2211yescharacteristic
18C2×Q8×D29C2211yescharacteristic
19C2×#90805C2213yes—
20C4×Q8×C29C2211yescharacteristic
21C4×Q8×C29C2213yes—
22C4×Q8×C29C2211yescharacteristic
23C4×Q8×C29C2213yes—
24C2×C4⋊C4×C29C2213yes—
25C2×C42×C29C2213yes—
26#11745309C2213yes—
27#11745308C2213yes—
28#11745308C2213yes—
29Q8×Dic29C2211yescharacteristic
30Q8×Dic29C2211yescharacteristic
31#11745306C2213yes—
32#11745292C2213yes—
33#11745291C2216yes—
34C4×C22⋊D29C2213yes—
35C4×C22⋊D29C2213yes—
36C4×C22⋊D29C2211yescharacteristic
37C4×C22⋊D29C2213yes—
38#11745288C2213yes—
39#11745286C2213yes—
40#11745260C2216yes—
41#11745259C2213yes—
42#11745258C2216yes—
43#11745257C2213yes—
44#11745256C2216yes—
45#11745255C2213yes—
46#11745254C2213yes—
47C4⋊C4×D29C2213yes—
48#11745252C2213yes—
49#11745251C2216yes—
50#11745250C2213yes—
51#11745249C2213yes—
52#11745238C2216yes—
53#11745237C2213yes—
54C4×D116C2213yes—
55C4×D116C2213yes—
56C4×D116C2213yes—
57#11745234C2213yes—
58#11745234C2213yes—
59#11745234C2216yes—
60C42×D29C2213yes—
61C42×D29C2213yes—
62#11745232C2213yes—
63C4×Dic58C2213yes—
64C4×Dic58C2213yes—
65C4×Dic58C2213yes—
66C2×Q8×C29—24no—
67C2×Q8×C29C2313yes—
68C2×Q8×C29C2311yescharacteristic
69C22×C4×C29C2313yes—
70C22×C4×C29C2313yes—
71C22×C4×C29C2311yescharacteristic
72C2×C22⋊D29C2313yes—
73C2×C22⋊D29C2311yescharacteristic
74#90809—24no—
75Q8×D29—24no—
76#90805—212no—
77C2×D116C2313yes—
78C2×D116C2313yes—
79C2×C4×D29C2313yes—
80C2×C4×D29C2313yes—
81C2×C4×D29C2311yescharacteristic
82C2×C4×D29C2313yes—
83C2×C4×D29C2313yes—
84C2×C4×D29C2313yes—
85C2×Dic58C2313yes—
86C2×Dic58C2313yes—
87C4⋊C4×C29C2313yes—
88C4⋊C4×C29C2313yes—
89C4⋊C4×C29C2316yes—
90C42×C29C2313yes—
91C42×C29C2313yes—
92C42×C29C2313yes—
93C42×C29C2313yes—
94C22⋊Dic29C2313yes—
95C22⋊Dic29C2311yescharacteristic
96#90781C2313yes—
97#90781C2313yes—
98#90781C2311yescharacteristic
99#90781C2313yes—
100#90781C2316yes—
101#90781C2316yes—
102#90781C2316yes—
103C4⋊Dic29C2313yes—
104C4⋊Dic29C2313yes—
105C4⋊Dic29C2313yes—
106C4⋊Dic29C2313yes—
107#90779C2316yes—
108#90779C2313yes—
109#90779C2313yes—
110#90779C2311yescharacteristic
111#90779C2313yes—
112#90779C2316yes—
113#90779C2316yes—
114C4×Dic29C2313yes—
115C4×Dic29C2313yes—
116C4×Dic29C2313yes—
117C4×Dic29C2313yes—
118C4×Dic29C2311yescharacteristic
119C4×Dic29C2313yes—
120C23×C29C2411yescharacteristic
121C22×D29C2413yes—
122C22×D29C2411yescharacteristic
123Q8×C29—26no—
124Q8×C29#4114yescomplemented
125C2×C4×C29—26no—
126C2×C4×C29—26no—
127C2×C4×C29—22no—
128C2×C4×C29C2413yes—
129C2×C4×C29C2411yescharacteristic
130C2×C4×C29C2413yes—
131C2×C4×C29C2413yes—
132C2×C4×C29C2413yes—
133C2×C4×C29C2411yescharacteristic
134C22⋊D29—26no—
135C22⋊D29#4114yescomplemented
136C2×Dic29C2411yescharacteristic
137C2×Dic29C2411yescharacteristic
138C2×Dic29C2413yes—
139C2×Dic29C2413yes—
140C2×Dic29C2413yes—
141C2×Dic29C2411yescharacteristic
142D116—26no—
143D116—26no—
144C4×D29—26no—
145C4×D29—26no—
146C4×D29—26no—
147C4×D29—22no—
148C4×D29—26no—
149C4×D29—26no—
150Dic58—26no—
151Dic58—26no—
152#3482—291nomaximal, Sylow
153C22×C29—21no—
154C22×C29—21no—
155C22×C29C2×#4112yes—
156C22×C29C2511yescharacteristic
157C2×D29—21no—
158C2×D29—21no—
159C2×D29—23no—
160C2×D29—23no—
161C2×D29—23no—
162C2×D29C2×#4112yes—
163C4×C29—23no—
164C4×C29—23no—
165C4×C29—23no—
166C4×C29—21no—
167C4×C29C2×#4116yes—
168C4×C292−1+412yes—
169Dic29—23no—
170Dic29—23no—
171Dic29—21no—
172Dic29—21no—
173Dic29—23no—
174Dic29C2×#4112yes—
175#557—291no—
176#556—293no—
177#552—293no—
178#552—293no—
179D4×Q8—291no—
180#548—291no—
181#548—291no—
182#547—293no—
183#533—293no—
184#529—293no—
185#529—293no—
186C4×#41—291no—
187C4×#41—293no—
188C2×C4×Q8—291no—
189C2×C4×Q8D2911yescharacteristic, complemented
190C2×C29—22no—
191C2×C29C22×#4111yescharacteristic
192C2×C29C22×#4111yescharacteristic
193C2×C29C2×2−1+411yescharacteristic
194D29—22no—
195D29—43no—
196C2×#41—291no—
197C2×#41—293no—
198C22×Q8—291no—
199C22×Q8C2×D2911yescharacteristic
200C4⋊Q8—293no—
201C4⋊Q8—293no—
202#126—296no—
203#126—296no—
204#125—293no—
205#125—296no—
206#125—293no—
207#124—293no—
208#124—293no—
209#123—296no—
210#123—296no—
211C22⋊Q8—293no—
212C22⋊Q8—293no—
213C22⋊Q8—293no—
214C22⋊Q8—296no—
215C22⋊Q8—293no—
216#121—293no—
217#121—293no—
218C4×Q8—291no—
219C4×Q8—291no—
220C4×Q8—293no—
221C4×Q8—293no—
222C4×Q8—293no—
223C4×Q8—293no—
224C4×Q8C2×D2911yescharacteristic
225C4×Q8C2×D2913yes—
226C4×Q8C2×D2911yescharacteristic
227C4×Q8C2×D2913yes—
228C4×D4—291no—
229C4×D4—293no—
230C4×D4—293no—
231C4×D4—293no—
232C4×D4—293no—
233C4×D4—293no—
234C4×D4—293no—
235C4×D4—293no—
236#117—293no—
237#117—293no—
238#117—293no—
239#117—293no—
240#117—296no—
241C2×C4⋊C4—293no—
242C2×C4⋊C4C2×D2913yes—
243C2×C42—293no—
244C2×C42—293no—
245C2×C42C2×D2913yes—
246C29#348211yescharacteristic, complemented, Sylow
247#41—5812no—
248#41—584no—
249C2×Q8—24no—
250C2×Q8—293no—
251C2×Q8—293no—
252C2×Q8—584no—
253C2×Q8C22×D2913yes—
254C2×Q8C22×D2911yescharacteristic
255C2×D4—291no—
256C2×D4—293no—
257C2×D4—293no—
258C2×D4—293no—
259C22×C4—293no—
260C22×C4—293no—
261C22×C4—293no—
262C22×C4—293no—
263C22×C4—291no—
264C22×C4—293no—
265C22×C4C22×D2913yes—
266C22×C4C22×D2913yes—
267C22×C4C22×D2911yescharacteristic
268C4⋊C4—293no—
269C4⋊C4—296no—
270C4⋊C4—291no—
271C4⋊C4—293no—
272C4⋊C4—293no—
273C4⋊C4—293no—
274C4⋊C4—293no—
275C4⋊C4—293no—
276C4⋊C4—293no—
277C4⋊C4—296no—
278C4⋊C4—296no—
279C4⋊C4C22×D2913yes—
280C4⋊C4C22×D2913yes—
281C4⋊C4C22×D2916yes—
282C22⋊C4—291no—
283C22⋊C4—293no—
284C22⋊C4—291no—
285C22⋊C4—293no—
286C22⋊C4—296no—
287C22⋊C4—293no—
288C22⋊C4—293no—
289C22⋊C4—296no—
290C22⋊C4—296no—
291C42—293no—
292C42—293no—
293C42—293no—
294C42—293no—
295C42—291no—
296C42—293no—
297C42C22×D2913yes—
298C42C22×D2913yes—
299C42C22×D2913yes—
300C42C22×D2913yes—
301C23—291no—
302C23—293no—
303C23C23×D2911yescharacteristic
304Q8—26no—
305Q8—586no—
306Q8—586no—
307Q8#9080514yescomplemented
308D4—294no—
309D4—586no—
310D4—586no—
311D4—586no—
312C2×C4—26no—
313C2×C4—26no—
314C2×C4—22no—
315C2×C4—291no—
316C2×C4—291no—
317C2×C4—291no—
318C2×C4—293no—
319C2×C4—293no—
320C2×C4—293no—
321C2×C4—586no—
322C2×C4—586no—
323C2×C4—586no—
324C2×C4—586no—
325C2×C4—582no—
326C2×C4—586no—
327C2×C4C23×D2913yes—
328C2×C4C23×D2911yescharacteristic
329C2×C4C23×D2913yes—
330C2×C4C23×D2913yes—
331C2×C4C23×D2913yes—
332C2×C4C23×D2911yescharacteristic
333C22—21no—
334C22—21no—
335C22—292no—
336C22—581no—
337C22—581no—
338C22—583no—
339C22—583no—
340C22—583no—
341C22#41×D2912yes—
342C22C24×D2911yescharacteristic
343C4—23no—
344C4—23no—
345C4—23no—
346C4—21no—
347C4—292no—
348C4—583no—
349C4—581no—
350C4—583no—
351C4—581no—
352C4—583no—
353C4C2×#9080516yes—
354C4#1174536212yes—
355C2—22no—
356C2—582no—
357C2—1163no—
358C2C2×#41×D2911yescharacteristic
359C2C22×#9080511yescharacteristic
360C2C2×#1174536211yescharacteristic
subgroupG/H
centerC2×C4C23×D29
commutator, socle, cosocleC22×C29C25
FrattiniC22C24×D29
FittingC2×C4×Q8×C29C2
hypercenterC2×C4×Q8D29
hypocenterC29#3482
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C2×C4 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
1. #14271889C2semidirect
2. #14271885C2semidirect
3. #14271854C2semidirect
4. #14271848C2semidirect
5. Q8×C22⋊D29C2semidirect
6. #14271825C2semidirect
7. #14271824C2semidirect
8. #14271814C2semidirect
9. #14271717C2semidirect
10. #14271700C2semidirect
11. #14271697C2semidirect
12. C4×#90809C2semidirect
13. C4×#90805C2semidirect
14. C4×Q8×D29C2semidirect
15. C2×C4×Q8×C29C2semidirect
124. Q8×C29#41semidirect
135. C22⋊D29#41semidirect
189. C2×C4×Q8D29semidirect
246. C29#3482semidirect
307. Q8#90805semidirect

Maximal subgroups

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

subgroupindex
#142718892
#142718852
#142718542
#142718482
Q8×C22⋊D292
#142718252
#142718242
#142718142
#142717172
#142717002
#142716972
C4×#908092
C4×#908052
C4×Q8×D292
C2×C4×Q8×C292
#348229