Finite Group Databasebeta

← #16829693

Subgroups — #16829693

Order 3712.

396 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#14271768C211yesmaximal, characteristic, complemented
2#14271643C211yesmaximal, characteristic, complemented
3#14271482C211yesmaximal, characteristic, complemented
4#14271477C211yesmaximal, characteristic, complemented
5#14271471C211yesmaximal, characteristic, complemented
6#14271464C211yesmaximal, characteristic, complemented
7#14271364C211yesmaximal, characteristic, complemented
8#14271359C211yesmaximal, characteristic, complemented
9#14271310C211yesmaximal, characteristic, complemented
10#14271310C211yesmaximal, characteristic, complemented
11#14271276C211yesmaximal, characteristic, complemented
12#14271265C211yesmaximal, characteristic, complemented
13C4×#90773C211yesmaximal, characteristic, complemented
14C4×D232C211yesmaximal, characteristic, complemented
15C29×#433C211yesmaximal, characteristic, complemented
16C2×#90805C2211yescharacteristic
17C29×#117C2211yescharacteristic
18#11745292C2211yescharacteristic
19#11745292C2211yescharacteristic
20C2×C4⋊Dic29C2211yescharacteristic
21C2×D232C2211yescharacteristic
22C2×D232C2211yescharacteristic
23C2×#90773C2211yescharacteristic
24C2×#90773C2211yescharacteristic
25#11745256—21no—
26#11745256—21no—
27#11745254—21no—
28C4⋊C4×D29—21no—
29#11745246—21no—
30#11745246—21no—
31#11745243—21no—
32#11745243—21no—
33#11745236C2211yescharacteristic
34C4×D116C2211yescharacteristic
35C4×D116C2211yescharacteristic
36C4×D116C2211yescharacteristic
37C4×D116C2211yescharacteristic
38#11745232C2211yescharacteristic
39C4×Dic58C2211yescharacteristic
40C4×Dic58C2211yescharacteristic
41C29×C4⋊C8C2211yescharacteristic
42C29×C4⋊C8C2211yescharacteristic
43C29×C22⋊C8C2211yescharacteristic
44C29×C22⋊C8C2211yescharacteristic
45C29×#97C2211yescharacteristic
46C4×C8×C29C2211yescharacteristic
47#11745169C2211yescharacteristic
48#11745169C2211yescharacteristic
49#11745169C2211yescharacteristic
50#11745169C2211yescharacteristic
51#11745169C2211yescharacteristic
52#11745169C2211yescharacteristic
53#11745166C2211yescharacteristic
54#11745166C2211yescharacteristic
55#11745165C2211yescharacteristic
56#11745165C2211yescharacteristic
57#11745164C2211yescharacteristic
58#11745164C2211yescharacteristic
59C22×C4×C29C2311yescharacteristic
60C2×C22⋊D29—21no—
61C2×C22⋊D29—21no—
62C2×C22⋊D29—21no—
63C22×Dic29—21no—
64#90805—22no—
65#90805—22no—
66C2×D116—21no—
67C2×D116—21no—
68C2×D116C2311yescharacteristic
69C2×D116C2311yescharacteristic
70C2×D116C2311yescharacteristic
71C2×C4×D29—21no—
72C2×C4×D29—21no—
73C2×C4×D29—21no—
74C2×C4×D29—21no—
75C2×C4×D29—21no—
76C2×Dic58C2311yescharacteristic
77C2×C8×C29C2311yescharacteristic
78C2×C8×C29C2311yescharacteristic
79C2×C8×C29C2311yescharacteristic
80C2×C8×C29C2311yescharacteristic
81C4⋊C4×C29D411yescharacteristic
82C4⋊C4×C29D411yescharacteristic
83C22⋊C4×C29D411yescharacteristic
84C22⋊C4×C29D411yescharacteristic
85C42×C29C2311yescharacteristic
86C42×C29C2311yescharacteristic
87#90781—21no—
88#90781—21no—
89#90781—21no—
90#90781—21no—
91#90781—21no—
92#90781—21no—
93C4⋊Dic29—21no—
94C4⋊Dic29C2311yescharacteristic
95C4⋊Dic29C2311yescharacteristic
96C4⋊Dic29C2311yescharacteristic
97C4⋊Dic29C2311yescharacteristic
98#90779—21no—
99#90779—21no—
100#90779—21no—
101#90779—21no—
102C4×Dic29—21no—
103C4×Dic29—21no—
104D232—22no—
105D232—22no—
106#90773—22no—
107#90773—22no—
108C23×C29C2×D411yescharacteristic
109C22×D29—21no—
110C22×D29—21no—
111C22×D29—21no—
112C2×C4×C29—21no—
113C2×C4×C29—21no—
114C2×C4×C29C2×D411yescharacteristic
115C2×C4×C29C2×D411yescharacteristic
116C2×C4×C29C2×D411yescharacteristic
117C2×C4×C29C2×D411yescharacteristic
118C2×C4×C29C2×D411yescharacteristic
119C2×C4×C29C2411yescharacteristic
120C22⋊D29—24no—
121C22⋊D29—81no—
122C22⋊D29—81no—
123C2×Dic29—21no—
124C2×Dic29—21no—
125C2×Dic29—21no—
126C2×Dic29—21no—
127C2×Dic29—21no—
128C2×Dic29—81no—
129D116—21no—
130D116—21no—
131D116—21no—
132D116—21no—
133D116—21no—
134D116—81no—
135D116—81no—
136D116#4112yes—
137C4×D29—24no—
138C4×D29—81no—
139C4×D29—81no—
140C4×D29—81no—
141C4×D29—81no—
142Dic58—21no—
143Dic58#4112yes—
144C8×C29—21no—
145C8×C29—21no—
146C8×C29—21no—
147C8×C29—21no—
148#3119—291nomaximal, Sylow
149C22×C29—21no—
150C22×C29—21no—
151C22×C29—21no—
152C22×C29C22×D411yescharacteristic
153C2×D29—22no—
154C2×D29—41no—
155C2×D29—41no—
156C2×D29—41no—
157C2×D29—41no—
158C2×D29—41no—
159C2×D29—41no—
160C2×D29—41no—
161C2×D29—41no—
162C4×C29—21no—
163C4×C29—21no—
164C4×C29—21no—
165C4×C29—21no—
166C4×C29—21no—
167C4×C29C2×#4111yescharacteristic
168C4×C29C2×#4111yescharacteristic
169Dic29—22no—
170Dic29—41no—
171Dic29—41no—
172Dic29—41no—
173Dic29—41no—
174#540—291no—
175#520—291no—
176#481—291no—
177#480—291no—
178#479—291no—
179#478—291no—
180#460—291no—
181#459—291no—
182#449—291no—
183#449—291no—
184#442—291no—
185#440—291no—
186C4×SD16—291no—
187C4×D8—291no—
188#433D2911yescharacteristic, complemented
189C2×C29—41no—
190C2×C29#52511yescharacteristic
191C2×C29#57611yescharacteristic
192C2×C29#57711yescharacteristic
193D29—42no—
194D29—81no—
195D29—81no—
196C2×#41—291no—
197C2×SD16—291no—
198C2×SD16—291no—
199C2×D8—291no—
200C2×D8—291no—
201#127—291no—
202#125—291no—
203#123—581no—
204#123—581no—
205#121—291no—
206#121—291no—
207#121—581no—
208#121—581no—
209C4×Q8—291no—
210C4×Q8—291no—
211C4×D4—291no—
212C4×D4—291no—
213C4×D4—291no—
214C4×D4—291no—
215C4×D4—581no—
216C4×D4—581no—
217#117—581no—
218#117C2×D2911yescharacteristic
219C2×C4⋊C4—291no—
220C2×C4⋊C4—581no—
221#107—291no—
222#107—291no—
223#106—291no—
224#106—291no—
225C4⋊C8C2×D2911yescharacteristic
226C4⋊C8C2×D2911yescharacteristic
227#103—291no—
228#103—291no—
229#102—291no—
230#102—291no—
231#102—291no—
232#102—291no—
233#102—291no—
234#102—291no—
235C22⋊C8C2×D2911yescharacteristic
236C22⋊C8C2×D2911yescharacteristic
237#97C2×D2911yescharacteristic
238C4×C8C2×D2911yescharacteristic
239C29#311911yescharacteristic, complemented, Sylow
240#41—582no—
241#41—582no—
242C2×Q8—291no—
243C2×D4—291no—
244C2×D4—291no—
245C2×D4—291no—
246C2×D4—581no—
247C2×D4—581no—
248C2×D4—581no—
249C2×D4—581no—
250C2×D4—581no—
251C22×C4—581no—
252C22×C4—581no—
253C22×C4—581no—
254C22×C4—581no—
255C22×C4—581no—
256C22×C4—581no—
257C22×C4C22×D2911yescharacteristic
258SD16—582no—
259SD16—582no—
260D8—582no—
261D8—582no—
262C2×C8C22×D2911yescharacteristic
263C2×C8C22×D2911yescharacteristic
264C2×C8C22×D2911yescharacteristic
265C2×C8C22×D2911yescharacteristic
266C4⋊C4—291no—
267C4⋊C4—291no—
268C4⋊C4—291no—
269C4⋊C4—291no—
270C4⋊C4—581no—
271C4⋊C4—581no—
272C4⋊C4—581no—
273C4⋊C4—581no—
274C4⋊C4—581no—
275C4⋊C4D11611yescharacteristic
276C4⋊C4D11611yescharacteristic
277C22⋊C4—581no—
278C22⋊C4—581no—
279C22⋊C4—581no—
280C22⋊C4—581no—
281C22⋊C4—581no—
282C22⋊C4—581no—
283C22⋊C4D11611yescharacteristic
284C22⋊C4D11611yescharacteristic
285C42—581no—
286C42—581no—
287C42C22×D2911yescharacteristic
288C42C22×D2911yescharacteristic
289C23—581no—
290C23—581no—
291C23—581no—
292C23C2×D11611yescharacteristic
293Q8—292no—
294Q8—581no—
295D4—292no—
296D4—584no—
297D4—581no—
298D4—581no—
299D4—581no—
300D4—581no—
301D4—581no—
302D4—2321no—
303D4—2321no—
304D4—2321no—
305D4—2321no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—584no—
309C2×C4—581no—
310C2×C4—581no—
311C2×C4—581no—
312C2×C4—581no—
313C2×C4—581no—
314C2×C4—2321no—
315C2×C4—2321no—
316C2×C4—2321no—
317C2×C4—2321no—
318C2×C4—2321no—
319C2×C4C2×D11611yescharacteristic
320C2×C4C2×D11611yescharacteristic
321C2×C4C2×D11611yescharacteristic
322C2×C4C2×D11611yescharacteristic
323C2×C4C2×D11611yescharacteristic
324C2×C4C23×D2911yescharacteristic
325C8—21no—
326C8—21no—
327C8—21no—
328C8—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—582no—
333C22—1161no—
334C22—1161no—
335C22—1161no—
336C22—1161no—
337C22—1161no—
338C22—1161no—
339C22—1161no—
340C22—1161no—
341C22C22×D11611yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—582no—
348C4—1161no—
349C4—1161no—
350C4—1161no—
351C4—1161no—
352C4#41×D2911yescharacteristic
353C4#41×D2911yescharacteristic
354C2—41no—
355C2—1162no—
356C2—2321no—
357C2—2321no—
358C2#1427167511yescharacteristic
359C2#1427196811yescharacteristic
360C2#1427197511yescharacteristic
subgroupG/H
centerC22C22×D116
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#433C2
socleC22×C29C22×D4
hypercenter#433D29
hypocenterC29#3119
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #14271768C2semidirect
2. #14271643C2semidirect
3. #14271482C2semidirect
4. #14271477C2semidirect
5. #14271471C2semidirect
6. #14271464C2semidirect
7. #14271364C2semidirect
8. #14271359C2semidirect
9. #14271310C2semidirect
10. #14271310C2semidirect
11. #14271276C2semidirect
12. #14271265C2semidirect
13. C4×#90773C2semidirect
14. C4×D232C2semidirect
15. C29×#433C2semidirect
188. #433D29semidirect
239. C29#3119semidirect

Maximal subgroups

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

subgroupindex
#142717682
#142716432
#142714822
#142714772
#142714712
#142714642
#142713642
#142713592
#142713102
#142712762
#142712652
C4×#907732
C4×D2322
C29×#4332
#311929