Finite Group Databasebeta

← #16829756

Subgroups — #16829756

Order 3712.

384 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271784C211yesmaximal, characteristic, complemented
2#14271643C211yesmaximal, characteristic, complemented
3#14271499C211yesmaximal, characteristic, complemented
4#14271477C211yesmaximal, characteristic, complemented
5#14271459C211yesmaximal, characteristic, complemented
6#14271444C211yesmaximal, characteristic, complemented
7#14271386C211yesmaximal, characteristic, complemented
8#14271379C211yesmaximal, characteristic, complemented
9#14271327C211yesmaximal, characteristic, complemented
10#14271310C211yesmaximal, characteristic
11#14271265C211yesmaximal, characteristic, complemented
12#14271265C211yesmaximal, characteristic, complemented
13C4×Dic116C211yesmaximal, characteristic, complemented
14C4×D232C211yesmaximal, characteristic, complemented
15C29×#433C211yesmaximal, characteristic, complemented
16C2×#90805C2211yescharacteristic
17C29×#117C2211yescharacteristic
18#11745292C2211yescharacteristic
19C2×C4⋊Dic29C2211yescharacteristic
20#11745286C2211yescharacteristic
21C2×Dic116C2211yescharacteristic
22C2×D232C2211yescharacteristic
23C2×#90773C2211yescharacteristic
24C2×#90773C2211yescharacteristic
25#11745260—21no—
26#11745258—21no—
27#11745254—21no—
28C4⋊C4×D29—21no—
29#11745247—21no—
30#11745245—21no—
31#11745243—21no—
32#11745243—21no—
33#11745237C2211yescharacteristic
34C4×D116C2211yescharacteristic
35C4×D116C2211yescharacteristic
36C4×D116C2211yescharacteristic
37#11745231C2211yescharacteristic
38C4×Dic58C2211yescharacteristic
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#11745166C2211yescharacteristic
52#11745166C2211yescharacteristic
53#11745166C2211yescharacteristic
54#11745166C2211yescharacteristic
55#11745164C2211yescharacteristic
56#11745164C2211yescharacteristic
57#11745164C2211yescharacteristic
58#11745164C2211yescharacteristic
59C22×C4×C29C2311yescharacteristic
60C2×C22⋊D29—21no—
61C2×C22⋊D29—21no—
62C22×Dic29—21no—
63#90805—22no—
64#90805—22no—
65C2×D116C2311yescharacteristic
66C2×D116C2311yescharacteristic
67C2×C4×D29—21no—
68C2×C4×D29—21no—
69C2×C4×D29—21no—
70C2×C4×D29—21no—
71C2×Dic58—21no—
72C2×Dic58C2311yescharacteristic
73C2×Dic58C2311yescharacteristic
74C2×C8×C29C2311yescharacteristic
75C2×C8×C29C2311yescharacteristic
76C2×C8×C29C2311yescharacteristic
77C2×C8×C29C2311yescharacteristic
78C4⋊C4×C29D411yescharacteristic
79C4⋊C4×C29D411yescharacteristic
80C22⋊C4×C29D411yescharacteristic
81C22⋊C4×C29D411yescharacteristic
82C42×C29C2311yescharacteristic
83C42×C29C2311yescharacteristic
84C22⋊Dic29—21no—
85#90781—21no—
86#90781—21no—
87#90781—21no—
88#90781—21no—
89#90781—21no—
90#90781—21no—
91C4⋊Dic29—21no—
92C4⋊Dic29—21no—
93C4⋊Dic29C2311yescharacteristic
94C4⋊Dic29C2311yescharacteristic
95C4⋊Dic29C2311yescharacteristic
96C4⋊Dic29C2311yescharacteristic
97#90779—21no—
98#90779—21no—
99#90779—21no—
100#90779—21no—
101C4×Dic29—21no—
102C4×Dic29—21no—
103C4×Dic29—21no—
104Dic116—22no—
105D232—22no—
106#90773—22no—
107#90773—22no—
108C23×C29C2×D411yescharacteristic
109C22×D29—21no—
110C22×D29—21no—
111C2×C4×C29—21no—
112C2×C4×C29—21no—
113C2×C4×C29C2×D411yescharacteristic
114C2×C4×C29C2×D411yescharacteristic
115C2×C4×C29C2×D411yescharacteristic
116C2×C4×C29C2×D411yescharacteristic
117C2×C4×C29C2×D411yescharacteristic
118C2×C4×C29C2411yescharacteristic
119C22⋊D29—24no—
120C22⋊D29—81no—
121C2×Dic29—21no—
122C2×Dic29—21no—
123C2×Dic29—21no—
124C2×Dic29—21no—
125C2×Dic29—21no—
126C2×Dic29—21no—
127C2×Dic29—81no—
128D116—21no—
129D116—21no—
130D116—21no—
131D116#4112yes—
132C4×D29—24no—
133C4×D29—81no—
134C4×D29—81no—
135C4×D29—81no—
136Dic58—21no—
137Dic58—21no—
138Dic58—21no—
139Dic58—81no—
140Dic58#4112yes—
141C8×C29—21no—
142C8×C29—21no—
143C8×C29—21no—
144C8×C29—21no—
145#3124—291nomaximal, Sylow
146C22×C29—21no—
147C22×C29—21no—
148C22×C29—21no—
149C22×C29C22×D411yescharacteristic
150C2×D29—22no—
151C2×D29—41no—
152C2×D29—41no—
153C2×D29—41no—
154C2×D29—41no—
155C2×D29—41no—
156C4×C29—21no—
157C4×C29—21no—
158C4×C29—21no—
159C4×C29—21no—
160C4×C29—21no—
161C4×C29C2×#4111yescharacteristic
162C4×C29C2×#4111yescharacteristic
163Dic29—22no—
164Dic29—41no—
165Dic29—41no—
166Dic29—41no—
167Dic29—41no—
168Dic29—41no—
169#542—291no—
170#520—291no—
171#484—291no—
172#480—291no—
173#477—291no—
174#474—291no—
175#464—291no—
176#463—291no—
177#452—291no—
178#449—291no—
179#440—291no—
180#440—291no—
181C4×Q16—291no—
182C4×D8—291no—
183#433D2911yescharacteristic, complemented
184C2×C29—41no—
185C2×C29#52511yescharacteristic
186C2×C29#57611yescharacteristic
187C2×C29#57811yescharacteristic
188D29—42no—
189D29—81no—
190C2×#41—291no—
191C2×Q16—291no—
192C2×SD16—291no—
193C2×SD16—291no—
194C2×D8—291no—
195C4⋊Q8—291no—
196#126—581no—
197#124—291no—
198#124—581no—
199#123—581no—
200C22⋊Q8—291no—
201C22⋊Q8—581no—
202#121—291no—
203C4×Q8—291no—
204C4×Q8—291no—
205C4×Q8—291no—
206C4×D4—291no—
207C4×D4—291no—
208C4×D4—291no—
209C4×D4—581no—
210C4×D4—581no—
211#117—581no—
212#117C2×D2911yescharacteristic
213C2×C4⋊C4—291no—
214C2×C4⋊C4—581no—
215#107—291no—
216#107—291no—
217#107—291no—
218#107—291no—
219C4⋊C8C2×D2911yescharacteristic
220C4⋊C8C2×D2911yescharacteristic
221#103—291no—
222#103—291no—
223#103—291no—
224#103—291no—
225#102—291no—
226#102—291no—
227#102—291no—
228#102—291no—
229C22⋊C8C2×D2911yescharacteristic
230C22⋊C8C2×D2911yescharacteristic
231#97C2×D2911yescharacteristic
232C4×C8C2×D2911yescharacteristic
233C29#312411yescharacteristic, complemented, Sylow
234#41—582no—
235#41—582no—
236C2×Q8—291no—
237C2×Q8—291no—
238C2×Q8—581no—
239C2×D4—291no—
240C2×D4—291no—
241C2×D4—581no—
242C2×D4—581no—
243C22×C4—581no—
244C22×C4—581no—
245C22×C4—581no—
246C22×C4—581no—
247C22×C4—581no—
248C22×C4C22×D2911yescharacteristic
249Q16—582no—
250SD16—582no—
251SD16—582no—
252D8—582no—
253C2×C8C22×D2911yescharacteristic
254C2×C8C22×D2911yescharacteristic
255C2×C8C22×D2911yescharacteristic
256C2×C8C22×D2911yescharacteristic
257C4⋊C4—291no—
258C4⋊C4—291no—
259C4⋊C4—291no—
260C4⋊C4—291no—
261C4⋊C4—581no—
262C4⋊C4—581no—
263C4⋊C4—581no—
264C4⋊C4—581no—
265C4⋊C4—581no—
266C4⋊C4—581no—
267C4⋊C4D11611yescharacteristic
268C4⋊C4D11611yescharacteristic
269C22⋊C4—581no—
270C22⋊C4—581no—
271C22⋊C4—581no—
272C22⋊C4—581no—
273C22⋊C4—581no—
274C22⋊C4—581no—
275C22⋊C4—581no—
276C22⋊C4D11611yescharacteristic
277C22⋊C4D11611yescharacteristic
278C42—581no—
279C42—581no—
280C42—581no—
281C42C22×D2911yescharacteristic
282C42C22×D2911yescharacteristic
283C23—581no—
284C23—581no—
285C23C2×D11611yescharacteristic
286Q8—292no—
287Q8—581no—
288Q8—581no—
289Q8—581no—
290Q8—2321no—
291D4—292no—
292D4—584no—
293D4—581no—
294D4—581no—
295D4—581no—
296D4—2321no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—584no—
300C2×C4—581no—
301C2×C4—581no—
302C2×C4—581no—
303C2×C4—581no—
304C2×C4—581no—
305C2×C4—581no—
306C2×C4—2321no—
307C2×C4—2321no—
308C2×C4—2321no—
309C2×C4—2321no—
310C2×C4C2×D11611yescharacteristic
311C2×C4C2×D11611yescharacteristic
312C2×C4C2×D11611yescharacteristic
313C2×C4C2×D11611yescharacteristic
314C2×C4C2×D11611yescharacteristic
315C2×C4C23×D2911yescharacteristic
316C8—21no—
317C8—21no—
318C8—21no—
319C8—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—582no—
324C22—1161no—
325C22—1161no—
326C22—1161no—
327C22—1161no—
328C22—1161no—
329C22C22×D11611yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—582no—
336C4—1161no—
337C4—1161no—
338C4—1161no—
339C4—1161no—
340C4—1161no—
341C4#41×D2911yescharacteristic
342C4#41×D2911yescharacteristic
343C2—41no—
344C2—1162no—
345C2—2321no—
346C2#1427167511yescharacteristic
347C2#1427196811yescharacteristic
348C2#1427198011yescharacteristic
subgroupG/H
centerC22C22×D116
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#433C2
socleC22×C29C22×D4
prime radical#14271310C2
hypercenter#433D29
hypocenterC29#3124
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. #14271784C2semidirect
2. #14271643C2semidirect
3. #14271499C2semidirect
4. #14271477C2semidirect
5. #14271459C2semidirect
6. #14271444C2semidirect
7. #14271386C2semidirect
8. #14271379C2semidirect
9. #14271327C2semidirect
11. #14271265C2semidirect
12. #14271265C2semidirect
13. C4×Dic116C2semidirect
14. C4×D232C2semidirect
15. C29×#433C2semidirect
183. #433D29semidirect
233. C29#3124semidirect

Maximal subgroups

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

subgroupindex
#142717842
#142716432
#142714992
#142714772
#142714592
#142714442
#142713862
#142713792
#142713272
#142713102
#142712652
C4×Dic1162
C4×D2322
C29×#4332
#312429