Finite Group Databasebeta

← #16829754

Subgroups — #16829754

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#14271498C211yesmaximal, characteristic, complemented
3#14271476C211yesmaximal, characteristic, complemented
4#14271458C211yesmaximal, characteristic, complemented
5#14271443C211yesmaximal, characteristic, complemented
6#14271385C211yesmaximal, characteristic, complemented
7#14271378C211yesmaximal, characteristic, complemented
8#14271325C211yesmaximal, characteristic, complemented
9#14271308C211yesmaximal, characteristic
10#14271263C211yesmaximal, characteristic, complemented
11#14271261C211yesmaximal, characteristic, complemented
12C4×#90785C211yesmaximal, characteristic, complemented
13C4×#90782C211yesmaximal, characteristic, complemented
14#14271224C211yesmaximal, characteristic, complemented
15C29×#520C211yesmaximal, characteristic, complemented
16C2×#41×C29C2211yescharacteristic
17C4×Q8×C29C2211yescharacteristic
18C4×Q8×C29C2211yescharacteristic
19C4×D4×C29—21no—
20C4×D4×C29—21no—
21C4×D4×C29C2211yescharacteristic
22C4×D4×C29C2211yescharacteristic
23C29×#117—21no—
24C29×#117C2211yescharacteristic
25C2×C4⋊C4×C29—21no—
26C2×C4⋊C4×C29C2211yescharacteristic
27C2×#90785C2211yescharacteristic
28C2×#90784C2211yescharacteristic
29C2×#90783C2211yescharacteristic
30C2×#90782C2211yescharacteristic
31#11745292C2211yescharacteristic
32#11745286C2211yescharacteristic
33#11745260—21no—
34#11745258—21no—
35#11745247—21no—
36#11745245—21no—
37#11745237C2211yescharacteristic
38C4×D116C2211yescharacteristic
39#11745231C2211yescharacteristic
40C4×Dic58C2211yescharacteristic
41#11745183C2211yescharacteristic
42#11745183C2211yescharacteristic
43#11745180C2211yescharacteristic
44#11745180C2211yescharacteristic
45C22⋊#6597C2211yescharacteristic
46C22⋊#6597C2211yescharacteristic
47#11745158C2211yescharacteristic
48#11745158C2211yescharacteristic
49#11745157C2211yescharacteristic
50#11745157C2211yescharacteristic
51#11745155C2211yescharacteristic
52#11745155C2211yescharacteristic
53#11745155C2211yescharacteristic
54#11745155C2211yescharacteristic
55C4⋊#6597C2211yescharacteristic
56C4⋊#6597C2211yescharacteristic
57#11745151C2211yescharacteristic
58C4×#6597C2211yescharacteristic
59#41×C29—22no—
60#41×C29—22no—
61C2×Q8×C29C2311yescharacteristic
62C2×D4×C29—21no—
63C2×D4×C29C2311yescharacteristic
64C22×C4×C29—21no—
65C22×C4×C29—21no—
66C22×C4×C29—21no—
67C22×C4×C29—21no—
68C22×C4×C29C2311yescharacteristic
69C2×C22⋊D29—21no—
70C2×D116C2311yescharacteristic
71C2×C4×D29—21no—
72C2×Dic58—21no—
73C2×Dic58C2311yescharacteristic
74C4⋊C4×C29—21no—
75C4⋊C4×C29—21no—
76C4⋊C4×C29—21no—
77C4⋊C4×C29D411yescharacteristic
78C4⋊C4×C29D411yescharacteristic
79C4⋊C4×C29C2311yescharacteristic
80C4⋊C4×C29C2311yescharacteristic
81C22⋊C4×C29—21no—
82C22⋊C4×C29—21no—
83C22⋊C4×C29D411yescharacteristic
84C22⋊C4×C29D411yescharacteristic
85C42×C29—21no—
86C42×C29—21no—
87C42×C29C2311yescharacteristic
88C42×C29C2311yescharacteristic
89C22⋊Dic29—21no—
90#90785—22no—
91#90784—22no—
92#90783—22no—
93#90782—22no—
94#90781—21no—
95#90781—21no—
96#90781—21no—
97#90781—21no—
98C4⋊Dic29—21no—
99C4⋊Dic29C2311yescharacteristic
100C4⋊Dic29C2311yescharacteristic
101#90779—21no—
102#90779—21no—
103C4×Dic29—21no—
104C2×#6597C2311yescharacteristic
105C2×#6597C2311yescharacteristic
106C2×#6597C2311yescharacteristic
107C2×#6597C2311yescharacteristic
108C23×C29—21no—
109C23×C29C2×D411yescharacteristic
110C22×D29—21no—
111Q8×C29—21no—
112Q8×C29#4112yes—
113D4×C29—24no—
114D4×C29—21no—
115D4×C29#4112yes—
116C2×C4×C29—24no—
117C2×C4×C29—21no—
118C2×C4×C29—21no—
119C2×C4×C29—21no—
120C2×C4×C29—21no—
121C2×C4×C29—21no—
122C2×C4×C29—81no—
123C2×C4×C29—81no—
124C2×C4×C29—81no—
125C2×C4×C29C2×D411yescharacteristic
126C2×C4×C29C2×D411yescharacteristic
127C2×C4×C29C2×D411yescharacteristic
128C2×C4×C29C2×D411yescharacteristic
129C2×C4×C29C2×D411yescharacteristic
130C2×C4×C29C2411yescharacteristic
131C22⋊D29—81no—
132C2×Dic29—21no—
133C2×Dic29—21no—
134C2×Dic29—21no—
135D116—21no—
136D116—21no—
137C4×D29—81no—
138Dic58—21no—
139Dic58—21no—
140Dic58—81no—
141#6597—21no—
142#6597—21no—
143#6597—21no—
144#6597—21no—
145#3124—291nomaximal, Sylow
146C22×C29—21no—
147C22×C29—22no—
148C22×C29—21no—
149C22×C29—21no—
150C22×C29—41no—
151C22×C29—41no—
152C22×C29C22×D411yescharacteristic
153C2×D29—41no—
154C2×D29—41no—
155C2×D29—41no—
156C4×C29—21no—
157C4×C29—22no—
158C4×C29—21no—
159C4×C29—21no—
160C4×C29—21no—
161C4×C29—21no—
162C4×C29—41no—
163C4×C29—41no—
164C4×C29C2×#4111yescharacteristic
165C4×C29C2×#4111yescharacteristic
166Dic29—41no—
167Dic29—41no—
168Dic29—41no—
169#542—291no—
170#520D2911yescharacteristic, complemented
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#433—291no—
184C2×C29—41no—
185C2×C29—42no—
186C2×C29#52511yescharacteristic
187C2×C29#57611yescharacteristic
188C2×C29#57811yescharacteristic
189D29—81no—
190C2×#41C2×D2911yescharacteristic
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×Q8C2×D2911yescharacteristic
205C4×Q8C2×D2911yescharacteristic
206C4×D4—21no—
207C4×D4—21no—
208C4×D4—291no—
209C4×D4C2×D2911yescharacteristic
210C4×D4C2×D2911yescharacteristic
211#117—21no—
212#117C2×D2911yescharacteristic
213C2×C4⋊C4—21no—
214C2×C4⋊C4C2×D2911yescharacteristic
215#107—291no—
216#107—291no—
217#107—291no—
218#107—291no—
219C4⋊C8—291no—
220C4⋊C8—291no—
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⋊C8—291no—
230C22⋊C8—291no—
231#97—291no—
232C4×C8—291no—
233C29#312411yescharacteristic, complemented, Sylow
234#41—22no—
235#41—22no—
236C2×Q8—291no—
237C2×Q8—581no—
238C2×Q8C22×D2911yescharacteristic
239C2×D4—21no—
240C2×D4—291no—
241C2×D4—581no—
242C2×D4C22×D2911yescharacteristic
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—581no—
248C22×C4C22×D2911yescharacteristic
249Q16—582no—
250SD16—582no—
251SD16—582no—
252D8—582no—
253C2×C8—291no—
254C2×C8—291no—
255C2×C8—291no—
256C2×C8—291no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—291no—
261C4⋊C4—291no—
262C4⋊C4—581no—
263C4⋊C4—581no—
264C4⋊C4—581no—
265C4⋊C4C22⋊D2911yescharacteristic
266C4⋊C4C22⋊D2911yescharacteristic
267C4⋊C4C22×D2911yescharacteristic
268C4⋊C4C22×D2911yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—581no—
272C22⋊C4—581no—
273C22⋊C4—581no—
274C22⋊C4—581no—
275C22⋊C4—581no—
276C22⋊C4C22⋊D2911yescharacteristic
277C22⋊C4C22⋊D2911yescharacteristic
278C42—21no—
279C42—21no—
280C42—581no—
281C42C22×D2911yescharacteristic
282C42C22×D2911yescharacteristic
283C23—21no—
284C23—581no—
285C23C2×C22⋊D2911yescharacteristic
286Q8—21no—
287Q8—581no—
288Q8—581no—
289Q8—2321no—
290Q8#9080512yes—
291D4—24no—
292D4—21no—
293D4—581no—
294D4—581no—
295D4—2321no—
296D4#9080512yes—
297C2×C4—24no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—581no—
307C2×C4—581no—
308C2×C4—581no—
309C2×C4—2321no—
310C2×C4C2×C22⋊D2911yescharacteristic
311C2×C4C2×C22⋊D2911yescharacteristic
312C2×C4C2×C22⋊D2911yescharacteristic
313C2×C4C2×C22⋊D2911yescharacteristic
314C2×C4C2×C22⋊D2911yescharacteristic
315C2×C4C23×D2911yescharacteristic
316C8—581no—
317C8—581no—
318C8—581no—
319C8—581no—
320C22—21no—
321C22—22no—
322C22—21no—
323C22—21no—
324C22—41no—
325C22—41no—
326C22—1161no—
327C22—1161no—
328C22—1161no—
329C22C22×C22⋊D2911yescharacteristic
330C4—21no—
331C4—22no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—41no—
337C4—41no—
338C4—1161no—
339C4—1161no—
340C4—1161no—
341C4C2×#9080511yescharacteristic
342C4C2×#9080511yescharacteristic
343C2—41no—
344C2—42no—
345C2—2321no—
346C2#1427167411yescharacteristic
347C2#1427196611yescharacteristic
348C2#1427197811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#520C2
socleC22×C29C22×D4
prime radical#14271308C2
hypercenter#520D29
hypocenterC29#3124
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ #117 ◁ #520

Complements

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

NH ≅ G/Ntype
1. #14271784C2semidirect
2. #14271498C2semidirect
3. #14271476C2semidirect
4. #14271458C2semidirect
5. #14271443C2semidirect
6. #14271385C2semidirect
7. #14271378C2semidirect
8. #14271325C2semidirect
10. #14271263C2semidirect
11. #14271261C2semidirect
12. C4×#90785C2semidirect
13. C4×#90782C2semidirect
14. #14271224C2semidirect
15. C29×#520C2semidirect
170. #520D29semidirect
233. C29#3124semidirect

Maximal subgroups

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

subgroupindex
#142717842
#142714982
#142714762
#142714582
#142714432
#142713852
#142713782
#142713252
#142713082
#142712632
#142712612
C4×#907852
C4×#907822
#142712242
C29×#5202
#312429