Finite Group Databasebeta

← #16829595

Subgroups — #16829595

Order 3712.

392 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
1C4×#90805C211yesmaximal, characteristic, complemented
2#14271501C211yesmaximal, characteristic, complemented
3#14271484C211yesmaximal, characteristic, complemented
4#14271467C211yesmaximal, characteristic, complemented
5#14271460C211yesmaximal, characteristic, complemented
6#14271382C211yesmaximal, characteristic, complemented
7#14271375C211yesmaximal, characteristic, complemented
8#14271323C211yesmaximal, characteristic, complemented
9#14271306C211yesmaximal, characteristic
10#14271273C211yesmaximal, characteristic, complemented
11#14271268C211yesmaximal, characteristic, complemented
12#14271263C211yesmaximal, characteristic, complemented
13#14271261C211yesmaximal, characteristic, complemented
14#14271220C211yesmaximal, characteristic, complemented
15C29×#529C211yesmaximal, characteristic, complemented
16C2×#90805C2211yescharacteristic
17C29×#126—21no—
18C29×#125C2211yescharacteristic
19C29×#124C2211yescharacteristic
20C29×#123—21no—
21C29×C22⋊Q8C2211yescharacteristic
22C29×#121C2211yescharacteristic
23C4×Q8×C29C2211yescharacteristic
24C4×D4×C29—21no—
25C4×D4×C29C2211yescharacteristic
26C29×#117—21no—
27C2×C42×C29C2211yescharacteristic
28C2×#90785C2211yescharacteristic
29C2×#90784C2211yescharacteristic
30C2×#90783C2211yescharacteristic
31C2×#90782C2211yescharacteristic
32C4×C22⋊D29—21no—
33C4×C22⋊D29—21no—
34#11745288C2211yescharacteristic
35C4×D116C2211yescharacteristic
36C4×D116C2211yescharacteristic
37#11745234—21no—
38C42×D29—21no—
39C4×Dic58C2211yescharacteristic
40C4×Dic58C2211yescharacteristic
41#11745183C2211yescharacteristic
42#11745183C2211yescharacteristic
43#11745180C2211yescharacteristic
44#11745180C2211yescharacteristic
45C22⋊#6597C2211yescharacteristic
46C22⋊#6597C2211yescharacteristic
47#11745158C2211yescharacteristic
48#11745158C2211yescharacteristic
49#11745157C2211yescharacteristic
50#11745157C2211yescharacteristic
51#11745156C2211yescharacteristic
52#11745156C2211yescharacteristic
53#11745155C2211yescharacteristic
54#11745155C2211yescharacteristic
55C4⋊#6597C2211yescharacteristic
56C4⋊#6597C2211yescharacteristic
57#11745151C2211yescharacteristic
58#11745151C2211yescharacteristic
59C2×Q8×C29C2311yescharacteristic
60C2×D4×C29—21no—
61C2×D4×C29C2311yescharacteristic
62C22×C4×C29—21no—
63C22×C4×C29D411yescharacteristic
64C22×C4×C29D411yescharacteristic
65C22×C4×C29C2311yescharacteristic
66C2×C22⋊D29—21no—
67#90805—22no—
68#90805—22no—
69C2×D116C2311yescharacteristic
70C2×C4×D29—21no—
71C2×C4×D29—21no—
72C2×C4×D29—21no—
73C2×Dic58C2311yescharacteristic
74C4⋊C4×C29—21no—
75C4⋊C4×C29—21no—
76C4⋊C4×C29—21no—
77C4⋊C4×C29—21no—
78C4⋊C4×C29C2311yescharacteristic
79C4⋊C4×C29C2311yescharacteristic
80C22⋊C4×C29—21no—
81C22⋊C4×C29—21no—
82C22⋊C4×C29—21no—
83C22⋊C4×C29—21no—
84C22⋊C4×C29—21no—
85C42×C29—21no—
86C42×C29D411yescharacteristic
87C42×C29D411yescharacteristic
88C42×C29C2311yescharacteristic
89C42×C29C2311yescharacteristic
90C22⋊Dic29—21no—
91#90785—22no—
92#90784—22no—
93#90783—22no—
94#90782—22no—
95#90781—21no—
96#90781—21no—
97C4⋊Dic29C2311yescharacteristic
98C4⋊Dic29C2311yescharacteristic
99#90779—21no—
100#90779—21no—
101C4×Dic29—21no—
102C4×Dic29—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—21no—
113D4×C29—21no—
114D4×C29—21no—
115D4×C29—42no—
116C2×C4×C29—21no—
117C2×C4×C29—21no—
118C2×C4×C29—21no—
119C2×C4×C29—21no—
120C2×C4×C29—21no—
121C2×C4×C29—41no—
122C2×C4×C29—41no—
123C2×C4×C29—42no—
124C2×C4×C29C2×D411yescharacteristic
125C2×C4×C29C2×D411yescharacteristic
126C2×C4×C29C2×D411yescharacteristic
127C2×C4×C29C2×D411yescharacteristic
128C2×C4×C29C2×D411yescharacteristic
129C2×C4×C29C2411yescharacteristic
130C22⋊D29—24no—
131C2×Dic29—21no—
132C2×Dic29—21no—
133C2×Dic29—21no—
134D116—21no—
135D116#4112yes—
136C4×D29—24no—
137C4×D29—42no—
138C4×D29—42no—
139Dic58—21no—
140Dic58#4112yes—
141#6597—21no—
142#6597—21no—
143#6597—21no—
144#6597—21no—
145#3111—291nomaximal, Sylow
146C22×C29—21no—
147C22×C29—21no—
148C22×C29—21no—
149C22×C29—41no—
150C22×C29—41no—
151C22×C29—41no—
152C22×C29C22×D411yescharacteristic
153C2×D29—22no—
154C2×D29—41no—
155C2×D29—41no—
156C4×C29—21no—
157C4×C29—21no—
158C4×C29—21no—
159C4×C29—21no—
160C4×C29—21no—
161C4×C29—41no—
162C4×C29—41no—
163C4×C29—41no—
164C4×C29C2×#4111yescharacteristic
165C4×C29C2×#4111yescharacteristic
166Dic29—22no—
167Dic29—41no—
168Dic29—41no—
169#529D2911yescharacteristic, complemented
170C4×#41—291no—
171#485—291no—
172#482—291no—
173#479—291no—
174#478—291no—
175#464—291no—
176#463—291no—
177#452—291no—
178#449—291no—
179#442—291no—
180#441—291no—
181#440—291no—
182#440—291no—
183#432—291no—
184C2×C29—41no—
185C2×C29—81no—
186C2×C29#52511yescharacteristic
187C2×C29#57511yescharacteristic
188C2×C29#57511yescharacteristic
189D29—42no—
190C2×#41—291no—
191C2×Q16—291no—
192C2×SD16—291no—
193C2×SD16—291no—
194C2×D8—291no—
195#126—21no—
196#125C2×D2911yescharacteristic
197#124C2×D2911yescharacteristic
198#123—21no—
199C22⋊Q8C2×D2911yescharacteristic
200#121C2×D2911yescharacteristic
201C4×Q8—291no—
202C4×Q8—291no—
203C4×Q8C2×D2911yescharacteristic
204C4×D4—21no—
205C4×D4—291no—
206C4×D4—291no—
207C4×D4—581no—
208C4×D4—581no—
209C4×D4C2×D2911yescharacteristic
210#117—21no—
211#117—291no—
212#117—581no—
213C2×C42—581no—
214C2×C42C2×D2911yescharacteristic
215#107—291no—
216#107—291no—
217#106—291no—
218#106—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—
232#97—291no—
233C29#311111yescharacteristic, complemented, Sylow
234#41—582no—
235#41—582no—
236C2×Q8—291no—
237C2×Q8C22×D2911yescharacteristic
238C2×D4—21no—
239C2×D4—291no—
240C2×D4—581no—
241C2×D4C22×D2911yescharacteristic
242C22×C4—21no—
243C22×C4—581no—
244C22×C4—581no—
245C22×C4—581no—
246C22×C4C22⋊D2911yescharacteristic
247C22×C4C22⋊D2911yescharacteristic
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—21no—
261C4⋊C4—291no—
262C4⋊C4—291no—
263C4⋊C4—581no—
264C4⋊C4—581no—
265C4⋊C4C22×D2911yescharacteristic
266C4⋊C4C22×D2911yescharacteristic
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—21no—
272C22⋊C4—581no—
273C22⋊C4—581no—
274C22⋊C4—581no—
275C42—21no—
276C42—581no—
277C42—581no—
278C42—581no—
279C42C22⋊D2911yescharacteristic
280C42C22⋊D2911yescharacteristic
281C42C22×D2911yescharacteristic
282C42C22×D2911yescharacteristic
283C23—21no—
284C23—581no—
285C23C2×C22⋊D2911yescharacteristic
286Q8—21no—
287Q8—21no—
288Q8—292no—
289Q8—581no—
290D4—21no—
291D4—21no—
292D4—42no—
293D4—292no—
294D4—584no—
295D4—581no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—42no—
304C2×C4—584no—
305C2×C4—581no—
306C2×C4—581no—
307C2×C4—581no—
308C2×C4—1162no—
309C2×C4—1162no—
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—21no—
322C22—21no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—582no—
327C22—1161no—
328C22—1161no—
329C22C22×C22⋊D2911yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—582no—
339C4—1161no—
340C4—1161no—
341C4#41×D2911yescharacteristic
342C4#41×D2911yescharacteristic
343C2—41no—
344C2—81no—
345C2—1162no—
346C2#1427167011yescharacteristic
347C2#1427196111yescharacteristic
348C2#1427196111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#529C2
socleC22×C29C22×D4
prime radical#14271306C2
hypercenter#529D29
hypocenterC29#3111
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. C4×#90805C2semidirect
2. #14271501C2semidirect
3. #14271484C2semidirect
4. #14271467C2semidirect
5. #14271460C2semidirect
6. #14271382C2semidirect
7. #14271375C2semidirect
8. #14271323C2semidirect
10. #14271273C2semidirect
11. #14271268C2semidirect
12. #14271263C2semidirect
13. #14271261C2semidirect
14. #14271220C2semidirect
15. C29×#529C2semidirect
169. #529D29semidirect
233. C29#3111semidirect

Maximal subgroups

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

subgroupindex
C4×#908052
#142715012
#142714842
#142714672
#142714602
#142713822
#142713752
#142713232
#142713062
#142712732
#142712682
#142712632
#142712612
#142712202
C29×#5292
#311129