Finite Group Databasebeta

← #16831473

Subgroups — #16831473

Order 3712.

394 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271863C211yesmaximal, characteristic, complemented
2#14271817C211yesmaximal, characteristic, complemented
3#14271532C211yesmaximal, characteristic, complemented
4#14271507C211yesmaximal, characteristic, complemented
5#14271495C211yesmaximal, characteristic, complemented
6#14271463C211yesmaximal, characteristic, complemented
7#14271408C211yesmaximal, characteristic, complemented
8#14271391C211yesmaximal, characteristic, complemented
9#14271368C211yesmaximal, characteristic, complemented
10#14271305C211yesmaximal, characteristic, complemented
11#14271305C211yesmaximal, characteristic, complemented
12#14271236C211yesmaximal, characteristic, complemented
13#14271161C211yesmaximal, characteristic, complemented
14#14271156C211yesmaximal, characteristic, complemented
15C29×#442C211yesmaximal, characteristic, complemented
16C2×#90807C2211yescharacteristic
17C2×#90807C2211yescharacteristic
18C2×D8×C29C2211yescharacteristic
19C4×D4×C29C2211yescharacteristic
20C4×D4×C29C2211yescharacteristic
21#11745300C2211yescharacteristic
22#11745300C2211yescharacteristic
23C2×#90783C2211yescharacteristic
24C2×#90783C2211yescharacteristic
25#11745292—21no—
26#11745291—21no—
27C4×C22⋊D29—21no—
28C2×C4⋊Dic29—21no—
29C2×#90772C2211yescharacteristic
30C2×C8×D29C2211yescharacteristic
31#11745259C2211yescharacteristic
32#11745259C2211yescharacteristic
33#11745254C2211yescharacteristic
34C4⋊C4×D29C2211yescharacteristic
35#11745248—21no—
36#11745248—21no—
37#11745246—21no—
38#11745241—21no—
39C4×D116C2211yescharacteristic
40#11745232C2211yescharacteristic
41#11745231C2211yescharacteristic
42C29×#106C2211yescharacteristic
43C29×#102C2211yescharacteristic
44C29×#102C2211yescharacteristic
45C29×#97C2211yescharacteristic
46#11745180C2211yescharacteristic
47#11745180C2211yescharacteristic
48#11745168C2211yescharacteristic
49#11745168C2211yescharacteristic
50#11745164C2211yescharacteristic
51#11745164C2211yescharacteristic
52#11745164C2211yescharacteristic
53#11745164C2211yescharacteristic
54#11745158C2211yescharacteristic
55#11745158C2211yescharacteristic
56#11745156C2211yescharacteristic
57#11745155C2211yescharacteristic
58C4⋊#6597C2211yescharacteristic
59C2×D4×C29C2311yescharacteristic
60C2×D4×C29C2311yescharacteristic
61C22×C4×C29—21no—
62C22×C4×C29—21no—
63C2×C22⋊D29—21no—
64C2×C22⋊D29—21no—
65C2×C22⋊D29—21no—
66C2×C22⋊D29—21no—
67C22×Dic29—21no—
68C22×Dic29—21no—
69#90807—22no—
70#90807—22no—
71#90807—41no—
72#90807—41no—
73C2×D116D411yescharacteristic
74C2×C4×D29—21no—
75C2×C4×D29C2311yescharacteristic
76C2×C4×D29C2311yescharacteristic
77C2×Dic58C2311yescharacteristic
78C2×Dic58C2311yescharacteristic
79D8×C29—22no—
80C2×C8×C29C2311yescharacteristic
81C2×C8×C29C2311yescharacteristic
82C4⋊C4×C29C2311yescharacteristic
83C4⋊C4×C29C2311yescharacteristic
84C22⋊C4×C29—21no—
85C22⋊C4×C29—21no—
86C42×C29C2311yescharacteristic
87C22⋊Dic29—21no—
88C22⋊Dic29—21no—
89#90783—41no—
90#90783—41no—
91#90781—21no—
92#90781—21no—
93#90781—21no—
94#90781D411yescharacteristic
95#90781D411yescharacteristic
96C4⋊Dic29—21no—
97C4⋊Dic29—21no—
98C4⋊Dic29—21no—
99C4⋊Dic29—21no—
100C4⋊Dic29D411yescharacteristic
101C4⋊Dic29C2311yescharacteristic
102C4⋊Dic29C2311yescharacteristic
103#90779—21no—
104#90779—21no—
105#90779—21no—
106C4×Dic29—21no—
107C2×#6597C2311yescharacteristic
108C2×#6597C2311yescharacteristic
109#90772—41no—
110C8×D29—41no—
111C23×C29—21no—
112C23×C29—21no—
113C22×D29C2×D411yescharacteristic
114C22×D29C2×D411yescharacteristic
115D4×C29—21no—
116D4×C29—21no—
117D4×C29—21no—
118D4×C29#4112yes—
119C2×C4×C29—21no—
120C2×C4×C29—21no—
121C2×C4×C29—42no—
122C2×C4×C29—81no—
123C2×C4×C29C2×D411yescharacteristic
124C2×C4×C29C2×D411yescharacteristic
125C2×C4×C29C2411yescharacteristic
126C22⋊D29—42no—
127C22⋊D29—42no—
128C22⋊D29—42no—
129C22⋊D29—81no—
130C2×Dic29—21no—
131C2×Dic29—21no—
132C2×Dic29—21no—
133C2×Dic29—21no—
134C2×Dic29—42no—
135C2×Dic29—42no—
136C2×Dic29C2×D411yescharacteristic
137C2×Dic29C2×D411yescharacteristic
138D116—41no—
139C4×D29—21no—
140C4×D29—21no—
141C4×D29—21no—
142C4×D29—21no—
143C4×D29—81no—
144Dic58—21no—
145Dic58—21no—
146Dic58—21no—
147Dic58—21no—
148C8×C29—21no—
149C8×C29—21no—
150#6597—21no—
151#6597—21no—
152#3307—291nomaximal, Sylow
153C22×C29—22no—
154C22×C29—41no—
155C22×C29—41no—
156C22×C29—41no—
157C22×C29—41no—
158C22×C29—41no—
159C22×C29C22×D411yescharacteristic
160C2×D29—21no—
161C2×D29—21no—
162C2×D29—21no—
163C2×D29—21no—
164C2×D29—21no—
165C2×D29—21no—
166C4×C29—21no—
167C4×C29—21no—
168C4×C29—41no—
169C4×C29—41no—
170C4×C29C2×#4111yescharacteristic
171C4×C29H(5,𝔽2)11yescharacteristic
172Dic29—21no—
173Dic29—21no—
174Dic29—41no—
175Dic29—41no—
176Dic29—41no—
177Dic29—41no—
178#553—291no—
179#547—291no—
180#491—291no—
181#485—291no—
182#483—291no—
183#478—291no—
184#468—291no—
185#465—291no—
186#461—291no—
187#449—291no—
188#449—291no—
189#442D2911yescharacteristic, complemented
190#435—291no—
191#417—291no—
192#416—291no—
193C2×C29—42no—
194C2×C29—81no—
195C2×C29#54611yescharacteristic
196C2×C29#57511yescharacteristic
197C2×C29#57711yescharacteristic
198D29—41no—
199D29—41no—
200C2×#41—291no—
201C2×#41—291no—
202C2×SD16—291no—
203C2×SD16—291no—
204C2×D8C2×D2911yescharacteristic
205C2×M16—291no—
206C22×C8—291no—
207C4⋊Q8—291no—
208#126—581no—
209#125—291no—
210#123—581no—
211#123—581no—
212#123—581no—
213C22⋊Q8—291no—
214C22⋊Q8—291no—
215#121—291no—
216#121—291no—
217#121—581no—
218#121—581no—
219C4×D4—291no—
220C4×D4—581no—
221C4×D4C2×D2911yescharacteristic
222C4×D4C2×D2911yescharacteristic
223#117—291no—
224C2×C4⋊C4—291no—
225C2×C4⋊C4—581no—
226#107—291no—
227#106—291no—
228#106C2×D2911yescharacteristic
229C4⋊C8—291no—
230#103—291no—
231#103—291no—
232#103—291no—
233#103—291no—
234#103—291no—
235#103—291no—
236#102—291no—
237#102—291no—
238#102C2×D2911yescharacteristic
239#102C2×D2911yescharacteristic
240C22⋊C8—291no—
241C22⋊C8—291no—
242#97C2×D2911yescharacteristic
243C29#330711yescharacteristic, complemented, Sylow
244#41—582no—
245#41—582no—
246#41—1161no—
247#41—1161no—
248C2×Q8—291no—
249C2×Q8—291no—
250C2×D4—291no—
251C2×D4—581no—
252C2×D4—581no—
253C2×D4—581no—
254C2×D4—581no—
255C2×D4C22×D2911yescharacteristic
256C2×D4C22×D2911yescharacteristic
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—291no—
260C22×C4—291no—
261C22×C4—581no—
262C22×C4—581no—
263C22×C4—581no—
264SD16—1161no—
265SD16—1161no—
266D8—22no—
267M16—1161no—
268C2×C8—291no—
269C2×C8—291no—
270C2×C8—1161no—
271C2×C8C22×D2911yescharacteristic
272C2×C8C22×D2911yescharacteristic
273C4⋊C4—291no—
274C4⋊C4—291no—
275C4⋊C4—291no—
276C4⋊C4—581no—
277C4⋊C4—581no—
278C4⋊C4—581no—
279C4⋊C4—581no—
280C4⋊C4—581no—
281C4⋊C4—581no—
282C4⋊C4—581no—
283C4⋊C4C22×D2911yescharacteristic
284C4⋊C4C22×D2911yescharacteristic
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—291no—
288C22⋊C4—291no—
289C22⋊C4—581no—
290C22⋊C4—581no—
291C22⋊C4—581no—
292C22⋊C4—581no—
293C22⋊C4—581no—
294C42—581no—
295C42C22×D2911yescharacteristic
296C23—21no—
297C23—21no—
298C23—291no—
299C23—291no—
300Q8—581no—
301Q8—581no—
302Q8—581no—
303Q8—581no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—1161no—
308D4—1162no—
309D4—1162no—
310D4—1162no—
311D4—2321no—
312D4#9080512yes—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—42no—
316C2×C4—81no—
317C2×C4—291no—
318C2×C4—291no—
319C2×C4—581no—
320C2×C4—581no—
321C2×C4—581no—
322C2×C4—581no—
323C2×C4—581no—
324C2×C4—581no—
325C2×C4—581no—
326C2×C4—581no—
327C2×C4—1162no—
328C2×C4—1162no—
329C2×C4—2321no—
330C2×C4D4×D2911yescharacteristic
331C2×C4D4×D2911yescharacteristic
332C2×C4C23×D2911yescharacteristic
333C8—21no—
334C8—21no—
335C8—581no—
336C8—581no—
337C22—22no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—581no—
344C22—581no—
345C22—581no—
346C22—581no—
347C22—581no—
348C22—581no—
349C22C2×D4×D2911yescharacteristic
350C4—21no—
351C4—21no—
352C4—41no—
353C4—41no—
354C4—581no—
355C4—581no—
356C4—1161no—
357C4—1161no—
358C4—1161no—
359C4—1161no—
360C4C2×#9080511yescharacteristic
361C4#1174536411yescharacteristic
362C2—42no—
363C2—81no—
364C2—1161no—
365C2—1161no—
366C2#1427180911yescharacteristic
367C2#1427195911yescharacteristic
368C2#1427197311yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#442C2
socleC22×C29C22×D4
hypercenter#442D29
hypocenterC29#3307
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #14271863C2semidirect
2. #14271817C2semidirect
3. #14271532C2semidirect
4. #14271507C2semidirect
5. #14271495C2semidirect
6. #14271463C2semidirect
7. #14271408C2semidirect
8. #14271391C2semidirect
9. #14271368C2semidirect
10. #14271305C2semidirect
11. #14271305C2semidirect
12. #14271236C2semidirect
13. #14271161C2semidirect
14. #14271156C2semidirect
15. C29×#442C2semidirect
189. #442D29semidirect
243. C29#3307semidirect

Maximal subgroups

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

subgroupindex
#142718632
#142718172
#142715322
#142715072
#142714952
#142714632
#142714082
#142713912
#142713682
#142713052
#142712362
#142711612
#142711562
C29×#4422
#330729