Finite Group Databasebeta

← #16831366

Subgroups — #16831366

Order 3712.

388 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271868C211yesmaximal, characteristic
2#14271826C211yesmaximal, characteristic
3#14271512C211yesmaximal, characteristic, complemented
4#14271500C211yesmaximal, characteristic, complemented
5#14271457C211yesmaximal, characteristic, complemented
6#14271405C211yesmaximal, characteristic, complemented
7#14271402C211yesmaximal, characteristic, complemented
8#14271372C211yesmaximal, characteristic, complemented
9#14271321C211yesmaximal, characteristic, complemented
10#14271320C211yesmaximal, characteristic, complemented
11#14271257C211yesmaximal, characteristic, complemented
12#14271226C211yesmaximal, characteristic
13C2×#11745158C211yesmaximal, characteristic, complemented
14#103×D29C211yesmaximal, characteristic, complemented
15C29×#484C211yesmaximal, characteristic, complemented
16C2×Q8×D29C2211yescharacteristic
17C22×Dic58C2211yescharacteristic
18C29×C22⋊Q8C2211yescharacteristic
19C2×C4⋊C4×C29C2211yescharacteristic
20#11745306C2211yescharacteristic
21C2×#90785C2211yescharacteristic
22C4×C22⋊D29—21no—
23C4×C22⋊D29C2211yescharacteristic
24#11745286—21no—
25#11745286C2211yescharacteristic
26C22×#6597C2211yescharacteristic
27C2×Dic116C2211yescharacteristic
28C2×Dic116C2211yescharacteristic
29C2×C8×D29C2211yescharacteristic
30#11745259C2211yescharacteristic
31#11745259C2211yescharacteristic
32#11745258—21no—
33#11745258—21no—
34C4⋊C4×D29C2211yescharacteristic
35#11745251—21no—
36#11745250—21no—
37#11745250C2211yescharacteristic
38#11745249C2211yescharacteristic
39#11745249C2211yescharacteristic
40#11745243—21no—
41#11745240—21no—
42C29×#107C2211yescharacteristic
43C29×#107C2211yescharacteristic
44C29×#103C2211yescharacteristic
45C29×#103C2211yescharacteristic
46C29×C22⋊C8C2211yescharacteristic
47#11745183C2211yescharacteristic
48#11745168C2211yescharacteristic
49#11745164C2211yescharacteristic
50#11745164C2211yescharacteristic
51#11745162C2211yescharacteristic
52C8×Dic29C2211yescharacteristic
53#11745158C2211yescharacteristic
54#11745158C2211yescharacteristic
55#11745158C2211yescharacteristic
56#11745158C2211yescharacteristic
57#11745158C2211yescharacteristic
58#11745155C2211yescharacteristic
59C2×Q8×C29C2311yescharacteristic
60C22×C4×C29—21no—
61C22×C4×C29C2311yescharacteristic
62C2×C22⋊D29D411yescharacteristic
63C22×Dic29—21no—
64Q8×D29—22no—
65Q8×D29—41no—
66C2×C4×D29—21no—
67C2×C4×D29—21no—
68C2×C4×D29C2311yescharacteristic
69C2×Dic58—22no—
70C2×Dic58—21no—
71C2×Dic58—21no—
72C2×Dic58—21no—
73C2×Dic58—41no—
74C2×Dic58C2311yescharacteristic
75C2×Dic58C2311yescharacteristic
76C2×Dic58C2311yescharacteristic
77C2×C8×C29C2311yescharacteristic
78C2×C8×C29C2311yescharacteristic
79C4⋊C4×C29—21no—
80C4⋊C4×C29—21no—
81C4⋊C4×C29C2311yescharacteristic
82C4⋊C4×C29C2311yescharacteristic
83C4⋊C4×C29C2311yescharacteristic
84C22⋊C4×C29—21no—
85C22⋊Dic29—21no—
86C22⋊Dic29D411yescharacteristic
87#90785—41no—
88#90781—21no—
89#90781—21no—
90#90781D411yescharacteristic
91C4⋊Dic29—21no—
92C4⋊Dic29—21no—
93C4⋊Dic29C2311yescharacteristic
94#90779—21no—
95#90779—21no—
96#90779—21no—
97#90779—21no—
98#90779—21no—
99#90779—21no—
100#90779—21no—
101#90779D411yescharacteristic
102C4×Dic29—21no—
103C4×Dic29—21no—
104C4×Dic29C2311yescharacteristic
105C2×#6597—41no—
106C2×#6597C2311yescharacteristic
107C2×#6597C2311yescharacteristic
108Dic116—22no—
109Dic116—41no—
110C8×D29—41no—
111C23×C29C2×D411yescharacteristic
112C22×D29C2×D411yescharacteristic
113Q8×C29—21no—
114Q8×C29—21no—
115C2×C4×C29—21no—
116C2×C4×C29—21no—
117C2×C4×C29—21no—
118C2×C4×C29—21no—
119C2×C4×C29—21no—
120C2×C4×C29—21no—
121C2×C4×C29—81no—
122C2×C4×C29C2×D411yescharacteristic
123C2×C4×C29C2411yescharacteristic
124C22⋊D29Q1614yescomplemented
125C2×Dic29—21no—
126C2×Dic29—21no—
127C2×Dic29—21no—
128C2×Dic29—21no—
129C2×Dic29—42no—
130C2×Dic29C2×D411yescharacteristic
131C2×Dic29C2×D411yescharacteristic
132C2×Dic29C2×D411yescharacteristic
133C4×D29—21no—
134C4×D29—21no—
135C4×D29—42no—
136C4×D29—81no—
137Dic58—21no—
138Dic58—21no—
139Dic58—21no—
140Dic58—21no—
141Dic58—21no—
142Dic58—42no—
143Dic58—42no—
144Dic58—81no—
145Dic58#4112yes—
146C8×C29—21no—
147C8×C29—21no—
148#6597—21no—
149#6597—21no—
150#3299—291nomaximal, Sylow
151C22×C29—21no—
152C22×C29—21no—
153C22×C29C2×Q1612yes—
154C22×C29C22×D411yescharacteristic
155C2×D29—21no—
156C2×D29—21no—
157C2×D29C2×Q1612yes—
158C4×C29—21no—
159C4×C29—41no—
160C4×C29—41no—
161C4×C29—41no—
162C4×C29—41no—
163C4×C29C2×#4111yescharacteristic
164C4×C29H(5,𝔽2)11yescharacteristic
165Dic29—22no—
166Dic29—21no—
167Dic29—21no—
168Dic29—41no—
169Dic29—41no—
170Dic29—41no—
171Dic29C2×Q1612yes—
172#554—291no—
173D4×Q8—291no—
174#487—291no—
175#484—291no—
176#484D2911yescharacteristic, complemented
177#477—291no—
178#467—291no—
179#467—291no—
180#462—291no—
181#451—291no—
182#451—291no—
183C4×Q16—291no—
184C8×D4—291no—
185C2×#103—291no—
186C2×#103—291no—
187C2×C29—22no—
188C2×C29#54611yescharacteristic
189C2×C29C22×Q1611yescharacteristic
190C2×C29#57711yescharacteristic
191D29—22no—
192C22×Q8—291no—
193C22×Q8—291no—
194C2×Q16—291no—
195C2×Q16—291no—
196C2×Q16—291no—
197C22×C8—291no—
198C22×C8—291no—
199C4⋊Q8—291no—
200C4⋊Q8—291no—
201C4⋊Q8—581no—
202#125—581no—
203C22⋊Q8—291no—
204C22⋊Q8—291no—
205C22⋊Q8—291no—
206C22⋊Q8—581no—
207C22⋊Q8—581no—
208C22⋊Q8—581no—
209C22⋊Q8—581no—
210C22⋊Q8C2×D2911yescharacteristic
211C4×Q8—291no—
212C4×Q8—291no—
213C4×D4—291no—
214C4×D4—581no—
215C4×D4—581no—
216C2×C4⋊C4—291no—
217C2×C4⋊C4C2×D2911yescharacteristic
218#107—291no—
219#107C2×D2911yescharacteristic
220#107C2×D2911yescharacteristic
221C4⋊C8—291no—
222#103—291no—
223#103—291no—
224#103—291no—
225#103—291no—
226#103—291no—
227#103—291no—
228#103—291no—
229#103—291no—
230#103C2×D2911yescharacteristic
231#103C2×D2911yescharacteristic
232C22⋊C8—291no—
233C22⋊C8C2×D2911yescharacteristic
234C4×C8—291no—
235C29#329911yescharacteristic, complemented, Sylow
236C2×Q8—291no—
237C2×Q8—291no—
238C2×Q8—291no—
239C2×Q8—581no—
240C2×Q8—581no—
241C2×Q8—582no—
242C2×Q8—581no—
243C2×Q8—582no—
244C2×Q8—1161no—
245C2×Q8—1161no—
246C2×Q8C22×D2911yescharacteristic
247C2×D4—291no—
248C22×C4—21no—
249C22×C4—291no—
250C22×C4—581no—
251C22×C4—581no—
252C22×C4—581no—
253C22×C4C22×D2911yescharacteristic
254Q16—582no—
255Q16—1161no—
256Q16—1161no—
257C2×C8—291no—
258C2×C8—291no—
259C2×C8—1161no—
260C2×C8—1161no—
261C2×C8C22×D2911yescharacteristic
262C2×C8C22×D2911yescharacteristic
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—291no—
266C4⋊C4—291no—
267C4⋊C4—581no—
268C4⋊C4—581no—
269C4⋊C4—581no—
270C4⋊C4—581no—
271C4⋊C4—581no—
272C4⋊C4—581no—
273C4⋊C4—581no—
274C4⋊C4—581no—
275C4⋊C4—581no—
276C4⋊C4C22×D2911yescharacteristic
277C4⋊C4C22×D2911yescharacteristic
278C4⋊C4C22×D2911yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—291no—
281C22⋊C4—291no—
282C22⋊C4—581no—
283C22⋊C4—581no—
284C22⋊C4—581no—
285C42—291no—
286C42—581no—
287C42—581no—
288C23—291no—
289C23D4×D2911yescharacteristic
290Q8—21no—
291Q8—21no—
292Q8—292no—
293Q8—581no—
294Q8—581no—
295Q8—581no—
296Q8—581no—
297Q8—581no—
298Q8—1162no—
299Q8—1162no—
300Q8—2321no—
301D4—294no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—81no—
309C2×C4—291no—
310C2×C4—291no—
311C2×C4—291no—
312C2×C4—581no—
313C2×C4—581no—
314C2×C4—581no—
315C2×C4—581no—
316C2×C4—581no—
317C2×C4—581no—
318C2×C4—1162no—
319C2×C4—1162no—
320C2×C4—2321no—
321C2×C4D4×D2911yescharacteristic
322C2×C4C23×D2911yescharacteristic
323C8—21no—
324C8—21no—
325C8—581no—
326C8—581no—
327C22—21no—
328C22—21no—
329C22—292no—
330C22—581no—
331C22—581no—
332C22Q16×D2912yes—
333C22C2×D4×D2911yescharacteristic
334C4—21no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—292no—
340C4—581no—
341C4—582no—
342C4—581no—
343C4—1161no—
344C4—1161no—
345C4—1161no—
346C4#41×D2911yescharacteristic
347C4#1174536411yescharacteristic
348C2—22no—
349C2—582no—
350C2#1427180511yescharacteristic
351C2C2×Q16×D2911yescharacteristic
352C2#1427197311yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#484C2
socleC22×C29C22×D4
prime radicalC2×C22⋊D29D4
hypercenter#484D29
hypocenterC29#3299
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
3. #14271512C2semidirect
4. #14271500C2semidirect
5. #14271457C2semidirect
6. #14271405C2semidirect
7. #14271402C2semidirect
8. #14271372C2semidirect
9. #14271321C2semidirect
10. #14271320C2semidirect
11. #14271257C2semidirect
13. C2×#11745158C2semidirect
14. #103×D29C2semidirect
15. C29×#484C2semidirect
124. C22⋊D29Q16semidirect
176. #484D29semidirect
235. C29#3299semidirect

Maximal subgroups

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

subgroupindex
#142718682
#142718262
#142715122
#142715002
#142714572
#142714052
#142714022
#142713722
#142713212
#142713202
#142712572
#142712262
C2×#117451582
#103×D292
C29×#4842
#329929