Finite Group Databasebeta

← #16831399

Subgroups — #16831399

Order 3712.

398 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#14271825C211yesmaximal, characteristic, complemented
3#14271518C211yesmaximal, characteristic, complemented
4#14271507C211yesmaximal, characteristic, complemented
5#14271483C211yesmaximal, characteristic, complemented
6#14271470C211yesmaximal, characteristic, complemented
7#14271398C211yesmaximal, characteristic, complemented
8#14271391C211yesmaximal, characteristic, complemented
9#14271378C211yesmaximal, characteristic, complemented
10#14271307C211yesmaximal, characteristic, complemented
11#14271300C211yesmaximal, characteristic, complemented
12C8×D116C211yesmaximal, characteristic, complemented
13#14271158C211yesmaximal, characteristic, complemented
14#103×D29C211yesmaximal, characteristic, complemented
15C4×SD16×C29C211yesmaximal, characteristic, complemented
16C2×#90809C2211yescharacteristic
17C2×Q8×D29C2211yescharacteristic
18C2×SD16×C29C2211yescharacteristic
19C4×Q8×C29C2211yescharacteristic
20C4×D4×C29C2211yescharacteristic
21#11745300C2211yescharacteristic
22#11745300C2211yescharacteristic
23C2×#90783C2211yescharacteristic
24C2×#90782C2211yescharacteristic
25#11745291—21no—
26C4×C22⋊D29—21no—
27C2×C8×D29C2211yescharacteristic
28C2×C8×D29C2211yescharacteristic
29#11745259—21no—
30#11745259C2211yescharacteristic
31#11745257—21no—
32#11745257C2211yescharacteristic
33#11745254C2211yescharacteristic
34C4⋊C4×D29C2211yescharacteristic
35#11745246—21no—
36#11745241—21no—
37#11745237—21no—
38#11745237C2211yescharacteristic
39C4×D116—21no—
40C4×D116C2211yescharacteristic
41#11745232C2211yescharacteristic
42C29×#106C2211yescharacteristic
43C29×#103C2211yescharacteristic
44C29×#102C2211yescharacteristic
45C4×C8×C29C2211yescharacteristic
46#11745183C2211yescharacteristic
47#11745183C2211yescharacteristic
48#11745169C2211yescharacteristic
49#11745169C2211yescharacteristic
50#11745168C2211yescharacteristic
51#11745168C2211yescharacteristic
52#11745164C2211yescharacteristic
53#11745164C2211yescharacteristic
54#11745158C2211yescharacteristic
55#11745157C2211yescharacteristic
56#11745156C2211yescharacteristic
57#11745155C2211yescharacteristic
58C4⋊#6597C2211yescharacteristic
59C2×Q8×C29C2311yescharacteristic
60C2×D4×C29C2311yescharacteristic
61C22×C4×C29—21no—
62C2×C22⋊D29—21no—
63C2×C22⋊D29—21no—
64#90809—22no—
65#90809—41no—
66Q8×D29—22no—
67Q8×D29—41no—
68C2×D116—21no—
69C2×D116—21no—
70C2×D116D411yescharacteristic
71C2×D116C2311yescharacteristic
72C2×C4×D29—21no—
73C2×C4×D29—21no—
74C2×C4×D29—21no—
75C2×C4×D29C2311yescharacteristic
76C2×C4×D29C2311yescharacteristic
77C2×Dic58—21no—
78C2×Dic58C2311yescharacteristic
79SD16×C29—22no—
80C2×C8×C29C2311yescharacteristic
81C2×C8×C29C2311yescharacteristic
82C4⋊C4×C29—21no—
83C4⋊C4×C29C2311yescharacteristic
84C4⋊C4×C29C2311yescharacteristic
85C22⋊C4×C29—21no—
86C42×C29—21no—
87C42×C29C2311yescharacteristic
88C22⋊Dic29—21no—
89C22⋊Dic29—21no—
90#90783—41no—
91#90782—41no—
92#90781—21no—
93#90781—21no—
94#90781—21no—
95#90781—21no—
96#90781—21no—
97#90781D411yescharacteristic
98#90781D411yescharacteristic
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
109C8×D29—41no—
110C8×D29—41no—
111C23×C29—21no—
112C22×D29—21no—
113C22×D29C2×D411yescharacteristic
114C22×D29C2×D411yescharacteristic
115Q8×C29—21no—
116Q8×C29#4112yes—
117D4×C29—21no—
118D4×C29—21no—
119C2×C4×C29—21no—
120C2×C4×C29—21no—
121C2×C4×C29—21no—
122C2×C4×C29—81no—
123C2×C4×C29C2×D411yescharacteristic
124C2×C4×C29C2×D411yescharacteristic
125C2×C4×C29C2411yescharacteristic
126C22⋊D29—42no—
127C22⋊D29—81no—
128C2×Dic29—21no—
129C2×Dic29—21no—
130C2×Dic29—21no—
131C2×Dic29C2×D411yescharacteristic
132C2×Dic29C2×D411yescharacteristic
133D116—22no—
134D116—21no—
135D116—21no—
136D116—42no—
137D116—42no—
138C4×D29—21no—
139C4×D29—21no—
140C4×D29—21no—
141C4×D29—21no—
142C4×D29—42no—
143C4×D29—42no—
144C4×D29—81no—
145Dic58—21no—
146Dic58—21no—
147Dic58—42no—
148C8×C29—21no—
149C8×C29—21no—
150#6597—21no—
151#6597—21no—
152#3301—291nomaximal, Sylow
153C22×C29—41no—
154C22×C29—41no—
155C22×C29—41no—
156C22×C29C22×D411yescharacteristic
157C2×D29—21no—
158C2×D29—21no—
159C2×D29—21no—
160C2×D29—21no—
161C2×D29—21no—
162C2×D29—41no—
163C2×D29—41no—
164C2×D29—41no—
165C2×D29#13512yes—
166C4×C29—22no—
167C4×C29—21no—
168C4×C29—21no—
169C4×C29—41no—
170C4×C29—41no—
171C4×C29C2×#4111yescharacteristic
172C4×C29H(5,𝔽2)11yescharacteristic
173Dic29—21no—
174Dic29—21no—
175Dic29—41no—
176Dic29—41no—
177Dic29—41no—
178#553—291no—
179#548—291no—
180#488—291no—
181#485—291no—
182#481—291no—
183#479—291no—
184#466—291no—
185#465—291no—
186#463—291no—
187#449—291no—
188#448—291no—
189C4×SD16D2911yescharacteristic, complemented
190C8×D4—291no—
191#416—291no—
192C2×#103—291no—
193C2×C29—81no—
194C2×C29#54611yescharacteristic
195C2×C29C2×#13511yescharacteristic
196C2×C29#57711yescharacteristic
197D29—22no—
198D29—41no—
199D29—81no—
200C2×#41—291no—
201C22×Q8—291no—
202C2×SD16—291no—
203C2×SD16C2×D2911yescharacteristic
204C2×D8—291no—
205C22×C8—291no—
206C22×C8—291no—
207#126—581no—
208#125—291no—
209#124—291no—
210#124—581no—
211#123—581no—
212C22⋊Q8—291no—
213C22⋊Q8—581no—
214#121—291no—
215#121—291no—
216#121—291no—
217#121—581no—
218#121—581no—
219C4×Q8C2×D2911yescharacteristic
220C4×D4—291no—
221C4×D4—581no—
222C4×D4—581no—
223C4×D4C2×D2911yescharacteristic
224#117—291no—
225C2×C4⋊C4—291no—
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#103C2×D2911yescharacteristic
236#102—291no—
237#102—291no—
238#102—291no—
239#102C2×D2911yescharacteristic
240C22⋊C8—291no—
241C22⋊C8—291no—
242C4×C8C2×D2911yescharacteristic
243C29#330111yescharacteristic, complemented, Sylow
244#41—582no—
245#41—1161no—
246C2×Q8—291no—
247C2×Q8—581no—
248C2×Q8—582no—
249C2×Q8—1161no—
250C2×Q8C22×D2911yescharacteristic
251C2×D4—291no—
252C2×D4—291no—
253C2×D4—581no—
254C2×D4—581no—
255C2×D4—581no—
256C2×D4—581no—
257C2×D4C22×D2911yescharacteristic
258C22×C4—21no—
259C22×C4—291no—
260C22×C4—291no—
261C22×C4—581no—
262C22×C4—581no—
263C22×C4—581no—
264SD16—22no—
265SD16—1161no—
266D8—1161no—
267C2×C8—291no—
268C2×C8—291no—
269C2×C8—1161no—
270C2×C8—1161no—
271C2×C8C22×D2911yescharacteristic
272C2×C8C22×D2911yescharacteristic
273C4⋊C4—21no—
274C4⋊C4—291no—
275C4⋊C4—291no—
276C4⋊C4—291no—
277C4⋊C4—581no—
278C4⋊C4—581no—
279C4⋊C4—581no—
280C4⋊C4—581no—
281C4⋊C4C22×D2911yescharacteristic
282C4⋊C4C22×D2911yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—291no—
285C22⋊C4—291no—
286C22⋊C4—581no—
287C22⋊C4—581no—
288C22⋊C4—581no—
289C22⋊C4—581no—
290C22⋊C4—581no—
291C22⋊C4—581no—
292C22⋊C4—581no—
293C42—21no—
294C42—581no—
295C42C22×D2911yescharacteristic
296C23—21no—
297C23—291no—
298C23—291no—
299C23—581no—
300Q8—21no—
301Q8—581no—
302Q8—581no—
303Q8—1162no—
304Q8#9080512yes—
305D4—21no—
306D4—21no—
307D4—582no—
308D4—581no—
309D4—581no—
310D4—1162no—
311D4—1162no—
312D4—1162no—
313D4—2321no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—81no—
318C2×C4—291no—
319C2×C4—291no—
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—41no—
338C22—41no—
339C22—41no—
340C22—292no—
341C22—581no—
342C22—581no—
343C22—581no—
344C22—581no—
345C22—581no—
346C22—1161no—
347C22—1161no—
348C22—1161no—
349C22C2×D4×D2911yescharacteristic
350C4—22no—
351C4—21no—
352C4—21no—
353C4—41no—
354C4—41no—
355C4—581no—
356C4—581no—
357C4—1161no—
358C4—1161no—
359C4—1161no—
360C4C2×#9080511yescharacteristic
361C4#1174536411yescharacteristic
362C2—81no—
363C2—582no—
364C2—1161no—
365C2—2321no—
366C2#1427180911yescharacteristic
367C2#135×D2911yescharacteristic
368C2#1427196911yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC4×SD16×C29C2
socleC22×C29C22×D4
hypercenterC4×SD16D29
hypocenterC29#3301
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #14271863C2semidirect
2. #14271825C2semidirect
3. #14271518C2semidirect
4. #14271507C2semidirect
5. #14271483C2semidirect
6. #14271470C2semidirect
7. #14271398C2semidirect
8. #14271391C2semidirect
9. #14271378C2semidirect
10. #14271307C2semidirect
11. #14271300C2semidirect
12. C8×D116C2semidirect
13. #14271158C2semidirect
14. #103×D29C2semidirect
15. C4×SD16×C29C2semidirect
189. C4×SD16D29semidirect
243. C29#3301semidirect

Maximal subgroups

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

subgroupindex
#142718632
#142718252
#142715182
#142715072
#142714832
#142714702
#142713982
#142713912
#142713782
#142713072
#142713002
C8×D1162
#142711582
#103×D292
C4×SD16×C292
#330129