Finite Group Databasebeta

← #16830906

Subgroups — #16830906

Order 3712.

358 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271786C211yesmaximal, characteristic, complemented
2#14271766C211yesmaximal, characteristic, complemented
3#14271472C211yesmaximal, characteristic, complemented
4#14271462C211yesmaximal, characteristic, complemented
5#14271452C211yesmaximal, characteristic, complemented
6#14271441C211yesmaximal, characteristic, complemented
7#14271414C211yesmaximal, characteristic, complemented
8#14271411C211yesmaximal, characteristic, complemented
9#14271399C211yesmaximal, characteristic, complemented
10#14271381C211yesmaximal, characteristic, complemented
11#14271380C211yesmaximal, characteristic, complemented
12#14271361C211yesmaximal, characteristic, complemented
13#14271357C211yesmaximal, characteristic, complemented
14#14271189C211yesmaximal, characteristic, complemented
15C29×#465C211yesmaximal, characteristic, complemented
16C2×SD16×C29C2211yescharacteristic
17C22×C8×C29C2211yescharacteristic
18C29×C22⋊Q8C2211yescharacteristic
19C29×#121C2211yescharacteristic
20#11745309C2211yescharacteristic
21Q8×Dic29C2211yescharacteristic
22C2×#90784C2211yescharacteristic
23#11745302C2211yescharacteristic
24#11745301—21no—
25#11745300—21no—
26D4×Dic29C2211yescharacteristic
27C2×#90782C2211yescharacteristic
28#11745292C2211yescharacteristic
29#11745292C2211yescharacteristic
30#11745288C2211yescharacteristic
31C2×#90777C2211yescharacteristic
32C2×D232C2211yescharacteristic
33#11745260—21no—
34#11745259—21no—
35#11745255C2211yescharacteristic
36#11745255C2211yescharacteristic
37#11745252C2211yescharacteristic
38#11745250C2211yescharacteristic
39#11745248—21no—
40#11745247—21no—
41#11745245—21no—
42#11745245—21no—
43C29×#106C2211yescharacteristic
44C29×#103C2211yescharacteristic
45C29×#102C2211yescharacteristic
46#11745183C2211yescharacteristic
47#11745180C2211yescharacteristic
48#11745169C2211yescharacteristic
49#11745169C2211yescharacteristic
50#11745166C2211yescharacteristic
51#11745162C2211yescharacteristic
52#11745162C2211yescharacteristic
53#11745162C2211yescharacteristic
54#11745162C2211yescharacteristic
55#11745157C2211yescharacteristic
56#11745157C2211yescharacteristic
57#11745156C2211yescharacteristic
58#11745155C2211yescharacteristic
59C2×Q8×C29C2311yescharacteristic
60C2×D4×C29—21no—
61C2×D4×C29C2311yescharacteristic
62C22×C4×C29C2311yescharacteristic
63C2×C22⋊D29—21no—
64C2×C22⋊D29—21no—
65C2×C22⋊D29—21no—
66C2×C22⋊D29—21no—
67C22×Dic29—21no—
68C2×D116C2311yescharacteristic
69C2×D116C2311yescharacteristic
70C2×C4×D29—21no—
71C2×C4×D29—21no—
72C2×Dic58—21no—
73SD16×C29—41no—
74C2×C8×C29—41no—
75C2×C8×C29C2311yescharacteristic
76C2×C8×C29C2311yescharacteristic
77C4⋊C4×C29—21no—
78C4⋊C4×C29C2311yescharacteristic
79C4⋊C4×C29C2311yescharacteristic
80C22⋊C4×C29—21no—
81C22⋊C4×C29—21no—
82C22⋊Dic29—21no—
83C22⋊Dic29D411yescharacteristic
84C22⋊Dic29D411yescharacteristic
85#90784—41no—
86#90782—41no—
87#90781—21no—
88#90781—21no—
89#90781—21no—
90#90781—21no—
91#90781—21no—
92#90781—21no—
93C4⋊Dic29—21no—
94C4⋊Dic29—21no—
95C4⋊Dic29D411yescharacteristic
96C4⋊Dic29D411yescharacteristic
97C4⋊Dic29C2311yescharacteristic
98C4⋊Dic29C2311yescharacteristic
99#90779—21no—
100#90779—21no—
101C4×Dic29—21no—
102C4×Dic29C2311yescharacteristic
103C4×Dic29C2311yescharacteristic
104#90777—41no—
105C2×#6597C2311yescharacteristic
106C2×#6597C2311yescharacteristic
107D232—41no—
108C23×C29—21no—
109C23×C29C2×D411yescharacteristic
110C22×D29—21no—
111C22×D29—21no—
112Q8×C29—21no—
113Q8×C29—21no—
114D4×C29—21no—
115D4×C29—21no—
116D4×C29—81no—
117C2×C4×C29—21no—
118C2×C4×C29—21no—
119C2×C4×C29—21no—
120C2×C4×C29—21no—
121C2×C4×C29—21no—
122C2×C4×C29C2×D411yescharacteristic
123C2×C4×C29C2411yescharacteristic
124C22⋊D29—81no—
125C22⋊D29—81no—
126C22⋊D29—81no—
127C22⋊D29—81no—
128C2×Dic29—21no—
129C2×Dic29—21no—
130C2×Dic29—81no—
131C2×Dic29C2×D411yescharacteristic
132C2×Dic29C2×D411yescharacteristic
133C2×Dic29C2×D411yescharacteristic
134C2×Dic29C2×D411yescharacteristic
135D116—21no—
136D116—21no—
137D116—21no—
138D116—21no—
139C4×D29—81no—
140C4×D29—81no—
141Dic58—81no—
142C8×C29—21no—
143C8×C29—21no—
144#6597—21no—
145#6597—21no—
146#3257—291nomaximal, Sylow
147C22×C29—21no—
148C22×C29—21no—
149C22×C29—21no—
150C22×C29—41no—
151C22×C29—41no—
152C22×C29—41no—
153C22×C29C22×D411yescharacteristic
154C2×D29—41no—
155C2×D29—41no—
156C2×D29—41no—
157C2×D29—41no—
158C2×D29—41no—
159C2×D29—41no—
160C4×C29—21no—
161C4×C29—41no—
162C4×C29—41no—
163C4×C29—41no—
164C4×C29H(5,𝔽2)11yescharacteristic
165C4×C292−1+411yescharacteristic
166Dic29—21no—
167Dic29—21no—
168Dic29—21no—
169Dic29—21no—
170Dic29—41no—
171Dic29—41no—
172#542—291no—
173#540—291no—
174#479—291no—
175#478—291no—
176#476—291no—
177#474—291no—
178#469—291no—
179#468—291no—
180#466—291no—
181#465D2911yescharacteristic, complemented
182#463—291no—
183#463—291no—
184#460—291no—
185#459—291no—
186#424—291no—
187C2×C29—41no—
188C2×C29—81no—
189C2×C29#53711yescharacteristic
190C2×C29#57611yescharacteristic
191C2×C29#57711yescharacteristic
192D29—81no—
193D29—81no—
194C2×SD16—291no—
195C2×SD16C2×D2911yescharacteristic
196C2×D8—291no—
197C2×D8—291no—
198C2×M16—291no—
199C22×C8C2×D2911yescharacteristic
200C4⋊Q8—291no—
201#127—291no—
202#126—581no—
203#125—291no—
204#124—291no—
205#124—581no—
206#123—581no—
207#123—581no—
208#123—581no—
209C22⋊Q8—581no—
210C22⋊Q8C2×D2911yescharacteristic
211#121—291no—
212#121—291no—
213#121—581no—
214#121—581no—
215#121C2×D2911yescharacteristic
216C4×Q8—291no—
217C4×D4—291no—
218C4×D4—291no—
219C4×D4—291no—
220#117—291no—
221#107—291no—
222#107—291no—
223#106—291no—
224#106C2×D2911yescharacteristic
225C4⋊C8—291no—
226C4⋊C8—291no—
227C4⋊C8—291no—
228C4⋊C8—291no—
229#103—291no—
230#103C2×D2911yescharacteristic
231#102—291no—
232#102—291no—
233#102—291no—
234#102—291no—
235#102—291no—
236#102C2×D2911yescharacteristic
237C29#325711yescharacteristic, complemented, Sylow
238C2×Q8—581no—
239C2×Q8C22×D2911yescharacteristic
240C2×D4—21no—
241C2×D4—291no—
242C2×D4—291no—
243C2×D4—581no—
244C2×D4—581no—
245C2×D4—581no—
246C2×D4—581no—
247C2×D4C22×D2911yescharacteristic
248C22×C4—581no—
249C22×C4—581no—
250C22×C4—581no—
251C22×C4C22×D2911yescharacteristic
252SD16—41no—
253SD16—1161no—
254D8—1161no—
255D8—1161no—
256M16—1161no—
257C2×C8—41no—
258C2×C8—291no—
259C2×C8—291no—
260C2×C8C22×D2911yescharacteristic
261C2×C8C22×D2911yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—291no—
264C4⋊C4—291no—
265C4⋊C4—291no—
266C4⋊C4—291no—
267C4⋊C4—581no—
268C4⋊C4—581no—
269C4⋊C4—581no—
270C4⋊C4—581no—
271C4⋊C4C22×D2911yescharacteristic
272C4⋊C4C22×D2911yescharacteristic
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—291no—
276C22⋊C4—291no—
277C22⋊C4—581no—
278C22⋊C4—581no—
279C22⋊C4—581no—
280C22⋊C4—581no—
281C22⋊C4—581no—
282C22⋊C4—581no—
283C22⋊C4—581no—
284C42—291no—
285C42—291no—
286C42—581no—
287C23—21no—
288C23—581no—
289C23—581no—
290C23D4×D2911yescharacteristic
291Q8—21no—
292Q8—21no—
293Q8—2321no—
294D4—21no—
295D4—21no—
296D4—81no—
297D4—581no—
298D4—581no—
299D4—581no—
300D4—581no—
301D4—2321no—
302D4—2321no—
303D4—2321no—
304D4—2321no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—291no—
311C2×C4—291no—
312C2×C4—291no—
313C2×C4—291no—
314C2×C4—581no—
315C2×C4—581no—
316C2×C4—2321no—
317C2×C4—2321no—
318C2×C4—2321no—
319C2×C4D4×D2911yescharacteristic
320C2×C4C23×D2911yescharacteristic
321C8—21no—
322C8—21no—
323C8—581no—
324C8—581no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—1161no—
332C22—1161no—
333C22—1161no—
334C22—1161no—
335C22—1161no—
336C22—1161no—
337C22C2×D4×D2911yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—581no—
343C4—581no—
344C4—581no—
345C4—581no—
346C4—1161no—
347C4—1161no—
348C4#1174535911yescharacteristic
349C4#1174536511yescharacteristic
350C2—41no—
351C2—81no—
352C2—2321no—
353C2—2321no—
354C2#1427174011yescharacteristic
355C2#1427196511yescharacteristic
356C2#1427196911yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#465C2
socleC22×C29C22×D4
hypercenter#465D29
hypocenterC29#3257
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #14271786C2semidirect
2. #14271766C2semidirect
3. #14271472C2semidirect
4. #14271462C2semidirect
5. #14271452C2semidirect
6. #14271441C2semidirect
7. #14271414C2semidirect
8. #14271411C2semidirect
9. #14271399C2semidirect
10. #14271381C2semidirect
11. #14271380C2semidirect
12. #14271361C2semidirect
13. #14271357C2semidirect
14. #14271189C2semidirect
15. C29×#465C2semidirect
181. #465D29semidirect
237. C29#3257semidirect

Maximal subgroups

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

subgroupindex
#142717862
#142717662
#142714722
#142714622
#142714522
#142714412
#142714142
#142714112
#142713992
#142713812
#142713802
#142713612
#142713572
#142711892
C29×#4652
#325729