Finite Group Databasebeta

← #16831336

Subgroups — #16831336

Order 3712.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271809C211yesmaximal, characteristic, complemented
2#14271520C211yesmaximal, characteristic, complemented
3#14271498C211yesmaximal, characteristic, complemented
4#14271487C211yesmaximal, characteristic, complemented
5#14271460C211yesmaximal, characteristic, complemented
6#14271397C211yesmaximal, characteristic, complemented
7#14271390C211yesmaximal, characteristic, complemented
8#14271378C211yesmaximal, characteristic, complemented
9#14271306C211yesmaximal, characteristic, complemented
10#14271296C211yesmaximal, characteristic, complemented
11C4×#90782C211yesmaximal, characteristic, complemented
12D4×#6597C211yesmaximal, characteristic, complemented
13#14271157C211yesmaximal, characteristic, complemented
14C2×#11745157C211yesmaximal, characteristic, complemented
15C29×#553C211yesmaximal, characteristic, complemented
16C2×#90805C2211yescharacteristic
17C22×D116C2211yescharacteristic
18C29×#126—21no—
19C29×#125C2211yescharacteristic, complemented
20C29×#123—21no—
21C29×#121—21no—
22C29×#121C2211yescharacteristic
23C29×#121C2211yescharacteristic, complemented
24C4×D4×C29—21no—
25C4×D4×C29C2211yescharacteristic
26C4×D4×C29C2211yescharacteristic, complemented
27C29×#117C2211yescharacteristic, complemented
28C2×C4⋊C4×C29C2211yescharacteristic
29#11745299—21no—
30C2×#90783C2211yescharacteristic, complemented
31C2×#90782C2211yescharacteristic
32C2×#90782C2211yescharacteristic
33#11745292C2211yescharacteristic
34#11745286C2211yescharacteristic
35C22×#6597C2211yescharacteristic
36C22×#6597C2211yescharacteristic, complemented
37#11745256—21no—
38#11745246—21no—
39C22⋊C4×D29—21no—
40#11745237C2211yescharacteristic
41C4×D116C2211yescharacteristic
42#11745180C2211yescharacteristic, complemented
43C22⋊#6597C2211yescharacteristic
44C22⋊#6597C2211yescharacteristic, complemented
45#11745158C2211yescharacteristic, complemented
46#11745158C2211yescharacteristic, complemented
47#11745158C2211yescharacteristic, complemented
48#11745157C2211yescharacteristic
49#11745157C2211yescharacteristic
50#11745157C2211yescharacteristic
51#11745157C2211yescharacteristic
52#11745157C2211yescharacteristic
53#11745157C2211yescharacteristic
54#11745156C2211yescharacteristic, complemented
55#11745155C2211yescharacteristic, complemented
56#11745155C2211yescharacteristic, complemented
57C4⋊#6597C2211yescharacteristic, complemented
58C4×#6597C2211yescharacteristic, complemented
59C23×D29—21no—
60C2×D4×C29—21no—
61C2×D4×C29—21no—
62C2×D4×C29D411yescharacteristic
63C2×D4×C29C2311yescharacteristic
64C22×C4×C29—21no—
65C22×C4×C29—21no—
66C22×C4×C29C2311yescharacteristic
67C22×C4×C29C2311yescharacteristic
68C2×C22⋊D29—21no—
69C2×C22⋊D29—21no—
70#90805—22no—
71#90805—41no—
72C2×D116—22no—
73C2×D116—21no—
74C2×D116—41no—
75C2×D116C2311yescharacteristic
76C2×D116C2311yescharacteristic
77C2×C4×D29—21no—
78C2×C4×D29—21no—
79C2×Dic58C2311yescharacteristic
80C4⋊C4×C29—21no—
81C4⋊C4×C29—21no—
82C4⋊C4×C29—21no—
83C4⋊C4×C29D411yescharacteristic
84C4⋊C4×C29C2311yescharacteristic
85C4⋊C4×C29C2311yescharacteristic
86C4⋊C4×C29C2311yescharacteristic
87C22⋊C4×C29—21no—
88C22⋊C4×C29—21no—
89C22⋊C4×C29—21no—
90C22⋊C4×C29—21no—
91C22⋊C4×C29D411yescharacteristic
92C22⋊C4×C29D411yescharacteristic
93C42×C29—21no—
94C42×C29C2311yescharacteristic
95C22⋊Dic29—21no—
96#90783—41no—
97#90782—22no—
98#90782—41no—
99#90781—21no—
100#90781—21no—
101#90781—21no—
102#90781—21no—
103C4⋊Dic29C2311yescharacteristic
104#90779—21no—
105C2×#6597—41no—
106C2×#6597—41no—
107C2×#6597C2311yescharacteristic
108C2×#6597C2311yescharacteristic
109C2×#6597C2311yescharacteristic
110C2×#6597C2311yescharacteristic
111C23×C29—21no—
112C23×C29C2×D411yescharacteristic
113C23×C29C2×D411yescharacteristic
114C22×D29—21no—
115C22×D29—21no—
116C22×D29—42no—
117C22×D29—42no—
118C22×D29—81no—
119D4×C29—22no—
120D4×C29—21no—
121D4×C29—21no—
122D4×C29—42no—
123D4×C29—81no—
124C2×C4×C29—21no—
125C2×C4×C29—21no—
126C2×C4×C29—21no—
127C2×C4×C29—21no—
128C2×C4×C29—21no—
129C2×C4×C29—21no—
130C2×C4×C29—21no—
131C2×C4×C29—81no—
132C2×C4×C29—81no—
133C2×C4×C29C2×D411yescharacteristic
134C2×C4×C29C2×D411yescharacteristic
135C2×C4×C29C2×D411yescharacteristic
136C2×C4×C29C2×D411yescharacteristic
137C2×C4×C29C2411yescharacteristic
138C22⋊D29—42no—
139C22⋊D29—81no—
140C2×Dic29—21no—
141C2×Dic29—21no—
142D116—21no—
143D116—21no—
144D116—21no—
145D116—42no—
146D116#4112yes—
147C4×D29—42no—
148C4×D29—81no—
149Dic58—21no—
150Dic58—21no—
151#6597—21no—
152#6597—21no—
153#6597—21no—
154#6597—21no—
155#3297—291nomaximal, Sylow
156C22×C29—21no—
157C22×C29—21no—
158C22×C29—21no—
159C22×C29—21no—
160C22×C29—21no—
161C22×C29—41no—
162C22×C29—41no—
163C22×C29—41no—
164C22×C29#13512yes—
165C22×C29C22×D411yescharacteristic
166C2×D29—22no—
167C2×D29—41no—
168C2×D29—41no—
169C2×D29—41no—
170C2×D29—41no—
171C2×D29—41no—
172C2×D29—84no—
173C4×C29—21no—
174C4×C29—21no—
175C4×C29—21no—
176C4×C29—21no—
177C4×C29—41no—
178C4×C29—41no—
179C4×C29—41no—
180C4×C29C2×#4111yescharacteristic
181C4×C29H(5,𝔽2)11yescharacteristic
182Dic29—41no—
183Dic29—41no—
184#553D2911yescharacteristic, complemented
185#546—291no—
186#488—291no—
187#484—291no—
188#482—291no—
189#478—291no—
190#466—291no—
191#465—291no—
192#463—291no—
193#449—291no—
194#447—291no—
195C4×D8—291no—
196C8×D4—291no—
197#416—291no—
198C2×#102—291no—
199C2×C29—22no—
200C2×C29—41no—
201C2×C29—81no—
202C2×C29#54611yescharacteristic
203C2×C29C2×#13511yescharacteristic
204C2×C29#57611yescharacteristic
205D29—42no—
206D29—81no—
207C2×#41—291no—
208C22×D4—291no—
209C2×SD16—291no—
210C2×D8—291no—
211C2×D8—291no—
212C22×C8—291no—
213C22×C8—291no—
214#126—21no—
215#125C2×D2911yescharacteristic, complemented
216#124—291no—
217#123—21no—
218#123—581no—
219C22⋊Q8—291no—
220#121—21no—
221#121—291no—
222#121—581no—
223#121C2×D2911yescharacteristic
224#121C2×D2911yescharacteristic, complemented
225#120—581no—
226C4×D4—21no—
227C4×D4—291no—
228C4×D4C2×D2911yescharacteristic
229C4×D4C2×D2911yescharacteristic, complemented
230#117C2×D2911yescharacteristic, complemented
231C2×C4⋊C4C2×D2911yescharacteristic
232C2×C22⋊C4—581no—
233#107—291no—
234#107—291no—
235#106—291no—
236C4⋊C8—291no—
237#103—291no—
238#103—291no—
239#103—291no—
240#102—291no—
241#102—291no—
242#102—291no—
243#102—291no—
244#102—291no—
245#102—291no—
246#102—291no—
247C22⋊C8—291no—
248C22⋊C8—291no—
249C4×C8—291no—
250C29#329711yescharacteristic, complemented, Sylow
251C24—581no—
252#41—582no—
253#41—1161no—
254C2×Q8—291no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—291no—
258C2×D4—291no—
259C2×D4—582no—
260C2×D4—581no—
261C2×D4—581no—
262C2×D4—581no—
263C2×D4—1161no—
264C2×D4C22⋊D2911yescharacteristic
265C2×D4C22×D2911yescharacteristic
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—581no—
269C22×C4—581no—
270C22×C4C22×D2911yescharacteristic
271C22×C4C22×D2911yescharacteristic
272SD16—1161no—
273D8—582no—
274D8—1161no—
275C2×C8—291no—
276C2×C8—291no—
277C2×C8—291no—
278C2×C8—291no—
279C2×C8—1161no—
280C2×C8—1161no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—291no—
285C4⋊C4—581no—
286C4⋊C4C22⋊D2911yescharacteristic
287C4⋊C4C22×D2911yescharacteristic
288C4⋊C4C22×D2911yescharacteristic
289C4⋊C4C22×D2911yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—581no—
295C22⋊C4—581no—
296C22⋊C4—581no—
297C22⋊C4—581no—
298C22⋊C4—581no—
299C22⋊C4C22⋊D2911yescharacteristic
300C22⋊C4C22⋊D2911yescharacteristic
301C42—21no—
302C42C22×D2911yescharacteristic
303C23—21no—
304C23—581no—
305C23—581no—
306C23—1162no—
307C23—1162no—
308C23—2321no—
309C23C2×C22⋊D2911yescharacteristic
310C23C2×C22⋊D2911yescharacteristic
311Q8—581no—
312Q8—581no—
313D4—22no—
314D4—21no—
315D4—21no—
316D4—42no—
317D4—81no—
318D4—292no—
319D4—581no—
320D4—581no—
321D4—581no—
322D4—1162no—
323D4—1162no—
324D4—2321no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—581no—
335C2×C4—581no—
336C2×C4—1162no—
337C2×C4—2321no—
338C2×C4C2×C22⋊D2911yescharacteristic
339C2×C4C2×C22⋊D2911yescharacteristic
340C2×C4C2×C22⋊D2911yescharacteristic
341C2×C4C2×C22⋊D2911yescharacteristic
342C2×C4C23×D2911yescharacteristic
343C8—581no—
344C8—581no—
345C8—581no—
346C8—581no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—582no—
356C22—1161no—
357C22—1161no—
358C22—1161no—
359C22—1161no—
360C22—1161no—
361C22—2324no—
362C22#1174531212yes—
363C22C22×C22⋊D2911yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—41no—
369C4—41no—
370C4—41no—
371C4—1161no—
372C4—1161no—
373C4#41×D2911yescharacteristic
374C4#1174536411yescharacteristic
375C2—22no—
376C2—41no—
377C2—81no—
378C2—1162no—
379C2—2321no—
380C2#1427180111yescharacteristic
381C2C2×#1174531211yescharacteristic
382C2#1427196611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#553C2
socleC22×C29C22×D4
hypercenter#553D29
hypocenterC29#3297
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. #14271809C2semidirect
2. #14271520C2semidirect
3. #14271498C2semidirect
4. #14271487C2semidirect
5. #14271460C2semidirect
6. #14271397C2semidirect
7. #14271390C2semidirect
8. #14271378C2semidirect
9. #14271306C2semidirect
10. #14271296C2semidirect
11. C4×#90782C2semidirect
12. D4×#6597C2semidirect
13. #14271157C2semidirect
14. C2×#11745157C2semidirect
15. C29×#553C2semidirect
19. C29×#125C22semidirect
23. C29×#121C22semidirect
26. C4×D4×C29C22semidirect
27. C29×#117C22semidirect
30. C2×#90783C22semidirect
36. C22×#6597C22semidirect
42. #11745180C22semidirect
44. C22⋊#6597C22semidirect
45. #11745158C22semidirect
46. #11745158C22semidirect
47. #11745158C22semidirect
54. #11745156C22semidirect
55. #11745155C22semidirect
56. #11745155C22semidirect
57. C4⋊#6597C22semidirect
58. C4×#6597C22semidirect
184. #553D29semidirect
215. #125C2×D29semidirect
224. #121C2×D29semidirect
229. C4×D4C2×D29semidirect
230. #117C2×D29semidirect
250. C29#3297semidirect

Maximal subgroups

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

subgroupindex
#142718092
#142715202
#142714982
#142714872
#142714602
#142713972
#142713902
#142713782
#142713062
#142712962
C4×#907822
D4×#65972
#142711572
C2×#117451572
C29×#5532
#329729