Finite Group Databasebeta

← #16831492

Subgroups — #16831492

Order 3712.

404 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271834C211yesmaximal, characteristic, complemented
2#14271529C211yesmaximal, characteristic, complemented
3#14271487C211yesmaximal, characteristic, complemented
4#14271476C211yesmaximal, characteristic, complemented
5#14271467C211yesmaximal, characteristic, complemented
6#14271414C211yesmaximal, characteristic, complemented
7#14271397C211yesmaximal, characteristic, complemented
8#14271358C211yesmaximal, characteristic, complemented
9#14271306C211yesmaximal, characteristic, complemented
10#14271306C211yesmaximal, characteristic, complemented
11#14271263C211yesmaximal, characteristic, complemented
12#14271235C211yesmaximal, characteristic, complemented
13#14271162C211yesmaximal, characteristic, complemented
14#14271157C211yesmaximal, characteristic, complemented
15C29×#553C211yesmaximal, characteristic, complemented
16C2×#90805C2211yescharacteristic
17C2×#90805C2211yescharacteristic
18C29×#126—21no—
19C29×#125C2211yescharacteristic
20C29×#123—21no—
21C29×#121—21no—
22C29×#121C2211yescharacteristic
23C29×#121C2211yescharacteristic
24C4×D4×C29—21no—
25C4×D4×C29C2211yescharacteristic
26C4×D4×C29C2211yescharacteristic
27C29×#117C2211yescharacteristic
28C2×C4⋊C4×C29C2211yescharacteristic
29#11745302—21no—
30C2×#90783C2211yescharacteristic
31C2×#90782C2211yescharacteristic
32C2×#90782C2211yescharacteristic
33#11745292C2211yescharacteristic
34#11745292C2211yescharacteristic
35C2×#90777C2211yescharacteristic
36C22×#6597C2211yescharacteristic
37#11745255—21no—
38#11745246—21no—
39#11745246—21no—
40#11745236C2211yescharacteristic
41C4×Dic58C2211yescharacteristic
42#11745180C2211yescharacteristic
43C22⋊#6597C2211yescharacteristic
44C22⋊#6597C2211yescharacteristic
45#11745158C2211yescharacteristic
46#11745158C2211yescharacteristic
47#11745158C2211yescharacteristic
48#11745157C2211yescharacteristic
49#11745157C2211yescharacteristic
50#11745157C2211yescharacteristic
51#11745157C2211yescharacteristic
52#11745157C2211yescharacteristic
53#11745157C2211yescharacteristic
54#11745156C2211yescharacteristic
55#11745155C2211yescharacteristic
56#11745155C2211yescharacteristic
57C4⋊#6597C2211yescharacteristic
58#11745151C2211yescharacteristic
59C2×D4×C29—21no—
60C2×D4×C29—21no—
61C2×D4×C29D411yescharacteristic
62C2×D4×C29C2311yescharacteristic
63C22×C4×C29—21no—
64C22×C4×C29—21no—
65C22×C4×C29C2311yescharacteristic
66C22×C4×C29C2311yescharacteristic
67C2×C22⋊D29—21no—
68C2×C22⋊D29—21no—
69C2×C22⋊D29—21no—
70C2×C22⋊D29—21no—
71#90805—22no—
72#90805—22no—
73#90805—41no—
74#90805—41no—
75C2×D116—21no—
76C2×D116—21no—
77C2×D116C2311yescharacteristic
78C2×D116C2311yescharacteristic
79C2×C4×D29—21no—
80C2×C4×D29—21no—
81C2×Dic58C2311yescharacteristic
82C4⋊C4×C29—21no—
83C4⋊C4×C29—21no—
84C4⋊C4×C29—21no—
85C4⋊C4×C29D411yescharacteristic
86C4⋊C4×C29C2311yescharacteristic
87C4⋊C4×C29C2311yescharacteristic
88C4⋊C4×C29C2311yescharacteristic
89C22⋊C4×C29—21no—
90C22⋊C4×C29—21no—
91C22⋊C4×C29—21no—
92C22⋊C4×C29—21no—
93C22⋊C4×C29D411yescharacteristic
94C22⋊C4×C29D411yescharacteristic
95C42×C29—21no—
96C42×C29C2311yescharacteristic
97#90783—22no—
98#90782—41no—
99#90782—41no—
100#90781—21no—
101#90781—21no—
102C4⋊Dic29C2311yescharacteristic
103#90779—21no—
104C4×Dic29—21no—
105#90777—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—
116D4×C29—21no—
117D4×C29—21no—
118D4×C29—41no—
119D4×C29—42no—
120D4×C29—81no—
121C2×C4×C29—21no—
122C2×C4×C29—21no—
123C2×C4×C29—21no—
124C2×C4×C29—21no—
125C2×C4×C29—21no—
126C2×C4×C29—21no—
127C2×C4×C29—21no—
128C2×C4×C29—81no—
129C2×C4×C29—81no—
130C2×C4×C29C2×D411yescharacteristic
131C2×C4×C29C2×D411yescharacteristic
132C2×C4×C29C2×D411yescharacteristic
133C2×C4×C29C2×D411yescharacteristic
134C2×C4×C29C2411yescharacteristic
135C22⋊D29—42no—
136C22⋊D29—42no—
137C22⋊D29—81no—
138C22⋊D29—81no—
139C2×Dic29—21no—
140C2×Dic29—21no—
141D116—21no—
142D116—21no—
143D116—21no—
144D116—21no—
145D116—42no—
146D116—81no—
147C4×D29—42no—
148C4×D29—42no—
149Dic58—21no—
150Dic58#4112yes—
151#6597—21no—
152#6597—21no—
153#6597—21no—
154#6597—21no—
155#3309—291nomaximal, Sylow
156C22×C29—21no—
157C22×C29—21no—
158C22×C29—21no—
159C22×C29—21no—
160C22×C29—21no—
161C22×C29—21no—
162C22×C29—41no—
163C22×C29—41no—
164C22×C29—41no—
165C22×C29C22×D411yescharacteristic
166C2×D29—41no—
167C2×D29—41no—
168C2×D29—41no—
169C2×D29—41no—
170C2×D29—41no—
171C2×D29—41no—
172C4×C29—21no—
173C4×C29—21no—
174C4×C29—21no—
175C4×C29—21no—
176C4×C29—41no—
177C4×C29—41no—
178C4×C29—41no—
179C4×C29C2×#4111yescharacteristic
180C4×C29H(5,𝔽2)11yescharacteristic
181Dic29—22no—
182Dic29—41no—
183#553D2911yescharacteristic, complemented
184#550—291no—
185#490—291no—
186#482—291no—
187#480—291no—
188#479—291no—
189#469—291no—
190#466—291no—
191#459—291no—
192#449—291no—
193#449—291no—
194#440—291no—
195#435—291no—
196#417—291no—
197#416—291no—
198C2×C29—41no—
199C2×C29—41no—
200C2×C29—81no—
201C2×C29#54611yescharacteristic
202C2×C29#57511yescharacteristic
203C2×C29#57611yescharacteristic
204D29—81no—
205D29—81no—
206C2×#41—291no—
207C2×#41—291no—
208C2×SD16—291no—
209C2×D8—291no—
210C2×D8—291no—
211C2×M16—291no—
212C22×C8—291no—
213#127—291no—
214#127—581no—
215#126—21no—
216#125C2×D2911yescharacteristic
217#123—21no—
218#121—21no—
219#121—291no—
220#121—291no—
221#121—581no—
222#121—581no—
223#121C2×D2911yescharacteristic
224#121C2×D2911yescharacteristic
225C4×Q8—291no—
226C4×D4—21no—
227C4×D4—581no—
228C4×D4C2×D2911yescharacteristic
229C4×D4C2×D2911yescharacteristic
230#117C2×D2911yescharacteristic
231C2×C4⋊C4C2×D2911yescharacteristic
232#107—291no—
233#107—291no—
234#106—291no—
235C4⋊C8—291no—
236#103—291no—
237#103—291no—
238#103—291no—
239#102—291no—
240#102—291no—
241#102—291no—
242#102—291no—
243#102—291no—
244#102—291no—
245#102—291no—
246C22⋊C8—291no—
247C22⋊C8—291no—
248#97—291no—
249C29#330911yescharacteristic, complemented, Sylow
250#41—582no—
251#41—582no—
252#41—1161no—
253#41—1161no—
254C2×Q8—291no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—291no—
258C2×D4—291no—
259C2×D4—581no—
260C2×D4—581no—
261C2×D4—581no—
262C2×D4—581no—
263C2×D4—581no—
264C2×D4—581no—
265C2×D4C22⋊D2911yescharacteristic
266C2×D4C22×D2911yescharacteristic
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—581no—
270C22×C4—581no—
271C22×C4C22×D2911yescharacteristic
272C22×C4C22×D2911yescharacteristic
273SD16—582no—
274D8—1161no—
275D8—1161no—
276M16—1161no—
277C2×C8—291no—
278C2×C8—291no—
279C2×C8—291no—
280C2×C8—291no—
281C2×C8—1161no—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—291no—
286C4⋊C4—581no—
287C4⋊C4C22⋊D2911yescharacteristic
288C4⋊C4C22×D2911yescharacteristic
289C4⋊C4C22×D2911yescharacteristic
290C4⋊C4C22×D2911yescharacteristic
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—21no—
295C22⋊C4—581no—
296C22⋊C4—581no—
297C22⋊C4C22⋊D2911yescharacteristic
298C22⋊C4C22⋊D2911yescharacteristic
299C42—21no—
300C42—581no—
301C42C22×D2911yescharacteristic
302C23—21no—
303C23—581no—
304C23—581no—
305C23C2×C22⋊D2911yescharacteristic
306C23C2×C22⋊D2911yescharacteristic
307Q8—292no—
308Q8—581no—
309D4—21no—
310D4—21no—
311D4—41no—
312D4—42no—
313D4—81no—
314D4—581no—
315D4—581no—
316D4—581no—
317D4—581no—
318D4—1162no—
319D4—1162no—
320D4—1162no—
321D4—2321no—
322D4—2321no—
323D4—2321no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4—581no—
334C2×C4—581no—
335C2×C4—1162no—
336C2×C4—1162no—
337C2×C4C2×C22⋊D2911yescharacteristic
338C2×C4C2×C22⋊D2911yescharacteristic
339C2×C4C2×C22⋊D2911yescharacteristic
340C2×C4C2×C22⋊D2911yescharacteristic
341C2×C4C23×D2911yescharacteristic
342C8—581no—
343C8—581no—
344C8—581no—
345C8—581no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—1161no—
356C22—1161no—
357C22—1161no—
358C22—1161no—
359C22—1161no—
360C22—1161no—
361C22C22×C22⋊D2911yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—582no—
370C4—1161no—
371C4#41×D2911yescharacteristic
372C4#1174536411yescharacteristic
373C2—41no—
374C2—41no—
375C2—81no—
376C2—2321no—
377C2—2321no—
378C2#1427180111yescharacteristic
379C2#1427196111yescharacteristic
380C2#1427196611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#553C2
socleC22×C29C22×D4
hypercenter#553D29
hypocenterC29#3309
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. #14271834C2semidirect
2. #14271529C2semidirect
3. #14271487C2semidirect
4. #14271476C2semidirect
5. #14271467C2semidirect
6. #14271414C2semidirect
7. #14271397C2semidirect
8. #14271358C2semidirect
9. #14271306C2semidirect
10. #14271306C2semidirect
11. #14271263C2semidirect
12. #14271235C2semidirect
13. #14271162C2semidirect
14. #14271157C2semidirect
15. C29×#553C2semidirect
183. #553D29semidirect
249. C29#3309semidirect

Maximal subgroups

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

subgroupindex
#142718342
#142715292
#142714872
#142714762
#142714672
#142714142
#142713972
#142713582
#142713062
#142712632
#142712352
#142711622
#142711572
C29×#5532
#330929