Finite Group Databasebeta

← #16832092

Subgroups — #16832092

Order 3712.

360 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271859C211yesmaximal, characteristic, complemented
2#14271562C211yesmaximal, characteristic, complemented
3#14271487C211yesmaximal, characteristic, complemented
4#14271484C211yesmaximal, characteristic, complemented
5#14271476C211yesmaximal, characteristic, complemented
6#14271474C211yesmaximal, characteristic, complemented
7#14271463C211yesmaximal, characteristic, complemented
8#14271460C211yesmaximal, characteristic, complemented
9#14271414C211yesmaximal, characteristic, complemented
10#14271414C211yesmaximal, characteristic, complemented
11C4×#90782C211yesmaximal, characteristic, complemented
12#14271241C211yesmaximal, characteristic, complemented
13#14271206C211yesmaximal, characteristic, complemented
14#14271203C211yesmaximal, characteristic, complemented
15C29×#553C211yesmaximal, characteristic, complemented
16C29×#126—21no—
17C29×#125C2211yescharacteristic
18C29×#123—21no—
19C29×#121—21no—
20C29×#121C2211yescharacteristic
21C29×#121C2211yescharacteristic
22C4×D4×C29—21no—
23C4×D4×C29C2211yescharacteristic
24C4×D4×C29C2211yescharacteristic
25C29×#117C2211yescharacteristic
26C2×C4⋊C4×C29C2211yescharacteristic
27#11745301—21no—
28C2×#90782C2211yescharacteristic
29#11745292C2211yescharacteristic
30#11745292C2211yescharacteristic
31#11745288C2211yescharacteristic
32C2×C4⋊Dic29C2211yescharacteristic
33C2×#90777C2211yescharacteristic
34C2×#90777C2211yescharacteristic
35#11745260—21no—
36#11745245—21no—
37#11745243—21no—
38C4×D116C2211yescharacteristic
39#11745232C2211yescharacteristic
40#11745180C2211yescharacteristic
41#11745180C2211yescharacteristic
42#11745180C2211yescharacteristic
43C22⋊#6597C2211yescharacteristic
44C22⋊#6597C2211yescharacteristic
45#11745157C2211yescharacteristic
46#11745157C2211yescharacteristic
47#11745157C2211yescharacteristic
48#11745156C2211yescharacteristic
49#11745156C2211yescharacteristic
50#11745156C2211yescharacteristic
51#11745156C2211yescharacteristic
52#11745155C2211yescharacteristic
53#11745155C2211yescharacteristic
54#11745155C2211yescharacteristic
55#11745155C2211yescharacteristic
56#11745155C2211yescharacteristic
57C4⋊#6597C2211yescharacteristic
58C4×#6597C2211yescharacteristic
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—
69C22×Dic29—21no—
70C2×D116C2311yescharacteristic
71C2×C4×D29—21no—
72C4⋊C4×C29—21no—
73C4⋊C4×C29—21no—
74C4⋊C4×C29—21no—
75C4⋊C4×C29D411yescharacteristic
76C4⋊C4×C29C2311yescharacteristic
77C4⋊C4×C29C2311yescharacteristic
78C4⋊C4×C29C2311yescharacteristic
79C22⋊C4×C29—21no—
80C22⋊C4×C29—21no—
81C22⋊C4×C29—21no—
82C22⋊C4×C29—21no—
83C22⋊C4×C29D411yescharacteristic
84C22⋊C4×C29D411yescharacteristic
85C42×C29—21no—
86C42×C29C2311yescharacteristic
87C22⋊Dic29—21no—
88#90782—22no—
89#90781—21no—
90#90781—21no—
91#90781—21no—
92C4⋊Dic29—21no—
93C4⋊Dic29C2311yescharacteristic
94C4⋊Dic29C2311yescharacteristic
95C4⋊Dic29C2311yescharacteristic
96#90779—21no—
97#90779—21no—
98C4×Dic29—21no—
99#90777—22no—
100#90777—22no—
101C2×#6597C2311yescharacteristic
102C2×#6597C2311yescharacteristic
103C2×#6597C2311yescharacteristic
104C2×#6597C2311yescharacteristic
105C23×C29—21no—
106C23×C29C2×D411yescharacteristic
107C23×C29C2×D411yescharacteristic
108C22×D29—21no—
109D4×C29—21no—
110D4×C29—21no—
111D4×C29—41no—
112D4×C29—42no—
113D4×C29—81no—
114C2×C4×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×C29—81no—
123C2×C4×C29C2×D411yescharacteristic
124C2×C4×C29C2×D411yescharacteristic
125C2×C4×C29C2×D411yescharacteristic
126C2×C4×C29C2×D411yescharacteristic
127C2×C4×C29C2411yescharacteristic
128C22⋊D29—42no—
129C22⋊D29—81no—
130C2×Dic29—21no—
131C2×Dic29—21no—
132C2×Dic29—21no—
133C2×Dic29—81no—
134D116—21no—
135D116—21no—
136C4×D29—81no—
137#6597—21no—
138#6597—21no—
139#6597—21no—
140#6597#4112yes—
141#3355—291nomaximal, Sylow
142C22×C29—21no—
143C22×C29—21no—
144C22×C29—21no—
145C22×C29—21no—
146C22×C29—21no—
147C22×C29—21no—
148C22×C29—41no—
149C22×C29—41no—
150C22×C29—41no—
151C22×C29C22×D411yescharacteristic
152C2×D29—41no—
153C2×D29—41no—
154C2×D29—41no—
155C4×C29—21no—
156C4×C29—21no—
157C4×C29—21no—
158C4×C29—21no—
159C4×C29—41no—
160C4×C29—41no—
161C4×C29—41no—
162C4×C29C2×#4111yescharacteristic
163C4×C292−1+411yescharacteristic
164Dic29—41no—
165Dic29—41no—
166Dic29—41no—
167#553—291no—
168#553D2911yescharacteristic, complemented
169#499—291no—
170#482—291no—
171#482—291no—
172#480—291no—
173#480—291no—
174#478—291no—
175#478—291no—
176#469—291no—
177#469—291no—
178C4×D8—291no—
179#436—291no—
180#428—291no—
181#428—291no—
182C2×C29—41no—
183C2×C29—41no—
184C2×C29—81no—
185C2×C29#54711yescharacteristic
186C2×C29#57511yescharacteristic
187C2×C29#57611yescharacteristic
188D29—81no—
189C2×D8—291no—
190C2×M16—291no—
191C2×M16—291no—
192#126—21no—
193#126—581no—
194#125—291no—
195#125C2×D2911yescharacteristic
196#123—21no—
197#123—581no—
198#121—21no—
199#121—291no—
200#121—291no—
201#121—581no—
202#121C2×D2911yescharacteristic
203#121C2×D2911yescharacteristic
204C4×D4—21no—
205C4×D4—291no—
206C4×D4—581no—
207C4×D4C2×D2911yescharacteristic
208C4×D4C2×D2911yescharacteristic
209#117—291no—
210#117C2×D2911yescharacteristic
211C2×C4⋊C4—291no—
212C2×C4⋊C4C2×D2911yescharacteristic
213#107—291no—
214#107—291no—
215#107—291no—
216#107—291no—
217#107—291no—
218#106—291no—
219#106—291no—
220#106—291no—
221#106—291no—
222C4⋊C8—291no—
223#102—291no—
224#102—291no—
225#102—291no—
226#102—291no—
227#102—291no—
228#102—291no—
229C22⋊C8—291no—
230C22⋊C8—291no—
231C4×C8—291no—
232C29#335511yescharacteristic, complemented, Sylow
233C2×D4—21no—
234C2×D4—21no—
235C2×D4—291no—
236C2×D4—581no—
237C2×D4—581no—
238C2×D4C22⋊D2911yescharacteristic
239C2×D4C22×D2911yescharacteristic
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—581no—
243C22×C4—581no—
244C22×C4C22×D2911yescharacteristic
245C22×C4C22×D2911yescharacteristic
246D8—582no—
247M16—582no—
248M16—582no—
249C2×C8—291no—
250C2×C8—291no—
251C2×C8—291no—
252C2×C8—291no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—291no—
257C4⋊C4—291no—
258C4⋊C4—291no—
259C4⋊C4—581no—
260C4⋊C4—581no—
261C4⋊C4—581no—
262C4⋊C4C22⋊D2911yescharacteristic
263C4⋊C4C22×D2911yescharacteristic
264C4⋊C4C22×D2911yescharacteristic
265C4⋊C4C22×D2911yescharacteristic
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—581no—
271C22⋊C4—581no—
272C22⋊C4—581no—
273C22⋊C4—581no—
274C22⋊C4C22⋊D2911yescharacteristic
275C22⋊C4C22⋊D2911yescharacteristic
276C42—21no—
277C42—581no—
278C42C22×D2911yescharacteristic
279C23—21no—
280C23—581no—
281C23C2×C22⋊D2911yescharacteristic
282C23C2×C22⋊D2911yescharacteristic
283D4—21no—
284D4—21no—
285D4—41no—
286D4—42no—
287D4—81no—
288D4—581no—
289D4—581no—
290D4—1162no—
291D4—2321no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4—581no—
302C2×C4—581no—
303C2×C4—581no—
304C2×C4—2321no—
305C2×C4—2321no—
306C2×C4C2×C22⋊D2911yescharacteristic
307C2×C4C2×C22⋊D2911yescharacteristic
308C2×C4C2×C22⋊D2911yescharacteristic
309C2×C4C2×C22⋊D2911yescharacteristic
310C2×C4C23×D2911yescharacteristic
311C8—292no—
312C8—581no—
313C8—581no—
314C8—581no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—1161no—
325C22—1161no—
326C22—1161no—
327C22C22×C22⋊D2911yescharacteristic
328C4—21no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—1161no—
336C4—1161no—
337C4—1161no—
338C4#41×D2911yescharacteristic
339C4#1174536511yescharacteristic
340C2—41no—
341C2—41no—
342C2—81no—
343C2—2321no—
344C2#1427181211yescharacteristic
345C2#1427196111yescharacteristic
346C2#1427196611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#553C2
socleC22×C29C22×D4
hypercenter#553D29
hypocenterC29#3355
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. #14271859C2semidirect
2. #14271562C2semidirect
3. #14271487C2semidirect
4. #14271484C2semidirect
5. #14271476C2semidirect
6. #14271474C2semidirect
7. #14271463C2semidirect
8. #14271460C2semidirect
9. #14271414C2semidirect
10. #14271414C2semidirect
11. C4×#90782C2semidirect
12. #14271241C2semidirect
13. #14271206C2semidirect
14. #14271203C2semidirect
15. C29×#553C2semidirect
168. #553D29semidirect
232. C29#3355semidirect

Maximal subgroups

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

subgroupindex
#142718592
#142715622
#142714872
#142714842
#142714762
#142714742
#142714632
#142714602
#142714142
C4×#907822
#142712412
#142712062
#142712032
C29×#5532
#335529