Finite Group Databasebeta

← #16829454

Subgroups — #16829454

Order 3712.

386 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271736C211yesmaximal, characteristic
2#14271644C211yesmaximal, characteristic
3#14271507C211yesmaximal, characteristic, complemented
4#14271505C211yesmaximal, characteristic, complemented
5#14271502C211yesmaximal, characteristic, complemented
6#14271501C211yesmaximal, characteristic, complemented
7#14271498C211yesmaximal, characteristic, complemented
8#14271497C211yesmaximal, characteristic, complemented
9#14271495C211yesmaximal, characteristic, complemented
10#14271202C211yesmaximal, characteristic, complemented
11#14271198C211yesmaximal, characteristic, complemented
12#14271170C211yesmaximal, characteristic, complemented
13#103×D29C211yesmaximal, characteristic, complemented
14#14271128C211yesmaximal, characteristic
15C29×#483C211yesmaximal, characteristic, complemented
16C2×Q8×D29C2211yescharacteristic
17C2×#90805C2211yescharacteristic
18C29×C22⋊Q8C2211yescharacteristic
19C2×C4⋊C4×C29C2211yescharacteristic
20#11745308C2211yescharacteristic
21C4×C22⋊D29—21no—
22C4×C22⋊D29—21no—
23#11745288C2211yescharacteristic
24#11745286C2211yescharacteristic
25C2×#90772C2211yescharacteristic
26C2×C8×D29C2211yescharacteristic
27#11745259C2211yescharacteristic
28#11745256—21no—
29#11745255—21no—
30#11745254C2211yescharacteristic
31#11745254C2211yescharacteristic
32#11745254C2211yescharacteristic
33C4⋊C4×D29C2211yescharacteristic
34C4⋊C4×D29C2211yescharacteristic
35#11745250—21no—
36#11745249—21no—
37#11745247—21no—
38#11745245—21no—
39C29×#106C2211yescharacteristic
40C29×#106C2211yescharacteristic
41C29×#103C2211yescharacteristic
42C29×#103C2211yescharacteristic
43C29×C22⋊C8C2211yescharacteristic
44#11745183C2211yescharacteristic
45#11745183C2211yescharacteristic
46C22⋊#6597C2211yescharacteristic
47#11745168C2211yescharacteristic
48#11745168C2211yescharacteristic
49#11745166C2211yescharacteristic
50#11745165C2211yescharacteristic
51#11745164C2211yescharacteristic
52#11745164C2211yescharacteristic
53#11745158C2211yescharacteristic
54#11745158C2211yescharacteristic
55#11745156C2211yescharacteristic
56#11745155C2211yescharacteristic
57#11745155C2211yescharacteristic
58#11745155C2211yescharacteristic
59C2×Q8×C29C2311yescharacteristic
60C22×C4×C29—21no—
61C22×C4×C29C2311yescharacteristic
62C2×C22⋊D29D411yescharacteristic
63C2×C22⋊D29D411yescharacteristic
64Q8×D29—22no—
65Q8×D29—22no—
66#90805—22no—
67#90805—22no—
68C2×D116D411yescharacteristic
69C2×C4×D29—21no—
70C2×C4×D29—21no—
71C2×C4×D29—21no—
72C2×C4×D29C2311yescharacteristic
73C2×C4×D29C2311yescharacteristic
74C2×Dic58—21no—
75C2×Dic58D411yescharacteristic
76C2×Dic58C2311yescharacteristic
77C2×C8×C29C2311yescharacteristic
78C2×C8×C29C2311yescharacteristic
79C4⋊C4×C29—21no—
80C4⋊C4×C29—21no—
81C4⋊C4×C29C2311yescharacteristic
82C4⋊C4×C29C2311yescharacteristic
83C4⋊C4×C29C2311yescharacteristic
84C22⋊C4×C29—21no—
85C22⋊Dic29—21no—
86C22⋊Dic29—21no—
87#90781—21no—
88#90781—21no—
89#90781—21no—
90#90781—21no—
91#90781—21no—
92C4⋊Dic29—21no—
93C4⋊Dic29C2311yescharacteristic
94C4⋊Dic29C2311yescharacteristic
95C4⋊Dic29C2311yescharacteristic
96#90779—21no—
97#90779—21no—
98#90779—21no—
99#90779—21no—
100C4×Dic29—21no—
101C4×Dic29—21no—
102C4×Dic29—21no—
103C4×Dic29—21no—
104C2×#6597C2311yescharacteristic
105C2×#6597C2311yescharacteristic
106#90772—22no—
107C8×D29—22no—
108C23×C29C2×D411yescharacteristic
109C22×D29C2×D411yescharacteristic
110C22×D29C2×D411yescharacteristic
111Q8×C29—21no—
112Q8×C29—21no—
113C2×C4×C29—21no—
114C2×C4×C29—21no—
115C2×C4×C29—21no—
116C2×C4×C29—21no—
117C2×C4×C29—21no—
118C2×C4×C29—21no—
119C2×C4×C29—81no—
120C2×C4×C29C2×D411yescharacteristic
121C2×C4×C29C2411yescharacteristic
122C22⋊D29—22no—
123C22⋊D29—22no—
124C2×Dic29—21no—
125C2×Dic29—21no—
126C2×Dic29—21no—
127C2×Dic29—21no—
128C2×Dic29C2×D411yescharacteristic
129C2×Dic29C2×D411yescharacteristic
130D116—22no—
131C4×D29—21no—
132C4×D29—21no—
133C4×D29—42no—
134C4×D29—81no—
135C4×D29—81no—
136C4×D29#4112yes—
137C4×D29#4112yes—
138Dic58—22no—
139Dic58—21no—
140Dic58—21no—
141Dic58—42no—
142C8×C29—21no—
143C8×C29—21no—
144#6597—21no—
145#6597—21no—
146#3097—291nomaximal, Sylow
147C22×C29—21no—
148C22×C29—21no—
149C22×C29—21no—
150C22×C29C22×D411yescharacteristic
151C2×D29—21no—
152C2×D29—21no—
153C2×D29—21no—
154C2×D29—21no—
155C2×D29—21no—
156C2×D29#12312yes—
157C4×C29—21no—
158C4×C29—41no—
159C4×C29—41no—
160C4×C29—41no—
161C4×C29—41no—
162C4×C29C2×#4111yescharacteristic
163C4×C29C2×#4111yescharacteristic
164Dic29—21no—
165Dic29—41no—
166Dic29—41no—
167Dic29—41no—
168Dic29—41no—
169Dic29#12312yes—
170#536—291no—
171#520—291no—
172#485—291no—
173#485—291no—
174#485—291no—
175#485—291no—
176#484—291no—
177#484—291no—
178#483—291no—
179#483D2911yescharacteristic, complemented
180#428—291no—
181#427—291no—
182#419—291no—
183C2×#103—291no—
184#408—291no—
185C2×C29—41no—
186C2×C29C2×#12311yescharacteristic
187C2×C29#57711yescharacteristic
188C2×C29#57811yescharacteristic
189D29—22no—
190D29—41no—
191C2×#41—291no—
192C22×Q8—291no—
193C2×M16—291no—
194C22×C8—291no—
195C4⋊Q8—581no—
196#124—581no—
197#123—581no—
198#123—581no—
199C22⋊Q8—291no—
200C22⋊Q8—291no—
201C22⋊Q8—291no—
202C22⋊Q8C2×D2911yescharacteristic
203C4×Q8—581no—
204C4×D4—581no—
205C4×D4—581no—
206C4×D4—581no—
207#117—291no—
208#117—291no—
209#117—291no—
210#117—291no—
211C2×C4⋊C4—291no—
212C2×C4⋊C4—291no—
213C2×C4⋊C4C2×D2911yescharacteristic
214#107—291no—
215#107—291no—
216#107—291no—
217#107—291no—
218#106—291no—
219#106—291no—
220#106C2×D2911yescharacteristic
221#106C2×D2911yescharacteristic
222#103—291no—
223#103—291no—
224#103—291no—
225#103—291no—
226#103—291no—
227#103—291no—
228#103C2×D2911yescharacteristic
229#103C2×D2911yescharacteristic
230C22⋊C8—291no—
231C22⋊C8—291no—
232C22⋊C8—291no—
233C22⋊C8C2×D2911yescharacteristic
234C29#309711yescharacteristic, complemented, Sylow
235#41—582no—
236#41—582no—
237C2×Q8—291no—
238C2×Q8—291no—
239C2×Q8—581no—
240C2×Q8—582no—
241C2×Q8—582no—
242C2×Q8C22×D2911yescharacteristic
243C2×D4—291no—
244C2×D4—291no—
245C2×D4—291no—
246C22×C4—21no—
247C22×C4—291no—
248C22×C4—291no—
249C22×C4—581no—
250C22×C4—581no—
251C22×C4—581no—
252C22×C4C22×D2911yescharacteristic
253M16—582no—
254C2×C8—291no—
255C2×C8—291no—
256C2×C8—582no—
257C2×C8C22×D2911yescharacteristic
258C2×C8C22×D2911yescharacteristic
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—291no—
262C4⋊C4—291no—
263C4⋊C4—291no—
264C4⋊C4—581no—
265C4⋊C4—581no—
266C4⋊C4—581no—
267C4⋊C4—581no—
268C4⋊C4—581no—
269C4⋊C4C22×D2911yescharacteristic
270C4⋊C4C22×D2911yescharacteristic
271C4⋊C4C22×D2911yescharacteristic
272C22⋊C4—21no—
273C22⋊C4—581no—
274C22⋊C4—581no—
275C22⋊C4—581no—
276C22⋊C4—581no—
277C22⋊C4—581no—
278C22⋊C4—581no—
279C22⋊C4—581no—
280C42—581no—
281C42—581no—
282C42—581no—
283C42—581no—
284C23—291no—
285C23—291no—
286C23D4×D2911yescharacteristic
287Q8—21no—
288Q8—21no—
289Q8—582no—
290Q8—581no—
291Q8—581no—
292Q8—1162no—
293D4—582no—
294D4—582no—
295D4—582no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—81no—
303C2×C4—291no—
304C2×C4—292no—
305C2×C4—292no—
306C2×C4—291no—
307C2×C4—581no—
308C2×C4—581no—
309C2×C4—581no—
310C2×C4—581no—
311C2×C4—581no—
312C2×C4—581no—
313C2×C4—1162no—
314C2×C4—2321no—
315C2×C4—2321no—
316C2×C4D4×D2911yescharacteristic
317C2×C4C23×D2911yescharacteristic
318C8—21no—
319C8—21no—
320C8—581no—
321C8—581no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—292no—
326C22—581no—
327C22—581no—
328C22—581no—
329C22—581no—
330C22—581no—
331C22C2×D4×D2911yescharacteristic
332C4—21no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—292no—
338C4—581no—
339C4—1161no—
340C4—1161no—
341C4—1161no—
342C4—1161no—
343C4#41×D2911yescharacteristic
344C4#41×D2911yescharacteristic
345C2—41no—
346C2—582no—
347C2—1161no—
348C2#123×D2911yescharacteristic
349C2#1427196911yescharacteristic
350C2#1427197911yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#483C2
socleC22×C29C22×D4
prime radicalC2×#90805C22
hypercenter#483D29
hypocenterC29#3097
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
3. #14271507C2semidirect
4. #14271505C2semidirect
5. #14271502C2semidirect
6. #14271501C2semidirect
7. #14271498C2semidirect
8. #14271497C2semidirect
9. #14271495C2semidirect
10. #14271202C2semidirect
11. #14271198C2semidirect
12. #14271170C2semidirect
13. #103×D29C2semidirect
15. C29×#483C2semidirect
179. #483D29semidirect
234. C29#3097semidirect

Maximal subgroups

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

subgroupindex
#142717362
#142716442
#142715072
#142715052
#142715022
#142715012
#142714982
#142714972
#142714952
#142712022
#142711982
#142711702
#103×D292
#142711282
C29×#4832
#309729