Finite Group Databasebeta

← #16829777

Subgroups — #16829777

Order 3712.

382 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271766C211yesmaximal, characteristic
2#14271641C211yesmaximal, characteristic, complemented
3#14271488C211yesmaximal, characteristic, complemented
4#14271484C211yesmaximal, characteristic, complemented
5#14271472C211yesmaximal, characteristic, complemented
6#14271468C211yesmaximal, characteristic, complemented
7#14271361C211yesmaximal, characteristic, complemented
8#14271361C211yesmaximal, characteristic, complemented
9#14271302C211yesmaximal, characteristic, complemented
10#14271266C211yesmaximal, characteristic, complemented
11#14271264C211yesmaximal, characteristic, complemented
12SD16×Dic29C211yesmaximal, characteristic, complemented
13#14271248C211yesmaximal, characteristic, complemented
14#14271221C211yesmaximal, characteristic, complemented
15C29×#448C211yesmaximal, characteristic, complemented
16C22×Q8×C29C2211yescharacteristic
17C2×SD16×C29C2211yescharacteristic
18C2×SD16×C29C2211yescharacteristic
19C29×#121C2211yescharacteristic
20Q8×Dic29—21no—
21Q8×Dic29—21no—
22Q8×Dic29C2211yescharacteristic
23Q8×Dic29C2211yescharacteristic
24Q8×Dic29C2211yescharacteristic
25Q8×Dic29C2211yescharacteristic
26C2×#90784C2211yescharacteristic
27C2×#90784C2211yescharacteristic
28#11745302C2211yescharacteristic
29#11745301—21no—
30#11745300—21no—
31D4×Dic29C2211yescharacteristic
32#11745292C2211yescharacteristic
33#11745288—21no—
34#11745288—21no—
35#11745288C2211yescharacteristic
36#11745288C2211yescharacteristic
37#11745255C2211yescharacteristic
38#11745252C2211yescharacteristic
39#11745248—21no—
40#11745245—21no—
41C29×#103C2211yescharacteristic
42C29×#103C2211yescharacteristic
43C29×C22⋊C8C2211yescharacteristic
44#11745183C2211yescharacteristic
45#11745183C2211yescharacteristic
46#11745180C2211yescharacteristic
47#11745180C2211yescharacteristic
48C22⋊#6597C2211yescharacteristic
49#11745169C2211yescharacteristic
50#11745169C2211yescharacteristic
51#11745166C2211yescharacteristic
52#11745165C2211yescharacteristic
53#11745163C2211yescharacteristic
54#11745162C2211yescharacteristic
55#11745162C2211yescharacteristic
56C8×Dic29C2211yescharacteristic
57#11745156C2211yescharacteristic
58#11745155C2211yescharacteristic
59C2×Q8×C29—22no—
60C2×Q8×C29—22no—
61C2×Q8×C29—21no—
62C2×Q8×C29C2311yescharacteristic
63C2×Q8×C29C2311yescharacteristic
64C2×D4×C29—21no—
65C2×D4×C29C2311yescharacteristic
66C22×C4×C29—21no—
67C22×C4×C29C2311yescharacteristic
68C2×C22⋊D29—21no—
69C2×C22⋊D29—21no—
70C2×C22⋊D29—21no—
71C22×Dic29—21no—
72C2×D116C2311yescharacteristic
73C2×C4×D29—21no—
74SD16×C29—22no—
75SD16×C29—22no—
76C2×C8×C29C2311yescharacteristic
77C2×C8×C29C2311yescharacteristic
78C4⋊C4×C29C2311yescharacteristic
79C22⋊C4×C29—21no—
80C22⋊Dic29—21no—
81C22⋊Dic29—21no—
82C22⋊Dic29D411yescharacteristic
83C22⋊Dic29D411yescharacteristic
84#90784—22no—
85#90784—22no—
86#90781—21no—
87#90781—21no—
88C4⋊Dic29—21no—
89C4⋊Dic29—21no—
90C4⋊Dic29—21no—
91C4⋊Dic29—21no—
92C4⋊Dic29—21no—
93C4⋊Dic29D411yescharacteristic
94C4⋊Dic29D411yescharacteristic
95C4⋊Dic29C2311yescharacteristic
96C4⋊Dic29C2311yescharacteristic
97C4⋊Dic29C2311yescharacteristic
98#90779—21no—
99C4×Dic29—21no—
100C4×Dic29—21no—
101C4×Dic29—21no—
102C4×Dic29—21no—
103C4×Dic29—21no—
104C4×Dic29C2311yescharacteristic
105C4×Dic29C2311yescharacteristic
106C2×#6597C2311yescharacteristic
107C2×#6597C2311yescharacteristic
108C23×C29—21no—
109C23×C29C2×D411yescharacteristic
110C22×D29—21no—
111Q8×C29—24no—
112Q8×C29—21no—
113Q8×C29—21no—
114Q8×C29#4112yes—
115Q8×C29#4112yes—
116D4×C29—21no—
117D4×C29—21no—
118D4×C29—81no—
119C2×C4×C29—24no—
120C2×C4×C29—21no—
121C2×C4×C29—21no—
122C2×C4×C29—21no—
123C2×C4×C29—21no—
124C2×C4×C29—21no—
125C2×C4×C29C2×D411yescharacteristic
126C2×C4×C29C2411yescharacteristic
127C22⋊D29—81no—
128C22⋊D29—81no—
129C22⋊D29—81no—
130C2×Dic29—21no—
131C2×Dic29—21no—
132C2×Dic29—21no—
133C2×Dic29—81no—
134C2×Dic29C2×D411yescharacteristic
135C2×Dic29C2×D411yescharacteristic
136C2×Dic29C2×D411yescharacteristic
137C2×Dic29C2×D411yescharacteristic
138D116—21no—
139D116—21no—
140C4×D29—81no—
141C8×C29—21no—
142C8×C29—21no—
143#6597—21no—
144#6597—21no—
145#3126—291nomaximal, Sylow
146C22×C29—21no—
147C22×C29—21no—
148C22×C29—21no—
149C22×C29—41no—
150C22×C29—41no—
151C22×C29—41no—
152C22×C29C22×D411yescharacteristic
153C2×D29—41no—
154C2×D29—41no—
155C2×D29—41no—
156C4×C29—22no—
157C4×C29—22no—
158C4×C29—21no—
159C4×C29—41no—
160C4×C29C2×#4111yescharacteristic
161C4×C29C2×#4111yescharacteristic
162Dic29—21no—
163Dic29—21no—
164Dic29—21no—
165Dic29—21no—
166Dic29—41no—
167Dic29—41no—
168Dic29—41no—
169#540—291no—
170#519—291no—
171#482—291no—
172#482—291no—
173#479—291no—
174#479—291no—
175#460—291no—
176#460—291no—
177#448—291no—
178#448D2911yescharacteristic, complemented
179#440—291no—
180#440—291no—
181C4×SD16—291no—
182C4×SD16—291no—
183#433—291no—
184C2×C29—41no—
185C2×C29—81no—
186C2×C29#52511yescharacteristic
187C2×C29#57711yescharacteristic
188C2×C29#57711yescharacteristic
189D29—81no—
190C22×Q8C2×D2911yescharacteristic
191C2×SD16—291no—
192C2×SD16—291no—
193C2×SD16C2×D2911yescharacteristic
194C2×SD16C2×D2911yescharacteristic
195#127—291no—
196#125—291no—
197#123—581no—
198#123—581no—
199#121—291no—
200#121—581no—
201#121—581no—
202#121C2×D2911yescharacteristic
203C4×Q8—291no—
204C4×Q8—291no—
205C4×Q8—291no—
206C4×Q8—291no—
207C4×Q8—581no—
208C4×Q8—581no—
209C4×D4—291no—
210C4×D4—291no—
211#117—291no—
212#117—291no—
213#117—581no—
214#117—581no—
215#107—291no—
216#107—291no—
217#106—291no—
218#106—291no—
219C4⋊C8—291no—
220C4⋊C8—291no—
221#103—291no—
222#103—291no—
223#103C2×D2911yescharacteristic
224#103C2×D2911yescharacteristic
225#102—291no—
226#102—291no—
227#102—291no—
228#102—291no—
229C22⋊C8—291no—
230C22⋊C8C2×D2911yescharacteristic
231#97—291no—
232C4×C8—291no—
233C29#312611yescharacteristic, complemented, Sylow
234C2×Q8—22no—
235C2×Q8—22no—
236C2×Q8—21no—
237C2×Q8C22×D2911yescharacteristic
238C2×Q8C22×D2911yescharacteristic
239C2×D4—21no—
240C2×D4—291no—
241C2×D4—581no—
242C2×D4—581no—
243C2×D4—581no—
244C2×D4C22×D2911yescharacteristic
245C22×C4—21no—
246C22×C4—581no—
247C22×C4—581no—
248C22×C4C22×D2911yescharacteristic
249SD16—22no—
250SD16—22no—
251SD16—582no—
252SD16—582no—
253C2×C8—291no—
254C2×C8—291no—
255C2×C8C22×D2911yescharacteristic
256C2×C8C22×D2911yescharacteristic
257C4⋊C4—291no—
258C4⋊C4—291no—
259C4⋊C4—291no—
260C4⋊C4—291no—
261C4⋊C4—291no—
262C4⋊C4—581no—
263C4⋊C4—581no—
264C4⋊C4—581no—
265C4⋊C4—581no—
266C4⋊C4—581no—
267C4⋊C4—581no—
268C4⋊C4C22×D2911yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—291no—
271C22⋊C4—291no—
272C22⋊C4—581no—
273C22⋊C4—581no—
274C22⋊C4—581no—
275C22⋊C4—581no—
276C42—291no—
277C42—291no—
278C42—581no—
279C42—581no—
280C42—581no—
281C42—581no—
282C42—581no—
283C23—21no—
284C23—581no—
285C23D4×D2911yescharacteristic
286Q8—24no—
287Q8—21no—
288Q8—21no—
289Q8#9080712yes—
290Q8#9080712yes—
291D4—21no—
292D4—21no—
293D4—81no—
294D4—581no—
295D4—581no—
296D4—2321no—
297D4—2321no—
298D4—2321no—
299C2×C4—24no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—291no—
306C2×C4—291no—
307C2×C4—291no—
308C2×C4—291no—
309C2×C4—581no—
310C2×C4—581no—
311C2×C4—581no—
312C2×C4—2321no—
313C2×C4—2321no—
314C2×C4D4×D2911yescharacteristic
315C2×C4C23×D2911yescharacteristic
316C8—21no—
317C8—21no—
318C8—581no—
319C8—581no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—1161no—
327C22—1161no—
328C22—1161no—
329C22C2×D4×D2911yescharacteristic
330C4—22no—
331C4—22no—
332C4—21no—
333C4—41no—
334C4—581no—
335C4—581no—
336C4—581no—
337C4—581no—
338C4—1161no—
339C4—1161no—
340C4—1161no—
341C4C2×#9080711yescharacteristic
342C4C2×#9080711yescharacteristic
343C2—41no—
344C2—81no—
345C2—2321no—
346C2#1427166911yescharacteristic
347C2#1427196911yescharacteristic
348C2#1427197211yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#448C2
socleC22×C29C22×D4
prime radical#14271766C2
hypercenter#448D29
hypocenterC29#3126
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
2. #14271641C2semidirect
3. #14271488C2semidirect
4. #14271484C2semidirect
5. #14271472C2semidirect
6. #14271468C2semidirect
7. #14271361C2semidirect
8. #14271361C2semidirect
9. #14271302C2semidirect
10. #14271266C2semidirect
11. #14271264C2semidirect
12. SD16×Dic29C2semidirect
13. #14271248C2semidirect
14. #14271221C2semidirect
15. C29×#448C2semidirect
178. #448D29semidirect
233. C29#3126semidirect

Maximal subgroups

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

subgroupindex
#142717662
#142716412
#142714882
#142714842
#142714722
#142714682
#142713612
#142713022
#142712662
#142712642
SD16×Dic292
#142712482
#142712212
C29×#4482
#312629