Finite Group Databasebeta

← #16829692

Subgroups — #16829692

Order 3712.

396 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271766C211yesmaximal, characteristic, complemented
2#14271646C211yesmaximal, characteristic, complemented
3#14271482C211yesmaximal, characteristic, complemented
4#14271474C211yesmaximal, characteristic, complemented
5#14271468C211yesmaximal, characteristic, complemented
6#14271465C211yesmaximal, characteristic, complemented
7#14271361C211yesmaximal, characteristic, complemented
8#14271356C211yesmaximal, characteristic, complemented
9#14271308C211yesmaximal, characteristic, complemented
10#14271275C211yesmaximal, characteristic, complemented
11#14271266C211yesmaximal, characteristic, complemented
12SD16×Dic29C211yesmaximal, characteristic, complemented
13#14271243C211yesmaximal, characteristic, complemented
14#14271221C211yesmaximal, characteristic, complemented
15C29×#449C211yesmaximal, characteristic, complemented
16C2×#41×C29C2211yescharacteristic
17C2×SD16×C29C2211yescharacteristic
18C2×D8×C29C2211yescharacteristic
19C29×#121C2211yescharacteristic
20Q8×Dic29C2211yescharacteristic
21Q8×Dic29C2211yescharacteristic
22C2×#90784C2211yescharacteristic
23#11745302C2211yescharacteristic
24#11745301—21no—
25#11745300—21no—
26D4×Dic29—21no—
27D4×Dic29—21no—
28D4×Dic29C2211yescharacteristic
29D4×Dic29C2211yescharacteristic
30D4×Dic29C2211yescharacteristic
31C2×#90782C2211yescharacteristic
32#11745292C2211yescharacteristic
33#11745288—21no—
34#11745288C2211yescharacteristic
35C2×C4⋊Dic29—21no—
36C2×C4⋊Dic29C2211yescharacteristic
37#11745255C2211yescharacteristic
38#11745252C2211yescharacteristic
39#11745248—21no—
40#11745245—21no—
41C29×#103C2211yescharacteristic
42C29×#102C2211yescharacteristic
43C29×C22⋊C8C2211yescharacteristic
44#11745183C2211yescharacteristic
45#11745180C2211yescharacteristic
46#11745180C2211yescharacteristic
47#11745180C2211yescharacteristic
48C22⋊#6597C2211yescharacteristic
49#11745169C2211yescharacteristic
50#11745169C2211yescharacteristic
51#11745165C2211yescharacteristic
52#11745165C2211yescharacteristic
53#11745163C2211yescharacteristic
54#11745162C2211yescharacteristic
55#11745162C2211yescharacteristic
56C8×Dic29C2211yescharacteristic
57#11745155C2211yescharacteristic
58#11745155C2211yescharacteristic
59#41×C29—22no—
60#41×C29—22no—
61C2×Q8×C29C2311yescharacteristic
62C2×D4×C29—21no—
63C2×D4×C29—21no—
64C2×D4×C29C2311yescharacteristic
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—
72C22×Dic29—21no—
73C22×Dic29—21no—
74C22×Dic29—21no—
75C2×D116C2311yescharacteristic
76C2×C4×D29—21no—
77SD16×C29—22no—
78D8×C29—22no—
79C2×C8×C29C2311yescharacteristic
80C2×C8×C29C2311yescharacteristic
81C4⋊C4×C29C2311yescharacteristic
82C22⋊C4×C29—21no—
83C22⋊Dic29—21no—
84C22⋊Dic29—21no—
85C22⋊Dic29—21no—
86C22⋊Dic29D411yescharacteristic
87C22⋊Dic29D411yescharacteristic
88#90784—22no—
89#90782—22no—
90#90781—21no—
91#90781—21no—
92C4⋊Dic29—21no—
93C4⋊Dic29—21no—
94C4⋊Dic29—21no—
95C4⋊Dic29—21no—
96C4⋊Dic29D411yescharacteristic
97C4⋊Dic29D411yescharacteristic
98C4⋊Dic29C2311yescharacteristic
99C4⋊Dic29C2311yescharacteristic
100C4⋊Dic29C2311yescharacteristic
101#90779—21no—
102C4×Dic29—21no—
103C4×Dic29—21no—
104C4×Dic29C2311yescharacteristic
105C4×Dic29C2311yescharacteristic
106C2×#6597C2311yescharacteristic
107C2×#6597C2311yescharacteristic
108C23×C29—21no—
109C23×C29—21no—
110C23×C29C2×D411yescharacteristic
111C22×D29—21no—
112Q8×C29—21no—
113Q8×C29#4112yes—
114D4×C29—24no—
115D4×C29—21no—
116D4×C29—21no—
117D4×C29—21no—
118D4×C29—81no—
119D4×C29#4112yes—
120C2×C4×C29—24no—
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×Dic29—81no—
135C2×Dic29—81no—
136C2×Dic29—81no—
137C2×Dic29C2×D411yescharacteristic
138C2×Dic29C2×D411yescharacteristic
139C2×Dic29C2×D411yescharacteristic
140C2×Dic29C2×D411yescharacteristic
141D116—21no—
142D116—21no—
143C4×D29—81no—
144C8×C29—21no—
145C8×C29—21no—
146#6597—21no—
147#6597—21no—
148#3119—291nomaximal, Sylow
149C22×C29—21no—
150C22×C29—22no—
151C22×C29—21no—
152C22×C29—21no—
153C22×C29—41no—
154C22×C29—41no—
155C22×C29—41no—
156C22×C29—41no—
157C22×C29—41no—
158C22×C29C22×D411yescharacteristic
159C2×D29—41no—
160C2×D29—41no—
161C2×D29—41no—
162C4×C29—21no—
163C4×C29—22no—
164C4×C29—41no—
165C4×C29C2×#4111yescharacteristic
166C4×C29C2×#4111yescharacteristic
167Dic29—21no—
168Dic29—21no—
169Dic29—21no—
170Dic29—21no—
171Dic29—41no—
172Dic29—41no—
173Dic29—41no—
174#540—291no—
175#520—291no—
176#481—291no—
177#480—291no—
178#479—291no—
179#478—291no—
180#460—291no—
181#459—291no—
182#449—291no—
183#449D2911yescharacteristic, complemented
184#442—291no—
185#440—291no—
186C4×SD16—291no—
187C4×D8—291no—
188#433—291no—
189C2×C29—41no—
190C2×C29—42no—
191C2×C29—81no—
192C2×C29#52511yescharacteristic
193C2×C29#57611yescharacteristic
194C2×C29#57711yescharacteristic
195D29—81no—
196C2×#41C2×D2911yescharacteristic
197C2×SD16—291no—
198C2×SD16C2×D2911yescharacteristic
199C2×D8—291no—
200C2×D8C2×D2911yescharacteristic
201#127—291no—
202#125—291no—
203#123—581no—
204#123—581no—
205#121—291no—
206#121—581no—
207#121—581no—
208#121C2×D2911yescharacteristic
209C4×Q8—291no—
210C4×Q8—291no—
211C4×D4—291no—
212C4×D4—291no—
213C4×D4—291no—
214C4×D4—291no—
215C4×D4—581no—
216C4×D4—581no—
217#117—291no—
218#117—581no—
219C2×C4⋊C4—291no—
220C2×C4⋊C4—581no—
221#107—291no—
222#107—291no—
223#106—291no—
224#106—291no—
225C4⋊C8—291no—
226C4⋊C8—291no—
227#103—291no—
228#103C2×D2911yescharacteristic
229#102—291no—
230#102—291no—
231#102—291no—
232#102—291no—
233#102—291no—
234#102C2×D2911yescharacteristic
235C22⋊C8—291no—
236C22⋊C8C2×D2911yescharacteristic
237#97—291no—
238C4×C8—291no—
239C29#311911yescharacteristic, complemented, Sylow
240#41—22no—
241#41—22no—
242C2×Q8C22×D2911yescharacteristic
243C2×D4—21no—
244C2×D4—21no—
245C2×D4—291no—
246C2×D4—581no—
247C2×D4—581no—
248C2×D4—581no—
249C2×D4C22×D2911yescharacteristic
250C2×D4C22×D2911yescharacteristic
251C22×C4—21no—
252C22×C4—581no—
253C22×C4—581no—
254C22×C4—581no—
255C22×C4—581no—
256C22×C4—581no—
257C22×C4C22×D2911yescharacteristic
258SD16—22no—
259SD16—582no—
260D8—22no—
261D8—582no—
262C2×C8—291no—
263C2×C8—291no—
264C2×C8C22×D2911yescharacteristic
265C2×C8C22×D2911yescharacteristic
266C4⋊C4—291no—
267C4⋊C4—291no—
268C4⋊C4—291no—
269C4⋊C4—291no—
270C4⋊C4—291no—
271C4⋊C4—581no—
272C4⋊C4—581no—
273C4⋊C4—581no—
274C4⋊C4—581no—
275C4⋊C4—581no—
276C4⋊C4C22×D2911yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—291no—
279C22⋊C4—291no—
280C22⋊C4—581no—
281C22⋊C4—581no—
282C22⋊C4—581no—
283C22⋊C4—581no—
284C22⋊C4—581no—
285C42—291no—
286C42—291no—
287C42—581no—
288C42—581no—
289C23—21no—
290C23—21no—
291C23—581no—
292C23D4×D2911yescharacteristic
293Q8—21no—
294Q8#9080712yes—
295D4—24no—
296D4—21no—
297D4—21no—
298D4—21no—
299D4—81no—
300D4—581no—
301D4—581no—
302D4—2321no—
303D4—2321no—
304D4—2321no—
305D4#9080712yes—
306C2×C4—24no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—291no—
312C2×C4—291no—
313C2×C4—291no—
314C2×C4—291no—
315C2×C4—581no—
316C2×C4—581no—
317C2×C4—581no—
318C2×C4—2321no—
319C2×C4—2321no—
320C2×C4—2321no—
321C2×C4—2321no—
322C2×C4—2321no—
323C2×C4D4×D2911yescharacteristic
324C2×C4C23×D2911yescharacteristic
325C8—21no—
326C8—21no—
327C8—581no—
328C8—581no—
329C22—21no—
330C22—22no—
331C22—21no—
332C22—21no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—1161no—
339C22—1161no—
340C22—1161no—
341C22C2×D4×D2911yescharacteristic
342C4—21no—
343C4—22no—
344C4—41no—
345C4—581no—
346C4—581no—
347C4—581no—
348C4—581no—
349C4—1161no—
350C4—1161no—
351C4—1161no—
352C4C2×#9080711yescharacteristic
353C4C2×#9080711yescharacteristic
354C2—41no—
355C2—42no—
356C2—81no—
357C2—2321no—
358C2#1427166911yescharacteristic
359C2#1427196711yescharacteristic
360C2#1427197011yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#449C2
socleC22×C29C22×D4
hypercenter#449D29
hypocenterC29#3119
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #14271766C2semidirect
2. #14271646C2semidirect
3. #14271482C2semidirect
4. #14271474C2semidirect
5. #14271468C2semidirect
6. #14271465C2semidirect
7. #14271361C2semidirect
8. #14271356C2semidirect
9. #14271308C2semidirect
10. #14271275C2semidirect
11. #14271266C2semidirect
12. SD16×Dic29C2semidirect
13. #14271243C2semidirect
14. #14271221C2semidirect
15. C29×#449C2semidirect
183. #449D29semidirect
239. C29#3119semidirect

Maximal subgroups

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

subgroupindex
#142717662
#142716462
#142714822
#142714742
#142714682
#142714652
#142713612
#142713562
#142713082
#142712752
#142712662
SD16×Dic292
#142712432
#142712212
C29×#4492
#311929