Finite Group Databasebeta

← #16829747

Subgroups — #16829747

Order 3712.

384 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#14271780C211yesmaximal, characteristic, complemented
2#14271646C211yesmaximal, characteristic, complemented
3#14271499C211yesmaximal, characteristic, complemented
4#14271474C211yesmaximal, characteristic, complemented
5#14271456C211yesmaximal, characteristic, complemented
6#14271441C211yesmaximal, characteristic, complemented
7#14271383C211yesmaximal, characteristic, complemented
8#14271376C211yesmaximal, characteristic, complemented
9#14271325C211yesmaximal, characteristic, complemented
10#14271264C211yesmaximal, characteristic, complemented
11#14271260C211yesmaximal, characteristic, complemented
12#14271255C211yesmaximal, characteristic, complemented
13D8×Dic29C211yesmaximal, characteristic, complemented
14#14271221C211yesmaximal, characteristic, complemented
15C29×#449C211yesmaximal, characteristic
16C2×#41×C29C2211yescharacteristic
17C2×SD16×C29C2211yescharacteristic
18C2×D8×C29C2211yescharacteristic
19C29×#121C2211yescharacteristic
20Q8×Dic29C2211yescharacteristic
21Q8×Dic29C2211yescharacteristic
22C2×#90785C2211yescharacteristic
23#11745298—21no—
24#11745298C2211yescharacteristic
25#11745297—21no—
26D4×Dic29—21no—
27D4×Dic29—21no—
28D4×Dic29C2211yescharacteristic
29D4×Dic29C2211yescharacteristic
30D4×Dic29C2211yescharacteristic
31C2×#90783C2211yescharacteristic
32#11745288—21no—
33#11745288C2211yescharacteristic
34C2×C4⋊Dic29—21no—
35C2×C4⋊Dic29C2211yescharacteristic
36#11745286C2211yescharacteristic
37#11745250C2211yescharacteristic
38#11745249C2211yescharacteristic
39#11745241—21no—
40#11745240—21no—
41C29×#103C2211yescharacteristic
42C29×#102C2211yescharacteristic
43C29×C22⋊C8C2211yescharacteristic
44#11745183C2211yescharacteristic
45#11745180C2211yescharacteristic
46#11745180C2211yescharacteristic
47#11745180C2211yescharacteristic
48C22⋊#6597C2211yescharacteristic
49#11745166C2211yescharacteristic
50#11745166C2211yescharacteristic
51#11745164C2211yescharacteristic
52#11745164C2211yescharacteristic
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
68C22×Dic29—21no—
69C22×Dic29—21no—
70C22×Dic29—21no—
71C22×Dic29—21no—
72C2×Dic58—21no—
73C2×Dic58C2311yescharacteristic
74SD16×C29—22no—
75D8×C29—22no—
76C2×C8×C29C2311yescharacteristic
77C2×C8×C29C2311yescharacteristic
78C4⋊C4×C29C2311yescharacteristic
79C22⋊C4×C29—21no—
80C22⋊Dic29—21no—
81C22⋊Dic29—21no—
82C22⋊Dic29—21no—
83C22⋊Dic29—21no—
84C22⋊Dic29—21no—
85C22⋊Dic29—21no—
86C22⋊Dic29D411yescharacteristic
87C22⋊Dic29D411yescharacteristic
88#90785—22no—
89#90783—22no—
90C4⋊Dic29—21no—
91C4⋊Dic29—21no—
92C4⋊Dic29—21no—
93C4⋊Dic29D411yescharacteristic
94C4⋊Dic29D411yescharacteristic
95C4⋊Dic29C2311yescharacteristic
96C4⋊Dic29C2311yescharacteristic
97C4⋊Dic29C2311yescharacteristic
98#90779—21no—
99#90779—21no—
100#90779—21no—
101C4×Dic29—21no—
102C4×Dic29—21no—
103C4×Dic29—21no—
104C4×Dic29C2311yescharacteristic
105C4×Dic29C2311yescharacteristic
106C2×#6597C2311yescharacteristic
107C2×#6597C2311yescharacteristic
108C23×C29—21no—
109C23×C29—21no—
110C23×C29C2×D411yescharacteristic
111Q8×C29—21no—
112Q8×C29#4112yes—
113D4×C29—24no—
114D4×C29—21no—
115D4×C29—21no—
116D4×C29—21no—
117D4×C29—81no—
118D4×C29#4112yes—
119C2×C4×C29—24no—
120C2×C4×C29—21no—
121C2×C4×C29—21no—
122C2×C4×C29—21no—
123C2×C4×C29—21no—
124C2×C4×C29C2×D411yescharacteristic
125C2×C4×C29C2411yescharacteristic
126C2×Dic29—21no—
127C2×Dic29—21no—
128C2×Dic29—21no—
129C2×Dic29—21no—
130C2×Dic29—81no—
131C2×Dic29—81no—
132C2×Dic29—81no—
133C2×Dic29—81no—
134C2×Dic29C2×D411yescharacteristic
135C2×Dic29C2×D411yescharacteristic
136C2×Dic29C2×D411yescharacteristic
137C2×Dic29C2×D411yescharacteristic
138Dic58—21no—
139Dic58—21no—
140Dic58—81no—
141C8×C29—21no—
142C8×C29—21no—
143#6597—21no—
144#6597—21no—
145#3124—291nomaximal, Sylow
146C22×C29—21no—
147C22×C29—22no—
148C22×C29—21no—
149C22×C29—21no—
150C22×C29—41no—
151C22×C29—41no—
152C22×C29—41no—
153C22×C29—41no—
154C22×C29—41no—
155C22×C29C22×D411yescharacteristic
156C4×C29—21no—
157C4×C29—22no—
158C4×C29—41no—
159C4×C29C2×#4111yescharacteristic
160C4×C29C2×#4111yescharacteristic
161Dic29—21no—
162Dic29—21no—
163Dic29—21no—
164Dic29—21no—
165Dic29—41no—
166Dic29—41no—
167Dic29—41no—
168Dic29—41no—
169#542—291no—
170#520—291no—
171#484—291no—
172#480—291no—
173#477—291no—
174#474—291no—
175#464—291no—
176#463—291no—
177#452—291no—
178#449D2911yescharacteristic
179#440—291no—
180#440—291no—
181C4×Q16—291no—
182C4×D8—291no—
183#433—291no—
184C2×C29—41no—
185C2×C29—42no—
186C2×C29—81no—
187C2×C29#52511yescharacteristic
188C2×C29#57611yescharacteristic
189C2×C29#57811yescharacteristic
190C2×#41C2×D2911yescharacteristic
191C2×Q16—291no—
192C2×SD16—291no—
193C2×SD16C2×D2911yescharacteristic
194C2×D8C2×D2911yescharacteristic
195C4⋊Q8—291no—
196#126—581no—
197#124—291no—
198#124—581no—
199#123—581no—
200C22⋊Q8—291no—
201C22⋊Q8—581no—
202#121C2×D2911yescharacteristic
203C4×Q8—291no—
204C4×Q8—291no—
205C4×Q8—291no—
206C4×D4—291no—
207C4×D4—291no—
208C4×D4—291no—
209C4×D4—581no—
210C4×D4—581no—
211#117—291no—
212#117—581no—
213C2×C4⋊C4—291no—
214C2×C4⋊C4—581no—
215#107—291no—
216#107—291no—
217#107—291no—
218#107—291no—
219C4⋊C8—291no—
220C4⋊C8—291no—
221#103—291no—
222#103—291no—
223#103—291no—
224#103C2×D2911yescharacteristic
225#102—291no—
226#102—291no—
227#102—291no—
228#102C2×D2911yescharacteristic
229C22⋊C8—291no—
230C22⋊C8C2×D2911yescharacteristic
231#97—291no—
232C4×C8—291no—
233C29#312411yescharacteristic, complemented, Sylow
234#41—22no—
235#41—22no—
236C2×Q8—291no—
237C2×Q8—581no—
238C2×Q8C22×D2911yescharacteristic
239C2×D4—21no—
240C2×D4—21no—
241C2×D4C22×D2911yescharacteristic
242C2×D4C22×D2911yescharacteristic
243C22×C4—21no—
244C22×C4—581no—
245C22×C4—581no—
246C22×C4—581no—
247C22×C4—581no—
248C22×C4C22×D2911yescharacteristic
249Q16—582no—
250SD16—22no—
251SD16—582no—
252D8—22no—
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—
276C22⋊C4—581no—
277C22⋊C4—581no—
278C42—291no—
279C42—291no—
280C42—581no—
281C42—581no—
282C42—581no—
283C23—21no—
284C23—21no—
285C23D4×D2911yescharacteristic
286Q8—21no—
287Q8—581no—
288Q8—581no—
289Q8—2321no—
290Q8#9080712yes—
291D4—24no—
292D4—21no—
293D4—21no—
294D4—21no—
295D4—81no—
296D4#9080712yes—
297C2×C4—24no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—291no—
303C2×C4—291no—
304C2×C4—291no—
305C2×C4—291no—
306C2×C4—581no—
307C2×C4—581no—
308C2×C4—581no—
309C2×C4—581no—
310C2×C4—2321no—
311C2×C4—2321no—
312C2×C4—2321no—
313C2×C4—2321no—
314C2×C4D4×D2911yescharacteristic
315C2×C4C23×D2911yescharacteristic
316C8—21no—
317C8—21no—
318C8—581no—
319C8—581no—
320C22—21no—
321C22—22no—
322C22—21no—
323C22—21no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22C2×D4×D2911yescharacteristic
330C4—21no—
331C4—22no—
332C4—41no—
333C4—581no—
334C4—581no—
335C4—581no—
336C4—581no—
337C4—1161no—
338C4—1161no—
339C4—1161no—
340C4—1161no—
341C4C2×#9080711yescharacteristic
342C4C2×#9080711yescharacteristic
343C2—41no—
344C2—42no—
345C2—81no—
346C2#1427166911yescharacteristic
347C2#1427196711yescharacteristic
348C2#1427197711yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
Fitting, prime radicalC29×#449C2
socleC22×C29C22×D4
hypercenter#449D29
hypocenterC29#3124
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. #14271780C2semidirect
2. #14271646C2semidirect
3. #14271499C2semidirect
4. #14271474C2semidirect
5. #14271456C2semidirect
6. #14271441C2semidirect
7. #14271383C2semidirect
8. #14271376C2semidirect
9. #14271325C2semidirect
10. #14271264C2semidirect
11. #14271260C2semidirect
12. #14271255C2semidirect
13. D8×Dic29C2semidirect
14. #14271221C2semidirect
233. C29#3124semidirect

Maximal subgroups

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

subgroupindex
#142717802
#142716462
#142714992
#142714742
#142714562
#142714412
#142713832
#142713762
#142713252
#142712642
#142712602
#142712552
D8×Dic292
#142712212
C29×#4492
#312429