Finite Group Databasebeta

← #16832194

Subgroups — #16832194

Order 3712.

396 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271872C211yesmaximal, characteristic, complemented
2#14271833C211yesmaximal, characteristic, complemented
3#14271527C211yesmaximal, characteristic, complemented
4#14271526C211yesmaximal, characteristic, complemented
5#14271508C211yesmaximal, characteristic, complemented
6#14271464C211yesmaximal, characteristic, complemented
7#14271461C211yesmaximal, characteristic, complemented
8#14271451C211yesmaximal, characteristic, complemented
9#14271356C211yesmaximal, characteristic, complemented
10#14271356C211yesmaximal, characteristic, complemented
11#14271292C211yesmaximal, characteristic, complemented
12#14271275C211yesmaximal, characteristic, complemented
13#14271273C211yesmaximal, characteristic, complemented
14D8×Dic29C211yesmaximal, characteristic, complemented
15C29×#459C211yesmaximal, characteristic, complemented
16C2×#90807—21no—
17C2×D8×C29C2211yescharacteristic
18C2×D8×C29C2211yescharacteristic
19C29×#127C2211yescharacteristic
20C4×D4×C29C2211yescharacteristic
21#11745302C2211yescharacteristic
22#11745302C2211yescharacteristic
23#11745301—21no—
24#11745301—21no—
25#11745300—21no—
26D4×Dic29C2211yescharacteristic
27D4×Dic29C2211yescharacteristic
28D4×Dic29C2211yescharacteristic
29D4×Dic29C2211yescharacteristic
30C2×#90782C2211yescharacteristic
31#11745286—21no—
32C2×#90779—21no—
33#11745252C2211yescharacteristic
34#11745250C2211yescharacteristic
35#11745240—21no—
36#11745240—21no—
37C4×D116C2211yescharacteristic
38#11745232C2211yescharacteristic
39C4×Dic58C2211yescharacteristic
40C29×C4⋊C8C2211yescharacteristic
41C29×#102C2211yescharacteristic
42C29×#102C2211yescharacteristic
43#11745180C2211yescharacteristic
44#11745180C2211yescharacteristic
45#11745180C2211yescharacteristic
46#11745180C2211yescharacteristic
47#11745180C2211yescharacteristic
48#11745169C2211yescharacteristic
49#11745169C2211yescharacteristic
50#11745166C2211yescharacteristic
51#11745165C2211yescharacteristic
52#11745163C2211yescharacteristic
53#11745162C2211yescharacteristic
54#11745162C2211yescharacteristic
55C8×Dic29C2211yescharacteristic
56#11745157C2211yescharacteristic
57#11745156C2211yescharacteristic
58#11745151C2211yescharacteristic
59C2×D4×C29—21no—
60C2×D4×C29—21no—
61C2×D4×C29C2311yescharacteristic
62C2×D4×C29C2311yescharacteristic
63C2×D4×C29C2311yescharacteristic
64C22×C4×C29—21no—
65C2×C22⋊D29—21no—
66C2×C22⋊D29—21no—
67C2×C22⋊D29—21no—
68C2×C22⋊D29—21no—
69C22×Dic29—21no—
70C22×Dic29—21no—
71C22×Dic29—21no—
72C22×Dic29—21no—
73#90807—44no—
74C2×D116C2311yescharacteristic
75C2×C4×D29—21no—
76C2×Dic58—21no—
77C2×Dic58D411yescharacteristic
78D8×C29—22no—
79D8×C29—22no—
80C2×C8×C29C2311yescharacteristic
81C2×C8×C29C2311yescharacteristic
82C4⋊C4×C29C2311yescharacteristic
83C22⋊C4×C29—21no—
84C42×C29C2311yescharacteristic
85C22⋊Dic29—21no—
86C22⋊Dic29—21no—
87C22⋊Dic29—21no—
88C22⋊Dic29—21no—
89#90782—22no—
90#90781—21no—
91C4⋊Dic29—21no—
92C4⋊Dic29D411yescharacteristic
93C4⋊Dic29C2311yescharacteristic
94C4⋊Dic29C2311yescharacteristic
95C4⋊Dic29C2311yescharacteristic
96#90779—21no—
97#90779—21no—
98#90779—21no—
99#90779—21no—
100#90779D411yescharacteristic
101#90779D411yescharacteristic
102C4×Dic29C2311yescharacteristic
103C4×Dic29C2311yescharacteristic
104C2×#6597C2311yescharacteristic
105C2×#6597C2311yescharacteristic
106C23×C29—21no—
107C23×C29—21no—
108C23×C29—21no—
109C22×D29—21no—
110D4×C29—21no—
111D4×C29—21no—
112D4×C29—21no—
113D4×C29—21no—
114D4×C29—21no—
115D4×C29—42no—
116D4×C29—81no—
117D4×C29#4112yescomplemented
118C2×C4×C29—21no—
119C2×C4×C29—81no—
120C2×C4×C29C2×D411yescharacteristic
121C2×C4×C29C2×D411yescharacteristic
122C2×C4×C29C2411yescharacteristic
123C22⋊D29—42no—
124C22⋊D29—42no—
125C22⋊D29—81no—
126C22⋊D29—81no—
127C2×Dic29—21no—
128C2×Dic29—21no—
129C2×Dic29—21no—
130C2×Dic29—42no—
131C2×Dic29—42no—
132C2×Dic29—42no—
133C2×Dic29—81no—
134C2×Dic29C2×D411yescharacteristic
135C2×Dic29C2×D411yescharacteristic
136C2×Dic29C2×D411yescharacteristic
137C2×Dic29C2×D411yescharacteristic
138D116—21no—
139D116—21no—
140C4×D29—42no—
141Dic58—22no—
142Dic58—81no—
143C8×C29—21no—
144C8×C29—21no—
145#6597—21no—
146#6597—21no—
147#3366—291nomaximal, Sylow
148C22×C29—22no—
149C22×C29—41no—
150C22×C29—41no—
151C22×C29—41no—
152C22×C29—41no—
153C22×C29—41no—
154C22×C29—41no—
155C22×C29—41no—
156C22×C29—41no—
157C22×C29C22×D411yescharacteristic
158C2×D29—41no—
159C2×D29—41no—
160C2×D29—41no—
161C4×C29—21no—
162C4×C29—21no—
163C4×C29—41no—
164C4×C29C2×#4111yescharacteristic
165C4×C292−1+411yescharacteristic
166Dic29—21no—
167Dic29—21no—
168Dic29—21no—
169Dic29—41no—
170Dic29—41no—
171Dic29—41no—
172Dic29AGL(1,ℤ/8)12yes—
173#554—291no—
174#550—291no—
175#490—291no—
176#490—291no—
177#486—291no—
178#478—291no—
179#478—291no—
180#476—291no—
181#459—291no—
182#459—291no—
183#459D2911yescharacteristic, complemented
184#446—291no—
185#442—291no—
186#442—291no—
187C4×D8—291no—
188C2×C29—42no—
189C2×C29—81no—
190C2×C29—81no—
191C2×C29#54811yescharacteristic
192C2×C29C2×AGL(1,ℤ/8)11yescharacteristic
193C2×C29#57611yescharacteristic
194D29—81no—
195C2×#41—581no—
196C2×D8—291no—
197C2×D8C2×D2911yescharacteristic
198C2×D8C2×D2911yescharacteristic
199C4⋊Q8—291no—
200#127—291no—
201#127—291no—
202#127C2×D2911yescharacteristic
203#125—291no—
204#125—291no—
205C22⋊Q8—581no—
206C22⋊Q8—581no—
207C22⋊Q8—581no—
208#121—581no—
209#121—581no—
210#121—581no—
211C4×Q8—291no—
212C4×D4—291no—
213C4×D4—291no—
214C4×D4—291no—
215C4×D4—291no—
216C4×D4—291no—
217C4×D4C2×D2911yescharacteristic
218C2×C4⋊C4—581no—
219#107—291no—
220#106—291no—
221#106—291no—
222C4⋊C8—291no—
223C4⋊C8—291no—
224C4⋊C8C2×D2911yescharacteristic
225#102—291no—
226#102—291no—
227#102—291no—
228#102—291no—
229#102—291no—
230#102—291no—
231#102—291no—
232#102—291no—
233#102C2×D2911yescharacteristic
234#102C2×D2911yescharacteristic
235#97—291no—
236#97—291no—
237C4×C8—291no—
238C29#336611yescharacteristic, complemented, Sylow
239#41—1164no—
240C2×Q8—291no—
241C2×Q8—581no—
242C2×D4—21no—
243C2×D4—21no—
244C2×D4—291no—
245C2×D4—581no—
246C2×D4—581no—
247C2×D4—581no—
248C2×D4—581no—
249C2×D4C22×D2911yescharacteristic
250C2×D4C22×D2911yescharacteristic
251C2×D4C22×D2911yescharacteristic
252C22×C4—21no—
253C22×C4—581no—
254C22×C4—581no—
255C22×C4—581no—
256C22×C4—581no—
257C22×C4—581no—
258D8—22no—
259D8—22no—
260D8—582no—
261C2×C8—291no—
262C2×C8—291no—
263C2×C8C22×D2911yescharacteristic
264C2×C8C22×D2911yescharacteristic
265C4⋊C4—291no—
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—581no—
279C22⋊C4—581no—
280C22⋊C4—581no—
281C22⋊C4—581no—
282C22⋊C4—581no—
283C42—291no—
284C42—291no—
285C42C22×D2911yescharacteristic
286C23—21no—
287C23—21no—
288C23—21no—
289C23—581no—
290Q8—582no—
291Q8—2321no—
292D4—21no—
293D4—21no—
294D4—21no—
295D4—21no—
296D4—21no—
297D4—42no—
298D4—81no—
299D4—581no—
300D4—581no—
301D4—1162no—
302D4—1162no—
303D4—2321no—
304D4—2321no—
305D4#9080712yescomplemented
306C2×C4—21no—
307C2×C4—81no—
308C2×C4—291no—
309C2×C4—291no—
310C2×C4—291no—
311C2×C4—291no—
312C2×C4—581no—
313C2×C4—581no—
314C2×C4—581no—
315C2×C4—1162no—
316C2×C4—1162no—
317C2×C4—1162no—
318C2×C4—1162no—
319C2×C4—2321no—
320C2×C4D4×D2911yescharacteristic
321C2×C4D4×D2911yescharacteristic
322C2×C4C23×D2911yescharacteristic
323C8—21no—
324C8—21no—
325C8—581no—
326C8—581no—
327C22—22no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—1161no—
337C22—1161no—
338C22—1161no—
339C22C2×D4×D2911yescharacteristic
340C4—21no—
341C4—21no—
342C4—41no—
343C4—292no—
344C4—581no—
345C4—581no—
346C4—581no—
347C4—1161no—
348C4—1161no—
349C4—1161no—
350C4C2×#9080711yescharacteristic
351C4#1174536511yescharacteristic
352C2—42no—
353C2—81no—
354C2—81no—
355C2—2321no—
356C2#1427181911yescharacteristic
357C2AGL(1,ℤ/8)×D2911yescharacteristic
358C2#1427196411yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#459C2
socleC22×C29C22×D4
hypercenter#459D29
hypocenterC29#3366
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #14271872C2semidirect
2. #14271833C2semidirect
3. #14271527C2semidirect
4. #14271526C2semidirect
5. #14271508C2semidirect
6. #14271464C2semidirect
7. #14271461C2semidirect
8. #14271451C2semidirect
9. #14271356C2semidirect
10. #14271356C2semidirect
11. #14271292C2semidirect
12. #14271275C2semidirect
13. #14271273C2semidirect
14. D8×Dic29C2semidirect
15. C29×#459C2semidirect
117. D4×C29#41semidirect
183. #459D29semidirect
238. C29#3366semidirect
305. D4#90807semidirect

Maximal subgroups

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

subgroupindex
#142718722
#142718332
#142715272
#142715262
#142715082
#142714642
#142714612
#142714512
#142713562
#142712922
#142712752
#142712732
D8×Dic292
C29×#4592
#336629