Finite Group Databasebeta

← C29×#3376 #16817090

Subgroups — C29×#3376 #16817090

Order 3712.

346 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#556C211yesmaximal, characteristic, complemented
2C29×#554C211yesmaximal, characteristic, complemented
3C29×#491C211yesmaximal, characteristic, complemented
4C29×#489C211yesmaximal, characteristic, complemented
5C29×#488C211yesmaximal, characteristic, complemented
6C29×#479C211yesmaximal, characteristic, complemented
7C29×#478C211yesmaximal, characteristic, complemented
8C29×#475C211yesmaximal, characteristic, complemented
9C29×#463C211yesmaximal, characteristic
10C29×#463C211yesmaximal, characteristic
11C29×#461C211yesmaximal, characteristic, complemented
12C29×#446C211yesmaximal, characteristic, complemented
13C29×#442C211yesmaximal, characteristic
14C29×#440C211yesmaximal, characteristic, complemented
15C4×SD16×C29C211yesmaximal, characteristic, complemented
16C2×SD16×C29C2211yescharacteristic
17C2×SD16×C29C2211yescharacteristic
18C2×D8×C29C2211yescharacteristic
19C29×C4⋊Q8C2211yescharacteristic
20C29×C4⋊Q8C2211yescharacteristic
21C29×#126—21no—
22C29×#126—21no—
23C29×#125C2211yescharacteristic
24C29×#125C2211yescharacteristic
25C29×#124C2211yescharacteristic
26C29×#124C2211yescharacteristic
27C29×C22⋊Q8—21no—
28C29×C22⋊Q8—21no—
29C29×C22⋊Q8—21no—
30C29×C22⋊Q8—21no—
31C4×Q8×C29C2211yescharacteristic
32C4×Q8×C29C2211yescharacteristic
33C4×Q8×C29C2211yescharacteristic
34C4×D4×C29C2211yescharacteristic
35C4×D4×C29C2211yescharacteristic
36C4×D4×C29C2211yescharacteristic
37C4×D4×C29C2211yescharacteristic
38C29×#117—21no—
39C2×C4⋊C4×C29—21no—
40C29×#107C2211yescharacteristic
41C29×#106C2211yescharacteristic
42C29×#106C2211yescharacteristic
43C29×C4⋊C8C2211yescharacteristic
44C29×C4⋊C8C2211yescharacteristic
45C29×C4⋊C8C2211yescharacteristic
46C29×#103C2211yescharacteristic
47C29×#103C2211yescharacteristic
48C29×#103C2211yescharacteristic
49C29×#103C2211yescharacteristic
50C29×#103C2211yescharacteristic
51C29×#103C2211yescharacteristic
52C29×#102C2211yescharacteristic
53C29×#102C2211yescharacteristic
54C29×#102C2211yescharacteristic
55C29×#102C2211yescharacteristic
56C29×#97C2211yescharacteristic
57C29×#97C2211yescharacteristic
58C4×C8×C29C2211yescharacteristic
59C2×Q8×C29—21no—
60C2×Q8×C29D411yescharacteristic
61C2×Q8×C29C2311yescharacteristic
62C2×Q8×C29C2311yescharacteristic
63C2×D4×C29C2311yescharacteristic
64C2×D4×C29C2311yescharacteristic
65C22×C4×C29—21no—
66C22×C4×C29—21no—
67C22×C4×C29—21no—
68C22×C4×C29—21no—
69SD16×C29—22no—
70SD16×C29—22no—
71D8×C29—22no—
72C2×C8×C29C2311yescharacteristic
73C2×C8×C29C2311yescharacteristic
74C2×C8×C29C2311yescharacteristic
75C2×C8×C29C2311yescharacteristic
76C4⋊C4×C29—21no—
77C4⋊C4×C29—21no—
78C4⋊C4×C29—21no—
79C4⋊C4×C29—21no—
80C4⋊C4×C29—21no—
81C4⋊C4×C29—21no—
82C4⋊C4×C29—21no—
83C4⋊C4×C29—21no—
84C4⋊C4×C29—21no—
85C4⋊C4×C29D411yescharacteristic
86C4⋊C4×C29D411yescharacteristic
87C4⋊C4×C29D411yescharacteristic
88C4⋊C4×C29C2311yescharacteristic
89C4⋊C4×C29C2311yescharacteristic
90C4⋊C4×C29C2311yescharacteristic
91C4⋊C4×C29C2311yescharacteristic
92C22⋊C4×C29—21no—
93C22⋊C4×C29—21no—
94C22⋊C4×C29—21no—
95C22⋊C4×C29—21no—
96C22⋊C4×C29—21no—
97C22⋊C4×C29—21no—
98C22⋊C4×C29—21no—
99C22⋊C4×C29—21no—
100C42×C29—21no—
101C42×C29—21no—
102C42×C29C2311yescharacteristic
103C42×C29C2311yescharacteristic
104C42×C29C2311yescharacteristic
105C23×C29—21no—
106C23×C29—21no—
107Q8×C29—21no—
108Q8×C29—21no—
109Q8×C29—21no—
110Q8×C29—21no—
111Q8×C29—41no—
112Q8×C29—81no—
113D4×C29—21no—
114D4×C29—21no—
115D4×C29—21no—
116D4×C29#4112yes—
117C2×C4×C29—21no—
118C2×C4×C29—21no—
119C2×C4×C29—21no—
120C2×C4×C29—21no—
121C2×C4×C29—21no—
122C2×C4×C29—21no—
123C2×C4×C29—42no—
124C2×C4×C29—42no—
125C2×C4×C29—81no—
126C2×C4×C29—81no—
127C2×C4×C29C2×D411yescharacteristic
128C2×C4×C29C2×D411yescharacteristic
129C2×C4×C29C2×D411yescharacteristic
130C2×C4×C29C2×D411yescharacteristic
131C2×C4×C29C2×D411yescharacteristic
132C2×C4×C29C2×D411yescharacteristic
133C2×C4×C29C2411yescharacteristic
134C8×C29—21no—
135C8×C29—21no—
136C8×C29—21no—
137C8×C29—21no—
138#3376C2911yesmaximal, characteristic, direct product factor, Sylow
139C22×C29—22no—
140C22×C29—41no—
141C22×C29—41no—
142C22×C29—41no—
143C22×C29—41no—
144C22×C29—41no—
145C22×C29C22×D411yescharacteristic
146C4×C29—21no—
147C4×C29—21no—
148C4×C29—21no—
149C4×C29—21no—
150C4×C29—21no—
151C4×C29—21no—
152C4×C29—41no—
153C4×C29—41no—
154C4×C29—41no—
155C4×C29—41no—
156C4×C29—41no—
157C4×C29—41no—
158C4×C29C2×#4111yescharacteristic
159C4×C292−1+411yescharacteristic
160#556C2×C2911yescharacteristic, complemented
161#554C2×C2911yescharacteristic, complemented
162#491C2×C2911yescharacteristic, complemented
163#489C2×C2911yescharacteristic, complemented
164#488C2×C2911yescharacteristic, complemented
165#479C2×C2911yescharacteristic, complemented
166#478C2×C2911yescharacteristic, complemented
167#475C2×C2911yescharacteristic, complemented
168#463C2×C2911yescharacteristic
169#463C2×C2911yescharacteristic
170#461C2×C2911yescharacteristic, complemented
171#446C2×C2911yescharacteristic, complemented
172#442C2×C2911yescharacteristic
173#440C2×C2911yescharacteristic, complemented
174C4×SD16C2×C2911yescharacteristic, complemented
175C2×C29—42no—
176C2×C29—81no—
177C2×C29#54811yescharacteristic
178C2×C29#57511yescharacteristic
179C2×C29#57711yescharacteristic
180C2×SD16C22×C2911yescharacteristic
181C2×SD16C22×C2911yescharacteristic
182C2×D8C22×C2911yescharacteristic
183C4⋊Q8C22×C2911yescharacteristic
184C4⋊Q8C22×C2911yescharacteristic
185#126—21no—
186#126—21no—
187#125C22×C2911yescharacteristic
188#125C22×C2911yescharacteristic
189#124C22×C2911yescharacteristic
190#124C22×C2911yescharacteristic
191C22⋊Q8—21no—
192C22⋊Q8—21no—
193C22⋊Q8—21no—
194C22⋊Q8—21no—
195C4×Q8C22×C2911yescharacteristic
196C4×Q8C22×C2911yescharacteristic
197C4×Q8C22×C2911yescharacteristic
198C4×D4C22×C2911yescharacteristic
199C4×D4C22×C2911yescharacteristic
200C4×D4C22×C2911yescharacteristic
201C4×D4C22×C2911yescharacteristic
202#117—21no—
203C2×C4⋊C4—21no—
204#107C22×C2911yescharacteristic
205#106C22×C2911yescharacteristic
206#106C22×C2911yescharacteristic
207C4⋊C8C22×C2911yescharacteristic
208C4⋊C8C22×C2911yescharacteristic
209C4⋊C8C22×C2911yescharacteristic
210#103C22×C2911yescharacteristic
211#103C22×C2911yescharacteristic
212#103C22×C2911yescharacteristic
213#103C22×C2911yescharacteristic
214#103C22×C2911yescharacteristic
215#103C22×C2911yescharacteristic
216#102C22×C2911yescharacteristic
217#102C22×C2911yescharacteristic
218#102C22×C2911yescharacteristic
219#102C22×C2911yescharacteristic
220#97C22×C2911yescharacteristic
221#97C22×C2911yescharacteristic
222C4×C8C22×C2911yescharacteristic
223C29#337611yescharacteristic, direct product factor, Sylow
224C2×Q8—21no—
225C2×Q8D4×C2911yescharacteristic
226C2×Q8C23×C2911yescharacteristic
227C2×Q8C23×C2911yescharacteristic
228C2×D4C23×C2911yescharacteristic
229C2×D4C23×C2911yescharacteristic
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234SD16—22no—
235SD16—22no—
236D8—22no—
237C2×C8C23×C2911yescharacteristic
238C2×C8C23×C2911yescharacteristic
239C2×C8C23×C2911yescharacteristic
240C2×C8C23×C2911yescharacteristic
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4D4×C2911yescharacteristic
251C4⋊C4D4×C2911yescharacteristic
252C4⋊C4D4×C2911yescharacteristic
253C4⋊C4C23×C2911yescharacteristic
254C4⋊C4C23×C2911yescharacteristic
255C4⋊C4C23×C2911yescharacteristic
256C4⋊C4C23×C2911yescharacteristic
257C22⋊C4—21no—
258C22⋊C4—21no—
259C22⋊C4—21no—
260C22⋊C4—21no—
261C22⋊C4—21no—
262C22⋊C4—21no—
263C22⋊C4—21no—
264C22⋊C4—21no—
265C42—21no—
266C42—21no—
267C42C23×C2911yescharacteristic
268C42C23×C2911yescharacteristic
269C42C23×C2911yescharacteristic
270C23—21no—
271C23—21no—
272Q8—21no—
273Q8—21no—
274Q8—21no—
275Q8—21no—
276Q8—41no—
277Q8—81no—
278D4—21no—
279D4—21no—
280D4—21no—
281D4#41×C2912yes—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—81no—
291C2×C4—81no—
292C2×C4C2×D4×C2911yescharacteristic
293C2×C4C2×D4×C2911yescharacteristic
294C2×C4C2×D4×C2911yescharacteristic
295C2×C4C2×D4×C2911yescharacteristic
296C2×C4C2×D4×C2911yescharacteristic
297C2×C4C2×D4×C2911yescharacteristic
298C2×C4C24×C2911yescharacteristic
299C8—21no—
300C8—21no—
301C8—21no—
302C8—21no—
303C22—22no—
304C22—41no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22—41no—
309C22C22×D4×C2911yescharacteristic
310C4—21no—
311C4—21no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—41no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4C2×#41×C2911yescharacteristic
323C4C29×2−1+411yescharacteristic
324C2—42no—
325C2—81no—
326C2C29×#54811yescharacteristic
327C2C29×#57511yescharacteristic
328C2C29×#57711yescharacteristic
subgroupG/H
center, socleC22×C29C22×D4
commutator, Frattini, cosocleC2×C4C24×C29
prime radicalC2×D8×C29C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C4×Q8×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C29×#556C2semidirect
2. C29×#554C2semidirect
3. C29×#491C2semidirect
4. C29×#489C2semidirect
5. C29×#488C2semidirect
6. C29×#479C2semidirect
7. C29×#478C2semidirect
8. C29×#475C2semidirect
11. C29×#461C2semidirect
12. C29×#446C2semidirect
14. C29×#440C2semidirect
15. C4×SD16×C29C2semidirect
138. #3376C29direct (N × H)
160. #556C2×C29semidirect
161. #554C2×C29semidirect
162. #491C2×C29semidirect
163. #489C2×C29semidirect
164. #488C2×C29semidirect
165. #479C2×C29semidirect
166. #478C2×C29semidirect
167. #475C2×C29semidirect
170. #461C2×C29semidirect
171. #446C2×C29semidirect
173. #440C2×C29semidirect
174. C4×SD16C2×C29semidirect
223. C29#3376direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#5562
C29×#5542
C29×#4912
C29×#4892
C29×#4882
C29×#4792
C29×#4782
C29×#4752
C29×#4632
C29×#4612
C29×#4462
C29×#4422
C29×#4402
C4×SD16×C292
#337629