Finite Group Databasebeta

← C29×#3121 #16816835

Subgroups — C29×#3121 #16816835

Order 3712.

370 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#542C211yesmaximal, characteristic
2C29×#519C211yesmaximal, characteristic, complemented
3C29×#485C211yesmaximal, characteristic, complemented
4C29×#482C211yesmaximal, characteristic
5C29×#477C211yesmaximal, characteristic, complemented
6C29×#475C211yesmaximal, characteristic, complemented
7C29×#464C211yesmaximal, characteristic, complemented
8C29×#464C211yesmaximal, characteristic, complemented
9C29×#451C211yesmaximal, characteristic, complemented
10C29×#448C211yesmaximal, characteristic
11C29×#441C211yesmaximal, characteristic, complemented
12C29×#440C211yesmaximal, characteristic, complemented
13C4×Q16×C29C211yesmaximal, characteristic, complemented
14C4×SD16×C29C211yesmaximal, characteristic, complemented
15C29×#433C211yesmaximal, characteristic, complemented
16C22×Q8×C29C2211yescharacteristic
17C2×Q16×C29C2211yescharacteristic
18C2×Q16×C29C2211yescharacteristic
19C2×SD16×C29C2211yescharacteristic
20C2×SD16×C29C2211yescharacteristic
21C29×C4⋊Q8C2211yescharacteristic
22C29×#126—21no—
23C29×#124—21no—
24C29×#124C2211yescharacteristic
25C29×#123—21no—
26C29×C22⋊Q8—21no—
27C29×C22⋊Q8C2211yescharacteristic
28C29×#121C2211yescharacteristic
29C4×Q8×C29—21no—
30C4×Q8×C29—21no—
31C4×Q8×C29C2211yescharacteristic
32C4×Q8×C29C2211yescharacteristic
33C4×Q8×C29C2211yescharacteristic
34C4×Q8×C29C2211yescharacteristic
35C4×Q8×C29C2211yescharacteristic
36C4×D4×C29C2211yescharacteristic
37C29×#117—21no—
38C29×#117—21no—
39C29×#117C2211yescharacteristic
40C29×#117C2211yescharacteristic
41C29×#107C2211yescharacteristic
42C29×#107C2211yescharacteristic
43C29×#106C2211yescharacteristic
44C29×#106C2211yescharacteristic
45C29×C4⋊C8C2211yescharacteristic
46C29×C4⋊C8C2211yescharacteristic
47C29×#103C2211yescharacteristic
48C29×#103C2211yescharacteristic
49C29×#103C2211yescharacteristic
50C29×#103C2211yescharacteristic
51C29×#103C2211yescharacteristic
52C29×#103C2211yescharacteristic
53C29×#102C2211yescharacteristic
54C29×#102C2211yescharacteristic
55C29×C22⋊C8C2211yescharacteristic
56C29×C22⋊C8C2211yescharacteristic
57C29×#97C2211yescharacteristic
58C4×C8×C29C2211yescharacteristic
59C2×Q8×C29—22no—
60C2×Q8×C29—22no—
61C2×Q8×C29—21no—
62C2×Q8×C29—21no—
63C2×Q8×C29C2311yescharacteristic
64C2×Q8×C29C2311yescharacteristic
65C2×Q8×C29C2311yescharacteristic
66C2×D4×C29—21no—
67C2×D4×C29C2311yescharacteristic
68C22×C4×C29—21no—
69C22×C4×C29—21no—
70C22×C4×C29C2311yescharacteristic
71Q16×C29—22no—
72Q16×C29—22no—
73SD16×C29—22no—
74SD16×C29—22no—
75C2×C8×C29C2311yescharacteristic
76C2×C8×C29C2311yescharacteristic
77C2×C8×C29C2311yescharacteristic
78C2×C8×C29C2311yescharacteristic
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×C29—21no—
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×C29D411yescharacteristic
99C22⋊C4×C29D411yescharacteristic
100C42×C29—21no—
101C42×C29—21no—
102C42×C29—21no—
103C42×C29—21no—
104C42×C29—21no—
105C42×C29—21no—
106C42×C29C2311yescharacteristic
107C42×C29C2311yescharacteristic
108C23×C29—21no—
109C23×C29C2×D411yescharacteristic
110Q8×C29—24no—
111Q8×C29—21no—
112Q8×C29—21no—
113Q8×C29—21no—
114Q8×C29—21no—
115Q8×C29—81no—
116Q8×C29#4112yes—
117Q8×C29#4112yes—
118D4×C29—21no—
119D4×C29—21no—
120D4×C29—81no—
121C2×C4×C29—24no—
122C2×C4×C29—21no—
123C2×C4×C29—21no—
124C2×C4×C29—21no—
125C2×C4×C29—21no—
126C2×C4×C29—21no—
127C2×C4×C29—21no—
128C2×C4×C29—21no—
129C2×C4×C29—21no—
130C2×C4×C29—21no—
131C2×C4×C29—81no—
132C2×C4×C29C2×D411yescharacteristic
133C2×C4×C29C2×D411yescharacteristic
134C2×C4×C29C2×D411yescharacteristic
135C2×C4×C29C2×D411yescharacteristic
136C2×C4×C29C2×D411yescharacteristic
137C2×C4×C29C2411yescharacteristic
138C8×C29—21no—
139C8×C29—21no—
140C8×C29—21no—
141C8×C29—21no—
142#3121C2911yesmaximal, characteristic, direct product factor, Sylow
143C22×C29—21no—
144C22×C29—21no—
145C22×C29—21no—
146C22×C29—41no—
147C22×C29—41no—
148C22×C29—41no—
149C22×C29C22×D411yescharacteristic
150C4×C29—22no—
151C4×C29—22no—
152C4×C29—21no—
153C4×C29—21no—
154C4×C29—21no—
155C4×C29—21no—
156C4×C29—21no—
157C4×C29—41no—
158C4×C29—41no—
159C4×C29—41no—
160C4×C29—41no—
161C4×C29—41no—
162C4×C29C2×#4111yescharacteristic
163C4×C29C2×#4111yescharacteristic
164#542C2×C2911yescharacteristic
165#519C2×C2911yescharacteristic, complemented
166#485C2×C2911yescharacteristic, complemented
167#482C2×C2911yescharacteristic
168#477C2×C2911yescharacteristic, complemented
169#475C2×C2911yescharacteristic, complemented
170#464C2×C2911yescharacteristic, complemented
171#464C2×C2911yescharacteristic, complemented
172#451C2×C2911yescharacteristic, complemented
173#448C2×C2911yescharacteristic
174#441C2×C2911yescharacteristic, complemented
175#440C2×C2911yescharacteristic, complemented
176C4×Q16C2×C2911yescharacteristic, complemented
177C4×SD16C2×C2911yescharacteristic, complemented
178#433C2×C2911yescharacteristic, complemented
179C2×C29—41no—
180C2×C29—81no—
181C2×C29#52511yescharacteristic
182C2×C29#57711yescharacteristic
183C2×C29#57811yescharacteristic
184C22×Q8C22×C2911yescharacteristic
185C2×Q16C22×C2911yescharacteristic
186C2×Q16C22×C2911yescharacteristic
187C2×SD16C22×C2911yescharacteristic
188C2×SD16C22×C2911yescharacteristic
189C4⋊Q8C22×C2911yescharacteristic
190#126—21no—
191#124—21no—
192#124C22×C2911yescharacteristic
193#123—21no—
194C22⋊Q8—21no—
195C22⋊Q8C22×C2911yescharacteristic
196#121C22×C2911yescharacteristic
197C4×Q8—21no—
198C4×Q8—21no—
199C4×Q8C22×C2911yescharacteristic
200C4×Q8C22×C2911yescharacteristic
201C4×Q8C22×C2911yescharacteristic
202C4×Q8C22×C2911yescharacteristic
203C4×Q8C22×C2911yescharacteristic
204C4×D4C22×C2911yescharacteristic
205#117—21no—
206#117—21no—
207#117C22×C2911yescharacteristic
208#117C22×C2911yescharacteristic
209#107C22×C2911yescharacteristic
210#107C22×C2911yescharacteristic
211#106C22×C2911yescharacteristic
212#106C22×C2911yescharacteristic
213C4⋊C8C22×C2911yescharacteristic
214C4⋊C8C22×C2911yescharacteristic
215#103C22×C2911yescharacteristic
216#103C22×C2911yescharacteristic
217#103C22×C2911yescharacteristic
218#103C22×C2911yescharacteristic
219#103C22×C2911yescharacteristic
220#103C22×C2911yescharacteristic
221#102C22×C2911yescharacteristic
222#102C22×C2911yescharacteristic
223C22⋊C8C22×C2911yescharacteristic
224C22⋊C8C22×C2911yescharacteristic
225#97C22×C2911yescharacteristic
226C4×C8C22×C2911yescharacteristic
227C29#312111yescharacteristic, direct product factor, Sylow
228C2×Q8—22no—
229C2×Q8—22no—
230C2×Q8—21no—
231C2×Q8—21no—
232C2×Q8C23×C2911yescharacteristic
233C2×Q8C23×C2911yescharacteristic
234C2×Q8C23×C2911yescharacteristic
235C2×D4—21no—
236C2×D4C23×C2911yescharacteristic
237C22×C4—21no—
238C22×C4—21no—
239C22×C4C23×C2911yescharacteristic
240Q16—22no—
241Q16—22no—
242SD16—22no—
243SD16—22no—
244C2×C8C23×C2911yescharacteristic
245C2×C8C23×C2911yescharacteristic
246C2×C8C23×C2911yescharacteristic
247C2×C8C23×C2911yescharacteristic
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4D4×C2911yescharacteristic
256C4⋊C4D4×C2911yescharacteristic
257C4⋊C4C23×C2911yescharacteristic
258C4⋊C4C23×C2911yescharacteristic
259C4⋊C4C23×C2911yescharacteristic
260C4⋊C4C23×C2911yescharacteristic
261C22⋊C4—21no—
262C22⋊C4—21no—
263C22⋊C4—21no—
264C22⋊C4—21no—
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4D4×C2911yescharacteristic
268C22⋊C4D4×C2911yescharacteristic
269C42—21no—
270C42—21no—
271C42—21no—
272C42—21no—
273C42—21no—
274C42—21no—
275C42C23×C2911yescharacteristic
276C42C23×C2911yescharacteristic
277C23—21no—
278C23C2×D4×C2911yescharacteristic
279Q8—24no—
280Q8—21no—
281Q8—21no—
282Q8—21no—
283Q8—21no—
284Q8—81no—
285Q8#41×C2912yes—
286Q8#41×C2912yes—
287D4—21no—
288D4—21no—
289D4—81no—
290C2×C4—24no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—81no—
301C2×C4C2×D4×C2911yescharacteristic
302C2×C4C2×D4×C2911yescharacteristic
303C2×C4C2×D4×C2911yescharacteristic
304C2×C4C2×D4×C2911yescharacteristic
305C2×C4C2×D4×C2911yescharacteristic
306C2×C4C24×C2911yescharacteristic
307C8—21no—
308C8—21no—
309C8—21no—
310C8—21no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22C22×D4×C2911yescharacteristic
318C4—22no—
319C4—22no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—21no—
325C4—41no—
326C4—41no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4C2×#41×C2911yescharacteristic
331C4C2×#41×C2911yescharacteristic
332C2—41no—
333C2—81no—
334C2C29×#52511yescharacteristic
335C2C29×#57711yescharacteristic
336C2C29×#57811yescharacteristic
subgroupG/H
center, socleC22×C29C22×D4
commutator, Frattini, cosocleC2×C4C24×C29
prime radicalC29×#121C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C29×#117 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#519C2semidirect
3. C29×#485C2semidirect
5. C29×#477C2semidirect
6. C29×#475C2semidirect
7. C29×#464C2semidirect
8. C29×#464C2semidirect
9. C29×#451C2semidirect
11. C29×#441C2semidirect
12. C29×#440C2semidirect
13. C4×Q16×C29C2semidirect
14. C4×SD16×C29C2semidirect
15. C29×#433C2semidirect
142. #3121C29direct (N × H)
165. #519C2×C29semidirect
166. #485C2×C29semidirect
168. #477C2×C29semidirect
169. #475C2×C29semidirect
170. #464C2×C29semidirect
171. #464C2×C29semidirect
172. #451C2×C29semidirect
174. #441C2×C29semidirect
175. #440C2×C29semidirect
176. C4×Q16C2×C29semidirect
177. C4×SD16C2×C29semidirect
178. #433C2×C29semidirect
227. C29#3121direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#5422
C29×#5192
C29×#4852
C29×#4822
C29×#4772
C29×#4752
C29×#4642
C29×#4512
C29×#4482
C29×#4412
C29×#4402
C4×Q16×C292
C4×SD16×C292
C29×#4332
#312129