Finite Group Databasebeta

← C29×#3315 #16817029

Subgroups — C29×#3315 #16817029

Order 3712.

382 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#552C211yesmaximal, characteristic, complemented
2C29×#547C211yesmaximal, characteristic
3C29×#491C211yesmaximal, characteristic, complemented
4C29×#485C211yesmaximal, characteristic, complemented
5C29×#484C211yesmaximal, characteristic, complemented
6C29×#478C211yesmaximal, characteristic, complemented
7C29×#470C211yesmaximal, characteristic, complemented
8C29×#467C211yesmaximal, characteristic, complemented
9C29×#462C211yesmaximal, characteristic, complemented
10C29×#452C211yesmaximal, characteristic, complemented
11C29×#452C211yesmaximal, characteristic, complemented
12C29×#440C211yesmaximal, characteristic, complemented
13C29×#435C211yesmaximal, characteristic, complemented
14C29×#417C211yesmaximal, characteristic, complemented
15C29×#416C211yesmaximal, characteristic, complemented
16C2×#41×C29C2211yescharacteristic
17C2×#41×C29C2211yescharacteristic
18C2×Q16×C29C2211yescharacteristic
19C2×Q16×C29C2211yescharacteristic
20C2×SD16×C29C2211yescharacteristic
21C2×M16×C29C2211yescharacteristic
22C22×C8×C29C2211yescharacteristic
23C29×C4⋊Q8C2211yescharacteristic
24C29×#126—21no—
25C29×#125—21no—
26C29×#125C2211yescharacteristic
27C29×#123—21no—
28C29×#123—21no—
29C29×#123—21no—
30C29×C22⋊Q8C2211yescharacteristic
31C29×C22⋊Q8C2211yescharacteristic
32C29×C22⋊Q8C2211yescharacteristic
33C29×C22⋊Q8C2211yescharacteristic
34C29×#121—21no—
35C4×Q8×C29C2211yescharacteristic
36C4×D4×C29C2211yescharacteristic
37C4×D4×C29C2211yescharacteristic
38C29×#117—21no—
39C29×#117C2211yescharacteristic
40C2×C4⋊C4×C29—21no—
41C2×C4⋊C4×C29C2211yescharacteristic
42C29×#107C2211yescharacteristic
43C29×#107C2211yescharacteristic
44C29×#106C2211yescharacteristic
45C29×C4⋊C8C2211yescharacteristic
46C29×#103C2211yescharacteristic
47C29×#103C2211yescharacteristic
48C29×#103C2211yescharacteristic
49C29×#103C2211yescharacteristic
50C29×#103C2211yescharacteristic
51C29×#103C2211yescharacteristic
52C29×#103C2211yescharacteristic
53C29×#102C2211yescharacteristic
54C29×#102C2211yescharacteristic
55C29×#102C2211yescharacteristic
56C29×C22⋊C8C2211yescharacteristic
57C29×C22⋊C8C2211yescharacteristic
58C29×#97C2211yescharacteristic
59#41×C29—22no—
60#41×C29—22no—
61#41×C29—41no—
62#41×C29—41no—
63C2×Q8×C29C2311yescharacteristic
64C2×Q8×C29C2311yescharacteristic
65C2×Q8×C29C2311yescharacteristic
66C2×D4×C29—21no—
67C2×D4×C29—21no—
68C2×D4×C29D411yescharacteristic
69C2×D4×C29C2311yescharacteristic
70C22×C4×C29—21no—
71C22×C4×C29—21no—
72C22×C4×C29—21no—
73C22×C4×C29—21no—
74C22×C4×C29C2311yescharacteristic
75C22×C4×C29C2311yescharacteristic
76Q16×C29—41no—
77Q16×C29—41no—
78SD16×C29—22no—
79M16×C29—41no—
80C2×C8×C29—41no—
81C2×C8×C29C2311yescharacteristic
82C2×C8×C29C2311yescharacteristic
83C2×C8×C29C2311yescharacteristic
84C2×C8×C29C2311yescharacteristic
85C4⋊C4×C29—21no—
86C4⋊C4×C29—21no—
87C4⋊C4×C29—21no—
88C4⋊C4×C29—21no—
89C4⋊C4×C29—21no—
90C4⋊C4×C29—21no—
91C4⋊C4×C29—21no—
92C4⋊C4×C29—21no—
93C4⋊C4×C29—21no—
94C4⋊C4×C29—21no—
95C4⋊C4×C29D411yescharacteristic
96C4⋊C4×C29C2311yescharacteristic
97C4⋊C4×C29C2311yescharacteristic
98C4⋊C4×C29C2311yescharacteristic
99C4⋊C4×C29C2311yescharacteristic
100C22⋊C4×C29—21no—
101C22⋊C4×C29—21no—
102C22⋊C4×C29—21no—
103C22⋊C4×C29—21no—
104C22⋊C4×C29—21no—
105C22⋊C4×C29—21no—
106C22⋊C4×C29D411yescharacteristic
107C22⋊C4×C29D411yescharacteristic
108C42×C29—21no—
109C42×C29—21no—
110C42×C29C2311yescharacteristic
111C23×C29—21no—
112C23×C29C2×D411yescharacteristic
113C23×C29C2×D411yescharacteristic
114Q8×C29—21no—
115Q8×C29—21no—
116Q8×C29—21no—
117Q8×C29—21no—
118Q8×C29—21no—
119Q8×C29—21no—
120D4×C29—21no—
121D4×C29—41no—
122D4×C29—42no—
123D4×C29—42no—
124D4×C29#4112yes—
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—21no—
132C2×C4×C29—21no—
133C2×C4×C29—21no—
134C2×C4×C29—21no—
135C2×C4×C29—21no—
136C2×C4×C29—42no—
137C2×C4×C29—42no—
138C2×C4×C29—42no—
139C2×C4×C29—42no—
140C2×C4×C29C2×D411yescharacteristic
141C2×C4×C29C2×D411yescharacteristic
142C2×C4×C29C2×D411yescharacteristic
143C2×C4×C29C2×D411yescharacteristic
144C2×C4×C29C2411yescharacteristic
145C8×C29—21no—
146C8×C29—21no—
147C8×C29—21no—
148C8×C29—21no—
149#3315C2911yesmaximal, characteristic, direct product factor, Sylow
150C22×C29—21no—
151C22×C29—21no—
152C22×C29—22no—
153C22×C29—21no—
154C22×C29—21no—
155C22×C29—21no—
156C22×C29—21no—
157C22×C29—41no—
158C22×C29—41no—
159C22×C29C22×D411yescharacteristic
160C4×C29—21no—
161C4×C29—21no—
162C4×C29—21no—
163C4×C29—21no—
164C4×C29—41no—
165C4×C29—41no—
166C4×C29—41no—
167C4×C29—41no—
168C4×C29—41no—
169C4×C29—41no—
170C4×C29—41no—
171C4×C29C2×#4111yescharacteristic
172C4×C29H(5,𝔽2)11yescharacteristic
173#552C2×C2911yescharacteristic, complemented
174#547C2×C2911yescharacteristic
175#491C2×C2911yescharacteristic, complemented
176#485C2×C2911yescharacteristic, complemented
177#484C2×C2911yescharacteristic, complemented
178#478C2×C2911yescharacteristic, complemented
179#470C2×C2911yescharacteristic, complemented
180#467C2×C2911yescharacteristic, complemented
181#462C2×C2911yescharacteristic, complemented
182#452C2×C2911yescharacteristic, complemented
183#452C2×C2911yescharacteristic, complemented
184#440C2×C2911yescharacteristic, complemented
185#435C2×C2911yescharacteristic, complemented
186#417C2×C2911yescharacteristic, complemented
187#416C2×C2911yescharacteristic, complemented
188C2×C29—41no—
189C2×C29—41no—
190C2×C29—42no—
191C2×C29#54611yescharacteristic
192C2×C29#57511yescharacteristic
193C2×C29#57811yescharacteristic
194C2×#41C22×C2911yescharacteristic
195C2×#41C22×C2911yescharacteristic
196C2×Q16C22×C2911yescharacteristic
197C2×Q16C22×C2911yescharacteristic
198C2×SD16C22×C2911yescharacteristic
199C2×M16C22×C2911yescharacteristic
200C22×C8C22×C2911yescharacteristic
201C4⋊Q8C22×C2911yescharacteristic
202#126—21no—
203#125—21no—
204#125C22×C2911yescharacteristic
205#123—21no—
206#123—21no—
207#123—21no—
208C22⋊Q8C22×C2911yescharacteristic
209C22⋊Q8C22×C2911yescharacteristic
210C22⋊Q8C22×C2911yescharacteristic
211C22⋊Q8C22×C2911yescharacteristic
212#121—21no—
213C4×Q8C22×C2911yescharacteristic
214C4×D4C22×C2911yescharacteristic
215C4×D4C22×C2911yescharacteristic
216#117—21no—
217#117C22×C2911yescharacteristic
218C2×C4⋊C4—21no—
219C2×C4⋊C4C22×C2911yescharacteristic
220#107C22×C2911yescharacteristic
221#107C22×C2911yescharacteristic
222#106C22×C2911yescharacteristic
223C4⋊C8C22×C2911yescharacteristic
224#103C22×C2911yescharacteristic
225#103C22×C2911yescharacteristic
226#103C22×C2911yescharacteristic
227#103C22×C2911yescharacteristic
228#103C22×C2911yescharacteristic
229#103C22×C2911yescharacteristic
230#103C22×C2911yescharacteristic
231#102C22×C2911yescharacteristic
232#102C22×C2911yescharacteristic
233#102C22×C2911yescharacteristic
234C22⋊C8C22×C2911yescharacteristic
235C22⋊C8C22×C2911yescharacteristic
236#97C22×C2911yescharacteristic
237C29#331511yescharacteristic, direct product factor, Sylow
238#41—22no—
239#41—22no—
240#41—41no—
241#41—41no—
242C2×Q8C23×C2911yescharacteristic
243C2×Q8C23×C2911yescharacteristic
244C2×Q8C23×C2911yescharacteristic
245C2×D4—21no—
246C2×D4—21no—
247C2×D4D4×C2911yescharacteristic
248C2×D4C23×C2911yescharacteristic
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4C23×C2911yescharacteristic
254C22×C4C23×C2911yescharacteristic
255Q16—41no—
256Q16—41no—
257SD16—22no—
258M16—41no—
259C2×C8—41no—
260C2×C8C23×C2911yescharacteristic
261C2×C8C23×C2911yescharacteristic
262C2×C8C23×C2911yescharacteristic
263C2×C8C23×C2911yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4D4×C2911yescharacteristic
275C4⋊C4C23×C2911yescharacteristic
276C4⋊C4C23×C2911yescharacteristic
277C4⋊C4C23×C2911yescharacteristic
278C4⋊C4C23×C2911yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4D4×C2911yescharacteristic
286C22⋊C4D4×C2911yescharacteristic
287C42—21no—
288C42—21no—
289C42C23×C2911yescharacteristic
290C23—21no—
291C23C2×D4×C2911yescharacteristic
292C23C2×D4×C2911yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—21no—
299D4—21no—
300D4—41no—
301D4—42no—
302D4—42no—
303D4#41×C2912yes—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4C2×D4×C2911yescharacteristic
320C2×C4C2×D4×C2911yescharacteristic
321C2×C4C2×D4×C2911yescharacteristic
322C2×C4C2×D4×C2911yescharacteristic
323C2×C4C24×C2911yescharacteristic
324C8—21no—
325C8—21no—
326C8—21no—
327C8—21no—
328C22—21no—
329C22—21no—
330C22—22no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—41no—
336C22—41no—
337C22C22×D4×C2911yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4C2×#41×C2911yescharacteristic
350C4C29×H(5,𝔽2)11yescharacteristic
351C2—41no—
352C2—41no—
353C2—42no—
354C2C29×#54611yescharacteristic
355C2C29×#57511yescharacteristic
356C2C29×#57811yescharacteristic
subgroupG/H
center, socleC22×C29C22×D4
commutator, Frattini, cosocleC2×C4C24×C29
prime radicalC29×#547C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C4×D4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C29×#552C2semidirect
3. C29×#491C2semidirect
4. C29×#485C2semidirect
5. C29×#484C2semidirect
6. C29×#478C2semidirect
7. C29×#470C2semidirect
8. C29×#467C2semidirect
9. C29×#462C2semidirect
10. C29×#452C2semidirect
11. C29×#452C2semidirect
12. C29×#440C2semidirect
13. C29×#435C2semidirect
14. C29×#417C2semidirect
15. C29×#416C2semidirect
149. #3315C29direct (N × H)
173. #552C2×C29semidirect
175. #491C2×C29semidirect
176. #485C2×C29semidirect
177. #484C2×C29semidirect
178. #478C2×C29semidirect
179. #470C2×C29semidirect
180. #467C2×C29semidirect
181. #462C2×C29semidirect
182. #452C2×C29semidirect
183. #452C2×C29semidirect
184. #440C2×C29semidirect
185. #435C2×C29semidirect
186. #417C2×C29semidirect
187. #416C2×C29semidirect
237. C29#3315direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#5522
C29×#5472
C29×#4912
C29×#4852
C29×#4842
C29×#4782
C29×#4702
C29×#4672
C29×#4622
C29×#4522
C29×#4402
C29×#4352
C29×#4172
C29×#4162
#331529