Finite Group Databasebeta

← C29×#3225 #16816939

Subgroups — C29×#3225 #16816939

Order 3712.

376 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#542C211yesmaximal, characteristic, complemented
2C29×#536C211yesmaximal, characteristic, complemented
3C29×#497C211yesmaximal, characteristic, complemented
4C29×#495C211yesmaximal, characteristic, complemented
5C29×#489C211yesmaximal, characteristic, complemented
6C29×#487C211yesmaximal, characteristic, complemented
7C29×#464C211yesmaximal, characteristic, complemented
8C29×#463C211yesmaximal, characteristic, complemented
9C29×#462C211yesmaximal, characteristic, complemented
10C29×#461C211yesmaximal, characteristic, complemented
11C29×#452C211yesmaximal, characteristic, complemented
12C29×#451C211yesmaximal, characteristic, complemented
13C29×#449C211yesmaximal, characteristic
14C29×#448C211yesmaximal, characteristic, complemented
15C29×#433C211yesmaximal, characteristic, complemented
16C2×#41×C29C2211yescharacteristic
17C22×Q8×C29C2211yescharacteristic
18C2×Q16×C29C2211yescharacteristic
19C2×Q16×C29C2211yescharacteristic
20C2×Q16×C29C2211yescharacteristic
21C2×SD16×C29C2211yescharacteristic
22C2×SD16×C29C2211yescharacteristic
23C2×SD16×C29C2211yescharacteristic
24C2×SD16×C29C2211yescharacteristic
25C2×D8×C29C2211yescharacteristic
26C29×C4⋊Q8C2211yescharacteristic
27C29×C4⋊Q8C2211yescharacteristic
28C29×C4⋊Q8C2211yescharacteristic
29C29×#126—21no—
30C29×#124—21no—
31C29×#124C2211yescharacteristic
32C29×#124C2211yescharacteristic
33C29×#124C2211yescharacteristic
34C29×#123—21no—
35C29×#123—21no—
36C29×#123—21no—
37C29×C22⋊Q8—21no—
38C29×C22⋊Q8—21no—
39C29×C22⋊Q8—21no—
40C29×C22⋊Q8C2211yescharacteristic
41C29×#121C2211yescharacteristic
42C4×Q8×C29C2211yescharacteristic
43C4×D4×C29C2211yescharacteristic
44C29×#117C2211yescharacteristic
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
59#41×C29—41no—
60#41×C29—41no—
61C2×Q8×C29—21no—
62C2×Q8×C29—21no—
63C2×Q8×C29—41no—
64C2×Q8×C29—41no—
65C2×Q8×C29C2311yescharacteristic
66C2×Q8×C29C2311yescharacteristic
67C2×Q8×C29C2311yescharacteristic
68C2×Q8×C29C2311yescharacteristic
69C2×D4×C29—21no—
70C2×D4×C29—21no—
71C2×D4×C29C2311yescharacteristic
72C2×D4×C29C2311yescharacteristic
73C22×C4×C29—21no—
74C22×C4×C29—21no—
75C22×C4×C29—21no—
76C22×C4×C29C2311yescharacteristic
77Q16×C29—41no—
78Q16×C29—41no—
79Q16×C29—41no—
80SD16×C29—41no—
81SD16×C29—41no—
82SD16×C29—41no—
83SD16×C29—41no—
84D8×C29—41no—
85C2×C8×C29C2311yescharacteristic
86C2×C8×C29C2311yescharacteristic
87C2×C8×C29C2311yescharacteristic
88C2×C8×C29C2311yescharacteristic
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×C29—21no—
96C4⋊C4×C29D411yescharacteristic
97C4⋊C4×C29D411yescharacteristic
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×C29—21no—
107C22⋊C4×C29—21no—
108C22⋊C4×C29—21no—
109C22⋊C4×C29D411yescharacteristic
110C22⋊C4×C29D411yescharacteristic
111C42×C29—21no—
112C42×C29C2311yescharacteristic
113C42×C29C2311yescharacteristic
114C23×C29—21no—
115C23×C29—21no—
116C23×C29C2×D411yescharacteristic
117Q8×C29—21no—
118Q8×C29—21no—
119Q8×C29—21no—
120Q8×C29—21no—
121Q8×C29—21no—
122Q8×C29—21no—
123Q8×C29—21no—
124Q8×C29—21no—
125Q8×C29—42no—
126Q8×C29—81no—
127D4×C29—21no—
128D4×C29—21no—
129D4×C29—21no—
130D4×C29—21no—
131D4×C29—42no—
132D4×C29—81no—
133C2×C4×C29—21no—
134C2×C4×C29—21no—
135C2×C4×C29—21no—
136C2×C4×C29—21no—
137C2×C4×C29—21no—
138C2×C4×C29—21no—
139C2×C4×C29—21no—
140C2×C4×C29—21no—
141C2×C4×C29—42no—
142C2×C4×C29—42no—
143C2×C4×C29—81no—
144C2×C4×C29C2×D411yescharacteristic
145C2×C4×C29C2×D411yescharacteristic
146C2×C4×C29C2×D411yescharacteristic
147C2×C4×C29C2×D411yescharacteristic
148C2×C4×C29C2×D411yescharacteristic
149C2×C4×C29C2411yescharacteristic
150C8×C29—21no—
151C8×C29—21no—
152C8×C29—21no—
153C8×C29—21no—
154#3225C2911yesmaximal, characteristic, direct product factor, Sylow
155C22×C29—21no—
156C22×C29—21no—
157C22×C29—21no—
158C22×C29—41no—
159C22×C29—41no—
160C22×C29—41no—
161C22×C29—41no—
162C22×C29—41no—
163C22×C29—41no—
164C22×C29C22×D411yescharacteristic
165C4×C29—21no—
166C4×C29—21no—
167C4×C29—21no—
168C4×C29—21no—
169C4×C29—21no—
170C4×C29—41no—
171C4×C29—41no—
172C4×C29—41no—
173C4×C29—41no—
174C4×C29—41no—
175C4×C29—41no—
176C4×C29H(5,𝔽2)11yescharacteristic
177C4×C29H(5,𝔽2)11yescharacteristic
178#542C2×C2911yescharacteristic, complemented
179#536C2×C2911yescharacteristic, complemented
180#497C2×C2911yescharacteristic, complemented
181#495C2×C2911yescharacteristic, complemented
182#489C2×C2911yescharacteristic, complemented
183#487C2×C2911yescharacteristic, complemented
184#464C2×C2911yescharacteristic, complemented
185#463C2×C2911yescharacteristic, complemented
186#462C2×C2911yescharacteristic, complemented
187#461C2×C2911yescharacteristic, complemented
188#452C2×C2911yescharacteristic, complemented
189#451C2×C2911yescharacteristic, complemented
190#449C2×C2911yescharacteristic
191#448C2×C2911yescharacteristic, complemented
192#433C2×C2911yescharacteristic, complemented
193C2×C29—41no—
194C2×C29—81no—
195C2×C29—81no—
196C2×C29#53511yescharacteristic
197C2×C29#57711yescharacteristic
198C2×C29#57811yescharacteristic
199C2×#41C22×C2911yescharacteristic
200C22×Q8C22×C2911yescharacteristic
201C2×Q16C22×C2911yescharacteristic
202C2×Q16C22×C2911yescharacteristic
203C2×Q16C22×C2911yescharacteristic
204C2×SD16C22×C2911yescharacteristic
205C2×SD16C22×C2911yescharacteristic
206C2×SD16C22×C2911yescharacteristic
207C2×SD16C22×C2911yescharacteristic
208C2×D8C22×C2911yescharacteristic
209C4⋊Q8C22×C2911yescharacteristic
210C4⋊Q8C22×C2911yescharacteristic
211C4⋊Q8C22×C2911yescharacteristic
212#126—21no—
213#124—21no—
214#124C22×C2911yescharacteristic
215#124C22×C2911yescharacteristic
216#124C22×C2911yescharacteristic
217#123—21no—
218#123—21no—
219#123—21no—
220C22⋊Q8—21no—
221C22⋊Q8—21no—
222C22⋊Q8—21no—
223C22⋊Q8C22×C2911yescharacteristic
224#121C22×C2911yescharacteristic
225C4×Q8C22×C2911yescharacteristic
226C4×D4C22×C2911yescharacteristic
227#117C22×C2911yescharacteristic
228C4⋊C8C22×C2911yescharacteristic
229C4⋊C8C22×C2911yescharacteristic
230#103C22×C2911yescharacteristic
231#103C22×C2911yescharacteristic
232#103C22×C2911yescharacteristic
233#103C22×C2911yescharacteristic
234#103C22×C2911yescharacteristic
235#103C22×C2911yescharacteristic
236#102C22×C2911yescharacteristic
237#102C22×C2911yescharacteristic
238C22⋊C8C22×C2911yescharacteristic
239C22⋊C8C22×C2911yescharacteristic
240#97C22×C2911yescharacteristic
241C4×C8C22×C2911yescharacteristic
242C29#322511yescharacteristic, direct product factor, Sylow
243#41—41no—
244#41—41no—
245C2×Q8—21no—
246C2×Q8—21no—
247C2×Q8—41no—
248C2×Q8—41no—
249C2×Q8C23×C2911yescharacteristic
250C2×Q8C23×C2911yescharacteristic
251C2×Q8C23×C2911yescharacteristic
252C2×Q8C23×C2911yescharacteristic
253C2×D4—21no—
254C2×D4—21no—
255C2×D4C23×C2911yescharacteristic
256C2×D4C23×C2911yescharacteristic
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4C23×C2911yescharacteristic
261Q16—41no—
262Q16—41no—
263Q16—41no—
264SD16—41no—
265SD16—41no—
266SD16—41no—
267SD16—41no—
268D8—41no—
269C2×C8C23×C2911yescharacteristic
270C2×C8C23×C2911yescharacteristic
271C2×C8C23×C2911yescharacteristic
272C2×C8C23×C2911yescharacteristic
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4D4×C2911yescharacteristic
281C4⋊C4D4×C2911yescharacteristic
282C4⋊C4C23×C2911yescharacteristic
283C4⋊C4C23×C2911yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4D4×C2911yescharacteristic
294C22⋊C4D4×C2911yescharacteristic
295C42—21no—
296C42C23×C2911yescharacteristic
297C42C23×C2911yescharacteristic
298C23—21no—
299C23—21no—
300C23C2×D4×C2911yescharacteristic
301Q8—21no—
302Q8—21no—
303Q8—21no—
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—21no—
308Q8—21no—
309Q8—42no—
310Q8—81no—
311D4—21no—
312D4—21no—
313D4—21no—
314D4—21no—
315D4—42no—
316D4—81no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—81no—
328C2×C4C2×D4×C2911yescharacteristic
329C2×C4C2×D4×C2911yescharacteristic
330C2×C4C2×D4×C2911yescharacteristic
331C2×C4C2×D4×C2911yescharacteristic
332C2×C4C2×D4×C2911yescharacteristic
333C2×C4C24×C2911yescharacteristic
334C8—21no—
335C8—21no—
336C8—21no—
337C8—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22C22×D4×C2911yescharacteristic
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4C29×H(5,𝔽2)11yescharacteristic
360C4C29×H(5,𝔽2)11yescharacteristic
361C2—41no—
362C2—81no—
363C2—81no—
364C2C29×#53511yescharacteristic
365C2C29×#57711yescharacteristic
366C2C29×#57811yescharacteristic
subgroupG/H
center, socleC22×C29C22×D4
commutator, Frattini, cosocleC2×C4C24×C29
prime radicalC29×#449C2
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
1. C29×#542C2semidirect
2. C29×#536C2semidirect
3. C29×#497C2semidirect
4. C29×#495C2semidirect
5. C29×#489C2semidirect
6. C29×#487C2semidirect
7. C29×#464C2semidirect
8. C29×#463C2semidirect
9. C29×#462C2semidirect
10. C29×#461C2semidirect
11. C29×#452C2semidirect
12. C29×#451C2semidirect
14. C29×#448C2semidirect
15. C29×#433C2semidirect
154. #3225C29direct (N × H)
178. #542C2×C29semidirect
179. #536C2×C29semidirect
180. #497C2×C29semidirect
181. #495C2×C29semidirect
182. #489C2×C29semidirect
183. #487C2×C29semidirect
184. #464C2×C29semidirect
185. #463C2×C29semidirect
186. #462C2×C29semidirect
187. #461C2×C29semidirect
188. #452C2×C29semidirect
189. #451C2×C29semidirect
191. #448C2×C29semidirect
192. #433C2×C29semidirect
242. C29#3225direct (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×#5362
C29×#4972
C29×#4952
C29×#4892
C29×#4872
C29×#4642
C29×#4632
C29×#4622
C29×#4612
C29×#4522
C29×#4512
C29×#4492
C29×#4482
C29×#4332
#322529