Finite Group Databasebeta

← C29×#12115 #20307015

Subgroups — C29×#12115 #20307015

Order 7424.

422 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3195C211yesmaximal, characteristic, complemented
2C29×#2191C212yesmaximal, complemented
3C29×#2010C211yesmaximal, characteristic
4C29×#1340C212yesmaximal, complemented
5C29×#1320C211yesmaximal, characteristic, complemented
6C29×#575C2211yescharacteristic
7C29×#525—21no—
8C2×C29×C22⋊Q8—21no—
9C29×#510—22no—
10C29×#483—22no—
11C29×#470—21no—
12C29×#470C2212yes—
13C29×#451—22no—
14C29×#421—21no—
15C29×#407C2211yescharacteristic
16C29×#360—22no—
17C29×#349C2212yes—
18C29×H(3,ℤ/4)C2211yescharacteristic
19C2×#41×C29—21no—
20C22×Q8×C29—21no—
21C23×C4×C29D411yescharacteristic
22C29×#137—41no—
23C29×AGL(1,ℤ/8)—41no—
24C29×#135—22no—
25C2×Q16×C29—21no—
26C2×Q16×C29D412yescomplemented
27C2×M16×C29D411yescharacteristic
28C2×M16×C29C2311yescharacteristic
29C29×#123—41no—
30C29×C22⋊Q8—22no—
31C29×C22⋊Q8—22no—
32C29×C22⋊Q8—41no—
33C29×C22⋊Q8—41no—
34C29×C22⋊Q8—41no—
35C29×#121—41no—
36C29×#120—41no—
37C4×D4×C29—42no—
38C29×#117—21no—
39C2×C4⋊C4×C29—21no—
40C2×C4⋊C4×C29—41no—
41C2×C22⋊C4×C29—41no—
42C29×Q32—42no—
43C29×SD32—42no—
44C29×M32—22no—
45C29×#106—21no—
46C29×#106D412yescomplemented
47C29×#104—42no—
48C29×#103—22no—
49C29×#103—22no—
50C29×C22⋊C8—22no—
51C24×C29D811yescharacteristic
52#41×C29—41no—
53#41×C29—41no—
54#41×C29—41no—
55#41×C29—41no—
56C2×Q8×C29—21no—
57C2×Q8×C29—22no—
58C2×Q8×C29—41no—
59C2×Q8×C29—81no—
60C2×Q8×C29—81no—
61C2×D4×C29—21no—
62C2×D4×C29—42no—
63C2×D4×C29—41no—
64C22×C4×C29—21no—
65C22×C4×C29—21no—
66C22×C4×C29—41no—
67C22×C4×C29—41no—
68C22×C4×C29—41no—
69C22×C4×C29—41no—
70C22×C4×C29—41no—
71C22×C4×C29D811yescharacteristic
72C22×C4×C29C2×D411yescharacteristic
73Q16×C29—22no—
74Q16×C29—42no—
75Q16×C29—81no—
76SD16×C29—42no—
77D8×C29—22no—
78M16×C29—41no—
79M16×C29—41no—
80C2×C8×C29—21no—
81C2×C8×C29C2×D412yes—
82C4⋊C4×C29—22no—
83C4⋊C4×C29—41no—
84C4⋊C4×C29—42no—
85C4⋊C4×C29—41no—
86C4⋊C4×C29—42no—
87C4⋊C4×C29—42no—
88C22⋊C4×C29—42no—
89C22⋊C4×C29—42no—
90C22⋊C4×C29—42no—
91C22⋊C4×C29—42no—
92C22⋊C4×C29—41no—
93C42×C29—22no—
94C16×C29—42no—
95#12115C2911yesmaximal, characteristic, direct product factor, Sylow
96C23×C29—21no—
97C23×C29—41no—
98C23×C29—42no—
99C23×C29—41no—
100C23×C29C2×D811yescharacteristic
101Q8×C29—41no—
102Q8×C29—42no—
103Q8×C29—41no—
104Q8×C29—42no—
105Q8×C29—82no—
106D4×C29—41no—
107D4×C29—41no—
108D4×C29—81no—
109D4×C29—84no—
110D4×C29—81no—
111C2×C4×C29—21no—
112C2×C4×C29—21no—
113C2×C4×C29—21no—
114C2×C4×C29—41no—
115C2×C4×C29—41no—
116C2×C4×C29—41no—
117C2×C4×C29—42no—
118C2×C4×C29—41no—
119C2×C4×C29—42no—
120C2×C4×C29—42no—
121C2×C4×C29—81no—
122C2×C4×C29—81no—
123C2×C4×C29—82no—
124C2×C4×C29—82no—
125C2×C4×C29—81no—
126C2×C4×C29#12011yescharacteristic
127C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
128C8×C29—22no—
129C8×C29—41no—
130#3195C2×C2911yescharacteristic, complemented
131#2191C2×C2912yescomplemented
132#2010C2×C2911yescharacteristic
133#1340C2×C2912yescomplemented
134#1320C2×C2911yescharacteristic, complemented
135C22×C29—22no—
136C22×C29—21no—
137C22×C29—41no—
138C22×C29—41no—
139C22×C29—42no—
140C22×C29—41no—
141C22×C29—81no—
142C22×C29—82no—
143C22×C29—81no—
144C22×C29#44711yescharacteristic
145C4×C29—21no—
146C4×C29—41no—
147C4×C29—82no—
148C4×C29—82no—
149C4×C29—81no—
150C4×C29—82no—
151C4×C29#45311yescharacteristic
152C4×C29B(4,𝔽2)11yescharacteristic
153#575C22×C2911yescharacteristic
154#525—21no—
155C2×C22⋊Q8—21no—
156#510—22no—
157#483—22no—
158#470—21no—
159#470C22×C2912yes—
160#451—22no—
161#421—21no—
162#407C22×C2911yescharacteristic
163#360—22no—
164#349C22×C2912yes—
165H(3,ℤ/4)C22×C2911yescharacteristic
166C2×C29—21no—
167C2×C29—41no—
168C2×C29—42no—
169C2×C29—161no—
170C2×C29#159511yescharacteristic
171C2×#41—21no—
172C22×Q8—21no—
173C23×C4D4×C2911yescharacteristic
174#137—41no—
175AGL(1,ℤ/8)—41no—
176#135—22no—
177C2×Q16—21no—
178C2×Q16D4×C2912yescomplemented
179C2×M16D4×C2911yescharacteristic
180C2×M16C23×C2911yescharacteristic
181#123—41no—
182C22⋊Q8—22no—
183C22⋊Q8—22no—
184C22⋊Q8—41no—
185C22⋊Q8—41no—
186C22⋊Q8—41no—
187#121—41no—
188#120—41no—
189C4×D4—42no—
190#117—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—41no—
193C2×C22⋊C4—41no—
194Q32—42no—
195SD32—42no—
196M32—22no—
197#106—21no—
198#106D4×C2912yescomplemented
199#104—42no—
200#103—22no—
201#103—22no—
202C22⋊C8—22no—
203C29#1211511yescharacteristic, direct product factor, Sylow
204C24D8×C2911yescharacteristic
205#41—41no—
206#41—41no—
207#41—41no—
208#41—41no—
209C2×Q8—21no—
210C2×Q8—22no—
211C2×Q8—41no—
212C2×Q8—81no—
213C2×Q8—81no—
214C2×D4—21no—
215C2×D4—42no—
216C2×D4—41no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—41no—
220C22×C4—41no—
221C22×C4—41no—
222C22×C4—41no—
223C22×C4—41no—
224C22×C4D8×C2911yescharacteristic
225C22×C4C2×D4×C2911yescharacteristic
226Q16—22no—
227Q16—42no—
228Q16—81no—
229SD16—42no—
230D8—22no—
231M16—41no—
232M16—41no—
233C2×C8—21no—
234C2×C8C2×D4×C2912yes—
235C4⋊C4—22no—
236C4⋊C4—41no—
237C4⋊C4—42no—
238C4⋊C4—41no—
239C4⋊C4—42no—
240C4⋊C4—42no—
241C22⋊C4—42no—
242C22⋊C4—42no—
243C22⋊C4—42no—
244C22⋊C4—42no—
245C22⋊C4—41no—
246C42—22no—
247C16—42no—
248C23—21no—
249C23—41no—
250C23—42no—
251C23—41no—
252C23C2×D8×C2911yescharacteristic
253Q8—41no—
254Q8—42no—
255Q8—41no—
256Q8—42no—
257Q8—82no—
258D4—41no—
259D4—41no—
260D4—81no—
261D4—84no—
262D4—81no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—42no—
270C2×C4—41no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—81no—
274C2×C4—81no—
275C2×C4—82no—
276C2×C4—82no—
277C2×C4—81no—
278C2×C4C29×#12011yescharacteristic
279C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
280C8—22no—
281C8—41no—
282C22—22no—
283C22—21no—
284C22—41no—
285C22—41no—
286C22—42no—
287C22—41no—
288C22—81no—
289C22—82no—
290C22—81no—
291C22C29×#44711yescharacteristic
292C4—21no—
293C4—41no—
294C4—82no—
295C4—82no—
296C4—81no—
297C4—82no—
298C4C29×#45311yescharacteristic
299C4C29×B(4,𝔽2)11yescharacteristic
300C2—21no—
301C2—41no—
302C2—42no—
303C2—161no—
304C2C29×#159511yescharacteristic
subgroupG/H
center, socleC2×C29#1595
commutator, Frattini, cosocleC2×M16C23×C29
prime radicalC29×#2010C2
LCSG ▷ C2×M16 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C29 ◁ C2×C4×C29 ◁ C2×M16×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C29×#3195C2semidirect
2. C29×#2191C2semidirect
4. C29×#1340C2semidirect
5. C29×#1320C2semidirect
26. C2×Q16×C29D4semidirect
46. C29×#106D4semidirect
95. #12115C29direct (N × H)
130. #3195C2×C29semidirect
131. #2191C2×C29semidirect
133. #1340C2×C29semidirect
134. #1320C2×C29semidirect
178. C2×Q16D4×C29semidirect
198. #106D4×C29semidirect
203. C29#12115direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#31952
C29×#21912
C29×#20102
C29×#13402
C29×#13202
#1211529