Finite Group Databasebeta

← C29×#12278 #20307178

Subgroups — C29×#12278 #20307178

Order 7424.

396 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 82 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×#3186C211yesmaximal, characteristic
2C29×#2232C212yesmaximal, complemented
3C29×#2075C211yesmaximal, characteristic, complemented
4C29×#1347C212yesmaximal, complemented
5C29×#1314C211yesmaximal, characteristic, complemented
6C2×C29×#121—21no—
7C29×#480—22no—
8C29×#466—21no—
9C29×#466C2212yes—
10C29×#447—22no—
11C2×C29×#107C2211yescharacteristic, complemented
12C2×C29×C22⋊C8C2211yescharacteristic
13C29×#380—21no—
14C29×#366—22no—
15C29×#357—22no—
16C29×C22⋊C16C2212yescomplemented
17C29×#340—21no—
18C29×#340C2211yescharacteristic, complemented
19C22×D4×C29—21no—
20C22×D4×C29—41no—
21C23×C4×C29D411yescharacteristic
22C2×D8×C29—21no—
23C2×D8×C29D412yes—
24C22×C8×C29D411yescharacteristic
25C22×C8×C29C2311yescharacteristic
26C29×#121—22no—
27C29×#121—22no—
28C29×#121—41no—
29C29×#121—41no—
30C2×C4⋊C4×C29—21no—
31C2×C4⋊C4×C29—21no—
32C2×C4⋊C4×C29—21no—
33C2×C22⋊C4×C29—41no—
34C2×C22⋊C4×C29—41no—
35C2×C16×C29—22no—
36C29×#107—21no—
37C29×#107—22no—
38C29×#107D412yes—
39C29×#102—22no—
40C29×#102—22no—
41C29×C22⋊C8—22no—
42C29×#95—41no—
43C24×C29—41no—
44C24×C29D811yescharacteristic
45C2×D4×C29—22no—
46C2×D4×C29—41no—
47C2×D4×C29—42no—
48C2×D4×C29—42no—
49C2×D4×C29—81no—
50C2×D4×C29—81no—
51C2×D4×C29—82no—
52C2×D4×C29—82no—
53C22×C4×C29—21no—
54C22×C4×C29—21no—
55C22×C4×C29—41no—
56C22×C4×C29—41no—
57C22×C4×C29—41no—
58C22×C4×C29—41no—
59C22×C4×C29—41no—
60C22×C4×C29D811yescharacteristic
61C22×C4×C29C2×D411yescharacteristic
62D8×C29—42no—
63D8×C29—81no—
64C2×C8×C29—21no—
65C2×C8×C29—41no—
66C2×C8×C29—41no—
67C2×C8×C29C2×D412yes—
68C4⋊C4×C29—22no—
69C4⋊C4×C29—41no—
70C4⋊C4×C29—41no—
71C4⋊C4×C29—41no—
72C4⋊C4×C29—41no—
73C4⋊C4×C29—41no—
74C22⋊C4×C29—42no—
75C22⋊C4×C29—42no—
76C22⋊C4×C29—82no—
77C16×C29—42no—
78#12278C2911yesmaximal, characteristic, direct product factor, Sylow
79C23×C29—21no—
80C23×C29—21no—
81C23×C29—41no—
82C23×C29—41no—
83C23×C29—42no—
84C23×C29—82no—
85C23×C29—82no—
86C23×C29—82no—
87C23×C29D1612yes—
88C23×C29C2×D811yescharacteristic
89D4×C29—42no—
90D4×C29—42no—
91D4×C29—82no—
92D4×C29—84no—
93D4×C29—82no—
94D4×C29—82no—
95C2×C4×C29—21no—
96C2×C4×C29—21no—
97C2×C4×C29—21no—
98C2×C4×C29—41no—
99C2×C4×C29—41no—
100C2×C4×C29—41no—
101C2×C4×C29—42no—
102C2×C4×C29—81no—
103C2×C4×C29—82no—
104C2×C4×C29—81no—
105C2×C4×C29—81no—
106C2×C4×C29—81no—
107C2×C4×C29—81no—
108C2×C4×C29—81no—
109C2×C4×C29—81no—
110C2×C4×C29#12011yescharacteristic
111C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
112C8×C29—22no—
113C8×C29—41no—
114#3186C2×C2911yescharacteristic
115#2232C2×C2912yescomplemented
116#2075C2×C2911yescharacteristic, complemented
117#1347C2×C2912yescomplemented
118#1314C2×C2911yescharacteristic, complemented
119C22×C29—21no—
120C22×C29—21no—
121C22×C29—22no—
122C22×C29—42no—
123C22×C29—41no—
124C22×C29—41no—
125C22×C29—81no—
126C22×C29—82no—
127C22×C29—82no—
128C22×C29—82no—
129C22×C29—164no—
130C22×C29#44711yescharacteristic
131C22×C29C2×D1611yescharacteristic
132C22×C29#50911yescharacteristic
133C4×C29—21no—
134C4×C29—41no—
135C4×C29—82no—
136C4×C29—161no—
137C4×C29—161no—
138C4×C29#45511yescharacteristic
139C4×C29#45811yescharacteristic
140C2×#121—21no—
141#480—22no—
142#466—21no—
143#466C22×C2912yes—
144#447—22no—
145C2×#107C22×C2911yescharacteristic, complemented
146C2×C22⋊C8C22×C2911yescharacteristic
147#380—21no—
148#366—22no—
149#357—22no—
150C22⋊C16C22×C2912yescomplemented
151#340—21no—
152#340C22×C2911yescharacteristic, complemented
153C2×C29—21no—
154C2×C29—21no—
155C2×C29—42no—
156C2×C29—162no—
157C2×C29#160711yescharacteristic
158C2×C29#218411yescharacteristic
159C2×C29#219111yescharacteristic
160C22×D4—21no—
161C22×D4—41no—
162C23×C4D4×C2911yescharacteristic
163C2×D8—21no—
164C2×D8D4×C2912yes—
165C22×C8D4×C2911yescharacteristic
166C22×C8C23×C2911yescharacteristic
167#121—22no—
168#121—22no—
169#121—41no—
170#121—41no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4—21no—
174C2×C22⋊C4—41no—
175C2×C22⋊C4—41no—
176C2×C16—22no—
177#107—21no—
178#107—22no—
179#107D4×C2912yes—
180#102—22no—
181#102—22no—
182C22⋊C8—22no—
183#95—41no—
184C29#1227811yescharacteristic, direct product factor, Sylow
185C24—41no—
186C24D8×C2911yescharacteristic
187C2×D4—22no—
188C2×D4—41no—
189C2×D4—42no—
190C2×D4—42no—
191C2×D4—81no—
192C2×D4—81no—
193C2×D4—82no—
194C2×D4—82no—
195C22×C4—21no—
196C22×C4—21no—
197C22×C4—41no—
198C22×C4—41no—
199C22×C4—41no—
200C22×C4—41no—
201C22×C4—41no—
202C22×C4D8×C2911yescharacteristic
203C22×C4C2×D4×C2911yescharacteristic
204D8—42no—
205D8—81no—
206C2×C8—21no—
207C2×C8—41no—
208C2×C8—41no—
209C2×C8C2×D4×C2912yes—
210C4⋊C4—22no—
211C4⋊C4—41no—
212C4⋊C4—41no—
213C4⋊C4—41no—
214C4⋊C4—41no—
215C4⋊C4—41no—
216C22⋊C4—42no—
217C22⋊C4—42no—
218C22⋊C4—82no—
219C16—42no—
220C23—21no—
221C23—21no—
222C23—41no—
223C23—41no—
224C23—42no—
225C23—82no—
226C23—82no—
227C23—82no—
228C23C29×D1612yes—
229C23C2×D8×C2911yescharacteristic
230D4—42no—
231D4—42no—
232D4—82no—
233D4—84no—
234D4—82no—
235D4—82no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—42no—
243C2×C4—81no—
244C2×C4—82no—
245C2×C4—81no—
246C2×C4—81no—
247C2×C4—81no—
248C2×C4—81no—
249C2×C4—81no—
250C2×C4—81no—
251C2×C4C29×#12011yescharacteristic
252C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
253C8—22no—
254C8—41no—
255C22—21no—
256C22—21no—
257C22—22no—
258C22—42no—
259C22—41no—
260C22—41no—
261C22—81no—
262C22—82no—
263C22—82no—
264C22—82no—
265C22—164no—
266C22C29×#44711yescharacteristic
267C22C2×C29×D1611yescharacteristic
268C22C29×#50911yescharacteristic
269C4—21no—
270C4—41no—
271C4—82no—
272C4—161no—
273C4—161no—
274C4C29×#45511yescharacteristic
275C4C29×#45811yescharacteristic
276C2—21no—
277C2—21no—
278C2—42no—
279C2—162no—
280C2C29×#160711yescharacteristic
281C2C29×#218411yescharacteristic
282C2C29×#219111yescharacteristic
subgroupG/H
center, socleC22×C29#447
commutator, Frattini, cosocleC22×C8C23×C29
prime radicalC29×#3186C2
LCSG ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C22×C4×C29 ◁ C2×C29×C22⋊C8 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#2232C2semidirect
3. C29×#2075C2semidirect
4. C29×#1347C2semidirect
5. C29×#1314C2semidirect
11. C2×C29×#107C22semidirect
16. C29×C22⋊C16C22semidirect
18. C29×#340C22semidirect
78. #12278C29direct (N × H)
115. #2232C2×C29semidirect
116. #2075C2×C29semidirect
117. #1347C2×C29semidirect
118. #1314C2×C29semidirect
145. C2×#107C22×C29semidirect
150. C22⋊C16C22×C29semidirect
152. #340C22×C29semidirect
184. C29#12278direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#31862
C29×#22322
C29×#20752
C29×#13472
C29×#13142
#1227829