Finite Group Databasebeta

← C29×#7103 #20302003

Subgroups — C29×#7103 #20302003

Order 7424.

692 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 692 conjugacy classes of subgroups — too many to draw. Only its 90 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×#1438C211yesmaximal, characteristic
2C29×#1280C212yesmaximal, complemented
3C23×D4×C29C411yescharacteristic
4C22×C22⋊C4×C29—22no—
5C2×C29×C22⋊C8—22no—
6C2×C29×#95C411yescharacteristic
7C2×C29×#95C2211yescharacteristic
8C25×C29—21no—
9C22×D4×C29—21no—
10C22×D4×C29—41no—
11C22×D4×C29—41no—
12C22×D4×C29—44no—
13C22×D4×C29C812yescomplemented
14C23×C4×C29—21no—
15C23×C4×C29C2×C411yescharacteristic
16C23×C4×C29D412yes—
17C22×C8×C29—42no—
18C2×C22⋊C4×C29—44no—
19C2×C22⋊C4×C29—44no—
20C2×C22⋊C4×C29—42no—
21C2×C22⋊C4×C29—42no—
22C29×C22⋊C8—24no—
23C29×C22⋊C8—42no—
24C29×#95—41no—
25C29×#95—41no—
26C24×C29—24no—
27C24×C29—22no—
28C24×C29—42no—
29C24×C29—42no—
30C24×C29—42no—
31C24×C29—41no—
32C24×C29—41no—
33C24×C29—42no—
34C24×C29—42no—
35C24×C29C22⋊C411yescharacteristic
36C2×D4×C29—42no—
37C2×D4×C29—42no—
38C2×D4×C29—44no—
39C2×D4×C29—44no—
40C2×D4×C29—48no—
41C2×D4×C29—44no—
42C2×D4×C29—44no—
43C22×C4×C29—22no—
44C22×C4×C29—21no—
45C22×C4×C29—21no—
46C22×C4×C29—22no—
47C22×C4×C29—22no—
48C22×C4×C29—42no—
49C22×C4×C29—42no—
50C22×C4×C29—42no—
51C22×C4×C29—42no—
52C22×C4×C29—41no—
53C22×C4×C29—41no—
54C22×C4×C29—42no—
55C22×C4×C29C2×C811yescharacteristic
56C22×C4×C29M1611yescharacteristic
57C22×C4×C29D812yes—
58C22×C4×C29SD1612yes—
59C2×C8×C29—44no—
60C2×C8×C29—82no—
61C2×C8×C29—82no—
62C22⋊C4×C29—48no—
63C22⋊C4×C29—48no—
64#7103C2911yesmaximal, characteristic, direct product factor, Sylow
65C23×C29—22no—
66C23×C29—21no—
67C23×C29—21no—
68C23×C29—24no—
69C23×C29—44no—
70C23×C29—44no—
71C23×C29—42no—
72C23×C29—44no—
73C23×C29—44no—
74C23×C29—44no—
75C23×C29—44no—
76C23×C29—42no—
77C23×C29—44no—
78C23×C29—44no—
79C23×C29—82no—
80C23×C29—82no—
81C23×C29—82no—
82C23×C29—82no—
83C23×C29—82no—
84C23×C29—82no—
85C23×C29—81no—
86C23×C29—81no—
87C23×C29—81no—
88C23×C29—81no—
89C23×C29C22⋊C811yescharacteristic
90C23×C29#9911yescharacteristic
91C23×C29#10011yescharacteristic
92C23×C29#10212yes—
93C23×C29#10412yes—
94D4×C29—44no—
95D4×C29—44no—
96D4×C29—48no—
97C2×C4×C29—21no—
98C2×C4×C29—21no—
99C2×C4×C29—22no—
100C2×C4×C29—22no—
101C2×C4×C29—42no—
102C2×C4×C29—42no—
103C2×C4×C29—42no—
104C2×C4×C29—42no—
105C2×C4×C29—42no—
106C2×C4×C29—42no—
107C2×C4×C29—41no—
108C2×C4×C29—41no—
109C2×C4×C29—44no—
110C2×C4×C29—42no—
111C2×C4×C29—82no—
112C2×C4×C29—81no—
113C2×C4×C29—82no—
114C2×C4×C29—81no—
115C8×C29—84no—
116#1438C2×C2911yescharacteristic
117#1280C2×C2912yescomplemented
118C22×C29—21no—
119C22×C29—21no—
120C22×C29—21no—
121C22×C29—21no—
122C22×C29—22no—
123C22×C29—22no—
124C22×C29—22no—
125C22×C29—22no—
126C22×C29—48no—
127C22×C29—44no—
128C22×C29—84no—
129C22×C29—84no—
130C22×C29—84no—
131C22×C29—82no—
132C22×C29—84no—
133C22×C29—84no—
134C22×C29—82no—
135C22×C29#32311yescharacteristic
136C22×C29D4⋊C812yes—
137C22×C29#32712yes—
138C22×C29#32911yescharacteristic
139C22×C29#33111yescharacteristic
140C22×C29AΣL(1,𝔽16)12yes—
141C22×C29#35311yescharacteristic
142C22×C29#35511yescharacteristic
143C4×C29—41no—
144C4×C29—41no—
145C4×C29—42no—
146C4×C29—42no—
147C4×C29—82no—
148C23×D4C4×C2911yescharacteristic
149C22×C22⋊C4—22no—
150C2×C22⋊C8—22no—
151C2×#95C4×C2911yescharacteristic
152C2×#95C22×C2911yescharacteristic
153C2×C29—21no—
154C2×C29—22no—
155C2×C29—21no—
156C2×C29—84no—
157C2×C29#127011yescharacteristic
158C2×C29#131611yescharacteristic
159C2×C29#131811yescharacteristic
160C2×C29#134312yes—
161C2×C29#134512yes—
162C25—21no—
163C22×D4—21no—
164C22×D4—41no—
165C22×D4—41no—
166C22×D4—44no—
167C22×D4C8×C2912yescomplemented
168C23×C4—21no—
169C23×C4C2×C4×C2911yescharacteristic
170C23×C4D4×C2912yes—
171C22×C8—42no—
172C2×C22⋊C4—44no—
173C2×C22⋊C4—44no—
174C2×C22⋊C4—42no—
175C2×C22⋊C4—42no—
176C22⋊C8—24no—
177C22⋊C8—42no—
178#95—41no—
179#95—41no—
180C29#710311yescharacteristic, direct product factor, Sylow
181C24—24no—
182C24—22no—
183C24—42no—
184C24—42no—
185C24—42no—
186C24—41no—
187C24—41no—
188C24—42no—
189C24—42no—
190C24C22⋊C4×C2911yescharacteristic
191C2×D4—42no—
192C2×D4—42no—
193C2×D4—44no—
194C2×D4—44no—
195C2×D4—48no—
196C2×D4—44no—
197C2×D4—44no—
198C22×C4—22no—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—22no—
202C22×C4—22no—
203C22×C4—42no—
204C22×C4—42no—
205C22×C4—42no—
206C22×C4—42no—
207C22×C4—41no—
208C22×C4—41no—
209C22×C4—42no—
210C22×C4C2×C8×C2911yescharacteristic
211C22×C4M16×C2911yescharacteristic
212C22×C4D8×C2912yes—
213C22×C4SD16×C2912yes—
214C2×C8—44no—
215C2×C8—82no—
216C2×C8—82no—
217C22⋊C4—48no—
218C22⋊C4—48no—
219C23—22no—
220C23—21no—
221C23—21no—
222C23—24no—
223C23—44no—
224C23—44no—
225C23—42no—
226C23—44no—
227C23—44no—
228C23—44no—
229C23—44no—
230C23—42no—
231C23—44no—
232C23—44no—
233C23—82no—
234C23—82no—
235C23—82no—
236C23—82no—
237C23—82no—
238C23—82no—
239C23—81no—
240C23—81no—
241C23—81no—
242C23—81no—
243C23C29×C22⋊C811yescharacteristic
244C23C29×#9911yescharacteristic
245C23C29×#10011yescharacteristic
246C23C29×#10212yes—
247C23C29×#10412yes—
248D4—44no—
249D4—44no—
250D4—48no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—44no—
264C2×C4—42no—
265C2×C4—82no—
266C2×C4—81no—
267C2×C4—82no—
268C2×C4—81no—
269C8—84no—
270C22—21no—
271C22—21no—
272C22—21no—
273C22—21no—
274C22—22no—
275C22—22no—
276C22—22no—
277C22—22no—
278C22—48no—
279C22—44no—
280C22—84no—
281C22—84no—
282C22—84no—
283C22—82no—
284C22—82no—
285C22—84no—
286C22—84no—
287C22C29×#32311yescharacteristic
288C22C29×D4⋊C812yes—
289C22C29×#32712yes—
290C22C29×#32911yescharacteristic
291C22C29×#33111yescharacteristic
292C22C29×AΣL(1,𝔽16)12yes—
293C22C29×#35311yescharacteristic
294C22C29×#35511yescharacteristic
295C4—41no—
296C4—41no—
297C4—42no—
298C4—42no—
299C4—82no—
300C2—21no—
301C2—22no—
302C2—21no—
303C2—84no—
304C2C29×#127011yescharacteristic
305C2C29×#131611yescharacteristic
306C2C29×#131811yescharacteristic
307C2C29×#134312yes—
308C2C29×#134512yes—
subgroupG/H
center, socleC23×C29#99
commutatorC22×C4C2×C8×C29
Frattini, cosocleC2×#95C22×C29
prime radicalC23×D4×C29C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C29 ◁ C24×C29 ◁ C2×C29×#95 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#1280C2semidirect
13. C22×D4×C29C8semidirect
64. #7103C29direct (N × H)
117. #1280C2×C29semidirect
167. C22×D4C8×C29semidirect
180. C29#7103direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#14382
C29×#12802
#710329