Finite Group Databasebeta

← C29×#12704 #20307604

Subgroups — C29×#12704 #20307604

Order 7424.

962 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 962 conjugacy classes of subgroups — too many to draw. Only its 150 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
1C2×C29×#536C211yesmaximal, characteristic
2C2×C29×#356C214yesmaximal, complemented
3C29×#1785C212yesmaximal
4C22×#41×C29C2211yescharacteristic
5C23×Q8×C29C411yescharacteristic
6C29×#536—28no—
7C2×C29×C4⋊Q8C2212yes—
8C2×C29×#124C412yes—
9C2×C29×#123—22no—
10C2×C29×C22⋊Q8—22no—
11C2×C29×#117C411yescharacteristic
12C2×C29×#101C2214yes—
13C2×C29×#100—22no—
14C29×#407—22no—
15C29×#356—28no—
16C2×#41×C29—24no—
17C2×#41×C29—42no—
18C2×#41×C29—42no—
19C22×Q8×C29—24no—
20C22×Q8×C29—21no—
21C22×Q8×C29—42no—
22C22×Q8×C29—42no—
23C22×Q8×C29C2×C412yes—
24C22×Q8×C29C2311yescharacteristic
25C22×D4×C29C2×C411yescharacteristic
26C22×D4×C29D412yes—
27C23×C4×C29—21no—
28C23×C4×C29C2×C411yescharacteristic
29C23×C4×C29D412yes—
30C2×M16×C29—24no—
31C29×C4⋊Q8—24no—
32C29×C4⋊Q8D418yes—
33C29×#124—24no—
34C29×#124—24no—
35C29×#123—216no—
36C29×C22⋊Q8—216no—
37C29×#117—24no—
38C2×C4⋊C4×C29—21no—
39C2×C4⋊C4×C29—24no—
40C2×C22⋊C4×C29—21no—
41C2×C22⋊C4×C29—24no—
42C2×C42×C29C2×C412yes—
43C29×#101—28no—
44C29×#100—44no—
45C29×C22⋊C8—44no—
46C24×C29C22⋊C412yes—
47C24×C29C22⋊C411yescharacteristic
48#41×C29—416no—
49C2×Q8×C29—24no—
50C2×Q8×C29—22no—
51C2×Q8×C29—41no—
52C2×Q8×C29—41no—
53C2×Q8×C29—416no—
54C2×Q8×C29—42no—
55C2×Q8×C29—42no—
56C2×Q8×C29—42no—
57C2×Q8×C29—42no—
58C2×Q8×C29C22⋊C414yes—
59C2×Q8×C29C2×D414yes—
60C2×D4×C29—24no—
61C2×D4×C29—22no—
62C2×D4×C29—24no—
63C2×D4×C29—41no—
64C2×D4×C29—41no—
65C2×D4×C29—42no—
66C22×C4×C29—22no—
67C22×C4×C29—22no—
68C22×C4×C29—22no—
69C22×C4×C29—24no—
70C22×C4×C29—22no—
71C22×C4×C29—22no—
72C22×C4×C29—24no—
73C22×C4×C29—24no—
74C22×C4×C29—42no—
75C22×C4×C29—42no—
76C22×C4×C29—42no—
77C22×C4×C29C22⋊C411yescharacteristic
78C22×C4×C29C22×C411yescharacteristic
79C22×C4×C29C2×D412yes—
80M16×C29—44no—
81M16×C29—44no—
82C2×C8×C29—44no—
83C4⋊C4×C29—24no—
84C4⋊C4×C29—216no—
85C22⋊C4×C29—24no—
86C22⋊C4×C29—216no—
87C42×C29—22no—
88C42×C29C22⋊C414yes—
89#12704C2911yesmaximal, characteristic, direct product factor, Sylow
90C23×C29—21no—
91C23×C29—21no—
92C23×C29—22no—
93C23×C29—22no—
94C23×C29—22no—
95C23×C29—42no—
96C23×C29—44no—
97C23×C29#9912yes—
98C23×C29C2×C22⋊C411yescharacteristic
99Q8×C29—44no—
100Q8×C29—44no—
101Q8×C29—48no—
102Q8×C29—44no—
103D4×C29—48no—
104D4×C29—44no—
105C2×C4×C29—28no—
106C2×C4×C29—21no—
107C2×C4×C29—22no—
108C2×C4×C29—21no—
109C2×C4×C29—21no—
110C2×C4×C29—22no—
111C2×C4×C29—21no—
112C2×C4×C29—24no—
113C2×C4×C29—24no—
114C2×C4×C29—48no—
115C2×C4×C29—44no—
116C2×C4×C29—48no—
117C2×C4×C29—42no—
118C2×C4×C29—42no—
119C2×C4×C29#9912yes—
120C2×C4×C29C2×C22⋊C412yes—
121C2×C4×C29#12014yes—
122C8×C29—84no—
123C2×#536C2×C2911yescharacteristic
124C2×#356C2×C2914yescomplemented
125#1785C2×C2912yes—
126C22×C29—22no—
127C22×C29—22no—
128C22×C29—42no—
129C22×C29—42no—
130C22×C29—44no—
131C22×C29—42no—
132C22×C29—44no—
133C22×C29—42no—
134C22×C29—82no—
135C22×C29#37911yescharacteristic
136C22×C29C2×#9911yescharacteristic
137C22×C29C2×#9911yescharacteristic
138C4×C29—24no—
139C4×C29—22no—
140C4×C29—22no—
141C4×C29—44no—
142C4×C29—44no—
143C22×#41C22×C2911yescharacteristic
144C23×Q8C4×C2911yescharacteristic
145#536—28no—
146C2×C4⋊Q8C22×C2912yes—
147C2×#124C4×C2912yes—
148C2×#123—22no—
149C2×C22⋊Q8—22no—
150C2×#117C4×C2911yescharacteristic
151C2×#101C22×C2914yes—
152C2×#100—22no—
153#407—22no—
154#356—28no—
155C2×C29—21no—
156C2×C29—21no—
157C2×C29—42no—
158C2×C29—82no—
159C2×C29#178111yescharacteristic
160C2×C29#213512yes—
161C2×#41—24no—
162C2×#41—42no—
163C2×#41—42no—
164C22×Q8—24no—
165C22×Q8—21no—
166C22×Q8—42no—
167C22×Q8—42no—
168C22×Q8C2×C4×C2912yes—
169C22×Q8C23×C2911yescharacteristic
170C22×D4C2×C4×C2911yescharacteristic
171C22×D4D4×C2912yes—
172C23×C4—21no—
173C23×C4C2×C4×C2911yescharacteristic
174C23×C4D4×C2912yes—
175C2×M16—24no—
176C4⋊Q8—24no—
177C4⋊Q8D4×C2918yes—
178#124—24no—
179#124—24no—
180#123—216no—
181C22⋊Q8—216no—
182#117—24no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—24no—
185C2×C22⋊C4—21no—
186C2×C22⋊C4—24no—
187C2×C42C2×C4×C2912yes—
188#101—28no—
189#100—44no—
190C22⋊C8—44no—
191C29#1270411yescharacteristic, direct product factor, Sylow
192C24C22⋊C4×C2912yes—
193C24C22⋊C4×C2911yescharacteristic
194#41—416no—
195C2×Q8—24no—
196C2×Q8—22no—
197C2×Q8—41no—
198C2×Q8—41no—
199C2×Q8—416no—
200C2×Q8—42no—
201C2×Q8—42no—
202C2×Q8—42no—
203C2×Q8—42no—
204C2×Q8C22⋊C4×C2914yes—
205C2×Q8C2×D4×C2914yes—
206C2×D4—24no—
207C2×D4—22no—
208C2×D4—24no—
209C2×D4—41no—
210C2×D4—41no—
211C2×D4—42no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—24no—
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—24no—
219C22×C4—24no—
220C22×C4—42no—
221C22×C4—42no—
222C22×C4—42no—
223C22×C4C22⋊C4×C2911yescharacteristic
224C22×C4C22×C4×C2911yescharacteristic
225C22×C4C2×D4×C2912yes—
226M16—44no—
227M16—44no—
228C2×C8—44no—
229C4⋊C4—24no—
230C4⋊C4—216no—
231C22⋊C4—24no—
232C22⋊C4—216no—
233C42—22no—
234C42C22⋊C4×C2914yes—
235C23—21no—
236C23—21no—
237C23—22no—
238C23—22no—
239C23—22no—
240C23—42no—
241C23—44no—
242C23C29×#9912yes—
243C23C2×C22⋊C4×C2911yescharacteristic
244Q8—44no—
245Q8—44no—
246Q8—48no—
247Q8—44no—
248D4—48no—
249D4—44no—
250C2×C4—28no—
251C2×C4—21no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—24no—
258C2×C4—24no—
259C2×C4—48no—
260C2×C4—48no—
261C2×C4—44no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4C29×#9912yes—
265C2×C4C2×C22⋊C4×C2912yes—
266C2×C4C29×#12014yes—
267C8—84no—
268C22—22no—
269C22—22no—
270C22—42no—
271C22—42no—
272C22—44no—
273C22—42no—
274C22—42no—
275C22—44no—
276C22—82no—
277C22C29×#37911yescharacteristic
278C22C2×C29×#9911yescharacteristic
279C22C2×C29×#9911yescharacteristic
280C4—24no—
281C4—22no—
282C4—22no—
283C4—44no—
284C4—44no—
285C2—21no—
286C2—21no—
287C2—42no—
288C2—82no—
289C2C29×#178111yescharacteristic
290C2C29×#213512yes—
subgroupG/H
center, socleC22×C29C2×#99
commutatorC22×C4C22×C4×C29
Frattini, cosocleC22×Q8C23×C29
prime radicalC22×#41×C29C22
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C22×C4×C29 ◁ C22×#41×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C29×#356C2semidirect
89. #12704C29direct (N × H)
124. C2×#356C2×C29semidirect
191. C29#12704direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#5362
C2×C29×#3562
C29×#17852
#1270429