Finite Group Databasebeta

← C29×#8457 #20303357

Subgroups — C29×#8457 #20303357

Order 7424.

746 conjugacy classes of subgroups; only the 154 normal subgroups are shown.

normal subgroups only

This group has 746 conjugacy classes of subgroups — too many to draw. Only its 154 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×#3501C211yesmaximal, characteristic
2C29×#1955C211yesmaximal, characteristic
3C29×#1552C212yesmaximal, complemented
4C29×#1531C212yesmaximal, complemented
5C29×#1466C211yesmaximal, characteristic
6C29×#554—22no—
7C29×#554—24no—
8D4×Q8×C29—22no—
9C29×#544C412yes—
10C29×#543—22no—
11C29×#533C2212yes—
12C2×C29×C22⋊Q8—22no—
13C29×#518C412yes—
14C2×C4×D4×C29C2211yescharacteristic
15C29×#432C2212yes—
16C2×C29×C4⋊C8C2211yescharacteristic
17C2×C29×C22⋊C8—22no—
18C2×C29×#97C2211yescharacteristic
19C29×#332—22no—
20C29×#332—22no—
21C29×#330—24no—
22C29×#323—22no—
23C22×Q8×C29—22no—
24C22×D4×C29C2×C411yescharacteristic
25C23×C4×C29D412yes—
26C22×C8×C29—21no—
27C22×C8×C29—21no—
28C29×C4⋊Q8—24no—
29C29×C4⋊Q8D412yes—
30C29×C4⋊Q8D412yes—
31C29×#125—24no—
32C29×#125D414yes—
33C29×C22⋊Q8—24no—
34C29×C22⋊Q8—24no—
35C29×C22⋊Q8—28no—
36C29×C22⋊Q8—28no—
37C29×C22⋊Q8—24no—
38C29×C22⋊Q8—22no—
39C29×C22⋊Q8—22no—
40C4×Q8×C29—22no—
41C4×Q8×C29—22no—
42C4×D4×C29—24no—
43C4×D4×C29—24no—
44C4×D4×C29—22no—
45C4×D4×C29—22no—
46C29×#117C2×C414yes—
47C2×C4⋊C4×C29—22no—
48C2×C4⋊C4×C29—24no—
49C2×C4⋊C4×C29C2×C411yescharacteristic
50C2×C22⋊C4×C29—24no—
51C2×C22⋊C4×C29D412yes—
52C2×C42×C29C2311yescharacteristic
53C29×C4⋊C8—22no—
54C29×C4⋊C8—22no—
55C29×C22⋊C8—22no—
56C29×C22⋊C8—44no—
57C29×#97—22no—
58C29×#97—22no—
59C24×C29C22⋊C412yes—
60C2×Q8×C29—24no—
61C2×Q8×C29—22no—
62C2×Q8×C29—22no—
63C2×Q8×C29—82no—
64C2×Q8×C29—82no—
65C2×D4×C29—24no—
66C2×D4×C29—22no—
67C22×C4×C29—24no—
68C22×C4×C29—24no—
69C22×C4×C29—22no—
70C22×C4×C29—22no—
71C22×C4×C29—42no—
72C22×C4×C29—42no—
73C22×C4×C29C22⋊C412yes—
74C22×C4×C29C22×C411yescharacteristic
75C22×C4×C29C2×D411yescharacteristic
76C22×C4×C29C2×D411yescharacteristic
77C2×C8×C29—22no—
78C2×C8×C29—41no—
79C2×C8×C29—41no—
80C2×C8×C29—42no—
81C2×C8×C29—41no—
82C2×C8×C29—42no—
83C4⋊C4×C29—24no—
84C4⋊C4×C29—28no—
85C4⋊C4×C29—22no—
86C4⋊C4×C29—24no—
87C4⋊C4×C29—22no—
88C4⋊C4×C29—24no—
89C4⋊C4×C29—22no—
90C4⋊C4×C29C22⋊C414yes—
91C4⋊C4×C29C22⋊C414yes—
92C22⋊C4×C29—28no—
93C22⋊C4×C29—24no—
94C22⋊C4×C29—24no—
95C42×C29—24no—
96C42×C29C2×D412yes—
97C42×C29C2×D412yes—
98#8457C2911yesmaximal, characteristic, direct product factor, Sylow
99C23×C29—22no—
100C23×C29—22no—
101C23×C29—42no—
102C23×C29—42no—
103C23×C29#10114yes—
104C23×C29C2×C22⋊C411yescharacteristic
105Q8×C29—42no—
106Q8×C29—42no—
107Q8×C29—82no—
108Q8×C29—84no—
109D4×C29—28no—
110C2×C4×C29—22no—
111C2×C4×C29—21no—
112C2×C4×C29—21no—
113C2×C4×C29—24no—
114C2×C4×C29—24no—
115C2×C4×C29—22no—
116C2×C4×C29—41no—
117C2×C4×C29—42no—
118C2×C4×C29—42no—
119C2×C4×C29—42no—
120C2×C4×C29—82no—
121C2×C4×C29—84no—
122C2×C4×C29—84no—
123C2×C4×C29C2×C22⋊C412yes—
124C2×C4×C29#12012yes—
125C2×C4×C29#12011yescharacteristic
126C2×C4×C29#12011yescharacteristic
127C8×C29—42no—
128C8×C29—82no—
129C8×C29—81no—
130#3501C2×C2911yescharacteristic
131#1955C2×C2911yescharacteristic
132#1552C2×C2912yescomplemented
133#1531C2×C2912yescomplemented
134#1466C2×C2911yescharacteristic
135C22×C29—21no—
136C22×C29—21no—
137C22×C29—24no—
138C22×C29—44no—
139C22×C29—42no—
140C22×C29—42no—
141C22×C29—82no—
142C22×C29#37911yescharacteristic
143C22×C29C2×#10112yes—
144C4×C29—21no—
145C4×C29—22no—
146C4×C29—22no—
147C4×C29—42no—
148C4×C29—44no—
149C4×C29—44no—
150C4×C29#45311yescharacteristic
151C4×C29#45511yescharacteristic
152#554—22no—
153#554—24no—
154D4×Q8—22no—
155#544C4×C2912yes—
156#543—22no—
157#533C22×C2912yes—
158C2×C22⋊Q8—22no—
159#518C4×C2912yes—
160C2×C4×D4C22×C2911yescharacteristic
161#432C22×C2912yes—
162C2×C4⋊C8C22×C2911yescharacteristic
163C2×C22⋊C8—22no—
164C2×#97C22×C2911yescharacteristic
165#332—22no—
166#332—22no—
167#330—24no—
168#323—22no—
169C2×C29—22no—
170C2×C29—44no—
171C2×C29#178411yescharacteristic
172C2×C29#179211yescharacteristic
173C2×C29#179411yescharacteristic
174C22×Q8—22no—
175C22×D4C2×C4×C2911yescharacteristic
176C23×C4D4×C2912yes—
177C22×C8—21no—
178C22×C8—21no—
179C4⋊Q8—24no—
180C4⋊Q8D4×C2912yes—
181C4⋊Q8D4×C2912yes—
182#125—24no—
183#125D4×C2914yes—
184C22⋊Q8—24no—
185C22⋊Q8—24no—
186C22⋊Q8—28no—
187C22⋊Q8—28no—
188C22⋊Q8—24no—
189C22⋊Q8—22no—
190C22⋊Q8—22no—
191C4×Q8—22no—
192C4×Q8—22no—
193C4×D4—24no—
194C4×D4—24no—
195C4×D4—22no—
196C4×D4—22no—
197#117C2×C4×C2914yes—
198C2×C4⋊C4—22no—
199C2×C4⋊C4—24no—
200C2×C4⋊C4C2×C4×C2911yescharacteristic
201C2×C22⋊C4—24no—
202C2×C22⋊C4D4×C2912yes—
203C2×C42C23×C2911yescharacteristic
204C4⋊C8—22no—
205C4⋊C8—22no—
206C22⋊C8—22no—
207C22⋊C8—44no—
208#97—22no—
209#97—22no—
210C29#845711yescharacteristic, direct product factor, Sylow
211C24C22⋊C4×C2912yes—
212C2×Q8—24no—
213C2×Q8—22no—
214C2×Q8—22no—
215C2×Q8—82no—
216C2×Q8—82no—
217C2×D4—24no—
218C2×D4—22no—
219C22×C4—24no—
220C22×C4—24no—
221C22×C4—22no—
222C22×C4—22no—
223C22×C4—42no—
224C22×C4—42no—
225C22×C4C22⋊C4×C2912yes—
226C22×C4C22×C4×C2911yescharacteristic
227C22×C4C2×D4×C2911yescharacteristic
228C22×C4C2×D4×C2911yescharacteristic
229C2×C8—22no—
230C2×C8—41no—
231C2×C8—41no—
232C2×C8—42no—
233C2×C8—42no—
234C2×C8—41no—
235C4⋊C4—24no—
236C4⋊C4—28no—
237C4⋊C4—22no—
238C4⋊C4—24no—
239C4⋊C4—22no—
240C4⋊C4—24no—
241C4⋊C4—22no—
242C4⋊C4C22⋊C4×C2914yes—
243C4⋊C4C22⋊C4×C2914yes—
244C22⋊C4—28no—
245C22⋊C4—24no—
246C22⋊C4—24no—
247C42—24no—
248C42C2×D4×C2912yes—
249C42C2×D4×C2912yes—
250C23—22no—
251C23—22no—
252C23—42no—
253C23—42no—
254C23C29×#10114yes—
255C23C2×C22⋊C4×C2911yescharacteristic
256Q8—42no—
257Q8—42no—
258Q8—82no—
259Q8—84no—
260D4—28no—
261C2×C4—22no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—24no—
265C2×C4—24no—
266C2×C4—22no—
267C2×C4—41no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—82no—
272C2×C4—84no—
273C2×C4—84no—
274C2×C4C2×C22⋊C4×C2912yes—
275C2×C4C29×#12012yes—
276C2×C4C29×#12011yescharacteristic
277C2×C4C29×#12011yescharacteristic
278C8—42no—
279C8—82no—
280C8—81no—
281C22—21no—
282C22—21no—
283C22—24no—
284C22—44no—
285C22—42no—
286C22—42no—
287C22—82no—
288C22C29×#37911yescharacteristic
289C22C2×C29×#10112yes—
290C4—22no—
291C4—21no—
292C4—22no—
293C4—42no—
294C4—44no—
295C4—44no—
296C4C29×#45311yescharacteristic
297C4C29×#45511yescharacteristic
298C2—22no—
299C2—44no—
300C2C29×#178411yescharacteristic
301C2C29×#179211yescharacteristic
302C2C29×#179411yescharacteristic
subgroupG/H
center, socleC22×C29#379
commutatorC22×C4C22×C4×C29
Frattini, cosocleC2×C42C23×C29
prime radicalC22×D4×C29C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C2×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
3. C29×#1552C2semidirect
4. C29×#1531C2semidirect
98. #8457C29direct (N × H)
132. #1552C2×C29semidirect
133. #1531C2×C29semidirect
210. C29#8457direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#35012
C29×#19552
C29×#15522
C29×#15312
C29×#14662
#845729