Finite Group Databasebeta

← C29×#10325 #20305225

Subgroups — C29×#10325 #20305225

Order 7424.

602 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 602 conjugacy classes of subgroups — too many to draw. Only its 122 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×#3189C211yesmaximal, characteristic
2C29×#2855C212yesmaximal
3C29×#1817C211yesmaximal, characteristic
4C29×#1520C212yesmaximal
5C29×#1289C211yesmaximal, characteristic
6C2×C29×C22⋊Q8C2212yes—
7C22×C42×C29C2211yescharacteristic
8C29×#484—22no—
9C29×#467—22no—
10C29×#451—22no—
11C2×C29×C22⋊C8C2211yescharacteristic
12C2×C29×C22⋊C8C2211yescharacteristic
13C29×#391—22no—
14C29×#389—22no—
15C29×#387—24no—
16C29×#385—22no—
17C29×#381—22no—
18C29×#380C2212yes—
19C29×#336—22no—
20C29×#328—24no—
21C22×Q8×C29D412yes—
22C23×C4×C29D411yescharacteristic
23C23×C4×C29D411yescharacteristic
24C23×C4×C29C2311yescharacteristic
25C2×Q16×C29—22no—
26C22×C8×C29—21no—
27C22×C8×C29D412yes—
28C29×C22⋊Q8—22no—
29C29×C22⋊Q8—22no—
30C29×C22⋊Q8—22no—
31C29×C22⋊Q8—22no—
32C2×C4⋊C4×C29—24no—
33C2×C4⋊C4×C29—22no—
34C2×C4⋊C4×C29—22no—
35C2×C4⋊C4×C29D412yes—
36C2×C22⋊C4×C29—22no—
37C2×C22⋊C4×C29—22no—
38C2×C42×C29—21no—
39C2×C42×C29—22no—
40C2×C42×C29—22no—
41C2×C42×C29—21no—
42C29×#107—22no—
43C29×#103—24no—
44C29×C22⋊C8—22no—
45C29×C22⋊C8—22no—
46C29×#95—24no—
47C29×#95—24no—
48C29×#95—24no—
49C29×#95D414yes—
50C24×C29C2×D411yescharacteristic
51C2×Q8×C29—22no—
52C2×Q8×C29—22no—
53C2×Q8×C29—44no—
54C22×C4×C29—22no—
55C22×C4×C29—22no—
56C22×C4×C29—21no—
57C22×C4×C29—21no—
58C22×C4×C29—21no—
59C22×C4×C29—22no—
60C22×C4×C29—22no—
61C22×C4×C29—24no—
62C22×C4×C29—22no—
63C22×C4×C29—42no—
64C22×C4×C29—42no—
65C22×C4×C29Q1612yescomplemented
66C22×C4×C29C2×D412yes—
67C22×C4×C29C2×D411yescharacteristic
68C22×C4×C29C2×D412yes—
69C22×C4×C29#4111yescharacteristic
70Q16×C29—82no—
71C2×C8×C29—22no—
72C2×C8×C29—42no—
73C2×C8×C29—42no—
74C2×C8×C29—41no—
75C4⋊C4×C29—22no—
76C4⋊C4×C29—22no—
77C4⋊C4×C29—44no—
78C4⋊C4×C29—48no—
79C4⋊C4×C29—42no—
80C4⋊C4×C29—42no—
81C22⋊C4×C29—42no—
82C22⋊C4×C29—42no—
83C22⋊C4×C29—42no—
84C22⋊C4×C29—42no—
85C42×C29—41no—
86C42×C29—42no—
87C42×C29—41no—
88#10325C2911yesmaximal, characteristic, direct product factor, Sylow
89C23×C29—41no—
90C23×C29—41no—
91C23×C29#12012yes—
92C23×C29#12111yescharacteristic
93C23×C29C2×Q1611yescharacteristic
94C23×C29#13511yescharacteristic
95C23×C29#13712yes—
96Q8×C29—44no—
97Q8×C29—82no—
98C2×C4×C29—24no—
99C2×C4×C29—22no—
100C2×C4×C29—24no—
101C2×C4×C29—22no—
102C2×C4×C29—24no—
103C2×C4×C29—22no—
104C2×C4×C29—42no—
105C2×C4×C29—41no—
106C2×C4×C29—42no—
107C2×C4×C29—41no—
108C2×C4×C29—41no—
109C2×C4×C29—41no—
110C2×C4×C29—42no—
111C2×C4×C29—41no—
112C2×C4×C29—44no—
113C2×C4×C29—44no—
114C2×C4×C29—44no—
115C2×C4×C29—44no—
116C2×C4×C29—42no—
117C2×C4×C29—42no—
118C2×C4×C29—44no—
119C2×C4×C29#12011yescharacteristic
120C2×C4×C29#12112yes—
121C2×C4×C29#12711yescharacteristic
122C8×C29—42no—
123C8×C29—81no—
124#3189C2×C2911yescharacteristic
125#2855C2×C2912yes—
126#1817C2×C2911yescharacteristic
127#1520C2×C2912yes—
128#1289C2×C2911yescharacteristic
129C22×C29—22no—
130C22×C29—21no—
131C22×C29—22no—
132C22×C29—21no—
133C22×C29—41no—
134C22×C29—41no—
135C22×C29—42no—
136C22×C29#39211yescharacteristic
137C22×C29#45112yes—
138C22×C29#45212yes—
139C22×C29#46711yescharacteristic
140C22×C29#47011yescharacteristic
141C4×C29—21no—
142C4×C29—22no—
143C4×C29—42no—
144C4×C29—42no—
145C4×C29—84no—
146C4×C29—82no—
147C4×C29—82no—
148C4×C29#45812yes—
149C2×C22⋊Q8C22×C2912yes—
150C22×C42C22×C2911yescharacteristic
151#484—22no—
152#467—22no—
153#451—22no—
154C2×C22⋊C8C22×C2911yescharacteristic
155C2×C22⋊C8C22×C2911yescharacteristic
156#391—22no—
157#389—22no—
158#387—24no—
159#385—22no—
160#381—22no—
161#380C22×C2912yes—
162#336—22no—
163#328—24no—
164C2×C29—22no—
165C2×C29—22no—
166C2×C29—21no—
167C2×C29—21no—
168C2×C29#200111yescharacteristic
169C2×C29#201011yescharacteristic
170C2×C29#202211yescharacteristic
171C22×Q8D4×C2912yes—
172C23×C4D4×C2911yescharacteristic
173C23×C4D4×C2911yescharacteristic
174C23×C4C23×C2911yescharacteristic
175C2×Q16—22no—
176C22×C8—21no—
177C22×C8D4×C2912yes—
178C22⋊Q8—22no—
179C22⋊Q8—22no—
180C22⋊Q8—22no—
181C22⋊Q8—22no—
182C2×C4⋊C4—24no—
183C2×C4⋊C4—22no—
184C2×C4⋊C4—22no—
185C2×C4⋊C4D4×C2912yes—
186C2×C22⋊C4—22no—
187C2×C22⋊C4—22no—
188C2×C42—21no—
189C2×C42—22no—
190C2×C42—22no—
191C2×C42—21no—
192#107—22no—
193#103—24no—
194C22⋊C8—22no—
195C22⋊C8—22no—
196#95—24no—
197#95—24no—
198#95—24no—
199#95D4×C2914yes—
200C29#1032511yescharacteristic, direct product factor, Sylow
201C24C2×D4×C2911yescharacteristic
202C2×Q8—22no—
203C2×Q8—22no—
204C2×Q8—44no—
205C22×C4—22no—
206C22×C4—22no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—22no—
211C22×C4—22no—
212C22×C4—24no—
213C22×C4—22no—
214C22×C4—42no—
215C22×C4—42no—
216C22×C4Q16×C2912yescomplemented
217C22×C4C2×D4×C2912yes—
218C22×C4C2×D4×C2911yescharacteristic
219C22×C4C2×D4×C2912yes—
220C22×C4#41×C2911yescharacteristic
221Q16—82no—
222C2×C8—22no—
223C2×C8—42no—
224C2×C8—42no—
225C2×C8—41no—
226C4⋊C4—22no—
227C4⋊C4—22no—
228C4⋊C4—44no—
229C4⋊C4—48no—
230C4⋊C4—42no—
231C4⋊C4—42no—
232C22⋊C4—42no—
233C22⋊C4—42no—
234C22⋊C4—42no—
235C22⋊C4—42no—
236C42—41no—
237C42—42no—
238C42—41no—
239C23—41no—
240C23—41no—
241C23C29×#12012yes—
242C23C29×#12111yescharacteristic
243C23C2×Q16×C2911yescharacteristic
244C23C29×#13511yescharacteristic
245C23C29×#13712yes—
246Q8—44no—
247Q8—82no—
248C2×C4—24no—
249C2×C4—22no—
250C2×C4—24no—
251C2×C4—22no—
252C2×C4—24no—
253C2×C4—22no—
254C2×C4—42no—
255C2×C4—41no—
256C2×C4—42no—
257C2×C4—41no—
258C2×C4—42no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—44no—
263C2×C4—44no—
264C2×C4—44no—
265C2×C4—44no—
266C2×C4—44no—
267C2×C4—42no—
268C2×C4—42no—
269C2×C4C29×#12011yescharacteristic
270C2×C4C29×#12112yes—
271C2×C4C29×#12711yescharacteristic
272C8—42no—
273C8—81no—
274C22—22no—
275C22—21no—
276C22—22no—
277C22—21no—
278C22—41no—
279C22—41no—
280C22—42no—
281C22C29×#39211yescharacteristic
282C22C29×#45112yes—
283C22C29×#45212yes—
284C22C29×#46711yescharacteristic
285C22C29×#47011yescharacteristic
286C4—21no—
287C4—22no—
288C4—42no—
289C4—42no—
290C4—84no—
291C4—82no—
292C4—82no—
293C4C29×#45812yes—
294C2—22no—
295C2—22no—
296C2—21no—
297C2—21no—
298C2C29×#200111yescharacteristic
299C2C29×#201011yescharacteristic
300C2C29×#202211yescharacteristic
subgroupG/H
center, socleC22×C29#392
commutator, Frattini, cosocleC23×C4C23×C29
prime radicalC24×C29C2×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C23×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
65. C22×C4×C29Q16semidirect
88. #10325C29direct (N × H)
200. C29#10325direct (N × H)
216. C22×C4Q16×C29semidirect

Maximal subgroups

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

subgroupindex
C29×#31892
C29×#28552
C29×#18172
C29×#15202
C29×#12892
#1032529