Finite Group Databasebeta

← C29×#11819 #20306719

Subgroups — C29×#11819 #20306719

Order 7424.

368 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 98 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×#2628C211yesmaximal, characteristic
2C29×#1822C211yesmaximal, characteristic
3C29×#1464C211yesmaximal, characteristic
4C29×#1354C214yesmaximal, complemented
5C2×C29×C4⋊Q8C411yescharacteristic
6C2×C29×#117C2211yescharacteristic
7C29×#432—21no—
8C29×#407—21no—
9C29×#400—21no—
10C29×#399—21no—
11C29×#395C2212yes—
12C29×#393C412yes—
13C29×#389—21no—
14C29×#382C411yescharacteristic
15C29×#380—21no—
16C29×#343—21no—
17C29×#343C2212yes—
18C29×#324C2212yes—
19C29×#323—21no—
20C22×Q8×C29C2×C412yes—
21C23×C4×C29D411yescharacteristic
22C2×M16×C29—22no—
23C29×C4⋊Q8—41no—
24C29×C4⋊Q8—41no—
25C29×#117—41no—
26C29×#117—41no—
27C2×C4⋊C4×C29—21no—
28C2×C4⋊C4×C29—21no—
29C2×C4⋊C4×C29—21no—
30C2×C4⋊C4×C29—22no—
31C2×C4⋊C4×C29D411yescharacteristic
32C2×C4⋊C4×C29C2311yescharacteristic
33C2×C22⋊C4×C29—22no—
34C2×C22⋊C4×C29C2×C411yescharacteristic
35C2×C22⋊C4×C29D411yescharacteristic
36C2×C42×C29C2×C411yescharacteristic
37C2×C42×C29D411yescharacteristic
38C29×C4⋊C8—41no—
39C29×C22⋊C8—22no—
40C29×C22⋊C8—41no—
41C29×C22⋊C8—41no—
42C29×#97—41no—
43C29×#95—21no—
44C29×#95—22no—
45C29×#95—22no—
46C29×#95C2×C412yes—
47C24×C29C22⋊C411yescharacteristic
48C2×Q8×C29—42no—
49C2×Q8×C29—82no—
50C22×C4×C29—21no—
51C22×C4×C29—21no—
52C22×C4×C29—22no—
53C22×C4×C29—22no—
54C22×C4×C29—22no—
55C22×C4×C29—41no—
56C22×C4×C29C22⋊C411yescharacteristic
57C22×C4×C29C22⋊C411yescharacteristic
58C22×C4×C29C22⋊C411yescharacteristic
59C22×C4×C29C22×C411yescharacteristic
60C22×C4×C29C2×D411yescharacteristic
61C22×C4×C29C2×D411yescharacteristic
62M16×C29—42no—
63M16×C29—42no—
64C2×C8×C29—42no—
65C2×C8×C29—42no—
66C4⋊C4×C29—41no—
67C4⋊C4×C29—41no—
68C4⋊C4×C29—42no—
69C4⋊C4×C29—42no—
70C4⋊C4×C29—41no—
71C4⋊C4×C29—41no—
72C4⋊C4×C29—82no—
73C22⋊C4×C29—41no—
74C22⋊C4×C29—41no—
75C22⋊C4×C29—82no—
76C42×C29—21no—
77C42×C29—21no—
78C42×C29—21no—
79C42×C29—21no—
80#11819C2911yesmaximal, characteristic, direct product factor, Sylow
81C23×C29—21no—
82C23×C29—21no—
83C23×C29—21no—
84C23×C29—41no—
85C23×C29—41no—
86C23×C29C2×C22⋊C411yescharacteristic
87Q8×C29—84no—
88C2×C4×C29—21no—
89C2×C4×C29—21no—
90C2×C4×C29—21no—
91C2×C4×C29—21no—
92C2×C4×C29—21no—
93C2×C4×C29—21no—
94C2×C4×C29—21no—
95C2×C4×C29—21no—
96C2×C4×C29—42no—
97C2×C4×C29—42no—
98C2×C4×C29—41no—
99C2×C4×C29—41no—
100C2×C4×C29—41no—
101C2×C4×C29—41no—
102C2×C4×C29—42no—
103C2×C4×C29—42no—
104C2×C4×C29—42no—
105C2×C4×C29—42no—
106C2×C4×C29—42no—
107C2×C4×C29—42no—
108C2×C4×C29#9911yescharacteristic
109C2×C4×C29#9911yescharacteristic
110C2×C4×C29#13712yes—
111C8×C29—82no—
112C8×C29—82no—
113#2628C2×C2911yescharacteristic
114#1822C2×C2911yescharacteristic
115#1464C2×C2911yescharacteristic
116#1354C2×C2914yescomplemented
117C22×C29—21no—
118C22×C29—21no—
119C22×C29—42no—
120C22×C29—41no—
121C22×C29—41no—
122C22×C29—41no—
123C22×C29—81no—
124C22×C29C2×#9911yescharacteristic
125C22×C29#41911yescharacteristic
126C22×C29#42111yescharacteristic
127C4×C29—22no—
128C4×C29—21no—
129C4×C29—21no—
130C4×C29—41no—
131C4×C29—41no—
132C4×C29—41no—
133C4×C29—41no—
134C4×C29—82no—
135C4×C29—82no—
136C2×C4⋊Q8C4×C2911yescharacteristic
137C2×#117C22×C2911yescharacteristic
138#432—21no—
139#407—21no—
140#400—21no—
141#399—21no—
142#395C22×C2912yes—
143#393C4×C2912yes—
144#389—21no—
145#382C4×C2911yescharacteristic
146#380—21no—
147#343—21no—
148#343C22×C2912yes—
149#324C22×C2912yes—
150#323—21no—
151C2×C29—21no—
152C2×C29—21no—
153C2×C29—81no—
154C2×C29#151111yescharacteristic
155C2×C29#212211yescharacteristic
156C2×C29#213511yescharacteristic
157C22×Q8C2×C4×C2912yes—
158C23×C4D4×C2911yescharacteristic
159C2×M16—22no—
160C4⋊Q8—41no—
161C4⋊Q8—41no—
162#117—41no—
163#117—41no—
164C2×C4⋊C4—21no—
165C2×C4⋊C4—21no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4D4×C2911yescharacteristic
169C2×C4⋊C4C23×C2911yescharacteristic
170C2×C22⋊C4—22no—
171C2×C22⋊C4C2×C4×C2911yescharacteristic
172C2×C22⋊C4D4×C2911yescharacteristic
173C2×C42C2×C4×C2911yescharacteristic
174C2×C42D4×C2911yescharacteristic
175C4⋊C8—41no—
176C22⋊C8—22no—
177C22⋊C8—41no—
178C22⋊C8—41no—
179#97—41no—
180#95—21no—
181#95—22no—
182#95—22no—
183#95C2×C4×C2912yes—
184C29#1181911yescharacteristic, direct product factor, Sylow
185C24C22⋊C4×C2911yescharacteristic
186C2×Q8—42no—
187C2×Q8—82no—
188C22×C4—22no—
189C22×C4—21no—
190C22×C4—21no—
191C22×C4—22no—
192C22×C4—22no—
193C22×C4—41no—
194C22×C4C22⋊C4×C2911yescharacteristic
195C22×C4C22⋊C4×C2911yescharacteristic
196C22×C4C22⋊C4×C2911yescharacteristic
197C22×C4C22×C4×C2911yescharacteristic
198C22×C4C2×D4×C2911yescharacteristic
199C22×C4C2×D4×C2911yescharacteristic
200M16—42no—
201M16—42no—
202C2×C8—42no—
203C2×C8—42no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—42no—
207C4⋊C4—42no—
208C4⋊C4—41no—
209C4⋊C4—41no—
210C4⋊C4—82no—
211C22⋊C4—41no—
212C22⋊C4—41no—
213C22⋊C4—82no—
214C42—21no—
215C42—21no—
216C42—21no—
217C42—21no—
218C23—21no—
219C23—21no—
220C23—21no—
221C23—41no—
222C23—41no—
223C23C2×C22⋊C4×C2911yescharacteristic
224Q8—84no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4C29×#9911yescharacteristic
246C2×C4C29×#9911yescharacteristic
247C2×C4C29×#13712yes—
248C8—82no—
249C8—82no—
250C22—21no—
251C22—21no—
252C22—42no—
253C22—41no—
254C22—41no—
255C22—41no—
256C22—81no—
257C22C2×C29×#9911yescharacteristic
258C22C29×#41911yescharacteristic
259C22C29×#42111yescharacteristic
260C4—22no—
261C4—21no—
262C4—21no—
263C4—41no—
264C4—41no—
265C4—41no—
266C4—41no—
267C4—82no—
268C4—82no—
269C2—21no—
270C2—21no—
271C2—81no—
272C2C29×#151111yescharacteristic
273C2C29×#212211yescharacteristic
274C2C29×#213511yescharacteristic
subgroupG/H
center, socleC22×C29C2×#99
commutatorC22×C4C22×C4×C29
Frattini, cosocleC2×C4⋊C4C23×C29
prime radicalC24×C29C22⋊C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C22×C4×C29 ◁ C2×C29×#117 ◁ G

Complements

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

NH ≅ G/Ntype
4. C29×#1354C2semidirect
80. #11819C29direct (N × H)
116. #1354C2×C29semidirect
184. C29#11819direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#26282
C29×#18222
C29×#14642
C29×#13542
#1181929