Finite Group Databasebeta

← C29×#10258 #20305158

Subgroups — C29×#10258 #20305158

Order 7424.

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

normal subgroups only

This group has 526 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×#3249C211yesmaximal, characteristic, complemented
2C29×#3077C212yesmaximal
3C29×#1954C211yesmaximal, characteristic
4C29×#1493C212yesmaximal, complemented
5C29×#1292C211yesmaximal, characteristic, complemented
6C29×#533C2212yes—
7C2×C4×D4×C29C2211yescharacteristic
8C29×#478—24no—
9C29×#477—22no—
10C29×#476—22no—
11C29×#474—22no—
12C29×#467—22no—
13C29×#462—22no—
14C29×#428—22no—
15C29×#423C2212yes—
16C2×C29×C4⋊C8C2211yescharacteristic
17C29×#418—22no—
18C2×C29×C22⋊C8—22no—
19C2×C4×C8×C29C2211yescharacteristic
20C29×Q8⋊C8—24no—
21C22×D4×C29D411yescharacteristic
22C23×C4×C29—21no—
23C2×Q16×C29—22no—
24C2×M16×C29—22no—
25C22×C8×C29—21no—
26C22×C8×C29D412yes—
27C29×C4⋊Q8D412yes—
28C29×C4⋊Q8D412yes—
29C29×#125—22no—
30C29×C22⋊Q8—22no—
31C29×C22⋊Q8—22no—
32C4×Q8×C29—22no—
33C4×Q8×C29—22no—
34C4×D4×C29—22no—
35C4×D4×C29—22no—
36C29×#117—22no—
37C2×C4⋊C4×C29D411yescharacteristic
38C2×C22⋊C4×C29—21no—
39C2×C42×C29C2311yescharacteristic
40C29×#107—24no—
41C29×#107—22no—
42C29×#106—24no—
43C29×C4⋊C8—22no—
44C29×C4⋊C8—22no—
45C29×C4⋊C8D414yes—
46C29×#103—24no—
47C29×#102—24no—
48C29×#102—24no—
49C29×C22⋊C8—44no—
50C4×C8×C29—22no—
51C24×C29—21no—
52C2×Q8×C29—22no—
53C2×Q8×C29—22no—
54C2×D4×C29—22no—
55C2×D4×C29—21no—
56C2×D4×C29—22no—
57C2×D4×C29Q1612yescomplemented
58C22×C4×C29—21no—
59C22×C4×C29—42no—
60C22×C4×C29—42no—
61C22×C4×C29—41no—
62C22×C4×C29—41no—
63C22×C4×C29C2×D411yescharacteristic
64C22×C4×C29C2×D411yescharacteristic
65C22×C4×C29#4111yescharacteristic
66Q16×C29—82no—
67M16×C29—42no—
68M16×C29—42no—
69C2×C8×C29—22no—
70C2×C8×C29—22no—
71C2×C8×C29—24no—
72C2×C8×C29—41no—
73C2×C8×C29—41no—
74C2×C8×C29—42no—
75C4⋊C4×C29—22no—
76C4⋊C4×C29—22no—
77C4⋊C4×C29—22no—
78C4⋊C4×C29—22no—
79C4⋊C4×C29—22no—
80C4⋊C4×C29—42no—
81C4⋊C4×C29—42no—
82C22⋊C4×C29—42no—
83C22⋊C4×C29—42no—
84C42×C29—42no—
85C42×C29C2×D412yes—
86C42×C29C2×D412yes—
87#10258C2911yesmaximal, characteristic, direct product factor, Sylow
88C23×C29—22no—
89C23×C29—42no—
90C23×C29—42no—
91C23×C29—41no—
92C23×C29—41no—
93C23×C29#12111yescharacteristic
94Q8×C29—44no—
95Q8×C29—42no—
96Q8×C29—42no—
97D4×C29—24no—
98D4×C29—42no—
99C2×C4×C29—21no—
100C2×C4×C29—21no—
101C2×C4×C29—41no—
102C2×C4×C29—42no—
103C2×C4×C29—42no—
104C2×C4×C29—42no—
105C2×C4×C29—41no—
106C2×C4×C29—82no—
107C2×C4×C29—81no—
108C2×C4×C29—81no—
109C2×C4×C29#12012yes—
110C2×C4×C29#12011yescharacteristic
111C2×C4×C29#12112yes—
112C2×C4×C29#12711yescharacteristic
113C2×C4×C29C2×Q1611yescharacteristic
114C2×C4×C29#13511yescharacteristic
115C2×C4×C29#13712yes—
116C8×C29—42no—
117C8×C29—44no—
118C8×C29—42no—
119#3249C2×C2911yescharacteristic, complemented
120#3077C2×C2912yes—
121#1954C2×C2911yescharacteristic
122#1493C2×C2912yescomplemented
123#1292C2×C2911yescharacteristic, complemented
124C22×C29—21no—
125C22×C29—21no—
126C22×C29—44no—
127C22×C29—42no—
128C22×C29—82no—
129C22×C29—81no—
130C22×C29—81no—
131C22×C29#39211yescharacteristic
132C22×C29#46711yescharacteristic
133C22×C29#47011yescharacteristic
134C4×C29—21no—
135C4×C29—22no—
136C4×C29—81no—
137C4×C29—82no—
138C4×C29—82no—
139C4×C29#45112yes—
140C4×C29#45212yes—
141C4×C29#45311yescharacteristic
142C4×C29#45411yescharacteristic
143#533C22×C2912yes—
144C2×C4×D4C22×C2911yescharacteristic
145#478—24no—
146#477—22no—
147#476—22no—
148#474—22no—
149#467—22no—
150#462—22no—
151#428—22no—
152#423C22×C2912yes—
153C2×C4⋊C8C22×C2911yescharacteristic
154#418—22no—
155C2×C22⋊C8—22no—
156C2×C4×C8C22×C2911yescharacteristic
157Q8⋊C8—24no—
158C2×C29—21no—
159C2×C29—21no—
160C2×C29—82no—
161C2×C29#200111yescharacteristic
162C2×C29#200611yescharacteristic
163C2×C29#201711yescharacteristic
164C22×D4D4×C2911yescharacteristic
165C23×C4—21no—
166C2×Q16—22no—
167C2×M16—22no—
168C22×C8—21no—
169C22×C8D4×C2912yes—
170C4⋊Q8D4×C2912yes—
171C4⋊Q8D4×C2912yes—
172#125—22no—
173C22⋊Q8—22no—
174C22⋊Q8—22no—
175C4×Q8—22no—
176C4×Q8—22no—
177C4×D4—22no—
178C4×D4—22no—
179#117—22no—
180C2×C4⋊C4D4×C2911yescharacteristic
181C2×C22⋊C4—21no—
182C2×C42C23×C2911yescharacteristic
183#107—24no—
184#107—22no—
185#106—24no—
186C4⋊C8—22no—
187C4⋊C8—22no—
188C4⋊C8D4×C2914yes—
189#103—24no—
190#102—24no—
191#102—24no—
192C22⋊C8—44no—
193C4×C8—22no—
194C29#1025811yescharacteristic, direct product factor, Sylow
195C24—21no—
196C2×Q8—22no—
197C2×Q8—22no—
198C2×D4—22no—
199C2×D4—21no—
200C2×D4—22no—
201C2×D4Q16×C2912yescomplemented
202C22×C4—21no—
203C22×C4—42no—
204C22×C4—42no—
205C22×C4—41no—
206C22×C4—41no—
207C22×C4C2×D4×C2911yescharacteristic
208C22×C4C2×D4×C2911yescharacteristic
209C22×C4#41×C2911yescharacteristic
210Q16—82no—
211M16—42no—
212M16—42no—
213C2×C8—22no—
214C2×C8—24no—
215C2×C8—22no—
216C2×C8—41no—
217C2×C8—41no—
218C2×C8—42no—
219C4⋊C4—22no—
220C4⋊C4—22no—
221C4⋊C4—22no—
222C4⋊C4—22no—
223C4⋊C4—22no—
224C4⋊C4—42no—
225C4⋊C4—42no—
226C22⋊C4—42no—
227C22⋊C4—42no—
228C42—42no—
229C42C2×D4×C2912yes—
230C42C2×D4×C2912yes—
231C23—22no—
232C23—42no—
233C23—42no—
234C23—41no—
235C23—41no—
236C23C29×#12111yescharacteristic
237Q8—44no—
238Q8—42no—
239Q8—42no—
240D4—24no—
241D4—42no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—41no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—41no—
249C2×C4—82no—
250C2×C4—81no—
251C2×C4—81no—
252C2×C4C29×#12012yes—
253C2×C4C29×#12011yescharacteristic
254C2×C4C29×#12112yes—
255C2×C4C29×#12711yescharacteristic
256C2×C4C2×Q16×C2911yescharacteristic
257C2×C4C29×#13511yescharacteristic
258C2×C4C29×#13712yes—
259C8—42no—
260C8—44no—
261C8—42no—
262C22—21no—
263C22—21no—
264C22—44no—
265C22—42no—
266C22—82no—
267C22—81no—
268C22—81no—
269C22C29×#39211yescharacteristic
270C22C29×#46711yescharacteristic
271C22C29×#47011yescharacteristic
272C4—21no—
273C4—22no—
274C4—81no—
275C4—82no—
276C4—82no—
277C4C29×#45112yes—
278C4C29×#45212yes—
279C4C29×#45311yescharacteristic
280C4C29×#45411yescharacteristic
281C2—21no—
282C2—21no—
283C2—82no—
284C2C29×#200111yescharacteristic
285C2C29×#200611yescharacteristic
286C2C29×#201711yescharacteristic
subgroupG/H
center, socleC22×C29#392
commutator, Frattini, cosocleC2×C42C23×C29
prime radicalC22×D4×C29D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C2×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C29×#3249C2semidirect
4. C29×#1493C2semidirect
5. C29×#1292C2semidirect
57. C2×D4×C29Q16semidirect
87. #10258C29direct (N × H)
119. #3249C2×C29semidirect
122. #1493C2×C29semidirect
123. #1292C2×C29semidirect
194. C29#10258direct (N × H)
201. C2×D4Q16×C29semidirect

Maximal subgroups

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

subgroupindex
C29×#32492
C29×#30772
C29×#19542
C29×#14932
C29×#12922
#1025829