Finite Group Databasebeta

← C29×#10856 #20305756

Subgroups — C29×#10856 #20305756

Order 7424.

810 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#423C211yesmaximal, characteristic
2C2×C29×#423C211yesmaximal, characteristic
3C4×C29×#117C211yesmaximal, characteristic
4C2×C29×#344C214yesmaximal
5C22×M16×C29C2212yes—
6C22×M16×C29C2212yes—
7C2×C29×#117C2212yes—
8C22×C42×C29C2211yescharacteristic
9C29×#423—22no—
10C29×#423—21no—
11C29×#423—21no—
12C29×#423—22no—
13C29×#423C412yescomplemented
14C29×#423C412yescomplemented
15C2×C29×C4⋊C8—22no—
16C2×C29×C4⋊C8C414yescomplemented
17C4×C4⋊C4×C29—22no—
18C4×C22⋊C4×C29C414yes—
19C29×#376—21no—
20C43×C29—21no—
21C29×#344—28no—
22C23×C4×C29C2×C412yes—
23C23×C4×C29C2311yescharacteristic
24C2×M16×C29—24no—
25C2×M16×C29—22no—
26C2×M16×C29—22no—
27C2×M16×C29—22no—
28C2×M16×C29—24no—
29C2×M16×C29—24no—
30C2×M16×C29—24no—
31C2×M16×C29C2×C414yes—
32C22×C8×C29—22no—
33C22×C8×C29C2×C414yes—
34C29×#117—22no—
35C29×#117—22no—
36C29×#117D414yes—
37C29×#117Q814yes—
38C2×C4⋊C4×C29—22no—
39C2×C22⋊C4×C29C2×C414yes—
40C2×C42×C29—22no—
41C2×C42×C29—24no—
42C2×C42×C29C2×C412yes—
43C2×C42×C29C2×C411yescharacteristic
44C2×C42×C29C2×C411yescharacteristic
45C2×C42×C29D412yes—
46C2×C42×C29D411yescharacteristic
47C2×C42×C29D411yescharacteristic
48C2×C42×C29D412yes—
49C2×C42×C29Q811yescharacteristic
50C2×C42×C29Q811yescharacteristic
51C29×C4⋊C8—24no—
52C29×C4⋊C8—24no—
53C29×C4⋊C8—24no—
54C29×C4⋊C8—24no—
55C29×#95—24no—
56C24×C29C22×C411yescharacteristic
57C22×C4×C29—24no—
58C22×C4×C29—44no—
59C22×C4×C29C4212yes—
60C22×C4×C29C4212yes—
61C22×C4×C29C22⋊C412yes—
62C22×C4×C29C22⋊C412yes—
63C22×C4×C29C4⋊C412yes—
64C22×C4×C29C4⋊C412yes—
65C22×C4×C29C22×C411yescharacteristic
66C22×C4×C29C22×C411yescharacteristic
67C22×C4×C29C2×D411yescharacteristic
68C22×C4×C29C2×D411yescharacteristic
69C22×C4×C29C2×D411yescharacteristic
70C22×C4×C29C2×D412yes—
71C22×C4×C29C2×Q811yescharacteristic
72C22×C4×C29C2×Q812yes—
73C22×C4×C29#4112yes—
74C22×C4×C29#4112yes—
75M16×C29—28no—
76M16×C29—44no—
77M16×C29—44no—
78M16×C29—42no—
79M16×C29—42no—
80C2×C8×C29—24no—
81C2×C8×C29—24no—
82C2×C8×C29—28no—
83C2×C8×C29—42no—
84C2×C8×C29—42no—
85C4⋊C4×C29—24no—
86C4⋊C4×C29—24no—
87C22⋊C4×C29—24no—
88C22⋊C4×C29C4⋊C418yes—
89C42×C29—24no—
90C42×C29—24no—
91C42×C29—48no—
92C42×C29C22⋊C412yes—
93C42×C29C22⋊C412yes—
94C42×C29C22⋊C412yes—
95C42×C29C22⋊C412yes—
96C42×C29C4⋊C412yes—
97C42×C29C4⋊C411yescharacteristic
98C42×C29C4⋊C411yescharacteristic
99C42×C29C4⋊C411yescharacteristic
100C42×C29C4⋊C412yes—
101C42×C29C4⋊C411yescharacteristic
102#10856C2911yesmaximal, characteristic, direct product factor, Sylow
103C23×C29—42no—
104C23×C29C2×C4211yescharacteristic
105C23×C29C2×C22⋊C411yescharacteristic
106C23×C29C2×C4⋊C411yescharacteristic
107C23×C29C2×C4⋊C412yes—
108C23×C29#11712yes—
109C2×C4×C29—24no—
110C2×C4×C29—24no—
111C2×C4×C29—24no—
112C2×C4×C29—28no—
113C2×C4×C29—42no—
114C2×C4×C29—42no—
115C2×C4×C29—42no—
116C2×C4×C29—48no—
117C2×C4×C29#9512yes—
118C2×C4×C29#9512yes—
119C2×C4×C29#9512yes—
120C2×C4×C29#9512yes—
121C2×C4×C29C2×C22⋊C411yescharacteristic
122C2×C4×C29C2×C22⋊C411yescharacteristic
123C2×C4×C29C2×C4⋊C411yescharacteristic
124C2×C4×C29C2×C4⋊C411yescharacteristic
125C2×C4×C29C4×D412yes—
126C2×C4×C29C4×D412yes—
127C2×C4×C29C4×Q812yes—
128C2×C4×C29C4×Q812yes—
129C2×C4×C29#12112yes—
130C2×C4×C29#12112yes—
131C2×C4×C29C22⋊Q812yes—
132C2×C4×C29C22⋊Q812yes—
133C2×C4×C29#12411yescharacteristic
134C2×C4×C29#12411yescharacteristic
135C2×C4×C29#12512yes—
136C2×C4×C29#12711yescharacteristic
137C2×C4×C29C4⋊Q812yes—
138C2×C4×C29C4⋊Q811yescharacteristic
139C8×C29—44no—
140C8×C29—44no—
141C2×#423C2×C2911yescharacteristic
142C2×#423C2×C2911yescharacteristic
143C4×#117C2×C2911yescharacteristic
144C2×#344C2×C2914yes—
145C22×C29—22no—
146C22×C29—22no—
147C22×C29—22no—
148C22×C29—42no—
149C22×C29—42no—
150C22×C29C2×#9511yescharacteristic
151C22×C29C4×C4⋊C412yes—
152C22×C29#38012yes—
153C22×C29#38211yescharacteristic
154C22×C29#38411yescharacteristic
155C4×C29—22no—
156C4×C29—22no—
157C4×C29—22no—
158C4×C29—48no—
159C4×C29#34414yescomplemented
160C4×C29#38912yes—
161C4×C29#38912yes—
162C4×C29#39011yescharacteristic
163C4×C29#39011yescharacteristic
164C4×C29#39111yescharacteristic
165C4×C29#39111yescharacteristic
166C22×M16C22×C2912yes—
167C22×M16C22×C2912yes—
168C2×#117C22×C2912yes—
169C22×C42C22×C2911yescharacteristic
170#423—22no—
171#423—22no—
172#423—21no—
173#423—21no—
174#423C4×C2912yescomplemented
175#423C4×C2912yescomplemented
176C2×C4⋊C8—22no—
177C2×C4⋊C8C4×C2914yescomplemented
178C4×C4⋊C4—22no—
179C4×C22⋊C4C4×C2914yes—
180#376—21no—
181C43—21no—
182#344—28no—
183C2×C29—22no—
184C2×C29—22no—
185C2×C29—21no—
186C2×C29—21no—
187C2×C29C4⋊#9511yescharacteristic
188C2×C29C2×#34412yes—
189C23×C4C2×C4×C2912yes—
190C23×C4C23×C2911yescharacteristic
191C2×M16—24no—
192C2×M16—22no—
193C2×M16—22no—
194C2×M16—22no—
195C2×M16—24no—
196C2×M16—24no—
197C2×M16—24no—
198C2×M16C2×C4×C2914yes—
199C22×C8—22no—
200C22×C8C2×C4×C2914yes—
201#117—22no—
202#117—22no—
203#117D4×C2914yes—
204#117Q8×C2914yes—
205C2×C4⋊C4—22no—
206C2×C22⋊C4C2×C4×C2914yes—
207C2×C42—22no—
208C2×C42—24no—
209C2×C42C2×C4×C2912yes—
210C2×C42C2×C4×C2911yescharacteristic
211C2×C42C2×C4×C2911yescharacteristic
212C2×C42D4×C2912yes—
213C2×C42D4×C2911yescharacteristic
214C2×C42D4×C2911yescharacteristic
215C2×C42D4×C2912yes—
216C2×C42Q8×C2911yescharacteristic
217C2×C42Q8×C2911yescharacteristic
218C4⋊C8—24no—
219C4⋊C8—24no—
220C4⋊C8—24no—
221C4⋊C8—24no—
222#95—24no—
223C29#1085611yescharacteristic, direct product factor, Sylow
224C24C22×C4×C2911yescharacteristic
225C22×C4—24no—
226C22×C4—44no—
227C22×C4C42×C2912yes—
228C22×C4C42×C2912yes—
229C22×C4C22⋊C4×C2912yes—
230C22×C4C22⋊C4×C2912yes—
231C22×C4C4⋊C4×C2912yes—
232C22×C4C4⋊C4×C2912yes—
233C22×C4C22×C4×C2911yescharacteristic
234C22×C4C22×C4×C2911yescharacteristic
235C22×C4C2×D4×C2911yescharacteristic
236C22×C4C2×D4×C2911yescharacteristic
237C22×C4C2×D4×C2911yescharacteristic
238C22×C4C2×D4×C2912yes—
239C22×C4C2×Q8×C2911yescharacteristic
240C22×C4C2×Q8×C2912yes—
241C22×C4#41×C2912yes—
242C22×C4#41×C2912yes—
243M16—28no—
244M16—44no—
245M16—44no—
246M16—42no—
247M16—42no—
248C2×C8—24no—
249C2×C8—24no—
250C2×C8—28no—
251C2×C8—42no—
252C2×C8—42no—
253C4⋊C4—24no—
254C4⋊C4—24no—
255C22⋊C4—24no—
256C22⋊C4C4⋊C4×C2918yes—
257C42—24no—
258C42—24no—
259C42—48no—
260C42C22⋊C4×C2912yes—
261C42C22⋊C4×C2912yes—
262C42C22⋊C4×C2912yes—
263C42C22⋊C4×C2912yes—
264C42C4⋊C4×C2912yes—
265C42C4⋊C4×C2911yescharacteristic
266C42C4⋊C4×C2911yescharacteristic
267C42C4⋊C4×C2911yescharacteristic
268C42C4⋊C4×C2912yes—
269C42C4⋊C4×C2911yescharacteristic
270C23—42no—
271C23C2×C42×C2911yescharacteristic
272C23C2×C22⋊C4×C2911yescharacteristic
273C23C2×C4⋊C4×C2911yescharacteristic
274C23C2×C4⋊C4×C2912yes—
275C23C29×#11712yes—
276C2×C4—24no—
277C2×C4—24no—
278C2×C4—24no—
279C2×C4—28no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—48no—
284C2×C4C29×#9512yes—
285C2×C4C29×#9512yes—
286C2×C4C29×#9512yes—
287C2×C4C29×#9512yes—
288C2×C4C2×C22⋊C4×C2911yescharacteristic
289C2×C4C2×C22⋊C4×C2911yescharacteristic
290C2×C4C2×C4⋊C4×C2911yescharacteristic
291C2×C4C2×C4⋊C4×C2911yescharacteristic
292C2×C4C4×D4×C2912yes—
293C2×C4C4×D4×C2912yes—
294C2×C4C4×Q8×C2912yes—
295C2×C4C4×Q8×C2912yes—
296C2×C4C29×#12112yes—
297C2×C4C29×#12112yes—
298C2×C4C29×C22⋊Q812yes—
299C2×C4C29×C22⋊Q812yes—
300C2×C4C29×#12411yescharacteristic
301C2×C4C29×#12411yescharacteristic
302C2×C4C29×#12512yes—
303C2×C4C29×#12711yescharacteristic
304C2×C4C29×C4⋊Q812yes—
305C2×C4C29×C4⋊Q811yescharacteristic
306C8—44no—
307C8—44no—
308C22—22no—
309C22—22no—
310C22—22no—
311C22—42no—
312C22—42no—
313C22C2×C29×#9511yescharacteristic
314C22C4×C4⋊C4×C2912yes—
315C22C29×#38012yes—
316C22C29×#38211yescharacteristic
317C22C29×#38411yescharacteristic
318C4—22no—
319C4—22no—
320C4—22no—
321C4—48no—
322C4C29×#34414yescomplemented
323C4C29×#38912yes—
324C4C29×#38912yes—
325C4C29×#39011yescharacteristic
326C4C29×#39011yescharacteristic
327C4C29×#39111yescharacteristic
328C4C29×#39111yescharacteristic
329C2—22no—
330C2—22no—
331C2—21no—
332C2—21no—
333C2C29×C4⋊#9511yescharacteristic
334C2C2×C29×#34412yes—
subgroupG/H
centerC2×C4×C29C2×C22⋊C4
commutatorC23C2×C42×C29
Frattini, cosocleC23×C4C23×C29
socleC22×C29C2×#95
prime radicalC24×C29C22×C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C29 ◁ C22×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
13. C29×#423C4semidirect
14. C29×#423C4semidirect
16. C2×C29×C4⋊C8C4semidirect
102. #10856C29direct (N × H)
159. C4×C29#344semidirect
174. #423C4×C29semidirect
175. #423C4×C29semidirect
177. C2×C4⋊C8C4×C29semidirect
223. C29#10856direct (N × H)
322. C4C29×#344semidirect

Maximal subgroups

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

subgroupindex
C2×C29×#4232
C4×C29×#1172
C2×C29×#3442
#1085629