Finite Group Databasebeta

← C29×#8556 #20303456

Subgroups — C29×#8556 #20303456

Order 7424.

842 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 842 conjugacy classes of subgroups — too many to draw. Only its 150 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
1C22×C29×#126C211yesmaximal, characteristic
2C29×#1821C212yesmaximal, complemented
3C29×#1463C212yesmaximal, complemented
4C29×#1462C212yesmaximal
5C2×C29×#126—24no—
6C2×C29×#126—24no—
7C2×C29×#126—24no—
8C22×C4⋊C4×C29C411yescharacteristic
9C22×C4⋊C4×C29C2211yescharacteristic
10C22×C4⋊C4×C29C2211yescharacteristic
11C22×C22⋊C4×C29C411yescharacteristic
12C22×C22⋊C4×C29C411yescharacteristic
13C22×C22⋊C4×C29C2211yescharacteristic
14C22×C42×C29C411yescharacteristic
15C29×#407C2214yes—
16C29×#343—24no—
17C29×#324—24no—
18C29×#323—24no—
19C25×C29C2×C411yescharacteristic
20C23×C4×C29C2×C411yescharacteristic
21C23×C4×C29C2×C411yescharacteristic
22C23×C4×C29C2×C411yescharacteristic
23C23×C4×C29C2×C411yescharacteristic
24C23×C4×C29C2×C411yescharacteristic
25C23×C4×C29C2311yescharacteristic
26C2×M16×C29—24no—
27C29×#126—232no—
28C2×C4⋊C4×C29—22no—
29C2×C4⋊C4×C29—22no—
30C2×C4⋊C4×C29—22no—
31C2×C4⋊C4×C29—22no—
32C2×C4⋊C4×C29—22no—
33C2×C4⋊C4×C29—22no—
34C2×C4⋊C4×C29—22no—
35C2×C4⋊C4×C29D414yes—
36C2×C4⋊C4×C29D414yes—
37C2×C22⋊C4×C29—22no—
38C2×C22⋊C4×C29—22no—
39C2×C22⋊C4×C29—22no—
40C2×C22⋊C4×C29—22no—
41C2×C22⋊C4×C29—22no—
42C2×C22⋊C4×C29—22no—
43C2×C22⋊C4×C29—22no—
44C2×C22⋊C4×C29—22no—
45C2×C22⋊C4×C29D414yes—
46C2×C42×C29—22no—
47C2×C42×C29—22no—
48C2×C42×C29—22no—
49C29×C22⋊C8—24no—
50C29×C22⋊C8—24no—
51C24×C29—21no—
52C24×C29—21no—
53C24×C29—42no—
54C24×C29—42no—
55C24×C29—42no—
56C24×C29C22⋊C412yes—
57C24×C29C22×C411yescharacteristic
58C22×C4×C29—21no—
59C22×C4×C29—21no—
60C22×C4×C29—21no—
61C22×C4×C29—21no—
62C22×C4×C29—21no—
63C22×C4×C29—21no—
64C22×C4×C29—21no—
65C22×C4×C29—21no—
66C22×C4×C29—21no—
67C22×C4×C29—21no—
68C22×C4×C29—42no—
69C22×C4×C29—42no—
70C22×C4×C29—42no—
71C22×C4×C29—42no—
72C22×C4×C29—42no—
73C22×C4×C29—42no—
74C22×C4×C29C22⋊C412yes—
75C22×C4×C29C22⋊C412yes—
76C22×C4×C29C22⋊C412yes—
77C22×C4×C29C22⋊C412yes—
78C22×C4×C29C22⋊C412yes—
79C22×C4×C29C2×D412yes—
80C22×C4×C29C2×D412yes—
81C22×C4×C29C2×D412yes—
82M16×C29—48no—
83C2×C8×C29—44no—
84C4⋊C4×C29—28no—
85C4⋊C4×C29—28no—
86C4⋊C4×C29—28no—
87C22⋊C4×C29—28no—
88C22⋊C4×C29—28no—
89C22⋊C4×C29—28no—
90C42×C29—28no—
91#8556C2911yesmaximal, characteristic, direct product factor, Sylow
92C23×C29—22no—
93C23×C29—22no—
94C23×C29—22no—
95C23×C29—22no—
96C23×C29—24no—
97C23×C29—42no—
98C23×C29—42no—
99C23×C29—42no—
100C23×C29—42no—
101C23×C29—42no—
102C23×C29—42no—
103C23×C29—42no—
104C23×C29—42no—
105C23×C29—88no—
106C23×C29C2×C22⋊C411yescharacteristic
107C23×C29C2×C22⋊C411yescharacteristic
108C23×C29C2×C22⋊C411yescharacteristic
109C2×C4×C29—24no—
110C2×C4×C29—22no—
111C2×C4×C29—22no—
112C2×C4×C29—22no—
113C2×C4×C29—22no—
114C2×C4×C29—22no—
115C2×C4×C29—24no—
116C2×C4×C29—42no—
117C2×C4×C29—42no—
118C2×C4×C29—42no—
119C2×C4×C29—42no—
120C2×C4×C29—42no—
121C2×C4×C29—42no—
122C2×C4×C29—42no—
123C2×C4×C29—42no—
124C2×C4×C29—42no—
125C2×C4×C29—42no—
126C2×C4×C29—42no—
127C2×C4×C29—42no—
128C2×C4×C29—42no—
129C2×C4×C29—42no—
130C2×C4×C29—42no—
131C2×C4×C29—42no—
132C2×C4×C29#12014yes—
133C8×C29—84no—
134C22×#126C2×C2911yescharacteristic
135#1821C2×C2912yescomplemented
136#1463C2×C2912yescomplemented
137#1462C2×C2912yes—
138C22×C29—28no—
139C22×C29—21no—
140C22×C29—21no—
141C22×C29—21no—
142C22×C29—21no—
143C22×C29—21no—
144C22×C29—21no—
145C22×C29—42no—
146C22×C29—42no—
147C22×C29—42no—
148C22×C29—84no—
149C22×C29—84no—
150C22×C29—84no—
151C22×C29#37911yescharacteristic
152C22×C29#41012yes—
153C22×C29#41312yes—
154C22×C29#41312yes—
155C4×C29—24no—
156C4×C29—42no—
157C4×C29—42no—
158C4×C29—42no—
159C4×C29—42no—
160C4×C29—42no—
161C2×#126—24no—
162C2×#126—24no—
163C2×#126—24no—
164C22×C4⋊C4C4×C2911yescharacteristic
165C22×C4⋊C4C22×C2911yescharacteristic
166C22×C4⋊C4C22×C2911yescharacteristic
167C22×C22⋊C4C4×C2911yescharacteristic
168C22×C22⋊C4C4×C2911yescharacteristic
169C22×C22⋊C4C22×C2911yescharacteristic
170C22×C42C4×C2911yescharacteristic
171#407C22×C2914yes—
172#343—24no—
173#324—24no—
174#323—24no—
175C2×C29—22no—
176C2×C29—22no—
177C2×C29—22no—
178C2×C29—82no—
179C2×C29#178211yescharacteristic
180C2×C29#178511yescharacteristic
181C2×C29#178511yescharacteristic
182C25C2×C4×C2911yescharacteristic
183C23×C4C2×C4×C2911yescharacteristic
184C23×C4C2×C4×C2911yescharacteristic
185C23×C4C2×C4×C2911yescharacteristic
186C23×C4C2×C4×C2911yescharacteristic
187C23×C4C2×C4×C2911yescharacteristic
188C23×C4C23×C2911yescharacteristic
189C2×M16—24no—
190#126—232no—
191C2×C4⋊C4—22no—
192C2×C4⋊C4—22no—
193C2×C4⋊C4—22no—
194C2×C4⋊C4—22no—
195C2×C4⋊C4—22no—
196C2×C4⋊C4—22no—
197C2×C4⋊C4—22no—
198C2×C4⋊C4D4×C2914yes—
199C2×C4⋊C4D4×C2914yes—
200C2×C22⋊C4—22no—
201C2×C22⋊C4—22no—
202C2×C22⋊C4—22no—
203C2×C22⋊C4—22no—
204C2×C22⋊C4—22no—
205C2×C22⋊C4—22no—
206C2×C22⋊C4—22no—
207C2×C22⋊C4—22no—
208C2×C22⋊C4D4×C2914yes—
209C2×C42—22no—
210C2×C42—22no—
211C2×C42—22no—
212C22⋊C8—24no—
213C22⋊C8—24no—
214C29#855611yescharacteristic, direct product factor, Sylow
215C24—21no—
216C24—21no—
217C24—42no—
218C24—42no—
219C24—42no—
220C24C22⋊C4×C2912yes—
221C24C22×C4×C2911yescharacteristic
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—42no—
233C22×C4—42no—
234C22×C4—42no—
235C22×C4—42no—
236C22×C4—42no—
237C22×C4—42no—
238C22×C4C22⋊C4×C2912yes—
239C22×C4C22⋊C4×C2912yes—
240C22×C4C22⋊C4×C2912yes—
241C22×C4C22⋊C4×C2912yes—
242C22×C4C22⋊C4×C2912yes—
243C22×C4C2×D4×C2912yes—
244C22×C4C2×D4×C2912yes—
245C22×C4C2×D4×C2912yes—
246M16—48no—
247C2×C8—44no—
248C4⋊C4—28no—
249C4⋊C4—28no—
250C4⋊C4—28no—
251C22⋊C4—28no—
252C22⋊C4—28no—
253C22⋊C4—28no—
254C42—28no—
255C23—22no—
256C23—22no—
257C23—22no—
258C23—22no—
259C23—24no—
260C23—42no—
261C23—42no—
262C23—42no—
263C23—42no—
264C23—42no—
265C23—42no—
266C23—42no—
267C23—42no—
268C23—88no—
269C23C2×C22⋊C4×C2911yescharacteristic
270C23C2×C22⋊C4×C2911yescharacteristic
271C23C2×C22⋊C4×C2911yescharacteristic
272C2×C4—24no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—24no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4C29×#12014yes—
296C8—84no—
297C22—28no—
298C22—21no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—21no—
303C22—21no—
304C22—42no—
305C22—42no—
306C22—42no—
307C22—84no—
308C22—84no—
309C22—84no—
310C22C29×#37911yescharacteristic
311C22C29×#41012yes—
312C22C29×#41312yes—
313C22C29×#41312yes—
314C4—24no—
315C4—42no—
316C4—42no—
317C4—42no—
318C4—42no—
319C4—42no—
320C2—22no—
321C2—22no—
322C2—22no—
323C2—82no—
324C2C29×#178211yescharacteristic
325C2C29×#178511yescharacteristic
326C2C29×#178511yescharacteristic
subgroupG/H
center, socleC22×C29#379
commutatorC24C22×C4×C29
Frattini, cosocleC23×C4C23×C29
prime radicalC25×C29C2×C4
LCSG ▷ C24 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C23×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#1821C2semidirect
3. C29×#1463C2semidirect
91. #8556C29direct (N × H)
135. #1821C2×C29semidirect
136. #1463C2×C29semidirect
214. C29#8556direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C29×#1262
C29×#18212
C29×#14632
C29×#14622
#855629