Finite Group Databasebeta

← C29×#17673 #20312573

Subgroups — C29×#17673 #20312573

Order 7424.

972 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3444C211yesmaximal, characteristic
2C29×#2920C212yesmaximal, complemented
3C29×#1537C212yesmaximal, complemented
4C29×#1536C212yesmaximal, complemented
5C29×#1529C218yesmaximal, complemented
6C29×#533C412yes—
7C29×#533C2211yescharacteristic
8C29×#532C412yes—
9C29×#532C2211yescharacteristic
10C29×#529—22no—
11C29×#529—22no—
12C29×#529C2214yes—
13C29×#525—22no—
14C29×#525C412yes—
15C4×#41×C29—22no—
16C4×#41×C29C412yes—
17C22×C42×C29C2211yescharacteristic
18C29×#432C2214yes—
19C29×#432C2214yes—
20C29×#431—22no—
21C29×#431—22no—
22C29×#423—22no—
23C29×#407—22no—
24C4×M16×C29C2214yes—
25C29×#330C2218yescomplemented
26C29×#329C2218yescomplemented
27C2×#41×C29—22no—
28C2×#41×C29C2×C412yes—
29C23×C4×C29C2×C411yescharacteristic
30C23×C4×C29D412yes—
31C2×M16×C29—24no—
32C29×C4⋊Q8C2×C411yescharacteristic
33C29×C4⋊Q8C2×C412yes—
34C29×#127C2×C411yescharacteristic
35C29×#126—24no—
36C29×#125—22no—
37C29×#125C2312yes—
38C29×#124—22no—
39C29×#124C2312yes—
40C29×#123—22no—
41C29×#123—24no—
42C29×C22⋊Q8—22no—
43C29×C22⋊Q8—22no—
44C29×C22⋊Q8C2×C414yes—
45C29×#121—22no—
46C29×#121—22no—
47C29×#121C2×C414yes—
48C29×#120—22no—
49C4×Q8×C29—22no—
50C4×Q8×C29—22no—
51C4×Q8×C29C2×C414yes—
52C4×D4×C29—24no—
53C4×D4×C29—24no—
54C4×D4×C29—24no—
55C4×D4×C29—22no—
56C4×D4×C29—22no—
57C4×D4×C29C2×C414yes—
58C29×#117—22no—
59C29×#117—22no—
60C29×#117—24no—
61C29×#117C2×C412yes—
62C2×C42×C29—22no—
63C2×C42×C29C2×C411yescharacteristic
64C2×C42×C29C2×C412yes—
65C2×C42×C29D412yes—
66C2×C42×C29D412yes—
67C2×C42×C29D412yes—
68C2×C42×C29C2311yescharacteristic
69C2×C42×C29C2312yes—
70C29×C4⋊C8—24no—
71C29×C4⋊C8—24no—
72C29×C22⋊C8—24no—
73C29×C22⋊C8—24no—
74C29×#97C2318yes—
75C4×C8×C29—24no—
76C24×C29C22⋊C411yescharacteristic
77#41×C29—48no—
78#41×C29—44no—
79C2×Q8×C29—22no—
80C2×Q8×C29C22×C412yes—
81C2×D4×C29—22no—
82C2×D4×C29—24no—
83C2×D4×C29—22no—
84C2×D4×C29C22×C412yes—
85C22×C4×C29—22no—
86C22×C4×C29—24no—
87C22×C4×C29—42no—
88C22×C4×C29—44no—
89C22×C4×C29C22⋊C412yes—
90C22×C4×C29C22⋊C412yes—
91C22×C4×C29C22⋊C412yes—
92C22×C4×C29C22⋊C412yes—
93C22×C4×C29C22⋊C411yescharacteristic
94C22×C4×C29C22×C411yescharacteristic
95C22×C4×C29C22×C412yes—
96C22×C4×C29C2×D412yes—
97C22×C4×C29C2×D412yes—
98C22×C4×C29C2×D412yes—
99M16×C29—48no—
100C2×C8×C29—28no—
101C4⋊C4×C29—22no—
102C4⋊C4×C29—22no—
103C4⋊C4×C29—24no—
104C4⋊C4×C29—24no—
105C4⋊C4×C29—24no—
106C4⋊C4×C29C22×C414yes—
107C22⋊C4×C29—24no—
108C22⋊C4×C29—22no—
109C22⋊C4×C29—24no—
110C22⋊C4×C29—24no—
111C22⋊C4×C29—24no—
112C42×C29—24no—
113C42×C29—22no—
114C42×C29C22⋊C411yescharacteristic
115C42×C29C22⋊C411yescharacteristic
116C42×C29C22⋊C412yes—
117C42×C29C22⋊C412yes—
118C42×C29C22×C412yes—
119C42×C29C22×C411yescharacteristic
120C42×C29C2×D412yes—
121C42×C29C2×D412yes—
122C42×C29C2×D412yes—
123C42×C29C2411yescharacteristic
124#17673C2911yesmaximal, characteristic, direct product factor, Sylow
125C23×C29—22no—
126C23×C29—41no—
127C23×C29—42no—
128C23×C29C2×C22⋊C411yescharacteristic
129C23×C29C2×C22⋊C412yes—
130Q8×C29—42no—
131Q8×C29—44no—
132D4×C29—42no—
133D4×C29—44no—
134D4×C29—44no—
135D4×C29—48no—
136C2×C4×C29—24no—
137C2×C4×C29—22no—
138C2×C4×C29—24no—
139C2×C4×C29—24no—
140C2×C4×C29—24no—
141C2×C4×C29—22no—
142C2×C4×C29—24no—
143C2×C4×C29—41no—
144C2×C4×C29—42no—
145C2×C4×C29—42no—
146C2×C4×C29—42no—
147C2×C4×C29—42no—
148C2×C4×C29—44no—
149C2×C4×C29—48no—
150C2×C4×C29C2×C22⋊C412yes—
151C2×C4×C29C2×C22⋊C412yes—
152C2×C4×C29C2×C22⋊C412yes—
153C2×C4×C29C2×C22⋊C411yescharacteristic
154C2×C4×C29C2×C22⋊C412yes—
155C2×C4×C29C23×C411yescharacteristic
156C2×C4×C29C22×D412yes—
157C8×C29—48no—
158#3444C2×C2911yescharacteristic
159#2920C2×C2912yescomplemented
160#1537C2×C2912yescomplemented
161#1536C2×C2912yescomplemented
162#1529C2×C2918yescomplemented
163C22×C29—21no—
164C22×C29—22no—
165C22×C29—22no—
166C22×C29—22no—
167C22×C29—22no—
168C22×C29—44no—
169C22×C29—42no—
170C22×C29—44no—
171C22×C29C22×C22⋊C411yescharacteristic
172C4×C29—22no—
173C4×C29—21no—
174C4×C29—22no—
175C4×C29—22no—
176C4×C29—22no—
177C4×C29—42no—
178C4×C29—44no—
179C4×C29#41312yes—
180C4×C29#42114yes—
181#533C4×C2912yes—
182#533C22×C2911yescharacteristic
183#532C4×C2912yes—
184#532C22×C2911yescharacteristic
185#529—22no—
186#529—22no—
187#529C22×C2914yes—
188#525—22no—
189#525C4×C2912yes—
190C4×#41—22no—
191C4×#41C4×C2912yes—
192C22×C42C22×C2911yescharacteristic
193#432C22×C2914yes—
194#432C22×C2914yes—
195#431—22no—
196#431—22no—
197#423—22no—
198#407—22no—
199C4×M16C22×C2914yes—
200#330C22×C2918yescomplemented
201#329C22×C2918yescomplemented
202C2×C29—41no—
203C2×C29—42no—
204C2×C29—82no—
205C2×C29C2×#41311yescharacteristic
206C2×C29C2×#42112yes—
207C2×#41—22no—
208C2×#41C2×C4×C2912yes—
209C23×C4C2×C4×C2911yescharacteristic
210C23×C4D4×C2912yes—
211C2×M16—24no—
212C4⋊Q8C2×C4×C2911yescharacteristic
213C4⋊Q8C2×C4×C2912yes—
214#127C2×C4×C2911yescharacteristic
215#126—24no—
216#125—22no—
217#125C23×C2912yes—
218#124—22no—
219#124C23×C2912yes—
220#123—22no—
221#123—24no—
222C22⋊Q8—22no—
223C22⋊Q8—22no—
224C22⋊Q8C2×C4×C2914yes—
225#121—22no—
226#121—22no—
227#121C2×C4×C2914yes—
228#120—22no—
229C4×Q8—22no—
230C4×Q8—22no—
231C4×Q8C2×C4×C2914yes—
232C4×D4—24no—
233C4×D4—24no—
234C4×D4—24no—
235C4×D4—22no—
236C4×D4—22no—
237C4×D4C2×C4×C2914yes—
238#117—22no—
239#117—22no—
240#117—24no—
241#117C2×C4×C2912yes—
242C2×C42—22no—
243C2×C42C2×C4×C2911yescharacteristic
244C2×C42C2×C4×C2912yes—
245C2×C42D4×C2912yes—
246C2×C42D4×C2912yes—
247C2×C42D4×C2912yes—
248C2×C42C23×C2912yes—
249C2×C42C23×C2911yescharacteristic
250C4⋊C8—24no—
251C4⋊C8—24no—
252C22⋊C8—24no—
253C22⋊C8—24no—
254#97C23×C2918yes—
255C4×C8—24no—
256C29#1767311yescharacteristic, direct product factor, Sylow
257C24C22⋊C4×C2911yescharacteristic
258#41—48no—
259#41—44no—
260C2×Q8—22no—
261C2×Q8C22×C4×C2912yes—
262C2×D4—22no—
263C2×D4—24no—
264C2×D4—22no—
265C2×D4C22×C4×C2912yes—
266C22×C4—22no—
267C22×C4—24no—
268C22×C4—42no—
269C22×C4—44no—
270C22×C4C22⋊C4×C2912yes—
271C22×C4C22⋊C4×C2912yes—
272C22×C4C22⋊C4×C2912yes—
273C22×C4C22⋊C4×C2912yes—
274C22×C4C22⋊C4×C2911yescharacteristic
275C22×C4C22×C4×C2911yescharacteristic
276C22×C4C22×C4×C2912yes—
277C22×C4C2×D4×C2912yes—
278C22×C4C2×D4×C2912yes—
279C22×C4C2×D4×C2912yes—
280M16—48no—
281C2×C8—28no—
282C4⋊C4—22no—
283C4⋊C4—22no—
284C4⋊C4—24no—
285C4⋊C4—24no—
286C4⋊C4—24no—
287C4⋊C4C22×C4×C2914yes—
288C22⋊C4—24no—
289C22⋊C4—22no—
290C22⋊C4—24no—
291C22⋊C4—24no—
292C22⋊C4—24no—
293C42—24no—
294C42—22no—
295C42C22⋊C4×C2911yescharacteristic
296C42C22⋊C4×C2911yescharacteristic
297C42C22⋊C4×C2912yes—
298C42C22⋊C4×C2912yes—
299C42C22×C4×C2912yes—
300C42C22×C4×C2911yescharacteristic
301C42C2×D4×C2912yes—
302C42C2×D4×C2912yes—
303C42C2×D4×C2912yes—
304C42C24×C2911yescharacteristic
305C23—22no—
306C23—41no—
307C23—42no—
308C23C2×C22⋊C4×C2911yescharacteristic
309C23C2×C22⋊C4×C2912yes—
310Q8—42no—
311Q8—44no—
312D4—42no—
313D4—44no—
314D4—44no—
315D4—48no—
316C2×C4—24no—
317C2×C4—22no—
318C2×C4—24no—
319C2×C4—24no—
320C2×C4—24no—
321C2×C4—22no—
322C2×C4—24no—
323C2×C4—41no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—44no—
329C2×C4—48no—
330C2×C4C2×C22⋊C4×C2912yes—
331C2×C4C2×C22⋊C4×C2912yes—
332C2×C4C2×C22⋊C4×C2912yes—
333C2×C4C2×C22⋊C4×C2911yescharacteristic
334C2×C4C2×C22⋊C4×C2912yes—
335C2×C4C23×C4×C2911yescharacteristic
336C2×C4C22×D4×C2912yes—
337C8—48no—
338C22—21no—
339C22—22no—
340C22—22no—
341C22—22no—
342C22—22no—
343C22—44no—
344C22—42no—
345C22—44no—
346C22C22×C22⋊C4×C2911yescharacteristic
347C4—22no—
348C4—21no—
349C4—22no—
350C4—22no—
351C4—22no—
352C4—42no—
353C4—44no—
354C4C29×#41312yes—
355C4C29×#42114yes—
356C2—41no—
357C2—42no—
358C2—82no—
359C2C2×C29×#41311yescharacteristic
360C2C2×C29×#42112yes—
subgroupG/H
center, socleC22×C29C22×C22⋊C4
commutatorC2×C4C23×C4×C29
Frattini, cosocleC42C24×C29
prime radicalC29×#3444C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C22×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#2920C2semidirect
3. C29×#1537C2semidirect
4. C29×#1536C2semidirect
5. C29×#1529C2semidirect
25. C29×#330C22semidirect
26. C29×#329C22semidirect
124. #17673C29direct (N × H)
159. #2920C2×C29semidirect
160. #1537C2×C29semidirect
161. #1536C2×C29semidirect
162. #1529C2×C29semidirect
200. #330C22×C29semidirect
201. #329C22×C29semidirect
256. C29#17673direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#34442
C29×#29202
C29×#15372
C29×#15362
C29×#15292
#1767329