Finite Group Databasebeta

← C29×#9313 #20304213

Subgroups — C29×#9313 #20304213

Order 7424.

428 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3115C211yesmaximal, characteristic
2C29×#2923C211yesmaximal, characteristic, complemented
3C29×#1530C211yesmaximal, characteristic, complemented
4C29×#1488C211yesmaximal, characteristic, complemented
5C29×#1484C211yesmaximal, characteristic, complemented
6C29×#1302C211yesmaximal, characteristic, complemented
7C29×#1291C211yesmaximal, characteristic, complemented
8C29×#532C2211yescharacteristic
9C4×#41×C29C2211yescharacteristic
10C29×#482—21no—
11C29×#475C411yescharacteristic
12C29×#474C411yescharacteristic
13C29×#460C411yescharacteristic
14C29×#459C411yescharacteristic
15C29×#449—21no—
16C29×#442—21no—
17C29×#440—21no—
18C29×#433—22no—
19C29×#432—22no—
20C29×#432C2211yescharacteristic
21C29×#432C2211yescharacteristic
22C29×#431C2211yescharacteristic
23C29×#424—21no—
24C29×#408—21no—
25C4×M16×C29C2211yescharacteristic
26C2×C29×#97C2211yescharacteristic
27C29×#329—22no—
28C29×Q8⋊C8—21no—
29C29×D4⋊C8—22no—
30C29×D4⋊C8—21no—
31C2×#41×C29—21no—
32C2×#41×C29D411yescharacteristic
33C2×SD16×C29—21no—
34C2×D8×C29—21no—
35C2×M16×C29—21no—
36C22×C8×C29—21no—
37C29×C4⋊Q8C2×C411yescharacteristic
38C29×#127C2×C411yescharacteristic
39C29×#124—21no—
40C29×#121—21no—
41C29×#121—21no—
42C4×Q8×C29C2×C411yescharacteristic
43C4×Q8×C29D411yescharacteristic
44C4×D4×C29—21no—
45C4×D4×C29—21no—
46C4×D4×C29—21no—
47C4×D4×C29—21no—
48C4×D4×C29C2×C411yescharacteristic
49C4×D4×C29D411yescharacteristic
50C29×#117—21no—
51C29×#117D411yescharacteristic
52C2×C42×C29—21no—
53C2×C42×C29C2311yescharacteristic
54C29×#107—21no—
55C29×#106—21no—
56C29×C4⋊C8—24no—
57C29×C4⋊C8—21no—
58C29×C4⋊C8—21no—
59C29×C4⋊C8C2×C411yescharacteristic
60C29×C4⋊C8C2×C411yescharacteristic
61C29×#103—21no—
62C29×#102—21no—
63C29×#102—21no—
64C29×#102—21no—
65C29×C22⋊C8—24no—
66C29×C22⋊C8—21no—
67C29×C22⋊C8—21no—
68C29×C22⋊C8—21no—
69C29×#97—21no—
70C29×#97—21no—
71C29×#97—21no—
72C29×#97—21no—
73C29×#97D412yes—
74C4×C8×C29—21no—
75C4×C8×C29D412yes—
76#41×C29—41no—
77#41×C29—41no—
78#41×C29—82no—
79C2×Q8×C29—21no—
80C2×Q8×C29C22⋊C411yescharacteristic
81C2×D4×C29—21no—
82C2×D4×C29—21no—
83C2×D4×C29—21no—
84C2×D4×C29—21no—
85C2×D4×C29—41no—
86C2×D4×C29C22⋊C411yescharacteristic
87C22×C4×C29—21no—
88C22×C4×C29—21no—
89C22×C4×C29—21no—
90C22×C4×C29—41no—
91C22×C4×C29C2×D411yescharacteristic
92C22×C4×C29#4111yescharacteristic
93C22×C4×C29#4111yescharacteristic
94SD16×C29—42no—
95D8×C29—42no—
96M16×C29—41no—
97M16×C29—41no—
98C2×C8×C29—21no—
99C2×C8×C29—21no—
100C2×C8×C29—22no—
101C2×C8×C29—22no—
102C2×C8×C29—41no—
103C2×C8×C29—41no—
104C2×C8×C29—41no—
105C2×C8×C29—41no—
106C4⋊C4×C29—21no—
107C4⋊C4×C29—21no—
108C4⋊C4×C29—21no—
109C4⋊C4×C29—21no—
110C4⋊C4×C29C22⋊C411yescharacteristic
111C4⋊C4×C29C22⋊C411yescharacteristic
112C22⋊C4×C29—21no—
113C22⋊C4×C29—21no—
114C22⋊C4×C29—21no—
115C22⋊C4×C29—41no—
116C22⋊C4×C29—41no—
117C42×C29—21no—
118C42×C29—21no—
119C42×C29—21no—
120C42×C29C22×C411yescharacteristic
121C42×C29C2×D411yescharacteristic
122C42×C29C2×D411yescharacteristic
123C42×C29C2×D411yescharacteristic
124#9313C2911yesmaximal, characteristic, direct product factor, Sylow
125C23×C29—21no—
126C23×C29—41no—
127C23×C29#12311yescharacteristic
128Q8×C29—21no—
129Q8×C29—21no—
130Q8×C29—81no—
131D4×C29—21no—
132D4×C29—21no—
133D4×C29—42no—
134D4×C29—42no—
135D4×C29—41no—
136D4×C29—41no—
137D4×C29—81no—
138D4×C29—82no—
139C2×C4×C29—21no—
140C2×C4×C29—21no—
141C2×C4×C29—21no—
142C2×C4×C29—21no—
143C2×C4×C29—21no—
144C2×C4×C29—41no—
145C2×C4×C29—41no—
146C2×C4×C29—42no—
147C2×C4×C29—41no—
148C2×C4×C29—81no—
149C2×C4×C29—81no—
150C2×C4×C29—82no—
151C2×C4×C29C2×C22⋊C411yescharacteristic
152C2×C4×C29C4×D411yescharacteristic
153C2×C4×C29C4×D411yescharacteristic
154C2×C4×C29#12011yescharacteristic
155C2×C4×C29#12111yescharacteristic
156C2×C4×C29#12111yescharacteristic
157C8×C29—42no—
158C8×C29—42no—
159C8×C29—41no—
160C8×C29—41no—
161C8×C29—81no—
162C8×C29—81no—
163#3115C2×C2911yescharacteristic
164#2923C2×C2911yescharacteristic, complemented
165#1530C2×C2911yescharacteristic, complemented
166#1488C2×C2911yescharacteristic, complemented
167#1484C2×C2911yescharacteristic, complemented
168#1302C2×C2911yescharacteristic, complemented
169#1291C2×C2911yescharacteristic, complemented
170C22×C29—21no—
171C22×C29—21no—
172C22×C29—21no—
173C22×C29—41no—
174C22×C29—41no—
175C22×C29—41no—
176C22×C29—81no—
177C22×C29—81no—
178C22×C29—81no—
179C22×C29#38611yescharacteristic
180C4×C29—21no—
181C4×C29—21no—
182C4×C29—21no—
183C4×C29—21no—
184C4×C29—21no—
185C4×C29—41no—
186C4×C29—41no—
187C4×C29—41no—
188C4×C29—81no—
189C4×C29#42111yescharacteristic
190C4×C29#42111yescharacteristic
191#532C22×C2911yescharacteristic
192C4×#41C22×C2911yescharacteristic
193#482—21no—
194#475C4×C2911yescharacteristic
195#474C4×C2911yescharacteristic
196#460C4×C2911yescharacteristic
197#459C4×C2911yescharacteristic
198#449—21no—
199#442—21no—
200#440—21no—
201#433—22no—
202#432—22no—
203#432C22×C2911yescharacteristic
204#432C22×C2911yescharacteristic
205#431C22×C2911yescharacteristic
206#424—21no—
207#408—21no—
208C4×M16C22×C2911yescharacteristic
209C2×#97C22×C2911yescharacteristic
210#329—22no—
211Q8⋊C8—21no—
212D4⋊C8—21no—
213D4⋊C8—22no—
214C2×C29—41no—
215C2×C29—81no—
216C2×C29—161no—
217C2×C29#188111yescharacteristic
218C2×C29#189711yescharacteristic
219C2×C29#190311yescharacteristic
220C2×#41—21no—
221C2×#41D4×C2911yescharacteristic
222C2×SD16—21no—
223C2×D8—21no—
224C2×M16—21no—
225C22×C8—21no—
226C4⋊Q8C2×C4×C2911yescharacteristic
227#127C2×C4×C2911yescharacteristic
228#124—21no—
229#121—21no—
230#121—21no—
231C4×Q8C2×C4×C2911yescharacteristic
232C4×Q8D4×C2911yescharacteristic
233C4×D4—21no—
234C4×D4—21no—
235C4×D4—21no—
236C4×D4—21no—
237C4×D4C2×C4×C2911yescharacteristic
238C4×D4D4×C2911yescharacteristic
239#117—21no—
240#117D4×C2911yescharacteristic
241C2×C42—21no—
242C2×C42C23×C2911yescharacteristic
243#107—21no—
244#106—21no—
245C4⋊C8—24no—
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8C2×C4×C2911yescharacteristic
249C4⋊C8C2×C4×C2911yescharacteristic
250#103—21no—
251#102—21no—
252#102—21no—
253#102—21no—
254C22⋊C8—24no—
255C22⋊C8—21no—
256C22⋊C8—21no—
257C22⋊C8—21no—
258#97—21no—
259#97—21no—
260#97—21no—
261#97—21no—
262#97D4×C2912yes—
263C4×C8—21no—
264C4×C8D4×C2912yes—
265C29#931311yescharacteristic, direct product factor, Sylow
266#41—41no—
267#41—41no—
268#41—82no—
269C2×Q8—21no—
270C2×Q8C22⋊C4×C2911yescharacteristic
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4—41no—
276C2×D4C22⋊C4×C2911yescharacteristic
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—41no—
281C22×C4C2×D4×C2911yescharacteristic
282C22×C4#41×C2911yescharacteristic
283C22×C4#41×C2911yescharacteristic
284SD16—42no—
285D8—42no—
286M16—41no—
287M16—41no—
288C2×C8—21no—
289C2×C8—21no—
290C2×C8—22no—
291C2×C8—22no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8—41no—
295C2×C8—41no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4C22⋊C4×C2911yescharacteristic
301C4⋊C4C22⋊C4×C2911yescharacteristic
302C22⋊C4—21no—
303C22⋊C4—21no—
304C22⋊C4—21no—
305C22⋊C4—41no—
306C22⋊C4—41no—
307C42—21no—
308C42—21no—
309C42—21no—
310C42C22×C4×C2911yescharacteristic
311C42C2×D4×C2911yescharacteristic
312C42C2×D4×C2911yescharacteristic
313C42C2×D4×C2911yescharacteristic
314C23—21no—
315C23—41no—
316C23C29×#12311yescharacteristic
317Q8—21no—
318Q8—21no—
319Q8—81no—
320D4—21no—
321D4—21no—
322D4—42no—
323D4—42no—
324D4—41no—
325D4—41no—
326D4—81no—
327D4—82no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—42no—
336C2×C4—41no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—82no—
340C2×C4C2×C22⋊C4×C2911yescharacteristic
341C2×C4C4×D4×C2911yescharacteristic
342C2×C4C4×D4×C2911yescharacteristic
343C2×C4C29×#12011yescharacteristic
344C2×C4C29×#12111yescharacteristic
345C2×C4C29×#12111yescharacteristic
346C8—42no—
347C8—42no—
348C8—41no—
349C8—41no—
350C8—81no—
351C8—81no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—81no—
359C22—81no—
360C22—81no—
361C22C29×#38611yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—21no—
367C4—41no—
368C4—41no—
369C4—41no—
370C4—81no—
371C4C29×#42111yescharacteristic
372C4C29×#42111yescharacteristic
373C2—41no—
374C2—81no—
375C2—161no—
376C2C29×#188111yescharacteristic
377C2C29×#189711yescharacteristic
378C2C29×#190311yescharacteristic
subgroupG/H
center, socleC22×C29#386
commutatorC42C22×C4×C29
Frattini, cosocleC2×C42C23×C29
prime radicalC29×#3115C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C2×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#2923C2semidirect
3. C29×#1530C2semidirect
4. C29×#1488C2semidirect
5. C29×#1484C2semidirect
6. C29×#1302C2semidirect
7. C29×#1291C2semidirect
124. #9313C29direct (N × H)
164. #2923C2×C29semidirect
165. #1530C2×C29semidirect
166. #1488C2×C29semidirect
167. #1484C2×C29semidirect
168. #1302C2×C29semidirect
169. #1291C2×C29semidirect
265. C29#9313direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#31152
C29×#29232
C29×#15302
C29×#14882
C29×#14842
C29×#13022
C29×#12912
#931329