Finite Group Databasebeta

← C29×#9766 #20304666

Subgroups — C29×#9766 #20304666

Order 7424.

396 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3167C211yesmaximal, characteristic
2C29×#1746C211yesmaximal, characteristic, complemented
3C29×#1568C211yesmaximal, characteristic, complemented
4C29×#1531C211yesmaximal, characteristic, complemented
5C29×#1530C211yesmaximal, characteristic
6C29×#1506C211yesmaximal, characteristic, complemented
7C29×#1505C211yesmaximal, characteristic
8C29×#533C2211yescharacteristic
9C29×#532C2211yescharacteristic
10C29×#498C411yescharacteristic, complemented
11C29×#492C411yescharacteristic, complemented
12C29×#487C411yescharacteristic, complemented
13C29×#486C411yescharacteristic, complemented
14C29×#465—21no—
15C29×#465—21no—
16C4×SD16×C29—21no—
17C4×SD16×C29—21no—
18C29×#432C2211yescharacteristic
19C29×#432C2211yescharacteristic
20C2×C29×#97C2211yescharacteristic
21C2×C4×C8×C29C2211yescharacteristic
22C29×#376C2211yescharacteristic
23C29×#336—21no—
24C29×#336—21no—
25C29×#335—21no—
26C29×#334—21no—
27C29×#330—22no—
28C29×#329—22no—
29C29×#328—22no—
30C29×#327—22no—
31C2×#41×C29—21no—
32C2×SD16×C29—21no—
33C2×SD16×C29—21no—
34C22×C8×C29—21no—
35C22×C8×C29D411yescharacteristic
36C22×C8×C29D411yescharacteristic
37C29×C4⋊Q8C2×C411yescharacteristic
38C29×C4⋊Q8C2×C411yescharacteristic
39C29×C4⋊Q8C2×C411yescharacteristic
40C29×#127C2×C411yescharacteristic
41C29×#125—21no—
42C29×#124—21no—
43C29×C22⋊Q8—21no—
44C29×C22⋊Q8—21no—
45C29×#121—21no—
46C29×#121—21no—
47C4×Q8×C29—21no—
48C4×Q8×C29—21no—
49C4×D4×C29—21no—
50C4×D4×C29—21no—
51C29×#117—21no—
52C2×C42×C29—21no—
53C2×C42×C29C2311yescharacteristic
54C29×#106—21no—
55C29×#106—21no—
56C29×C4⋊C8—21no—
57C29×C4⋊C8—21no—
58C29×#103—21no—
59C29×#103—21no—
60C29×#102—21no—
61C29×#102—21no—
62C29×C22⋊C8—21no—
63C29×C22⋊C8—21no—
64C29×#97—21no—
65C29×#97—21no—
66C29×#97—21no—
67C29×#97D412yes—
68C4×C8×C29C2×C411yescharacteristic
69C4×C8×C29C2×C411yescharacteristic
70C4×C8×C29D411yescharacteristic
71C4×C8×C29D411yescharacteristic
72C29×#95—21no—
73C29×#95D412yes—
74#41×C29—82no—
75C2×Q8×C29—21no—
76C2×Q8×C29—21no—
77C2×Q8×C29—21no—
78C2×D4×C29—21no—
79C2×D4×C29—21no—
80C2×D4×C29—21no—
81C2×D4×C29—41no—
82C22×C4×C29—22no—
83C22×C4×C29—41no—
84C22×C4×C29C2×D411yescharacteristic
85C22×C4×C29C2×D411yescharacteristic
86C22×C4×C29#4111yescharacteristic
87SD16×C29—42no—
88SD16×C29—42no—
89C2×C8×C29—22no—
90C2×C8×C29—41no—
91C2×C8×C29—41no—
92C2×C8×C29—41no—
93C2×C8×C29—41no—
94C2×C8×C29—41no—
95C2×C8×C29—41no—
96C2×C8×C29C22⋊C411yescharacteristic
97C2×C8×C29C22⋊C411yescharacteristic
98C2×C8×C29C22⋊C411yescharacteristic
99C2×C8×C29C22⋊C411yescharacteristic
100C4⋊C4×C29—21no—
101C4⋊C4×C29—21no—
102C4⋊C4×C29—21no—
103C4⋊C4×C29—21no—
104C4⋊C4×C29—21no—
105C4⋊C4×C29—21no—
106C4⋊C4×C29—41no—
107C4⋊C4×C29—41no—
108C22⋊C4×C29—41no—
109C22⋊C4×C29—41no—
110C22⋊C4×C29—41no—
111C42×C29—41no—
112C42×C29—41no—
113C42×C29—41no—
114C42×C29C22×C411yescharacteristic
115C42×C29C2×D411yescharacteristic
116C42×C29C2×D411yescharacteristic
117C42×C29#4111yescharacteristic
118#9766C2911yesmaximal, characteristic, direct product factor, Sylow
119C23×C29—41no—
120C23×C29#12111yescharacteristic
121Q8×C29—41no—
122Q8×C29—41no—
123Q8×C29—81no—
124Q8×C29—81no—
125D4×C29—41no—
126D4×C29—41no—
127D4×C29—81no—
128D4×C29—81no—
129D4×C29—82no—
130C2×C4×C29—22no—
131C2×C4×C29—21no—
132C2×C4×C29—21no—
133C2×C4×C29—41no—
134C2×C4×C29—42no—
135C2×C4×C29—42no—
136C2×C4×C29—41no—
137C2×C4×C29—41no—
138C2×C4×C29—41no—
139C2×C4×C29—42no—
140C2×C4×C29—82no—
141C2×C4×C29C2×C22⋊C411yescharacteristic
142C2×C4×C29C4×D411yescharacteristic
143C2×C4×C29C4×D411yescharacteristic
144C2×C4×C29#12111yescharacteristic
145C2×C4×C29#12411yescharacteristic
146C2×C4×C29#12711yescharacteristic
147C8×C29—21no—
148C8×C29—21no—
149C8×C29—21no—
150C8×C29—21no—
151C8×C29—42no—
152C8×C29—81no—
153C8×C29—81no—
154#3167C2×C2911yescharacteristic
155#1746C2×C2911yescharacteristic, complemented
156#1568C2×C2911yescharacteristic, complemented
157#1531C2×C2911yescharacteristic, complemented
158#1530C2×C2911yescharacteristic
159#1506C2×C2911yescharacteristic, complemented
160#1505C2×C2911yescharacteristic
161C22×C29—21no—
162C22×C29—21no—
163C22×C29—81no—
164C22×C29—81no—
165C22×C29—81no—
166C22×C29#39011yescharacteristic
167C22×C29#47112yes—
168C4×C29—21no—
169C4×C29—21no—
170C4×C29—21no—
171C4×C29—21no—
172C4×C29—21no—
173C4×C29—82no—
174C4×C29—81no—
175C4×C29—81no—
176C4×C29—81no—
177C4×C29#42111yescharacteristic
178C4×C29#42111yescharacteristic
179#533C22×C2911yescharacteristic
180#532C22×C2911yescharacteristic
181#498C4×C2911yescharacteristic, complemented
182#492C4×C2911yescharacteristic, complemented
183#487C4×C2911yescharacteristic, complemented
184#486C4×C2911yescharacteristic, complemented
185#465—21no—
186#465—21no—
187C4×SD16—21no—
188C4×SD16—21no—
189#432C22×C2911yescharacteristic
190#432C22×C2911yescharacteristic
191C2×#97C22×C2911yescharacteristic
192C2×C4×C8C22×C2911yescharacteristic
193#376C22×C2911yescharacteristic
194#336—21no—
195#336—21no—
196#335—21no—
197#334—21no—
198#330—22no—
199#329—22no—
200#328—22no—
201#327—22no—
202C2×C29—22no—
203C2×C29—161no—
204C2×C29#196311yescharacteristic
205C2×C29#197611yescharacteristic
206C2×C29#197711yescharacteristic
207C2×#41—21no—
208C2×SD16—21no—
209C2×SD16—21no—
210C22×C8—21no—
211C22×C8D4×C2911yescharacteristic
212C22×C8D4×C2911yescharacteristic
213C4⋊Q8C2×C4×C2911yescharacteristic
214C4⋊Q8C2×C4×C2911yescharacteristic
215C4⋊Q8C2×C4×C2911yescharacteristic
216#127C2×C4×C2911yescharacteristic
217#125—21no—
218#124—21no—
219C22⋊Q8—21no—
220C22⋊Q8—21no—
221#121—21no—
222#121—21no—
223C4×Q8—21no—
224C4×Q8—21no—
225C4×D4—21no—
226C4×D4—21no—
227#117—21no—
228C2×C42—21no—
229C2×C42C23×C2911yescharacteristic
230#106—21no—
231#106—21no—
232C4⋊C8—21no—
233C4⋊C8—21no—
234#103—21no—
235#103—21no—
236#102—21no—
237#102—21no—
238C22⋊C8—21no—
239C22⋊C8—21no—
240#97—21no—
241#97—21no—
242#97—21no—
243#97D4×C2912yes—
244C4×C8C2×C4×C2911yescharacteristic
245C4×C8C2×C4×C2911yescharacteristic
246C4×C8D4×C2911yescharacteristic
247C4×C8D4×C2911yescharacteristic
248#95—21no—
249#95D4×C2912yes—
250C29#976611yescharacteristic, direct product factor, Sylow
251#41—82no—
252C2×Q8—21no—
253C2×Q8—21no—
254C2×Q8—21no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—41no—
259C22×C4—22no—
260C22×C4—41no—
261C22×C4C2×D4×C2911yescharacteristic
262C22×C4C2×D4×C2911yescharacteristic
263C22×C4#41×C2911yescharacteristic
264SD16—42no—
265SD16—42no—
266C2×C8—22no—
267C2×C8—41no—
268C2×C8—41no—
269C2×C8—41no—
270C2×C8—41no—
271C2×C8—41no—
272C2×C8—41no—
273C2×C8C22⋊C4×C2911yescharacteristic
274C2×C8C22⋊C4×C2911yescharacteristic
275C2×C8C22⋊C4×C2911yescharacteristic
276C2×C8C22⋊C4×C2911yescharacteristic
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C22⋊C4—41no—
288C42—41no—
289C42—41no—
290C42—41no—
291C42C22×C4×C2911yescharacteristic
292C42C2×D4×C2911yescharacteristic
293C42C2×D4×C2911yescharacteristic
294C42#41×C2911yescharacteristic
295C23—41no—
296C23C29×#12111yescharacteristic
297Q8—41no—
298Q8—41no—
299Q8—81no—
300Q8—81no—
301D4—41no—
302D4—41no—
303D4—81no—
304D4—81no—
305D4—82no—
306C2×C4—22no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—41no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—82no—
317C2×C4C2×C22⋊C4×C2911yescharacteristic
318C2×C4C4×D4×C2911yescharacteristic
319C2×C4C4×D4×C2911yescharacteristic
320C2×C4C29×#12111yescharacteristic
321C2×C4C29×#12411yescharacteristic
322C2×C4C29×#12711yescharacteristic
323C8—21no—
324C8—21no—
325C8—21no—
326C8—21no—
327C8—42no—
328C8—81no—
329C8—81no—
330C22—21no—
331C22—21no—
332C22—81no—
333C22—81no—
334C22—81no—
335C22C29×#39011yescharacteristic
336C22C29×#47112yes—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—82no—
343C4—81no—
344C4—81no—
345C4—81no—
346C4C29×#42111yescharacteristic
347C4C29×#42111yescharacteristic
348C2—22no—
349C2—161no—
350C2C29×#196311yescharacteristic
351C2C29×#197611yescharacteristic
352C2C29×#197711yescharacteristic
subgroupG/H
center, socleC22×C29#390
commutatorC42C22×C4×C29
Frattini, cosocleC2×C42C23×C29
prime radicalC29×#532C22
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×#1746C2semidirect
3. C29×#1568C2semidirect
4. C29×#1531C2semidirect
6. C29×#1506C2semidirect
10. C29×#498C4semidirect
11. C29×#492C4semidirect
12. C29×#487C4semidirect
13. C29×#486C4semidirect
118. #9766C29direct (N × H)
155. #1746C2×C29semidirect
156. #1568C2×C29semidirect
157. #1531C2×C29semidirect
159. #1506C2×C29semidirect
181. #498C4×C29semidirect
182. #492C4×C29semidirect
183. #487C4×C29semidirect
184. #486C4×C29semidirect
250. C29#9766direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#31672
C29×#17462
C29×#15682
C29×#15312
C29×#15302
C29×#15062
C29×#15052
#976629