Finite Group Databasebeta

← C29×#9352 #20304252

Subgroups — C29×#9352 #20304252

Order 7424.

414 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3080C211yesmaximal, characteristic
2C29×#2971C211yesmaximal, characteristic
3C29×#1528C211yesmaximal, characteristic, complemented
4C29×#1488C211yesmaximal, characteristic
5C29×#1470C211yesmaximal, characteristic, complemented
6C29×#1307C211yesmaximal, characteristic, complemented
7C29×#1299C211yesmaximal, characteristic, complemented
8C2×C29×#125C2211yescharacteristic
9C4×#41×C29C2211yescharacteristic
10C29×#479—21no—
11C29×#479—21no—
12C29×#478—21no—
13C29×#478—21no—
14C8×Q8×C29—21no—
15C29×#436—22no—
16C29×#436—21no—
17C29×#432—21no—
18C29×#432C2211yescharacteristic
19C29×#432C2211yescharacteristic
20C29×#431C2211yescharacteristic
21C29×#428C411yescharacteristic
22C29×#428C411yescharacteristic
23C29×#423C2211yescharacteristic
24C29×#417C411yescharacteristic
25C29×#417C411yescharacteristic
26C4×M16×C29—21no—
27C4×M16×C29C2211yescharacteristic
28C29×#330—21no—
29C29×#330—21no—
30C29×Q8⋊C8—21no—
31C29×D4⋊C8—21no—
32C29×#324—22no—
33C2×#41×C29C2×C411yescharacteristic
34C2×M16×C29—22no—
35C2×M16×C29—21no—
36C2×M16×C29C2×C411yescharacteristic
37C2×M16×C29C2×C411yescharacteristic
38C29×#125—21no—
39C29×#125—21no—
40C29×#125—21no—
41C29×#125—21no—
42C4×Q8×C29D411yescharacteristic
43C4×Q8×C29D411yescharacteristic
44C4×D4×C29—21no—
45C4×D4×C29—21no—
46C4×D4×C29D411yescharacteristic
47C4×D4×C29D411yescharacteristic
48C29×#117—21no—
49C29×#117C2×C411yescharacteristic
50C2×C4⋊C4×C29—21no—
51C2×C4⋊C4×C29—21no—
52C2×C4⋊C4×C29C2×C411yescharacteristic
53C2×C4⋊C4×C29C2×C411yescharacteristic
54C2×C42×C29—21no—
55C2×C42×C29C2311yescharacteristic
56C29×#107—21no—
57C29×#107—21no—
58C29×#106—21no—
59C29×#106—21no—
60C29×C4⋊C8—22no—
61C29×C4⋊C8—21no—
62C29×C4⋊C8—21no—
63C29×C4⋊C8—21no—
64C29×C4⋊C8—21no—
65C29×C4⋊C8—21no—
66C29×#103—21no—
67C29×#103—21no—
68C29×#102—21no—
69C29×#102—21no—
70C29×C22⋊C8—22no—
71C29×C22⋊C8—21no—
72C29×C22⋊C8—21no—
73C29×C22⋊C8D412yes—
74C29×#97—21no—
75C29×#97—21no—
76C29×#97D411yescharacteristic
77C29×#97D411yescharacteristic
78C4×C8×C29—22no—
79C4×C8×C29—21no—
80C4×C8×C29—21no—
81#41×C29—22no—
82#41×C29—41no—
83C2×Q8×C29C22⋊C411yescharacteristic
84C2×D4×C29—21no—
85C2×D4×C29C22⋊C411yescharacteristic
86C22×C4×C29—21no—
87C22×C4×C29—21no—
88C22×C4×C29—21no—
89C22×C4×C29—21no—
90C22×C4×C29—21no—
91C22×C4×C29C22×C411yescharacteristic
92C22×C4×C29C2×D411yescharacteristic
93C22×C4×C29#4111yescharacteristic
94M16×C29—42no—
95M16×C29—44no—
96M16×C29—41no—
97M16×C29—41no—
98C2×C8×C29—21no—
99C2×C8×C29—21no—
100C2×C8×C29—21no—
101C2×C8×C29—22no—
102C2×C8×C29—21no—
103C2×C8×C29—41no—
104C2×C8×C29—41no—
105C4⋊C4×C29—21no—
106C4⋊C4×C29—21no—
107C4⋊C4×C29—21no—
108C4⋊C4×C29—21no—
109C4⋊C4×C29—21no—
110C4⋊C4×C29—21no—
111C4⋊C4×C29—41no—
112C4⋊C4×C29—41no—
113C4⋊C4×C29—41no—
114C4⋊C4×C29—41no—
115C4⋊C4×C29C22⋊C411yescharacteristic
116C4⋊C4×C29C22⋊C411yescharacteristic
117C22⋊C4×C29—21no—
118C22⋊C4×C29—21no—
119C22⋊C4×C29—21no—
120C42×C29—21no—
121C42×C29—21no—
122C42×C29—21no—
123C42×C29C2×D411yescharacteristic
124C42×C29C2×D411yescharacteristic
125C42×C29C2×D411yescharacteristic
126C42×C29#4111yescharacteristic
127#9352C2911yesmaximal, characteristic, direct product factor, Sylow
128C23×C29—21no—
129C23×C29C4×D411yescharacteristic
130Q8×C29—21no—
131Q8×C29#10112yes—
132D4×C29—21no—
133D4×C29—21no—
134D4×C29—42no—
135C2×C4×C29—21no—
136C2×C4×C29—21no—
137C2×C4×C29—21no—
138C2×C4×C29—21no—
139C2×C4×C29—21no—
140C2×C4×C29—41no—
141C2×C4×C29—41no—
142C2×C4×C29—42no—
143C2×C4×C29—42no—
144C2×C4×C29—42no—
145C2×C4×C29—41no—
146C2×C4×C29—41no—
147C2×C4×C29—81no—
148C2×C4×C29—81no—
149C2×C4×C29C2×C22⋊C411yescharacteristic
150C2×C4×C29C4×D411yescharacteristic
151C2×C4×C29#12011yescharacteristic
152C2×C4×C29#12111yescharacteristic
153C2×C4×C29#12111yescharacteristic
154C2×C4×C29#12311yescharacteristic
155C8×C29—22no—
156C8×C29—42no—
157C8×C29—41no—
158C8×C29—41no—
159C8×C29—41no—
160C8×C29—81no—
161C8×C29—81no—
162#3080C2×C2911yescharacteristic
163#2971C2×C2911yescharacteristic
164#1528C2×C2911yescharacteristic, complemented
165#1488C2×C2911yescharacteristic
166#1470C2×C2911yescharacteristic, complemented
167#1307C2×C2911yescharacteristic, complemented
168#1299C2×C2911yescharacteristic, complemented
169C22×C29—21no—
170C22×C29—21no—
171C22×C29—21no—
172C22×C29—41no—
173C22×C29—41no—
174C22×C29—41no—
175C22×C29#38611yescharacteristic
176C4×C29—21no—
177C4×C29—21no—
178C4×C29—21no—
179C4×C29—22no—
180C4×C29—21no—
181C4×C29—21no—
182C4×C29—41no—
183C4×C29—41no—
184C4×C29—81no—
185C4×C29—81no—
186C4×C29C2×#10111yescharacteristic
187C4×C29#41311yescharacteristic
188C2×#125C22×C2911yescharacteristic
189C4×#41C22×C2911yescharacteristic
190#479—21no—
191#479—21no—
192#478—21no—
193#478—21no—
194C8×Q8—21no—
195#436—21no—
196#436—22no—
197#432—21no—
198#432C22×C2911yescharacteristic
199#432C22×C2911yescharacteristic
200#431C22×C2911yescharacteristic
201#428C4×C2911yescharacteristic
202#428C4×C2911yescharacteristic
203#423C22×C2911yescharacteristic
204#417C4×C2911yescharacteristic
205#417C4×C2911yescharacteristic
206C4×M16—21no—
207C4×M16C22×C2911yescharacteristic
208#330—21no—
209#330—21no—
210Q8⋊C8—21no—
211D4⋊C8—21no—
212#324—22no—
213C2×C29—41no—
214C2×C29—81no—
215C2×C29#188111yescharacteristic
216C2×C29#190111yescharacteristic
217C2×C29#190611yescharacteristic
218C2×#41C2×C4×C2911yescharacteristic
219C2×M16—22no—
220C2×M16—21no—
221C2×M16C2×C4×C2911yescharacteristic
222C2×M16C2×C4×C2911yescharacteristic
223#125—21no—
224#125—21no—
225#125—21no—
226#125—21no—
227C4×Q8D4×C2911yescharacteristic
228C4×Q8D4×C2911yescharacteristic
229C4×D4—21no—
230C4×D4—21no—
231C4×D4D4×C2911yescharacteristic
232C4×D4D4×C2911yescharacteristic
233#117—21no—
234#117C2×C4×C2911yescharacteristic
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4C2×C4×C2911yescharacteristic
238C2×C4⋊C4C2×C4×C2911yescharacteristic
239C2×C42—21no—
240C2×C42C23×C2911yescharacteristic
241#107—21no—
242#107—21no—
243#106—21no—
244#106—21no—
245C4⋊C8—22no—
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8—21no—
249C4⋊C8—21no—
250C4⋊C8—21no—
251#103—21no—
252#103—21no—
253#102—21no—
254#102—21no—
255C22⋊C8—22no—
256C22⋊C8—21no—
257C22⋊C8—21no—
258C22⋊C8D4×C2912yes—
259#97—21no—
260#97—21no—
261#97D4×C2911yescharacteristic
262#97D4×C2911yescharacteristic
263C4×C8—22no—
264C4×C8—21no—
265C4×C8—21no—
266C29#935211yescharacteristic, direct product factor, Sylow
267#41—22no—
268#41—41no—
269C2×Q8C22⋊C4×C2911yescharacteristic
270C2×D4—21no—
271C2×D4C22⋊C4×C2911yescharacteristic
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4C22×C4×C2911yescharacteristic
278C22×C4C2×D4×C2911yescharacteristic
279C22×C4#41×C2911yescharacteristic
280M16—42no—
281M16—44no—
282M16—41no—
283M16—41no—
284C2×C8—21no—
285C2×C8—21no—
286C2×C8—21no—
287C2×C8—22no—
288C2×C8—21no—
289C2×C8—41no—
290C2×C8—41no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4C22⋊C4×C2911yescharacteristic
302C4⋊C4C22⋊C4×C2911yescharacteristic
303C22⋊C4—21no—
304C22⋊C4—21no—
305C22⋊C4—21no—
306C42—21no—
307C42—21no—
308C42—21no—
309C42C2×D4×C2911yescharacteristic
310C42C2×D4×C2911yescharacteristic
311C42C2×D4×C2911yescharacteristic
312C42#41×C2911yescharacteristic
313C23—21no—
314C23C4×D4×C2911yescharacteristic
315Q8—21no—
316Q8C29×#10112yes—
317D4—21no—
318D4—21no—
319D4—42no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4C2×C22⋊C4×C2911yescharacteristic
335C2×C4C4×D4×C2911yescharacteristic
336C2×C4C29×#12011yescharacteristic
337C2×C4C29×#12111yescharacteristic
338C2×C4C29×#12111yescharacteristic
339C2×C4C29×#12311yescharacteristic
340C8—22no—
341C8—42no—
342C8—41no—
343C8—41no—
344C8—41no—
345C8—81no—
346C8—81no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22C29×#38611yescharacteristic
354C4—21no—
355C4—21no—
356C4—21no—
357C4—21no—
358C4—21no—
359C4—22no—
360C4—41no—
361C4—41no—
362C4—81no—
363C4—81no—
364C4C2×C29×#10111yescharacteristic
365C4C29×#41311yescharacteristic
366C2—41no—
367C2—81no—
368C2C29×#188111yescharacteristic
369C2C29×#190111yescharacteristic
370C2C29×#190611yescharacteristic
subgroupG/H
center, socleC22×C29#386
commutatorC22×C4C22×C4×C29
Frattini, cosocleC2×C42C23×C29
prime radicalC2×#41×C29C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C2×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
3. C29×#1528C2semidirect
5. C29×#1470C2semidirect
6. C29×#1307C2semidirect
7. C29×#1299C2semidirect
127. #9352C29direct (N × H)
164. #1528C2×C29semidirect
166. #1470C2×C29semidirect
167. #1307C2×C29semidirect
168. #1299C2×C29semidirect
266. C29#9352direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#30802
C29×#29712
C29×#15282
C29×#14882
C29×#14702
C29×#13072
C29×#12992
#935229