Finite Group Databasebeta

← C29×#9094 #20303994

Subgroups — C29×#9094 #20303994

Order 7424.

488 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#2983C211yesmaximal, characteristic, complemented
2C2×C29×#440C211yesmaximal, characteristic
3C29×#1479C211yesmaximal, characteristic, complemented
4C29×#1478C211yesmaximal, characteristic
5C29×#1460C211yesmaximal, characteristic
6C29×#1281C211yesmaximal, characteristic, complemented
7C29×#1275C211yesmaximal, characteristic, complemented
8C22×SD16×C29C411yescharacteristic
9C2×C4×Q8×C29C2211yescharacteristic
10C2×C4×D4×C29C2211yescharacteristic
11C29×#446—22no—
12C29×#446—22no—
13C29×#440—22no—
14C29×#440—22no—
15C29×#432—22no—
16C29×#431C2211yescharacteristic
17C29×#431C2211yescharacteristic
18C29×#431C2211yescharacteristic
19C29×#431C2211yescharacteristic
20C2×C29×#107C411yescharacteristic
21C2×C29×#103C411yescharacteristic
22C2×C29×#102C411yescharacteristic
23C2×C29×#97C2211yescharacteristic
24C29×Q8⋊C8—22no—
25C29×D4⋊C8—22no—
26C29×#323—22no—
27C22×Q8×C29C2×C411yescharacteristic
28C22×D4×C29C2×C411yescharacteristic
29C23×C4×C29—21no—
30C2×SD16×C29—22no—
31C2×SD16×C29—22no—
32C2×SD16×C29—22no—
33C22×C8×C29C2×C411yescharacteristic
34C22×C8×C29C2×C411yescharacteristic
35C4×Q8×C29—21no—
36C4×Q8×C29—21no—
37C4×Q8×C29D412yes—
38C4×Q8×C29D412yes—
39C4×D4×C29—21no—
40C4×D4×C29—21no—
41C4×D4×C29—21no—
42C4×D4×C29—21no—
43C2×C4⋊C4×C29—21no—
44C2×C4⋊C4×C29C2×C411yescharacteristic
45C2×C4⋊C4×C29C2×C411yescharacteristic
46C2×C22⋊C4×C29—21no—
47C2×C42×C29—21no—
48C2×C42×C29C2311yescharacteristic
49C29×#107—22no—
50C29×C4⋊C8—24no—
51C29×C4⋊C8—21no—
52C29×C4⋊C8—21no—
53C29×C4⋊C8—21no—
54C29×C4⋊C8—21no—
55C29×#103—22no—
56C29×#102—22no—
57C29×C22⋊C8—21no—
58C29×C22⋊C8—21no—
59C29×C22⋊C8—21no—
60C29×C22⋊C8D412yes—
61C29×#97—24no—
62C29×#97—21no—
63C29×#97—21no—
64C4×C8×C29—21no—
65C4×C8×C29—21no—
66C4×C8×C29—21no—
67C4×C8×C29D412yes—
68C24×C29—21no—
69C2×Q8×C29—21no—
70C2×Q8×C29—21no—
71C2×Q8×C29—21no—
72C2×Q8×C29—21no—
73C2×Q8×C29—21no—
74C2×Q8×C29C22⋊C412yes—
75C2×D4×C29—21no—
76C2×D4×C29—21no—
77C2×D4×C29—21no—
78C2×D4×C29—21no—
79C2×D4×C29—21no—
80C2×D4×C29M1612yes—
81C22×C4×C29—21no—
82C22×C4×C29—21no—
83C22×C4×C29—21no—
84C22×C4×C29—41no—
85C22×C4×C29—41no—
86C22×C4×C29—82no—
87C22×C4×C29C22×C411yescharacteristic
88C22×C4×C29C2×D411yescharacteristic
89C22×C4×C29#4111yescharacteristic
90SD16×C29—28no—
91C2×C8×C29—21no—
92C2×C8×C29—21no—
93C2×C8×C29—21no—
94C2×C8×C29—22no—
95C2×C8×C29—22no—
96C2×C8×C29—21no—
97C2×C8×C29—21no—
98C2×C8×C29—41no—
99C2×C8×C29—41no—
100C2×C8×C29M1612yes—
101C4⋊C4×C29—21no—
102C4⋊C4×C29—22no—
103C4⋊C4×C29—22no—
104C4⋊C4×C29—21no—
105C4⋊C4×C29—21no—
106C4⋊C4×C29C22⋊C412yes—
107C22⋊C4×C29—41no—
108C22⋊C4×C29—41no—
109C42×C29—22no—
110C42×C29—22no—
111C42×C29C2×D411yescharacteristic
112C42×C29C2×D411yescharacteristic
113C42×C29C2×D411yescharacteristic
114C42×C29#4111yescharacteristic
115#9094C2911yesmaximal, characteristic, direct product factor, Sylow
116C23×C29—22no—
117C23×C29—41no—
118C23×C29—41no—
119C23×C29—81no—
120C23×C29—81no—
121C23×C29C4×D411yescharacteristic
122Q8×C29—22no—
123Q8×C29—22no—
124Q8×C29—41no—
125Q8×C29—41no—
126D4×C29—22no—
127D4×C29—22no—
128D4×C29—41no—
129D4×C29—41no—
130C2×C4×C29—22no—
131C2×C4×C29—22no—
132C2×C4×C29—41no—
133C2×C4×C29—41no—
134C2×C4×C29—41no—
135C2×C4×C29—41no—
136C2×C4×C29—41no—
137C2×C4×C29—82no—
138C2×C4×C29—82no—
139C2×C4×C29—81no—
140C2×C4×C29—81no—
141C2×C4×C29C2×C22⋊C411yescharacteristic
142C2×C4×C29C4×D411yescharacteristic
143C2×C4×C29#12011yescharacteristic
144C2×C4×C29#12111yescharacteristic
145C2×C4×C29#12111yescharacteristic
146C2×C4×C29#12311yescharacteristic
147C2×C4×C29C2×M1611yescharacteristic
148C2×C4×C29C2×M1611yescharacteristic
149C2×C4×C29#13111yescharacteristic
150C2×C4×C29#13111yescharacteristic
151C8×C29—22no—
152C8×C29—42no—
153C8×C29—42no—
154C8×C29—41no—
155C8×C29—81no—
156C8×C29—81no—
157#2983C2×C2911yescharacteristic, complemented
158C2×#440C2×C2911yescharacteristic
159#1479C2×C2911yescharacteristic, complemented
160#1478C2×C2911yescharacteristic
161#1460C2×C2911yescharacteristic
162#1281C2×C2911yescharacteristic, complemented
163#1275C2×C2911yescharacteristic, complemented
164C22×C29—21no—
165C22×C29—21no—
166C22×C29—42no—
167C22×C29—82no—
168C22×C29—82no—
169C22×C29—81no—
170C22×C29—81no—
171C22×C29#38611yescharacteristic
172C22×C29#43511yescharacteristic
173C22×C29#43611yescharacteristic
174C4×C29—21no—
175C4×C29—21no—
176C4×C29—21no—
177C4×C29—21no—
178C4×C29—42no—
179C4×C29—42no—
180C4×C29—81no—
181C4×C29#40711yescharacteristic
182C4×C29#40811yescharacteristic
183C4×C29#43511yescharacteristic
184C4×C29#43611yescharacteristic
185C22×SD16C4×C2911yescharacteristic
186C2×C4×Q8C22×C2911yescharacteristic
187C2×C4×D4C22×C2911yescharacteristic
188#446—22no—
189#446—22no—
190#440—22no—
191#440—22no—
192#432—22no—
193#431C22×C2911yescharacteristic
194#431C22×C2911yescharacteristic
195#431C22×C2911yescharacteristic
196#431C22×C2911yescharacteristic
197C2×#107C4×C2911yescharacteristic
198C2×#103C4×C2911yescharacteristic
199C2×#102C4×C2911yescharacteristic
200C2×#97C22×C2911yescharacteristic
201Q8⋊C8—22no—
202D4⋊C8—22no—
203#323—22no—
204C2×C29—21no—
205C2×C29—21no—
206C2×C29—82no—
207C2×C29#187011yescharacteristic
208C2×C29#190311yescharacteristic
209C2×C29#190511yescharacteristic
210C22×Q8C2×C4×C2911yescharacteristic
211C22×D4C2×C4×C2911yescharacteristic
212C23×C4—21no—
213C2×SD16—22no—
214C2×SD16—22no—
215C2×SD16—22no—
216C22×C8C2×C4×C2911yescharacteristic
217C22×C8C2×C4×C2911yescharacteristic
218C4×Q8—21no—
219C4×Q8—21no—
220C4×Q8D4×C2912yes—
221C4×Q8D4×C2912yes—
222C4×D4—21no—
223C4×D4—21no—
224C4×D4—21no—
225C4×D4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4C2×C4×C2911yescharacteristic
228C2×C4⋊C4C2×C4×C2911yescharacteristic
229C2×C22⋊C4—21no—
230C2×C42—21no—
231C2×C42C23×C2911yescharacteristic
232#107—22no—
233C4⋊C8—24no—
234C4⋊C8—21no—
235C4⋊C8—21no—
236C4⋊C8—21no—
237C4⋊C8—21no—
238#103—22no—
239#102—22no—
240C22⋊C8—21no—
241C22⋊C8—21no—
242C22⋊C8—21no—
243C22⋊C8D4×C2912yes—
244#97—24no—
245#97—21no—
246#97—21no—
247C4×C8—21no—
248C4×C8—21no—
249C4×C8—21no—
250C4×C8D4×C2912yes—
251C29#909411yescharacteristic, direct product factor, Sylow
252C24—21no—
253C2×Q8—21no—
254C2×Q8—21no—
255C2×Q8—21no—
256C2×Q8—21no—
257C2×Q8—21no—
258C2×Q8C22⋊C4×C2912yes—
259C2×D4—21no—
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4M16×C2912yes—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—82no—
271C22×C4C22×C4×C2911yescharacteristic
272C22×C4C2×D4×C2911yescharacteristic
273C22×C4#41×C2911yescharacteristic
274SD16—28no—
275C2×C8—21no—
276C2×C8—21no—
277C2×C8—21no—
278C2×C8—22no—
279C2×C8—22no—
280C2×C8—21no—
281C2×C8—21no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8M16×C2912yes—
285C4⋊C4—21no—
286C4⋊C4—22no—
287C4⋊C4—22no—
288C4⋊C4—21no—
289C4⋊C4—21no—
290C4⋊C4C22⋊C4×C2912yes—
291C22⋊C4—41no—
292C22⋊C4—41no—
293C42—22no—
294C42—22no—
295C42C2×D4×C2911yescharacteristic
296C42C2×D4×C2911yescharacteristic
297C42C2×D4×C2911yescharacteristic
298C42#41×C2911yescharacteristic
299C23—22no—
300C23—41no—
301C23—41no—
302C23—81no—
303C23—81no—
304C23C4×D4×C2911yescharacteristic
305Q8—22no—
306Q8—22no—
307Q8—41no—
308Q8—41no—
309D4—22no—
310D4—22no—
311D4—41no—
312D4—41no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—82no—
321C2×C4—82no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4C2×C22⋊C4×C2911yescharacteristic
325C2×C4C4×D4×C2911yescharacteristic
326C2×C4C29×#12011yescharacteristic
327C2×C4C29×#12111yescharacteristic
328C2×C4C29×#12111yescharacteristic
329C2×C4C29×#12311yescharacteristic
330C2×C4C2×M16×C2911yescharacteristic
331C2×C4C2×M16×C2911yescharacteristic
332C2×C4C29×#13111yescharacteristic
333C2×C4C29×#13111yescharacteristic
334C8—22no—
335C8—42no—
336C8—42no—
337C8—41no—
338C8—81no—
339C8—81no—
340C22—21no—
341C22—21no—
342C22—42no—
343C22—82no—
344C22—82no—
345C22—81no—
346C22—81no—
347C22C29×#38611yescharacteristic
348C22C29×#43511yescharacteristic
349C22C29×#43611yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—42no—
355C4—42no—
356C4—81no—
357C4C29×#40711yescharacteristic
358C4C29×#40811yescharacteristic
359C4C29×#43511yescharacteristic
360C4C29×#43611yescharacteristic
361C2—21no—
362C2—21no—
363C2—82no—
364C2C29×#187011yescharacteristic
365C2C29×#190311yescharacteristic
366C2C29×#190511yescharacteristic
subgroupG/H
center, socleC22×C29#386
commutatorC22×C4C22×C4×C29
Frattini, cosocleC2×C42C23×C29
prime radicalC22×D4×C29C2×C4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C2×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C29×#2983C2semidirect
3. C29×#1479C2semidirect
6. C29×#1281C2semidirect
7. C29×#1275C2semidirect
115. #9094C29direct (N × H)
157. #2983C2×C29semidirect
159. #1479C2×C29semidirect
162. #1281C2×C29semidirect
163. #1275C2×C29semidirect
251. C29#9094direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#29832
C2×C29×#4402
C29×#14792
C29×#14782
C29×#14602
C29×#12812
C29×#12752
#909429