Finite Group Databasebeta

← C29×#9357 #20304257

Subgroups — C29×#9357 #20304257

Order 7424.

456 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×#3079C211yesmaximal, characteristic
2C29×#2990C211yesmaximal, characteristic
3C29×#1966C211yesmaximal, characteristic, complemented
4C29×#1549C211yesmaximal, characteristic, complemented
5C29×#1489C211yesmaximal, characteristic
6C29×#1309C211yesmaximal, characteristic, complemented
7C29×#1299C211yesmaximal, characteristic, complemented
8C2×C29×C4⋊Q8C2211yescharacteristic
9C4×#41×C29C2211yescharacteristic
10C29×#477—21no—
11C29×#476—21no—
12C29×#475—21no—
13C29×#474—21no—
14C29×#446—21no—
15C29×#435—22no—
16C8×D4×C29—21no—
17C29×#432—21no—
18C29×#431C2211yescharacteristic
19C29×#428C412yes—
20C29×#423C2211yescharacteristic
21C29×#423C2211yescharacteristic
22C29×#423C2211yescharacteristic
23C2×C29×C4⋊C8—21no—
24C29×#417C412yes—
25C2×C29×#101—22no—
26C4×M16×C29C2211yescharacteristic
27C29×#332—21no—
28C29×#332—21no—
29C29×Q8⋊C8—21no—
30C29×D4⋊C8—21no—
31C2×#41×C29C2×C411yescharacteristic
32C22×Q8×C29—21no—
33C2×M16×C29—21no—
34C2×M16×C29—21no—
35C2×M16×C29C2×C412yes—
36C2×M16×C29D412yes—
37C22×C8×C29—22no—
38C29×C4⋊Q8—21no—
39C29×C4⋊Q8—21no—
40C29×C4⋊Q8—21no—
41C29×C4⋊Q8—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×C29C2×C412yes—
52C2×C42×C29—21no—
53C2×C42×C29C2311yescharacteristic
54C29×#107—22no—
55C29×#106—22no—
56C29×C4⋊C8—22no—
57C29×C4⋊C8—21no—
58C29×C4⋊C8—21no—
59C29×C4⋊C8—21no—
60C29×C4⋊C8—21no—
61C29×C4⋊C8—21no—
62C29×C4⋊C8—21no—
63C29×C4⋊C8D411yescharacteristic
64C29×C4⋊C8D411yescharacteristic
65C29×#103—22no—
66C29×#102—22no—
67C29×#101—44no—
68C29×C22⋊C8—22no—
69C29×C22⋊C8—21no—
70C29×#97—22no—
71C29×#97—21no—
72C4×C8×C29—21no—
73C4×C8×C29—21no—
74#41×C29—22no—
75#41×C29—41no—
76C2×Q8×C29—42no—
77C2×Q8×C29—42no—
78C2×Q8×C29—41no—
79C2×Q8×C29—41no—
80C2×Q8×C29C22⋊C411yescharacteristic
81C2×D4×C29—21no—
82C2×D4×C29C22⋊C411yescharacteristic
83C22×C4×C29—21no—
84C22×C4×C29—21no—
85C22×C4×C29—21no—
86C22×C4×C29—22no—
87C22×C4×C29C22×C411yescharacteristic
88C22×C4×C29C2×D411yescharacteristic
89C22×C4×C29#4111yescharacteristic
90M16×C29—22no—
91M16×C29—41no—
92M16×C29—42no—
93M16×C29—42no—
94M16×C29—81no—
95C2×C8×C29—22no—
96C2×C8×C29—21no—
97C2×C8×C29—22no—
98C2×C8×C29—21no—
99C2×C8×C29—41no—
100C2×C8×C29—41no—
101C2×C8×C29—82no—
102C4⋊C4×C29—21no—
103C4⋊C4×C29—21no—
104C4⋊C4×C29—22no—
105C4⋊C4×C29—22no—
106C4⋊C4×C29—41no—
107C4⋊C4×C29—41no—
108C4⋊C4×C29C22⋊C411yescharacteristic
109C4⋊C4×C29C22⋊C411yescharacteristic
110C22⋊C4×C29—21no—
111C22⋊C4×C29—21no—
112C22⋊C4×C29—21no—
113C42×C29—21no—
114C42×C29—21no—
115C42×C29—21no—
116C42×C29C2×D411yescharacteristic
117C42×C29C2×D411yescharacteristic
118C42×C29C2×D411yescharacteristic
119C42×C29#4111yescharacteristic
120#9357C2911yesmaximal, characteristic, direct product factor, Sylow
121C23×C29—21no—
122C23×C29C4×D411yescharacteristic
123Q8×C29—21no—
124Q8×C29—21no—
125Q8×C29—82no—
126Q8×C29—81no—
127Q8×C29—81no—
128D4×C29—21no—
129D4×C29—42no—
130D4×C29#10112yescomplemented
131C2×C4×C29—21no—
132C2×C4×C29—21no—
133C2×C4×C29—21no—
134C2×C4×C29—21no—
135C2×C4×C29—21no—
136C2×C4×C29—21no—
137C2×C4×C29—21no—
138C2×C4×C29—21no—
139C2×C4×C29—21no—
140C2×C4×C29—42no—
141C2×C4×C29—41no—
142C2×C4×C29—41no—
143C2×C4×C29—41no—
144C2×C4×C29—41no—
145C2×C4×C29—44no—
146C2×C4×C29—42no—
147C2×C4×C29C2×C22⋊C411yescharacteristic
148C2×C4×C29C4×D411yescharacteristic
149C2×C4×C29#12011yescharacteristic
150C2×C4×C29#12111yescharacteristic
151C2×C4×C29#12111yescharacteristic
152C2×C4×C29#12311yescharacteristic
153C8×C29—42no—
154C8×C29—42no—
155C8×C29—41no—
156C8×C29—42no—
157C8×C29—41no—
158C8×C29—81no—
159#3079C2×C2911yescharacteristic
160#2990C2×C2911yescharacteristic
161#1966C2×C2911yescharacteristic, complemented
162#1549C2×C2911yescharacteristic, complemented
163#1489C2×C2911yescharacteristic
164#1309C2×C2911yescharacteristic, complemented
165#1299C2×C2911yescharacteristic, complemented
166C22×C29—21no—
167C22×C29—21no—
168C22×C29—22no—
169C22×C29—21no—
170C22×C29—41no—
171C22×C29—41no—
172C22×C29#38611yescharacteristic
173C4×C29—21no—
174C4×C29—21no—
175C4×C29—21no—
176C4×C29—41no—
177C4×C29—41no—
178C4×C29—41no—
179C4×C29—82no—
180C4×C29C2×#10111yescharacteristic
181C4×C29#41311yescharacteristic
182C4×C29#45311yescharacteristic
183C4×C29#45411yescharacteristic
184C4×C29#47111yescharacteristic
185C4×C29#47311yescharacteristic
186C2×C4⋊Q8C22×C2911yescharacteristic
187C4×#41C22×C2911yescharacteristic
188#477—21no—
189#476—21no—
190#475—21no—
191#474—21no—
192#446—21no—
193#435—22no—
194C8×D4—21no—
195#432—21no—
196#431C22×C2911yescharacteristic
197#428C4×C2912yes—
198#423C22×C2911yescharacteristic
199#423C22×C2911yescharacteristic
200#423C22×C2911yescharacteristic
201C2×C4⋊C8—21no—
202#417C4×C2912yes—
203C2×#101—22no—
204C4×M16C22×C2911yescharacteristic
205#332—21no—
206#332—21no—
207Q8⋊C8—21no—
208D4⋊C8—21no—
209C2×C29—41no—
210C2×C29—42no—
211C2×C29#188311yescharacteristic
212C2×C29#190111yescharacteristic
213C2×C29#190811yescharacteristic
214C2×#41C2×C4×C2911yescharacteristic
215C22×Q8—21no—
216C2×M16—21no—
217C2×M16—21no—
218C2×M16C2×C4×C2912yes—
219C2×M16D4×C2912yes—
220C22×C8—22no—
221C4⋊Q8—21no—
222C4⋊Q8—21no—
223C4⋊Q8—21no—
224C4⋊Q8—21no—
225C4×Q8D4×C2911yescharacteristic
226C4×Q8D4×C2911yescharacteristic
227C4×D4—21no—
228C4×D4—21no—
229C4×D4D4×C2911yescharacteristic
230C4×D4D4×C2911yescharacteristic
231#117—21no—
232#117C2×C4×C2911yescharacteristic
233C2×C4⋊C4—21no—
234C2×C4⋊C4C2×C4×C2912yes—
235C2×C42—21no—
236C2×C42C23×C2911yescharacteristic
237#107—22no—
238#106—22no—
239C4⋊C8—22no—
240C4⋊C8—21no—
241C4⋊C8—21no—
242C4⋊C8—21no—
243C4⋊C8—21no—
244C4⋊C8—21no—
245C4⋊C8—21no—
246C4⋊C8D4×C2911yescharacteristic
247C4⋊C8D4×C2911yescharacteristic
248#103—22no—
249#102—22no—
250#101—44no—
251C22⋊C8—22no—
252C22⋊C8—21no—
253#97—22no—
254#97—21no—
255C4×C8—21no—
256C4×C8—21no—
257C29#935711yescharacteristic, direct product factor, Sylow
258#41—22no—
259#41—41no—
260C2×Q8—42no—
261C2×Q8—42no—
262C2×Q8—41no—
263C2×Q8—41no—
264C2×Q8C22⋊C4×C2911yescharacteristic
265C2×D4—21no—
266C2×D4C22⋊C4×C2911yescharacteristic
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—22no—
271C22×C4C22×C4×C2911yescharacteristic
272C22×C4C2×D4×C2911yescharacteristic
273C22×C4#41×C2911yescharacteristic
274M16—22no—
275M16—41no—
276M16—42no—
277M16—42no—
278M16—81no—
279C2×C8—22no—
280C2×C8—21no—
281C2×C8—21no—
282C2×C8—22no—
283C2×C8—41no—
284C2×C8—41no—
285C2×C8—82no—
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—22no—
289C4⋊C4—22no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4C22⋊C4×C2911yescharacteristic
293C4⋊C4C22⋊C4×C2911yescharacteristic
294C22⋊C4—21no—
295C22⋊C4—21no—
296C22⋊C4—21no—
297C42—21no—
298C42—21no—
299C42—21no—
300C42C2×D4×C2911yescharacteristic
301C42C2×D4×C2911yescharacteristic
302C42C2×D4×C2911yescharacteristic
303C42#41×C2911yescharacteristic
304C23—21no—
305C23C4×D4×C2911yescharacteristic
306Q8—21no—
307Q8—21no—
308Q8—82no—
309Q8—81no—
310Q8—81no—
311D4—21no—
312D4—42no—
313D4C29×#10112yescomplemented
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—42no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—44no—
329C2×C4—42no—
330C2×C4C2×C22⋊C4×C2911yescharacteristic
331C2×C4C4×D4×C2911yescharacteristic
332C2×C4C29×#12011yescharacteristic
333C2×C4C29×#12111yescharacteristic
334C2×C4C29×#12111yescharacteristic
335C2×C4C29×#12311yescharacteristic
336C8—42no—
337C8—41no—
338C8—42no—
339C8—41no—
340C8—42no—
341C8—81no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—22no—
346C22—41no—
347C22—41no—
348C22C29×#38611yescharacteristic
349C4—21no—
350C4—21no—
351C4—21no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—82no—
356C4C2×C29×#10111yescharacteristic
357C4C29×#41311yescharacteristic
358C4C29×#45311yescharacteristic
359C4C29×#45411yescharacteristic
360C4C29×#47111yescharacteristic
361C4C29×#47311yescharacteristic
362C2—41no—
363C2—42no—
364C2C29×#188311yescharacteristic
365C2C29×#190111yescharacteristic
366C2C29×#190811yescharacteristic
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×#1966C2semidirect
4. C29×#1549C2semidirect
6. C29×#1309C2semidirect
7. C29×#1299C2semidirect
120. #9357C29direct (N × H)
130. D4×C29#101semidirect
161. #1966C2×C29semidirect
162. #1549C2×C29semidirect
164. #1309C2×C29semidirect
165. #1299C2×C29semidirect
257. C29#9357direct (N × H)
313. D4C29×#101semidirect

Maximal subgroups

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

subgroupindex
C29×#30792
C29×#29902
C29×#19662
C29×#15492
C29×#14892
C29×#13092
C29×#12992
#935729