Finite Group Databasebeta

← C29×#9319 #20304219

Subgroups — C29×#9319 #20304219

Order 7424.

458 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3079C211yesmaximal, characteristic
2C29×#2989C211yesmaximal, characteristic
3C29×#1987C211yesmaximal, characteristic, complemented
4C29×#1806C211yesmaximal, characteristic
5C29×#1548C211yesmaximal, characteristic, complemented
6C29×#1303C211yesmaximal, characteristic, complemented
7C29×#1292C211yesmaximal, characteristic, complemented
8C2×C29×C4⋊Q8C2211yescharacteristic
9C4×#41×C29C2211yescharacteristic
10C29×#477—21no—
11C29×#476—21no—
12C29×#475C412yescomplemented
13C29×#474C412yescomplemented
14C29×#446—21no—
15C29×#436—21no—
16C29×#435—22no—
17C29×#432—21no—
18C29×#431C2211yescharacteristic
19C29×#428—21no—
20C29×#423—21no—
21C29×#423C2211yescharacteristic
22C29×#423C2211yescharacteristic
23C2×C29×C4⋊C8C2211yescharacteristic
24C2×C29×#104—21no—
25C29×#417—21no—
26C4×C4⋊C4×C29C2211yescharacteristic
27C29×#340—22no—
28C29×#339—21no—
29C29×#333—21no—
30C29×#333—21no—
31C2×#41×C29D411yescharacteristic
32C22×Q8×C29—21no—
33C2×M16×C29—21no—
34C2×M16×C29—22no—
35C2×M16×C29—21no—
36C22×C8×C29D412yes—
37C29×C4⋊Q8—21no—
38C29×C4⋊Q8—21no—
39C29×C4⋊Q8—21no—
40C29×C4⋊Q8C2×C412yes—
41C4×Q8×C29C2×C411yescharacteristic
42C4×Q8×C29D411yescharacteristic
43C4×D4×C29—21no—
44C4×D4×C29—21no—
45C4×D4×C29C2×C411yescharacteristic
46C4×D4×C29D411yescharacteristic
47C29×#117—21no—
48C29×#117D411yescharacteristic
49C2×C4⋊C4×C29—21no—
50C2×C4⋊C4×C29—21no—
51C2×C4⋊C4×C29—21no—
52C2×C42×C29—21no—
53C2×C42×C29—21no—
54C2×C42×C29C2311yescharacteristic
55C29×#107—22no—
56C29×#106—22no—
57C29×C4⋊C8—22no—
58C29×C4⋊C8—21no—
59C29×C4⋊C8—21no—
60C29×C4⋊C8—21no—
61C29×C4⋊C8—21no—
62C29×C4⋊C8—21no—
63C29×C4⋊C8C2×C412yes—
64C29×C4⋊C8D411yescharacteristic
65C29×C4⋊C8D411yescharacteristic
66C29×#104—42no—
67C29×#103—22no—
68C29×#102—22no—
69C29×C22⋊C8—22no—
70C29×C22⋊C8—21no—
71C29×#97—22no—
72C4×C8×C29—21no—
73C29×#95—21no—
74#41×C29—21no—
75#41×C29—21no—
76#41×C29—21no—
77#41×C29—21no—
78C2×Q8×C29—22no—
79C2×Q8×C29—41no—
80C2×Q8×C29—82no—
81C2×Q8×C29C22⋊C411yescharacteristic
82C2×D4×C29—21no—
83C2×D4×C29C22⋊C411yescharacteristic
84C22×C4×C29—21no—
85C22×C4×C29—21no—
86C22×C4×C29—21no—
87C22×C4×C29—41no—
88C22×C4×C29—41no—
89C22×C4×C29C2×D411yescharacteristic
90C22×C4×C29C2×D411yescharacteristic
91C22×C4×C29#4111yescharacteristic
92M16×C29—41no—
93M16×C29—41no—
94M16×C29—41no—
95M16×C29—41no—
96M16×C29—82no—
97C2×C8×C29—22no—
98C2×C8×C29—22no—
99C2×C8×C29—21no—
100C2×C8×C29—21no—
101C2×C8×C29—42no—
102C2×C8×C29—41no—
103C4⋊C4×C29—21no—
104C4⋊C4×C29—21no—
105C4⋊C4×C29—22no—
106C4⋊C4×C29—22no—
107C4⋊C4×C29—22no—
108C4⋊C4×C29—41no—
109C4⋊C4×C29—41no—
110C4⋊C4×C29—41no—
111C4⋊C4×C29C22⋊C411yescharacteristic
112C4⋊C4×C29C22⋊C411yescharacteristic
113C22⋊C4×C29—21no—
114C22⋊C4×C29—21no—
115C22⋊C4×C29—21no—
116C42×C29—21no—
117C42×C29—21no—
118C42×C29—21no—
119C42×C29—41no—
120C42×C29—41no—
121C42×C29C22×C411yescharacteristic
122C42×C29C2×D411yescharacteristic
123C42×C29C2×D411yescharacteristic
124C42×C29#4111yescharacteristic
125#9319C2911yesmaximal, characteristic, direct product factor, Sylow
126C23×C29—21no—
127C23×C29#12111yescharacteristic
128Q8×C29—21no—
129Q8×C29—21no—
130Q8×C29—82no—
131Q8×C29—82no—
132D4×C29—21no—
133D4×C29—21no—
134D4×C29—41no—
135D4×C29—41no—
136C2×C4×C29—21no—
137C2×C4×C29—21no—
138C2×C4×C29—21no—
139C2×C4×C29—21no—
140C2×C4×C29—21no—
141C2×C4×C29—41no—
142C2×C4×C29—41no—
143C2×C4×C29—41no—
144C2×C4×C29—41no—
145C2×C4×C29—41no—
146C2×C4×C29—42no—
147C2×C4×C29—42no—
148C2×C4×C29—81no—
149C2×C4×C29—81no—
150C2×C4×C29—82no—
151C2×C4×C29—81no—
152C2×C4×C29C2×C22⋊C411yescharacteristic
153C2×C4×C29C4×D411yescharacteristic
154C2×C4×C29C4×D411yescharacteristic
155C2×C4×C29#12011yescharacteristic
156C2×C4×C29#12111yescharacteristic
157C2×C4×C29#12311yescharacteristic
158C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
159C2×C4×C29#13711yescharacteristic
160C2×C4×C29#13711yescharacteristic
161C2×C4×C29#13711yescharacteristic
162C8×C29—42no—
163C8×C29—42no—
164C8×C29—41no—
165C8×C29—41no—
166C8×C29—81no—
167#3079C2×C2911yescharacteristic
168#2989C2×C2911yescharacteristic
169#1987C2×C2911yescharacteristic, complemented
170#1806C2×C2911yescharacteristic
171#1548C2×C2911yescharacteristic, complemented
172#1303C2×C2911yescharacteristic, complemented
173#1292C2×C2911yescharacteristic, complemented
174C22×C29—21no—
175C22×C29—21no—
176C22×C29—41no—
177C22×C29—41no—
178C22×C29—41no—
179C22×C29#38611yescharacteristic
180C22×C29#46811yescharacteristic
181C22×C29#47011yescharacteristic
182C4×C29—21no—
183C4×C29—21no—
184C4×C29—21no—
185C4×C29—41no—
186C4×C29—41no—
187C4×C29—41no—
188C4×C29—82no—
189C4×C29—82no—
190C4×C29#41711yescharacteristic
191C4×C29#41911yescharacteristic
192C4×C29#45511yescharacteristic
193C4×C29#45611yescharacteristic
194C4×C29#46811yescharacteristic
195C4×C29#47011yescharacteristic
196C2×C4⋊Q8C22×C2911yescharacteristic
197C4×#41C22×C2911yescharacteristic
198#477—21no—
199#476—21no—
200#475C4×C2912yescomplemented
201#474C4×C2912yescomplemented
202#446—21no—
203#436—21no—
204#435—22no—
205#432—21no—
206#431C22×C2911yescharacteristic
207#428—21no—
208#423—21no—
209#423C22×C2911yescharacteristic
210#423C22×C2911yescharacteristic
211C2×C4⋊C8C22×C2911yescharacteristic
212C2×#104—21no—
213#417—21no—
214C4×C4⋊C4C22×C2911yescharacteristic
215#340—22no—
216#339—21no—
217#333—21no—
218#333—21no—
219C2×C29—21no—
220C2×C29—21no—
221C2×C29—81no—
222C2×C29#188211yescharacteristic
223C2×C29#189411yescharacteristic
224C2×C29#190311yescharacteristic
225C2×#41D4×C2911yescharacteristic
226C22×Q8—21no—
227C2×M16—21no—
228C2×M16—22no—
229C2×M16—21no—
230C22×C8D4×C2912yes—
231C4⋊Q8—21no—
232C4⋊Q8—21no—
233C4⋊Q8—21no—
234C4⋊Q8C2×C4×C2912yes—
235C4×Q8C2×C4×C2911yescharacteristic
236C4×Q8D4×C2911yescharacteristic
237C4×D4—21no—
238C4×D4—21no—
239C4×D4C2×C4×C2911yescharacteristic
240C4×D4D4×C2911yescharacteristic
241#117—21no—
242#117D4×C2911yescharacteristic
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C42—21no—
247C2×C42—21no—
248C2×C42C23×C2911yescharacteristic
249#107—22no—
250#106—22no—
251C4⋊C8—22no—
252C4⋊C8—21no—
253C4⋊C8—21no—
254C4⋊C8—21no—
255C4⋊C8—21no—
256C4⋊C8—21no—
257C4⋊C8C2×C4×C2912yes—
258C4⋊C8D4×C2911yescharacteristic
259C4⋊C8D4×C2911yescharacteristic
260#104—42no—
261#103—22no—
262#102—22no—
263C22⋊C8—22no—
264C22⋊C8—21no—
265#97—22no—
266C4×C8—21no—
267#95—21no—
268C29#931911yescharacteristic, direct product factor, Sylow
269#41—21no—
270#41—21no—
271#41—21no—
272#41—21no—
273C2×Q8—22no—
274C2×Q8—41no—
275C2×Q8—82no—
276C2×Q8C22⋊C4×C2911yescharacteristic
277C2×D4—21no—
278C2×D4C22⋊C4×C2911yescharacteristic
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4C2×D4×C2911yescharacteristic
285C22×C4C2×D4×C2911yescharacteristic
286C22×C4#41×C2911yescharacteristic
287M16—41no—
288M16—41no—
289M16—41no—
290M16—41no—
291M16—82no—
292C2×C8—22no—
293C2×C8—21no—
294C2×C8—21no—
295C2×C8—22no—
296C2×C8—42no—
297C2×C8—41no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—22no—
301C4⋊C4—22no—
302C4⋊C4—22no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4C22⋊C4×C2911yescharacteristic
307C4⋊C4C22⋊C4×C2911yescharacteristic
308C22⋊C4—21no—
309C22⋊C4—21no—
310C22⋊C4—21no—
311C42—21no—
312C42—21no—
313C42—21no—
314C42—41no—
315C42—41no—
316C42C22×C4×C2911yescharacteristic
317C42C2×D4×C2911yescharacteristic
318C42C2×D4×C2911yescharacteristic
319C42#41×C2911yescharacteristic
320C23—21no—
321C23C29×#12111yescharacteristic
322Q8—21no—
323Q8—21no—
324Q8—82no—
325Q8—82no—
326D4—21no—
327D4—21no—
328D4—41no—
329D4—41no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—81no—
343C2×C4—82no—
344C2×C4—81no—
345C2×C4—81no—
346C2×C4C2×C22⋊C4×C2911yescharacteristic
347C2×C4C4×D4×C2911yescharacteristic
348C2×C4C4×D4×C2911yescharacteristic
349C2×C4C29×#12011yescharacteristic
350C2×C4C29×#12111yescharacteristic
351C2×C4C29×#12311yescharacteristic
352C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
353C2×C4C29×#13711yescharacteristic
354C2×C4C29×#13711yescharacteristic
355C2×C4C29×#13711yescharacteristic
356C8—42no—
357C8—41no—
358C8—41no—
359C8—42no—
360C8—81no—
361C22—21no—
362C22—21no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22C29×#38611yescharacteristic
367C22C29×#46811yescharacteristic
368C22C29×#47011yescharacteristic
369C4—21no—
370C4—21no—
371C4—21no—
372C4—41no—
373C4—41no—
374C4—41no—
375C4—82no—
376C4—82no—
377C4C29×#41711yescharacteristic
378C4C29×#41911yescharacteristic
379C4C29×#45511yescharacteristic
380C4C29×#45611yescharacteristic
381C4C29×#46811yescharacteristic
382C4C29×#47011yescharacteristic
383C2—21no—
384C2—21no—
385C2—81no—
386C2C29×#188211yescharacteristic
387C2C29×#189411yescharacteristic
388C2C29×#190311yescharacteristic
subgroupG/H
center, socleC22×C29#386
commutatorC42C22×C4×C29
Frattini, cosocleC2×C42C23×C29
prime radicalC2×#41×C29D4
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
3. C29×#1987C2semidirect
5. C29×#1548C2semidirect
6. C29×#1303C2semidirect
7. C29×#1292C2semidirect
12. C29×#475C4semidirect
13. C29×#474C4semidirect
125. #9319C29direct (N × H)
169. #1987C2×C29semidirect
171. #1548C2×C29semidirect
172. #1303C2×C29semidirect
173. #1292C2×C29semidirect
200. #475C4×C29semidirect
201. #474C4×C29semidirect
268. C29#9319direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#30792
C29×#29892
C29×#19872
C29×#18062
C29×#15482
C29×#13032
C29×#12922
#931929