Finite Group Databasebeta

← C29×#9175 #20304075

Subgroups — C29×#9175 #20304075

Order 7424.

566 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3077C211yesmaximal, characteristic
2C29×#2349C211yesmaximal, characteristic
3C29×#1518C211yesmaximal, characteristic, complemented
4C29×#1503C211yesmaximal, characteristic, complemented
5C29×#1478C211yesmaximal, characteristic
6C29×#1303C211yesmaximal, characteristic, complemented
7C29×#1286C211yesmaximal, characteristic, complemented
8C29×#533C2211yescharacteristic
9C2×C4×D4×C29—21no—
10C2×C4×D4×C29C2211yescharacteristic
11C29×#478—22no—
12C29×#476C412yescomplemented
13C29×#474C412yescomplemented
14C29×#431C2211yescharacteristic
15C29×#431C2211yescharacteristic
16C29×#428—21no—
17C29×#423C2211yescharacteristic
18C29×#418—21no—
19C29×#389—21no—
20C29×#385—22no—
21C29×#382C2211yescharacteristic
22C29×#380—21no—
23C4×C4⋊C4×C29C2211yescharacteristic
24C2×C29×#95—21no—
25C29×#328—21no—
26C29×#328—21no—
27C29×#328—22no—
28C29×D4⋊C8—22no—
29C22×D4×C29D411yescharacteristic
30C23×C4×C29—21no—
31C23×C4×C29—22no—
32C2×M16×C29—21no—
33C29×C4⋊Q8C2×C411yescharacteristic, complemented
34C29×C4⋊Q8C2×C411yescharacteristic, complemented
35C29×#125—21no—
36C29×C22⋊Q8—21no—
37C29×C22⋊Q8—21no—
38C4×Q8×C29—21no—
39C4×Q8×C29—21no—
40C4×D4×C29—21no—
41C4×D4×C29—21no—
42C4×D4×C29—42no—
43C4×D4×C29—42no—
44C4×D4×C29C2×C412yes—
45C4×D4×C29D412yes—
46C29×#117—21no—
47C2×C4⋊C4×C29—21no—
48C2×C4⋊C4×C29—21no—
49C2×C4⋊C4×C29—22no—
50C2×C4⋊C4×C29D411yescharacteristic
51C2×C22⋊C4×C29—21no—
52C2×C22⋊C4×C29—22no—
53C2×C42×C29—21no—
54C2×C42×C29C2311yescharacteristic
55C29×#107—22no—
56C29×#106—22no—
57C29×C4⋊C8—21no—
58C29×C4⋊C8—21no—
59C29×C4⋊C8—21no—
60C29×C4⋊C8C2×C412yescomplemented
61C29×#102—22no—
62C29×#102—22no—
63C29×C22⋊C8—21no—
64C29×C22⋊C8—21no—
65C4×C8×C29—21no—
66C4×C8×C29—21no—
67C29×#95—22no—
68C29×#95—21no—
69C29×#95D411yescharacteristic
70C29×#95D411yescharacteristic
71C29×#95D412yes—
72C24×C29—21no—
73C2×Q8×C29—21no—
74C2×Q8×C29—21no—
75C2×D4×C29—21no—
76C2×D4×C29—21no—
77C2×D4×C29—21no—
78C2×D4×C29C22⋊C412yes—
79C2×D4×C29SD1612yes—
80C2×D4×C29Q1612yes—
81C22×C4×C29—21no—
82C22×C4×C29—21no—
83C22×C4×C29—22no—
84C22×C4×C29—22no—
85C22×C4×C29—21no—
86C22×C4×C29—22no—
87C22×C4×C29—44no—
88C22×C4×C29—44no—
89C22×C4×C29—82no—
90C22×C4×C29—82no—
91C22×C4×C29C2×D411yescharacteristic
92C22×C4×C29C2×D411yescharacteristic
93C22×C4×C29C2×D411yescharacteristic
94M16×C29—41no—
95M16×C29—41no—
96C2×C8×C29—22no—
97C2×C8×C29—41no—
98C2×C8×C29—41no—
99C4⋊C4×C29—21no—
100C4⋊C4×C29—21no—
101C4⋊C4×C29—21no—
102C4⋊C4×C29—21no—
103C4⋊C4×C29—21no—
104C4⋊C4×C29—42no—
105C4⋊C4×C29—41no—
106C4⋊C4×C29—41no—
107C4⋊C4×C29—41no—
108C4⋊C4×C29—41no—
109C4⋊C4×C29—82no—
110C4⋊C4×C29C22⋊C412yes—
111C22⋊C4×C29—22no—
112C22⋊C4×C29—22no—
113C22⋊C4×C29—44no—
114C22⋊C4×C29—41no—
115C42×C29—41no—
116C42×C29—41no—
117C42×C29—41no—
118C42×C29C22×C411yescharacteristic
119C42×C29C2×D411yescharacteristic
120C42×C29#4111yescharacteristic
121C42×C29#4111yescharacteristic
122#9175C2911yesmaximal, characteristic, direct product factor, Sylow
123C23×C29—22no—
124C23×C29—22no—
125C23×C29—22no—
126C23×C29—42no—
127C23×C29—42no—
128C23×C29#12011yescharacteristic
129Q8×C29—81no—
130Q8×C29—81no—
131D4×C29—22no—
132D4×C29—22no—
133D4×C29—22no—
134D4×C29#10314yes—
135C2×C4×C29—22no—
136C2×C4×C29—22no—
137C2×C4×C29—41no—
138C2×C4×C29—41no—
139C2×C4×C29—42no—
140C2×C4×C29—41no—
141C2×C4×C29—41no—
142C2×C4×C29—41no—
143C2×C4×C29—41no—
144C2×C4×C29—42no—
145C2×C4×C29—42no—
146C2×C4×C29—41no—
147C2×C4×C29—41no—
148C2×C4×C29—41no—
149C2×C4×C29—42no—
150C2×C4×C29—82no—
151C2×C4×C29—82no—
152C2×C4×C29—88no—
153C2×C4×C29C2×C22⋊C411yescharacteristic
154C2×C4×C29C4×D411yescharacteristic
155C2×C4×C29C4×D411yescharacteristic
156C2×C4×C29#12111yescharacteristic
157C2×C4×C29#12111yescharacteristic
158C2×C4×C29#12311yescharacteristic
159C2×C4×C29C2×SD1611yescharacteristic
160C2×C4×C29C2×Q1611yescharacteristic
161C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
162C2×C4×C29#13711yescharacteristic
163C8×C29—42no—
164C8×C29—81no—
165C8×C29—81no—
166#3077C2×C2911yescharacteristic
167#2349C2×C2911yescharacteristic
168#1518C2×C2911yescharacteristic, complemented
169#1503C2×C2911yescharacteristic, complemented
170#1478C2×C2911yescharacteristic
171#1303C2×C2911yescharacteristic, complemented
172#1286C2×C2911yescharacteristic, complemented
173C22×C29—21no—
174C22×C29—21no—
175C22×C29—24no—
176C22×C29—44no—
177C22×C29—44no—
178C22×C29—42no—
179C22×C29—42no—
180C22×C29#38611yescharacteristic
181C22×C29#45011yescharacteristic
182C22×C29#45111yescharacteristic
183C4×C29—21no—
184C4×C29—21no—
185C4×C29—21no—
186C4×C29—21no—
187C4×C29—42no—
188C4×C29—42no—
189C4×C29—81no—
190C4×C29—82no—
191C4×C29—81no—
192C4×C29—81no—
193C4×C29C2×#10311yescharacteristic
194C4×C29#41711yescharacteristic
195C4×C29#48311yescharacteristic
196C4×C29#48411yescharacteristic
197#533C22×C2911yescharacteristic
198C2×C4×D4—21no—
199C2×C4×D4C22×C2911yescharacteristic
200#478—22no—
201#476C4×C2912yescomplemented
202#474C4×C2912yescomplemented
203#431C22×C2911yescharacteristic
204#431C22×C2911yescharacteristic
205#428—21no—
206#423C22×C2911yescharacteristic
207#418—21no—
208#389—21no—
209#385—22no—
210#382C22×C2911yescharacteristic
211#380—21no—
212C4×C4⋊C4C22×C2911yescharacteristic
213C2×#95—21no—
214#328—21no—
215#328—21no—
216#328—22no—
217D4⋊C8—22no—
218C2×C29—21no—
219C2×C29—21no—
220C2×C29—44no—
221C2×C29#187211yescharacteristic
222C2×C29#190411yescharacteristic
223C2×C29#190611yescharacteristic
224C22×D4D4×C2911yescharacteristic
225C23×C4—21no—
226C23×C4—22no—
227C2×M16—21no—
228C4⋊Q8C2×C4×C2911yescharacteristic, complemented
229C4⋊Q8C2×C4×C2911yescharacteristic, complemented
230#125—21no—
231C22⋊Q8—21no—
232C22⋊Q8—21no—
233C4×Q8—21no—
234C4×Q8—21no—
235C4×D4—21no—
236C4×D4—21no—
237C4×D4—42no—
238C4×D4—42no—
239C4×D4C2×C4×C2912yes—
240C4×D4D4×C2912yes—
241#117—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—22no—
245C2×C4⋊C4D4×C2911yescharacteristic
246C2×C22⋊C4—21no—
247C2×C22⋊C4—22no—
248C2×C42—21no—
249C2×C42C23×C2911yescharacteristic
250#107—22no—
251#106—22no—
252C4⋊C8—21no—
253C4⋊C8—21no—
254C4⋊C8—21no—
255C4⋊C8C2×C4×C2912yescomplemented
256#102—22no—
257#102—22no—
258C22⋊C8—21no—
259C22⋊C8—21no—
260C4×C8—21no—
261C4×C8—21no—
262#95—22no—
263#95—21no—
264#95D4×C2911yescharacteristic
265#95D4×C2911yescharacteristic
266#95D4×C2912yes—
267C29#917511yescharacteristic, direct product factor, Sylow
268C24—21no—
269C2×Q8—21no—
270C2×Q8—21no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4C22⋊C4×C2912yes—
275C2×D4SD16×C2912yes—
276C2×D4Q16×C2912yes—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—21no—
283C22×C4—44no—
284C22×C4—44no—
285C22×C4—82no—
286C22×C4—82no—
287C22×C4C2×D4×C2911yescharacteristic
288C22×C4C2×D4×C2911yescharacteristic
289C22×C4C2×D4×C2911yescharacteristic
290M16—41no—
291M16—41no—
292C2×C8—22no—
293C2×C8—41no—
294C2×C8—41no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—42no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—82no—
306C4⋊C4C22⋊C4×C2912yes—
307C22⋊C4—22no—
308C22⋊C4—22no—
309C22⋊C4—44no—
310C22⋊C4—41no—
311C42—41no—
312C42—41no—
313C42—41no—
314C42C22×C4×C2911yescharacteristic
315C42C2×D4×C2911yescharacteristic
316C42#41×C2911yescharacteristic
317C42#41×C2911yescharacteristic
318C23—22no—
319C23—22no—
320C23—22no—
321C23—42no—
322C23—42no—
323C23C29×#12011yescharacteristic
324Q8—81no—
325Q8—81no—
326D4—22no—
327D4—22no—
328D4—22no—
329D4C29×#10314yes—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—42no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—41no—
342C2×C4—42no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—82no—
346C2×C4—82no—
347C2×C4—88no—
348C2×C4C2×C22⋊C4×C2911yescharacteristic
349C2×C4C4×D4×C2911yescharacteristic
350C2×C4C4×D4×C2911yescharacteristic
351C2×C4C29×#12111yescharacteristic
352C2×C4C29×#12111yescharacteristic
353C2×C4C29×#12311yescharacteristic
354C2×C4C2×SD16×C2911yescharacteristic
355C2×C4C2×Q16×C2911yescharacteristic
356C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
357C2×C4C29×#13711yescharacteristic
358C8—42no—
359C8—81no—
360C8—81no—
361C22—21no—
362C22—21no—
363C22—24no—
364C22—44no—
365C22—44no—
366C22—42no—
367C22—42no—
368C22C29×#38611yescharacteristic
369C22C29×#45011yescharacteristic
370C22C29×#45111yescharacteristic
371C4—21no—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—42no—
376C4—42no—
377C4—82no—
378C4—81no—
379C4—81no—
380C4—81no—
381C4C2×C29×#10311yescharacteristic
382C4C29×#41711yescharacteristic
383C4C29×#48311yescharacteristic
384C4C29×#48411yescharacteristic
385C2—21no—
386C2—21no—
387C2—44no—
388C2C29×#187211yescharacteristic
389C2C29×#190411yescharacteristic
390C2C29×#190611yescharacteristic
subgroupG/H
center, socleC22×C29#386
commutatorC42C22×C4×C29
Frattini, cosocleC2×C42C23×C29
prime radicalC22×D4×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×#1518C2semidirect
4. C29×#1503C2semidirect
6. C29×#1303C2semidirect
7. C29×#1286C2semidirect
12. C29×#476C4semidirect
13. C29×#474C4semidirect
33. C29×C4⋊Q8C2×C4semidirect
34. C29×C4⋊Q8C2×C4semidirect
60. C29×C4⋊C8C2×C4semidirect
122. #9175C29direct (N × H)
168. #1518C2×C29semidirect
169. #1503C2×C29semidirect
171. #1303C2×C29semidirect
172. #1286C2×C29semidirect
201. #476C4×C29semidirect
202. #474C4×C29semidirect
228. C4⋊Q8C2×C4×C29semidirect
229. C4⋊Q8C2×C4×C29semidirect
255. C4⋊C8C2×C4×C29semidirect
267. C29#9175direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#30772
C29×#23492
C29×#15182
C29×#15032
C29×#14782
C29×#13032
C29×#12862
#917529