Finite Group Databasebeta

← C29×#10466 #20305366

Subgroups — C29×#10466 #20305366

Order 7424.

420 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3037C211yesmaximal, characteristic
2C29×#1805C211yesmaximal, characteristic, complemented
3C29×#1571C211yesmaximal, characteristic, complemented
4C29×#1540C211yesmaximal, characteristic
5C29×#1517C211yesmaximal, characteristic
6C29×#1461C211yesmaximal, characteristic, complemented
7C29×#1286C211yesmaximal, characteristic, complemented
8C2×C29×#137—21no—
9C29×#532C2211yescharacteristic
10C2×C4×Q8×C29C2211yescharacteristic
11C29×#464—22no—
12C29×#462—21no—
13C29×#460—21no—
14C29×#431C2211yescharacteristic
15C29×#431C2211yescharacteristic
16C29×#423C2211yescharacteristic
17C2×C29×C4⋊C8C2211yescharacteristic
18C29×#417—21no—
19C2×C29×#103—21no—
20C29×#382C2211yescharacteristic
21C29×#340—21no—
22C29×#335—22no—
23C29×#332—21no—
24C29×#331—21no—
25C29×#327—22no—
26C29×#324—22no—
27C2×#41×C29—21no—
28C22×Q8×C29D411yescharacteristic
29C29×#137—42no—
30C29×#137—42no—
31C2×Q16×C29—22no—
32C2×SD16×C29—22no—
33C2×M16×C29—21no—
34C22×C8×C29—21no—
35C29×C4⋊Q8D411yescharacteristic
36C29×#127D411yescharacteristic
37C29×#124—21no—
38C29×#121—21no—
39C29×#121—21no—
40C4×Q8×C29—21no—
41C4×Q8×C29—21no—
42C4×Q8×C29—21no—
43C4×Q8×C29—21no—
44C4×D4×C29—21no—
45C4×D4×C29—21no—
46C2×C4⋊C4×C29—21no—
47C2×C4⋊C4×C29—21no—
48C2×C4⋊C4×C29D411yescharacteristic
49C2×C42×C29—21no—
50C2×C42×C29C2311yescharacteristic
51C29×C4⋊C8—21no—
52C29×C4⋊C8—21no—
53C29×C4⋊C8—21no—
54C29×C4⋊C8—21no—
55C29×C4⋊C8—21no—
56C29×C4⋊C8D412yes—
57C29×#103—22no—
58C29×#103—42no—
59C29×#102—22no—
60C29×C22⋊C8—21no—
61C29×C22⋊C8D412yes—
62C4×C8×C29—21no—
63C4×C8×C29—21no—
64C29×#95—21no—
65C29×#95—21no—
66#41×C29—41no—
67#41×C29—41no—
68#41×C29—41no—
69#41×C29—41no—
70C2×Q8×C29—21no—
71C2×Q8×C29—21no—
72C2×Q8×C29—21no—
73C2×Q8×C29—21no—
74C2×Q8×C29—21no—
75C2×Q8×C29—21no—
76C2×Q8×C29D812yes—
77C2×D4×C29—21no—
78C2×D4×C29—21no—
79C2×D4×C29—21no—
80C2×D4×C29—41no—
81C22×C4×C29—21no—
82C22×C4×C29—21no—
83C22×C4×C29—41no—
84C22×C4×C29—41no—
85C22×C4×C29C2×D411yescharacteristic
86C22×C4×C29C2×D411yescharacteristic
87C22×C4×C29#4111yescharacteristic
88Q16×C29—44no—
89SD16×C29—44no—
90M16×C29—41no—
91M16×C29—41no—
92C2×C8×C29—22no—
93C2×C8×C29—22no—
94C2×C8×C29—41no—
95C2×C8×C29—41no—
96C2×C8×C29—41no—
97C2×C8×C29—41no—
98C4⋊C4×C29—21no—
99C4⋊C4×C29—21no—
100C4⋊C4×C29—21no—
101C4⋊C4×C29—21no—
102C4⋊C4×C29—41no—
103C4⋊C4×C29—41no—
104C4⋊C4×C29—41no—
105C4⋊C4×C29—41no—
106C22⋊C4×C29—41no—
107C22⋊C4×C29—41no—
108C42×C29—41no—
109C42×C29—41no—
110C42×C29C2×D411yescharacteristic
111C42×C29C2×D411yescharacteristic
112C42×C29#4111yescharacteristic
113C42×C29#4111yescharacteristic
114#10466C2911yesmaximal, characteristic, direct product factor, Sylow
115C23×C29—41no—
116C23×C29#12111yescharacteristic
117Q8×C29—22no—
118Q8×C29—22no—
119Q8×C29—41no—
120Q8×C29—41no—
121Q8×C29—41no—
122Q8×C29—41no—
123D4×C29—41no—
124D4×C29—41no—
125D4×C29—81no—
126D4×C29—81no—
127D4×C29—81no—
128D4×C29—81no—
129C2×C4×C29—22no—
130C2×C4×C29—41no—
131C2×C4×C29—41no—
132C2×C4×C29—41no—
133C2×C4×C29—41no—
134C2×C4×C29—41no—
135C2×C4×C29—41no—
136C2×C4×C29—81no—
137C2×C4×C29—81no—
138C2×C4×C29—81no—
139C2×C4×C29—81no—
140C2×C4×C29—81no—
141C2×C4×C29—81no—
142C2×C4×C29#12011yescharacteristic
143C2×C4×C29#12111yescharacteristic
144C2×C4×C29#12111yescharacteristic
145C2×C4×C29#12311yescharacteristic
146C2×C4×C29#12311yescharacteristic
147C2×C4×C29#12411yescharacteristic
148C2×C4×C29C2×D811yescharacteristic
149C2×C4×C29#13511yescharacteristic
150C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C29#13711yescharacteristic
152C8×C29—42no—
153C8×C29—42no—
154C8×C29—81no—
155C8×C29—81no—
156#3037C2×C2911yescharacteristic
157#1805C2×C2911yescharacteristic, complemented
158#1571C2×C2911yescharacteristic, complemented
159#1540C2×C2911yescharacteristic
160#1517C2×C2911yescharacteristic
161#1461C2×C2911yescharacteristic, complemented
162#1286C2×C2911yescharacteristic, complemented
163C22×C29—21no—
164C22×C29—21no—
165C22×C29—81no—
166C22×C29—81no—
167C22×C29—81no—
168C22×C29#39411yescharacteristic
169C22×C29#46611yescharacteristic
170C22×C29#46811yescharacteristic
171C4×C29—21no—
172C4×C29—21no—
173C4×C29—21no—
174C4×C29—21no—
175C4×C29—42no—
176C4×C29—81no—
177C4×C29—81no—
178C4×C29—161no—
179C4×C29#44711yescharacteristic
180C4×C29#45211yescharacteristic
181C4×C29#48011yescharacteristic
182C4×C29#48211yescharacteristic
183C2×#137—21no—
184#532C22×C2911yescharacteristic
185C2×C4×Q8C22×C2911yescharacteristic
186#464—22no—
187#462—21no—
188#460—21no—
189#431C22×C2911yescharacteristic
190#431C22×C2911yescharacteristic
191#423C22×C2911yescharacteristic
192C2×C4⋊C8C22×C2911yescharacteristic
193#417—21no—
194C2×#103—21no—
195#382C22×C2911yescharacteristic
196#340—21no—
197#335—22no—
198#332—21no—
199#331—21no—
200#327—22no—
201#324—22no—
202C2×C29—21no—
203C2×C29—21no—
204C2×C29—161no—
205C2×C29#203311yescharacteristic
206C2×C29#204911yescharacteristic
207C2×C29#205311yescharacteristic
208C2×#41—21no—
209C22×Q8D4×C2911yescharacteristic
210#137—42no—
211#137—42no—
212C2×Q16—22no—
213C2×SD16—22no—
214C2×M16—21no—
215C22×C8—21no—
216C4⋊Q8D4×C2911yescharacteristic
217#127D4×C2911yescharacteristic
218#124—21no—
219#121—21no—
220#121—21no—
221C4×Q8—21no—
222C4×Q8—21no—
223C4×Q8—21no—
224C4×Q8—21no—
225C4×D4—21no—
226C4×D4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4D4×C2911yescharacteristic
230C2×C42—21no—
231C2×C42C23×C2911yescharacteristic
232C4⋊C8—21no—
233C4⋊C8—21no—
234C4⋊C8—21no—
235C4⋊C8—21no—
236C4⋊C8—21no—
237C4⋊C8D4×C2912yes—
238#103—22no—
239#103—42no—
240#102—22no—
241C22⋊C8—21no—
242C22⋊C8D4×C2912yes—
243C4×C8—21no—
244C4×C8—21no—
245#95—21no—
246#95—21no—
247C29#1046611yescharacteristic, direct product factor, Sylow
248#41—41no—
249#41—41no—
250#41—41no—
251#41—41no—
252C2×Q8—21no—
253C2×Q8—21no—
254C2×Q8—21no—
255C2×Q8—21no—
256C2×Q8—21no—
257C2×Q8—21no—
258C2×Q8D8×C2912yes—
259C2×D4—21no—
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—41no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4C2×D4×C2911yescharacteristic
268C22×C4C2×D4×C2911yescharacteristic
269C22×C4#41×C2911yescharacteristic
270Q16—44no—
271SD16—44no—
272M16—41no—
273M16—41no—
274C2×C8—22no—
275C2×C8—22no—
276C2×C8—41no—
277C2×C8—41no—
278C2×C8—41no—
279C2×C8—41no—
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C22⋊C4—41no—
289C22⋊C4—41no—
290C42—41no—
291C42—41no—
292C42C2×D4×C2911yescharacteristic
293C42C2×D4×C2911yescharacteristic
294C42#41×C2911yescharacteristic
295C42#41×C2911yescharacteristic
296C23—41no—
297C23C29×#12111yescharacteristic
298Q8—22no—
299Q8—22no—
300Q8—41no—
301Q8—41no—
302Q8—41no—
303Q8—41no—
304D4—41no—
305D4—41no—
306D4—81no—
307D4—81no—
308D4—81no—
309D4—81no—
310C2×C4—22no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4C29×#12011yescharacteristic
324C2×C4C29×#12111yescharacteristic
325C2×C4C29×#12111yescharacteristic
326C2×C4C29×#12311yescharacteristic
327C2×C4C29×#12311yescharacteristic
328C2×C4C29×#12411yescharacteristic
329C2×C4C2×D8×C2911yescharacteristic
330C2×C4C29×#13511yescharacteristic
331C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
332C2×C4C29×#13711yescharacteristic
333C8—42no—
334C8—42no—
335C8—81no—
336C8—81no—
337C22—21no—
338C22—21no—
339C22—81no—
340C22—81no—
341C22—81no—
342C22C29×#39411yescharacteristic
343C22C29×#46611yescharacteristic
344C22C29×#46811yescharacteristic
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—42no—
350C4—81no—
351C4—81no—
352C4—161no—
353C4C29×#44711yescharacteristic
354C4C29×#45211yescharacteristic
355C4C29×#48011yescharacteristic
356C4C29×#48211yescharacteristic
357C2—21no—
358C2—21no—
359C2—161no—
360C2C29×#203311yescharacteristic
361C2C29×#204911yescharacteristic
362C2C29×#205311yescharacteristic
subgroupG/H
center, socleC22×C29#394
commutator, Frattini, cosocleC2×C42C23×C29
prime radicalC29×#532C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C2×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#1805C2semidirect
3. C29×#1571C2semidirect
6. C29×#1461C2semidirect
7. C29×#1286C2semidirect
114. #10466C29direct (N × H)
157. #1805C2×C29semidirect
158. #1571C2×C29semidirect
161. #1461C2×C29semidirect
162. #1286C2×C29semidirect
247. C29#10466direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#30372
C29×#18052
C29×#15712
C29×#15402
C29×#15172
C29×#14612
C29×#12862
#1046629