Finite Group Databasebeta

← C29×#13033 #20307933

Subgroups — C29×#13033 #20307933

Order 7424.

498 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#509C211yesmaximal, characteristic
2C29×#2948C211yesmaximal, characteristic, complemented
3C29×#2145C211yesmaximal, characteristic, complemented
4C29×#2140C211yesmaximal, characteristic, complemented
5C29×#1976C211yesmaximal, characteristic, complemented
6C29×#1384C211yesmaximal, characteristic, complemented
7C29×#1378C211yesmaximal, characteristic, complemented
8C2×C29×#135C2211yescharacteristic
9C22×D8×C29C2211yescharacteristic
10C29×#518—21no—
11C29×#509—22no—
12C29×#509—22no—
13C2×C29×SD32C412yescomplemented
14C2×C29×D16C412yescomplemented
15C2×C29×M32C2211yescharacteristic
16C2×C29×M32C2211yescharacteristic
17C29×#442—22no—
18C4×D8×C29—22no—
19C29×#427C2211yescharacteristic
20C29×#427C2211yescharacteristic
21C29×#421—21no—
22C29×#418—21no—
23C29×#410—21no—
24C29×#405C2211yescharacteristic
25C29×#360—22no—
26C29×#357—22no—
27C2×#41×C29—21no—
28C22×D4×C29—21no—
29C29×#135—21no—
30C29×#135—21no—
31C29×#135—21no—
32C29×#135—21no—
33C2×Q16×C29C2×C411yescharacteristic, complemented
34C2×SD16×C29—21no—
35C2×D8×C29—21no—
36C2×D8×C29—21no—
37C2×D8×C29—21no—
38C2×D8×C29C2×C412yes—
39C2×D8×C29C2×C411yescharacteristic, complemented
40C2×D8×C29D412yes—
41C2×D8×C29D412yes—
42C2×M16×C29D411yescharacteristic
43C22×C8×C29C2311yescharacteristic
44C4×D4×C29—24no—
45C4×D4×C29—42no—
46C29×#117—21no—
47C29×#117—21no—
48C29×#117D411yescharacteristic
49C2×C22⋊C4×C29—42no—
50C29×SD32—24no—
51C29×D16—24no—
52C29×M32—21no—
53C29×M32—21no—
54C29×M32—21no—
55C29×M32—21no—
56C2×C16×C29—21no—
57C2×C16×C29C2×C412yescomplemented
58C29×#107—21no—
59C29×#107—21no—
60C29×#106—21no—
61C29×#106D412yes—
62C29×#104—42no—
63C29×#102—24no—
64C29×#99—42no—
65C29×#97—21no—
66C4×C8×C29—21no—
67C24×C29—41no—
68#41×C29—41no—
69#41×C29—41no—
70#41×C29—41no—
71#41×C29—41no—
72C2×Q8×C29—21no—
73C2×D4×C29—22no—
74C2×D4×C29—21no—
75C2×D4×C29—22no—
76C2×D4×C29—22no—
77C2×D4×C29—41no—
78C2×D4×C29—41no—
79C2×D4×C29—41no—
80C2×D4×C29—41no—
81C22×C4×C29—44no—
82C22×C4×C29—41no—
83C22×C4×C29C2×D411yescharacteristic
84Q16×C29—21no—
85Q16×C29—21no—
86SD16×C29—41no—
87SD16×C29—41no—
88D8×C29—21no—
89D8×C29—22no—
90D8×C29—21no—
91D8×C29—22no—
92D8×C29—22no—
93D8×C29C22⋊C414yes—
94M16×C29—21no—
95M16×C29—21no—
96C2×C8×C29—21no—
97C2×C8×C29C22×C411yescharacteristic
98C2×C8×C29C2×D411yescharacteristic
99C2×C8×C29C2×D411yescharacteristic
100C2×C8×C29C2×D411yescharacteristic
101C2×C8×C29#4111yescharacteristic
102C2×C8×C29#4111yescharacteristic
103C4⋊C4×C29—21no—
104C4⋊C4×C29—22no—
105C4⋊C4×C29—41no—
106C22⋊C4×C29—44no—
107C22⋊C4×C29—41no—
108C22⋊C4×C29—41no—
109C22⋊C4×C29D812yes—
110C42×C29—21no—
111C42×C29—41no—
112C42×C29—41no—
113C16×C29—22no—
114C16×C29—41no—
115#13033C2911yesmaximal, characteristic, direct product factor, Sylow
116C23×C29—42no—
117C23×C29—42no—
118C23×C29—42no—
119C23×C29—41no—
120C23×C29—162no—
121C23×C29C2×D811yescharacteristic
122Q8×C29—41no—
123Q8×C29—41no—
124D4×C29—24no—
125D4×C29—41no—
126D4×C29—42no—
127D4×C29—41no—
128D4×C29—42no—
129D4×C29—42no—
130D4×C29—81no—
131D4×C29—81no—
132C2×C4×C29—22no—
133C2×C4×C29—41no—
134C2×C4×C29—42no—
135C2×C4×C29—81no—
136C2×C4×C29—81no—
137C2×C4×C29—81no—
138C2×C4×C29—164no—
139C2×C4×C29C4×D411yescharacteristic
140C2×C4×C29#12011yescharacteristic
141C2×C4×C29#12111yescharacteristic
142C2×C4×C29#13511yescharacteristic
143C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
144C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
145C8×C29—41no—
146C8×C29C2×C22⋊C411yescharacteristic
147C8×C29C4×D411yescharacteristic
148C8×C29#12111yescharacteristic
149C8×C29#12311yescharacteristic
150C2×#509C2×C2911yescharacteristic
151#2948C2×C2911yescharacteristic, complemented
152#2145C2×C2911yescharacteristic, complemented
153#2140C2×C2911yescharacteristic, complemented
154#1976C2×C2911yescharacteristic, complemented
155#1384C2×C2911yescharacteristic, complemented
156#1378C2×C2911yescharacteristic, complemented
157C22×C29—41no—
158C22×C29—44no—
159C22×C29—84no—
160C22×C29—81no—
161C22×C29—162no—
162C22×C29—162no—
163C22×C29—161no—
164C22×C29C4×D811yescharacteristic
165C22×C29#44711yescharacteristic
166C22×C29#45911yescharacteristic
167C4×C29—42no—
168C4×C29—82no—
169C4×C29—81no—
170C4×C29—161no—
171C4×C29#38611yescharacteristic
172C4×C29#44211yescharacteristic
173C4×C29#44911yescharacteristic
174C4×C29#46311yescharacteristic
175C2×#135C22×C2911yescharacteristic
176C22×D8C22×C2911yescharacteristic
177#518—21no—
178#509—22no—
179#509—22no—
180C2×SD32C4×C2912yescomplemented
181C2×D16C4×C2912yescomplemented
182C2×M32C22×C2911yescharacteristic
183C2×M32C22×C2911yescharacteristic
184#442—22no—
185C4×D8—22no—
186#427C22×C2911yescharacteristic
187#427C22×C2911yescharacteristic
188#421—21no—
189#418—21no—
190#410—21no—
191#405C22×C2911yescharacteristic
192#360—22no—
193#357—22no—
194C2×C29—21no—
195C2×C29—21no—
196C2×C29—21no—
197C2×C29—84no—
198C2×C29—161no—
199C2×C29#187911yescharacteristic
200C2×#41—21no—
201C22×D4—21no—
202#135—21no—
203#135—21no—
204#135—21no—
205#135—21no—
206C2×Q16C2×C4×C2911yescharacteristic, complemented
207C2×SD16—21no—
208C2×D8—21no—
209C2×D8—21no—
210C2×D8—21no—
211C2×D8C2×C4×C2912yes—
212C2×D8C2×C4×C2911yescharacteristic, complemented
213C2×D8D4×C2912yes—
214C2×D8D4×C2912yes—
215C2×M16D4×C2911yescharacteristic
216C22×C8C23×C2911yescharacteristic
217C4×D4—24no—
218C4×D4—42no—
219#117—21no—
220#117—21no—
221#117D4×C2911yescharacteristic
222C2×C22⋊C4—42no—
223SD32—24no—
224D16—24no—
225M32—21no—
226M32—21no—
227M32—21no—
228M32—21no—
229C2×C16—21no—
230C2×C16C2×C4×C2912yescomplemented
231#107—21no—
232#107—21no—
233#106—21no—
234#106D4×C2912yes—
235#104—42no—
236#102—24no—
237#99—42no—
238#97—21no—
239C4×C8—21no—
240C29#1303311yescharacteristic, direct product factor, Sylow
241C24—41no—
242#41—41no—
243#41—41no—
244#41—41no—
245#41—41no—
246C2×Q8—21no—
247C2×D4—22no—
248C2×D4—21no—
249C2×D4—22no—
250C2×D4—22no—
251C2×D4—41no—
252C2×D4—41no—
253C2×D4—41no—
254C2×D4—41no—
255C22×C4—44no—
256C22×C4—41no—
257C22×C4C2×D4×C2911yescharacteristic
258Q16—21no—
259Q16—21no—
260SD16—41no—
261SD16—41no—
262D8—21no—
263D8—22no—
264D8—21no—
265D8—22no—
266D8—22no—
267D8C22⋊C4×C2914yes—
268M16—21no—
269M16—21no—
270C2×C8—21no—
271C2×C8C22×C4×C2911yescharacteristic
272C2×C8C2×D4×C2911yescharacteristic
273C2×C8C2×D4×C2911yescharacteristic
274C2×C8C2×D4×C2911yescharacteristic
275C2×C8#41×C2911yescharacteristic
276C2×C8#41×C2911yescharacteristic
277C4⋊C4—21no—
278C4⋊C4—22no—
279C4⋊C4—41no—
280C22⋊C4—44no—
281C22⋊C4—41no—
282C22⋊C4—41no—
283C22⋊C4D8×C2912yes—
284C42—21no—
285C42—41no—
286C42—41no—
287C16—22no—
288C16—41no—
289C23—42no—
290C23—42no—
291C23—42no—
292C23—41no—
293C23—162no—
294C23C2×D8×C2911yescharacteristic
295Q8—41no—
296Q8—41no—
297D4—24no—
298D4—42no—
299D4—41no—
300D4—42no—
301D4—42no—
302D4—41no—
303D4—81no—
304D4—81no—
305C2×C4—22no—
306C2×C4—41no—
307C2×C4—42no—
308C2×C4—81no—
309C2×C4—81no—
310C2×C4—81no—
311C2×C4—164no—
312C2×C4C4×D4×C2911yescharacteristic
313C2×C4C29×#12011yescharacteristic
314C2×C4C29×#12111yescharacteristic
315C2×C4C29×#13511yescharacteristic
316C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
317C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
318C8—41no—
319C8C2×C22⋊C4×C2911yescharacteristic
320C8C4×D4×C2911yescharacteristic
321C8C29×#12111yescharacteristic
322C8C29×#12311yescharacteristic
323C22—41no—
324C22—44no—
325C22—84no—
326C22—81no—
327C22—162no—
328C22—162no—
329C22—161no—
330C22C4×D8×C2911yescharacteristic
331C22C29×#44711yescharacteristic
332C22C29×#45911yescharacteristic
333C4—42no—
334C4—82no—
335C4—81no—
336C4—161no—
337C4C29×#38611yescharacteristic
338C4C29×#44211yescharacteristic
339C4C29×#44911yescharacteristic
340C4C29×#46311yescharacteristic
341C2—21no—
342C2—21no—
343C2—21no—
344C2—84no—
345C2—161no—
346C2C29×#187911yescharacteristic
subgroupG/H
center, socleC2×C29#1879
commutatorC2×C8C22×C4×C29
Frattini, cosocleC22×C8C23×C29
prime radicalC2×C29×#509C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C29 ◁ C22×C4×C29 ◁ C29×#405 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#2948C2semidirect
3. C29×#2145C2semidirect
4. C29×#2140C2semidirect
5. C29×#1976C2semidirect
6. C29×#1384C2semidirect
7. C29×#1378C2semidirect
13. C2×C29×SD32C4semidirect
14. C2×C29×D16C4semidirect
33. C2×Q16×C29C2×C4semidirect
39. C2×D8×C29C2×C4semidirect
57. C2×C16×C29C2×C4semidirect
115. #13033C29direct (N × H)
151. #2948C2×C29semidirect
152. #2145C2×C29semidirect
153. #2140C2×C29semidirect
154. #1976C2×C29semidirect
155. #1384C2×C29semidirect
156. #1378C2×C29semidirect
180. C2×SD32C4×C29semidirect
181. C2×D16C4×C29semidirect
206. C2×Q16C2×C4×C29semidirect
212. C2×D8C2×C4×C29semidirect
230. C2×C16C2×C4×C29semidirect
240. C29#13033direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#5092
C29×#29482
C29×#21452
C29×#21402
C29×#19762
C29×#13842
C29×#13782
#1303329