Finite Group Databasebeta

← C29×#13013 #20307913

Subgroups — C29×#13013 #20307913

Order 7424.

526 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C29×SD32C211yesmaximal, characteristic
2C2×C4×Q16×C29C211yesmaximal, characteristic, complemented
3C2×C29×#358C211yesmaximal, characteristic, complemented
4C2×C29×#357C211yesmaximal, characteristic
5C29×#1970C211yesmaximal, characteristic
6C29×#1380C211yesmaximal, characteristic, complemented
7C29×#1374C211yesmaximal, characteristic, complemented
8C22×Q16×C29C2211yescharacteristic
9C22×D8×C29C2211yescharacteristic
10C2×C4×Q8×C29—21no—
11C2×C29×SD32—22no—
12C2×C29×SD32—22no—
13C2×C29×SD32C414yescomplemented
14C22×C16×C29C2211yescharacteristic
15C22×C16×C29C2211yescharacteristic
16C4×Q16×C29—22no—
17C4×Q16×C29—22no—
18C2×C29×#107C2211yescharacteristic
19C2×C29×#107C2211yescharacteristic
20C2×C29×#103—21no—
21C2×C29×#102—21no—
22C2×C4×C8×C29C2211yescharacteristic
23C29×#390—21no—
24C29×#358—22no—
25C29×#357—22no—
26C22×Q8×C29—21no—
27C22×D4×C29—21no—
28C2×Q16×C29—21no—
29C2×Q16×C29—21no—
30C2×Q16×C29—21no—
31C2×Q16×C29C2×C412yes—
32C2×Q16×C29D412yes—
33C2×Q16×C29D412yes—
34C2×D8×C29—21no—
35C2×D8×C29—21no—
36C2×D8×C29—21no—
37C2×D8×C29—21no—
38C2×D8×C29—21no—
39C2×D8×C29C2×C412yes—
40C22×C8×C29D411yescharacteristic
41C22×C8×C29C2311yescharacteristic
42C4×Q8×C29—24no—
43C4×Q8×C29—42no—
44C2×C4⋊C4×C29—21no—
45C2×C4⋊C4×C29—21no—
46C2×C4⋊C4×C29—41no—
47C2×C22⋊C4×C29—41no—
48C2×C22⋊C4×C29—41no—
49C2×C42×C29—41no—
50C2×C42×C29D411yescharacteristic
51C29×SD32—28no—
52C2×C16×C29—21no—
53C2×C16×C29—21no—
54C2×C16×C29—21no—
55C2×C16×C29—21no—
56C2×C16×C29—21no—
57C2×C16×C29C2×C412yes—
58C29×#107—21no—
59C29×#107—21no—
60C29×#107—21no—
61C29×#107D412yes—
62C29×#103—24no—
63C29×#102—42no—
64C4×C8×C29—21no—
65C4×C8×C29—21no—
66C24×C29—41no—
67C2×Q8×C29—22no—
68C2×Q8×C29—22no—
69C2×Q8×C29—22no—
70C2×Q8×C29—41no—
71C2×Q8×C29—41no—
72C2×Q8×C29—41no—
73C2×D4×C29—22no—
74C2×D4×C29—41no—
75C2×D4×C29—41no—
76C2×D4×C29—41no—
77C2×D4×C29—41no—
78C2×D4×C29—41no—
79C22×C4×C29—41no—
80C22×C4×C29—41no—
81C22×C4×C29—41no—
82C22×C4×C29D811yescharacteristic
83C22×C4×C29D811yescharacteristic
84C22×C4×C29C2×D411yescharacteristic
85Q16×C29—22no—
86Q16×C29—22no—
87Q16×C29—22no—
88Q16×C29C22⋊C414yescomplemented
89D8×C29—22no—
90D8×C29—22no—
91D8×C29—41no—
92D8×C29—41no—
93C2×C8×C29—21no—
94C2×C8×C29—21no—
95C2×C8×C29—21no—
96C2×C8×C29C22×C411yescharacteristic
97C2×C8×C29C2×D411yescharacteristic
98C2×C8×C29C2×D411yescharacteristic
99C2×C8×C29C2×D411yescharacteristic
100C2×C8×C29#4111yescharacteristic
101C2×C8×C29#4111yescharacteristic
102C4⋊C4×C29—22no—
103C4⋊C4×C29—44no—
104C4⋊C4×C29—41no—
105C4⋊C4×C29—41no—
106C4⋊C4×C29—41no—
107C22⋊C4×C29—82no—
108C22⋊C4×C29—82no—
109C42×C29—21no—
110C42×C29—21no—
111C42×C29—44no—
112C16×C29—22no—
113C16×C29—41no—
114#13013C2911yesmaximal, characteristic, direct product factor, Sylow
115C23×C29—42no—
116C23×C29—81no—
117C23×C29—81no—
118C23×C29—81no—
119C23×C29—81no—
120C23×C29—81no—
121C23×C29—81no—
122C23×C29C2×D811yescharacteristic
123Q8×C29—24no—
124Q8×C29—42no—
125Q8×C29—42no—
126Q8×C29—42no—
127D4×C29—42no—
128D4×C29—42no—
129D4×C29—81no—
130D4×C29—81no—
131C2×C4×C29—21no—
132C2×C4×C29—21no—
133C2×C4×C29—21no—
134C2×C4×C29—21no—
135C2×C4×C29—21no—
136C2×C4×C29—42no—
137C2×C4×C29—42no—
138C2×C4×C29—42no—
139C2×C4×C29—42no—
140C2×C4×C29—81no—
141C2×C4×C29—81no—
142C2×C4×C29—81no—
143C2×C4×C29—81no—
144C2×C4×C29—81no—
145C2×C4×C29SD3212yescomplemented
146C2×C4×C29C4×D411yescharacteristic
147C2×C4×C29#12011yescharacteristic
148C2×C4×C29#12111yescharacteristic
149C2×C4×C29#13511yescharacteristic
150C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
152C8×C29—41no—
153C8×C29C2×C22⋊C411yescharacteristic
154C8×C29C4×D411yescharacteristic
155C8×C29#12111yescharacteristic
156C8×C29#12311yescharacteristic
157C22×SD32C2×C2911yescharacteristic
158C2×C4×Q16C2×C2911yescharacteristic, complemented
159C2×#358C2×C2911yescharacteristic, complemented
160C2×#357C2×C2911yescharacteristic
161#1970C2×C2911yescharacteristic
162#1380C2×C2911yescharacteristic, complemented
163#1374C2×C2911yescharacteristic, complemented
164C22×C29—82no—
165C22×C29—82no—
166C22×C29—82no—
167C22×C29—161no—
168C22×C29—161no—
169C22×C29—161no—
170C22×C29—161no—
171C22×C29C4×D811yescharacteristic
172C22×C29#44711yescharacteristic
173C22×C29#45911yescharacteristic
174C22×C29C2×SD3211yescharacteristic
175C22×C29#50811yescharacteristic
176C22×C29#50911yescharacteristic
177C22×C29#51011yescharacteristic
178C4×C29—22no—
179C4×C29—44no—
180C4×C29—41no—
181C4×C29—82no—
182C4×C29—161no—
183C4×C29#38611yescharacteristic
184C4×C29#44211yescharacteristic
185C4×C29#44911yescharacteristic
186C4×C29#46311yescharacteristic
187C22×Q16C22×C2911yescharacteristic
188C22×D8C22×C2911yescharacteristic
189C2×C4×Q8—21no—
190C2×SD32—22no—
191C2×SD32—22no—
192C2×SD32C4×C2914yescomplemented
193C22×C16C22×C2911yescharacteristic
194C22×C16C22×C2911yescharacteristic
195C4×Q16—22no—
196C4×Q16—22no—
197C2×#107C22×C2911yescharacteristic
198C2×#107C22×C2911yescharacteristic
199C2×#103—21no—
200C2×#102—21no—
201C2×C4×C8C22×C2911yescharacteristic
202#390—21no—
203#358—22no—
204#357—22no—
205C2×C29—162no—
206C2×C29#187911yescharacteristic
207C2×C29C4×SD3211yescharacteristic
208C2×C29#217511yescharacteristic
209C2×C29#218511yescharacteristic
210C2×C29#218611yescharacteristic
211C2×C29#220711yescharacteristic
212C2×C29#221111yescharacteristic
213C22×Q8—21no—
214C22×D4—21no—
215C2×Q16—21no—
216C2×Q16—21no—
217C2×Q16—21no—
218C2×Q16C2×C4×C2912yes—
219C2×Q16D4×C2912yes—
220C2×Q16D4×C2912yes—
221C2×D8—21no—
222C2×D8—21no—
223C2×D8—21no—
224C2×D8—21no—
225C2×D8—21no—
226C2×D8C2×C4×C2912yes—
227C22×C8D4×C2911yescharacteristic
228C22×C8C23×C2911yescharacteristic
229C4×Q8—24no—
230C4×Q8—42no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—41no—
234C2×C22⋊C4—41no—
235C2×C22⋊C4—41no—
236C2×C42—41no—
237C2×C42D4×C2911yescharacteristic
238SD32—28no—
239C2×C16—21no—
240C2×C16—21no—
241C2×C16—21no—
242C2×C16—21no—
243C2×C16—21no—
244C2×C16C2×C4×C2912yes—
245#107—21no—
246#107—21no—
247#107—21no—
248#107D4×C2912yes—
249#103—24no—
250#102—42no—
251C4×C8—21no—
252C4×C8—21no—
253C29#1301311yescharacteristic, direct product factor, Sylow
254C24—41no—
255C2×Q8—22no—
256C2×Q8—22no—
257C2×Q8—22no—
258C2×Q8—41no—
259C2×Q8—41no—
260C2×Q8—41no—
261C2×D4—22no—
262C2×D4—41no—
263C2×D4—41no—
264C2×D4—41no—
265C2×D4—41no—
266C2×D4—41no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4D8×C2911yescharacteristic
271C22×C4D8×C2911yescharacteristic
272C22×C4C2×D4×C2911yescharacteristic
273Q16—22no—
274Q16—22no—
275Q16—22no—
276Q16C22⋊C4×C2914yescomplemented
277D8—22no—
278D8—22no—
279D8—41no—
280D8—41no—
281C2×C8—21no—
282C2×C8—21no—
283C2×C8—21no—
284C2×C8C22×C4×C2911yescharacteristic
285C2×C8C2×D4×C2911yescharacteristic
286C2×C8C2×D4×C2911yescharacteristic
287C2×C8C2×D4×C2911yescharacteristic
288C2×C8#41×C2911yescharacteristic
289C2×C8#41×C2911yescharacteristic
290C4⋊C4—22no—
291C4⋊C4—44no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C22⋊C4—82no—
296C22⋊C4—82no—
297C42—21no—
298C42—21no—
299C42—44no—
300C16—22no—
301C16—41no—
302C23—42no—
303C23—81no—
304C23—81no—
305C23—81no—
306C23—81no—
307C23—81no—
308C23—81no—
309C23C2×D8×C2911yescharacteristic
310Q8—24no—
311Q8—42no—
312Q8—42no—
313Q8—42no—
314D4—42no—
315D4—42no—
316D4—81no—
317D4—81no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—81no—
330C2×C4—81no—
331C2×C4—81no—
332C2×C4C29×SD3212yescomplemented
333C2×C4C4×D4×C2911yescharacteristic
334C2×C4C29×#12011yescharacteristic
335C2×C4C29×#12111yescharacteristic
336C2×C4C29×#13511yescharacteristic
337C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
338C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
339C8—41no—
340C8C2×C22⋊C4×C2911yescharacteristic
341C8C4×D4×C2911yescharacteristic
342C8C29×#12111yescharacteristic
343C8C29×#12311yescharacteristic
344C22—82no—
345C22—82no—
346C22—82no—
347C22—161no—
348C22—161no—
349C22—161no—
350C22—161no—
351C22C4×D8×C2911yescharacteristic
352C22C29×#44711yescharacteristic
353C22C29×#45911yescharacteristic
354C22C2×C29×SD3211yescharacteristic
355C22C29×#50811yescharacteristic
356C22C29×#50911yescharacteristic
357C22C29×#51011yescharacteristic
358C4—22no—
359C4—41no—
360C4—44no—
361C4—82no—
362C4—161no—
363C4C29×#38611yescharacteristic
364C4C29×#44211yescharacteristic
365C4C29×#44911yescharacteristic
366C4C29×#46311yescharacteristic
367C2—162no—
368C2C29×#187911yescharacteristic
369C2C4×C29×SD3211yescharacteristic
370C2C29×#217511yescharacteristic
371C2C29×#218511yescharacteristic
372C2C29×#218611yescharacteristic
373C2C29×#220711yescharacteristic
374C2C29×#221111yescharacteristic
subgroupG/H
center, socleC23×C29C2×D8
commutatorC2×C8C22×C4×C29
Frattini, cosocleC22×C8C23×C29
prime radicalC22×D8×C29C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C29 ◁ C2×C42×C29 ◁ C2×C4×C8×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×Q16×C29C2semidirect
3. C2×C29×#358C2semidirect
6. C29×#1380C2semidirect
7. C29×#1374C2semidirect
13. C2×C29×SD32C4semidirect
88. Q16×C29C22⋊C4semidirect
114. #13013C29direct (N × H)
145. C2×C4×C29SD32semidirect
158. C2×C4×Q16C2×C29semidirect
159. C2×#358C2×C29semidirect
162. #1380C2×C29semidirect
163. #1374C2×C29semidirect
192. C2×SD32C4×C29semidirect
253. C29#13013direct (N × H)
276. Q16C22⋊C4×C29semidirect
332. C2×C4C29×SD32semidirect

Maximal subgroups

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

subgroupindex
C22×C29×SD322
C2×C4×Q16×C292
C2×C29×#3582
C2×C29×#3572
C29×#19702
C29×#13802
C29×#13742
#1301329