Finite Group Databasebeta

← C29×#13022 #20307922

Subgroups — C29×#13022 #20307922

Order 7424.

494 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#509C211yesmaximal, characteristic
2C29×#2951C211yesmaximal, characteristic, complemented
3C2×C29×#359C211yesmaximal, characteristic, complemented
4C2×C29×#357C211yesmaximal, characteristic, complemented
5C29×#1978C211yesmaximal, characteristic, complemented
6C29×#1387C211yesmaximal, characteristic, complemented
7C29×#1379C211yesmaximal, characteristic, complemented
8C2×C29×#135C2211yescharacteristic
9C22×D8×C29C2211yescharacteristic
10C29×#520—21no—
11C29×#509—22no—
12C29×#509C414yescomplemented
13C2×C29×SD32—21no—
14C2×C29×D16—21no—
15C2×C29×M32C2211yescharacteristic
16C22×C16×C29C2211yescharacteristic
17C29×#440—22no—
18C4×Q16×C29—21no—
19C4×D8×C29—21no—
20C2×C29×#108C2211yescharacteristic
21C2×C29×#107C2211yescharacteristic
22C29×#418—21no—
23C29×#417—21no—
24C2×C29×#100—21no—
25C29×#405C2211yescharacteristic
26C29×#359—22no—
27C29×#357—22no—
28C2×#41×C29—21no—
29C22×D4×C29—21no—
30C29×#135—21no—
31C29×#135—21no—
32C29×#135C2×C412yes—
33C29×#135D412yes—
34C2×Q16×C29D411yescharacteristic
35C2×SD16×C29—21no—
36C2×D8×C29—21no—
37C2×D8×C29—21no—
38C2×D8×C29—21no—
39C2×D8×C29—21no—
40C2×D8×C29—21no—
41C2×D8×C29C2×C412yescomplemented
42C2×D8×C29D411yescharacteristic
43C2×M16×C29—21no—
44C2×M16×C29D411yescharacteristic
45C22×C8×C29C2311yescharacteristic
46C4×Q8×C29—22no—
47C4×D4×C29—22no—
48C4×D4×C29—42no—
49C29×#117—41no—
50C29×#117D411yescharacteristic
51C2×C4⋊C4×C29—21no—
52C2×C4⋊C4×C29—41no—
53C29×SD32—24no—
54C29×D16—24no—
55C29×M32—21no—
56C29×M32C2×C412yescomplemented
57C2×C16×C29—21no—
58C2×C16×C29—21no—
59C2×C16×C29—21no—
60C2×C16×C29—21no—
61C29×#108—21no—
62C29×#108—21no—
63C29×#107—21no—
64C29×#107D412yes—
65C29×#103—22no—
66C29×#102—22no—
67C29×#102—41no—
68C29×#102—41no—
69C29×#100—42no—
70C29×#97—21no—
71C4×C8×C29—21no—
72C24×C29—41no—
73#41×C29—22no—
74#41×C29—22no—
75#41×C29—41no—
76#41×C29—41no—
77C2×Q8×C29—21no—
78C2×D4×C29—22no—
79C2×D4×C29—21no—
80C2×D4×C29—41no—
81C2×D4×C29—41no—
82C2×D4×C29—41no—
83C2×D4×C29—41no—
84C2×D4×C29—41no—
85C2×D4×C29—41no—
86C22×C4×C29—42no—
87C22×C4×C29—41no—
88C22×C4×C29—41no—
89C22×C4×C29C2×D411yescharacteristic
90Q16×C29—21no—
91Q16×C29C22⋊C412yes—
92SD16×C29—22no—
93SD16×C29—22no—
94D8×C29—22no—
95D8×C29—22no—
96D8×C29—21no—
97D8×C29—41no—
98D8×C29—41no—
99D8×C29C22⋊C412yes—
100M16×C29—21no—
101M16×C29—21no—
102M16×C29—41no—
103M16×C29—41no—
104C2×C8×C29—21no—
105C2×C8×C29—41no—
106C2×C8×C29C22×C411yescharacteristic
107C2×C8×C29C2×D411yescharacteristic
108C2×C8×C29C2×D411yescharacteristic
109C2×C8×C29C2×D411yescharacteristic
110C2×C8×C29#4111yescharacteristic
111C2×C8×C29#4111yescharacteristic
112C4⋊C4×C29—22no—
113C4⋊C4×C29—42no—
114C4⋊C4×C29—41no—
115C4⋊C4×C29D811yescharacteristic
116C4⋊C4×C29D811yescharacteristic
117C22⋊C4×C29—21no—
118C22⋊C4×C29—42no—
119C42×C29—21no—
120C42×C29—42no—
121C16×C29—22no—
122C16×C29—41no—
123#13022C2911yesmaximal, characteristic, direct product factor, Sylow
124C23×C29—41no—
125C23×C29—42no—
126C23×C29—81no—
127C23×C29—81no—
128C23×C29—161no—
129C23×C29—161no—
130C23×C29AGL(1,ℤ/8)11yescharacteristic
131Q8×C29—22no—
132Q8×C29—41no—
133D4×C29—22no—
134D4×C29—42no—
135D4×C29—42no—
136D4×C29—42no—
137D4×C29—42no—
138D4×C29—41no—
139D4×C29—81no—
140D4×C29—81no—
141C2×C4×C29—21no—
142C2×C4×C29—21no—
143C2×C4×C29—41no—
144C2×C4×C29—42no—
145C2×C4×C29—42no—
146C2×C4×C29—42no—
147C2×C4×C29—162no—
148C2×C4×C29—161no—
149C2×C4×C29C4×D411yescharacteristic
150C2×C4×C29#12011yescharacteristic
151C2×C4×C29#12111yescharacteristic
152C2×C4×C29C2×D811yescharacteristic
153C2×C4×C29#13511yescharacteristic
154C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
155C8×C29—41no—
156C8×C29—81no—
157C8×C29C2×C22⋊C411yescharacteristic
158C8×C29C4×D411yescharacteristic
159C8×C29#12111yescharacteristic
160C8×C29#12311yescharacteristic
161C2×#509C2×C2911yescharacteristic
162#2951C2×C2911yescharacteristic, complemented
163C2×#359C2×C2911yescharacteristic, complemented
164C2×#357C2×C2911yescharacteristic, complemented
165#1978C2×C2911yescharacteristic, complemented
166#1387C2×C2911yescharacteristic, complemented
167#1379C2×C2911yescharacteristic, complemented
168C22×C29—21no—
169C22×C29—21no—
170C22×C29—42no—
171C22×C29—81no—
172C22×C29—81no—
173C22×C29—82no—
174C22×C29—162no—
175C22×C29—162no—
176C22×C29—161no—
177C22×C29—161no—
178C22×C29#44211yescharacteristic
179C22×C29#44711yescharacteristic
180C22×C29#46311yescharacteristic
181C4×C29—42no—
182C4×C29—41no—
183C4×C29—41no—
184C4×C29—82no—
185C4×C29#38611yescharacteristic
186C4×C29C4×D811yescharacteristic
187C4×C29#44911yescharacteristic
188C4×C29#45911yescharacteristic
189C2×#135C22×C2911yescharacteristic
190C22×D8C22×C2911yescharacteristic
191#520—21no—
192#509—22no—
193#509C4×C2914yescomplemented
194C2×SD32—21no—
195C2×D16—21no—
196C2×M32C22×C2911yescharacteristic
197C22×C16C22×C2911yescharacteristic
198#440—22no—
199C4×Q16—21no—
200C4×D8—21no—
201C2×#108C22×C2911yescharacteristic
202C2×#107C22×C2911yescharacteristic
203#418—21no—
204#417—21no—
205C2×#100—21no—
206#405C22×C2911yescharacteristic
207#359—22no—
208#357—22no—
209C2×C29—21no—
210C2×C29—21no—
211C2×C29—82no—
212C2×C29—162no—
213C2×C29#187911yescharacteristic
214C2×C29#219211yescharacteristic
215C2×C29#219311yescharacteristic
216C2×#41—21no—
217C22×D4—21no—
218#135—21no—
219#135—21no—
220#135C2×C4×C2912yes—
221#135D4×C2912yes—
222C2×Q16D4×C2911yescharacteristic
223C2×SD16—21no—
224C2×D8—21no—
225C2×D8—21no—
226C2×D8—21no—
227C2×D8—21no—
228C2×D8—21no—
229C2×D8C2×C4×C2912yescomplemented
230C2×D8D4×C2911yescharacteristic
231C2×M16—21no—
232C2×M16D4×C2911yescharacteristic
233C22×C8C23×C2911yescharacteristic
234C4×Q8—22no—
235C4×D4—22no—
236C4×D4—42no—
237#117—41no—
238#117D4×C2911yescharacteristic
239C2×C4⋊C4—21no—
240C2×C4⋊C4—41no—
241SD32—24no—
242D16—24no—
243M32—21no—
244M32C2×C4×C2912yescomplemented
245C2×C16—21no—
246C2×C16—21no—
247C2×C16—21no—
248C2×C16—21no—
249#108—21no—
250#108—21no—
251#107—21no—
252#107D4×C2912yes—
253#103—22no—
254#102—22no—
255#102—41no—
256#102—41no—
257#100—42no—
258#97—21no—
259C4×C8—21no—
260C29#1302211yescharacteristic, direct product factor, Sylow
261C24—41no—
262#41—22no—
263#41—22no—
264#41—41no—
265#41—41no—
266C2×Q8—21no—
267C2×D4—22no—
268C2×D4—21no—
269C2×D4—41no—
270C2×D4—41no—
271C2×D4—41no—
272C2×D4—41no—
273C2×D4—41no—
274C2×D4—41no—
275C22×C4—42no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4C2×D4×C2911yescharacteristic
279Q16—21no—
280Q16C22⋊C4×C2912yes—
281SD16—22no—
282SD16—22no—
283D8—22no—
284D8—22no—
285D8—21no—
286D8—41no—
287D8—41no—
288D8C22⋊C4×C2912yes—
289M16—21no—
290M16—21no—
291M16—41no—
292M16—41no—
293C2×C8—21no—
294C2×C8—41no—
295C2×C8C22×C4×C2911yescharacteristic
296C2×C8C2×D4×C2911yescharacteristic
297C2×C8C2×D4×C2911yescharacteristic
298C2×C8C2×D4×C2911yescharacteristic
299C2×C8#41×C2911yescharacteristic
300C2×C8#41×C2911yescharacteristic
301C4⋊C4—22no—
302C4⋊C4—42no—
303C4⋊C4—41no—
304C4⋊C4D8×C2911yescharacteristic
305C4⋊C4D8×C2911yescharacteristic
306C22⋊C4—21no—
307C22⋊C4—42no—
308C42—21no—
309C42—42no—
310C16—22no—
311C16—41no—
312C23—41no—
313C23—42no—
314C23—81no—
315C23—81no—
316C23—161no—
317C23—161no—
318C23C29×AGL(1,ℤ/8)11yescharacteristic
319Q8—22no—
320Q8—41no—
321D4—22no—
322D4—42no—
323D4—42no—
324D4—42no—
325D4—41no—
326D4—42no—
327D4—81no—
328D4—81no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—41no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—162no—
336C2×C4—161no—
337C2×C4C4×D4×C2911yescharacteristic
338C2×C4C29×#12011yescharacteristic
339C2×C4C29×#12111yescharacteristic
340C2×C4C2×D8×C2911yescharacteristic
341C2×C4C29×#13511yescharacteristic
342C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
343C8—41no—
344C8—81no—
345C8C2×C22⋊C4×C2911yescharacteristic
346C8C4×D4×C2911yescharacteristic
347C8C29×#12111yescharacteristic
348C8C29×#12311yescharacteristic
349C22—21no—
350C22—21no—
351C22—42no—
352C22—81no—
353C22—81no—
354C22—82no—
355C22—162no—
356C22—162no—
357C22—161no—
358C22—161no—
359C22C29×#44211yescharacteristic
360C22C29×#44711yescharacteristic
361C22C29×#46311yescharacteristic
362C4—41no—
363C4—41no—
364C4—42no—
365C4—82no—
366C4C29×#38611yescharacteristic
367C4C4×D8×C2911yescharacteristic
368C4C29×#44911yescharacteristic
369C4C29×#45911yescharacteristic
370C2—21no—
371C2—21no—
372C2—82no—
373C2—162no—
374C2C29×#187911yescharacteristic
375C2C29×#219211yescharacteristic
376C2C29×#219311yescharacteristic
subgroupG/H
center, socleC22×C29#447
commutatorC2×C8C22×C4×C29
Frattini, cosocleC22×C8C23×C29
prime radicalC2×C29×#509C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C22×C4×C29 ◁ C29×#405 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#2951C2semidirect
3. C2×C29×#359C2semidirect
4. C2×C29×#357C2semidirect
5. C29×#1978C2semidirect
6. C29×#1387C2semidirect
7. C29×#1379C2semidirect
12. C29×#509C4semidirect
41. C2×D8×C29C2×C4semidirect
56. C29×M32C2×C4semidirect
123. #13022C29direct (N × H)
162. #2951C2×C29semidirect
163. C2×#359C2×C29semidirect
164. C2×#357C2×C29semidirect
165. #1978C2×C29semidirect
166. #1387C2×C29semidirect
167. #1379C2×C29semidirect
193. #509C4×C29semidirect
229. C2×D8C2×C4×C29semidirect
244. M32C2×C4×C29semidirect
260. C29#13022direct (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×#29512
C2×C29×#3592
C2×C29×#3572
C29×#19782
C29×#13872
C29×#13792
#1302229