Finite Group Databasebeta

← C29×#19406 #20314306

Subgroups — C29×#19406 #20314306

Order 7424.

598 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3228C211yesmaximal, characteristic
2C29×#3112C211yesmaximal, characteristic
3C29×#3104C211yesmaximal, characteristic, complemented
4C29×#2982C211yesmaximal, characteristic, complemented
5C29×#1682C212yesmaximal, complemented
6C29×#1678C212yesmaximal, complemented
7C29×#1676C212yesmaximal, complemented
8C29×#1672C212yesmaximal, complemented
9C29×#1572C211yesmaximal, characteristic, complemented
10C29×#1554C211yesmaximal, characteristic, complemented
11C29×#1543C211yesmaximal, characteristic
12C29×#533C2211yescharacteristic
13C29×#532C2211yescharacteristic
14C2×C4×Q8×C29C2211yescharacteristic
15C29×#500C2211yescharacteristic
16C29×#498C2211yescharacteristic
17C29×#486C2211yescharacteristic
18C29×#486C2211yescharacteristic
19C29×#484—21no—
20C29×#482—22no—
21C29×#480—21no—
22C29×#478—22no—
23C29×#477C2212yes—
24C29×#477C2212yes—
25C29×#462C2212yes—
26C29×#460C2212yes—
27C29×#451—21no—
28C29×#448—21no—
29C8×Q8×C29—22no—
30C8×Q8×C29C2212yes—
31C8×Q8×C29C2212yes—
32C29×#440—22no—
33C4×Q16×C29—22no—
34C29×#432C2211yescharacteristic
35C29×#431—22no—
36C29×#431C2211yescharacteristic
37C29×#431C2211yescharacteristic
38C29×#431C2211yescharacteristic
39C29×#335C2212yes—
40C29×#334C2212yes—
41C29×#333C2212yes—
42C29×#333C2212yes—
43C29×#332C2212yes—
44C29×#331C2212yes—
45C2×#41×C29—21no—
46C22×Q8×C29D411yescharacteristic
47C2×Q16×C29—22no—
48C2×SD16×C29—22no—
49C29×C4⋊Q8C2311yescharacteristic
50C29×C4⋊Q8C2311yescharacteristic
51C29×C4⋊Q8C2311yescharacteristic
52C29×#127C2311yescharacteristic
53C29×#125—21no—
54C29×#124—21no—
55C29×C22⋊Q8—21no—
56C29×C22⋊Q8—21no—
57C29×#121—21no—
58C29×#121—21no—
59C4×Q8×C29—21no—
60C4×Q8×C29—21no—
61C4×Q8×C29—21no—
62C4×Q8×C29—21no—
63C4×Q8×C29D412yes—
64C4×Q8×C29C2312yes—
65C4×D4×C29—21no—
66C4×D4×C29—21no—
67C29×#117—21no—
68C2×C4⋊C4×C29—21no—
69C2×C4⋊C4×C29D411yescharacteristic
70C2×C42×C29—21no—
71C2×C42×C29C2311yescharacteristic
72C29×#107—22no—
73C29×#107—22no—
74C29×#107—22no—
75C29×#106—22no—
76C29×C4⋊C8—22no—
77C29×C4⋊C8—22no—
78C29×C4⋊C8D412yes—
79C29×C4⋊C8C2312yes—
80C29×C4⋊C8C2312yes—
81C29×C4⋊C8C2312yes—
82C29×#103—22no—
83C29×#103—22no—
84C29×#103—22no—
85C29×#102—22no—
86C29×#102—22no—
87C29×#102—22no—
88C29×C22⋊C8—21no—
89C29×C22⋊C8—21no—
90C29×C22⋊C8—21no—
91C29×C22⋊C8D412yes—
92C29×#97—21no—
93C4×C8×C29—22no—
94C4×C8×C29—22no—
95C4×C8×C29—21no—
96C4×C8×C29—21no—
97C4×C8×C29C2311yescharacteristic
98C4×C8×C29C2311yescharacteristic
99#41×C29—82no—
100C2×Q8×C29—24no—
101C2×Q8×C29—21no—
102C2×Q8×C29—21no—
103C2×Q8×C29—21no—
104C2×Q8×C29—21no—
105C2×Q8×C29C2×D412yes—
106C2×D4×C29—21no—
107C2×D4×C29—21no—
108C2×D4×C29—21no—
109C2×D4×C29—41no—
110C22×C4×C29—21no—
111C22×C4×C29—21no—
112C22×C4×C29—41no—
113C22×C4×C29C2×D411yescharacteristic
114C22×C4×C29C2×D411yescharacteristic
115C22×C4×C29#4111yescharacteristic
116Q16×C29—44no—
117SD16×C29—44no—
118C2×C8×C29—22no—
119C2×C8×C29—22no—
120C2×C8×C29—22no—
121C2×C8×C29C2×D412yes—
122C2×C8×C29C2×D412yes—
123C4⋊C4×C29—22no—
124C4⋊C4×C29—21no—
125C4⋊C4×C29—22no—
126C4⋊C4×C29—21no—
127C4⋊C4×C29—21no—
128C4⋊C4×C29—21no—
129C4⋊C4×C29—21no—
130C4⋊C4×C29—21no—
131C4⋊C4×C29—21no—
132C4⋊C4×C29—41no—
133C4⋊C4×C29—41no—
134C4⋊C4×C29C2×D412yes—
135C22⋊C4×C29—41no—
136C22⋊C4×C29—41no—
137C22⋊C4×C29—41no—
138C42×C29—22no—
139C42×C29—22no—
140C42×C29—41no—
141C42×C29C2×D411yescharacteristic
142C42×C29C2×D411yescharacteristic
143C42×C29#4111yescharacteristic
144C42×C29C2411yescharacteristic
145#19406C2911yesmaximal, characteristic, direct product factor, Sylow
146C23×C29—41no—
147C23×C29#12111yescharacteristic
148Q8×C29—24no—
149Q8×C29—22no—
150Q8×C29—42no—
151Q8×C29—81no—
152Q8×C29—81no—
153Q8×C29#13514yes—
154D4×C29—42no—
155D4×C29—42no—
156D4×C29—81no—
157D4×C29—82no—
158C2×C4×C29—24no—
159C2×C4×C29—22no—
160C2×C4×C29—22no—
161C2×C4×C29—22no—
162C2×C4×C29—22no—
163C2×C4×C29—41no—
164C2×C4×C29—41no—
165C2×C4×C29—41no—
166C2×C4×C29—41no—
167C2×C4×C29—82no—
168C2×C4×C29—81no—
169C2×C4×C29#12111yescharacteristic
170C2×C4×C29#12111yescharacteristic
171C2×C4×C29#12111yescharacteristic
172C2×C4×C29C22×D411yescharacteristic
173C2×C4×C29C22×D411yescharacteristic
174C2×C4×C29C2×#4111yescharacteristic
175C8×C29—22no—
176C8×C29—22no—
177C8×C29—42no—
178C8×C29—42no—
179C8×C29—42no—
180#3228C2×C2911yescharacteristic
181#3112C2×C2911yescharacteristic
182#3104C2×C2911yescharacteristic, complemented
183#2982C2×C2911yescharacteristic, complemented
184#1682C2×C2912yescomplemented
185#1678C2×C2912yescomplemented
186#1676C2×C2912yescomplemented
187#1672C2×C2912yescomplemented
188#1572C2×C2911yescharacteristic, complemented
189#1554C2×C2911yescharacteristic, complemented
190#1543C2×C2911yescharacteristic
191C22×C29—21no—
192C22×C29—21no—
193C22×C29—21no—
194C22×C29—81no—
195C22×C29—81no—
196C22×C29—81no—
197C22×C29C2×#12111yescharacteristic
198C4×C29—21no—
199C4×C29—24no—
200C4×C29—21no—
201C4×C29—21no—
202C4×C29—21no—
203C4×C29—42no—
204C4×C29—81no—
205C4×C29—81no—
206C4×C29—81no—
207C4×C29C2×#13512yes—
208C4×C29#57812yes—
209#533C22×C2911yescharacteristic
210#532C22×C2911yescharacteristic
211C2×C4×Q8C22×C2911yescharacteristic
212#500C22×C2911yescharacteristic
213#498C22×C2911yescharacteristic
214#486C22×C2911yescharacteristic
215#486C22×C2911yescharacteristic
216#484—21no—
217#482—22no—
218#480—21no—
219#478—22no—
220#477C22×C2912yes—
221#477C22×C2912yes—
222#462C22×C2912yes—
223#460C22×C2912yes—
224#451—21no—
225#448—21no—
226C8×Q8—22no—
227C8×Q8C22×C2912yes—
228C8×Q8C22×C2912yes—
229#440—22no—
230C4×Q16—22no—
231#432C22×C2911yescharacteristic
232#431—22no—
233#431C22×C2911yescharacteristic
234#431C22×C2911yescharacteristic
235#431C22×C2911yescharacteristic
236#335C22×C2912yes—
237#334C22×C2912yes—
238#333C22×C2912yes—
239#333C22×C2912yes—
240#332C22×C2912yes—
241#331C22×C2912yes—
242C2×C29—41no—
243C2×C29—161no—
244C2×C29#304411yescharacteristic
245C2×C29#305011yescharacteristic
246C2×C29#306811yescharacteristic
247C2×#41—21no—
248C22×Q8D4×C2911yescharacteristic
249C2×Q16—22no—
250C2×SD16—22no—
251C4⋊Q8C23×C2911yescharacteristic
252C4⋊Q8C23×C2911yescharacteristic
253C4⋊Q8C23×C2911yescharacteristic
254#127C23×C2911yescharacteristic
255#125—21no—
256#124—21no—
257C22⋊Q8—21no—
258C22⋊Q8—21no—
259#121—21no—
260#121—21no—
261C4×Q8—21no—
262C4×Q8—21no—
263C4×Q8—21no—
264C4×Q8—21no—
265C4×Q8D4×C2912yes—
266C4×Q8C23×C2912yes—
267C4×D4—21no—
268C4×D4—21no—
269#117—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4D4×C2911yescharacteristic
272C2×C42—21no—
273C2×C42C23×C2911yescharacteristic
274#107—22no—
275#107—22no—
276#107—22no—
277#106—22no—
278C4⋊C8—22no—
279C4⋊C8—22no—
280C4⋊C8D4×C2912yes—
281C4⋊C8C23×C2912yes—
282C4⋊C8C23×C2912yes—
283C4⋊C8C23×C2912yes—
284#103—22no—
285#103—22no—
286#103—22no—
287#102—22no—
288#102—22no—
289#102—22no—
290C22⋊C8—21no—
291C22⋊C8—21no—
292C22⋊C8—21no—
293C22⋊C8D4×C2912yes—
294#97—21no—
295C4×C8—22no—
296C4×C8—22no—
297C4×C8—21no—
298C4×C8—21no—
299C4×C8C23×C2911yescharacteristic
300C4×C8C23×C2911yescharacteristic
301C29#1940611yescharacteristic, direct product factor, Sylow
302#41—82no—
303C2×Q8—24no—
304C2×Q8—21no—
305C2×Q8—21no—
306C2×Q8—21no—
307C2×Q8—21no—
308C2×Q8C2×D4×C2912yes—
309C2×D4—21no—
310C2×D4—21no—
311C2×D4—21no—
312C2×D4—41no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—41no—
316C22×C4C2×D4×C2911yescharacteristic
317C22×C4C2×D4×C2911yescharacteristic
318C22×C4#41×C2911yescharacteristic
319Q16—44no—
320SD16—44no—
321C2×C8—22no—
322C2×C8—22no—
323C2×C8—22no—
324C2×C8C2×D4×C2912yes—
325C2×C8C2×D4×C2912yes—
326C4⋊C4—22no—
327C4⋊C4—21no—
328C4⋊C4—22no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—21no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4C2×D4×C2912yes—
338C22⋊C4—41no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C42—22no—
342C42—22no—
343C42—41no—
344C42C2×D4×C2911yescharacteristic
345C42C2×D4×C2911yescharacteristic
346C42#41×C2911yescharacteristic
347C42C24×C2911yescharacteristic
348C23—41no—
349C23C29×#12111yescharacteristic
350Q8—24no—
351Q8—22no—
352Q8—42no—
353Q8—81no—
354Q8—81no—
355Q8C29×#13514yes—
356D4—42no—
357D4—42no—
358D4—81no—
359D4—82no—
360C2×C4—24no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—82no—
370C2×C4—81no—
371C2×C4C29×#12111yescharacteristic
372C2×C4C29×#12111yescharacteristic
373C2×C4C29×#12111yescharacteristic
374C2×C4C22×D4×C2911yescharacteristic
375C2×C4C22×D4×C2911yescharacteristic
376C2×C4C2×#41×C2911yescharacteristic
377C8—22no—
378C8—22no—
379C8—42no—
380C8—42no—
381C8—42no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—81no—
386C22—81no—
387C22—81no—
388C22C2×C29×#12111yescharacteristic
389C4—21no—
390C4—24no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—42no—
395C4—81no—
396C4—81no—
397C4—81no—
398C4C2×C29×#13512yes—
399C4C29×#57812yes—
400C2—41no—
401C2—161no—
402C2C29×#304411yescharacteristic
403C2C29×#305011yescharacteristic
404C2C29×#306811yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#532C22
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×#3104C2semidirect
4. C29×#2982C2semidirect
5. C29×#1682C2semidirect
6. C29×#1678C2semidirect
7. C29×#1676C2semidirect
8. C29×#1672C2semidirect
9. C29×#1572C2semidirect
10. C29×#1554C2semidirect
145. #19406C29direct (N × H)
182. #3104C2×C29semidirect
183. #2982C2×C29semidirect
184. #1682C2×C29semidirect
185. #1678C2×C29semidirect
186. #1676C2×C29semidirect
187. #1672C2×C29semidirect
188. #1572C2×C29semidirect
189. #1554C2×C29semidirect
301. C29#19406direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#32282
C29×#31122
C29×#31042
C29×#29822
C29×#16822
C29×#16782
C29×#16762
C29×#16722
C29×#15722
C29×#15542
C29×#15432
#1940629