Finite Group Databasebeta

← C29×#33808 #20328708

Subgroups — C29×#33808 #20328708

Order 7424.

442 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3177C211yesmaximal, characteristic
2C29×#3164C211yesmaximal, characteristic
3C29×#2255C211yesmaximal, characteristic, complemented
4C29×#2253C211yesmaximal, characteristic, complemented
5C29×#2245C211yesmaximal, characteristic, complemented
6C29×#2241C211yesmaximal, characteristic, complemented
7C29×#2237C211yesmaximal, characteristic
8C29×#2237C211yesmaximal, characteristic
9C29×#2236C211yesmaximal, characteristic
10C29×#2235C211yesmaximal, characteristic
11C29×#2229C211yesmaximal, characteristic, complemented
12C29×#2229C211yesmaximal, characteristic, complemented
13C29×#2227C211yesmaximal, characteristic, complemented
14C29×#2225C211yesmaximal, characteristic, complemented
15C29×#2164C211yesmaximal, characteristic
16C29×#544—21no—
17C29×#541—21no—
18C29×#501—21no—
19C29×#501—21no—
20C29×#500C2211yescharacteristic
21C29×#500C2211yescharacteristic
22C29×#499C2211yescharacteristic
23C29×#499C2211yescharacteristic
24C29×#499C2211yescharacteristic
25C29×#494C2211yescharacteristic
26C29×#491—21no—
27C29×#470—21no—
28C29×#467C2211yescharacteristic
29C29×#467C2211yescharacteristic
30C29×#441—21no—
31C4×Q16×C29C2211yescharacteristic
32C4×Q16×C29C2211yescharacteristic
33C29×#428—21no—
34C29×#427C2211yescharacteristic
35C2×C29×#107C2211yescharacteristic
36C29×#405C2211yescharacteristic
37C29×#367C2211yescharacteristic
38C29×#367C2211yescharacteristic
39C29×#367C2211yescharacteristic
40C29×#367C2211yescharacteristic
41C29×#366C2211yescharacteristic
42C29×#366C2211yescharacteristic
43C29×#366C2211yescharacteristic
44C29×#366C2211yescharacteristic
45C29×C4⋊C16C2211yescharacteristic
46C29×C4⋊C16C2211yescharacteristic
47C29×#358C2211yescharacteristic
48C29×#358C2211yescharacteristic
49C29×#358C2211yescharacteristic
50C29×#358C2211yescharacteristic
51C29×#358C2211yescharacteristic
52C29×#358C2211yescharacteristic
53C29×#358C2211yescharacteristic
54C29×#358C2211yescharacteristic
55C29×C22⋊C16C2211yescharacteristic
56C29×C22⋊C16C2211yescharacteristic
57C29×#346C2211yescharacteristic
58C4×C16×C29C2211yescharacteristic
59C2×Q16×C29—21no—
60C2×Q16×C29C2311yescharacteristic
61C2×Q16×C29C2311yescharacteristic
62C2×M16×C29D411yescharacteristic
63C22×C8×C29C2311yescharacteristic
64C29×C4⋊Q8—21no—
65C29×C4⋊Q8—21no—
66C29×C4⋊Q8—21no—
67C29×C4⋊Q8—41no—
68C29×#126—41no—
69C29×#126—41no—
70C29×#125—21no—
71C29×#125—21no—
72C29×#125—21no—
73C29×#125—41no—
74C29×#125—41no—
75C29×#125—41no—
76C29×C22⋊Q8—21no—
77C29×C22⋊Q8—21no—
78C29×C22⋊Q8—41no—
79C29×C22⋊Q8—41no—
80C4×Q8×C29—21no—
81C4×Q8×C29—21no—
82C29×#117—21no—
83C29×#117D411yescharacteristic
84C2×C4⋊C4×C29—21no—
85C2×C16×C29C2311yescharacteristic
86C2×C16×C29C2311yescharacteristic
87C2×C16×C29C2311yescharacteristic
88C2×C16×C29C2311yescharacteristic
89C29×#107—21no—
90C29×#107—21no—
91C29×#107—21no—
92C29×#107C2311yescharacteristic
93C29×#107C2311yescharacteristic
94C29×#107C2311yescharacteristic
95C29×#107C2311yescharacteristic
96C29×#107C2311yescharacteristic
97C29×#107C2311yescharacteristic
98C29×#106—21no—
99C29×#106—21no—
100C29×#106—21no—
101C29×#106—21no—
102C29×#103—21no—
103C29×#103—21no—
104C29×#103—21no—
105C29×#103—21no—
106C29×#97D411yescharacteristic
107C29×#97D411yescharacteristic
108C4×C8×C29C2311yescharacteristic
109C4×C8×C29C2311yescharacteristic
110C2×Q8×C29—21no—
111C2×Q8×C29—21no—
112C2×Q8×C29—41no—
113C2×Q8×C29—41no—
114C22×C4×C29—41no—
115C22×C4×C29C2×D411yescharacteristic
116Q16×C29—21no—
117Q16×C29—21no—
118Q16×C29—21no—
119Q16×C29—21no—
120Q16×C29—42no—
121M16×C29—22no—
122C2×C8×C29—21no—
123C2×C8×C29—21no—
124C2×C8×C29C2×D411yescharacteristic
125C2×C8×C29C2×D411yescharacteristic
126C2×C8×C29C2×D411yescharacteristic
127C2×C8×C29C2411yescharacteristic
128C4⋊C4×C29—21no—
129C4⋊C4×C29—21no—
130C4⋊C4×C29—21no—
131C4⋊C4×C29—21no—
132C4⋊C4×C29—21no—
133C4⋊C4×C29—21no—
134C4⋊C4×C29—41no—
135C4⋊C4×C29—41no—
136C4⋊C4×C29—41no—
137C4⋊C4×C29—41no—
138C4⋊C4×C29—41no—
139C4⋊C4×C29—41no—
140C4⋊C4×C29—41no—
141C4⋊C4×C29—41no—
142C4⋊C4×C29—41no—
143C4⋊C4×C29—41no—
144C4⋊C4×C29—41no—
145C4⋊C4×C29—41no—
146C4⋊C4×C29—41no—
147C4⋊C4×C29—41no—
148C4⋊C4×C29—41no—
149C4⋊C4×C29D811yescharacteristic
150C4⋊C4×C29D811yescharacteristic
151C22⋊C4×C29—41no—
152C22⋊C4×C29—41no—
153C22⋊C4×C29—41no—
154C22⋊C4×C29D811yescharacteristic
155C22⋊C4×C29D811yescharacteristic
156C42×C29—41no—
157C42×C29—41no—
158C42×C29—41no—
159C42×C29C2×D411yescharacteristic
160C42×C29C2×D411yescharacteristic
161C16×C29—21no—
162C16×C29—21no—
163C16×C29—21no—
164C16×C29—21no—
165#33808C2911yesmaximal, characteristic, direct product factor, Sylow
166C23×C29C2×D811yescharacteristic
167Q8×C29—41no—
168Q8×C29—41no—
169Q8×C29—41no—
170Q8×C29—41no—
171Q8×C29—161no—
172Q8×C29—161no—
173C2×C4×C29—21no—
174C2×C4×C29—21no—
175C2×C4×C29—41no—
176C2×C4×C29—41no—
177C2×C4×C29—41no—
178C2×C4×C29—41no—
179C2×C4×C29—41no—
180C2×C4×C29—41no—
181C2×C4×C29—41no—
182C2×C4×C29—41no—
183C2×C4×C29—161no—
184C2×C4×C29C2×D811yescharacteristic
185C2×C4×C29C2×D811yescharacteristic
186C2×C4×C29C2×D811yescharacteristic
187C2×C4×C29C2×D811yescharacteristic
188C2×C4×C29C2×D811yescharacteristic
189C2×C4×C29C22×D411yescharacteristic
190C8×C29—21no—
191C8×C29—21no—
192C8×C29#13712yes—
193C8×C292−1+411yescharacteristic
194C8×C292−1+411yescharacteristic
195#3177C2×C2911yescharacteristic
196#3164C2×C2911yescharacteristic
197#2255C2×C2911yescharacteristic, complemented
198#2253C2×C2911yescharacteristic, complemented
199#2245C2×C2911yescharacteristic, complemented
200#2241C2×C2911yescharacteristic, complemented
201#2237C2×C2911yescharacteristic
202#2237C2×C2911yescharacteristic
203#2236C2×C2911yescharacteristic
204#2235C2×C2911yescharacteristic
205#2229C2×C2911yescharacteristic, complemented
206#2229C2×C2911yescharacteristic, complemented
207#2227C2×C2911yescharacteristic, complemented
208#2225C2×C2911yescharacteristic, complemented
209#2164C2×C2911yescharacteristic
210C22×C29—21no—
211C22×C29—21no—
212C22×C29—21no—
213C22×C29C22×D811yescharacteristic
214C4×C29—21no—
215C4×C29—21no—
216C4×C29—21no—
217C4×C29—21no—
218C4×C29—21no—
219C4×C29—81no—
220C4×C29—81no—
221C4×C29—81no—
222C4×C29—81no—
223C4×C29—81no—
224C4×C29—81no—
225C4×C29—81no—
226C4×C29—81no—
227C4×C29#53611yescharacteristic
228C4×C29C2×#13711yescharacteristic
229#544—21no—
230#541—21no—
231#501—21no—
232#501—21no—
233#500C22×C2911yescharacteristic
234#500C22×C2911yescharacteristic
235#499C22×C2911yescharacteristic
236#499C22×C2911yescharacteristic
237#499C22×C2911yescharacteristic
238#494C22×C2911yescharacteristic
239#491—21no—
240#470—21no—
241#467C22×C2911yescharacteristic
242#467C22×C2911yescharacteristic
243#441—21no—
244C4×Q16C22×C2911yescharacteristic
245C4×Q16C22×C2911yescharacteristic
246#428—21no—
247#427C22×C2911yescharacteristic
248C2×#107C22×C2911yescharacteristic
249#405C22×C2911yescharacteristic
250#367C22×C2911yescharacteristic
251#367C22×C2911yescharacteristic
252#367C22×C2911yescharacteristic
253#367C22×C2911yescharacteristic
254#366C22×C2911yescharacteristic
255#366C22×C2911yescharacteristic
256#366C22×C2911yescharacteristic
257#366C22×C2911yescharacteristic
258C4⋊C16C22×C2911yescharacteristic
259C4⋊C16C22×C2911yescharacteristic
260#358C22×C2911yescharacteristic
261#358C22×C2911yescharacteristic
262#358C22×C2911yescharacteristic
263#358C22×C2911yescharacteristic
264#358C22×C2911yescharacteristic
265#358C22×C2911yescharacteristic
266#358C22×C2911yescharacteristic
267#358C22×C2911yescharacteristic
268C22⋊C16C22×C2911yescharacteristic
269C22⋊C16C22×C2911yescharacteristic
270#346C22×C2911yescharacteristic
271C4×C16C22×C2911yescharacteristic
272C2×C29—41no—
273C2×C29#322611yescharacteristic
274C2×C29#341611yescharacteristic
275C2×C29#341711yescharacteristic
276C2×Q16—21no—
277C2×Q16C23×C2911yescharacteristic
278C2×Q16C23×C2911yescharacteristic
279C2×M16D4×C2911yescharacteristic
280C22×C8C23×C2911yescharacteristic
281C4⋊Q8—21no—
282C4⋊Q8—21no—
283C4⋊Q8—21no—
284C4⋊Q8—41no—
285#126—41no—
286#126—41no—
287#125—21no—
288#125—21no—
289#125—21no—
290#125—41no—
291#125—41no—
292#125—41no—
293C22⋊Q8—21no—
294C22⋊Q8—21no—
295C22⋊Q8—41no—
296C22⋊Q8—41no—
297C4×Q8—21no—
298C4×Q8—21no—
299#117—21no—
300#117D4×C2911yescharacteristic
301C2×C4⋊C4—21no—
302C2×C16C23×C2911yescharacteristic
303C2×C16C23×C2911yescharacteristic
304C2×C16C23×C2911yescharacteristic
305C2×C16C23×C2911yescharacteristic
306#107—21no—
307#107—21no—
308#107—21no—
309#107C23×C2911yescharacteristic
310#107C23×C2911yescharacteristic
311#107C23×C2911yescharacteristic
312#107C23×C2911yescharacteristic
313#107C23×C2911yescharacteristic
314#107C23×C2911yescharacteristic
315#106—21no—
316#106—21no—
317#106—21no—
318#106—21no—
319#103—21no—
320#103—21no—
321#103—21no—
322#103—21no—
323#97D4×C2911yescharacteristic
324#97D4×C2911yescharacteristic
325C4×C8C23×C2911yescharacteristic
326C4×C8C23×C2911yescharacteristic
327C29#3380811yescharacteristic, direct product factor, Sylow
328C2×Q8—21no—
329C2×Q8—21no—
330C2×Q8—41no—
331C2×Q8—41no—
332C22×C4—41no—
333C22×C4C2×D4×C2911yescharacteristic
334Q16—21no—
335Q16—21no—
336Q16—21no—
337Q16—21no—
338Q16—42no—
339M16—22no—
340C2×C8—21no—
341C2×C8—21no—
342C2×C8C2×D4×C2911yescharacteristic
343C2×C8C2×D4×C2911yescharacteristic
344C2×C8C2×D4×C2911yescharacteristic
345C2×C8C24×C2911yescharacteristic
346C4⋊C4—21no—
347C4⋊C4—21no—
348C4⋊C4—21no—
349C4⋊C4—21no—
350C4⋊C4—21no—
351C4⋊C4—21no—
352C4⋊C4—41no—
353C4⋊C4—41no—
354C4⋊C4—41no—
355C4⋊C4—41no—
356C4⋊C4—41no—
357C4⋊C4—41no—
358C4⋊C4—41no—
359C4⋊C4—41no—
360C4⋊C4—41no—
361C4⋊C4—41no—
362C4⋊C4—41no—
363C4⋊C4—41no—
364C4⋊C4—41no—
365C4⋊C4—41no—
366C4⋊C4—41no—
367C4⋊C4D8×C2911yescharacteristic
368C4⋊C4D8×C2911yescharacteristic
369C22⋊C4—41no—
370C22⋊C4—41no—
371C22⋊C4—41no—
372C22⋊C4D8×C2911yescharacteristic
373C22⋊C4D8×C2911yescharacteristic
374C42—41no—
375C42—41no—
376C42—41no—
377C42C2×D4×C2911yescharacteristic
378C42C2×D4×C2911yescharacteristic
379C16—21no—
380C16—21no—
381C16—21no—
382C16—21no—
383C23C2×D8×C2911yescharacteristic
384Q8—41no—
385Q8—41no—
386Q8—41no—
387Q8—41no—
388Q8—161no—
389Q8—161no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—161no—
401C2×C4C2×D8×C2911yescharacteristic
402C2×C4C2×D8×C2911yescharacteristic
403C2×C4C2×D8×C2911yescharacteristic
404C2×C4C2×D8×C2911yescharacteristic
405C2×C4C2×D8×C2911yescharacteristic
406C2×C4C22×D4×C2911yescharacteristic
407C8—21no—
408C8—21no—
409C8C29×#13712yes—
410C8C29×2−1+411yescharacteristic
411C8C29×2−1+411yescharacteristic
412C22—21no—
413C22—21no—
414C22—21no—
415C22C22×D8×C2911yescharacteristic
416C4—21no—
417C4—21no—
418C4—21no—
419C4—21no—
420C4—21no—
421C4—81no—
422C4—81no—
423C4—81no—
424C4—81no—
425C4—81no—
426C4—81no—
427C4—81no—
428C4—81no—
429C4C29×#53611yescharacteristic
430C4C2×C29×#13711yescharacteristic
431C2—41no—
432C2C29×#322611yescharacteristic
433C2C29×#341611yescharacteristic
434C2C29×#341711yescharacteristic
subgroupG/H
center, socleC22×C29C22×D8
commutator, Frattini, cosocleC2×C8C24×C29
prime radicalC23×C29C2×D8
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C29×#117 ◁ C29×#405 ◁ G

Complements

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

NH ≅ G/Ntype
3. C29×#2255C2semidirect
4. C29×#2253C2semidirect
5. C29×#2245C2semidirect
6. C29×#2241C2semidirect
11. C29×#2229C2semidirect
12. C29×#2229C2semidirect
13. C29×#2227C2semidirect
14. C29×#2225C2semidirect
165. #33808C29direct (N × H)
197. #2255C2×C29semidirect
198. #2253C2×C29semidirect
199. #2245C2×C29semidirect
200. #2241C2×C29semidirect
205. #2229C2×C29semidirect
206. #2229C2×C29semidirect
207. #2227C2×C29semidirect
208. #2225C2×C29semidirect
327. C29#33808direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#31772
C29×#31642
C29×#22552
C29×#22532
C29×#22452
C29×#22412
C29×#22372
C29×#22362
C29×#22352
C29×#22292
C29×#22272
C29×#22252
C29×#21642
#3380829