Finite Group Databasebeta

← C29×#33810 #20328710

Subgroups — C29×#33810 #20328710

Order 7424.

454 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3175C211yesmaximal, characteristic
2C29×#3164C211yesmaximal, characteristic, complemented
3C29×#2255C211yesmaximal, characteristic, complemented
4C29×#2254C211yesmaximal, characteristic, complemented
5C29×#2243C211yesmaximal, characteristic, complemented
6C29×#2242C211yesmaximal, characteristic, complemented
7C29×#2237C211yesmaximal, characteristic, complemented
8C29×#2235C211yesmaximal, characteristic, complemented
9C29×#2234C211yesmaximal, characteristic
10C29×#2233C211yesmaximal, characteristic
11C29×#2229C211yesmaximal, characteristic, complemented
12C29×#2228C211yesmaximal, characteristic, complemented
13C29×#2226C211yesmaximal, characteristic, complemented
14C29×#2225C211yesmaximal, characteristic, complemented
15C29×#2164C211yesmaximal, characteristic, complemented
16C29×#544—21no—
17C29×#542—21no—
18C29×#501—21no—
19C29×#501—21no—
20C29×#500C2211yescharacteristic
21C29×#500C2211yescharacteristic
22C29×#500C2211yescharacteristic
23C29×#499C2211yescharacteristic
24C29×#499C2211yescharacteristic
25C29×#495C2211yescharacteristic
26C29×#489—21no—
27C29×#468—21no—
28C29×#467C2211yescharacteristic
29C29×#466C2211yescharacteristic
30C29×#440—21no—
31C4×Q16×C29C2211yescharacteristic
32C4×D8×C29C2211yescharacteristic
33C29×#428—21no—
34C29×#427C2211yescharacteristic
35C2×C29×#107C2211yescharacteristic
36C29×#405C2211yescharacteristic
37C29×#367C2211yescharacteristic
38C29×#367C2211yescharacteristic
39C29×#367C2211yescharacteristic
40C29×#367C2211yescharacteristic
41C29×#367C2211yescharacteristic
42C29×#367C2211yescharacteristic
43C29×#366C2211yescharacteristic
44C29×#366C2211yescharacteristic
45C29×C4⋊C16C2211yescharacteristic
46C29×C4⋊C16C2211yescharacteristic
47C29×#358C2211yescharacteristic
48C29×#358C2211yescharacteristic
49C29×#358C2211yescharacteristic
50C29×#358C2211yescharacteristic
51C29×#357C2211yescharacteristic
52C29×#357C2211yescharacteristic
53C29×#357C2211yescharacteristic
54C29×#357C2211yescharacteristic
55C29×C22⋊C16C2211yescharacteristic
56C29×C22⋊C16C2211yescharacteristic
57C29×#346C2211yescharacteristic
58C4×C16×C29C2211yescharacteristic
59C2×Q16×C29C2311yescharacteristic
60C2×SD16×C29—21no—
61C2×D8×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×#125—21no—
70C29×#125—21no—
71C29×#125—41no—
72C29×#124—21no—
73C29×#124—41no—
74C29×#123—41no—
75C29×C22⋊Q8—21no—
76C29×C22⋊Q8—41no—
77C29×C22⋊Q8—41no—
78C29×C22⋊Q8—41no—
79C29×#121—21no—
80C4×Q8×C29—21no—
81C4×D4×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×#107—21no—
93C29×#107C2311yescharacteristic
94C29×#107C2311yescharacteristic
95C29×#107C2311yescharacteristic
96C29×#107C2311yescharacteristic
97C29×#107C2311yescharacteristic
98C29×#107C2311yescharacteristic
99C29×#106—21no—
100C29×#106—21no—
101C29×#106—21no—
102C29×#103—21no—
103C29×#103—21no—
104C29×#102—21no—
105C29×#102—21no—
106C29×#97D411yescharacteristic
107C29×#97D411yescharacteristic
108C4×C8×C29C2311yescharacteristic
109C4×C8×C29C2311yescharacteristic
110C2×Q8×C29—21no—
111C2×Q8×C29—41no—
112C2×Q8×C29—41no—
113C2×Q8×C29—41no—
114C2×D4×C29—21no—
115C2×D4×C29—41no—
116C22×C4×C29—41no—
117C22×C4×C29—41no—
118C22×C4×C29C2×D411yescharacteristic
119Q16×C29—21no—
120Q16×C29—21no—
121SD16×C29—42no—
122D8×C29—21no—
123D8×C29—21no—
124M16×C29—22no—
125C2×C8×C29—21no—
126C2×C8×C29—21no—
127C2×C8×C29C2×D411yescharacteristic
128C2×C8×C29C2×D411yescharacteristic
129C2×C8×C29C2×D411yescharacteristic
130C2×C8×C29C2411yescharacteristic
131C4⋊C4×C29—21no—
132C4⋊C4×C29—21no—
133C4⋊C4×C29—21no—
134C4⋊C4×C29—21no—
135C4⋊C4×C29—21no—
136C4⋊C4×C29—21no—
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×C29D811yescharacteristic
148C4⋊C4×C29D811yescharacteristic
149C22⋊C4×C29—41no—
150C22⋊C4×C29—41no—
151C22⋊C4×C29—41no—
152C22⋊C4×C29—41no—
153C22⋊C4×C29—41no—
154C22⋊C4×C29—41no—
155C22⋊C4×C29D811yescharacteristic
156C22⋊C4×C29D811yescharacteristic
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#33810C2911yesmaximal, characteristic, direct product factor, Sylow
166C23×C29—41no—
167C23×C29C2×D811yescharacteristic
168Q8×C29—41no—
169Q8×C29—41no—
170Q8×C29—161no—
171Q8×C29—161no—
172Q8×C29—161no—
173D4×C29—41no—
174D4×C29—41no—
175D4×C29—161no—
176C2×C4×C29—21no—
177C2×C4×C29—21no—
178C2×C4×C29—41no—
179C2×C4×C29—41no—
180C2×C4×C29—41no—
181C2×C4×C29—41no—
182C2×C4×C29—41no—
183C2×C4×C29—41no—
184C2×C4×C29—41no—
185C2×C4×C29—161no—
186C2×C4×C29—161no—
187C2×C4×C29C2×D811yescharacteristic
188C2×C4×C29C2×D811yescharacteristic
189C2×C4×C29C2×D811yescharacteristic
190C2×C4×C29C2×D811yescharacteristic
191C2×C4×C29C2×D811yescharacteristic
192C2×C4×C29C22×D411yescharacteristic
193C8×C29—21no—
194C8×C29—21no—
195C8×C29#13712yes—
196C8×C292−1+411yescharacteristic
197C8×C292−1+411yescharacteristic
198#3175C2×C2911yescharacteristic
199#3164C2×C2911yescharacteristic, complemented
200#2255C2×C2911yescharacteristic, complemented
201#2254C2×C2911yescharacteristic, complemented
202#2243C2×C2911yescharacteristic, complemented
203#2242C2×C2911yescharacteristic, complemented
204#2237C2×C2911yescharacteristic, complemented
205#2235C2×C2911yescharacteristic, complemented
206#2234C2×C2911yescharacteristic
207#2233C2×C2911yescharacteristic
208#2229C2×C2911yescharacteristic, complemented
209#2228C2×C2911yescharacteristic, complemented
210#2226C2×C2911yescharacteristic, complemented
211#2225C2×C2911yescharacteristic, complemented
212#2164C2×C2911yescharacteristic, complemented
213C22×C29—21no—
214C22×C29—21no—
215C22×C29—21no—
216C22×C29—81no—
217C22×C29—81no—
218C22×C29—81no—
219C22×C29C22×D811yescharacteristic
220C4×C29—21no—
221C4×C29—21no—
222C4×C29—21no—
223C4×C29—21no—
224C4×C29—21no—
225C4×C29—81no—
226C4×C29—81no—
227C4×C29—81no—
228C4×C29—81no—
229C4×C29—81no—
230C4×C29—81no—
231C4×C29—81no—
232C4×C29#53611yescharacteristic
233C4×C29C2×#13711yescharacteristic
234#544—21no—
235#542—21no—
236#501—21no—
237#501—21no—
238#500C22×C2911yescharacteristic
239#500C22×C2911yescharacteristic
240#500C22×C2911yescharacteristic
241#499C22×C2911yescharacteristic
242#499C22×C2911yescharacteristic
243#495C22×C2911yescharacteristic
244#489—21no—
245#468—21no—
246#467C22×C2911yescharacteristic
247#466C22×C2911yescharacteristic
248#440—21no—
249C4×Q16C22×C2911yescharacteristic
250C4×D8C22×C2911yescharacteristic
251#428—21no—
252#427C22×C2911yescharacteristic
253C2×#107C22×C2911yescharacteristic
254#405C22×C2911yescharacteristic
255#367C22×C2911yescharacteristic
256#367C22×C2911yescharacteristic
257#367C22×C2911yescharacteristic
258#367C22×C2911yescharacteristic
259#367C22×C2911yescharacteristic
260#367C22×C2911yescharacteristic
261#366C22×C2911yescharacteristic
262#366C22×C2911yescharacteristic
263C4⋊C16C22×C2911yescharacteristic
264C4⋊C16C22×C2911yescharacteristic
265#358C22×C2911yescharacteristic
266#358C22×C2911yescharacteristic
267#358C22×C2911yescharacteristic
268#358C22×C2911yescharacteristic
269#357C22×C2911yescharacteristic
270#357C22×C2911yescharacteristic
271#357C22×C2911yescharacteristic
272#357C22×C2911yescharacteristic
273C22⋊C16C22×C2911yescharacteristic
274C22⋊C16C22×C2911yescharacteristic
275#346C22×C2911yescharacteristic
276C4×C16C22×C2911yescharacteristic
277C2×C29—41no—
278C2×C29—161no—
279C2×C29#322611yescharacteristic
280C2×C29#341611yescharacteristic
281C2×C29#341611yescharacteristic
282C2×Q16C23×C2911yescharacteristic
283C2×SD16—21no—
284C2×D8C23×C2911yescharacteristic
285C2×M16D4×C2911yescharacteristic
286C22×C8C23×C2911yescharacteristic
287C4⋊Q8—21no—
288C4⋊Q8—21no—
289C4⋊Q8—21no—
290C4⋊Q8—41no—
291#126—41no—
292#125—21no—
293#125—21no—
294#125—41no—
295#124—21no—
296#124—41no—
297#123—41no—
298C22⋊Q8—21no—
299C22⋊Q8—41no—
300C22⋊Q8—41no—
301C22⋊Q8—41no—
302#121—21no—
303C4×Q8—21no—
304C4×D4—21no—
305#117—21no—
306#117D4×C2911yescharacteristic
307C2×C4⋊C4—21no—
308C2×C16C23×C2911yescharacteristic
309C2×C16C23×C2911yescharacteristic
310C2×C16C23×C2911yescharacteristic
311C2×C16C23×C2911yescharacteristic
312#107—21no—
313#107—21no—
314#107—21no—
315#107—21no—
316#107C23×C2911yescharacteristic
317#107C23×C2911yescharacteristic
318#107C23×C2911yescharacteristic
319#107C23×C2911yescharacteristic
320#107C23×C2911yescharacteristic
321#107C23×C2911yescharacteristic
322#106—21no—
323#106—21no—
324#106—21no—
325#103—21no—
326#103—21no—
327#102—21no—
328#102—21no—
329#97D4×C2911yescharacteristic
330#97D4×C2911yescharacteristic
331C4×C8C23×C2911yescharacteristic
332C4×C8C23×C2911yescharacteristic
333C29#3381011yescharacteristic, direct product factor, Sylow
334C2×Q8—21no—
335C2×Q8—41no—
336C2×Q8—41no—
337C2×Q8—41no—
338C2×D4—21no—
339C2×D4—41no—
340C22×C4—41no—
341C22×C4—41no—
342C22×C4C2×D4×C2911yescharacteristic
343Q16—21no—
344Q16—21no—
345SD16—42no—
346D8—21no—
347D8—21no—
348M16—22no—
349C2×C8—21no—
350C2×C8—21no—
351C2×C8C2×D4×C2911yescharacteristic
352C2×C8C2×D4×C2911yescharacteristic
353C2×C8C2×D4×C2911yescharacteristic
354C2×C8C24×C2911yescharacteristic
355C4⋊C4—21no—
356C4⋊C4—21no—
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4—41no—
362C4⋊C4—41no—
363C4⋊C4—41no—
364C4⋊C4—41no—
365C4⋊C4—41no—
366C4⋊C4—41no—
367C4⋊C4—41no—
368C4⋊C4—41no—
369C4⋊C4—41no—
370C4⋊C4—41no—
371C4⋊C4D8×C2911yescharacteristic
372C4⋊C4D8×C2911yescharacteristic
373C22⋊C4—41no—
374C22⋊C4—41no—
375C22⋊C4—41no—
376C22⋊C4—41no—
377C22⋊C4—41no—
378C22⋊C4—41no—
379C22⋊C4D8×C2911yescharacteristic
380C22⋊C4D8×C2911yescharacteristic
381C42—41no—
382C42—41no—
383C42C2×D4×C2911yescharacteristic
384C42C2×D4×C2911yescharacteristic
385C16—21no—
386C16—21no—
387C16—21no—
388C16—21no—
389C23—41no—
390C23C2×D8×C2911yescharacteristic
391Q8—41no—
392Q8—41no—
393Q8—161no—
394Q8—161no—
395Q8—161no—
396D4—41no—
397D4—41no—
398D4—161no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—161no—
409C2×C4—161no—
410C2×C4C2×D8×C2911yescharacteristic
411C2×C4C2×D8×C2911yescharacteristic
412C2×C4C2×D8×C2911yescharacteristic
413C2×C4C2×D8×C2911yescharacteristic
414C2×C4C2×D8×C2911yescharacteristic
415C2×C4C22×D4×C2911yescharacteristic
416C8—21no—
417C8—21no—
418C8C29×#13712yes—
419C8C29×2−1+411yescharacteristic
420C8C29×2−1+411yescharacteristic
421C22—21no—
422C22—21no—
423C22—21no—
424C22—81no—
425C22—81no—
426C22—81no—
427C22C22×D8×C2911yescharacteristic
428C4—21no—
429C4—21no—
430C4—21no—
431C4—21no—
432C4—21no—
433C4—81no—
434C4—81no—
435C4—81no—
436C4—81no—
437C4—81no—
438C4—81no—
439C4—81no—
440C4C29×#53611yescharacteristic
441C4C2×C29×#13711yescharacteristic
442C2—41no—
443C2—161no—
444C2C29×#322611yescharacteristic
445C2C29×#341611yescharacteristic
446C2C29×#341611yescharacteristic
subgroupG/H
center, socleC22×C29C22×D8
commutator, Frattini, cosocleC2×C8C24×C29
prime radicalC29×#466C22
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
2. C29×#3164C2semidirect
3. C29×#2255C2semidirect
4. C29×#2254C2semidirect
5. C29×#2243C2semidirect
6. C29×#2242C2semidirect
7. C29×#2237C2semidirect
8. C29×#2235C2semidirect
11. C29×#2229C2semidirect
12. C29×#2228C2semidirect
13. C29×#2226C2semidirect
14. C29×#2225C2semidirect
15. C29×#2164C2semidirect
165. #33810C29direct (N × H)
199. #3164C2×C29semidirect
200. #2255C2×C29semidirect
201. #2254C2×C29semidirect
202. #2243C2×C29semidirect
203. #2242C2×C29semidirect
204. #2237C2×C29semidirect
205. #2235C2×C29semidirect
208. #2229C2×C29semidirect
209. #2228C2×C29semidirect
210. #2226C2×C29semidirect
211. #2225C2×C29semidirect
212. #2164C2×C29semidirect
333. C29#33810direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#31752
C29×#31642
C29×#22552
C29×#22542
C29×#22432
C29×#22422
C29×#22372
C29×#22352
C29×#22342
C29×#22332
C29×#22292
C29×#22282
C29×#22262
C29×#22252
C29×#21642
#3381029