Finite Group Databasebeta

← C29×#33646 #20328546

Subgroups — C29×#33646 #20328546

Order 7424.

628 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3050C211yesmaximal, characteristic
2C22×C29×#107C211yesmaximal, characteristic, complemented
3C29×#2236C212yesmaximal, complemented
4C29×#2235C212yesmaximal, complemented
5C29×#2233C212yesmaximal, complemented
6C29×#2232C212yesmaximal, complemented
7C29×#2159C212yesmaximal, complemented
8C29×#2139C212yesmaximal, complemented
9C29×#2112C211yesmaximal, characteristic, complemented
10C2×C29×#135C2211yescharacteristic
11C23×C8×C29C2211yescharacteristic
12C29×#525—21no—
13C22×C4⋊C4×C29—21no—
14C2×C29×M32C2212yes—
15C29×#467C2211yescharacteristic
16C29×#467C2211yescharacteristic
17C29×#466C2211yescharacteristic
18C29×#466C2211yescharacteristic
19C29×#465—21no—
20C29×#465—21no—
21C29×#427C2211yescharacteristic
22C2×C29×#107—21no—
23C2×C29×#107—21no—
24C2×C29×#107—21no—
25C2×C29×#107C2212yes—
26C2×C29×#107C2212yes—
27C2×C29×#107C2212yes—
28C29×#416—21no—
29C29×#367C2214yescomplemented
30C29×#366C2214yescomplemented
31C29×#358C2214yescomplemented
32C29×#357C2214yescomplemented
33C29×C22⋊C16C2212yes—
34C29×C22⋊C16C2212yes—
35C2×#41×C29—21no—
36C23×C4×C29—41no—
37C23×C4×C29D411yescharacteristic
38C29×#135—24no—
39C2×Q16×C29C2311yescharacteristic
40C2×SD16×C29—21no—
41C2×D8×C29C2311yescharacteristic
42C22×C8×C29—24no—
43C22×C8×C29D411yescharacteristic
44C22×C8×C29D411yescharacteristic
45C22×C8×C29D411yescharacteristic
46C22×C8×C29C2311yescharacteristic
47C22×C8×C29C2311yescharacteristic
48C22×C8×C29C2311yescharacteristic
49C29×#123—41no—
50C29×C22⋊Q8—21no—
51C29×C22⋊Q8—21no—
52C29×#121—21no—
53C29×#121—21no—
54C29×#120—41no—
55C4×D4×C29—41no—
56C4×D4×C29—41no—
57C29×#117—21no—
58C2×C4⋊C4×C29—22no—
59C2×C4⋊C4×C29—22no—
60C2×C4⋊C4×C29—22no—
61C2×C4⋊C4×C29—41no—
62C2×C4⋊C4×C29—41no—
63C2×C4⋊C4×C29—41no—
64C29×M32—24no—
65C2×C16×C29C2314yes—
66C29×#107—22no—
67C29×#107—22no—
68C29×#107—22no—
69C29×#107C2314yes—
70C29×#107C2311yescharacteristic
71C29×#107C2311yescharacteristic
72C29×#106—21no—
73C29×#103—21no—
74C29×#103—21no—
75C29×#102—21no—
76C29×#102—21no—
77C24×C29D811yescharacteristic
78#41×C29—42no—
79#41×C29—42no—
80C2×Q8×C29—21no—
81C2×D4×C29—21no—
82C2×D4×C29—41no—
83C2×D4×C29—41no—
84C2×D4×C29—41no—
85C22×C4×C29—22no—
86C22×C4×C29—22no—
87C22×C4×C29—42no—
88C22×C4×C29—42no—
89C22×C4×C29—42no—
90C22×C4×C29—41no—
91C22×C4×C29—84no—
92C22×C4×C29D811yescharacteristic
93C22×C4×C29D811yescharacteristic
94C22×C4×C29D811yescharacteristic
95C22×C4×C29C2×D411yescharacteristic
96C22×C4×C29C2×D411yescharacteristic
97C22×C4×C29C2×D411yescharacteristic
98Q16×C29—22no—
99SD16×C29—42no—
100D8×C29—22no—
101C2×C8×C29—22no—
102C2×C8×C29—22no—
103C2×C8×C29—22no—
104C2×C8×C29—22no—
105C2×C8×C29—22no—
106C2×C8×C29C2×D411yescharacteristic
107C2×C8×C29C2×D411yescharacteristic
108C2×C8×C29C2×D411yescharacteristic
109C2×C8×C29#4114yes—
110C2×C8×C29C2411yescharacteristic
111C4⋊C4×C29—24no—
112C4⋊C4×C29—21no—
113C4⋊C4×C29—21no—
114C4⋊C4×C29—42no—
115C4⋊C4×C29—42no—
116C4⋊C4×C29—42no—
117C4⋊C4×C29—41no—
118C4⋊C4×C29—41no—
119C22⋊C4×C29—41no—
120C22⋊C4×C29—41no—
121C22⋊C4×C29—41no—
122C22⋊C4×C29—41no—
123C22⋊C4×C29—41no—
124C42×C29—41no—
125C16×C29—24no—
126#33646C2911yesmaximal, characteristic, direct product factor, Sylow
127C23×C29—22no—
128C23×C29—22no—
129C23×C29—22no—
130C23×C29—41no—
131C23×C29C2×D811yescharacteristic
132C23×C29C2×D811yescharacteristic
133C23×C29C2×D811yescharacteristic
134Q8×C29—41no—
135Q8×C29—41no—
136D4×C29—41no—
137D4×C29—41no—
138D4×C29—82no—
139D4×C29—82no—
140D4×C29—82no—
141C2×C4×C29—22no—
142C2×C4×C29—21no—
143C2×C4×C29—21no—
144C2×C4×C29—21no—
145C2×C4×C29—21no—
146C2×C4×C29—22no—
147C2×C4×C29—22no—
148C2×C4×C29—41no—
149C2×C4×C29—41no—
150C2×C4×C29—41no—
151C2×C4×C29—44no—
152C2×C4×C29—84no—
153C2×C4×C29—84no—
154C2×C4×C29—84no—
155C2×C4×C29—82no—
156C2×C4×C29#12312yes—
157C2×C4×C29C2×D811yescharacteristic
158C2×C4×C29C2×D811yescharacteristic
159C2×C4×C29C2×D811yescharacteristic
160C2×C4×C29#13712yes—
161C2×C4×C29C22×D411yescharacteristic
162C8×C29—21no—
163C8×C29—21no—
164C8×C29#12312yes—
165C8×C29C2×#4112yes—
166#3050C2×C2911yescharacteristic
167C22×#107C2×C2911yescharacteristic, complemented
168#2236C2×C2912yescomplemented
169#2235C2×C2912yescomplemented
170#2233C2×C2912yescomplemented
171#2232C2×C2912yescomplemented
172#2159C2×C2912yescomplemented
173#2139C2×C2912yescomplemented
174#2112C2×C2911yescharacteristic, complemented
175C22×C29—28no—
176C22×C29—21no—
177C22×C29—21no—
178C22×C29—21no—
179C22×C29—21no—
180C22×C29—21no—
181C22×C29—21no—
182C22×C29—81no—
183C22×C29—81no—
184C22×C29—81no—
185C22×C29#48012yes—
186C22×C29#50912yes—
187C22×C29#51012yes—
188C22×C29C22×D811yescharacteristic
189C4×C29—21no—
190C4×C29—21no—
191C4×C29—81no—
192C4×C29—84no—
193C4×C29—81no—
194C4×C29—81no—
195C4×C29#48012yes—
196C4×C29C2×#12311yescharacteristic
197C4×C29C2×#13711yescharacteristic
198C2×#135C22×C2911yescharacteristic
199C23×C8C22×C2911yescharacteristic
200#525—21no—
201C22×C4⋊C4—21no—
202C2×M32C22×C2912yes—
203#467C22×C2911yescharacteristic
204#467C22×C2911yescharacteristic
205#466C22×C2911yescharacteristic
206#466C22×C2911yescharacteristic
207#465—21no—
208#465—21no—
209#427C22×C2911yescharacteristic
210C2×#107—21no—
211C2×#107—21no—
212C2×#107—21no—
213C2×#107C22×C2912yes—
214C2×#107C22×C2912yes—
215C2×#107C22×C2912yes—
216#416—21no—
217#367C22×C2914yescomplemented
218#366C22×C2914yescomplemented
219#358C22×C2914yescomplemented
220#357C22×C2914yescomplemented
221C22⋊C16C22×C2912yes—
222C22⋊C16C22×C2912yes—
223C2×C29—22no—
224C2×C29—22no—
225C2×C29—22no—
226C2×C29—161no—
227C2×C29C2×#48011yescharacteristic
228C2×C29C2×#50911yescharacteristic
229C2×C29C2×#51011yescharacteristic
230C2×#41—21no—
231C23×C4—41no—
232C23×C4D4×C2911yescharacteristic
233#135—24no—
234C2×Q16C23×C2911yescharacteristic
235C2×SD16—21no—
236C2×D8C23×C2911yescharacteristic
237C22×C8—24no—
238C22×C8D4×C2911yescharacteristic
239C22×C8D4×C2911yescharacteristic
240C22×C8D4×C2911yescharacteristic
241C22×C8C23×C2911yescharacteristic
242C22×C8C23×C2911yescharacteristic
243C22×C8C23×C2911yescharacteristic
244#123—41no—
245C22⋊Q8—21no—
246C22⋊Q8—21no—
247#121—21no—
248#121—21no—
249#120—41no—
250C4×D4—41no—
251C4×D4—41no—
252#117—21no—
253C2×C4⋊C4—22no—
254C2×C4⋊C4—22no—
255C2×C4⋊C4—22no—
256C2×C4⋊C4—41no—
257C2×C4⋊C4—41no—
258C2×C4⋊C4—41no—
259M32—24no—
260C2×C16C23×C2914yes—
261#107—22no—
262#107—22no—
263#107—22no—
264#107C23×C2914yes—
265#107C23×C2911yescharacteristic
266#107C23×C2911yescharacteristic
267#106—21no—
268#103—21no—
269#103—21no—
270#102—21no—
271#102—21no—
272C29#3364611yescharacteristic, direct product factor, Sylow
273C24D8×C2911yescharacteristic
274#41—42no—
275#41—42no—
276C2×Q8—21no—
277C2×D4—21no—
278C2×D4—41no—
279C2×D4—41no—
280C2×D4—41no—
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—42no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—41no—
287C22×C4—84no—
288C22×C4D8×C2911yescharacteristic
289C22×C4D8×C2911yescharacteristic
290C22×C4D8×C2911yescharacteristic
291C22×C4C2×D4×C2911yescharacteristic
292C22×C4C2×D4×C2911yescharacteristic
293C22×C4C2×D4×C2911yescharacteristic
294Q16—22no—
295SD16—42no—
296D8—22no—
297C2×C8—22no—
298C2×C8—22no—
299C2×C8—22no—
300C2×C8—22no—
301C2×C8—22no—
302C2×C8C2×D4×C2911yescharacteristic
303C2×C8C2×D4×C2911yescharacteristic
304C2×C8C2×D4×C2911yescharacteristic
305C2×C8#41×C2914yes—
306C2×C8C24×C2911yescharacteristic
307C4⋊C4—21no—
308C4⋊C4—21no—
309C4⋊C4—24no—
310C4⋊C4—42no—
311C4⋊C4—42no—
312C4⋊C4—42no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C22⋊C4—41no—
316C22⋊C4—41no—
317C22⋊C4—41no—
318C22⋊C4—41no—
319C22⋊C4—41no—
320C42—41no—
321C16—24no—
322C23—22no—
323C23—22no—
324C23—22no—
325C23—41no—
326C23C2×D8×C2911yescharacteristic
327C23C2×D8×C2911yescharacteristic
328C23C2×D8×C2911yescharacteristic
329Q8—41no—
330Q8—41no—
331D4—41no—
332D4—41no—
333D4—82no—
334D4—82no—
335D4—82no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—44no—
347C2×C4—84no—
348C2×C4—84no—
349C2×C4—84no—
350C2×C4—82no—
351C2×C4C29×#12312yes—
352C2×C4C2×D8×C2911yescharacteristic
353C2×C4C2×D8×C2911yescharacteristic
354C2×C4C2×D8×C2911yescharacteristic
355C2×C4C29×#13712yes—
356C2×C4C22×D4×C2911yescharacteristic
357C8—21no—
358C8—21no—
359C8C29×#12312yes—
360C8C2×#41×C2912yes—
361C22—28no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—81no—
369C22—81no—
370C22—81no—
371C22C29×#48012yes—
372C22C29×#50912yes—
373C22C29×#51012yes—
374C22C22×D8×C2911yescharacteristic
375C4—21no—
376C4—21no—
377C4—81no—
378C4—84no—
379C4—81no—
380C4—81no—
381C4C29×#48012yes—
382C4C2×C29×#12311yescharacteristic
383C4C2×C29×#13711yescharacteristic
384C2—22no—
385C2—22no—
386C2—22no—
387C2—161no—
388C2C2×C29×#48011yescharacteristic
389C2C2×C29×#50911yescharacteristic
390C2C2×C29×#51011yescharacteristic
subgroupG/H
center, socleC22×C29C22×D8
commutator, Frattini, cosocleC2×C8C24×C29
prime radicalC29×#3050C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C23×C4×C29 ◁ C23×C8×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C29×#107C2semidirect
3. C29×#2236C2semidirect
4. C29×#2235C2semidirect
5. C29×#2233C2semidirect
6. C29×#2232C2semidirect
7. C29×#2159C2semidirect
8. C29×#2139C2semidirect
9. C29×#2112C2semidirect
29. C29×#367C22semidirect
30. C29×#366C22semidirect
31. C29×#358C22semidirect
32. C29×#357C22semidirect
126. #33646C29direct (N × H)
167. C22×#107C2×C29semidirect
168. #2236C2×C29semidirect
169. #2235C2×C29semidirect
170. #2233C2×C29semidirect
171. #2232C2×C29semidirect
172. #2159C2×C29semidirect
173. #2139C2×C29semidirect
174. #2112C2×C29semidirect
217. #367C22×C29semidirect
218. #366C22×C29semidirect
219. #358C22×C29semidirect
220. #357C22×C29semidirect
272. C29#33646direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#30502
C22×C29×#1072
C29×#22362
C29×#22352
C29×#22332
C29×#22322
C29×#21592
C29×#21392
C29×#21122
#3364629