Finite Group Databasebeta

← C29×#10174 #20305074

Subgroups — C29×#10174 #20305074

Order 7424.

578 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3226C211yesmaximal, characteristic
2C2×C29×#500C211yesmaximal, characteristic, complemented
3C29×#3152C211yesmaximal, characteristic
4C29×#1966C211yesmaximal, characteristic, complemented
5C29×#1546C211yesmaximal, characteristic, complemented
6C29×#1492C211yesmaximal, characteristic
7C29×#1278C211yesmaximal, characteristic, complemented
8C2×C29×#137—22no—
9C29×#532C2211yescharacteristic
10C2×C29×C4⋊Q8C2211yescharacteristic
11C2×C29×C4⋊Q8C2211yescharacteristic
12C29×#500—22no—
13C29×#500—21no—
14C29×#500—22no—
15C29×#497—22no—
16C29×#494—21no—
17C29×#492—21no—
18C29×#486—21no—
19C29×#480—22no—
20C29×#474—22no—
21C29×#431C2211yescharacteristic
22C2×C29×#107—22no—
23C29×#423C2211yescharacteristic
24C2×C29×#101—22no—
25C4×M16×C29C2211yescharacteristic
26C2×C4×C8×C29C2211yescharacteristic
27C29×#332—22no—
28C29×D4⋊C8—22no—
29C2×#41×C29—21no—
30C22×Q8×C29—21no—
31C22×Q8×C29—21no—
32C29×#137—44no—
33C29×#137—44no—
34C2×Q16×C29—24no—
35C2×SD16×C29—24no—
36C2×M16×C29—21no—
37C2×M16×C29D412yes—
38C22×C8×C29—21no—
39C29×C4⋊Q8—21no—
40C29×C4⋊Q8—21no—
41C29×C4⋊Q8—21no—
42C29×C4⋊Q8—21no—
43C29×C4⋊Q8—21no—
44C29×C4⋊Q8—21no—
45C29×C4⋊Q8—21no—
46C29×C4⋊Q8D411yescharacteristic
47C29×C4⋊Q8D412yes—
48C29×#127D411yescharacteristic
49C29×#124—21no—
50C29×#121—21no—
51C29×#121—21no—
52C4×D4×C29—21no—
53C4×D4×C29—21no—
54C2×C4⋊C4×C29—21no—
55C2×C4⋊C4×C29—21no—
56C2×C4⋊C4×C29—21no—
57C2×C4⋊C4×C29D412yes—
58C2×C42×C29C2311yescharacteristic
59C29×#107—28no—
60C29×#107—24no—
61C29×C4⋊C8—21no—
62C29×C4⋊C8—21no—
63C29×C4⋊C8D412yes—
64C29×#102—24no—
65C29×#101—44no—
66C29×C22⋊C8—21no—
67C29×#97—21no—
68C4×C8×C29—21no—
69C4×C8×C29—21no—
70C4×C8×C29—21no—
71C4×C8×C29D412yes—
72#41×C29—42no—
73#41×C29—42no—
74C2×Q8×C29—21no—
75C2×Q8×C29—22no—
76C2×Q8×C29—41no—
77C2×Q8×C29—41no—
78C2×Q8×C29—41no—
79C2×Q8×C29—42no—
80C2×Q8×C29—42no—
81C2×Q8×C29—42no—
82C2×Q8×C29—42no—
83C2×D4×C29—21no—
84C2×D4×C29—21no—
85C2×D4×C29—21no—
86C2×D4×C29—41no—
87C22×C4×C29—22no—
88C22×C4×C29—41no—
89C22×C4×C29—41no—
90C22×C4×C29C2×D411yescharacteristic
91C22×C4×C29C2×D411yescharacteristic
92C22×C4×C29#4111yescharacteristic
93Q16×C29—48no—
94SD16×C29—48no—
95M16×C29—22no—
96M16×C29—42no—
97M16×C29D814yes—
98C2×C8×C29—24no—
99C2×C8×C29—22no—
100C2×C8×C29—22no—
101C2×C8×C29—22no—
102C2×C8×C29—41no—
103C4⋊C4×C29—22no—
104C4⋊C4×C29—22no—
105C4⋊C4×C29—22no—
106C4⋊C4×C29—21no—
107C4⋊C4×C29—22no—
108C4⋊C4×C29—21no—
109C4⋊C4×C29—41no—
110C4⋊C4×C29—41no—
111C4⋊C4×C29—41no—
112C4⋊C4×C29—41no—
113C22⋊C4×C29—41no—
114C22⋊C4×C29—41no—
115C42×C29C2×D411yescharacteristic
116C42×C29C2×D411yescharacteristic
117C42×C29C2×D411yescharacteristic
118C42×C29C2×D411yescharacteristic
119#10174C2911yesmaximal, characteristic, direct product factor, Sylow
120C23×C29—41no—
121C23×C29#12111yescharacteristic
122Q8×C29—44no—
123Q8×C29—42no—
124Q8×C29—82no—
125Q8×C29—81no—
126Q8×C29—81no—
127Q8×C29—81no—
128Q8×C29—81no—
129D4×C29—42no—
130D4×C29—42no—
131D4×C29—42no—
132D4×C29—82no—
133C2×C4×C29—22no—
134C2×C4×C29—22no—
135C2×C4×C29—41no—
136C2×C4×C29—42no—
137C2×C4×C29—42no—
138C2×C4×C29—44no—
139C2×C4×C29—82no—
140C2×C4×C29—81no—
141C2×C4×C29—81no—
142C2×C4×C29#12011yescharacteristic
143C2×C4×C29#12011yescharacteristic
144C2×C4×C29#12011yescharacteristic
145C2×C4×C29#12111yescharacteristic
146C2×C4×C29#12111yescharacteristic
147C2×C4×C29#12711yescharacteristic
148C2×C4×C29C2×D812yes—
149C2×C4×C29AGL(1,ℤ/8)12yes—
150C8×C29—24no—
151C8×C29—24no—
152C8×C29—42no—
153C8×C29—81no—
154#3226C2×C2911yescharacteristic
155C2×#500C2×C2911yescharacteristic, complemented
156#3152C2×C2911yescharacteristic
157#1966C2×C2911yescharacteristic, complemented
158#1546C2×C2911yescharacteristic, complemented
159#1492C2×C2911yescharacteristic
160#1278C2×C2911yescharacteristic, complemented
161C22×C29—21no—
162C22×C29—21no—
163C22×C29—81no—
164C22×C29—81no—
165C22×C29—81no—
166C22×C29#39211yescharacteristic
167C22×C29#45912yes—
168C4×C29—21no—
169C4×C29—21no—
170C4×C29—82no—
171C4×C29—81no—
172C4×C29—82no—
173C4×C29#44712yes—
174C4×C29#45612yes—
175C4×C29#47312yes—
176C4×C29#49311yescharacteristic
177C4×C29#49611yescharacteristic
178C2×#137—22no—
179#532C22×C2911yescharacteristic
180C2×C4⋊Q8C22×C2911yescharacteristic
181C2×C4⋊Q8C22×C2911yescharacteristic
182#500—22no—
183#500—21no—
184#500—22no—
185#497—22no—
186#494—21no—
187#492—21no—
188#486—21no—
189#480—22no—
190#474—22no—
191#431C22×C2911yescharacteristic
192C2×#107—22no—
193#423C22×C2911yescharacteristic
194C2×#101—22no—
195C4×M16C22×C2911yescharacteristic
196C2×C4×C8C22×C2911yescharacteristic
197#332—22no—
198D4⋊C8—22no—
199C2×C29—22no—
200C2×C29—161no—
201C2×C29#200511yescharacteristic
202C2×C29#201111yescharacteristic
203C2×C29#202011yescharacteristic
204C2×#41—21no—
205C22×Q8—21no—
206C22×Q8—21no—
207#137—44no—
208#137—44no—
209C2×Q16—24no—
210C2×SD16—24no—
211C2×M16—21no—
212C2×M16D4×C2912yes—
213C22×C8—21no—
214C4⋊Q8—21no—
215C4⋊Q8—21no—
216C4⋊Q8—21no—
217C4⋊Q8—21no—
218C4⋊Q8—21no—
219C4⋊Q8—21no—
220C4⋊Q8—21no—
221C4⋊Q8D4×C2912yes—
222C4⋊Q8D4×C2911yescharacteristic
223#127D4×C2911yescharacteristic
224#124—21no—
225#121—21no—
226#121—21no—
227C4×D4—21no—
228C4×D4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4D4×C2912yes—
233C2×C42C23×C2911yescharacteristic
234#107—28no—
235#107—24no—
236C4⋊C8—21no—
237C4⋊C8—21no—
238C4⋊C8D4×C2912yes—
239#102—24no—
240#101—44no—
241C22⋊C8—21no—
242#97—21no—
243C4×C8—21no—
244C4×C8—21no—
245C4×C8—21no—
246C4×C8D4×C2912yes—
247C29#1017411yescharacteristic, direct product factor, Sylow
248#41—42no—
249#41—42no—
250C2×Q8—21no—
251C2×Q8—22no—
252C2×Q8—41no—
253C2×Q8—41no—
254C2×Q8—41no—
255C2×Q8—42no—
256C2×Q8—42no—
257C2×Q8—42no—
258C2×Q8—42no—
259C2×D4—21no—
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—41no—
263C22×C4—22no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4C2×D4×C2911yescharacteristic
267C22×C4C2×D4×C2911yescharacteristic
268C22×C4#41×C2911yescharacteristic
269Q16—48no—
270SD16—48no—
271M16—22no—
272M16—42no—
273M16D8×C2914yes—
274C2×C8—24no—
275C2×C8—22no—
276C2×C8—22no—
277C2×C8—22no—
278C2×C8—41no—
279C4⋊C4—22no—
280C4⋊C4—22no—
281C4⋊C4—22no—
282C4⋊C4—21no—
283C4⋊C4—22no—
284C4⋊C4—21no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C22⋊C4—41no—
290C22⋊C4—41no—
291C42C2×D4×C2911yescharacteristic
292C42C2×D4×C2911yescharacteristic
293C42C2×D4×C2911yescharacteristic
294C42C2×D4×C2911yescharacteristic
295C23—41no—
296C23C29×#12111yescharacteristic
297Q8—44no—
298Q8—42no—
299Q8—82no—
300Q8—81no—
301Q8—81no—
302Q8—81no—
303Q8—81no—
304D4—42no—
305D4—42no—
306D4—42no—
307D4—82no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—44no—
311C2×C4—41no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—82no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4C29×#12011yescharacteristic
318C2×C4C29×#12011yescharacteristic
319C2×C4C29×#12011yescharacteristic
320C2×C4C29×#12111yescharacteristic
321C2×C4C29×#12111yescharacteristic
322C2×C4C29×#12711yescharacteristic
323C2×C4C2×D8×C2912yes—
324C2×C4C29×AGL(1,ℤ/8)12yes—
325C8—24no—
326C8—24no—
327C8—42no—
328C8—81no—
329C22—21no—
330C22—21no—
331C22—81no—
332C22—81no—
333C22—81no—
334C22C29×#39211yescharacteristic
335C22C29×#45912yes—
336C4—21no—
337C4—21no—
338C4—82no—
339C4—81no—
340C4—82no—
341C4C29×#44712yes—
342C4C29×#45612yes—
343C4C29×#47312yes—
344C4C29×#49311yescharacteristic
345C4C29×#49611yescharacteristic
346C2—22no—
347C2—161no—
348C2C29×#200511yescharacteristic
349C2C29×#201111yescharacteristic
350C2C29×#202011yescharacteristic
subgroupG/H
center, socleC22×C29#392
commutator, Frattini, cosocleC2×C42C23×C29
prime radicalC29×#532C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C2×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C29×#500C2semidirect
4. C29×#1966C2semidirect
5. C29×#1546C2semidirect
7. C29×#1278C2semidirect
119. #10174C29direct (N × H)
155. C2×#500C2×C29semidirect
157. #1966C2×C29semidirect
158. #1546C2×C29semidirect
160. #1278C2×C29semidirect
247. C29#10174direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#32262
C2×C29×#5002
C29×#31522
C29×#19662
C29×#15462
C29×#14922
C29×#12782
#1017429