Finite Group Databasebeta

← C29×#9048 #20303948

Subgroups — C29×#9048 #20303948

Order 7424.

424 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3104C211yesmaximal, characteristic
2C29×#2961C211yesmaximal, characteristic
3C29×#1985C211yesmaximal, characteristic
4C29×#1542C211yesmaximal, characteristic
5C29×#1487C211yesmaximal, characteristic
6C29×#1301C211yesmaximal, characteristic
7C29×#1281C211yesmaximal, characteristic
8C29×#533C2211yescharacteristic
9C2×C4×Q8×C29C2211yescharacteristic
10C29×#484C412yes—
11C29×#477—21no—
12C29×#462—21no—
13C29×#451C412yes—
14C29×#446—22no—
15C29×#446—22no—
16C4×Q16×C29—22no—
17C29×#431C2211yescharacteristic
18C29×#431C2211yescharacteristic
19C29×#424—21no—
20C29×#423C2211yescharacteristic
21C2×C29×C4⋊C8C2211yescharacteristic
22C29×#405—21no—
23C2×C29×#97C2211yescharacteristic
24C29×#336—21no—
25C29×#336—21no—
26C29×#333—21no—
27C29×#332—21no—
28C29×Q8⋊C8—22no—
29C22×Q8×C29C2×C411yescharacteristic
30C2×Q16×C29—22no—
31C2×M16×C29—21no—
32C22×C8×C29—21no—
33C22×C8×C29D411yescharacteristic
34C22×C8×C29D411yescharacteristic
35C29×C4⋊Q8D411yescharacteristic
36C29×C4⋊Q8D411yescharacteristic
37C29×#125—21no—
38C29×C22⋊Q8—21no—
39C29×C22⋊Q8C2×C412yes—
40C4×Q8×C29—21no—
41C4×Q8×C29—21no—
42C4×Q8×C29—21no—
43C4×Q8×C29—21no—
44C4×Q8×C29—21no—
45C4×Q8×C29D412yes—
46C29×#117—21no—
47C2×C4⋊C4×C29—21no—
48C2×C4⋊C4×C29C2×C411yescharacteristic
49C2×C42×C29—21no—
50C2×C42×C29C2311yescharacteristic
51C29×#107—22no—
52C29×C4⋊C8—24no—
53C29×C4⋊C8—21no—
54C29×C4⋊C8—21no—
55C29×C4⋊C8—21no—
56C29×C4⋊C8—21no—
57C29×C4⋊C8—21no—
58C29×C4⋊C8D412yes—
59C29×#103—22no—
60C29×#103—22no—
61C29×C22⋊C8—21no—
62C29×C22⋊C8C2×C412yes—
63C29×#97—22no—
64C29×#97—21no—
65C29×#97—21no—
66C4×C8×C29—22no—
67C4×C8×C29—21no—
68C4×C8×C29—21no—
69C2×Q8×C29—21no—
70C2×Q8×C29—21no—
71C2×Q8×C29—21no—
72C2×Q8×C29—42no—
73C2×Q8×C29C22⋊C412yes—
74C22×C4×C29—21no—
75C22×C4×C29—21no—
76C22×C4×C29C22×C411yescharacteristic
77C22×C4×C29C2×D411yescharacteristic
78C22×C4×C29#4111yescharacteristic
79Q16×C29—44no—
80M16×C29—41no—
81M16×C29—41no—
82C2×C8×C29—21no—
83C2×C8×C29—21no—
84C2×C8×C29—22no—
85C2×C8×C29—21no—
86C2×C8×C29—22no—
87C2×C8×C29—21no—
88C2×C8×C29—21no—
89C2×C8×C29—41no—
90C2×C8×C29—41no—
91C2×C8×C29—41no—
92C2×C8×C29—41no—
93C2×C8×C29Q1612yescomplemented
94C4⋊C4×C29—22no—
95C4⋊C4×C29—21no—
96C4⋊C4×C29—21no—
97C4⋊C4×C29—21no—
98C4⋊C4×C29—22no—
99C4⋊C4×C29—21no—
100C4⋊C4×C29—21no—
101C4⋊C4×C29—41no—
102C4⋊C4×C29—41no—
103C4⋊C4×C29C22⋊C412yes—
104C22⋊C4×C29—22no—
105C42×C29—22no—
106C42×C29—41no—
107C42×C29—41no—
108C42×C29C2×D411yescharacteristic
109C42×C29C2×D411yescharacteristic
110C42×C29C2×D411yescharacteristic
111C42×C29#4111yescharacteristic
112#9048C2911yesmaximal, characteristic, direct product factor, Sylow
113C23×C29C4×D411yescharacteristic
114Q8×C29—22no—
115Q8×C29—22no—
116Q8×C29—42no—
117Q8×C29—41no—
118Q8×C29—41no—
119Q8×C29—81no—
120C2×C4×C29—22no—
121C2×C4×C29—22no—
122C2×C4×C29—22no—
123C2×C4×C29—41no—
124C2×C4×C29—41no—
125C2×C4×C29—41no—
126C2×C4×C29—41no—
127C2×C4×C29—42no—
128C2×C4×C29—41no—
129C2×C4×C29C2×C22⋊C411yescharacteristic
130C2×C4×C29C4×D411yescharacteristic
131C2×C4×C29#12011yescharacteristic
132C2×C4×C29#12111yescharacteristic
133C2×C4×C29#12111yescharacteristic
134C2×C4×C29#12311yescharacteristic
135C2×C4×C29C2×Q1611yescharacteristic
136C2×C4×C29#13511yescharacteristic
137C2×C4×C29#13711yescharacteristic
138C2×C4×C29#13711yescharacteristic
139C8×C29—22no—
140C8×C29—42no—
141C8×C29—41no—
142C8×C29—42no—
143C8×C29—81no—
144C8×C29—81no—
145#3104C2×C2911yescharacteristic
146#2961C2×C2911yescharacteristic
147#1985C2×C2911yescharacteristic
148#1542C2×C2911yescharacteristic
149#1487C2×C2911yescharacteristic
150#1301C2×C2911yescharacteristic
151#1281C2×C2911yescharacteristic
152C22×C29—21no—
153C22×C29—21no—
154C22×C29#38611yescharacteristic
155C22×C29C4×Q1611yescharacteristic
156C22×C29#44111yescharacteristic
157C4×C29—21no—
158C4×C29—21no—
159C4×C29—21no—
160C4×C29—21no—
161C4×C29—42no—
162C4×C29—42no—
163C4×C29—42no—
164C4×C29—81no—
165C4×C29#45111yescharacteristic
166C4×C29#45211yescharacteristic
167C4×C29#46211yescharacteristic
168C4×C29#46411yescharacteristic
169#533C22×C2911yescharacteristic
170C2×C4×Q8C22×C2911yescharacteristic
171#484C4×C2912yes—
172#477—21no—
173#462—21no—
174#451C4×C2912yes—
175#446—22no—
176#446—22no—
177C4×Q16—22no—
178#431C22×C2911yescharacteristic
179#431C22×C2911yescharacteristic
180#424—21no—
181#423C22×C2911yescharacteristic
182C2×C4⋊C8C22×C2911yescharacteristic
183#405—21no—
184C2×#97C22×C2911yescharacteristic
185#336—21no—
186#336—21no—
187#333—21no—
188#332—21no—
189Q8⋊C8—22no—
190C2×C29—21no—
191C2×C29—21no—
192C2×C29#187811yescharacteristic
193C2×C29#188111yescharacteristic
194C2×C29#189111yescharacteristic
195C22×Q8C2×C4×C2911yescharacteristic
196C2×Q16—22no—
197C2×M16—21no—
198C22×C8—21no—
199C22×C8D4×C2911yescharacteristic
200C22×C8D4×C2911yescharacteristic
201C4⋊Q8D4×C2911yescharacteristic
202C4⋊Q8D4×C2911yescharacteristic
203#125—21no—
204C22⋊Q8—21no—
205C22⋊Q8C2×C4×C2912yes—
206C4×Q8—21no—
207C4×Q8—21no—
208C4×Q8—21no—
209C4×Q8—21no—
210C4×Q8—21no—
211C4×Q8D4×C2912yes—
212#117—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4C2×C4×C2911yescharacteristic
215C2×C42—21no—
216C2×C42C23×C2911yescharacteristic
217#107—22no—
218C4⋊C8—24no—
219C4⋊C8—21no—
220C4⋊C8—21no—
221C4⋊C8—21no—
222C4⋊C8—21no—
223C4⋊C8—21no—
224C4⋊C8D4×C2912yes—
225#103—22no—
226#103—22no—
227C22⋊C8—21no—
228C22⋊C8C2×C4×C2912yes—
229#97—22no—
230#97—21no—
231#97—21no—
232C4×C8—22no—
233C4×C8—21no—
234C4×C8—21no—
235C29#904811yescharacteristic, direct product factor, Sylow
236C2×Q8—21no—
237C2×Q8—21no—
238C2×Q8—21no—
239C2×Q8—42no—
240C2×Q8C22⋊C4×C2912yes—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4C22×C4×C2911yescharacteristic
244C22×C4C2×D4×C2911yescharacteristic
245C22×C4#41×C2911yescharacteristic
246Q16—44no—
247M16—41no—
248M16—41no—
249C2×C8—21no—
250C2×C8—21no—
251C2×C8—22no—
252C2×C8—22no—
253C2×C8—21no—
254C2×C8—21no—
255C2×C8—21no—
256C2×C8—41no—
257C2×C8—41no—
258C2×C8—41no—
259C2×C8—41no—
260C2×C8Q16×C2912yescomplemented
261C4⋊C4—22no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—22no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4C22⋊C4×C2912yes—
271C22⋊C4—22no—
272C42—22no—
273C42—41no—
274C42—41no—
275C42C2×D4×C2911yescharacteristic
276C42C2×D4×C2911yescharacteristic
277C42C2×D4×C2911yescharacteristic
278C42#41×C2911yescharacteristic
279C23C4×D4×C2911yescharacteristic
280Q8—22no—
281Q8—22no—
282Q8—42no—
283Q8—41no—
284Q8—41no—
285Q8—81no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—42no—
294C2×C4—41no—
295C2×C4C2×C22⋊C4×C2911yescharacteristic
296C2×C4C4×D4×C2911yescharacteristic
297C2×C4C29×#12011yescharacteristic
298C2×C4C29×#12111yescharacteristic
299C2×C4C29×#12111yescharacteristic
300C2×C4C29×#12311yescharacteristic
301C2×C4C2×Q16×C2911yescharacteristic
302C2×C4C29×#13511yescharacteristic
303C2×C4C29×#13711yescharacteristic
304C2×C4C29×#13711yescharacteristic
305C8—22no—
306C8—42no—
307C8—41no—
308C8—42no—
309C8—81no—
310C8—81no—
311C22—21no—
312C22—21no—
313C22C29×#38611yescharacteristic
314C22C4×Q16×C2911yescharacteristic
315C22C29×#44111yescharacteristic
316C4—21no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—42no—
321C4—42no—
322C4—42no—
323C4—81no—
324C4C29×#45111yescharacteristic
325C4C29×#45211yescharacteristic
326C4C29×#46211yescharacteristic
327C4C29×#46411yescharacteristic
328C2—21no—
329C2—21no—
330C2C29×#187811yescharacteristic
331C2C29×#188111yescharacteristic
332C2C29×#189111yescharacteristic
subgroupG/H
centerC2×C4×C29#120
commutatorC22×C4C22×C4×C29
Frattini, cosocleC2×C42C23×C29
socleC22×C29#386
prime radicalC23×C29C4×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C29 ◁ C2×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
93. C2×C8×C29Q16semidirect
112. #9048C29direct (N × H)
235. C29#9048direct (N × H)
260. C2×C8Q16×C29semidirect

Maximal subgroups

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

subgroupindex
C29×#31042
C29×#29612
C29×#19852
C29×#15422
C29×#14872
C29×#13012
C29×#12812
#904829