Finite Group Databasebeta

← C29×#9050 #20303950

Subgroups — C29×#9050 #20303950

Order 7424.

476 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3101C211yesmaximal, characteristic
2C29×#2961C211yesmaximal, characteristic, complemented
3C29×#1955C211yesmaximal, characteristic
4C29×#1542C211yesmaximal, characteristic, complemented
5C29×#1486C211yesmaximal, characteristic
6C29×#1301C211yesmaximal, characteristic, complemented
7C29×#1281C211yesmaximal, characteristic, complemented
8C29×#533C2211yescharacteristic
9C2×C4×D4×C29C2211yescharacteristic
10C29×#483C412yes—
11C29×#476—21no—
12C29×#461—21no—
13C29×#450C412yes—
14C29×#446—22no—
15C29×#446—22no—
16C4×SD16×C29—22no—
17C29×#431C2211yescharacteristic
18C29×#431C2211yescharacteristic
19C29×#424—21no—
20C29×#423C2211yescharacteristic
21C2×C29×C4⋊C8C2211yescharacteristic
22C2×C29×C22⋊C8—21no—
23C2×C29×C22⋊C8—21no—
24C29×#405—21no—
25C2×C29×#97C2211yescharacteristic
26C29×#333—21no—
27C29×#332—21no—
28C29×D4⋊C8—22no—
29C22×D4×C29C2×C411yescharacteristic
30C23×C4×C29—21no—
31C2×SD16×C29—22no—
32C2×M16×C29—21no—
33C22×C8×C29—21no—
34C22×C8×C29D411yescharacteristic
35C22×C8×C29D411yescharacteristic
36C29×C4⋊Q8D411yescharacteristic
37C29×C4⋊Q8D411yescharacteristic
38C29×#125—21no—
39C29×C22⋊Q8—21no—
40C29×C22⋊Q8C2×C412yes—
41C4×Q8×C29—21no—
42C4×Q8×C29D412yes—
43C4×D4×C29—21no—
44C4×D4×C29—21no—
45C4×D4×C29—21no—
46C4×D4×C29—21no—
47C29×#117—21no—
48C2×C4⋊C4×C29C2×C411yescharacteristic
49C2×C22⋊C4×C29—21no—
50C2×C42×C29C2311yescharacteristic
51C29×#106—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×#102—22no—
61C29×C22⋊C8—21no—
62C29×C22⋊C8—42no—
63C29×C22⋊C8—42no—
64C29×C22⋊C8C2×C412yes—
65C29×#97—22no—
66C29×#97—21no—
67C29×#97—21no—
68C4×C8×C29—22no—
69C4×C8×C29—21no—
70C4×C8×C29—21no—
71C24×C29—21no—
72C2×Q8×C29—21no—
73C2×Q8×C29C22⋊C412yes—
74C2×D4×C29—21no—
75C2×D4×C29—21no—
76C2×D4×C29—42no—
77C22×C4×C29—21no—
78C22×C4×C29—41no—
79C22×C4×C29—41no—
80C22×C4×C29—41no—
81C22×C4×C29—41no—
82C22×C4×C29—41no—
83C22×C4×C29—41no—
84C22×C4×C29C22×C411yescharacteristic
85C22×C4×C29C2×D411yescharacteristic
86C22×C4×C29#4111yescharacteristic
87SD16×C29—44no—
88M16×C29—41no—
89M16×C29—41no—
90C2×C8×C29—21no—
91C2×C8×C29—21no—
92C2×C8×C29—22no—
93C2×C8×C29—21no—
94C2×C8×C29—22no—
95C2×C8×C29—21no—
96C2×C8×C29—21no—
97C2×C8×C29—41no—
98C2×C8×C29—41no—
99C2×C8×C29—41no—
100C2×C8×C29—41no—
101C2×C8×C29SD1612yescomplemented
102C4⋊C4×C29—22no—
103C4⋊C4×C29—21no—
104C4⋊C4×C29—21no—
105C4⋊C4×C29—21no—
106C4⋊C4×C29—22no—
107C4⋊C4×C29—21no—
108C4⋊C4×C29—21no—
109C4⋊C4×C29C22⋊C412yes—
110C22⋊C4×C29—22no—
111C22⋊C4×C29—41no—
112C22⋊C4×C29—41no—
113C42×C29—22no—
114C42×C29C2×D411yescharacteristic
115C42×C29C2×D411yescharacteristic
116C42×C29C2×D411yescharacteristic
117C42×C29#4111yescharacteristic
118#9050C2911yesmaximal, characteristic, direct product factor, Sylow
119C23×C29—22no—
120C23×C29—41no—
121C23×C29—41no—
122C23×C29—41no—
123C23×C29—41no—
124C23×C29—41no—
125C23×C29—41no—
126C23×C29C4×D411yescharacteristic
127Q8×C29—42no—
128Q8×C29—81no—
129D4×C29—22no—
130D4×C29—22no—
131D4×C29—41no—
132D4×C29—41no—
133C2×C4×C29—22no—
134C2×C4×C29—22no—
135C2×C4×C29—41no—
136C2×C4×C29—41no—
137C2×C4×C29—41no—
138C2×C4×C29—41no—
139C2×C4×C29—41no—
140C2×C4×C29—81no—
141C2×C4×C29—81no—
142C2×C4×C29—81no—
143C2×C4×C29—81no—
144C2×C4×C29C2×C22⋊C411yescharacteristic
145C2×C4×C29C4×D411yescharacteristic
146C2×C4×C29#12011yescharacteristic
147C2×C4×C29#12111yescharacteristic
148C2×C4×C29#12111yescharacteristic
149C2×C4×C29#12311yescharacteristic
150C2×C4×C29C2×SD1611yescharacteristic
151C2×C4×C29#13511yescharacteristic
152C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C29#13711yescharacteristic
154C8×C29—22no—
155C8×C29—42no—
156C8×C29—41no—
157C8×C29—42no—
158C8×C29—81no—
159C8×C29—81no—
160#3101C2×C2911yescharacteristic
161#2961C2×C2911yescharacteristic, complemented
162#1955C2×C2911yescharacteristic
163#1542C2×C2911yescharacteristic, complemented
164#1486C2×C2911yescharacteristic
165#1301C2×C2911yescharacteristic, complemented
166#1281C2×C2911yescharacteristic, complemented
167C22×C29—21no—
168C22×C29—21no—
169C22×C29—42no—
170C22×C29—42no—
171C22×C29—42no—
172C22×C29—81no—
173C22×C29—81no—
174C22×C29—81no—
175C22×C29—81no—
176C22×C29#38611yescharacteristic
177C22×C29C4×SD1611yescharacteristic
178C22×C29#44011yescharacteristic
179C4×C29—21no—
180C4×C29—21no—
181C4×C29—21no—
182C4×C29—21no—
183C4×C29—42no—
184C4×C29—42no—
185C4×C29—81no—
186C4×C29#44811yescharacteristic
187C4×C29#44911yescharacteristic
188C4×C29#46011yescharacteristic
189C4×C29#46411yescharacteristic
190#533C22×C2911yescharacteristic
191C2×C4×D4C22×C2911yescharacteristic
192#483C4×C2912yes—
193#476—21no—
194#461—21no—
195#450C4×C2912yes—
196#446—22no—
197#446—22no—
198C4×SD16—22no—
199#431C22×C2911yescharacteristic
200#431C22×C2911yescharacteristic
201#424—21no—
202#423C22×C2911yescharacteristic
203C2×C4⋊C8C22×C2911yescharacteristic
204C2×C22⋊C8—21no—
205C2×C22⋊C8—21no—
206#405—21no—
207C2×#97C22×C2911yescharacteristic
208#333—21no—
209#332—21no—
210D4⋊C8—22no—
211C2×C29—21no—
212C2×C29—21no—
213C2×C29—82no—
214C2×C29#188011yescharacteristic
215C2×C29#188111yescharacteristic
216C2×C29#189111yescharacteristic
217C22×D4C2×C4×C2911yescharacteristic
218C23×C4—21no—
219C2×SD16—22no—
220C2×M16—21no—
221C22×C8—21no—
222C22×C8D4×C2911yescharacteristic
223C22×C8D4×C2911yescharacteristic
224C4⋊Q8D4×C2911yescharacteristic
225C4⋊Q8D4×C2911yescharacteristic
226#125—21no—
227C22⋊Q8—21no—
228C22⋊Q8C2×C4×C2912yes—
229C4×Q8—21no—
230C4×Q8D4×C2912yes—
231C4×D4—21no—
232C4×D4—21no—
233C4×D4—21no—
234C4×D4—21no—
235#117—21no—
236C2×C4⋊C4C2×C4×C2911yescharacteristic
237C2×C22⋊C4—21no—
238C2×C42C23×C2911yescharacteristic
239#106—22no—
240C4⋊C8—24no—
241C4⋊C8—21no—
242C4⋊C8—21no—
243C4⋊C8—21no—
244C4⋊C8—21no—
245C4⋊C8—21no—
246C4⋊C8D4×C2912yes—
247#103—22no—
248#102—22no—
249C22⋊C8—21no—
250C22⋊C8—42no—
251C22⋊C8—42no—
252C22⋊C8C2×C4×C2912yes—
253#97—22no—
254#97—21no—
255#97—21no—
256C4×C8—22no—
257C4×C8—21no—
258C4×C8—21no—
259C29#905011yescharacteristic, direct product factor, Sylow
260C24—21no—
261C2×Q8—21no—
262C2×Q8C22⋊C4×C2912yes—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—42no—
266C22×C4—21no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4C22×C4×C2911yescharacteristic
274C22×C4C2×D4×C2911yescharacteristic
275C22×C4#41×C2911yescharacteristic
276SD16—44no—
277M16—41no—
278M16—41no—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8—22no—
282C2×C8—22no—
283C2×C8—21no—
284C2×C8—21no—
285C2×C8—21no—
286C2×C8—41no—
287C2×C8—41no—
288C2×C8—41no—
289C2×C8—41no—
290C2×C8SD16×C2912yescomplemented
291C4⋊C4—22no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—22no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4C22⋊C4×C2912yes—
299C22⋊C4—22no—
300C22⋊C4—41no—
301C22⋊C4—41no—
302C42—22no—
303C42C2×D4×C2911yescharacteristic
304C42C2×D4×C2911yescharacteristic
305C42C2×D4×C2911yescharacteristic
306C42#41×C2911yescharacteristic
307C23—22no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23C4×D4×C2911yescharacteristic
315Q8—42no—
316Q8—81no—
317D4—22no—
318D4—22no—
319D4—41no—
320D4—41no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—81no—
329C2×C4—81no—
330C2×C4—81no—
331C2×C4—81no—
332C2×C4C2×C22⋊C4×C2911yescharacteristic
333C2×C4C4×D4×C2911yescharacteristic
334C2×C4C29×#12011yescharacteristic
335C2×C4C29×#12111yescharacteristic
336C2×C4C29×#12111yescharacteristic
337C2×C4C29×#12311yescharacteristic
338C2×C4C2×SD16×C2911yescharacteristic
339C2×C4C29×#13511yescharacteristic
340C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
341C2×C4C29×#13711yescharacteristic
342C8—22no—
343C8—42no—
344C8—41no—
345C8—42no—
346C8—81no—
347C8—81no—
348C22—21no—
349C22—21no—
350C22—42no—
351C22—42no—
352C22—42no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22—81no—
357C22C29×#38611yescharacteristic
358C22C4×SD16×C2911yescharacteristic
359C22C29×#44011yescharacteristic
360C4—21no—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—42no—
365C4—42no—
366C4—81no—
367C4C29×#44811yescharacteristic
368C4C29×#44911yescharacteristic
369C4C29×#46011yescharacteristic
370C4C29×#46411yescharacteristic
371C2—21no—
372C2—21no—
373C2—82no—
374C2C29×#188011yescharacteristic
375C2C29×#188111yescharacteristic
376C2C29×#189111yescharacteristic
subgroupG/H
centerC2×C4×C29#120
commutatorC22×C4C22×C4×C29
Frattini, cosocleC2×C42C23×C29
socleC22×C29#386
prime radicalC22×D4×C29C2×C4
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
2. C29×#2961C2semidirect
4. C29×#1542C2semidirect
6. C29×#1301C2semidirect
7. C29×#1281C2semidirect
101. C2×C8×C29SD16semidirect
118. #9050C29direct (N × H)
161. #2961C2×C29semidirect
163. #1542C2×C29semidirect
165. #1301C2×C29semidirect
166. #1281C2×C29semidirect
259. C29#9050direct (N × H)
290. C2×C8SD16×C29semidirect

Maximal subgroups

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

subgroupindex
C29×#31012
C29×#29612
C29×#19552
C29×#15422
C29×#14862
C29×#13012
C29×#12812
#905029