Finite Group Databasebeta

← C29×#9266 #20304166

Subgroups — C29×#9266 #20304166

Order 7424.

400 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3232C211yesmaximal, characteristic
2C29×#2968C211yesmaximal, characteristic
3C29×#1532C211yesmaximal, characteristic
4C2×C29×#330C211yesmaximal, characteristic, complemented
5C29×#1470C211yesmaximal, characteristic, complemented
6C29×#1302C211yesmaximal, characteristic, complemented
7C29×#1281C211yesmaximal, characteristic, complemented
8C29×#529C2211yescharacteristic
9C2×C29×#125C2211yescharacteristic
10C29×#499—21no—
11C29×#488—21no—
12C29×#484C411yescharacteristic
13C29×#483C411yescharacteristic
14C29×#481C411yescharacteristic
15C29×#480C411yescharacteristic
16C29×#479—21no—
17C29×#478—21no—
18C29×#446—21no—
19C29×#435—21no—
20C29×#435—21no—
21C8×D4×C29—21no—
22C29×#433—21no—
23C29×#432C2211yescharacteristic
24C29×#431C2211yescharacteristic
25C29×#431C2211yescharacteristic
26C29×#405—21no—
27C2×C29×#97C2211yescharacteristic
28C2×C29×#97C2211yescharacteristic
29C29×#330—21no—
30C29×#330—21no—
31C29×#330—21no—
32C29×#329—21no—
33C29×#324—21no—
34C29×#324—21no—
35C2×M16×C29—21no—
36C22×C8×C29—21no—
37C22×C8×C29—21no—
38C22×C8×C29—21no—
39C29×#126—21no—
40C29×#125—21no—
41C29×#125—21no—
42C29×#125—21no—
43C29×#125—21no—
44C29×#125D411yescharacteristic
45C29×#124D411yescharacteristic
46C29×#123—21no—
47C29×C22⋊Q8C2×C411yescharacteristic
48C29×#121C2×C411yescharacteristic
49C4×Q8×C29D411yescharacteristic
50C4×D4×C29—21no—
51C4×D4×C29D411yescharacteristic
52C29×#117—21no—
53C2×C4⋊C4×C29—21no—
54C2×C4⋊C4×C29—21no—
55C2×C4⋊C4×C29C2×C411yescharacteristic
56C2×C4⋊C4×C29C2×C411yescharacteristic
57C2×C42×C29C2311yescharacteristic
58C29×#107—21no—
59C29×#107—21no—
60C29×#106—21no—
61C29×#106—21no—
62C29×C4⋊C8—21no—
63C29×C4⋊C8—21no—
64C29×C4⋊C8—21no—
65C29×C4⋊C8—21no—
66C29×C4⋊C8—21no—
67C29×#103—21no—
68C29×#103—21no—
69C29×#102—21no—
70C29×#102—21no—
71C29×C22⋊C8—21no—
72C29×C22⋊C8—21no—
73C29×C22⋊C8—21no—
74C29×C22⋊C8C2×C411yescharacteristic
75C29×C22⋊C8C2×C411yescharacteristic
76C29×C22⋊C8D411yescharacteristic
77C29×C22⋊C8D411yescharacteristic
78C29×#97—21no—
79C29×#97—21no—
80C29×#97—21no—
81C29×#97—21no—
82C29×#97—21no—
83C29×#97D411yescharacteristic
84C29×#97D411yescharacteristic
85C4×C8×C29—21no—
86C4×C8×C29—21no—
87C4×C8×C29—21no—
88C2×Q8×C29C22⋊C411yescharacteristic
89C2×D4×C29—21no—
90C2×D4×C29C22⋊C411yescharacteristic
91C22×C4×C29—21no—
92C22×C4×C29—21no—
93C22×C4×C29—21no—
94C22×C4×C29C22×C411yescharacteristic
95C22×C4×C29C2×D411yescharacteristic
96C22×C4×C29#4111yescharacteristic
97M16×C29—42no—
98C2×C8×C29—21no—
99C2×C8×C29—22no—
100C2×C8×C29—21no—
101C2×C8×C29—21no—
102C2×C8×C29—21no—
103C2×C8×C29—21no—
104C2×C8×C29—21no—
105C2×C8×C29—42no—
106C2×C8×C29—42no—
107C2×C8×C29—41no—
108C2×C8×C29—41no—
109C2×C8×C29—41no—
110C4⋊C4×C29—21no—
111C4⋊C4×C29—21no—
112C4⋊C4×C29—21no—
113C4⋊C4×C29—21no—
114C4⋊C4×C29—21no—
115C4⋊C4×C29—21no—
116C4⋊C4×C29—21no—
117C4⋊C4×C29—21no—
118C4⋊C4×C29—41no—
119C4⋊C4×C29—41no—
120C4⋊C4×C29—41no—
121C4⋊C4×C29—41no—
122C4⋊C4×C29C22⋊C411yescharacteristic
123C4⋊C4×C29C22⋊C411yescharacteristic
124C22⋊C4×C29—21no—
125C22⋊C4×C29—21no—
126C22⋊C4×C29—21no—
127C22⋊C4×C29—21no—
128C22⋊C4×C29—21no—
129C42×C29—21no—
130C42×C29C2×D411yescharacteristic
131C42×C29C2×D411yescharacteristic
132C42×C29C2×D411yescharacteristic
133C42×C29#4111yescharacteristic
134#9266C2911yesmaximal, characteristic, direct product factor, Sylow
135C23×C29—21no—
136C23×C29C4×D411yescharacteristic
137Q8×C29—41no—
138D4×C29—41no—
139D4×C29—41no—
140D4×C29—41no—
141C2×C4×C29—21no—
142C2×C4×C29—21no—
143C2×C4×C29—21no—
144C2×C4×C29—21no—
145C2×C4×C29—21no—
146C2×C4×C29—41no—
147C2×C4×C29—41no—
148C2×C4×C29—41no—
149C2×C4×C29—41no—
150C2×C4×C29—41no—
151C2×C4×C29—41no—
152C2×C4×C29—41no—
153C2×C4×C29—41no—
154C2×C4×C29—81no—
155C2×C4×C29C2×C22⋊C411yescharacteristic
156C2×C4×C29C4×D411yescharacteristic
157C2×C4×C29#12011yescharacteristic
158C2×C4×C29#12111yescharacteristic
159C2×C4×C29#12111yescharacteristic
160C2×C4×C29#12311yescharacteristic
161C8×C29—22no—
162C8×C29—41no—
163C8×C29—41no—
164C8×C29—42no—
165C8×C29—41no—
166C8×C29—41no—
167C8×C29—41no—
168C8×C29—81no—
169#3232C2×C2911yescharacteristic
170#2968C2×C2911yescharacteristic
171#1532C2×C2911yescharacteristic
172C2×#330C2×C2911yescharacteristic, complemented
173#1470C2×C2911yescharacteristic, complemented
174#1302C2×C2911yescharacteristic, complemented
175#1281C2×C2911yescharacteristic, complemented
176C22×C29—21no—
177C22×C29—21no—
178C22×C29—41no—
179C22×C29—41no—
180C22×C29—41no—
181C22×C29#38611yescharacteristic
182C22×C29#44311yescharacteristic
183C22×C29#44411yescharacteristic
184C4×C29—21no—
185C4×C29—21no—
186C4×C29—21no—
187C4×C29—21no—
188C4×C29—21no—
189C4×C29—21no—
190C4×C29—41no—
191C4×C29—41no—
192C4×C29—41no—
193C4×C29—81no—
194C4×C29—81no—
195#529C22×C2911yescharacteristic
196C2×#125C22×C2911yescharacteristic
197#499—21no—
198#488—21no—
199#484C4×C2911yescharacteristic
200#483C4×C2911yescharacteristic
201#481C4×C2911yescharacteristic
202#480C4×C2911yescharacteristic
203#479—21no—
204#478—21no—
205#446—21no—
206#435—21no—
207#435—21no—
208C8×D4—21no—
209#433—21no—
210#432C22×C2911yescharacteristic
211#431C22×C2911yescharacteristic
212#431C22×C2911yescharacteristic
213#405—21no—
214C2×#97C22×C2911yescharacteristic
215C2×#97C22×C2911yescharacteristic
216#330—21no—
217#330—21no—
218#330—21no—
219#329—21no—
220#324—21no—
221#324—21no—
222C2×C29—21no—
223C2×C29—21no—
224C2×C29—81no—
225C2×C29#187611yescharacteristic
226C2×C29#190611yescharacteristic
227C2×C29#191511yescharacteristic
228C2×M16—21no—
229C22×C8—21no—
230C22×C8—21no—
231C22×C8—21no—
232#126—21no—
233#125—21no—
234#125—21no—
235#125—21no—
236#125—21no—
237#125D4×C2911yescharacteristic
238#124D4×C2911yescharacteristic
239#123—21no—
240C22⋊Q8C2×C4×C2911yescharacteristic
241#121C2×C4×C2911yescharacteristic
242C4×Q8D4×C2911yescharacteristic
243C4×D4—21no—
244C4×D4D4×C2911yescharacteristic
245#117—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4C2×C4×C2911yescharacteristic
249C2×C4⋊C4C2×C4×C2911yescharacteristic
250C2×C42C23×C2911yescharacteristic
251#107—21no—
252#107—21no—
253#106—21no—
254#106—21no—
255C4⋊C8—21no—
256C4⋊C8—21no—
257C4⋊C8—21no—
258C4⋊C8—21no—
259C4⋊C8—21no—
260#103—21no—
261#103—21no—
262#102—21no—
263#102—21no—
264C22⋊C8—21no—
265C22⋊C8—21no—
266C22⋊C8—21no—
267C22⋊C8C2×C4×C2911yescharacteristic
268C22⋊C8C2×C4×C2911yescharacteristic
269C22⋊C8D4×C2911yescharacteristic
270C22⋊C8D4×C2911yescharacteristic
271#97—21no—
272#97—21no—
273#97—21no—
274#97—21no—
275#97—21no—
276#97D4×C2911yescharacteristic
277#97D4×C2911yescharacteristic
278C4×C8—21no—
279C4×C8—21no—
280C4×C8—21no—
281C29#926611yescharacteristic, direct product factor, Sylow
282C2×Q8C22⋊C4×C2911yescharacteristic
283C2×D4—21no—
284C2×D4C22⋊C4×C2911yescharacteristic
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4C22×C4×C2911yescharacteristic
289C22×C4C2×D4×C2911yescharacteristic
290C22×C4#41×C2911yescharacteristic
291M16—42no—
292C2×C8—21no—
293C2×C8—22no—
294C2×C8—21no—
295C2×C8—21no—
296C2×C8—21no—
297C2×C8—21no—
298C2×C8—21no—
299C2×C8—42no—
300C2×C8—42no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—41no—
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4C22⋊C4×C2911yescharacteristic
317C4⋊C4C22⋊C4×C2911yescharacteristic
318C22⋊C4—21no—
319C22⋊C4—21no—
320C22⋊C4—21no—
321C22⋊C4—21no—
322C22⋊C4—21no—
323C42—21no—
324C42C2×D4×C2911yescharacteristic
325C42C2×D4×C2911yescharacteristic
326C42C2×D4×C2911yescharacteristic
327C42#41×C2911yescharacteristic
328C23—21no—
329C23C4×D4×C2911yescharacteristic
330Q8—41no—
331D4—41no—
332D4—41no—
333D4—41no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—81no—
348C2×C4C2×C22⋊C4×C2911yescharacteristic
349C2×C4C4×D4×C2911yescharacteristic
350C2×C4C29×#12011yescharacteristic
351C2×C4C29×#12111yescharacteristic
352C2×C4C29×#12111yescharacteristic
353C2×C4C29×#12311yescharacteristic
354C8—22no—
355C8—41no—
356C8—41no—
357C8—42no—
358C8—41no—
359C8—41no—
360C8—41no—
361C8—81no—
362C22—21no—
363C22—21no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22C29×#38611yescharacteristic
368C22C29×#44311yescharacteristic
369C22C29×#44411yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—41no—
377C4—41no—
378C4—41no—
379C4—81no—
380C4—81no—
381C2—21no—
382C2—21no—
383C2—81no—
384C2C29×#187611yescharacteristic
385C2C29×#190611yescharacteristic
386C2C29×#191511yescharacteristic
subgroupG/H
center, socleC22×C29#386
commutatorC22×C4C22×C4×C29
Frattini, cosocleC2×C42C23×C29
prime radicalC29×#121C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C2×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C29×#330C2semidirect
5. C29×#1470C2semidirect
6. C29×#1302C2semidirect
7. C29×#1281C2semidirect
134. #9266C29direct (N × H)
172. C2×#330C2×C29semidirect
173. #1470C2×C29semidirect
174. #1302C2×C29semidirect
175. #1281C2×C29semidirect
281. C29#9266direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#32322
C29×#29682
C29×#15322
C2×C29×#3302
C29×#14702
C29×#13022
C29×#12812
#926629