Finite Group Databasebeta

← C29×#9354 #20304254

Subgroups — C29×#9354 #20304254

Order 7424.

470 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3039C211yesmaximal, characteristic
2C29×#2991C211yesmaximal, characteristic
3C29×#1997C211yesmaximal, characteristic, complemented
4C29×#1548C211yesmaximal, characteristic, complemented
5C29×#1489C211yesmaximal, characteristic
6C29×#1309C211yesmaximal, characteristic, complemented
7C29×#1299C211yesmaximal, characteristic, complemented
8C2×C29×#137C412yes—
9C2×C29×C4⋊Q8C2211yescharacteristic
10C4×#41×C29C2211yescharacteristic
11C29×#462—21no—
12C29×#462—21no—
13C29×#461—21no—
14C29×#461—21no—
15C8×Q8×C29—21no—
16C29×#436—22no—
17C29×#436—21no—
18C29×#431—21no—
19C29×#431C2211yescharacteristic
20C29×#423—21no—
21C29×#423C2211yescharacteristic
22C29×#423C2211yescharacteristic
23C29×#423C2211yescharacteristic
24C29×#419C412yes—
25C4×M16×C29C2211yescharacteristic
26C29×#343—22no—
27C29×#333—21no—
28C29×#333—21no—
29C29×Q8⋊C8—21no—
30C29×D4⋊C8—21no—
31C2×#41×C29C2×C411yescharacteristic
32C22×Q8×C29C2×C412yes—
33C29×#137—44no—
34C2×Q16×C29—22no—
35C2×SD16×C29—22no—
36C2×M16×C29—22no—
37C2×M16×C29—21no—
38C2×M16×C29—21no—
39C2×M16×C29C2×C412yes—
40C2×M16×C29D412yes—
41C29×C4⋊Q8—21no—
42C29×C4⋊Q8—21no—
43C29×C4⋊Q8—21no—
44C29×C4⋊Q8—21no—
45C4×Q8×C29D411yescharacteristic
46C4×Q8×C29D411yescharacteristic
47C4×D4×C29—21no—
48C4×D4×C29—21no—
49C4×D4×C29D411yescharacteristic
50C4×D4×C29D411yescharacteristic
51C29×#117—21no—
52C29×#117C2×C411yescharacteristic
53C2×C4⋊C4×C29—21no—
54C2×C4⋊C4×C29—21no—
55C2×C42×C29—21no—
56C2×C42×C29C2311yescharacteristic
57C29×C4⋊C8—22no—
58C29×C4⋊C8—21no—
59C29×C4⋊C8—21no—
60C29×C4⋊C8—21no—
61C29×C4⋊C8—21no—
62C29×C4⋊C8—21no—
63C29×C4⋊C8—21no—
64C29×C4⋊C8D411yescharacteristic
65C29×C4⋊C8D411yescharacteristic
66C29×#103—22no—
67C29×#103—22no—
68C29×C22⋊C8—22no—
69C29×C22⋊C8—21no—
70C29×#97—21no—
71C4×C8×C29—22no—
72C4×C8×C29—21no—
73C4×C8×C29—21no—
74#41×C29—22no—
75#41×C29—41no—
76C2×Q8×C29—22no—
77C2×Q8×C29—22no—
78C2×Q8×C29—42no—
79C2×Q8×C29—42no—
80C2×Q8×C29C22⋊C411yescharacteristic
81C2×D4×C29—21no—
82C2×D4×C29C22⋊C411yescharacteristic
83C22×C4×C29—21no—
84C22×C4×C29—21no—
85C22×C4×C29—21no—
86C22×C4×C29—22no—
87C22×C4×C29C22×C411yescharacteristic
88C22×C4×C29C2×D411yescharacteristic
89C22×C4×C29#4111yescharacteristic
90Q16×C29—44no—
91SD16×C29—44no—
92M16×C29—22no—
93M16×C29—41no—
94M16×C29—42no—
95M16×C29—42no—
96M16×C29—82no—
97M16×C29—81no—
98C2×C8×C29—22no—
99C2×C8×C29—21no—
100C2×C8×C29—22no—
101C2×C8×C29—21no—
102C2×C8×C29—41no—
103C2×C8×C29—41no—
104C4⋊C4×C29—21no—
105C4⋊C4×C29—21no—
106C4⋊C4×C29—41no—
107C4⋊C4×C29—41no—
108C4⋊C4×C29—41no—
109C4⋊C4×C29—41no—
110C4⋊C4×C29C22⋊C411yescharacteristic
111C4⋊C4×C29C22⋊C411yescharacteristic
112C22⋊C4×C29—21no—
113C22⋊C4×C29—21no—
114C22⋊C4×C29—21no—
115C42×C29—21no—
116C42×C29—21no—
117C42×C29—21no—
118C42×C29C2×D411yescharacteristic
119C42×C29C2×D411yescharacteristic
120C42×C29C2×D411yescharacteristic
121C42×C29#4111yescharacteristic
122#9354C2911yesmaximal, characteristic, direct product factor, Sylow
123C23×C29—21no—
124C23×C29C4×D411yescharacteristic
125Q8×C29—21no—
126Q8×C29—42no—
127Q8×C29—42no—
128Q8×C29—82no—
129Q8×C29#10012yes—
130D4×C29—21no—
131D4×C29—21no—
132D4×C29—42no—
133C2×C4×C29—21no—
134C2×C4×C29—21no—
135C2×C4×C29—21no—
136C2×C4×C29—21no—
137C2×C4×C29—21no—
138C2×C4×C29—21no—
139C2×C4×C29—21no—
140C2×C4×C29—21no—
141C2×C4×C29—21no—
142C2×C4×C29—42no—
143C2×C4×C29—41no—
144C2×C4×C29—41no—
145C2×C4×C29—41no—
146C2×C4×C29—41no—
147C2×C4×C29—42no—
148C2×C4×C29—82no—
149C2×C4×C29C2×C22⋊C411yescharacteristic
150C2×C4×C29C4×D411yescharacteristic
151C2×C4×C29#12011yescharacteristic
152C2×C4×C29#12111yescharacteristic
153C2×C4×C29#12111yescharacteristic
154C2×C4×C29#12311yescharacteristic
155C8×C29—42no—
156C8×C29—42no—
157C8×C29—42no—
158C8×C29—41no—
159C8×C29—41no—
160C8×C29—81no—
161#3039C2×C2911yescharacteristic
162#2991C2×C2911yescharacteristic
163#1997C2×C2911yescharacteristic, complemented
164#1548C2×C2911yescharacteristic, complemented
165#1489C2×C2911yescharacteristic
166#1309C2×C2911yescharacteristic, complemented
167#1299C2×C2911yescharacteristic, complemented
168C22×C29—21no—
169C22×C29—21no—
170C22×C29—21no—
171C22×C29—41no—
172C22×C29—41no—
173C22×C29—41no—
174C22×C29#38611yescharacteristic
175C4×C29—21no—
176C4×C29—21no—
177C4×C29—22no—
178C4×C29—21no—
179C4×C29—41no—
180C4×C29—41no—
181C4×C29—82no—
182C4×C29C2×#10011yescharacteristic
183C4×C29#41311yescharacteristic
184C4×C29#45511yescharacteristic
185C4×C29#45611yescharacteristic
186C4×C29#47111yescharacteristic
187C4×C29#47311yescharacteristic
188C2×#137C4×C2912yes—
189C2×C4⋊Q8C22×C2911yescharacteristic
190C4×#41C22×C2911yescharacteristic
191#462—21no—
192#462—21no—
193#461—21no—
194#461—21no—
195C8×Q8—21no—
196#436—22no—
197#436—21no—
198#431—21no—
199#431C22×C2911yescharacteristic
200#423—21no—
201#423C22×C2911yescharacteristic
202#423C22×C2911yescharacteristic
203#423C22×C2911yescharacteristic
204#419C4×C2912yes—
205C4×M16C22×C2911yescharacteristic
206#343—22no—
207#333—21no—
208#333—21no—
209Q8⋊C8—21no—
210D4⋊C8—21no—
211C2×C29—41no—
212C2×C29—81no—
213C2×C29#188211yescharacteristic
214C2×C29#190011yescharacteristic
215C2×C29#190811yescharacteristic
216C2×#41C2×C4×C2911yescharacteristic
217C22×Q8C2×C4×C2912yes—
218#137—44no—
219C2×Q16—22no—
220C2×SD16—22no—
221C2×M16—22no—
222C2×M16—21no—
223C2×M16—21no—
224C2×M16C2×C4×C2912yes—
225C2×M16D4×C2912yes—
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8—21no—
229C4⋊Q8—21no—
230C4×Q8D4×C2911yescharacteristic
231C4×Q8D4×C2911yescharacteristic
232C4×D4—21no—
233C4×D4—21no—
234C4×D4D4×C2911yescharacteristic
235C4×D4D4×C2911yescharacteristic
236#117—21no—
237#117C2×C4×C2911yescharacteristic
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C42—21no—
241C2×C42C23×C2911yescharacteristic
242C4⋊C8—22no—
243C4⋊C8—21no—
244C4⋊C8—21no—
245C4⋊C8—21no—
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8—21no—
249C4⋊C8D4×C2911yescharacteristic
250C4⋊C8D4×C2911yescharacteristic
251#103—22no—
252#103—22no—
253C22⋊C8—22no—
254C22⋊C8—21no—
255#97—21no—
256C4×C8—22no—
257C4×C8—21no—
258C4×C8—21no—
259C29#935411yescharacteristic, direct product factor, Sylow
260#41—22no—
261#41—41no—
262C2×Q8—22no—
263C2×Q8—22no—
264C2×Q8—42no—
265C2×Q8—42no—
266C2×Q8C22⋊C4×C2911yescharacteristic
267C2×D4—21no—
268C2×D4C22⋊C4×C2911yescharacteristic
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—22no—
273C22×C4C22×C4×C2911yescharacteristic
274C22×C4C2×D4×C2911yescharacteristic
275C22×C4#41×C2911yescharacteristic
276Q16—44no—
277SD16—44no—
278M16—22no—
279M16—41no—
280M16—42no—
281M16—42no—
282M16—82no—
283M16—81no—
284C2×C8—22no—
285C2×C8—21no—
286C2×C8—22no—
287C2×C8—21no—
288C2×C8—41no—
289C2×C8—41no—
290C4⋊C4—21no—
291C4⋊C4—21no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4C22⋊C4×C2911yescharacteristic
297C4⋊C4C22⋊C4×C2911yescharacteristic
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—21no—
301C42—21no—
302C42—21no—
303C42—21no—
304C42C2×D4×C2911yescharacteristic
305C42C2×D4×C2911yescharacteristic
306C42C2×D4×C2911yescharacteristic
307C42#41×C2911yescharacteristic
308C23—21no—
309C23C4×D4×C2911yescharacteristic
310Q8—21no—
311Q8—42no—
312Q8—42no—
313Q8—82no—
314Q8C29×#10012yes—
315D4—21no—
316D4—21no—
317D4—42no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—42no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—42no—
333C2×C4—82no—
334C2×C4C2×C22⋊C4×C2911yescharacteristic
335C2×C4C4×D4×C2911yescharacteristic
336C2×C4C29×#12011yescharacteristic
337C2×C4C29×#12111yescharacteristic
338C2×C4C29×#12111yescharacteristic
339C2×C4C29×#12311yescharacteristic
340C8—42no—
341C8—42no—
342C8—41no—
343C8—41no—
344C8—42no—
345C8—81no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22C29×#38611yescharacteristic
353C4—21no—
354C4—21no—
355C4—21no—
356C4—22no—
357C4—41no—
358C4—41no—
359C4—82no—
360C4C2×C29×#10011yescharacteristic
361C4C29×#41311yescharacteristic
362C4C29×#45511yescharacteristic
363C4C29×#45611yescharacteristic
364C4C29×#47111yescharacteristic
365C4C29×#47311yescharacteristic
366C2—41no—
367C2—81no—
368C2C29×#188211yescharacteristic
369C2C29×#190011yescharacteristic
370C2C29×#190811yescharacteristic
subgroupG/H
center, socleC22×C29#386
commutatorC22×C4C22×C4×C29
Frattini, cosocleC2×C42C23×C29
prime radicalC2×#41×C29C2×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
3. C29×#1997C2semidirect
4. C29×#1548C2semidirect
6. C29×#1309C2semidirect
7. C29×#1299C2semidirect
122. #9354C29direct (N × H)
163. #1997C2×C29semidirect
164. #1548C2×C29semidirect
166. #1309C2×C29semidirect
167. #1299C2×C29semidirect
259. C29#9354direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#30392
C29×#29912
C29×#19972
C29×#15482
C29×#14892
C29×#13092
C29×#12992
#935429