Finite Group Databasebeta

← C29×#8842 #20303742

Subgroups — C29×#8842 #20303742

Order 7424.

420 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#2989C211yesmaximal, characteristic
2C29×#1831C211yesmaximal, characteristic, complemented
3C4×C29×#104C211yesmaximal, characteristic
4C29×#1565C211yesmaximal, characteristic, complemented
5C29×#1477C211yesmaximal, characteristic
6C29×#1283C211yesmaximal, characteristic, complemented
7C29×#1276C211yesmaximal, characteristic, complemented
8C4×#41×C29C2211yescharacteristic
9C29×#446—21no—
10C29×#436—21no—
11C29×#435—22no—
12C29×#432—21no—
13C29×#431C2211yescharacteristic
14C29×#431C2211yescharacteristic
15C29×#423—21no—
16C2×C29×C4⋊C8C2211yescharacteristic
17C2×C29×C4⋊C8C2211yescharacteristic
18C2×C29×#104C411yescharacteristic
19C2×C29×#104C411yescharacteristic
20C4×M16×C29C2211yescharacteristic
21C43×C29C2211yescharacteristic
22C29×#339C411yescharacteristic
23C29×#339C411yescharacteristic
24C29×#336—22no—
25C29×#335—21no—
26C29×#334—21no—
27C29×Q8⋊C8—21no—
28C29×D4⋊C8—21no—
29C2×#41×C29C2×C411yescharacteristic
30C2×M16×C29—22no—
31C2×M16×C29C2×C411yescharacteristic
32C2×M16×C29C2×C411yescharacteristic
33C22×C8×C29—21no—
34C22×C8×C29D412yes—
35C4×Q8×C29D411yescharacteristic
36C4×Q8×C29Q811yescharacteristic
37C4×D4×C29—21no—
38C4×D4×C29—21no—
39C4×D4×C29D411yescharacteristic
40C4×D4×C29Q811yescharacteristic
41C29×#117—21no—
42C29×#117C2×C411yescharacteristic
43C2×C42×C29—21no—
44C2×C42×C29—21no—
45C2×C42×C29—21no—
46C2×C42×C29C2×C411yescharacteristic
47C2×C42×C29C2×C411yescharacteristic
48C2×C42×C29C2311yescharacteristic
49C29×C4⋊C8—22no—
50C29×C4⋊C8—21no—
51C29×C4⋊C8—21no—
52C29×C4⋊C8—21no—
53C29×C4⋊C8—21no—
54C29×C4⋊C8—21no—
55C29×C4⋊C8D411yescharacteristic
56C29×C4⋊C8D411yescharacteristic
57C29×#104—22no—
58C29×#104—22no—
59C29×C22⋊C8—22no—
60C29×C22⋊C8—21no—
61C29×C22⋊C8—21no—
62C29×#97—22no—
63C29×#97—21no—
64C4×C8×C29—21no—
65C4×C8×C29—21no—
66C4×C8×C29—21no—
67#41×C29—21no—
68#41×C29—21no—
69#41×C29—21no—
70#41×C29—21no—
71C2×Q8×C29C4⋊C411yescharacteristic
72C2×D4×C29—21no—
73C2×D4×C29C4⋊C411yescharacteristic
74C22×C4×C29—21no—
75C22×C4×C29—21no—
76C22×C4×C29—21no—
77C22×C4×C29—21no—
78C22×C4×C29—21no—
79C22×C4×C29C22×C411yescharacteristic
80C22×C4×C29C2×D411yescharacteristic
81C22×C4×C29#4111yescharacteristic
82M16×C29—21no—
83M16×C29—21no—
84M16×C29—21no—
85M16×C29—82no—
86M16×C29M1612yescomplemented
87C2×C8×C29—21no—
88C2×C8×C29—21no—
89C2×C8×C29—22no—
90C2×C8×C29—21no—
91C2×C8×C29—21no—
92C2×C8×C29—42no—
93C2×C8×C29—42no—
94C2×C8×C29—41no—
95C2×C8×C29—41no—
96C4⋊C4×C29—21no—
97C4⋊C4×C29—21no—
98C4⋊C4×C29C4⋊C411yescharacteristic
99C4⋊C4×C29C4⋊C411yescharacteristic
100C22⋊C4×C29—21no—
101C22⋊C4×C29—21no—
102C22⋊C4×C29—21no—
103C42×C29—21no—
104C42×C29—21no—
105C42×C29—21no—
106C42×C29—21no—
107C42×C29—21no—
108C42×C29—21no—
109C42×C29—41no—
110C42×C29—41no—
111C42×C29—42no—
112C42×C29M1612yescomplemented
113C42×C29C2×D411yescharacteristic
114C42×C29C2×D411yescharacteristic
115C42×C29C2×Q811yescharacteristic
116C42×C29#4111yescharacteristic
117#8842C2911yesmaximal, characteristic, direct product factor, Sylow
118C23×C29—21no—
119C23×C29C4×D411yescharacteristic
120Q8×C29—21no—
121Q8×C29—21no—
122D4×C29—21no—
123D4×C29—21no—
124D4×C29—41no—
125D4×C29—41no—
126C2×C4×C29—21no—
127C2×C4×C29—21no—
128C2×C4×C29—22no—
129C2×C4×C29—21no—
130C2×C4×C29—21no—
131C2×C4×C29—21no—
132C2×C4×C29—22no—
133C2×C4×C29—41no—
134C2×C4×C29—41no—
135C2×C4×C29—41no—
136C2×C4×C29—41no—
137C2×C4×C29—41no—
138C2×C4×C29—41no—
139C2×C4×C29—41no—
140C2×C4×C29—41no—
141C2×C4×C29—41no—
142C2×C4×C29—81no—
143C2×C4×C29C2×C4⋊C411yescharacteristic
144C2×C4×C29C4×D411yescharacteristic
145C2×C4×C29#12011yescharacteristic
146C2×C4×C29C22⋊Q811yescharacteristic
147C2×C4×C29C22⋊Q811yescharacteristic
148C2×C4×C29#12311yescharacteristic
149C2×C4×C29C2×M1611yescharacteristic
150C2×C4×C29C2×M1611yescharacteristic
151C2×C4×C29#13111yescharacteristic
152C2×C4×C29#13111yescharacteristic
153C8×C29—22no—
154C8×C29—41no—
155C8×C29—41no—
156C8×C29—42no—
157C8×C29—41no—
158C8×C29—81no—
159C8×C29—81no—
160#2989C2×C2911yescharacteristic
161#1831C2×C2911yescharacteristic, complemented
162C4×#104C2×C2911yescharacteristic
163#1565C2×C2911yescharacteristic, complemented
164#1477C2×C2911yescharacteristic
165#1283C2×C2911yescharacteristic, complemented
166#1276C2×C2911yescharacteristic, complemented
167C22×C29—21no—
168C22×C29—21no—
169C22×C29—41no—
170C22×C29—41no—
171C22×C29—41no—
172C22×C29#38511yescharacteristic
173C22×C29#43511yescharacteristic
174C22×C29#43611yescharacteristic
175C4×C29—21no—
176C4×C29—21no—
177C4×C29—21no—
178C4×C29—42no—
179C4×C29—42no—
180C4×C29—41no—
181C4×C29—41no—
182C4×C29—41no—
183C4×C29#42311yescharacteristic
184C4×C29#42411yescharacteristic
185C4×C29#43511yescharacteristic
186C4×C29#43611yescharacteristic
187C4×C29#45411yescharacteristic
188C4×C29#45511yescharacteristic
189C4×#41C22×C2911yescharacteristic
190#446—21no—
191#436—21no—
192#435—22no—
193#432—21no—
194#431C22×C2911yescharacteristic
195#431C22×C2911yescharacteristic
196#423—21no—
197C2×C4⋊C8C22×C2911yescharacteristic
198C2×C4⋊C8C22×C2911yescharacteristic
199C2×#104C4×C2911yescharacteristic
200C2×#104C4×C2911yescharacteristic
201C4×M16C22×C2911yescharacteristic
202C43C22×C2911yescharacteristic
203#339C4×C2911yescharacteristic
204#339C4×C2911yescharacteristic
205#336—22no—
206#335—21no—
207#334—21no—
208Q8⋊C8—21no—
209D4⋊C8—21no—
210C2×C29—21no—
211C2×C29—21no—
212C2×C29—81no—
213C2×C29#185111yescharacteristic
214C2×C29#186011yescharacteristic
215C2×C29#186111yescharacteristic
216C2×#41C2×C4×C2911yescharacteristic
217C2×M16—22no—
218C2×M16C2×C4×C2911yescharacteristic
219C2×M16C2×C4×C2911yescharacteristic
220C22×C8—21no—
221C22×C8D4×C2912yes—
222C4×Q8D4×C2911yescharacteristic
223C4×Q8Q8×C2911yescharacteristic
224C4×D4—21no—
225C4×D4—21no—
226C4×D4D4×C2911yescharacteristic
227C4×D4Q8×C2911yescharacteristic
228#117—21no—
229#117C2×C4×C2911yescharacteristic
230C2×C42—21no—
231C2×C42—21no—
232C2×C42—21no—
233C2×C42C2×C4×C2911yescharacteristic
234C2×C42C2×C4×C2911yescharacteristic
235C2×C42C23×C2911yescharacteristic
236C4⋊C8—22no—
237C4⋊C8—21no—
238C4⋊C8—21no—
239C4⋊C8—21no—
240C4⋊C8—21no—
241C4⋊C8—21no—
242C4⋊C8D4×C2911yescharacteristic
243C4⋊C8D4×C2911yescharacteristic
244#104—22no—
245#104—22no—
246C22⋊C8—22no—
247C22⋊C8—21no—
248C22⋊C8—21no—
249#97—22no—
250#97—21no—
251C4×C8—21no—
252C4×C8—21no—
253C4×C8—21no—
254C29#884211yescharacteristic, direct product factor, Sylow
255#41—21no—
256#41—21no—
257#41—21no—
258#41—21no—
259C2×Q8C4⋊C4×C2911yescharacteristic
260C2×D4—21no—
261C2×D4C4⋊C4×C2911yescharacteristic
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4C22×C4×C2911yescharacteristic
268C22×C4C2×D4×C2911yescharacteristic
269C22×C4#41×C2911yescharacteristic
270M16—21no—
271M16—21no—
272M16—21no—
273M16—82no—
274M16M16×C2912yescomplemented
275C2×C8—21no—
276C2×C8—21no—
277C2×C8—21no—
278C2×C8—21no—
279C2×C8—22no—
280C2×C8—42no—
281C2×C8—42no—
282C2×C8—41no—
283C2×C8—41no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4C4⋊C4×C2911yescharacteristic
287C4⋊C4C4⋊C4×C2911yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—21no—
291C42—21no—
292C42—21no—
293C42—21no—
294C42—21no—
295C42—21no—
296C42—21no—
297C42—41no—
298C42—41no—
299C42—42no—
300C42M16×C2912yescomplemented
301C42C2×D4×C2911yescharacteristic
302C42C2×D4×C2911yescharacteristic
303C42C2×Q8×C2911yescharacteristic
304C42#41×C2911yescharacteristic
305C23—21no—
306C23C4×D4×C2911yescharacteristic
307Q8—21no—
308Q8—21no—
309D4—21no—
310D4—21no—
311D4—41no—
312D4—41no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—81no—
330C2×C4C2×C4⋊C4×C2911yescharacteristic
331C2×C4C4×D4×C2911yescharacteristic
332C2×C4C29×#12011yescharacteristic
333C2×C4C29×C22⋊Q811yescharacteristic
334C2×C4C29×C22⋊Q811yescharacteristic
335C2×C4C29×#12311yescharacteristic
336C2×C4C2×M16×C2911yescharacteristic
337C2×C4C2×M16×C2911yescharacteristic
338C2×C4C29×#13111yescharacteristic
339C2×C4C29×#13111yescharacteristic
340C8—22no—
341C8—41no—
342C8—41no—
343C8—42no—
344C8—41no—
345C8—81no—
346C8—81no—
347C22—21no—
348C22—21no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22C29×#38511yescharacteristic
353C22C29×#43511yescharacteristic
354C22C29×#43611yescharacteristic
355C4—21no—
356C4—21no—
357C4—21no—
358C4—42no—
359C4—42no—
360C4—41no—
361C4—41no—
362C4—41no—
363C4C29×#42311yescharacteristic
364C4C29×#42411yescharacteristic
365C4C29×#43511yescharacteristic
366C4C29×#43611yescharacteristic
367C4C29×#45411yescharacteristic
368C4C29×#45511yescharacteristic
369C2—21no—
370C2—21no—
371C2—81no—
372C2C29×#185111yescharacteristic
373C2C29×#186011yescharacteristic
374C2C29×#186111yescharacteristic
subgroupG/H
centerC2×C4×C29#120
commutatorC22×C4C22×C4×C29
Frattini, cosocleC2×C42C23×C29
socleC22×C29#385
prime radicalC2×#41×C29C2×C4
LCSG ▷ C22×C4 ▷ C2 ▷ 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×#1831C2semidirect
4. C29×#1565C2semidirect
6. C29×#1283C2semidirect
7. C29×#1276C2semidirect
86. M16×C29M16semidirect
112. C42×C29M16semidirect
117. #8842C29direct (N × H)
161. #1831C2×C29semidirect
163. #1565C2×C29semidirect
165. #1283C2×C29semidirect
166. #1276C2×C29semidirect
254. C29#8842direct (N × H)
274. M16M16×C29semidirect
300. C42M16×C29semidirect

Maximal subgroups

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

subgroupindex
C29×#29892
C29×#18312
C4×C29×#1042
C29×#15652
C29×#14772
C29×#12832
C29×#12762
#884229