Finite Group Databasebeta

← C29×#9291 #20304191

Subgroups — C29×#9291 #20304191

Order 7424.

494 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3226C211yesmaximal, characteristic
2C29×#2932C211yesmaximal, characteristic
3C29×#1960C211yesmaximal, characteristic, complemented
4C29×#1546C211yesmaximal, characteristic, complemented
5C29×#1517C211yesmaximal, characteristic
6C29×#1286C211yesmaximal, characteristic, complemented
7C29×#1275C211yesmaximal, characteristic, complemented
8C2×C29×#131—21no—
9C29×#532C2211yescharacteristic
10C2×C29×C4⋊Q8C2211yescharacteristic
11C29×#500C412yescomplemented
12C29×#486C412yescomplemented
13C29×#480—22no—
14C29×#474—22no—
15C29×#435—22no—
16C29×#435—22no—
17C29×#431C2211yescharacteristic
18C29×#431C2211yescharacteristic
19C29×#423C2211yescharacteristic
20C2×C29×#103—21no—
21C2×C29×#103—21no—
22C29×#408—21no—
23C2×C29×#97C2211yescharacteristic
24C29×#382C2211yescharacteristic
25C29×#332—22no—
26C29×#327—22no—
27C2×#41×C29—21no—
28C22×Q8×C29—21no—
29C29×#131—42no—
30C29×#131—42no—
31C2×M16×C29—22no—
32C2×M16×C29—21no—
33C22×C8×C29—22no—
34C22×C8×C29D411yescharacteristic
35C22×C8×C29D411yescharacteristic
36C29×C4⋊Q8—21no—
37C29×C4⋊Q8—21no—
38C29×C4⋊Q8—21no—
39C29×C4⋊Q8C2×C412yes—
40C29×C4⋊Q8C2×C411yescharacteristic
41C29×#127C2×C411yescharacteristic
42C29×#124—21no—
43C29×#121—21no—
44C29×#121D412yes—
45C4×D4×C29—21no—
46C4×D4×C29D412yes—
47C2×C4⋊C4×C29—21no—
48C2×C4⋊C4×C29—21no—
49C2×C4⋊C4×C29—21no—
50C2×C42×C29C2311yescharacteristic
51C29×#107—24no—
52C29×C4⋊C8—21no—
53C29×C4⋊C8—21no—
54C29×C4⋊C8—21no—
55C29×C4⋊C8D412yes—
56C29×#103—42no—
57C29×#103—42no—
58C29×#102—24no—
59C29×C22⋊C8—24no—
60C29×C22⋊C8—21no—
61C29×C22⋊C8—21no—
62C29×#97—21no—
63C29×#97—21no—
64C4×C8×C29—21no—
65C4×C8×C29C2×C412yes—
66C29×#95—21no—
67C29×#95—21no—
68#41×C29—41no—
69#41×C29—41no—
70#41×C29—41no—
71#41×C29—41no—
72C2×Q8×C29—21no—
73C2×Q8×C29—22no—
74C2×Q8×C29—41no—
75C2×Q8×C29—41no—
76C2×Q8×C29—41no—
77C2×Q8×C29—41no—
78C2×Q8×C29—41no—
79C2×D4×C29—22no—
80C2×D4×C29—21no—
81C2×D4×C29—21no—
82C2×D4×C29C22⋊C412yes—
83C22×C4×C29—22no—
84C22×C4×C29—41no—
85C22×C4×C29—41no—
86C22×C4×C29C2×D411yescharacteristic
87C22×C4×C29C2×D411yescharacteristic
88C22×C4×C29#4111yescharacteristic
89M16×C29—44no—
90M16×C29—41no—
91M16×C29—41no—
92C2×C8×C29—21no—
93C2×C8×C29—21no—
94C2×C8×C29—22no—
95C2×C8×C29—22no—
96C2×C8×C29—21no—
97C2×C8×C29—21no—
98C2×C8×C29—21no—
99C2×C8×C29—44no—
100C2×C8×C29—41no—
101C2×C8×C29D812yes—
102C4⋊C4×C29—21no—
103C4⋊C4×C29—22no—
104C4⋊C4×C29—22no—
105C4⋊C4×C29—41no—
106C4⋊C4×C29—41no—
107C4⋊C4×C29—41no—
108C4⋊C4×C29—41no—
109C4⋊C4×C29C22⋊C412yes—
110C22⋊C4×C29—22no—
111C22⋊C4×C29—22no—
112C42×C29C22×C411yescharacteristic
113C42×C29C2×D411yescharacteristic
114C42×C29C2×D411yescharacteristic
115C42×C29#4111yescharacteristic
116#9291C2911yesmaximal, characteristic, direct product factor, Sylow
117C23×C29—22no—
118C23×C29#12111yescharacteristic
119Q8×C29—41no—
120Q8×C29—41no—
121Q8×C29—42no—
122Q8×C29—42no—
123Q8×C29—81no—
124Q8×C29—81no—
125D4×C29—42no—
126D4×C29—42no—
127D4×C29—42no—
128D4×C29—41no—
129D4×C29—41no—
130D4×C29—81no—
131C2×C4×C29—22no—
132C2×C4×C29—41no—
133C2×C4×C29—41no—
134C2×C4×C29—42no—
135C2×C4×C29—42no—
136C2×C4×C29—42no—
137C2×C4×C29—81no—
138C2×C4×C29—81no—
139C2×C4×C29—81no—
140C2×C4×C29—81no—
141C2×C4×C29—81no—
142C2×C4×C29C2×C22⋊C411yescharacteristic
143C2×C4×C29C4×D411yescharacteristic
144C2×C4×C29C4×D411yescharacteristic
145C2×C4×C29#12011yescharacteristic
146C2×C4×C29#12111yescharacteristic
147C2×C4×C29#12311yescharacteristic
148C2×C4×C29C2×D811yescharacteristic
149C2×C4×C29#13511yescharacteristic
150C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
152C8×C29—22no—
153C8×C29—42no—
154C8×C29—42no—
155C8×C29—41no—
156C8×C29—81no—
157#3226C2×C2911yescharacteristic
158#2932C2×C2911yescharacteristic
159#1960C2×C2911yescharacteristic, complemented
160#1546C2×C2911yescharacteristic, complemented
161#1517C2×C2911yescharacteristic
162#1286C2×C2911yescharacteristic, complemented
163#1275C2×C2911yescharacteristic, complemented
164C22×C29—21no—
165C22×C29—21no—
166C22×C29—42no—
167C22×C29—42no—
168C22×C29—42no—
169C22×C29#38611yescharacteristic
170C22×C29#45911yescharacteristic
171C22×C29#46311yescharacteristic
172C4×C29—21no—
173C4×C29—21no—
174C4×C29—21no—
175C4×C29—21no—
176C4×C29—42no—
177C4×C29—82no—
178C4×C29—161no—
179C4×C29C4×D811yescharacteristic
180C4×C29#44211yescharacteristic
181C4×C29#44711yescharacteristic
182C4×C29#44911yescharacteristic
183C2×#131—21no—
184#532C22×C2911yescharacteristic
185C2×C4⋊Q8C22×C2911yescharacteristic
186#500C4×C2912yescomplemented
187#486C4×C2912yescomplemented
188#480—22no—
189#474—22no—
190#435—22no—
191#435—22no—
192#431C22×C2911yescharacteristic
193#431C22×C2911yescharacteristic
194#423C22×C2911yescharacteristic
195C2×#103—21no—
196C2×#103—21no—
197#408—21no—
198C2×#97C22×C2911yescharacteristic
199#382C22×C2911yescharacteristic
200#332—22no—
201#327—22no—
202C2×C29—21no—
203C2×C29—21no—
204C2×C29—82no—
205C2×C29#187911yescharacteristic
206C2×C29#190211yescharacteristic
207C2×C29#190911yescharacteristic
208C2×#41—21no—
209C22×Q8—21no—
210#131—42no—
211#131—42no—
212C2×M16—22no—
213C2×M16—21no—
214C22×C8—22no—
215C22×C8D4×C2911yescharacteristic
216C22×C8D4×C2911yescharacteristic
217C4⋊Q8—21no—
218C4⋊Q8—21no—
219C4⋊Q8—21no—
220C4⋊Q8C2×C4×C2912yes—
221C4⋊Q8C2×C4×C2911yescharacteristic
222#127C2×C4×C2911yescharacteristic
223#124—21no—
224#121—21no—
225#121D4×C2912yes—
226C4×D4—21no—
227C4×D4D4×C2912yes—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C42C23×C2911yescharacteristic
232#107—24no—
233C4⋊C8—21no—
234C4⋊C8—21no—
235C4⋊C8—21no—
236C4⋊C8D4×C2912yes—
237#103—42no—
238#103—42no—
239#102—24no—
240C22⋊C8—24no—
241C22⋊C8—21no—
242C22⋊C8—21no—
243#97—21no—
244#97—21no—
245C4×C8—21no—
246C4×C8C2×C4×C2912yes—
247#95—21no—
248#95—21no—
249C29#929111yescharacteristic, direct product factor, Sylow
250#41—41no—
251#41—41no—
252#41—41no—
253#41—41no—
254C2×Q8—21no—
255C2×Q8—22no—
256C2×Q8—41no—
257C2×Q8—41no—
258C2×Q8—41no—
259C2×Q8—41no—
260C2×Q8—41no—
261C2×D4—22no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4C22⋊C4×C2912yes—
265C22×C4—22no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4C2×D4×C2911yescharacteristic
269C22×C4C2×D4×C2911yescharacteristic
270C22×C4#41×C2911yescharacteristic
271M16—44no—
272M16—41no—
273M16—41no—
274C2×C8—21no—
275C2×C8—21no—
276C2×C8—22no—
277C2×C8—21no—
278C2×C8—22no—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8—44no—
282C2×C8—41no—
283C2×C8D8×C2912yes—
284C4⋊C4—21no—
285C4⋊C4—22no—
286C4⋊C4—22no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4C22⋊C4×C2912yes—
292C22⋊C4—22no—
293C22⋊C4—22no—
294C42C22×C4×C2911yescharacteristic
295C42C2×D4×C2911yescharacteristic
296C42C2×D4×C2911yescharacteristic
297C42#41×C2911yescharacteristic
298C23—22no—
299C23C29×#12111yescharacteristic
300Q8—41no—
301Q8—41no—
302Q8—42no—
303Q8—42no—
304Q8—81no—
305Q8—81no—
306D4—42no—
307D4—42no—
308D4—42no—
309D4—41no—
310D4—41no—
311D4—81no—
312C2×C4—22no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4C2×C22⋊C4×C2911yescharacteristic
324C2×C4C4×D4×C2911yescharacteristic
325C2×C4C4×D4×C2911yescharacteristic
326C2×C4C29×#12011yescharacteristic
327C2×C4C29×#12111yescharacteristic
328C2×C4C29×#12311yescharacteristic
329C2×C4C2×D8×C2911yescharacteristic
330C2×C4C29×#13511yescharacteristic
331C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
332C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
333C8—22no—
334C8—42no—
335C8—42no—
336C8—41no—
337C8—81no—
338C22—21no—
339C22—21no—
340C22—42no—
341C22—42no—
342C22—42no—
343C22C29×#38611yescharacteristic
344C22C29×#45911yescharacteristic
345C22C29×#46311yescharacteristic
346C4—21no—
347C4—21no—
348C4—21no—
349C4—21no—
350C4—42no—
351C4—82no—
352C4—161no—
353C4C4×D8×C2911yescharacteristic
354C4C29×#44211yescharacteristic
355C4C29×#44711yescharacteristic
356C4C29×#44911yescharacteristic
357C2—21no—
358C2—21no—
359C2—82no—
360C2C29×#187911yescharacteristic
361C2C29×#190211yescharacteristic
362C2C29×#190911yescharacteristic
subgroupG/H
center, socleC22×C29#386
commutatorC42C22×C4×C29
Frattini, cosocleC2×C42C23×C29
prime radicalC29×#532C22
LCSG ▷ C42 ▷ 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×#1960C2semidirect
4. C29×#1546C2semidirect
6. C29×#1286C2semidirect
7. C29×#1275C2semidirect
11. C29×#500C4semidirect
12. C29×#486C4semidirect
116. #9291C29direct (N × H)
159. #1960C2×C29semidirect
160. #1546C2×C29semidirect
162. #1286C2×C29semidirect
163. #1275C2×C29semidirect
186. #500C4×C29semidirect
187. #486C4×C29semidirect
249. C29#9291direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#32262
C29×#29322
C29×#19602
C29×#15462
C29×#15172
C29×#12862
C29×#12752
#929129