Finite Group Databasebeta

← C29×#9271 #20304171

Subgroups — C29×#9271 #20304171

Order 7424.

496 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3226C211yesmaximal, characteristic
2C29×#2935C211yesmaximal, characteristic
3C29×#1966C211yesmaximal, characteristic, complemented
4C29×#1547C211yesmaximal, characteristic
5C2×C29×#332C211yesmaximal, characteristic, complemented
6C29×#1301C211yesmaximal, characteristic, complemented
7C29×#1283C211yesmaximal, characteristic, complemented
8C2×C29×#131—21no—
9C29×#532C2211yescharacteristic
10C2×C29×C4⋊Q8C2211yescharacteristic
11C29×#500—21no—
12C29×#486—21no—
13C29×#480C414yes—
14C29×#474—22no—
15C29×#436—21no—
16C29×#435—22no—
17C8×D4×C29—21no—
18C29×#431C2211yescharacteristic
19C29×#423C2211yescharacteristic
20C2×C29×C4⋊C8C2211yescharacteristic
21C2×C29×C4⋊C8C2211yescharacteristic
22C2×C29×#101—21no—
23C2×C29×#101—21no—
24C29×#408—21no—
25C4×M16×C29C2211yescharacteristic
26C29×#332—21no—
27C29×#332—21no—
28C29×#332—21no—
29C29×#331—21no—
30C2×#41×C29—21no—
31C22×Q8×C29—21no—
32C29×#131—42no—
33C29×#131—42no—
34C2×M16×C29—22no—
35C2×M16×C29—21no—
36C2×M16×C29D411yescharacteristic
37C2×M16×C29D411yescharacteristic
38C22×C8×C29—22no—
39C22×C8×C29—21no—
40C22×C8×C29—21no—
41C29×C4⋊Q8—21no—
42C29×C4⋊Q8—21no—
43C29×C4⋊Q8—21no—
44C29×C4⋊Q8—21no—
45C29×C4⋊Q8D411yescharacteristic
46C29×#127D411yescharacteristic
47C29×#124—21no—
48C29×#121—21no—
49C29×#121C2×C412yes—
50C4×D4×C29—21no—
51C4×D4×C29D412yes—
52C2×C4⋊C4×C29—21no—
53C2×C4⋊C4×C29C2×C412yes—
54C2×C42×C29C2311yescharacteristic
55C29×#107—24no—
56C29×C4⋊C8—21no—
57C29×C4⋊C8—21no—
58C29×C4⋊C8—21no—
59C29×C4⋊C8—21no—
60C29×C4⋊C8—21no—
61C29×C4⋊C8—21no—
62C29×C4⋊C8D411yescharacteristic
63C29×C4⋊C8D411yescharacteristic
64C29×#102—24no—
65C29×#101—42no—
66C29×#101—42no—
67C29×C22⋊C8—22no—
68C29×C22⋊C8—22no—
69C29×C22⋊C8C2×C412yes—
70C29×#97—21no—
71C4×C8×C29—21no—
72C4×C8×C29—21no—
73#41×C29—41no—
74#41×C29—41no—
75#41×C29—41no—
76#41×C29—41no—
77C2×Q8×C29—21no—
78C2×Q8×C29—41no—
79C2×Q8×C29—41no—
80C2×Q8×C29—41no—
81C2×Q8×C29—41no—
82C2×Q8×C29—41no—
83C2×Q8×C29—41no—
84C2×D4×C29—22no—
85C2×D4×C29—21no—
86C2×D4×C29—21no—
87C2×D4×C29C22⋊C412yes—
88C22×C4×C29—22no—
89C22×C4×C29—22no—
90C22×C4×C29C22×C411yescharacteristic
91C22×C4×C29C2×D411yescharacteristic
92C22×C4×C29#4111yescharacteristic
93M16×C29—21no—
94M16×C29—21no—
95M16×C29—21no—
96M16×C29—44no—
97M16×C29—41no—
98M16×C29—41no—
99M16×C29D812yes—
100C2×C8×C29—21no—
101C2×C8×C29—22no—
102C2×C8×C29—21no—
103C2×C8×C29—21no—
104C2×C8×C29—21no—
105C2×C8×C29—44no—
106C2×C8×C29—41no—
107C2×C8×C29—41no—
108C2×C8×C29—41no—
109C2×C8×C29—41no—
110C2×C8×C29—81no—
111C4⋊C4×C29—21no—
112C4⋊C4×C29—22no—
113C4⋊C4×C29—22no—
114C4⋊C4×C29—41no—
115C4⋊C4×C29—41no—
116C4⋊C4×C29C22⋊C412yes—
117C22⋊C4×C29—22no—
118C22⋊C4×C29—22no—
119C42×C29C2×D411yescharacteristic
120C42×C29C2×D411yescharacteristic
121C42×C29C2×D411yescharacteristic
122C42×C29#4111yescharacteristic
123#9271C2911yesmaximal, characteristic, direct product factor, Sylow
124C23×C29—22no—
125C23×C29C4×D411yescharacteristic
126Q8×C29—41no—
127Q8×C29—41no—
128Q8×C29—81no—
129Q8×C29—81no—
130Q8×C29—81no—
131Q8×C29—81no—
132D4×C29—42no—
133D4×C29—42no—
134D4×C29—42no—
135D4×C29—41no—
136D4×C29—41no—
137D4×C29—41no—
138D4×C29—41no—
139C2×C4×C29—21no—
140C2×C4×C29—21no—
141C2×C4×C29—22no—
142C2×C4×C29—41no—
143C2×C4×C29—42no—
144C2×C4×C29—42no—
145C2×C4×C29—42no—
146C2×C4×C29—42no—
147C2×C4×C29—42no—
148C2×C4×C29C2×C22⋊C411yescharacteristic
149C2×C4×C29C4×D411yescharacteristic
150C2×C4×C29#12011yescharacteristic
151C2×C4×C29#12111yescharacteristic
152C2×C4×C29#12111yescharacteristic
153C2×C4×C29#12311yescharacteristic
154C2×C4×C29C2×D811yescharacteristic
155C2×C4×C29#13511yescharacteristic
156C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
158C8×C29—22no—
159C8×C29—42no—
160C8×C29—41no—
161C8×C29—41no—
162C8×C29—41no—
163C8×C29—81no—
164C8×C29—81no—
165#3226C2×C2911yescharacteristic
166#2935C2×C2911yescharacteristic
167#1966C2×C2911yescharacteristic, complemented
168#1547C2×C2911yescharacteristic
169C2×#332C2×C2911yescharacteristic, complemented
170#1301C2×C2911yescharacteristic, complemented
171#1283C2×C2911yescharacteristic, complemented
172C22×C29—21no—
173C22×C29—21no—
174C22×C29—42no—
175C22×C29—42no—
176C22×C29—42no—
177C22×C29#38611yescharacteristic
178C22×C29C4×D811yescharacteristic
179C22×C29#44211yescharacteristic
180C4×C29—21no—
181C4×C29—21no—
182C4×C29—21no—
183C4×C29—42no—
184C4×C29—82no—
185C4×C29#44711yescharacteristic
186C4×C29#44911yescharacteristic
187C4×C29#45911yescharacteristic
188C4×C29#46311yescharacteristic
189C4×C29#47111yescharacteristic
190C4×C29#47311yescharacteristic
191C2×#131—21no—
192#532C22×C2911yescharacteristic
193C2×C4⋊Q8C22×C2911yescharacteristic
194#500—21no—
195#486—21no—
196#480C4×C2914yes—
197#474—22no—
198#436—21no—
199#435—22no—
200C8×D4—21no—
201#431C22×C2911yescharacteristic
202#423C22×C2911yescharacteristic
203C2×C4⋊C8C22×C2911yescharacteristic
204C2×C4⋊C8C22×C2911yescharacteristic
205C2×#101—21no—
206C2×#101—21no—
207#408—21no—
208C4×M16C22×C2911yescharacteristic
209#332—21no—
210#332—21no—
211#332—21no—
212#331—21no—
213C2×C29—21no—
214C2×C29—21no—
215C2×C29—82no—
216C2×C29#187911yescharacteristic
217C2×C29#190811yescharacteristic
218C2×C29#191511yescharacteristic
219C2×#41—21no—
220C22×Q8—21no—
221#131—42no—
222#131—42no—
223C2×M16—22no—
224C2×M16—21no—
225C2×M16D4×C2911yescharacteristic
226C2×M16D4×C2911yescharacteristic
227C22×C8—22no—
228C22×C8—21no—
229C22×C8—21no—
230C4⋊Q8—21no—
231C4⋊Q8—21no—
232C4⋊Q8—21no—
233C4⋊Q8—21no—
234C4⋊Q8D4×C2911yescharacteristic
235#127D4×C2911yescharacteristic
236#124—21no—
237#121—21no—
238#121C2×C4×C2912yes—
239C4×D4—21no—
240C4×D4D4×C2912yes—
241C2×C4⋊C4—21no—
242C2×C4⋊C4C2×C4×C2912yes—
243C2×C42C23×C2911yescharacteristic
244#107—24no—
245C4⋊C8—21no—
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8—21no—
249C4⋊C8—21no—
250C4⋊C8—21no—
251C4⋊C8D4×C2911yescharacteristic
252C4⋊C8D4×C2911yescharacteristic
253#102—24no—
254#101—42no—
255#101—42no—
256C22⋊C8—22no—
257C22⋊C8—22no—
258C22⋊C8C2×C4×C2912yes—
259#97—21no—
260C4×C8—21no—
261C4×C8—21no—
262C29#927111yescharacteristic, direct product factor, Sylow
263#41—41no—
264#41—41no—
265#41—41no—
266#41—41no—
267C2×Q8—21no—
268C2×Q8—41no—
269C2×Q8—41no—
270C2×Q8—41no—
271C2×Q8—41no—
272C2×Q8—41no—
273C2×Q8—41no—
274C2×D4—22no—
275C2×D4—21no—
276C2×D4—21no—
277C2×D4C22⋊C4×C2912yes—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4C22×C4×C2911yescharacteristic
281C22×C4C2×D4×C2911yescharacteristic
282C22×C4#41×C2911yescharacteristic
283M16—21no—
284M16—21no—
285M16—21no—
286M16—44no—
287M16—41no—
288M16—41no—
289M16D8×C2912yes—
290C2×C8—21no—
291C2×C8—22no—
292C2×C8—21no—
293C2×C8—21no—
294C2×C8—21no—
295C2×C8—44no—
296C2×C8—41no—
297C2×C8—41no—
298C2×C8—41no—
299C2×C8—41no—
300C2×C8—81no—
301C4⋊C4—21no—
302C4⋊C4—22no—
303C4⋊C4—22no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4C22⋊C4×C2912yes—
307C22⋊C4—22no—
308C22⋊C4—22no—
309C42C2×D4×C2911yescharacteristic
310C42C2×D4×C2911yescharacteristic
311C42C2×D4×C2911yescharacteristic
312C42#41×C2911yescharacteristic
313C23—22no—
314C23C4×D4×C2911yescharacteristic
315Q8—41no—
316Q8—41no—
317Q8—81no—
318Q8—81no—
319Q8—81no—
320Q8—81no—
321D4—42no—
322D4—42no—
323D4—42no—
324D4—41no—
325D4—41no—
326D4—41no—
327D4—41no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—22no—
331C2×C4—41no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4C2×C22⋊C4×C2911yescharacteristic
338C2×C4C4×D4×C2911yescharacteristic
339C2×C4C29×#12011yescharacteristic
340C2×C4C29×#12111yescharacteristic
341C2×C4C29×#12111yescharacteristic
342C2×C4C29×#12311yescharacteristic
343C2×C4C2×D8×C2911yescharacteristic
344C2×C4C29×#13511yescharacteristic
345C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
346C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
347C8—22no—
348C8—42no—
349C8—41no—
350C8—41no—
351C8—41no—
352C8—81no—
353C8—81no—
354C22—21no—
355C22—21no—
356C22—42no—
357C22—42no—
358C22—42no—
359C22C29×#38611yescharacteristic
360C22C4×D8×C2911yescharacteristic
361C22C29×#44211yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—42no—
366C4—82no—
367C4C29×#44711yescharacteristic
368C4C29×#44911yescharacteristic
369C4C29×#45911yescharacteristic
370C4C29×#46311yescharacteristic
371C4C29×#47111yescharacteristic
372C4C29×#47311yescharacteristic
373C2—21no—
374C2—21no—
375C2—82no—
376C2C29×#187911yescharacteristic
377C2C29×#190811yescharacteristic
378C2C29×#191511yescharacteristic
subgroupG/H
center, socleC22×C29#386
commutatorC22×C4C22×C4×C29
Frattini, cosocleC2×C42C23×C29
prime radicalC29×#532C22
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×#1966C2semidirect
5. C2×C29×#332C2semidirect
6. C29×#1301C2semidirect
7. C29×#1283C2semidirect
123. #9271C29direct (N × H)
167. #1966C2×C29semidirect
169. C2×#332C2×C29semidirect
170. #1301C2×C29semidirect
171. #1283C2×C29semidirect
262. C29#9271direct (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×#29352
C29×#19662
C29×#15472
C2×C29×#3322
C29×#13012
C29×#12832
#927129