Finite Group Databasebeta

← C29×#9181 #20304081

Subgroups — C29×#9181 #20304081

Order 7424.

548 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3036C211yesmaximal, characteristic
2C29×#2357C211yesmaximal, characteristic, complemented
3C29×#1517C211yesmaximal, characteristic, complemented
4C29×#1502C211yesmaximal, characteristic, complemented
5C29×#1478C211yesmaximal, characteristic, complemented
6C29×#1303C211yesmaximal, characteristic, complemented
7C29×#1286C211yesmaximal, characteristic, complemented
8C2×C29×AGL(1,ℤ/8)—21no—
9C29×#532C2211yescharacteristic
10C2×C4×D4×C29C2211yescharacteristic
11C29×#463—22no—
12C29×#461C412yescomplemented
13C29×#459C412yescomplemented
14C29×#431C2211yescharacteristic
15C29×#431C2211yescharacteristic
16C29×#423C2211yescharacteristic
17C29×#417—21no—
18C29×#390—21no—
19C29×#388—22no—
20C29×#382C2211yescharacteristic
21C29×#381—21no—
22C4×C4⋊C4×C29—21no—
23C4×C4⋊C4×C29C2211yescharacteristic
24C4×C22⋊C4×C29—21no—
25C29×#327—21no—
26C29×#327—21no—
27C29×#327—22no—
28C29×D4⋊C8—22no—
29C2×#41×C29—21no—
30C22×D4×C29D411yescharacteristic
31C23×C4×C29—21no—
32C29×AGL(1,ℤ/8)—42no—
33C29×AGL(1,ℤ/8)—42no—
34C2×SD16×C29—22no—
35C2×D8×C29—22no—
36C2×M16×C29—21no—
37C29×C4⋊Q8C2×C411yescharacteristic
38C29×#127C2×C411yescharacteristic
39C29×#124—21no—
40C29×#121—21no—
41C29×#121—21no—
42C4×D4×C29—21no—
43C4×D4×C29—21no—
44C4×D4×C29—21no—
45C4×D4×C29—21no—
46C4×D4×C29C2×C412yes—
47C4×D4×C29D412yes—
48C2×C4⋊C4×C29—21no—
49C2×C4⋊C4×C29—21no—
50C2×C4⋊C4×C29D411yescharacteristic
51C2×C22⋊C4×C29—21no—
52C2×C22⋊C4×C29—22no—
53C2×C22⋊C4×C29—22no—
54C2×C42×C29—21no—
55C2×C42×C29—22no—
56C2×C42×C29C2311yescharacteristic
57C29×C4⋊C8—21no—
58C29×C4⋊C8—21no—
59C29×C4⋊C8—21no—
60C29×C4⋊C8C2×C412yes—
61C29×#103—22no—
62C29×#102—22no—
63C29×C22⋊C8—21no—
64C29×C22⋊C8—21no—
65C4×C8×C29—21no—
66C4×C8×C29—21no—
67C29×#95—22no—
68C29×#95—21no—
69C29×#95D411yescharacteristic
70C29×#95D411yescharacteristic
71C29×#95D412yes—
72C24×C29—21no—
73#41×C29—41no—
74#41×C29—41no—
75#41×C29—41no—
76#41×C29—41no—
77C2×Q8×C29—21no—
78C2×D4×C29—21no—
79C2×D4×C29—21no—
80C2×D4×C29—21no—
81C2×D4×C29—21no—
82C2×D4×C29—21no—
83C2×D4×C29—21no—
84C2×D4×C29—21no—
85C2×D4×C29—21no—
86C2×D4×C29—41no—
87C2×D4×C29C22⋊C412yes—
88C22×C4×C29—21no—
89C22×C4×C29—21no—
90C22×C4×C29—22no—
91C22×C4×C29—22no—
92C22×C4×C29—22no—
93C22×C4×C29—21no—
94C22×C4×C29—41no—
95C22×C4×C29—82no—
96C22×C4×C29C2×D411yescharacteristic
97C22×C4×C29C2×D411yescharacteristic
98C22×C4×C29C2×D411yescharacteristic
99SD16×C29—44no—
100D8×C29—44no—
101M16×C29—41no—
102M16×C29—41no—
103C2×C8×C29—22no—
104C2×C8×C29—41no—
105C2×C8×C29—41no—
106C4⋊C4×C29—21no—
107C4⋊C4×C29—21no—
108C4⋊C4×C29—21no—
109C4⋊C4×C29—42no—
110C4⋊C4×C29—41no—
111C4⋊C4×C29—41no—
112C4⋊C4×C29C22⋊C412yes—
113C22⋊C4×C29—22no—
114C22⋊C4×C29—22no—
115C22⋊C4×C29—44no—
116C22⋊C4×C29—41no—
117C22⋊C4×C29—41no—
118C22⋊C4×C29—82no—
119C42×C29—41no—
120C42×C29—41no—
121C42×C29—82no—
122C42×C29C22×C411yescharacteristic
123C42×C29C2×D411yescharacteristic
124C42×C29#4111yescharacteristic
125C42×C29#4111yescharacteristic
126#9181C2911yesmaximal, characteristic, direct product factor, Sylow
127C23×C29—22no—
128C23×C29—42no—
129C23×C29—42no—
130C23×C29—41no—
131C23×C29—41no—
132C23×C29—41no—
133C23×C29#12011yescharacteristic
134Q8×C29—41no—
135Q8×C29—41no—
136D4×C29—22no—
137D4×C29—22no—
138D4×C29—41no—
139D4×C29—41no—
140D4×C29—41no—
141D4×C29—41no—
142D4×C29—81no—
143D4×C29—81no—
144D4×C29—81no—
145D4×C29—81no—
146C2×C4×C29—22no—
147C2×C4×C29—22no—
148C2×C4×C29—41no—
149C2×C4×C29—41no—
150C2×C4×C29—41no—
151C2×C4×C29—42no—
152C2×C4×C29—41no—
153C2×C4×C29—42no—
154C2×C4×C29—42no—
155C2×C4×C29—41no—
156C2×C4×C29—41no—
157C2×C4×C29—41no—
158C2×C4×C29—41no—
159C2×C4×C29—42no—
160C2×C4×C29—82no—
161C2×C4×C29—82no—
162C2×C4×C29—81no—
163C2×C4×C29—81no—
164C2×C4×C29C2×C22⋊C411yescharacteristic
165C2×C4×C29C4×D411yescharacteristic
166C2×C4×C29C4×D411yescharacteristic
167C2×C4×C29#12111yescharacteristic
168C2×C4×C29#12111yescharacteristic
169C2×C4×C29#12311yescharacteristic
170C2×C4×C29#13511yescharacteristic
171C2×C4×C29#13511yescharacteristic
172C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
173C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
174C8×C29—42no—
175C8×C29—81no—
176C8×C29—81no—
177#3036C2×C2911yescharacteristic
178#2357C2×C2911yescharacteristic, complemented
179#1517C2×C2911yescharacteristic, complemented
180#1502C2×C2911yescharacteristic, complemented
181#1478C2×C2911yescharacteristic, complemented
182#1303C2×C2911yescharacteristic, complemented
183#1286C2×C2911yescharacteristic, complemented
184C22×C29—21no—
185C22×C29—21no—
186C22×C29—42no—
187C22×C29—42no—
188C22×C29—42no—
189C22×C29—82no—
190C22×C29—82no—
191C22×C29—81no—
192C22×C29—81no—
193C22×C29—81no—
194C22×C29#38611yescharacteristic
195C22×C29#44911yescharacteristic
196C22×C29#44911yescharacteristic
197C4×C29—21no—
198C4×C29—21no—
199C4×C29—21no—
200C4×C29—21no—
201C4×C29—42no—
202C4×C29—42no—
203C4×C29—81no—
204C4×C29—82no—
205C4×C29—81no—
206C4×C29#41611yescharacteristic
207C4×C29#41811yescharacteristic
208C4×C29#48211yescharacteristic
209C4×C29#48211yescharacteristic
210C2×AGL(1,ℤ/8)—21no—
211#532C22×C2911yescharacteristic
212C2×C4×D4C22×C2911yescharacteristic
213#463—22no—
214#461C4×C2912yescomplemented
215#459C4×C2912yescomplemented
216#431C22×C2911yescharacteristic
217#431C22×C2911yescharacteristic
218#423C22×C2911yescharacteristic
219#417—21no—
220#390—21no—
221#388—22no—
222#382C22×C2911yescharacteristic
223#381—21no—
224C4×C4⋊C4—21no—
225C4×C4⋊C4C22×C2911yescharacteristic
226C4×C22⋊C4—21no—
227#327—21no—
228#327—21no—
229#327—22no—
230D4⋊C8—22no—
231C2×C29—21no—
232C2×C29—21no—
233C2×C29—82no—
234C2×C29—161no—
235C2×C29#187511yescharacteristic
236C2×C29#190411yescharacteristic
237C2×C29#190611yescharacteristic
238C2×#41—21no—
239C22×D4D4×C2911yescharacteristic
240C23×C4—21no—
241AGL(1,ℤ/8)—42no—
242AGL(1,ℤ/8)—42no—
243C2×SD16—22no—
244C2×D8—22no—
245C2×M16—21no—
246C4⋊Q8C2×C4×C2911yescharacteristic
247#127C2×C4×C2911yescharacteristic
248#124—21no—
249#121—21no—
250#121—21no—
251C4×D4—21no—
252C4×D4—21no—
253C4×D4—21no—
254C4×D4—21no—
255C4×D4C2×C4×C2912yes—
256C4×D4D4×C2912yes—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4D4×C2911yescharacteristic
260C2×C22⋊C4—21no—
261C2×C22⋊C4—22no—
262C2×C22⋊C4—22no—
263C2×C42—21no—
264C2×C42—22no—
265C2×C42C23×C2911yescharacteristic
266C4⋊C8—21no—
267C4⋊C8—21no—
268C4⋊C8—21no—
269C4⋊C8C2×C4×C2912yes—
270#103—22no—
271#102—22no—
272C22⋊C8—21no—
273C22⋊C8—21no—
274C4×C8—21no—
275C4×C8—21no—
276#95—22no—
277#95—21no—
278#95D4×C2911yescharacteristic
279#95D4×C2911yescharacteristic
280#95D4×C2912yes—
281C29#918111yescharacteristic, direct product factor, Sylow
282C24—21no—
283#41—41no—
284#41—41no—
285#41—41no—
286#41—41no—
287C2×Q8—21no—
288C2×D4—21no—
289C2×D4—21no—
290C2×D4—21no—
291C2×D4—21no—
292C2×D4—21no—
293C2×D4—21no—
294C2×D4—21no—
295C2×D4—21no—
296C2×D4—41no—
297C2×D4C22⋊C4×C2912yes—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—22no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—21no—
304C22×C4—41no—
305C22×C4—82no—
306C22×C4C2×D4×C2911yescharacteristic
307C22×C4C2×D4×C2911yescharacteristic
308C22×C4C2×D4×C2911yescharacteristic
309SD16—44no—
310D8—44no—
311M16—41no—
312M16—41no—
313C2×C8—22no—
314C2×C8—41no—
315C2×C8—41no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—42no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4C22⋊C4×C2912yes—
323C22⋊C4—22no—
324C22⋊C4—22no—
325C22⋊C4—44no—
326C22⋊C4—41no—
327C22⋊C4—41no—
328C22⋊C4—82no—
329C42—41no—
330C42—41no—
331C42—82no—
332C42C22×C4×C2911yescharacteristic
333C42C2×D4×C2911yescharacteristic
334C42#41×C2911yescharacteristic
335C42#41×C2911yescharacteristic
336C23—22no—
337C23—42no—
338C23—42no—
339C23—41no—
340C23—41no—
341C23—41no—
342C23C29×#12011yescharacteristic
343Q8—41no—
344Q8—41no—
345D4—22no—
346D4—22no—
347D4—41no—
348D4—41no—
349D4—41no—
350D4—41no—
351D4—81no—
352D4—81no—
353D4—81no—
354D4—81no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—42no—
361C2×C4—41no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—42no—
368C2×C4—41no—
369C2×C4—82no—
370C2×C4—82no—
371C2×C4—81no—
372C2×C4—81no—
373C2×C4C2×C22⋊C4×C2911yescharacteristic
374C2×C4C4×D4×C2911yescharacteristic
375C2×C4C4×D4×C2911yescharacteristic
376C2×C4C29×#12111yescharacteristic
377C2×C4C29×#12111yescharacteristic
378C2×C4C29×#12311yescharacteristic
379C2×C4C29×#13511yescharacteristic
380C2×C4C29×#13511yescharacteristic
381C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
382C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
383C8—42no—
384C8—81no—
385C8—81no—
386C22—21no—
387C22—21no—
388C22—42no—
389C22—42no—
390C22—42no—
391C22—82no—
392C22—82no—
393C22—81no—
394C22—81no—
395C22—81no—
396C22C29×#38611yescharacteristic
397C22C29×#44911yescharacteristic
398C22C29×#44911yescharacteristic
399C4—21no—
400C4—21no—
401C4—21no—
402C4—21no—
403C4—42no—
404C4—42no—
405C4—81no—
406C4—82no—
407C4—81no—
408C4C29×#41611yescharacteristic
409C4C29×#41811yescharacteristic
410C4C29×#48211yescharacteristic
411C4C29×#48211yescharacteristic
412C2—21no—
413C2—21no—
414C2—82no—
415C2—161no—
416C2C29×#187511yescharacteristic
417C2C29×#190411yescharacteristic
418C2C29×#190611yescharacteristic
subgroupG/H
center, socleC22×C29#386
commutatorC42C22×C4×C29
Frattini, cosocleC2×C42C23×C29
prime radicalC29×#3036C2
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
2. C29×#2357C2semidirect
3. C29×#1517C2semidirect
4. C29×#1502C2semidirect
5. C29×#1478C2semidirect
6. C29×#1303C2semidirect
7. C29×#1286C2semidirect
12. C29×#461C4semidirect
13. C29×#459C4semidirect
126. #9181C29direct (N × H)
178. #2357C2×C29semidirect
179. #1517C2×C29semidirect
180. #1502C2×C29semidirect
181. #1478C2×C29semidirect
182. #1303C2×C29semidirect
183. #1286C2×C29semidirect
214. #461C4×C29semidirect
215. #459C4×C29semidirect
281. C29#9181direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#30362
C29×#23572
C29×#15172
C29×#15022
C29×#14782
C29×#13032
C29×#12862
#918129