Finite Group Databasebeta

← C29×#10458 #20305358

Subgroups — C29×#10458 #20305358

Order 7424.

428 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3037C211yesmaximal, characteristic
2C29×#1801C211yesmaximal, characteristic, complemented
3C29×#1567C211yesmaximal, characteristic, complemented
4C29×#1547C211yesmaximal, characteristic
5C29×#1492C211yesmaximal, characteristic
6C2×C29×Q8⋊C8C211yesmaximal, characteristic, complemented
7C29×#1292C211yesmaximal, characteristic, complemented
8C2×C29×#137—21no—
9C29×#532C2211yescharacteristic
10C2×C4×Q8×C29C2211yescharacteristic
11C29×#464—22no—
12C29×#462—21no—
13C29×#460—21no—
14C29×#423C2211yescharacteristic
15C29×#423C2211yescharacteristic
16C29×#423C2211yescharacteristic
17C2×C29×C4⋊C8C2211yescharacteristic
18C29×#417—21no—
19C2×C29×#101—21no—
20C2×C4×C8×C29C2211yescharacteristic
21C29×#343—21no—
22C29×#335—22no—
23C29×#332—21no—
24C29×#331—21no—
25C29×Q8⋊C8—21no—
26C29×Q8⋊C8—21no—
27C29×D4⋊C8—21no—
28C29×D4⋊C8—21no—
29C2×#41×C29—21no—
30C22×Q8×C29D411yescharacteristic
31C29×#137—42no—
32C29×#137—42no—
33C2×Q16×C29—22no—
34C2×SD16×C29—22no—
35C2×M16×C29—21no—
36C2×M16×C29—21no—
37C2×M16×C29—21no—
38C22×C8×C29—21no—
39C22×C8×C29—21no—
40C29×C4⋊Q8D411yescharacteristic
41C29×#127D411yescharacteristic
42C29×#124—21no—
43C29×#121—21no—
44C29×#121—21no—
45C4×Q8×C29—21no—
46C4×Q8×C29—21no—
47C4×Q8×C29—21no—
48C4×Q8×C29—21no—
49C4×D4×C29—21no—
50C4×D4×C29—21no—
51C2×C4⋊C4×C29—21no—
52C2×C4⋊C4×C29D411yescharacteristic
53C2×C42×C29—21no—
54C2×C42×C29C2311yescharacteristic
55C29×C4⋊C8—21no—
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⋊C8D412yes—
63C29×#103—22no—
64C29×#102—22no—
65C29×#101—42no—
66C4×C8×C29—21no—
67C4×C8×C29D411yescharacteristic
68C4×C8×C29D411yescharacteristic
69#41×C29—41no—
70#41×C29—41no—
71#41×C29—41no—
72#41×C29—41no—
73C2×Q8×C29—21no—
74C2×Q8×C29—21no—
75C2×Q8×C29—21no—
76C2×Q8×C29—21no—
77C2×Q8×C29—21no—
78C2×Q8×C29—21no—
79C2×Q8×C29D812yes—
80C2×D4×C29—21no—
81C2×D4×C29—21no—
82C2×D4×C29—21no—
83C2×D4×C29—41no—
84C22×C4×C29—21no—
85C22×C4×C29—21no—
86C22×C4×C29—41no—
87C22×C4×C29C2×D411yescharacteristic
88C22×C4×C29#4111yescharacteristic
89C22×C4×C29#4111yescharacteristic
90Q16×C29—44no—
91SD16×C29—44no—
92M16×C29—41no—
93M16×C29—41no—
94M16×C29—41no—
95M16×C29—41no—
96M16×C29—41no—
97M16×C29—41no—
98C2×C8×C29—21no—
99C2×C8×C29—22no—
100C2×C8×C29—21no—
101C2×C8×C29—42no—
102C2×C8×C29—41no—
103C2×C8×C29—41no—
104C2×C8×C29—41no—
105C2×C8×C29—81no—
106C4⋊C4×C29—21no—
107C4⋊C4×C29—21no—
108C4⋊C4×C29—21no—
109C4⋊C4×C29—21no—
110C4⋊C4×C29—41no—
111C4⋊C4×C29—41no—
112C22⋊C4×C29—41no—
113C22⋊C4×C29—41no—
114C42×C29—41no—
115C42×C29—41no—
116C42×C29C2×D411yescharacteristic
117C42×C29C2×D411yescharacteristic
118C42×C29C2×D411yescharacteristic
119C42×C29#4111yescharacteristic
120#10458C2911yesmaximal, characteristic, direct product factor, Sylow
121C23×C29—41no—
122C23×C29#12311yescharacteristic
123Q8×C29—22no—
124Q8×C29—22no—
125Q8×C29—41no—
126Q8×C29—41no—
127Q8×C29—41no—
128Q8×C29—41no—
129D4×C29—41no—
130D4×C29—41no—
131D4×C29—41no—
132D4×C29—41no—
133D4×C29—81no—
134D4×C29—81no—
135D4×C29—81no—
136C2×C4×C29—21no—
137C2×C4×C29—21no—
138C2×C4×C29—22no—
139C2×C4×C29—41no—
140C2×C4×C29—41no—
141C2×C4×C29—41no—
142C2×C4×C29—41no—
143C2×C4×C29—41no—
144C2×C4×C29—81no—
145C2×C4×C29—81no—
146C2×C4×C29—81no—
147C2×C4×C29#12011yescharacteristic
148C2×C4×C29#12111yescharacteristic
149C2×C4×C29#12111yescharacteristic
150C2×C4×C29#12111yescharacteristic
151C2×C4×C29#12311yescharacteristic
152C2×C4×C29#12411yescharacteristic
153C2×C4×C29C2×D811yescharacteristic
154C2×C4×C29#13511yescharacteristic
155C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
156C2×C4×C29#13711yescharacteristic
157C8×C29—22no—
158C8×C29—41no—
159C8×C29—42no—
160C8×C29—81no—
161C8×C29—81no—
162C8×C29—81no—
163#3037C2×C2911yescharacteristic
164#1801C2×C2911yescharacteristic, complemented
165#1567C2×C2911yescharacteristic, complemented
166#1547C2×C2911yescharacteristic
167#1492C2×C2911yescharacteristic
168C2×Q8⋊C8C2×C2911yescharacteristic, complemented
169#1292C2×C2911yescharacteristic, complemented
170C22×C29—21no—
171C22×C29—21no—
172C22×C29—81no—
173C22×C29—81no—
174C22×C29—81no—
175C22×C29#39411yescharacteristic
176C22×C29#48011yescharacteristic
177C22×C29#48211yescharacteristic
178C4×C29—21no—
179C4×C29—21no—
180C4×C29—21no—
181C4×C29—42no—
182C4×C29—81no—
183C4×C29—81no—
184C4×C29#44711yescharacteristic
185C4×C29#45211yescharacteristic
186C4×C29#46611yescharacteristic
187C4×C29#46811yescharacteristic
188C4×C29#47111yescharacteristic
189C4×C29#47311yescharacteristic
190C2×#137—21no—
191#532C22×C2911yescharacteristic
192C2×C4×Q8C22×C2911yescharacteristic
193#464—22no—
194#462—21no—
195#460—21no—
196#423C22×C2911yescharacteristic
197#423C22×C2911yescharacteristic
198#423C22×C2911yescharacteristic
199C2×C4⋊C8C22×C2911yescharacteristic
200#417—21no—
201C2×#101—21no—
202C2×C4×C8C22×C2911yescharacteristic
203#343—21no—
204#335—22no—
205#332—21no—
206#331—21no—
207Q8⋊C8—21no—
208Q8⋊C8—21no—
209D4⋊C8—21no—
210D4⋊C8—21no—
211C2×C29—21no—
212C2×C29—21no—
213C2×C29—161no—
214C2×C29#203311yescharacteristic
215C2×C29#205011yescharacteristic
216C2×C29#205211yescharacteristic
217C2×#41—21no—
218C22×Q8D4×C2911yescharacteristic
219#137—42no—
220#137—42no—
221C2×Q16—22no—
222C2×SD16—22no—
223C2×M16—21no—
224C2×M16—21no—
225C2×M16—21no—
226C22×C8—21no—
227C22×C8—21no—
228C4⋊Q8D4×C2911yescharacteristic
229#127D4×C2911yescharacteristic
230#124—21no—
231#121—21no—
232#121—21no—
233C4×Q8—21no—
234C4×Q8—21no—
235C4×Q8—21no—
236C4×Q8—21no—
237C4×D4—21no—
238C4×D4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4D4×C2911yescharacteristic
241C2×C42—21no—
242C2×C42C23×C2911yescharacteristic
243C4⋊C8—21no—
244C4⋊C8—21no—
245C4⋊C8—21no—
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8—21no—
249C4⋊C8—21no—
250C4⋊C8D4×C2912yes—
251#103—22no—
252#102—22no—
253#101—42no—
254C4×C8—21no—
255C4×C8D4×C2911yescharacteristic
256C4×C8D4×C2911yescharacteristic
257C29#1045811yescharacteristic, direct product factor, Sylow
258#41—41no—
259#41—41no—
260#41—41no—
261#41—41no—
262C2×Q8—21no—
263C2×Q8—21no—
264C2×Q8—21no—
265C2×Q8—21no—
266C2×Q8—21no—
267C2×Q8—21no—
268C2×Q8D8×C2912yes—
269C2×D4—21no—
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—41no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—41no—
276C22×C4C2×D4×C2911yescharacteristic
277C22×C4#41×C2911yescharacteristic
278C22×C4#41×C2911yescharacteristic
279Q16—44no—
280SD16—44no—
281M16—41no—
282M16—41no—
283M16—41no—
284M16—41no—
285M16—41no—
286M16—41no—
287C2×C8—21no—
288C2×C8—22no—
289C2×C8—21no—
290C2×C8—42no—
291C2×C8—41no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8—81no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C22⋊C4—41no—
302C22⋊C4—41no—
303C42—41no—
304C42—41no—
305C42C2×D4×C2911yescharacteristic
306C42C2×D4×C2911yescharacteristic
307C42C2×D4×C2911yescharacteristic
308C42#41×C2911yescharacteristic
309C23—41no—
310C23C29×#12311yescharacteristic
311Q8—22no—
312Q8—22no—
313Q8—41no—
314Q8—41no—
315Q8—41no—
316Q8—41no—
317D4—41no—
318D4—41no—
319D4—41no—
320D4—41no—
321D4—81no—
322D4—81no—
323D4—81no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—22no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4C29×#12011yescharacteristic
336C2×C4C29×#12111yescharacteristic
337C2×C4C29×#12111yescharacteristic
338C2×C4C29×#12111yescharacteristic
339C2×C4C29×#12311yescharacteristic
340C2×C4C29×#12411yescharacteristic
341C2×C4C2×D8×C2911yescharacteristic
342C2×C4C29×#13511yescharacteristic
343C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
344C2×C4C29×#13711yescharacteristic
345C8—22no—
346C8—41no—
347C8—42no—
348C8—81no—
349C8—81no—
350C8—81no—
351C22—21no—
352C22—21no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22C29×#39411yescharacteristic
357C22C29×#48011yescharacteristic
358C22C29×#48211yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—42no—
363C4—81no—
364C4—81no—
365C4C29×#44711yescharacteristic
366C4C29×#45211yescharacteristic
367C4C29×#46611yescharacteristic
368C4C29×#46811yescharacteristic
369C4C29×#47111yescharacteristic
370C4C29×#47311yescharacteristic
371C2—21no—
372C2—21no—
373C2—161no—
374C2C29×#203311yescharacteristic
375C2C29×#205011yescharacteristic
376C2C29×#205211yescharacteristic
subgroupG/H
center, socleC22×C29#394
commutator, Frattini, cosocleC2×C42C23×C29
prime radicalC29×#532C22
LCSG ▷ C2×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×#1801C2semidirect
3. C29×#1567C2semidirect
6. C2×C29×Q8⋊C8C2semidirect
7. C29×#1292C2semidirect
120. #10458C29direct (N × H)
164. #1801C2×C29semidirect
165. #1567C2×C29semidirect
168. C2×Q8⋊C8C2×C29semidirect
169. #1292C2×C29semidirect
257. C29#10458direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#30372
C29×#18012
C29×#15672
C29×#15472
C29×#14922
C2×C29×Q8⋊C82
C29×#12922
#1045829