Finite Group Databasebeta

← C29×#10193 #20305093

Subgroups — C29×#10193 #20305093

Order 7424.

592 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3246C211yesmaximal, characteristic, complemented
2C29×#3205C211yesmaximal, characteristic
3C29×#3138C211yesmaximal, characteristic, complemented
4C29×#1982C211yesmaximal, characteristic, complemented
5C29×#1980C211yesmaximal, characteristic, complemented
6C29×#1503C211yesmaximal, characteristic, complemented
7C29×#1283C211yesmaximal, characteristic, complemented
8C29×#533C2211yescharacteristic
9C29×#532C2211yescharacteristic
10C2×C29×#127C2211yescharacteristic
11C29×#493—21no—
12C29×#490—22no—
13C29×#486—21no—
14C29×#486—21no—
15C29×#486—21no—
16C29×#476—21no—
17C29×#475—21no—
18C29×#465—22no—
19C29×#461—21no—
20C29×#460—21no—
21C29×#459—22no—
22C29×#447—22no—
23C29×#431C2211yescharacteristic
24C2×C29×C4⋊C8C2211yescharacteristic
25C2×C29×#104—22no—
26C29×#418—22no—
27C2×C29×#102—22no—
28C4×M16×C29C2211yescharacteristic
29C4×C4⋊C4×C29C2211yescharacteristic
30C29×#328—22no—
31C2×#41×C29—21no—
32C22×D4×C29—21no—
33C22×D4×C29—21no—
34C22×D4×C29—21no—
35C2×SD16×C29—22no—
36C2×D8×C29—24no—
37C2×M16×C29D412yes—
38C22×C8×C29D412yes—
39C29×C4⋊Q8D411yescharacteristic
40C29×C4⋊Q8D411yescharacteristic
41C29×C4⋊Q8D411yescharacteristic
42C29×#127—21no—
43C29×#127—21no—
44C29×#127—21no—
45C29×#127D412yes—
46C29×#127D411yescharacteristic
47C29×#125—21no—
48C29×#124—21no—
49C29×C22⋊Q8—21no—
50C29×C22⋊Q8—21no—
51C29×#121—21no—
52C29×#121—21no—
53C4×Q8×C29—21no—
54C4×Q8×C29—21no—
55C4×D4×C29—21no—
56C4×D4×C29—21no—
57C29×#117—21no—
58C2×C4⋊C4×C29—21no—
59C2×C42×C29—21no—
60C2×C42×C29C2311yescharacteristic
61C29×#106—22no—
62C29×C4⋊C8—21no—
63C29×C4⋊C8—21no—
64C29×C4⋊C8—21no—
65C29×#104—44no—
66C29×#103—22no—
67C29×#102—24no—
68C29×#102—22no—
69C29×#102—24no—
70C29×#102—24no—
71C29×#102—44no—
72C29×C22⋊C8D412yes—
73C29×#97—21no—
74C4×C8×C29—21no—
75C4×C8×C29—21no—
76C29×#95—21no—
77C24×C29—41no—
78#41×C29—42no—
79#41×C29—42no—
80C2×Q8×C29—21no—
81C2×Q8×C29—21no—
82C2×Q8×C29—21no—
83C2×D4×C29—21no—
84C2×D4×C29—21no—
85C2×D4×C29—22no—
86C2×D4×C29—22no—
87C2×D4×C29—21no—
88C2×D4×C29—22no—
89C2×D4×C29—42no—
90C2×D4×C29—42no—
91C2×D4×C29—41no—
92C2×D4×C29—41no—
93C2×D4×C29—41no—
94C2×D4×C29—41no—
95C2×D4×C29—42no—
96C2×D4×C29—42no—
97C2×D4×C29—82no—
98C22×C4×C29—41no—
99C22×C4×C29—41no—
100C22×C4×C29C2×D411yescharacteristic
101C22×C4×C29C2×D411yescharacteristic
102C22×C4×C29C2×D411yescharacteristic
103SD16×C29—82no—
104D8×C29—84no—
105M16×C29—22no—
106M16×C29—22no—
107C2×C8×C29—22no—
108C2×C8×C29—22no—
109C2×C8×C29—22no—
110C2×C8×C29—42no—
111C4⋊C4×C29—22no—
112C4⋊C4×C29—21no—
113C4⋊C4×C29—21no—
114C4⋊C4×C29—21no—
115C4⋊C4×C29—21no—
116C4⋊C4×C29—21no—
117C4⋊C4×C29—21no—
118C4⋊C4×C29—41no—
119C4⋊C4×C29—41no—
120C4⋊C4×C29—41no—
121C22⋊C4×C29—41no—
122C22⋊C4×C29—41no—
123C22⋊C4×C29—41no—
124C42×C29—41no—
125C42×C29—42no—
126C42×C29C2×D411yescharacteristic
127C42×C29C2×D411yescharacteristic
128C42×C29C2×D411yescharacteristic
129C42×C29#4111yescharacteristic
130#10193C2911yesmaximal, characteristic, direct product factor, Sylow
131C23×C29—41no—
132C23×C29—42no—
133C23×C29—82no—
134C23×C29—82no—
135C23×C29—81no—
136C23×C29—81no—
137C23×C29#12711yescharacteristic
138Q8×C29—41no—
139Q8×C29—41no—
140Q8×C29—42no—
141Q8×C29—81no—
142D4×C29—42no—
143D4×C29—44no—
144D4×C29—44no—
145D4×C29—44no—
146D4×C29—41no—
147D4×C29—41no—
148D4×C29—42no—
149D4×C29—82no—
150D4×C29—81no—
151D4×C29—81no—
152D4×C29—81no—
153D4×C29—81no—
154D4×C29—82no—
155C2×C4×C29—21no—
156C2×C4×C29—21no—
157C2×C4×C29—41no—
158C2×C4×C29—42no—
159C2×C4×C29—41no—
160C2×C4×C29—41no—
161C2×C4×C29—41no—
162C2×C4×C29—81no—
163C2×C4×C29—81no—
164C2×C4×C29—82no—
165C2×C4×C29#12011yescharacteristic
166C2×C4×C29#12011yescharacteristic
167C2×C4×C29#12011yescharacteristic
168C2×C4×C29#12111yescharacteristic
169C2×C4×C29#12111yescharacteristic
170C2×C4×C29#12111yescharacteristic
171C2×C4×C29#13512yes—
172C2×C4×C29AGL(1,ℤ/8)12yes—
173C8×C29—42no—
174C8×C29—42no—
175C8×C29—42no—
176#3246C2×C2911yescharacteristic, complemented
177#3205C2×C2911yescharacteristic
178#3138C2×C2911yescharacteristic, complemented
179#1982C2×C2911yescharacteristic, complemented
180#1980C2×C2911yescharacteristic, complemented
181#1503C2×C2911yescharacteristic, complemented
182#1283C2×C2911yescharacteristic, complemented
183C22×C29—21no—
184C22×C29—21no—
185C22×C29—82no—
186C22×C29—81no—
187C22×C29—82no—
188C22×C29—81no—
189C22×C29—81no—
190C22×C29—82no—
191C22×C29—162no—
192C22×C29—162no—
193C22×C29#39211yescharacteristic
194C22×C29#49511yescharacteristic
195C22×C29#49611yescharacteristic
196C4×C29—21no—
197C4×C29—21no—
198C4×C29—21no—
199C4×C29—82no—
200C4×C29—81no—
201C4×C29—81no—
202C4×C29—81no—
203C4×C29#44912yes—
204C4×C29#45311yescharacteristic
205C4×C29#45411yescharacteristic
206C4×C29#46312yes—
207#533C22×C2911yescharacteristic
208#532C22×C2911yescharacteristic
209C2×#127C22×C2911yescharacteristic
210#493—21no—
211#490—22no—
212#486—21no—
213#486—21no—
214#486—21no—
215#476—21no—
216#475—21no—
217#465—22no—
218#461—21no—
219#460—21no—
220#459—22no—
221#447—22no—
222#431C22×C2911yescharacteristic
223C2×C4⋊C8C22×C2911yescharacteristic
224C2×#104—22no—
225#418—22no—
226C2×#102—22no—
227C4×M16C22×C2911yescharacteristic
228C4×C4⋊C4C22×C2911yescharacteristic
229#328—22no—
230C2×C29—21no—
231C2×C29—21no—
232C2×C29—161no—
233C2×C29—162no—
234C2×C29#200611yescharacteristic
235C2×C29#200811yescharacteristic
236C2×C29#201211yescharacteristic
237C2×#41—21no—
238C22×D4—21no—
239C22×D4—21no—
240C22×D4—21no—
241C2×SD16—22no—
242C2×D8—24no—
243C2×M16D4×C2912yes—
244C22×C8D4×C2912yes—
245C4⋊Q8D4×C2911yescharacteristic
246C4⋊Q8D4×C2911yescharacteristic
247C4⋊Q8D4×C2911yescharacteristic
248#127—21no—
249#127—21no—
250#127—21no—
251#127D4×C2912yes—
252#127D4×C2911yescharacteristic
253#125—21no—
254#124—21no—
255C22⋊Q8—21no—
256C22⋊Q8—21no—
257#121—21no—
258#121—21no—
259C4×Q8—21no—
260C4×Q8—21no—
261C4×D4—21no—
262C4×D4—21no—
263#117—21no—
264C2×C4⋊C4—21no—
265C2×C42—21no—
266C2×C42C23×C2911yescharacteristic
267#106—22no—
268C4⋊C8—21no—
269C4⋊C8—21no—
270C4⋊C8—21no—
271#104—44no—
272#103—22no—
273#102—24no—
274#102—24no—
275#102—24no—
276#102—22no—
277#102—44no—
278C22⋊C8D4×C2912yes—
279#97—21no—
280C4×C8—21no—
281C4×C8—21no—
282#95—21no—
283C29#1019311yescharacteristic, direct product factor, Sylow
284C24—41no—
285#41—42no—
286#41—42no—
287C2×Q8—21no—
288C2×Q8—21no—
289C2×Q8—21no—
290C2×D4—22no—
291C2×D4—21no—
292C2×D4—22no—
293C2×D4—21no—
294C2×D4—21no—
295C2×D4—22no—
296C2×D4—42no—
297C2×D4—42no—
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—41no—
301C2×D4—41no—
302C2×D4—42no—
303C2×D4—42no—
304C2×D4—82no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4C2×D4×C2911yescharacteristic
308C22×C4C2×D4×C2911yescharacteristic
309C22×C4C2×D4×C2911yescharacteristic
310SD16—82no—
311D8—84no—
312M16—22no—
313M16—22no—
314C2×C8—22no—
315C2×C8—22no—
316C2×C8—22no—
317C2×C8—42no—
318C4⋊C4—22no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C22⋊C4—41no—
329C22⋊C4—41no—
330C22⋊C4—41no—
331C42—41no—
332C42—42no—
333C42C2×D4×C2911yescharacteristic
334C42C2×D4×C2911yescharacteristic
335C42C2×D4×C2911yescharacteristic
336C42#41×C2911yescharacteristic
337C23—41no—
338C23—42no—
339C23—82no—
340C23—82no—
341C23—81no—
342C23—81no—
343C23C29×#12711yescharacteristic
344Q8—41no—
345Q8—41no—
346Q8—42no—
347Q8—81no—
348D4—42no—
349D4—44no—
350D4—44no—
351D4—44no—
352D4—41no—
353D4—41no—
354D4—42no—
355D4—82no—
356D4—81no—
357D4—81no—
358D4—81no—
359D4—81no—
360D4—82no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—41no—
364C2×C4—42no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—81no—
369C2×C4—81no—
370C2×C4—82no—
371C2×C4C29×#12011yescharacteristic
372C2×C4C29×#12011yescharacteristic
373C2×C4C29×#12011yescharacteristic
374C2×C4C29×#12111yescharacteristic
375C2×C4C29×#12111yescharacteristic
376C2×C4C29×#12111yescharacteristic
377C2×C4C29×#13512yes—
378C2×C4C29×AGL(1,ℤ/8)12yes—
379C8—42no—
380C8—42no—
381C8—42no—
382C22—21no—
383C22—21no—
384C22—82no—
385C22—81no—
386C22—82no—
387C22—81no—
388C22—81no—
389C22—82no—
390C22—162no—
391C22—162no—
392C22C29×#39211yescharacteristic
393C22C29×#49511yescharacteristic
394C22C29×#49611yescharacteristic
395C4—21no—
396C4—21no—
397C4—21no—
398C4—82no—
399C4—81no—
400C4—81no—
401C4—81no—
402C4C29×#44912yes—
403C4C29×#45311yescharacteristic
404C4C29×#45411yescharacteristic
405C4C29×#46312yes—
406C2—21no—
407C2—21no—
408C2—162no—
409C2—161no—
410C2C29×#200611yescharacteristic
411C2C29×#200811yescharacteristic
412C2C29×#201211yescharacteristic
subgroupG/H
center, socleC22×C29#392
commutator, Frattini, cosocleC2×C42C23×C29
prime radicalC29×#3205C2
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
1. C29×#3246C2semidirect
3. C29×#3138C2semidirect
4. C29×#1982C2semidirect
5. C29×#1980C2semidirect
6. C29×#1503C2semidirect
7. C29×#1283C2semidirect
130. #10193C29direct (N × H)
176. #3246C2×C29semidirect
178. #3138C2×C29semidirect
179. #1982C2×C29semidirect
180. #1980C2×C29semidirect
181. #1503C2×C29semidirect
182. #1283C2×C29semidirect
283. C29#10193direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#32462
C29×#32052
C29×#31382
C29×#19822
C29×#19802
C29×#15032
C29×#12832
#1019329