Finite Group Databasebeta

← C29×#9349 #20304249

Subgroups — C29×#9349 #20304249

Order 7424.

474 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3040C211yesmaximal, characteristic
2C29×#2970C211yesmaximal, characteristic, complemented
3C29×#1527C211yesmaximal, characteristic, complemented
4C29×#1488C211yesmaximal, characteristic, complemented
5C29×#1469C211yesmaximal, characteristic, complemented
6C29×#1307C211yesmaximal, characteristic, complemented
7C29×#1299C211yesmaximal, characteristic, complemented
8C2×C29×#137C411yescharacteristic
9C2×C29×AGL(1,ℤ/8)C411yescharacteristic
10C2×C29×#124C2211yescharacteristic
11C4×#41×C29C2211yescharacteristic
12C29×#464—21no—
13C29×#464—21no—
14C29×#463—21no—
15C29×#463—21no—
16C29×#446—21no—
17C29×#435—22no—
18C8×D4×C29—21no—
19C29×#432—21no—
20C29×#432C2211yescharacteristic
21C29×#432C2211yescharacteristic
22C29×#431C2211yescharacteristic
23C29×#423C2211yescharacteristic
24C29×#419C411yescharacteristic
25C29×#418C411yescharacteristic
26C4×M16×C29C2211yescharacteristic
27C2×C29×#97—21no—
28C29×#329—21no—
29C29×#329—21no—
30C29×Q8⋊C8—21no—
31C29×D4⋊C8—21no—
32C29×#323—22no—
33C2×#41×C29C2×C411yescharacteristic
34C22×Q8×C29C2×C411yescharacteristic
35C22×D4×C29C2×C411yescharacteristic
36C29×#137—42no—
37C29×AGL(1,ℤ/8)—42no—
38C2×Q16×C29—21no—
39C2×SD16×C29—21no—
40C2×SD16×C29—21no—
41C2×D8×C29—21no—
42C2×M16×C29—21no—
43C2×M16×C29C2×C411yescharacteristic
44C2×M16×C29C2×C411yescharacteristic
45C22×C8×C29—22no—
46C29×#124—21no—
47C29×#124—21no—
48C29×#124—21no—
49C29×#124—21no—
50C4×Q8×C29D411yescharacteristic
51C4×Q8×C29D411yescharacteristic
52C4×D4×C29—21no—
53C4×D4×C29—21no—
54C4×D4×C29D411yescharacteristic
55C4×D4×C29D411yescharacteristic
56C29×#117—21no—
57C29×#117C2×C411yescharacteristic
58C2×C22⋊C4×C29—21no—
59C2×C22⋊C4×C29—21no—
60C2×C42×C29—21no—
61C2×C42×C29C2311yescharacteristic
62C29×C4⋊C8—22no—
63C29×C4⋊C8—21no—
64C29×C4⋊C8—21no—
65C29×C4⋊C8—21no—
66C29×C4⋊C8—21no—
67C29×C4⋊C8—21no—
68C29×#103—21no—
69C29×#103—21no—
70C29×#102—21no—
71C29×#102—21no—
72C29×C22⋊C8—22no—
73C29×C22⋊C8—21no—
74C29×C22⋊C8—21no—
75C29×C22⋊C8D412yes—
76C29×#97—22no—
77C29×#97—21no—
78C29×#97—21no—
79C29×#97D411yescharacteristic
80C29×#97D411yescharacteristic
81C4×C8×C29—21no—
82C4×C8×C29—21no—
83C24×C29—21no—
84#41×C29—22no—
85#41×C29—41no—
86C2×Q8×C29—21no—
87C2×Q8×C29—21no—
88C2×Q8×C29—41no—
89C2×Q8×C29—41no—
90C2×Q8×C29C22⋊C411yescharacteristic
91C2×D4×C29—21no—
92C2×D4×C29—21no—
93C2×D4×C29—21no—
94C2×D4×C29—41no—
95C2×D4×C29—41no—
96C2×D4×C29C22⋊C411yescharacteristic
97C22×C4×C29—21no—
98C22×C4×C29—21no—
99C22×C4×C29—21no—
100C22×C4×C29—21no—
101C22×C4×C29C22×C411yescharacteristic
102C22×C4×C29C2×D411yescharacteristic
103C22×C4×C29#4111yescharacteristic
104Q16×C29—42no—
105SD16×C29—42no—
106SD16×C29—42no—
107D8×C29—42no—
108M16×C29—42no—
109M16×C29—41no—
110M16×C29—41no—
111C2×C8×C29—21no—
112C2×C8×C29—21no—
113C2×C8×C29—21no—
114C2×C8×C29—22no—
115C2×C8×C29—21no—
116C2×C8×C29—44no—
117C2×C8×C29—41no—
118C2×C8×C29—41no—
119C4⋊C4×C29—21no—
120C4⋊C4×C29—21no—
121C4⋊C4×C29C22⋊C411yescharacteristic
122C4⋊C4×C29C22⋊C411yescharacteristic
123C22⋊C4×C29—21no—
124C22⋊C4×C29—21no—
125C22⋊C4×C29—21no—
126C22⋊C4×C29—41no—
127C22⋊C4×C29—41no—
128C22⋊C4×C29—41no—
129C22⋊C4×C29—41no—
130C42×C29—21no—
131C42×C29—21no—
132C42×C29—21no—
133C42×C29C2×D411yescharacteristic
134C42×C29C2×D411yescharacteristic
135C42×C29C2×D411yescharacteristic
136C42×C29#4111yescharacteristic
137#9349C2911yesmaximal, characteristic, direct product factor, Sylow
138C23×C29—21no—
139C23×C29—42no—
140C23×C29—41no—
141C23×C29—81no—
142C23×C29—81no—
143C23×C29C4×D411yescharacteristic
144Q8×C29—21no—
145Q8×C29—21no—
146Q8×C29—41no—
147Q8×C29—41no—
148Q8×C29—81no—
149D4×C29—21no—
150D4×C29—42no—
151D4×C29—41no—
152D4×C29—41no—
153D4×C29—81no—
154D4×C29#10012yes—
155C2×C4×C29—21no—
156C2×C4×C29—21no—
157C2×C4×C29—21no—
158C2×C4×C29—21no—
159C2×C4×C29—21no—
160C2×C4×C29—41no—
161C2×C4×C29—41no—
162C2×C4×C29—42no—
163C2×C4×C29—42no—
164C2×C4×C29—41no—
165C2×C4×C29—81no—
166C2×C4×C29—81no—
167C2×C4×C29C2×C22⋊C411yescharacteristic
168C2×C4×C29C4×D411yescharacteristic
169C2×C4×C29#12011yescharacteristic
170C2×C4×C29#12111yescharacteristic
171C2×C4×C29#12111yescharacteristic
172C2×C4×C29#12311yescharacteristic
173C8×C29—22no—
174C8×C29—42no—
175C8×C29—41no—
176C8×C29—41no—
177C8×C29—41no—
178C8×C29—81no—
179C8×C29—81no—
180#3040C2×C2911yescharacteristic
181#2970C2×C2911yescharacteristic, complemented
182#1527C2×C2911yescharacteristic, complemented
183#1488C2×C2911yescharacteristic, complemented
184#1469C2×C2911yescharacteristic, complemented
185#1307C2×C2911yescharacteristic, complemented
186#1299C2×C2911yescharacteristic, complemented
187C22×C29—21no—
188C22×C29—21no—
189C22×C29—22no—
190C22×C29—21no—
191C22×C29—41no—
192C22×C29—41no—
193C22×C29—81no—
194C22×C29—81no—
195C22×C29—81no—
196C22×C29—162no—
197C22×C29#38611yescharacteristic
198C4×C29—21no—
199C4×C29—21no—
200C4×C29—21no—
201C4×C29—21no—
202C4×C29—21no—
203C4×C29—41no—
204C4×C29—41no—
205C4×C29—41no—
206C4×C29—81no—
207C4×C29C2×#10011yescharacteristic
208C4×C29#41311yescharacteristic
209C2×#137C4×C2911yescharacteristic
210C2×AGL(1,ℤ/8)C4×C2911yescharacteristic
211C2×#124C22×C2911yescharacteristic
212C4×#41C22×C2911yescharacteristic
213#464—21no—
214#464—21no—
215#463—21no—
216#463—21no—
217#446—21no—
218#435—22no—
219C8×D4—21no—
220#432—21no—
221#432C22×C2911yescharacteristic
222#432C22×C2911yescharacteristic
223#431C22×C2911yescharacteristic
224#423C22×C2911yescharacteristic
225#419C4×C2911yescharacteristic
226#418C4×C2911yescharacteristic
227C4×M16C22×C2911yescharacteristic
228C2×#97—21no—
229#329—21no—
230#329—21no—
231Q8⋊C8—21no—
232D4⋊C8—21no—
233#323—22no—
234C2×C29—41no—
235C2×C29—42no—
236C2×C29—161no—
237C2×C29#188111yescharacteristic
238C2×C29#190011yescharacteristic
239C2×C29#190611yescharacteristic
240C2×#41C2×C4×C2911yescharacteristic
241C22×Q8C2×C4×C2911yescharacteristic
242C22×D4C2×C4×C2911yescharacteristic
243#137—42no—
244AGL(1,ℤ/8)—42no—
245C2×Q16—21no—
246C2×SD16—21no—
247C2×SD16—21no—
248C2×D8—21no—
249C2×M16—21no—
250C2×M16C2×C4×C2911yescharacteristic
251C2×M16C2×C4×C2911yescharacteristic
252C22×C8—22no—
253#124—21no—
254#124—21no—
255#124—21no—
256#124—21no—
257C4×Q8D4×C2911yescharacteristic
258C4×Q8D4×C2911yescharacteristic
259C4×D4—21no—
260C4×D4—21no—
261C4×D4D4×C2911yescharacteristic
262C4×D4D4×C2911yescharacteristic
263#117—21no—
264#117C2×C4×C2911yescharacteristic
265C2×C22⋊C4—21no—
266C2×C22⋊C4—21no—
267C2×C42—21no—
268C2×C42C23×C2911yescharacteristic
269C4⋊C8—22no—
270C4⋊C8—21no—
271C4⋊C8—21no—
272C4⋊C8—21no—
273C4⋊C8—21no—
274C4⋊C8—21no—
275#103—21no—
276#103—21no—
277#102—21no—
278#102—21no—
279C22⋊C8—22no—
280C22⋊C8—21no—
281C22⋊C8—21no—
282C22⋊C8D4×C2912yes—
283#97—22no—
284#97—21no—
285#97—21no—
286#97D4×C2911yescharacteristic
287#97D4×C2911yescharacteristic
288C4×C8—21no—
289C4×C8—21no—
290C29#934911yescharacteristic, direct product factor, Sylow
291C24—21no—
292#41—22no—
293#41—41no—
294C2×Q8—21no—
295C2×Q8—21no—
296C2×Q8—41no—
297C2×Q8—41no—
298C2×Q8C22⋊C4×C2911yescharacteristic
299C2×D4—21no—
300C2×D4—21no—
301C2×D4—21no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4C22⋊C4×C2911yescharacteristic
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4C22×C4×C2911yescharacteristic
310C22×C4C2×D4×C2911yescharacteristic
311C22×C4#41×C2911yescharacteristic
312Q16—42no—
313SD16—42no—
314SD16—42no—
315D8—42no—
316M16—42no—
317M16—41no—
318M16—41no—
319C2×C8—21no—
320C2×C8—21no—
321C2×C8—21no—
322C2×C8—21no—
323C2×C8—22no—
324C2×C8—44no—
325C2×C8—41no—
326C2×C8—41no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4C22⋊C4×C2911yescharacteristic
330C4⋊C4C22⋊C4×C2911yescharacteristic
331C22⋊C4—21no—
332C22⋊C4—21no—
333C22⋊C4—21no—
334C22⋊C4—41no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C42—21no—
339C42—21no—
340C42—21no—
341C42C2×D4×C2911yescharacteristic
342C42C2×D4×C2911yescharacteristic
343C42C2×D4×C2911yescharacteristic
344C42#41×C2911yescharacteristic
345C23—21no—
346C23—42no—
347C23—41no—
348C23—81no—
349C23—81no—
350C23C4×D4×C2911yescharacteristic
351Q8—21no—
352Q8—21no—
353Q8—41no—
354Q8—41no—
355Q8—81no—
356D4—21no—
357D4—42no—
358D4—41no—
359D4—41no—
360D4—81no—
361D4C29×#10012yes—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—41no—
372C2×C4—81no—
373C2×C4—81no—
374C2×C4C2×C22⋊C4×C2911yescharacteristic
375C2×C4C4×D4×C2911yescharacteristic
376C2×C4C29×#12011yescharacteristic
377C2×C4C29×#12111yescharacteristic
378C2×C4C29×#12111yescharacteristic
379C2×C4C29×#12311yescharacteristic
380C8—22no—
381C8—42no—
382C8—41no—
383C8—41no—
384C8—41no—
385C8—81no—
386C8—81no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—22no—
391C22—41no—
392C22—41no—
393C22—81no—
394C22—81no—
395C22—81no—
396C22—162no—
397C22C29×#38611yescharacteristic
398C4—21no—
399C4—21no—
400C4—21no—
401C4—21no—
402C4—21no—
403C4—41no—
404C4—41no—
405C4—41no—
406C4—81no—
407C4C2×C29×#10011yescharacteristic
408C4C29×#41311yescharacteristic
409C2—41no—
410C2—42no—
411C2—161no—
412C2C29×#188111yescharacteristic
413C2C29×#190011yescharacteristic
414C2C29×#190611yescharacteristic
subgroupG/H
center, socleC22×C29#386
commutatorC22×C4C22×C4×C29
Frattini, cosocleC2×C42C23×C29
prime radicalC2×C29×AGL(1,ℤ/8)C4
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
2. C29×#2970C2semidirect
3. C29×#1527C2semidirect
4. C29×#1488C2semidirect
5. C29×#1469C2semidirect
6. C29×#1307C2semidirect
7. C29×#1299C2semidirect
137. #9349C29direct (N × H)
181. #2970C2×C29semidirect
182. #1527C2×C29semidirect
183. #1488C2×C29semidirect
184. #1469C2×C29semidirect
185. #1307C2×C29semidirect
186. #1299C2×C29semidirect
290. C29#9349direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#30402
C29×#29702
C29×#15272
C29×#14882
C29×#14692
C29×#13072
C29×#12992
#934929