Finite Group Databasebeta

← C29×#9165 #20304065

Subgroups — C29×#9165 #20304065

Order 7424.

486 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3110C211yesmaximal, characteristic
2C29×#2974C211yesmaximal, characteristic
3C29×#1762C211yesmaximal, characteristic
4C29×#1531C211yesmaximal, characteristic, complemented
5C29×#1503C211yesmaximal, characteristic, complemented
6C29×#1302C211yesmaximal, characteristic, complemented
7C29×#1285C211yesmaximal, characteristic, complemented
8C29×#533C2211yescharacteristic
9C2×C4×D4×C29C2211yescharacteristic
10C29×#484—21no—
11C29×#474C411yescharacteristic, complemented
12C29×#474C411yescharacteristic, complemented
13C29×#461C411yescharacteristic, complemented
14C29×#461C411yescharacteristic, complemented
15C29×#450—21no—
16C29×#440—21no—
17C29×#440—21no—
18C29×#436—21no—
19C29×#435—22no—
20C8×D4×C29—21no—
21C29×#432C2211yescharacteristic
22C29×#432C2211yescharacteristic
23C29×#431C2211yescharacteristic
24C2×C29×#102—21no—
25C29×#407—21no—
26C2×C29×C22⋊C8—21no—
27C2×C29×#97C2211yescharacteristic
28C4×C4⋊C4×C29C2211yescharacteristic
29C29×#340—21no—
30C29×#330—22no—
31C29×#328—21no—
32C29×#328—21no—
33C22×D4×C29D411yescharacteristic
34C23×C4×C29—21no—
35C2×SD16×C29—21no—
36C2×SD16×C29—21no—
37C2×M16×C29—22no—
38C22×C8×C29—21no—
39C22×C8×C29—22no—
40C29×C4⋊Q8C2×C411yescharacteristic
41C29×C4⋊Q8C2×C411yescharacteristic
42C29×#125—21no—
43C29×C22⋊Q8—21no—
44C29×C22⋊Q8—21no—
45C4×Q8×C29—21no—
46C4×Q8×C29—21no—
47C4×D4×C29—21no—
48C4×D4×C29—21no—
49C4×D4×C29C2×C411yescharacteristic
50C4×D4×C29C2×C411yescharacteristic
51C4×D4×C29D411yescharacteristic
52C4×D4×C29D411yescharacteristic
53C29×#117—21no—
54C2×C4⋊C4×C29—21no—
55C2×C4⋊C4×C29D411yescharacteristic
56C2×C22⋊C4×C29—21no—
57C2×C42×C29—21no—
58C2×C42×C29C2311yescharacteristic
59C29×#107—21no—
60C29×#107—21no—
61C29×C4⋊C8—21no—
62C29×C4⋊C8—21no—
63C29×C4⋊C8C2×C411yescharacteristic
64C29×C4⋊C8C2×C411yescharacteristic
65C29×#103—21no—
66C29×#103—21no—
67C29×#102—24no—
68C29×#102—21no—
69C29×#102—21no—
70C29×C22⋊C8—22no—
71C29×C22⋊C8—22no—
72C29×C22⋊C8—21no—
73C29×C22⋊C8—21no—
74C29×C22⋊C8D411yescharacteristic
75C29×C22⋊C8D411yescharacteristic
76C29×#97—21no—
77C29×#97—21no—
78C29×#97—21no—
79C29×#97D412yes—
80C4×C8×C29—21no—
81C29×#95—21no—
82C24×C29—21no—
83C2×Q8×C29—21no—
84C2×Q8×C29—21no—
85C2×D4×C29—22no—
86C2×D4×C29—21no—
87C2×D4×C29—41no—
88C2×D4×C29C22⋊C411yescharacteristic
89C2×D4×C29C22⋊C411yescharacteristic
90C22×C4×C29—21no—
91C22×C4×C29—21no—
92C22×C4×C29—21no—
93C22×C4×C29—21no—
94C22×C4×C29—21no—
95C22×C4×C29—41no—
96C22×C4×C29—82no—
97C22×C4×C29C2×D411yescharacteristic
98C22×C4×C29C2×D411yescharacteristic
99C22×C4×C29#4111yescharacteristic
100SD16×C29—42no—
101SD16×C29—42no—
102M16×C29—82no—
103C2×C8×C29—22no—
104C2×C8×C29—21no—
105C2×C8×C29—21no—
106C2×C8×C29—21no—
107C2×C8×C29—22no—
108C2×C8×C29—21no—
109C2×C8×C29—41no—
110C2×C8×C29—41no—
111C2×C8×C29—82no—
112C4⋊C4×C29—21no—
113C4⋊C4×C29—22no—
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—
121C4⋊C4×C29C22⋊C411yescharacteristic
122C4⋊C4×C29C22⋊C411yescharacteristic
123C22⋊C4×C29—21no—
124C22⋊C4×C29—21no—
125C22⋊C4×C29—21no—
126C22⋊C4×C29—21no—
127C22⋊C4×C29—41no—
128C42×C29—41no—
129C42×C29—81no—
130C42×C29C22×C411yescharacteristic
131C42×C29C2×D411yescharacteristic
132C42×C29C2×D411yescharacteristic
133C42×C29#4111yescharacteristic
134#9165C2911yesmaximal, characteristic, direct product factor, Sylow
135C23×C29—21no—
136C23×C29—21no—
137C23×C29—42no—
138C23×C29—41no—
139C23×C29—41no—
140C23×C29—81no—
141C23×C29#12111yescharacteristic
142Q8×C29—41no—
143Q8×C29—41no—
144Q8×C29—81no—
145D4×C29—21no—
146D4×C29—21no—
147D4×C29—21no—
148D4×C29—42no—
149D4×C29#10412yes—
150C2×C4×C29—21no—
151C2×C4×C29—21no—
152C2×C4×C29—21no—
153C2×C4×C29—21no—
154C2×C4×C29—21no—
155C2×C4×C29—21no—
156C2×C4×C29—41no—
157C2×C4×C29—42no—
158C2×C4×C29—42no—
159C2×C4×C29—42no—
160C2×C4×C29—41no—
161C2×C4×C29—41no—
162C2×C4×C29—81no—
163C2×C4×C29—81no—
164C2×C4×C29—81no—
165C2×C4×C29—81no—
166C2×C4×C29—81no—
167C2×C4×C29C2×C22⋊C411yescharacteristic
168C2×C4×C29C4×D411yescharacteristic
169C2×C4×C29C4×D411yescharacteristic
170C2×C4×C29#12011yescharacteristic
171C2×C4×C29#12111yescharacteristic
172C2×C4×C29#12311yescharacteristic
173C8×C29—42no—
174C8×C29—41no—
175C8×C29—42no—
176C8×C29—41no—
177C8×C29—41no—
178C8×C29—41no—
179#3110C2×C2911yescharacteristic
180#2974C2×C2911yescharacteristic
181#1762C2×C2911yescharacteristic
182#1531C2×C2911yescharacteristic, complemented
183#1503C2×C2911yescharacteristic, complemented
184#1302C2×C2911yescharacteristic, complemented
185#1285C2×C2911yescharacteristic, complemented
186C22×C29—21no—
187C22×C29—21no—
188C22×C29—22no—
189C22×C29—41no—
190C22×C29—41no—
191C22×C29—41no—
192C22×C29—41no—
193C22×C29—41no—
194C22×C29—82no—
195C22×C29—82no—
196C22×C29#38611yescharacteristic
197C22×C29#47111yescharacteristic
198C22×C29#47311yescharacteristic
199C4×C29—21no—
200C4×C29—21no—
201C4×C29—21no—
202C4×C29—21no—
203C4×C29—21no—
204C4×C29—41no—
205C4×C29—41no—
206C4×C29—82no—
207C4×C29—81no—
208C4×C29—81no—
209C4×C29C2×#10411yescharacteristic
210C4×C29#42111yescharacteristic
211#533C22×C2911yescharacteristic
212C2×C4×D4C22×C2911yescharacteristic
213#484—21no—
214#474C4×C2911yescharacteristic, complemented
215#474C4×C2911yescharacteristic, complemented
216#461C4×C2911yescharacteristic, complemented
217#461C4×C2911yescharacteristic, complemented
218#450—21no—
219#440—21no—
220#440—21no—
221#436—21no—
222#435—22no—
223C8×D4—21no—
224#432C22×C2911yescharacteristic
225#432C22×C2911yescharacteristic
226#431C22×C2911yescharacteristic
227C2×#102—21no—
228#407—21no—
229C2×C22⋊C8—21no—
230C2×#97C22×C2911yescharacteristic
231C4×C4⋊C4C22×C2911yescharacteristic
232#340—21no—
233#330—22no—
234#328—21no—
235#328—21no—
236C2×C29—21no—
237C2×C29—21no—
238C2×C29—42no—
239C2×C29—81no—
240C2×C29#187111yescharacteristic
241C2×C29#190411yescharacteristic
242C2×C29#190811yescharacteristic
243C22×D4D4×C2911yescharacteristic
244C23×C4—21no—
245C2×SD16—21no—
246C2×SD16—21no—
247C2×M16—22no—
248C22×C8—21no—
249C22×C8—22no—
250C4⋊Q8C2×C4×C2911yescharacteristic
251C4⋊Q8C2×C4×C2911yescharacteristic
252#125—21no—
253C22⋊Q8—21no—
254C22⋊Q8—21no—
255C4×Q8—21no—
256C4×Q8—21no—
257C4×D4—21no—
258C4×D4—21no—
259C4×D4C2×C4×C2911yescharacteristic
260C4×D4C2×C4×C2911yescharacteristic
261C4×D4D4×C2911yescharacteristic
262C4×D4D4×C2911yescharacteristic
263#117—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4D4×C2911yescharacteristic
266C2×C22⋊C4—21no—
267C2×C42—21no—
268C2×C42C23×C2911yescharacteristic
269#107—21no—
270#107—21no—
271C4⋊C8—21no—
272C4⋊C8—21no—
273C4⋊C8C2×C4×C2911yescharacteristic
274C4⋊C8C2×C4×C2911yescharacteristic
275#103—21no—
276#103—21no—
277#102—24no—
278#102—21no—
279#102—21no—
280C22⋊C8—22no—
281C22⋊C8—22no—
282C22⋊C8—21no—
283C22⋊C8—21no—
284C22⋊C8D4×C2911yescharacteristic
285C22⋊C8D4×C2911yescharacteristic
286#97—21no—
287#97—21no—
288#97—21no—
289#97D4×C2912yes—
290C4×C8—21no—
291#95—21no—
292C29#916511yescharacteristic, direct product factor, Sylow
293C24—21no—
294C2×Q8—21no—
295C2×Q8—21no—
296C2×D4—22no—
297C2×D4—21no—
298C2×D4—41no—
299C2×D4C22⋊C4×C2911yescharacteristic
300C2×D4C22⋊C4×C2911yescharacteristic
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—41no—
307C22×C4—82no—
308C22×C4C2×D4×C2911yescharacteristic
309C22×C4C2×D4×C2911yescharacteristic
310C22×C4#41×C2911yescharacteristic
311SD16—42no—
312SD16—42no—
313M16—82no—
314C2×C8—22no—
315C2×C8—21no—
316C2×C8—21no—
317C2×C8—21no—
318C2×C8—21no—
319C2×C8—22no—
320C2×C8—41no—
321C2×C8—41no—
322C2×C8—82no—
323C4⋊C4—21no—
324C4⋊C4—22no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4C22⋊C4×C2911yescharacteristic
333C4⋊C4C22⋊C4×C2911yescharacteristic
334C22⋊C4—21no—
335C22⋊C4—21no—
336C22⋊C4—21no—
337C22⋊C4—21no—
338C22⋊C4—41no—
339C42—41no—
340C42—81no—
341C42C22×C4×C2911yescharacteristic
342C42C2×D4×C2911yescharacteristic
343C42C2×D4×C2911yescharacteristic
344C42#41×C2911yescharacteristic
345C23—21no—
346C23—21no—
347C23—42no—
348C23—41no—
349C23—41no—
350C23—81no—
351C23C29×#12111yescharacteristic
352Q8—41no—
353Q8—41no—
354Q8—81no—
355D4—21no—
356D4—21no—
357D4—21no—
358D4—42no—
359D4C29×#10412yes—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—41no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—81no—
373C2×C4—81no—
374C2×C4—81no—
375C2×C4—81no—
376C2×C4—81no—
377C2×C4C2×C22⋊C4×C2911yescharacteristic
378C2×C4C4×D4×C2911yescharacteristic
379C2×C4C4×D4×C2911yescharacteristic
380C2×C4C29×#12011yescharacteristic
381C2×C4C29×#12111yescharacteristic
382C2×C4C29×#12311yescharacteristic
383C8—42no—
384C8—41no—
385C8—42no—
386C8—41no—
387C8—41no—
388C8—41no—
389C22—21no—
390C22—21no—
391C22—22no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—82no—
398C22—82no—
399C22C29×#38611yescharacteristic
400C22C29×#47111yescharacteristic
401C22C29×#47311yescharacteristic
402C4—21no—
403C4—21no—
404C4—21no—
405C4—21no—
406C4—21no—
407C4—41no—
408C4—41no—
409C4—82no—
410C4—81no—
411C4—81no—
412C4C2×C29×#10411yescharacteristic
413C4C29×#42111yescharacteristic
414C2—21no—
415C2—21no—
416C2—42no—
417C2—81no—
418C2C29×#187111yescharacteristic
419C2C29×#190411yescharacteristic
420C2C29×#190811yescharacteristic
subgroupG/H
center, socleC22×C29#386
commutatorC42C22×C4×C29
Frattini, cosocleC2×C42C23×C29
prime radicalC22×D4×C29D4
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
4. C29×#1531C2semidirect
5. C29×#1503C2semidirect
6. C29×#1302C2semidirect
7. C29×#1285C2semidirect
11. C29×#474C4semidirect
12. C29×#474C4semidirect
13. C29×#461C4semidirect
14. C29×#461C4semidirect
134. #9165C29direct (N × H)
182. #1531C2×C29semidirect
183. #1503C2×C29semidirect
184. #1302C2×C29semidirect
185. #1285C2×C29semidirect
214. #474C4×C29semidirect
215. #474C4×C29semidirect
216. #461C4×C29semidirect
217. #461C4×C29semidirect
292. C29#9165direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#31102
C29×#29742
C29×#17622
C29×#15312
C29×#15032
C29×#13022
C29×#12852
#916529