Finite Group Databasebeta

← C29×#9331 #20304231

Subgroups — C29×#9331 #20304231

Order 7424.

438 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3196C211yesmaximal, characteristic
2C29×#2978C211yesmaximal, characteristic
3C29×#1516C211yesmaximal, characteristic
4C29×#1511C211yesmaximal, characteristic, complemented
5C29×#1472C211yesmaximal, characteristic, complemented
6C29×#1306C211yesmaximal, characteristic, complemented
7C29×#1293C211yesmaximal, characteristic, complemented
8C29×#525C2211yescharacteristic
9C2×C29×C22⋊Q8C2211yescharacteristic
10C29×#485—21no—
11C29×#484C411yescharacteristic, complemented
12C29×#481C411yescharacteristic, complemented
13C29×#470—21no—
14C29×#468—21no—
15C29×#452—21no—
16C29×#451C411yescharacteristic, complemented
17C29×#448C411yescharacteristic, complemented
18C29×#436—21no—
19C29×#436—21no—
20C29×#435—21no—
21C29×#435—21no—
22C29×#433—21no—
23C29×#408—21no—
24C29×#407C2211yescharacteristic
25C29×#407C2211yescharacteristic
26C29×#407C2211yescharacteristic
27C2×C29×C22⋊C8C2211yescharacteristic
28C29×#381C2211yescharacteristic
29C29×#328—21no—
30C29×#328—21no—
31C29×#328—21no—
32C29×#327—21no—
33C29×#324—21no—
34C29×#324—21no—
35C2×#41×C29D411yescharacteristic
36C22×Q8×C29C2×C411yescharacteristic
37C23×C4×C29C2311yescharacteristic
38C2×Q16×C29—21no—
39C2×SD16×C29—21no—
40C2×M16×C29—21no—
41C2×M16×C29—21no—
42C2×M16×C29—21no—
43C2×M16×C29—21no—
44C22×C8×C29—21no—
45C22×C8×C29—21no—
46C29×#123—21no—
47C29×C22⋊Q8—21no—
48C29×C22⋊Q8—21no—
49C29×C22⋊Q8—21no—
50C29×C22⋊Q8—21no—
51C29×C22⋊Q8C2×C411yescharacteristic
52C29×C22⋊Q8D411yescharacteristic
53C29×#121C2×C411yescharacteristic
54C29×#121D411yescharacteristic
55C29×#120—21no—
56C4×D4×C29—21no—
57C4×D4×C29—21no—
58C29×#117D411yescharacteristic
59C2×C4⋊C4×C29—21no—
60C2×C4⋊C4×C29C2×C411yescharacteristic
61C2×C22⋊C4×C29—21no—
62C2×C22⋊C4×C29—21no—
63C29×#107—21no—
64C29×#106—21no—
65C29×C4⋊C8—21no—
66C29×C4⋊C8—21no—
67C29×#103—21no—
68C29×#103—21no—
69C29×#103—21no—
70C29×#102—21no—
71C29×C22⋊C8—21no—
72C29×C22⋊C8—21no—
73C29×C22⋊C8—21no—
74C29×C22⋊C8—21no—
75C29×C22⋊C8—21no—
76C29×C22⋊C8—21no—
77C29×C22⋊C8—21no—
78C29×C22⋊C8C2×C411yescharacteristic
79C29×C22⋊C8C2×C411yescharacteristic
80C29×C22⋊C8D411yescharacteristic
81C29×C22⋊C8D411yescharacteristic
82C29×C22⋊C8D411yescharacteristic
83C29×C22⋊C8D411yescharacteristic
84C29×#97—21no—
85C4×C8×C29—21no—
86C29×#95—21no—
87C29×#95—21no—
88C24×C29#4111yescharacteristic
89#41×C29—81no—
90C2×Q8×C29—21no—
91C2×Q8×C29—21no—
92C2×Q8×C29—81no—
93C2×Q8×C29C22⋊C411yescharacteristic
94C2×D4×C29—21no—
95C2×D4×C29—21no—
96C2×D4×C29—21no—
97C2×D4×C29C22⋊C411yescharacteristic
98C22×C4×C29—21no—
99C22×C4×C29—21no—
100C22×C4×C29—21no—
101C22×C4×C29—41no—
102C22×C4×C29—81no—
103C22×C4×C29C22×C411yescharacteristic
104C22×C4×C29C2×D411yescharacteristic
105C22×C4×C29C2×D411yescharacteristic
106C22×C4×C29C2×D411yescharacteristic
107C22×C4×C29C2×D411yescharacteristic
108C22×C4×C29#4111yescharacteristic
109Q16×C29—81no—
110SD16×C29—81no—
111M16×C29—81no—
112M16×C29—81no—
113M16×C29—81no—
114M16×C29—81no—
115C2×C8×C29—21no—
116C2×C8×C29—21no—
117C2×C8×C29—21no—
118C2×C8×C29—21no—
119C2×C8×C29—21no—
120C2×C8×C29—21no—
121C2×C8×C29—41no—
122C2×C8×C29—81no—
123C2×C8×C29—81no—
124C4⋊C4×C29—21no—
125C4⋊C4×C29—21no—
126C4⋊C4×C29—21no—
127C4⋊C4×C29—21no—
128C4⋊C4×C29—41no—
129C4⋊C4×C29—41no—
130C4⋊C4×C29C22⋊C411yescharacteristic
131C4⋊C4×C29C22⋊C411yescharacteristic
132C22⋊C4×C29—21no—
133C22⋊C4×C29—21no—
134C22⋊C4×C29—21no—
135C22⋊C4×C29—21no—
136C22⋊C4×C29—21no—
137C22⋊C4×C29—41no—
138C22⋊C4×C29—41no—
139C22⋊C4×C29—81no—
140C42×C29—21no—
141#9331C2911yesmaximal, characteristic, direct product factor, Sylow
142C23×C29—21no—
143C23×C29—41no—
144C23×C29—41no—
145C23×C29—41no—
146C23×C29C4×D411yescharacteristic
147C23×C29#12111yescharacteristic
148C23×C29#12311yescharacteristic
149Q8×C29—41no—
150Q8×C29—41no—
151Q8×C29—41no—
152Q8×C29—81no—
153D4×C29—41no—
154D4×C29—81no—
155D4×C29—81no—
156D4×C29—81no—
157C2×C4×C29—21no—
158C2×C4×C29—21no—
159C2×C4×C29—21no—
160C2×C4×C29—41no—
161C2×C4×C29—41no—
162C2×C4×C29—41no—
163C2×C4×C29—41no—
164C2×C4×C29—41no—
165C2×C4×C29—41no—
166C2×C4×C29—41no—
167C2×C4×C29—41no—
168C2×C4×C29—42no—
169C2×C4×C29—41no—
170C2×C4×C29—41no—
171C2×C4×C29—81no—
172C2×C4×C29—81no—
173C2×C4×C29—81no—
174C2×C4×C29—81no—
175C2×C4×C29C2×C22⋊C411yescharacteristic
176C2×C4×C29C4×D411yescharacteristic
177C2×C4×C29#12011yescharacteristic
178C2×C4×C29#12111yescharacteristic
179C8×C29—41no—
180C8×C29—41no—
181C8×C29—41no—
182C8×C29—41no—
183C8×C29—41no—
184C8×C29—41no—
185C8×C29—81no—
186#3196C2×C2911yescharacteristic
187#2978C2×C2911yescharacteristic
188#1516C2×C2911yescharacteristic
189#1511C2×C2911yescharacteristic, complemented
190#1472C2×C2911yescharacteristic, complemented
191#1306C2×C2911yescharacteristic, complemented
192#1293C2×C2911yescharacteristic, complemented
193C22×C29—21no—
194C22×C29—21no—
195C22×C29—21no—
196C22×C29—21no—
197C22×C29—21no—
198C22×C29—21no—
199C22×C29—21no—
200C22×C29—21no—
201C22×C29—21no—
202C22×C29—41no—
203C22×C29—41no—
204C22×C29—41no—
205C22×C29—82no—
206C22×C29#38611yescharacteristic
207C4×C29—21no—
208C4×C29—21no—
209C4×C29—21no—
210C4×C29—21no—
211C4×C29—41no—
212C4×C29—41no—
213C4×C29—41no—
214C4×C29—81no—
215C4×C29—81no—
216C4×C29—161no—
217#525C22×C2911yescharacteristic
218C2×C22⋊Q8C22×C2911yescharacteristic
219#485—21no—
220#484C4×C2911yescharacteristic, complemented
221#481C4×C2911yescharacteristic, complemented
222#470—21no—
223#468—21no—
224#452—21no—
225#451C4×C2911yescharacteristic, complemented
226#448C4×C2911yescharacteristic, complemented
227#436—21no—
228#436—21no—
229#435—21no—
230#435—21no—
231#433—21no—
232#408—21no—
233#407C22×C2911yescharacteristic
234#407C22×C2911yescharacteristic
235#407C22×C2911yescharacteristic
236C2×C22⋊C8C22×C2911yescharacteristic
237#381C22×C2911yescharacteristic
238#328—21no—
239#328—21no—
240#328—21no—
241#327—21no—
242#324—21no—
243#324—21no—
244C2×C29—41no—
245C2×C29—41no—
246C2×C29—41no—
247C2×C29—81no—
248C2×C29#188111yescharacteristic
249C2×C29#190211yescharacteristic
250C2×C29#191311yescharacteristic
251C2×#41D4×C2911yescharacteristic
252C22×Q8C2×C4×C2911yescharacteristic
253C23×C4C23×C2911yescharacteristic
254C2×Q16—21no—
255C2×SD16—21no—
256C2×M16—21no—
257C2×M16—21no—
258C2×M16—21no—
259C2×M16—21no—
260C22×C8—21no—
261C22×C8—21no—
262#123—21no—
263C22⋊Q8—21no—
264C22⋊Q8—21no—
265C22⋊Q8—21no—
266C22⋊Q8—21no—
267C22⋊Q8C2×C4×C2911yescharacteristic
268C22⋊Q8D4×C2911yescharacteristic
269#121C2×C4×C2911yescharacteristic
270#121D4×C2911yescharacteristic
271#120—21no—
272C4×D4—21no—
273C4×D4—21no—
274#117D4×C2911yescharacteristic
275C2×C4⋊C4—21no—
276C2×C4⋊C4C2×C4×C2911yescharacteristic
277C2×C22⋊C4—21no—
278C2×C22⋊C4—21no—
279#107—21no—
280#106—21no—
281C4⋊C8—21no—
282C4⋊C8—21no—
283#103—21no—
284#103—21no—
285#103—21no—
286#102—21no—
287C22⋊C8—21no—
288C22⋊C8—21no—
289C22⋊C8—21no—
290C22⋊C8—21no—
291C22⋊C8—21no—
292C22⋊C8—21no—
293C22⋊C8—21no—
294C22⋊C8C2×C4×C2911yescharacteristic
295C22⋊C8C2×C4×C2911yescharacteristic
296C22⋊C8D4×C2911yescharacteristic
297C22⋊C8D4×C2911yescharacteristic
298C22⋊C8D4×C2911yescharacteristic
299C22⋊C8D4×C2911yescharacteristic
300#97—21no—
301C4×C8—21no—
302#95—21no—
303#95—21no—
304C29#933111yescharacteristic, direct product factor, Sylow
305C24#41×C2911yescharacteristic
306#41—81no—
307C2×Q8—21no—
308C2×Q8—21no—
309C2×Q8—81no—
310C2×Q8C22⋊C4×C2911yescharacteristic
311C2×D4—21no—
312C2×D4—21no—
313C2×D4—21no—
314C2×D4C22⋊C4×C2911yescharacteristic
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—41no—
319C22×C4—81no—
320C22×C4C22×C4×C2911yescharacteristic
321C22×C4C2×D4×C2911yescharacteristic
322C22×C4C2×D4×C2911yescharacteristic
323C22×C4C2×D4×C2911yescharacteristic
324C22×C4C2×D4×C2911yescharacteristic
325C22×C4#41×C2911yescharacteristic
326Q16—81no—
327SD16—81no—
328M16—81no—
329M16—81no—
330M16—81no—
331M16—81no—
332C2×C8—21no—
333C2×C8—21no—
334C2×C8—21no—
335C2×C8—21no—
336C2×C8—21no—
337C2×C8—21no—
338C2×C8—41no—
339C2×C8—81no—
340C2×C8—81no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—41no—
346C4⋊C4—41no—
347C4⋊C4C22⋊C4×C2911yescharacteristic
348C4⋊C4C22⋊C4×C2911yescharacteristic
349C22⋊C4—21no—
350C22⋊C4—21no—
351C22⋊C4—21no—
352C22⋊C4—21no—
353C22⋊C4—21no—
354C22⋊C4—41no—
355C22⋊C4—41no—
356C22⋊C4—81no—
357C42—21no—
358C23—21no—
359C23—41no—
360C23—41no—
361C23—41no—
362C23C4×D4×C2911yescharacteristic
363C23C29×#12111yescharacteristic
364C23C29×#12311yescharacteristic
365Q8—41no—
366Q8—41no—
367Q8—41no—
368Q8—81no—
369D4—41no—
370D4—81no—
371D4—81no—
372D4—81no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—42no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—81no—
388C2×C4—81no—
389C2×C4—81no—
390C2×C4—81no—
391C2×C4C2×C22⋊C4×C2911yescharacteristic
392C2×C4C4×D4×C2911yescharacteristic
393C2×C4C29×#12011yescharacteristic
394C2×C4C29×#12111yescharacteristic
395C8—41no—
396C8—41no—
397C8—41no—
398C8—41no—
399C8—41no—
400C8—41no—
401C8—81no—
402C22—21no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—21no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—82no—
415C22C29×#38611yescharacteristic
416C4—21no—
417C4—21no—
418C4—21no—
419C4—21no—
420C4—41no—
421C4—41no—
422C4—41no—
423C4—81no—
424C4—81no—
425C4—161no—
426C2—41no—
427C2—41no—
428C2—41no—
429C2—81no—
430C2C29×#188111yescharacteristic
431C2C29×#190211yescharacteristic
432C2C29×#191311yescharacteristic
subgroupG/H
center, socleC22×C29#386
commutatorC22×C4C22×C4×C29
Frattini, cosocleC23×C4C23×C29
prime radicalC29×#525C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C23×C4×C29 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. C29×#1511C2semidirect
5. C29×#1472C2semidirect
6. C29×#1306C2semidirect
7. C29×#1293C2semidirect
11. C29×#484C4semidirect
12. C29×#481C4semidirect
16. C29×#451C4semidirect
17. C29×#448C4semidirect
141. #9331C29direct (N × H)
189. #1511C2×C29semidirect
190. #1472C2×C29semidirect
191. #1306C2×C29semidirect
192. #1293C2×C29semidirect
220. #484C4×C29semidirect
221. #481C4×C29semidirect
225. #451C4×C29semidirect
226. #448C4×C29semidirect
304. C29#9331direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#31962
C29×#29782
C29×#15162
C29×#15112
C29×#14722
C29×#13062
C29×#12932
#933129