Finite Group Databasebeta

← C29×#9209 #20304109

Subgroups — C29×#9209 #20304109

Order 7424.

456 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3076C211yesmaximal, characteristic
2C29×#2965C211yesmaximal, characteristic
3C29×#1806C211yesmaximal, characteristic
4C29×#1503C211yesmaximal, characteristic, complemented
5C29×#1493C211yesmaximal, characteristic, complemented
6C29×#1301C211yesmaximal, characteristic, complemented
7C29×#1279C211yesmaximal, characteristic, complemented
8C29×#533C2211yescharacteristic
9C4×#41×C29C2211yescharacteristic
10C29×#479—21no—
11C29×#478—21no—
12C29×#477C411yescharacteristic, complemented
13C29×#476C411yescharacteristic, complemented
14C29×#475C411yescharacteristic, complemented
15C29×#474C411yescharacteristic, complemented
16C29×#446—21no—
17C29×#436—21no—
18C29×#435—22no—
19C29×#431—21no—
20C29×#431C2211yescharacteristic
21C29×#427—21no—
22C29×#423C2211yescharacteristic
23C2×C29×C4⋊C8C2211yescharacteristic
24C2×C29×#104—21no—
25C29×#416—21no—
26C4×M16×C29—21no—
27C2×C4×C8×C29C2211yescharacteristic
28C4×C4⋊C4×C29C2211yescharacteristic
29C29×#339—21no—
30C29×#328—22no—
31C29×Q8⋊C8—21no—
32C29×Q8⋊C8—21no—
33C2×#41×C29D411yescharacteristic
34C2×M16×C29—22no—
35C2×M16×C29—21no—
36C22×C8×C29—21no—
37C22×C8×C29—21no—
38C29×C4⋊Q8C2×C411yescharacteristic
39C29×C4⋊Q8C2×C411yescharacteristic
40C29×#125—21no—
41C29×C22⋊Q8—21no—
42C29×C22⋊Q8—21no—
43C4×Q8×C29—21no—
44C4×Q8×C29—21no—
45C4×Q8×C29C2×C411yescharacteristic
46C4×Q8×C29D411yescharacteristic
47C4×D4×C29—21no—
48C4×D4×C29—21no—
49C4×D4×C29C2×C411yescharacteristic
50C4×D4×C29D411yescharacteristic
51C29×#117—21no—
52C29×#117—21no—
53C29×#117D411yescharacteristic
54C2×C4⋊C4×C29—21no—
55C2×C42×C29—21no—
56C2×C42×C29—21no—
57C2×C42×C29C2311yescharacteristic
58C29×#107—21no—
59C29×#107—21no—
60C29×#106—21no—
61C29×#106—21no—
62C29×C4⋊C8—22no—
63C29×C4⋊C8—21no—
64C29×C4⋊C8—21no—
65C29×C4⋊C8—21no—
66C29×C4⋊C8—21no—
67C29×C4⋊C8C2×C411yescharacteristic
68C29×C4⋊C8C2×C411yescharacteristic
69C29×#104—42no—
70C29×#103—21no—
71C29×#103—21no—
72C29×#102—21no—
73C29×#102—21no—
74C29×C22⋊C8—22no—
75C29×C22⋊C8D412yes—
76C29×#97—22no—
77C4×C8×C29—21no—
78C4×C8×C29—21no—
79C4×C8×C29D411yescharacteristic
80C4×C8×C29D411yescharacteristic
81C29×#95—21no—
82#41×C29—21no—
83#41×C29—21no—
84#41×C29—21no—
85#41×C29—21no—
86C2×Q8×C29—21no—
87C2×Q8×C29—21no—
88C2×Q8×C29C22⋊C411yescharacteristic
89C2×D4×C29—21no—
90C2×D4×C29C22⋊C411yescharacteristic
91C22×C4×C29—21no—
92C22×C4×C29—21no—
93C22×C4×C29—21no—
94C22×C4×C29—41no—
95C22×C4×C29C2×D411yescharacteristic
96C22×C4×C29C2×D411yescharacteristic
97C22×C4×C29#4111yescharacteristic
98M16×C29—44no—
99M16×C29—41no—
100M16×C29—41no—
101C2×C8×C29—21no—
102C2×C8×C29—21no—
103C2×C8×C29—21no—
104C2×C8×C29—21no—
105C2×C8×C29—22no—
106C2×C8×C29—42no—
107C2×C8×C29—41no—
108C2×C8×C29—41no—
109C2×C8×C29—41no—
110C4⋊C4×C29—21no—
111C4⋊C4×C29—21no—
112C4⋊C4×C29—22no—
113C4⋊C4×C29—21no—
114C4⋊C4×C29—21no—
115C4⋊C4×C29—21no—
116C4⋊C4×C29—21no—
117C4⋊C4×C29—41no—
118C4⋊C4×C29—41no—
119C4⋊C4×C29—41no—
120C4⋊C4×C29C22⋊C411yescharacteristic
121C4⋊C4×C29C22⋊C411yescharacteristic
122C22⋊C4×C29—21no—
123C22⋊C4×C29—21no—
124C22⋊C4×C29—21no—
125C22⋊C4×C29—41no—
126C42×C29—21no—
127C42×C29—21no—
128C42×C29—21no—
129C42×C29—41no—
130C42×C29—41no—
131C42×C29—41no—
132C42×C29C22×C411yescharacteristic
133C42×C29C2×D411yescharacteristic
134C42×C29C2×D411yescharacteristic
135C42×C29#4111yescharacteristic
136#9209C2911yesmaximal, characteristic, direct product factor, Sylow
137C23×C29—21no—
138C23×C29#12111yescharacteristic
139Q8×C29—21no—
140Q8×C29—21no—
141Q8×C29—41no—
142Q8×C29—41no—
143Q8×C29—81no—
144D4×C29—21no—
145D4×C29—21no—
146D4×C29—41no—
147D4×C29—41no—
148C2×C4×C29—21no—
149C2×C4×C29—21no—
150C2×C4×C29—21no—
151C2×C4×C29—21no—
152C2×C4×C29—21no—
153C2×C4×C29—41no—
154C2×C4×C29—42no—
155C2×C4×C29—41no—
156C2×C4×C29—41no—
157C2×C4×C29—41no—
158C2×C4×C29—41no—
159C2×C4×C29—42no—
160C2×C4×C29—41no—
161C2×C4×C29—41no—
162C2×C4×C29—81no—
163C2×C4×C29—81no—
164C2×C4×C29C2×C22⋊C411yescharacteristic
165C2×C4×C29C4×D411yescharacteristic
166C2×C4×C29C4×D411yescharacteristic
167C2×C4×C29#12011yescharacteristic
168C2×C4×C29#12111yescharacteristic
169C2×C4×C29#12311yescharacteristic
170C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
171C2×C4×C29#13711yescharacteristic
172C2×C4×C29#13711yescharacteristic
173C2×C4×C29#13711yescharacteristic
174C8×C29—22no—
175C8×C29—41no—
176C8×C29—42no—
177C8×C29—41no—
178C8×C29—41no—
179C8×C29—81no—
180#3076C2×C2911yescharacteristic
181#2965C2×C2911yescharacteristic
182#1806C2×C2911yescharacteristic
183#1503C2×C2911yescharacteristic, complemented
184#1493C2×C2911yescharacteristic, complemented
185#1301C2×C2911yescharacteristic, complemented
186#1279C2×C2911yescharacteristic, complemented
187C22×C29—21no—
188C22×C29—21no—
189C22×C29—41no—
190C22×C29—41no—
191C22×C29—41no—
192C22×C29#38611yescharacteristic
193C22×C29#46811yescharacteristic
194C22×C29#47011yescharacteristic
195C4×C29—21no—
196C4×C29—21no—
197C4×C29—21no—
198C4×C29—41no—
199C4×C29—41no—
200C4×C29—41no—
201C4×C29—82no—
202C4×C29—81no—
203C4×C29—81no—
204C4×C29#41711yescharacteristic
205C4×C29#41911yescharacteristic
206C4×C29#44311yescharacteristic
207C4×C29#44411yescharacteristic
208C4×C29#46811yescharacteristic
209C4×C29#47011yescharacteristic
210#533C22×C2911yescharacteristic
211C4×#41C22×C2911yescharacteristic
212#479—21no—
213#478—21no—
214#477C4×C2911yescharacteristic, complemented
215#476C4×C2911yescharacteristic, complemented
216#475C4×C2911yescharacteristic, complemented
217#474C4×C2911yescharacteristic, complemented
218#446—21no—
219#436—21no—
220#435—22no—
221#431—21no—
222#431C22×C2911yescharacteristic
223#427—21no—
224#423C22×C2911yescharacteristic
225C2×C4⋊C8C22×C2911yescharacteristic
226C2×#104—21no—
227#416—21no—
228C4×M16—21no—
229C2×C4×C8C22×C2911yescharacteristic
230C4×C4⋊C4C22×C2911yescharacteristic
231#339—21no—
232#328—22no—
233Q8⋊C8—21no—
234Q8⋊C8—21no—
235C2×C29—21no—
236C2×C29—21no—
237C2×C29—81no—
238C2×C29#187611yescharacteristic
239C2×C29#189411yescharacteristic
240C2×C29#190611yescharacteristic
241C2×#41D4×C2911yescharacteristic
242C2×M16—22no—
243C2×M16—21no—
244C22×C8—21no—
245C22×C8—21no—
246C4⋊Q8C2×C4×C2911yescharacteristic
247C4⋊Q8C2×C4×C2911yescharacteristic
248#125—21no—
249C22⋊Q8—21no—
250C22⋊Q8—21no—
251C4×Q8—21no—
252C4×Q8—21no—
253C4×Q8C2×C4×C2911yescharacteristic
254C4×Q8D4×C2911yescharacteristic
255C4×D4—21no—
256C4×D4—21no—
257C4×D4C2×C4×C2911yescharacteristic
258C4×D4D4×C2911yescharacteristic
259#117—21no—
260#117—21no—
261#117D4×C2911yescharacteristic
262C2×C4⋊C4—21no—
263C2×C42—21no—
264C2×C42—21no—
265C2×C42C23×C2911yescharacteristic
266#107—21no—
267#107—21no—
268#106—21no—
269#106—21no—
270C4⋊C8—22no—
271C4⋊C8—21no—
272C4⋊C8—21no—
273C4⋊C8—21no—
274C4⋊C8—21no—
275C4⋊C8C2×C4×C2911yescharacteristic
276C4⋊C8C2×C4×C2911yescharacteristic
277#104—42no—
278#103—21no—
279#103—21no—
280#102—21no—
281#102—21no—
282C22⋊C8—22no—
283C22⋊C8D4×C2912yes—
284#97—22no—
285C4×C8—21no—
286C4×C8—21no—
287C4×C8D4×C2911yescharacteristic
288C4×C8D4×C2911yescharacteristic
289#95—21no—
290C29#920911yescharacteristic, direct product factor, Sylow
291#41—21no—
292#41—21no—
293#41—21no—
294#41—21no—
295C2×Q8—21no—
296C2×Q8—21no—
297C2×Q8C22⋊C4×C2911yescharacteristic
298C2×D4—21no—
299C2×D4C22⋊C4×C2911yescharacteristic
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—41no—
304C22×C4C2×D4×C2911yescharacteristic
305C22×C4C2×D4×C2911yescharacteristic
306C22×C4#41×C2911yescharacteristic
307M16—44no—
308M16—41no—
309M16—41no—
310C2×C8—21no—
311C2×C8—21no—
312C2×C8—21no—
313C2×C8—21no—
314C2×C8—22no—
315C2×C8—42no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—41no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—22no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4C22⋊C4×C2911yescharacteristic
330C4⋊C4C22⋊C4×C2911yescharacteristic
331C22⋊C4—21no—
332C22⋊C4—21no—
333C22⋊C4—21no—
334C22⋊C4—41no—
335C42—21no—
336C42—21no—
337C42—21no—
338C42—41no—
339C42—41no—
340C42—41no—
341C42C22×C4×C2911yescharacteristic
342C42C2×D4×C2911yescharacteristic
343C42C2×D4×C2911yescharacteristic
344C42#41×C2911yescharacteristic
345C23—21no—
346C23C29×#12111yescharacteristic
347Q8—21no—
348Q8—21no—
349Q8—41no—
350Q8—41no—
351Q8—81no—
352D4—21no—
353D4—21no—
354D4—41no—
355D4—41no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—41no—
362C2×C4—42no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—42no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—81no—
371C2×C4—81no—
372C2×C4C2×C22⋊C4×C2911yescharacteristic
373C2×C4C4×D4×C2911yescharacteristic
374C2×C4C4×D4×C2911yescharacteristic
375C2×C4C29×#12011yescharacteristic
376C2×C4C29×#12111yescharacteristic
377C2×C4C29×#12311yescharacteristic
378C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
379C2×C4C29×#13711yescharacteristic
380C2×C4C29×#13711yescharacteristic
381C2×C4C29×#13711yescharacteristic
382C8—22no—
383C8—41no—
384C8—42no—
385C8—41no—
386C8—41no—
387C8—81no—
388C22—21no—
389C22—21no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22C29×#38611yescharacteristic
394C22C29×#46811yescharacteristic
395C22C29×#47011yescharacteristic
396C4—21no—
397C4—21no—
398C4—21no—
399C4—41no—
400C4—41no—
401C4—41no—
402C4—82no—
403C4—81no—
404C4—81no—
405C4C29×#41711yescharacteristic
406C4C29×#41911yescharacteristic
407C4C29×#44311yescharacteristic
408C4C29×#44411yescharacteristic
409C4C29×#46811yescharacteristic
410C4C29×#47011yescharacteristic
411C2—21no—
412C2—21no—
413C2—81no—
414C2C29×#187611yescharacteristic
415C2C29×#189411yescharacteristic
416C2C29×#190611yescharacteristic
subgroupG/H
centerC2×C4×C29#121
commutatorC42C22×C4×C29
Frattini, cosocleC2×C42C23×C29
socleC22×C29#386
prime radicalC2×#41×C29D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C29 ◁ C2×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
4. C29×#1503C2semidirect
5. C29×#1493C2semidirect
6. C29×#1301C2semidirect
7. C29×#1279C2semidirect
12. C29×#477C4semidirect
13. C29×#476C4semidirect
14. C29×#475C4semidirect
15. C29×#474C4semidirect
136. #9209C29direct (N × H)
183. #1503C2×C29semidirect
184. #1493C2×C29semidirect
185. #1301C2×C29semidirect
186. #1279C2×C29semidirect
214. #477C4×C29semidirect
215. #476C4×C29semidirect
216. #475C4×C29semidirect
217. #474C4×C29semidirect
290. C29#9209direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#30762
C29×#29652
C29×#18062
C29×#15032
C29×#14932
C29×#13012
C29×#12792
#920929