Finite Group Databasebeta

← C29×#8911 #20303811

Subgroups — C29×#8911 #20303811

Order 7424.

484 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#2379C211yesmaximal, characteristic
2C29×#1959C211yesmaximal, characteristic
3C29×#1847C211yesmaximal, characteristic, complemented
4C29×#1836C211yesmaximal, characteristic, complemented
5C2×C29×#329C211yesmaximal, characteristic
6C29×#1295C211yesmaximal, characteristic, complemented
7C29×#1295C211yesmaximal, characteristic, complemented
8C2×C29×#124C2211yescharacteristic
9C2×C29×#107—21no—
10C2×C29×#106—21no—
11C2×C29×#103—21no—
12C2×C29×#102—21no—
13C2×C29×#97C2211yescharacteristic
14C2×C29×#97C2211yescharacteristic
15C2×C29×#97C2211yescharacteristic
16C29×#391—21no—
17C29×#388—21no—
18C29×#388—21no—
19C29×#386—21no—
20C29×#385—21no—
21C29×#385—21no—
22C29×#384C2211yescharacteristic
23C29×#382C2211yescharacteristic
24C29×#382C2211yescharacteristic
25C29×#340—21no—
26C29×#340—21no—
27C29×#329C414yescomplemented
28C22×Q8×C29D411yescharacteristic
29C22×D4×C29D411yescharacteristic
30C23×C4×C29—21no—
31C22×C8×C29—21no—
32C22×C8×C29—21no—
33C22×C8×C29—21no—
34C29×#124—21no—
35C29×#124—21no—
36C29×#124C2×C412yes—
37C29×#124Q812yes—
38C2×C4⋊C4×C29—21no—
39C2×C4⋊C4×C29—21no—
40C2×C4⋊C4×C29—21no—
41C2×C4⋊C4×C29—21no—
42C2×C4⋊C4×C29D411yescharacteristic
43C2×C4⋊C4×C29D411yescharacteristic
44C2×C4⋊C4×C29D411yescharacteristic
45C2×C4⋊C4×C29D411yescharacteristic
46C2×C22⋊C4×C29—21no—
47C2×C22⋊C4×C29—21no—
48C2×C22⋊C4×C29—21no—
49C2×C22⋊C4×C29—21no—
50C2×C22⋊C4×C29—21no—
51C2×C42×C29—21no—
52C2×C42×C29C2311yescharacteristic
53C29×#107—42no—
54C29×#106—42no—
55C29×#103—42no—
56C29×#102—42no—
57C29×#97—21no—
58C29×#97—21no—
59C29×#97—21no—
60C29×#97—21no—
61C29×#97C2×C412yescomplemented
62C29×#97C2×C412yescomplemented
63C29×#95—21no—
64C29×#95—21no—
65C29×#95—21no—
66C29×#95—21no—
67C29×#95—21no—
68C29×#95—21no—
69C24×C29—21no—
70C2×Q8×C29—21no—
71C2×Q8×C29—41no—
72C2×Q8×C29—41no—
73C2×Q8×C29C4⋊C412yes—
74C2×D4×C29—21no—
75C2×D4×C29—41no—
76C2×D4×C29—41no—
77C2×D4×C29C4⋊C412yes—
78C22×C4×C29—21no—
79C22×C4×C29—21no—
80C22×C4×C29—21no—
81C22×C4×C29—21no—
82C22×C4×C29—21no—
83C22×C4×C29—41no—
84C22×C4×C29—81no—
85C22×C4×C29—81no—
86C22×C4×C29—81no—
87C22×C4×C29C2×D411yescharacteristic
88C22×C4×C29C2×D411yescharacteristic
89C22×C4×C29C2×D411yescharacteristic
90C2×C8×C29—22no—
91C2×C8×C29—22no—
92C2×C8×C29—22no—
93C2×C8×C29—22no—
94C2×C8×C29—22no—
95C2×C8×C29—41no—
96C2×C8×C29—41no—
97C2×C8×C29—41no—
98C2×C8×C29—41no—
99C4⋊C4×C29—41no—
100C4⋊C4×C29—41no—
101C4⋊C4×C29—41no—
102C4⋊C4×C29—41no—
103C4⋊C4×C29—42no—
104C4⋊C4×C29—41no—
105C4⋊C4×C29—41no—
106C4⋊C4×C29—41no—
107C4⋊C4×C29—41no—
108C4⋊C4×C29—81no—
109C22⋊C4×C29—22no—
110C22⋊C4×C29—22no—
111C22⋊C4×C29—22no—
112C22⋊C4×C29—22no—
113C22⋊C4×C29—81no—
114C22⋊C4×C29—81no—
115C22⋊C4×C29—81no—
116C42×C29—81no—
117C42×C29C22×C411yescharacteristic
118C42×C29C2×Q811yescharacteristic
119C42×C29#4111yescharacteristic
120C42×C29#4111yescharacteristic
121#8911C2911yesmaximal, characteristic, direct product factor, Sylow
122C23×C29—22no—
123C23×C29—41no—
124C23×C29—41no—
125C23×C29—41no—
126C23×C29—41no—
127C23×C29—41no—
128C23×C29—41no—
129C23×C29#12011yescharacteristic
130Q8×C29—42no—
131Q8×C29—81no—
132D4×C29—42no—
133D4×C29—81no—
134C2×C4×C29—21no—
135C2×C4×C29—21no—
136C2×C4×C29—21no—
137C2×C4×C29—21no—
138C2×C4×C29—21no—
139C2×C4×C29—21no—
140C2×C4×C29—22no—
141C2×C4×C29—41no—
142C2×C4×C29—41no—
143C2×C4×C29—41no—
144C2×C4×C29—41no—
145C2×C4×C29—41no—
146C2×C4×C29—41no—
147C2×C4×C29—41no—
148C2×C4×C29—41no—
149C2×C4×C29—41no—
150C2×C4×C29—41no—
151C2×C4×C29—41no—
152C2×C4×C29—41no—
153C2×C4×C29—41no—
154C2×C4×C29—41no—
155C2×C4×C29—84no—
156C2×C4×C29—81no—
157C2×C4×C29—81no—
158C2×C4×C29—81no—
159C2×C4×C29C2×C4⋊C411yescharacteristic
160C2×C4×C29C4×D411yescharacteristic
161C2×C4×C29C4×D411yescharacteristic
162C2×C4×C29C22⋊Q811yescharacteristic
163C2×C4×C29C22⋊Q811yescharacteristic
164C2×C4×C29#12311yescharacteristic
165C8×C29—24no—
166C8×C29—42no—
167C8×C29—42no—
168#2379C2×C2911yescharacteristic
169#1959C2×C2911yescharacteristic
170#1847C2×C2911yescharacteristic, complemented
171#1836C2×C2911yescharacteristic, complemented
172C2×#329C2×C2911yescharacteristic
173#1295C2×C2911yescharacteristic, complemented
174#1295C2×C2911yescharacteristic, complemented
175C22×C29—42no—
176C22×C29—42no—
177C22×C29—42no—
178C22×C29—81no—
179C22×C29—81no—
180C22×C29—81no—
181C22×C29—81no—
182C22×C29#38511yescharacteristic
183C22×C29#45311yescharacteristic
184C22×C29#45311yescharacteristic
185C22×C29#45411yescharacteristic
186C22×C29#45511yescharacteristic
187C22×C29#45511yescharacteristic
188C22×C29#45611yescharacteristic
189C4×C29—21no—
190C4×C29—21no—
191C4×C29—21no—
192C4×C29—21no—
193C4×C29—21no—
194C4×C29—21no—
195C4×C29—42no—
196C4×C29—81no—
197C4×C29—81no—
198C4×C29—81no—
199C4×C29—81no—
200C4×C29—161no—
201C2×#124C22×C2911yescharacteristic
202C2×#107—21no—
203C2×#106—21no—
204C2×#103—21no—
205C2×#102—21no—
206C2×#97C22×C2911yescharacteristic
207C2×#97C22×C2911yescharacteristic
208C2×#97C22×C2911yescharacteristic
209#391—21no—
210#388—21no—
211#388—21no—
212#386—21no—
213#385—21no—
214#385—21no—
215#384C22×C2911yescharacteristic
216#382C22×C2911yescharacteristic
217#382C22×C2911yescharacteristic
218#340—21no—
219#340—21no—
220#329C4×C2914yescomplemented
221C2×C29—82no—
222C2×C29#165611yescharacteristic
223C2×C29#165911yescharacteristic
224C2×C29#166111yescharacteristic
225C2×C29#166411yescharacteristic
226C2×C29#185611yescharacteristic
227C2×C29#185911yescharacteristic
228C2×C29#186011yescharacteristic
229C22×Q8D4×C2911yescharacteristic
230C22×D4D4×C2911yescharacteristic
231C23×C4—21no—
232C22×C8—21no—
233C22×C8—21no—
234C22×C8—21no—
235#124—21no—
236#124—21no—
237#124C2×C4×C2912yes—
238#124Q8×C2912yes—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4D4×C2911yescharacteristic
244C2×C4⋊C4D4×C2911yescharacteristic
245C2×C4⋊C4D4×C2911yescharacteristic
246C2×C4⋊C4D4×C2911yescharacteristic
247C2×C22⋊C4—21no—
248C2×C22⋊C4—21no—
249C2×C22⋊C4—21no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—21no—
252C2×C42—21no—
253C2×C42C23×C2911yescharacteristic
254#107—42no—
255#106—42no—
256#103—42no—
257#102—42no—
258#97—21no—
259#97—21no—
260#97—21no—
261#97—21no—
262#97C2×C4×C2912yescomplemented
263#97C2×C4×C2912yescomplemented
264#95—21no—
265#95—21no—
266#95—21no—
267#95—21no—
268#95—21no—
269#95—21no—
270C29#891111yescharacteristic, direct product factor, Sylow
271C24—21no—
272C2×Q8—21no—
273C2×Q8—41no—
274C2×Q8—41no—
275C2×Q8C4⋊C4×C2912yes—
276C2×D4—21no—
277C2×D4—41no—
278C2×D4—41no—
279C2×D4C4⋊C4×C2912yes—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—41no—
286C22×C4—81no—
287C22×C4—81no—
288C22×C4—81no—
289C22×C4C2×D4×C2911yescharacteristic
290C22×C4C2×D4×C2911yescharacteristic
291C22×C4C2×D4×C2911yescharacteristic
292C2×C8—22no—
293C2×C8—22no—
294C2×C8—22no—
295C2×C8—22no—
296C2×C8—22no—
297C2×C8—41no—
298C2×C8—41no—
299C2×C8—41no—
300C2×C8—41no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4—42no—
310C4⋊C4—81no—
311C22⋊C4—22no—
312C22⋊C4—22no—
313C22⋊C4—22no—
314C22⋊C4—22no—
315C22⋊C4—81no—
316C22⋊C4—81no—
317C22⋊C4—81no—
318C42—81no—
319C42C22×C4×C2911yescharacteristic
320C42C2×Q8×C2911yescharacteristic
321C42#41×C2911yescharacteristic
322C42#41×C2911yescharacteristic
323C23—22no—
324C23—41no—
325C23—41no—
326C23—41no—
327C23—41no—
328C23—41no—
329C23—41no—
330C23C29×#12011yescharacteristic
331Q8—42no—
332Q8—81no—
333D4—42no—
334D4—81no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—22no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—84no—
357C2×C4—81no—
358C2×C4—81no—
359C2×C4—81no—
360C2×C4C2×C4⋊C4×C2911yescharacteristic
361C2×C4C4×D4×C2911yescharacteristic
362C2×C4C4×D4×C2911yescharacteristic
363C2×C4C29×C22⋊Q811yescharacteristic
364C2×C4C29×C22⋊Q811yescharacteristic
365C2×C4C29×#12311yescharacteristic
366C8—24no—
367C8—42no—
368C8—42no—
369C22—42no—
370C22—42no—
371C22—42no—
372C22—81no—
373C22—81no—
374C22—81no—
375C22—81no—
376C22C29×#38511yescharacteristic
377C22C29×#45311yescharacteristic
378C22C29×#45311yescharacteristic
379C22C29×#45411yescharacteristic
380C22C29×#45511yescharacteristic
381C22C29×#45511yescharacteristic
382C22C29×#45611yescharacteristic
383C4—21no—
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—21no—
389C4—42no—
390C4—81no—
391C4—81no—
392C4—81no—
393C4—81no—
394C4—161no—
395C2—82no—
396C2C29×#165611yescharacteristic
397C2C29×#165911yescharacteristic
398C2C29×#166111yescharacteristic
399C2C29×#166411yescharacteristic
400C2C29×#185611yescharacteristic
401C2C29×#185911yescharacteristic
402C2C29×#186011yescharacteristic
subgroupG/H
center, socleC23×C29#120
commutatorC42C22×C4×C29
Frattini, cosocleC2×C42C23×C29
prime radicalC22×D4×C29D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C29 ◁ C2×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
3. C29×#1847C2semidirect
4. C29×#1836C2semidirect
6. C29×#1295C2semidirect
7. C29×#1295C2semidirect
27. C29×#329C4semidirect
61. C29×#97C2×C4semidirect
62. C29×#97C2×C4semidirect
121. #8911C29direct (N × H)
170. #1847C2×C29semidirect
171. #1836C2×C29semidirect
173. #1295C2×C29semidirect
174. #1295C2×C29semidirect
220. #329C4×C29semidirect
262. #97C2×C4×C29semidirect
263. #97C2×C4×C29semidirect
270. C29#8911direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#23792
C29×#19592
C29×#18472
C29×#18362
C2×C29×#3292
C29×#12952
#891129