Finite Group Databasebeta

← #3301×C229 #44420362

Subgroups — #3301×C229 #44420362

Order 29312.

398 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#553×C229C211yesmaximal, characteristic, complemented
2#548×C229C211yesmaximal, characteristic, complemented
3#488×C229C211yesmaximal, characteristic, complemented
4#485×C229C211yesmaximal, characteristic, complemented
5#481×C229C211yesmaximal, characteristic, complemented
6#479×C229C211yesmaximal, characteristic, complemented
7#466×C229C211yesmaximal, characteristic, complemented
8#465×C229C211yesmaximal, characteristic, complemented
9#463×C229C211yesmaximal, characteristic, complemented
10#449×C229C211yesmaximal, characteristic, complemented
11#448×C229C211yesmaximal, characteristic, complemented
12C4×SD16×C229C211yesmaximal, characteristic, complemented
13C8×D4×C229C211yesmaximal, characteristic, complemented
14#416×C229C211yesmaximal, characteristic, complemented
15C2×#103×C229C211yesmaximal, characteristic, complemented
16C2×#41×C229C2211yescharacteristic
17C22×Q8×C229C2211yescharacteristic
18C2×SD16×C229C2211yescharacteristic
19C2×SD16×C229C2211yescharacteristic
20C2×D8×C229C2211yescharacteristic
21C22×C8×C229C2211yescharacteristic
22C22×C8×C229C2211yescharacteristic
23#126×C229—21no—
24#125×C229C2211yescharacteristic
25#124×C229—21no—
26#124×C229C2211yescharacteristic
27#123×C229—21no—
28C22⋊Q8×C229—21no—
29C22⋊Q8×C229C2211yescharacteristic
30#121×C229—21no—
31#121×C229—21no—
32#121×C229C2211yescharacteristic
33#121×C229C2211yescharacteristic
34#121×C229C2211yescharacteristic
35C4×Q8×C229C2211yescharacteristic
36C4×D4×C229—21no—
37C4×D4×C229—21no—
38C4×D4×C229C2211yescharacteristic
39C4×D4×C229C2211yescharacteristic
40#117×C229C2211yescharacteristic
41C2×C4⋊C4×C229C2211yescharacteristic
42#107×C229C2211yescharacteristic
43#106×C229C2211yescharacteristic
44#106×C229C2211yescharacteristic
45C4⋊C8×C229C2211yescharacteristic
46#103×C229C2211yescharacteristic
47#103×C229C2211yescharacteristic
48#103×C229C2211yescharacteristic
49#103×C229C2211yescharacteristic
50#103×C229C2211yescharacteristic
51#103×C229C2211yescharacteristic
52#102×C229C2211yescharacteristic
53#102×C229C2211yescharacteristic
54#102×C229C2211yescharacteristic
55#102×C229C2211yescharacteristic
56C22⋊C8×C229C2211yescharacteristic
57C22⋊C8×C229C2211yescharacteristic
58C4×C8×C229C2211yescharacteristic
59#41×C229—22no—
60#41×C229—41no—
61C2×Q8×C229—21no—
62C2×Q8×C229—22no—
63C2×Q8×C229—41no—
64C2×Q8×C229C2311yescharacteristic
65C2×Q8×C229C2311yescharacteristic
66C2×D4×C229—21no—
67C2×D4×C229—21no—
68C2×D4×C229—21no—
69C2×D4×C229—21no—
70C2×D4×C229D411yescharacteristic
71C2×D4×C229C2311yescharacteristic
72C2×D4×C229C2311yescharacteristic
73C22×C4×C229—21no—
74C22×C4×C229—21no—
75C22×C4×C229—21no—
76C22×C4×C229—21no—
77C22×C4×C229C2311yescharacteristic
78C22×C4×C229C2311yescharacteristic
79SD16×C229—22no—
80SD16×C229—41no—
81D8×C229—41no—
82C2×C8×C229—41no—
83C2×C8×C229—41no—
84C2×C8×C229C2311yescharacteristic
85C2×C8×C229C2311yescharacteristic
86C2×C8×C229C2311yescharacteristic
87C2×C8×C229C2311yescharacteristic
88C4⋊C4×C229—21no—
89C4⋊C4×C229—21no—
90C4⋊C4×C229—21no—
91C4⋊C4×C229—21no—
92C4⋊C4×C229—21no—
93C4⋊C4×C229D411yescharacteristic
94C4⋊C4×C229C2311yescharacteristic
95C4⋊C4×C229C2311yescharacteristic
96C4⋊C4×C229C2311yescharacteristic
97C4⋊C4×C229C2311yescharacteristic
98C22⋊C4×C229—21no—
99C22⋊C4×C229—21no—
100C22⋊C4×C229—21no—
101C22⋊C4×C229—21no—
102C22⋊C4×C229—21no—
103C22⋊C4×C229—21no—
104C22⋊C4×C229—21no—
105C22⋊C4×C229—21no—
106C22⋊C4×C229D411yescharacteristic
107C22⋊C4×C229D411yescharacteristic
108C42×C229—21no—
109C42×C229—21no—
110C42×C229C2311yescharacteristic
111C23×C229—21no—
112C23×C229—21no—
113C23×C229C2×D411yescharacteristic
114C23×C229C2×D411yescharacteristic
115Q8×C229—21no—
116Q8×C229—21no—
117Q8×C229—21no—
118Q8×C229—42no—
119Q8×C229#4112yes—
120D4×C229—22no—
121D4×C229—21no—
122D4×C229—21no—
123D4×C229—21no—
124D4×C229—21no—
125D4×C229—42no—
126D4×C229—42no—
127D4×C229—42no—
128D4×C229—81no—
129C2×C4×C229—21no—
130C2×C4×C229—21no—
131C2×C4×C229—21no—
132C2×C4×C229—21no—
133C2×C4×C229—21no—
134C2×C4×C229—21no—
135C2×C4×C229—21no—
136C2×C4×C229—21no—
137C2×C4×C229—21no—
138C2×C4×C229—21no—
139C2×C4×C229—42no—
140C2×C4×C229—42no—
141C2×C4×C229—81no—
142C2×C4×C229—81no—
143C2×C4×C229C2×D411yescharacteristic
144C2×C4×C229C2×D411yescharacteristic
145C2×C4×C229C2×D411yescharacteristic
146C2×C4×C229C2×D411yescharacteristic
147C2×C4×C229C2411yescharacteristic
148C8×C229—21no—
149C8×C229—21no—
150C8×C229—21no—
151C8×C229—21no—
152C22×C229—21no—
153C22×C229—21no—
154C22×C229—21no—
155C22×C229—21no—
156C22×C229—21no—
157C22×C229—41no—
158C22×C229—41no—
159C22×C229—41no—
160C22×C229—41no—
161C22×C229—41no—
162C22×C229—41no—
163C22×C229#13512yes—
164C22×C229C22×D411yescharacteristic
165C4×C229—21no—
166C4×C229—21no—
167C4×C229—22no—
168C4×C229—21no—
169C4×C229—21no—
170C4×C229—41no—
171C4×C229—41no—
172C4×C229—41no—
173C4×C229—41no—
174C4×C229—41no—
175C4×C229C2×#4111yescharacteristic
176C4×C229H(5,𝔽2)11yescharacteristic
177C2×C229—22no—
178C2×C229—41no—
179C2×C229—81no—
180C2×C229—81no—
181C2×C229#54611yescharacteristic
182C2×C229C2×#13511yescharacteristic
183C2×C229#57711yescharacteristic
184C229#330111yescharacteristic, direct product factor, Sylow
185#3301C22911yesmaximal, characteristic, direct product factor, Sylow
186#553C2×C22911yescharacteristic, complemented
187#548C2×C22911yescharacteristic, complemented
188#488C2×C22911yescharacteristic, complemented
189#485C2×C22911yescharacteristic, complemented
190#481C2×C22911yescharacteristic, complemented
191#479C2×C22911yescharacteristic, complemented
192#466C2×C22911yescharacteristic, complemented
193#465C2×C22911yescharacteristic, complemented
194#463C2×C22911yescharacteristic, complemented
195#449C2×C22911yescharacteristic, complemented
196#448C2×C22911yescharacteristic, complemented
197C4×SD16C2×C22911yescharacteristic, complemented
198C8×D4C2×C22911yescharacteristic, complemented
199#416C2×C22911yescharacteristic, complemented
200C2×#103C2×C22911yescharacteristic, complemented
201C2×#41C22×C22911yescharacteristic
202C22×Q8C22×C22911yescharacteristic
203C2×SD16C22×C22911yescharacteristic
204C2×SD16C22×C22911yescharacteristic
205C2×D8C22×C22911yescharacteristic
206C22×C8C22×C22911yescharacteristic
207C22×C8C22×C22911yescharacteristic
208#126—21no—
209#125C22×C22911yescharacteristic
210#124—21no—
211#124C22×C22911yescharacteristic
212#123—21no—
213C22⋊Q8—21no—
214C22⋊Q8C22×C22911yescharacteristic
215#121—21no—
216#121—21no—
217#121C22×C22911yescharacteristic
218#121C22×C22911yescharacteristic
219#121C22×C22911yescharacteristic
220C4×Q8C22×C22911yescharacteristic
221C4×D4—21no—
222C4×D4—21no—
223C4×D4C22×C22911yescharacteristic
224C4×D4C22×C22911yescharacteristic
225#117C22×C22911yescharacteristic
226C2×C4⋊C4C22×C22911yescharacteristic
227#107C22×C22911yescharacteristic
228#106C22×C22911yescharacteristic
229#106C22×C22911yescharacteristic
230C4⋊C8C22×C22911yescharacteristic
231#103C22×C22911yescharacteristic
232#103C22×C22911yescharacteristic
233#103C22×C22911yescharacteristic
234#103C22×C22911yescharacteristic
235#103C22×C22911yescharacteristic
236#103C22×C22911yescharacteristic
237#102C22×C22911yescharacteristic
238#102C22×C22911yescharacteristic
239#102C22×C22911yescharacteristic
240#102C22×C22911yescharacteristic
241C22⋊C8C22×C22911yescharacteristic
242C22⋊C8C22×C22911yescharacteristic
243C4×C8C22×C22911yescharacteristic
244#41—22no—
245#41—41no—
246C2×Q8—21no—
247C2×Q8—22no—
248C2×Q8—41no—
249C2×Q8C23×C22911yescharacteristic
250C2×Q8C23×C22911yescharacteristic
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—21no—
254C2×D4—21no—
255C2×D4D4×C22911yescharacteristic
256C2×D4C23×C22911yescharacteristic
257C2×D4C23×C22911yescharacteristic
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4C23×C22911yescharacteristic
263C22×C4C23×C22911yescharacteristic
264SD16—22no—
265SD16—41no—
266D8—41no—
267C2×C8—41no—
268C2×C8—41no—
269C2×C8C23×C22911yescharacteristic
270C2×C8C23×C22911yescharacteristic
271C2×C8C23×C22911yescharacteristic
272C2×C8C23×C22911yescharacteristic
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4D4×C22911yescharacteristic
279C4⋊C4C23×C22911yescharacteristic
280C4⋊C4C23×C22911yescharacteristic
281C4⋊C4C23×C22911yescharacteristic
282C4⋊C4C23×C22911yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4D4×C22911yescharacteristic
292C22⋊C4D4×C22911yescharacteristic
293C42—21no—
294C42—21no—
295C42C23×C22911yescharacteristic
296C23—21no—
297C23—21no—
298C23C2×D4×C22911yescharacteristic
299C23C2×D4×C22911yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—21no—
303Q8—42no—
304Q8#41×C22912yes—
305D4—22no—
306D4—21no—
307D4—21no—
308D4—21no—
309D4—21no—
310D4—42no—
311D4—42no—
312D4—42no—
313D4—81no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—81no—
327C2×C4—81no—
328C2×C4C2×D4×C22911yescharacteristic
329C2×C4C2×D4×C22911yescharacteristic
330C2×C4C2×D4×C22911yescharacteristic
331C2×C4C2×D4×C22911yescharacteristic
332C2×C4C24×C22911yescharacteristic
333C8—21no—
334C8—21no—
335C8—21no—
336C8—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22#135×C22912yes—
349C22C22×D4×C22911yescharacteristic
350C4—21no—
351C4—21no—
352C4—22no—
353C4—21no—
354C4—21no—
355C4—41no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4C2×#41×C22911yescharacteristic
361C4H(5,𝔽2)×C22911yescharacteristic
362C2—22no—
363C2—41no—
364C2—81no—
365C2—81no—
366C2#546×C22911yescharacteristic
367C2C2×#135×C22911yescharacteristic
368C2#577×C22911yescharacteristic
subgroupG/H
center, socleC22×C229C22×D4
commutator, Frattini, cosocleC2×C4C24×C229
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C229 ◁ C4×D4×C229 ◁ G

Complements

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

NH ≅ G/Ntype
1. #553×C229C2semidirect
2. #548×C229C2semidirect
3. #488×C229C2semidirect
4. #485×C229C2semidirect
5. #481×C229C2semidirect
6. #479×C229C2semidirect
7. #466×C229C2semidirect
8. #465×C229C2semidirect
9. #463×C229C2semidirect
10. #449×C229C2semidirect
11. #448×C229C2semidirect
12. C4×SD16×C229C2semidirect
13. C8×D4×C229C2semidirect
14. #416×C229C2semidirect
15. C2×#103×C229C2semidirect
184. C229#3301direct (N × H)
185. #3301C229direct (N × H)
186. #553C2×C229semidirect
187. #548C2×C229semidirect
188. #488C2×C229semidirect
189. #485C2×C229semidirect
190. #481C2×C229semidirect
191. #479C2×C229semidirect
192. #466C2×C229semidirect
193. #465C2×C229semidirect
194. #463C2×C229semidirect
195. #449C2×C229semidirect
196. #448C2×C229semidirect
197. C4×SD16C2×C229semidirect
198. C8×D4C2×C229semidirect
199. #416C2×C229semidirect
200. C2×#103C2×C229semidirect

Maximal subgroups

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

subgroupindex
#553×C2292
#548×C2292
#488×C2292
#485×C2292
#481×C2292
#479×C2292
#466×C2292
#465×C2292
#463×C2292
#449×C2292
#448×C2292
C4×SD16×C2292
C8×D4×C2292
#416×C2292
C2×#103×C2292
#3301229