Finite Group Databasebeta

← #46821055

Subgroups — #46821055

Order 34432.

386 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771134C211yesmaximal, characteristic
2C4×Q8×D269C211yesmaximal, characteristic, complemented
3#31770939C211yesmaximal, characteristic, complemented
4#31770922C211yesmaximal, characteristic
5#31770913C211yesmaximal, characteristic, complemented
6#31770912C211yesmaximal, characteristic, complemented
7#31770824C211yesmaximal, characteristic, complemented
8#31770759C211yesmaximal, characteristic, complemented
9#31770742C211yesmaximal, characteristic
10#31770712C211yesmaximal, characteristic, complemented
11#31770709C211yesmaximal, characteristic, complemented
12#31770706C211yesmaximal, characteristic, complemented
13#31770702C211yesmaximal, characteristic, complemented
14#31770661C211yesmaximal, characteristic, complemented
15#464×C269C211yesmaximal, characteristic, complemented
16C2×Q8×D269C2211yescharacteristic
17C2×#16864392C2211yescharacteristic
18C2×#16864390C2211yescharacteristic
19#22575446—21no—
20#22575445C2211yescharacteristic
21#22575435—21no—
22#22575429C2211yescharacteristic
23#22575424C2211yescharacteristic
24Q8×Dic269C2211yescharacteristic
25Q8×Dic269C2211yescharacteristic
26C4×Dic538—21no—
27C4×Dic538C2211yescharacteristic
28#22575418—21no—
29#22575418C2211yescharacteristic
30D4×Dic269C2211yescharacteristic
31#22575413—21no—
32#22575409—21no—
33C4⋊C4×D269—21no—
34C4⋊C4×D269C2211yescharacteristic
35C42×D269—21no—
36C42×D269C2211yescharacteristic
37#22575387C2211yescharacteristic
38#22575386C2211yescharacteristic
39#22575385C2211yescharacteristic
40#22575384C2211yescharacteristic
41C4⋊#14524130C2211yescharacteristic
42#22575378C2211yescharacteristic
43#22575378C2211yescharacteristic
44#22575377C2211yescharacteristic
45#22575377C2211yescharacteristic
46#22575377C2211yescharacteristic
47#22575374C2211yescharacteristic
48#22575365C2211yescharacteristic
49#22575365C2211yescharacteristic
50#22575363C2211yescharacteristic
51#22575363C2211yescharacteristic
52C2×Q16×C269C2211yescharacteristic
53C2×SD16×C269C2211yescharacteristic
54#124×C269C2211yescharacteristic
55C4×Q8×C269C2211yescharacteristic
56C4⋊C8×C269C2211yescharacteristic
57#103×C269C2211yescharacteristic
58#102×C269C2211yescharacteristic
59C2×Dic538—21no—
60C2×Dic538C2311yescharacteristic
61Q8×D269—22no—
62Q8×D269—22no—
63C2×C22⋊D269—21no—
64C22×Dic269—21no—
65C2×C4×D269—21no—
66C2×C4×D269—21no—
67C2×C4×D269D411yescharacteristic
68C2×C4×D269D411yescharacteristic
69C2×C4×D269C2311yescharacteristic
70#16864392—22no—
71#16864390—22no—
72C2×#14524130C2311yescharacteristic
73C2×#14524130C2311yescharacteristic
74C4⋊Dic269—21no—
75C4⋊Dic269—21no—
76C4⋊Dic269C2311yescharacteristic
77C4⋊Dic269C2311yescharacteristic
78C4⋊Dic269C2311yescharacteristic
79#16864381—21no—
80#16864381—21no—
81#16864381—21no—
82#16864381—21no—
83#16864381—21no—
84#16864381—21no—
85C22⋊Dic269—21no—
86C22⋊Dic269—21no—
87#16864379—21no—
88C4×Dic269—21no—
89C4×Dic269—21no—
90C4×Dic269—21no—
91C4×Dic269—21no—
92C4×Dic269D411yescharacteristic
93C4×Dic269D411yescharacteristic
94C4×Dic269C2311yescharacteristic
95C2×Q8×C269C2311yescharacteristic
96C2×Q8×C269C2311yescharacteristic
97C2×D4×C269C2311yescharacteristic
98Q16×C269—22no—
99SD16×C269—22no—
100C2×C8×C269C2311yescharacteristic
101C2×C8×C269C2311yescharacteristic
102C4⋊C4×C269—21no—
103C4⋊C4×C269C2311yescharacteristic
104C22⋊C4×C269—21no—
105C22⋊C4×C269—21no—
106C42×C269—21no—
107C42×C269C2311yescharacteristic
108C22×D269C2×D411yescharacteristic
109Dic538—24no—
110Dic538—21no—
111Dic538#4112yes—
112C22⋊D269—42no—
113C2×Dic269—21no—
114C2×Dic269—21no—
115C2×Dic269—21no—
116C2×Dic269—21no—
117C2×Dic269—42no—
118C2×Dic269C2×D411yescharacteristic
119C2×Dic269C2×D411yescharacteristic
120C2×Dic269C2×D411yescharacteristic
121C4×D269—24no—
122C4×D269—22no—
123C4×D269—21no—
124C4×D269—21no—
125C4×D269—41no—
126C4×D269—42no—
127#14524130—21no—
128#14524130—21no—
129C23×C269—21no—
130Q8×C269—21no—
131Q8×C269—21no—
132Q8×C269—21no—
133Q8×C269#4112yes—
134D4×C269—21no—
135D4×C269—21no—
136C2×C4×C269—21no—
137C2×C4×C269—21no—
138C2×C4×C269—21no—
139C2×C4×C269C2×D411yescharacteristic
140C2×C4×C269C2×D411yescharacteristic
141C2×C4×C269C2411yescharacteristic
142C8×C269—21no—
143C8×C269—21no—
144C22×C269—41no—
145C22×C269—41no—
146C22×C269—41no—
147C22×C269C22×D411yescharacteristic
148C2×D269—21no—
149C2×D269—21no—
150C2×D269#13712yes—
151C4×C269—22no—
152C4×C269—21no—
153C4×C269—21no—
154C4×C269—41no—
155C4×C269—41no—
156C4×C269C2×#4111yescharacteristic
157C4×C269C2×#4111yescharacteristic
158Dic269—22no—
159Dic269—21no—
160Dic269—21no—
161Dic269—21no—
162Dic269—41no—
163Dic269—41no—
164Dic269—41no—
165C2×C269—81no—
166C2×C269#52511yescharacteristic
167C2×C269C2×#13711yescharacteristic
168C2×C269#57511yescharacteristic
169D269—22no—
170C269#311711yescharacteristic, complemented, Sylow
171#3117—2691nomaximal, Sylow
172#529—2691no—
173C2×C4×Q8—2691no—
174#484—2691no—
175#481—2691no—
176#479—2691no—
177#479—2691no—
178#464—2691no—
179#464D26911yescharacteristic, complemented
180#451—2691no—
181#448—2691no—
182#441—2691no—
183#441—2691no—
184#440—2691no—
185#440—2691no—
186#432—2691no—
187C22×Q8—2691no—
188C2×Q16—2691no—
189C2×Q16C2×D26911yescharacteristic
190C2×SD16—2691no—
191C2×SD16C2×D26911yescharacteristic
192#126—5381no—
193#125—2691no—
194#124C2×D26911yescharacteristic
195#123—5381no—
196C22⋊Q8—2691no—
197#121—2691no—
198C4×Q8—2691no—
199C4×Q8—2691no—
200C4×Q8—2691no—
201C4×Q8—2691no—
202C4×Q8—5381no—
203C4×Q8—5381no—
204C4×Q8C2×D26911yescharacteristic
205C4×D4—2691no—
206C4×D4—5381no—
207#117—5381no—
208C2×C4⋊C4—2691no—
209C2×C4⋊C4—5381no—
210C2×C42—2691no—
211C2×C42—5381no—
212#107—2691no—
213#107—2691no—
214#106—2691no—
215#106—2691no—
216C4⋊C8—2691no—
217C4⋊C8C2×D26911yescharacteristic
218#103—2691no—
219#103—2691no—
220#103—2691no—
221#103—2691no—
222#103—2691no—
223#103C2×D26911yescharacteristic
224#102—2691no—
225#102C2×D26911yescharacteristic
226C22⋊C8—2691no—
227C22⋊C8—2691no—
228#97—2691no—
229#97—2691no—
230C2×Q8—2691no—
231C2×Q8—5381no—
232C2×Q8—5382no—
233C2×Q8—5382no—
234C2×Q8C22×D26911yescharacteristic
235C2×Q8C22×D26911yescharacteristic
236C2×D4—5381no—
237C2×D4C22×D26911yescharacteristic
238C22×C4—2691no—
239C22×C4—2691no—
240C22×C4—2691no—
241C22×C4—5381no—
242C22×C4—5381no—
243C22×C4—5381no—
244Q16—22no—
245Q16—5382no—
246SD16—22no—
247SD16—5382no—
248C2×C8—2691no—
249C2×C8—2691no—
250C2×C8C22×D26911yescharacteristic
251C2×C8C22×D26911yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—2691no—
254C4⋊C4—2691no—
255C4⋊C4—2691no—
256C4⋊C4—5381no—
257C4⋊C4—5381no—
258C4⋊C4—5381no—
259C4⋊C4—5381no—
260C4⋊C4—5381no—
261C4⋊C4—5381no—
262C4⋊C4—5381no—
263C4⋊C4—5381no—
264C4⋊C4C22×D26911yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—5381no—
268C22⋊C4—5381no—
269C22⋊C4—5381no—
270C42—21no—
271C42—2691no—
272C42—2691no—
273C42—2691no—
274C42—5381no—
275C42—5381no—
276C42—5381no—
277C42—5381no—
278C42C22×D26911yescharacteristic
279C23—21no—
280C23—2691no—
281Q8—21no—
282Q8—21no—
283Q8—21no—
284Q8—2692no—
285Q8—5384no—
286Q8—5381no—
287Q8#1686440112yes—
288D4—21no—
289D4—21no—
290D4—10762no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—2691no—
295C2×C4—2691no—
296C2×C4—2691no—
297C2×C4—5382no—
298C2×C4—5384no—
299C2×C4—5381no—
300C2×C4—5381no—
301C2×C4—5381no—
302C2×C4—5381no—
303C2×C4—5381no—
304C2×C4—5381no—
305C2×C4—10761no—
306C2×C4—10762no—
307C2×C4—10762no—
308C2×C4D4×D26911yescharacteristic
309C2×C4D4×D26911yescharacteristic
310C2×C4C23×D26911yescharacteristic
311C8—21no—
312C8—21no—
313C8—5381no—
314C8—5381no—
315C22—41no—
316C22—41no—
317C22—41no—
318C22—2692no—
319C22—5381no—
320C22—5381no—
321C22C2×D4×D26911yescharacteristic
322C4—21no—
323C4—21no—
324C4—22no—
325C4—41no—
326C4—41no—
327C4—5381no—
328C4—5381no—
329C4—5381no—
330C4—5382no—
331C4—10761no—
332C4—10761no—
333C4—10761no—
334C4#41×D26911yescharacteristic
335C4C2×#1686440111yescharacteristic
336C2—81no—
337C2—5382no—
338C2#3177111511yescharacteristic
339C2#137×D26911yescharacteristic
340C2#3177140211yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#464×C269C2
socleC22×C269C22×D4
prime radical#22575424C22
hypercenter#464D269
hypocenterC269#3117
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
2. C4×Q8×D269C2semidirect
3. #31770939C2semidirect
5. #31770913C2semidirect
6. #31770912C2semidirect
7. #31770824C2semidirect
8. #31770759C2semidirect
10. #31770712C2semidirect
11. #31770709C2semidirect
12. #31770706C2semidirect
13. #31770702C2semidirect
14. #31770661C2semidirect
15. #464×C269C2semidirect
170. C269#3117semidirect
179. #464D269semidirect

Maximal subgroups

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

subgroupindex
#317711342
C4×Q8×D2692
#317709392
#317709222
#317709132
#317709122
#317708242
#317707592
#317707422
#317707122
#317707092
#317707062
#317707022
#317706612
#464×C2692
#3117269