Finite Group Databasebeta

← #46822299

Subgroups — #46822299

Order 34432.

358 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771228C211yesmaximal, characteristic, complemented
2#31771208C211yesmaximal, characteristic, complemented
3#31770914C211yesmaximal, characteristic, complemented
4#31770904C211yesmaximal, characteristic, complemented
5#31770894C211yesmaximal, characteristic, complemented
6#31770883C211yesmaximal, characteristic, complemented
7#31770856C211yesmaximal, characteristic, complemented
8#31770853C211yesmaximal, characteristic, complemented
9#31770841C211yesmaximal, characteristic, complemented
10#31770823C211yesmaximal, characteristic, complemented
11#31770822C211yesmaximal, characteristic, complemented
12#31770803C211yesmaximal, characteristic, complemented
13#31770799C211yesmaximal, characteristic, complemented
14#31770631C211yesmaximal, characteristic, complemented
15#465×C269C211yesmaximal, characteristic, complemented
16C2×#16864389C2211yescharacteristic
17C2×D2152C2211yescharacteristic
18C2×#16864387C2211yescharacteristic
19C2×#16864386C2211yescharacteristic
20#22575452C2211yescharacteristic
21#22575449C2211yescharacteristic
22#22575448—21no—
23#22575444C2211yescharacteristic
24#22575442C2211yescharacteristic
25#22575439—21no—
26#22575437—21no—
27#22575435—21no—
28#22575435—21no—
29#22575433—21no—
30#22575427C2211yescharacteristic
31#22575427C2211yescharacteristic
32#22575425—21no—
33#22575424—21no—
34Q8×Dic269C2211yescharacteristic
35D4×Dic269C2211yescharacteristic
36#22575415C2211yescharacteristic
37#22575415C2211yescharacteristic
38#22575412C2211yescharacteristic
39#22575387C2211yescharacteristic
40#22575386C2211yescharacteristic
41#22575384C2211yescharacteristic
42#22575382C2211yescharacteristic
43#22575382C2211yescharacteristic
44#22575382C2211yescharacteristic
45#22575382C2211yescharacteristic
46#22575377C2211yescharacteristic
47#22575375C2211yescharacteristic
48#22575375C2211yescharacteristic
49#22575374C2211yescharacteristic
50#22575373C2211yescharacteristic
51#22575373C2211yescharacteristic
52C2×SD16×C269C2211yescharacteristic
53C22×C8×C269C2211yescharacteristic
54C22⋊Q8×C269C2211yescharacteristic
55#121×C269C2211yescharacteristic
56#106×C269C2211yescharacteristic
57#103×C269C2211yescharacteristic
58#102×C269C2211yescharacteristic
59C2×Dic538—21no—
60C2×D1076C2311yescharacteristic
61C2×D1076C2311yescharacteristic
62C2×C22⋊D269—21no—
63C2×C22⋊D269—21no—
64C2×C22⋊D269—21no—
65C2×C22⋊D269—21no—
66C22×Dic269—21no—
67C2×C4×D269—21no—
68C2×C4×D269—21no—
69#16864389—41no—
70D2152—41no—
71#16864387—41no—
72#16864386—41no—
73C2×#14524130C2311yescharacteristic
74C2×#14524130C2311yescharacteristic
75C4⋊Dic269—21no—
76C4⋊Dic269—21no—
77C4⋊Dic269D411yescharacteristic
78C4⋊Dic269D411yescharacteristic
79C4⋊Dic269C2311yescharacteristic
80C4⋊Dic269C2311yescharacteristic
81#16864381—21no—
82#16864381—21no—
83C22⋊Dic269—21no—
84C22⋊Dic269D411yescharacteristic
85C22⋊Dic269D411yescharacteristic
86#16864379—21no—
87#16864379—21no—
88#16864379—21no—
89#16864379—21no—
90#16864379—21no—
91#16864379—21no—
92C4×Dic269—21no—
93C4×Dic269C2311yescharacteristic
94C4×Dic269C2311yescharacteristic
95C2×Q8×C269C2311yescharacteristic
96C2×D4×C269—21no—
97C2×D4×C269C2311yescharacteristic
98C22×C4×C269C2311yescharacteristic
99SD16×C269—41no—
100C2×C8×C269—41no—
101C2×C8×C269C2311yescharacteristic
102C2×C8×C269C2311yescharacteristic
103C4⋊C4×C269—21no—
104C4⋊C4×C269C2311yescharacteristic
105C4⋊C4×C269C2311yescharacteristic
106C22⋊C4×C269—21no—
107C22⋊C4×C269—21no—
108C22×D269—21no—
109C22×D269—21no—
110Dic538—81no—
111D1076—21no—
112D1076—21no—
113D1076—21no—
114D1076—21no—
115C22⋊D269—81no—
116C22⋊D269—81no—
117C22⋊D269—81no—
118C22⋊D269—81no—
119C2×Dic269—21no—
120C2×Dic269—21no—
121C2×Dic269—81no—
122C2×Dic269C2×D411yescharacteristic
123C2×Dic269C2×D411yescharacteristic
124C2×Dic269C2×D411yescharacteristic
125C2×Dic269C2×D411yescharacteristic
126C4×D269—81no—
127C4×D269—81no—
128#14524130—21no—
129#14524130—21no—
130C23×C269—21no—
131C23×C269C2×D411yescharacteristic
132Q8×C269—21no—
133Q8×C269—21no—
134D4×C269—21no—
135D4×C269—21no—
136D4×C269—81no—
137C2×C4×C269—21no—
138C2×C4×C269—21no—
139C2×C4×C269—21no—
140C2×C4×C269—21no—
141C2×C4×C269—21no—
142C2×C4×C269C2×D411yescharacteristic
143C2×C4×C269C2411yescharacteristic
144C8×C269—21no—
145C8×C269—21no—
146C22×C269—21no—
147C22×C269—21no—
148C22×C269—21no—
149C22×C269—41no—
150C22×C269—41no—
151C22×C269—41no—
152C22×C269C22×D411yescharacteristic
153C2×D269—41no—
154C2×D269—41no—
155C2×D269—41no—
156C2×D269—41no—
157C2×D269—41no—
158C2×D269—41no—
159C4×C269—21no—
160C4×C269—41no—
161C4×C269—41no—
162C4×C269—41no—
163C4×C269H(5,𝔽2)11yescharacteristic
164C4×C2692−1+411yescharacteristic
165Dic269—21no—
166Dic269—21no—
167Dic269—21no—
168Dic269—21no—
169Dic269—41no—
170Dic269—41no—
171C2×C269—41no—
172C2×C269—81no—
173C2×C269#53711yescharacteristic
174C2×C269#57611yescharacteristic
175C2×C269#57711yescharacteristic
176D269—81no—
177D269—81no—
178C269#325711yescharacteristic, complemented, Sylow
179#3257—2691nomaximal, Sylow
180#542—2691no—
181#540—2691no—
182#479—2691no—
183#478—2691no—
184#476—2691no—
185#474—2691no—
186#469—2691no—
187#468—2691no—
188#466—2691no—
189#465D26911yescharacteristic, complemented
190#463—2691no—
191#463—2691no—
192#460—2691no—
193#459—2691no—
194#424—2691no—
195C2×SD16—2691no—
196C2×SD16C2×D26911yescharacteristic
197C2×D8—2691no—
198C2×D8—2691no—
199C2×M16—2691no—
200C22×C8C2×D26911yescharacteristic
201C4⋊Q8—2691no—
202#127—2691no—
203#126—5381no—
204#125—2691no—
205#124—2691no—
206#124—5381no—
207#123—5381no—
208#123—5381no—
209#123—5381no—
210C22⋊Q8—5381no—
211C22⋊Q8C2×D26911yescharacteristic
212#121—2691no—
213#121—2691no—
214#121—5381no—
215#121—5381no—
216#121C2×D26911yescharacteristic
217C4×Q8—2691no—
218C4×D4—2691no—
219C4×D4—2691no—
220C4×D4—2691no—
221#117—2691no—
222#107—2691no—
223#107—2691no—
224#106—2691no—
225#106C2×D26911yescharacteristic
226C4⋊C8—2691no—
227C4⋊C8—2691no—
228C4⋊C8—2691no—
229C4⋊C8—2691no—
230#103—2691no—
231#103C2×D26911yescharacteristic
232#102—2691no—
233#102—2691no—
234#102—2691no—
235#102—2691no—
236#102—2691no—
237#102C2×D26911yescharacteristic
238C2×Q8—5381no—
239C2×Q8C22×D26911yescharacteristic
240C2×D4—21no—
241C2×D4—2691no—
242C2×D4—2691no—
243C2×D4—5381no—
244C2×D4—5381no—
245C2×D4—5381no—
246C2×D4—5381no—
247C2×D4C22×D26911yescharacteristic
248C22×C4—5381no—
249C22×C4—5381no—
250C22×C4—5381no—
251C22×C4C22×D26911yescharacteristic
252SD16—41no—
253SD16—10761no—
254D8—10761no—
255D8—10761no—
256M16—10761no—
257C2×C8—41no—
258C2×C8—2691no—
259C2×C8—2691no—
260C2×C8C22×D26911yescharacteristic
261C2×C8C22×D26911yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—2691no—
264C4⋊C4—2691no—
265C4⋊C4—2691no—
266C4⋊C4—2691no—
267C4⋊C4—5381no—
268C4⋊C4—5381no—
269C4⋊C4—5381no—
270C4⋊C4—5381no—
271C4⋊C4C22×D26911yescharacteristic
272C4⋊C4C22×D26911yescharacteristic
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—2691no—
276C22⋊C4—2691no—
277C22⋊C4—5381no—
278C22⋊C4—5381no—
279C22⋊C4—5381no—
280C22⋊C4—5381no—
281C22⋊C4—5381no—
282C22⋊C4—5381no—
283C22⋊C4—5381no—
284C42—2691no—
285C42—2691no—
286C42—5381no—
287C23—21no—
288C23—5381no—
289C23—5381no—
290C23D4×D26911yescharacteristic
291Q8—21no—
292Q8—21no—
293Q8—21521no—
294D4—21no—
295D4—21no—
296D4—81no—
297D4—5381no—
298D4—5381no—
299D4—5381no—
300D4—5381no—
301D4—21521no—
302D4—21521no—
303D4—21521no—
304D4—21521no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—2691no—
311C2×C4—2691no—
312C2×C4—2691no—
313C2×C4—2691no—
314C2×C4—5381no—
315C2×C4—5381no—
316C2×C4—21521no—
317C2×C4—21521no—
318C2×C4—21521no—
319C2×C4D4×D26911yescharacteristic
320C2×C4C23×D26911yescharacteristic
321C8—21no—
322C8—21no—
323C8—5381no—
324C8—5381no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—10761no—
332C22—10761no—
333C22—10761no—
334C22—10761no—
335C22—10761no—
336C22—10761no—
337C22C2×D4×D26911yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—5381no—
343C4—5381no—
344C4—5381no—
345C4—5381no—
346C4—10761no—
347C4—10761no—
348C4#2257549811yescharacteristic
349C4#2257550011yescharacteristic
350C2—41no—
351C2—81no—
352C2—21521no—
353C2—21521no—
354C2#3177118211yescharacteristic
355C2#3177140711yescharacteristic
356C2#3177141111yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#465×C269C2
socleC22×C269C22×D4
hypercenter#465D269
hypocenterC269#3257
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #31771228C2semidirect
2. #31771208C2semidirect
3. #31770914C2semidirect
4. #31770904C2semidirect
5. #31770894C2semidirect
6. #31770883C2semidirect
7. #31770856C2semidirect
8. #31770853C2semidirect
9. #31770841C2semidirect
10. #31770823C2semidirect
11. #31770822C2semidirect
12. #31770803C2semidirect
13. #31770799C2semidirect
14. #31770631C2semidirect
15. #465×C269C2semidirect
178. C269#3257semidirect
189. #465D269semidirect

Maximal subgroups

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

subgroupindex
#317712282
#317712082
#317709142
#317709042
#317708942
#317708832
#317708562
#317708532
#317708412
#317708232
#317708222
#317708032
#317707992
#317706312
#465×C2692
#3257269