Finite Group Databasebeta

← #46821086

Subgroups — #46821086

Order 34432.

396 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771210C211yesmaximal, characteristic, complemented
2#31771085C211yesmaximal, characteristic, complemented
3#31770924C211yesmaximal, characteristic, complemented
4#31770919C211yesmaximal, characteristic, complemented
5#31770913C211yesmaximal, characteristic, complemented
6#31770906C211yesmaximal, characteristic, complemented
7#31770806C211yesmaximal, characteristic, complemented
8#31770801C211yesmaximal, characteristic, complemented
9#31770752C211yesmaximal, characteristic, complemented
10#31770752C211yesmaximal, characteristic, complemented
11#31770718C211yesmaximal, characteristic, complemented
12#31770707C211yesmaximal, characteristic, complemented
13C4×#16864391C211yesmaximal, characteristic, complemented
14C4×D2152C211yesmaximal, characteristic, complemented
15#433×C269C211yesmaximal, characteristic, complemented
16C2×#16864402C2211yescharacteristic
17C2×#16864391C2211yescharacteristic
18C2×#16864391C2211yescharacteristic
19C2×D2152C2211yescharacteristic
20C2×D2152C2211yescharacteristic
21#22575450C2211yescharacteristic
22#22575445C2211yescharacteristic
23#22575438—21no—
24#22575438—21no—
25#22575427C2211yescharacteristic
26#22575427C2211yescharacteristic
27#22575426—21no—
28#22575426—21no—
29C4×Dic538C2211yescharacteristic
30C4×Dic538C2211yescharacteristic
31C4×D1076C2211yescharacteristic
32C4×D1076C2211yescharacteristic
33C4×D1076C2211yescharacteristic
34C4×D1076C2211yescharacteristic
35#22575413—21no—
36#22575413—21no—
37#22575411—21no—
38C2×C4⋊Dic269C2211yescharacteristic
39C4⋊C4×D269—21no—
40#22575387C2211yescharacteristic
41#22575387C2211yescharacteristic
42#22575385C2211yescharacteristic
43#22575385C2211yescharacteristic
44#22575378C2211yescharacteristic
45#22575378C2211yescharacteristic
46#22575375C2211yescharacteristic
47#22575375C2211yescharacteristic
48#22575375C2211yescharacteristic
49#22575375C2211yescharacteristic
50#22575375C2211yescharacteristic
51#22575375C2211yescharacteristic
52#117×C269C2211yescharacteristic
53C4⋊C8×C269C2211yescharacteristic
54C4⋊C8×C269C2211yescharacteristic
55C22⋊C8×C269C2211yescharacteristic
56C22⋊C8×C269C2211yescharacteristic
57#97×C269C2211yescharacteristic
58C4×C8×C269C2211yescharacteristic
59#16864402—22no—
60#16864402—22no—
61C2×Dic538C2311yescharacteristic
62C2×D1076—21no—
63C2×D1076—21no—
64C2×D1076C2311yescharacteristic
65C2×D1076C2311yescharacteristic
66C2×D1076C2311yescharacteristic
67C2×C22⋊D269—21no—
68C2×C22⋊D269—21no—
69C2×C22⋊D269—21no—
70C22×Dic269—21no—
71C2×C4×D269—21no—
72C2×C4×D269—21no—
73C2×C4×D269—21no—
74C2×C4×D269—21no—
75C2×C4×D269—21no—
76#16864391—22no—
77#16864391—22no—
78D2152—22no—
79D2152—22no—
80C4⋊Dic269—21no—
81C4⋊Dic269C2311yescharacteristic
82C4⋊Dic269C2311yescharacteristic
83C4⋊Dic269C2311yescharacteristic
84C4⋊Dic269C2311yescharacteristic
85#16864381—21no—
86#16864381—21no—
87#16864381—21no—
88#16864381—21no—
89#16864379—21no—
90#16864379—21no—
91#16864379—21no—
92#16864379—21no—
93#16864379—21no—
94#16864379—21no—
95C4×Dic269—21no—
96C4×Dic269—21no—
97C22×C4×C269C2311yescharacteristic
98C2×C8×C269C2311yescharacteristic
99C2×C8×C269C2311yescharacteristic
100C2×C8×C269C2311yescharacteristic
101C2×C8×C269C2311yescharacteristic
102C4⋊C4×C269D411yescharacteristic
103C4⋊C4×C269D411yescharacteristic
104C22⋊C4×C269D411yescharacteristic
105C22⋊C4×C269D411yescharacteristic
106C42×C269C2311yescharacteristic
107C42×C269C2311yescharacteristic
108C22×D269—21no—
109C22×D269—21no—
110C22×D269—21no—
111Dic538—21no—
112Dic538#4112yes—
113D1076—21no—
114D1076—21no—
115D1076—21no—
116D1076—21no—
117D1076—21no—
118D1076—81no—
119D1076—81no—
120D1076#4112yes—
121C22⋊D269—24no—
122C22⋊D269—81no—
123C22⋊D269—81no—
124C2×Dic269—21no—
125C2×Dic269—21no—
126C2×Dic269—21no—
127C2×Dic269—21no—
128C2×Dic269—21no—
129C2×Dic269—81no—
130C4×D269—24no—
131C4×D269—81no—
132C4×D269—81no—
133C4×D269—81no—
134C4×D269—81no—
135C23×C269C2×D411yescharacteristic
136C2×C4×C269—21no—
137C2×C4×C269—21no—
138C2×C4×C269C2×D411yescharacteristic
139C2×C4×C269C2×D411yescharacteristic
140C2×C4×C269C2×D411yescharacteristic
141C2×C4×C269C2×D411yescharacteristic
142C2×C4×C269C2×D411yescharacteristic
143C2×C4×C269C2411yescharacteristic
144C8×C269—21no—
145C8×C269—21no—
146C8×C269—21no—
147C8×C269—21no—
148C22×C269—21no—
149C22×C269—21no—
150C22×C269—21no—
151C22×C269C22×D411yescharacteristic
152C2×D269—22no—
153C2×D269—41no—
154C2×D269—41no—
155C2×D269—41no—
156C2×D269—41no—
157C2×D269—41no—
158C2×D269—41no—
159C2×D269—41no—
160C2×D269—41no—
161C4×C269—21no—
162C4×C269—21no—
163C4×C269—21no—
164C4×C269—21no—
165C4×C269—21no—
166C4×C269C2×#4111yescharacteristic
167C4×C269C2×#4111yescharacteristic
168Dic269—22no—
169Dic269—41no—
170Dic269—41no—
171Dic269—41no—
172Dic269—41no—
173C2×C269—41no—
174C2×C269#52511yescharacteristic
175C2×C269#57611yescharacteristic
176C2×C269#57711yescharacteristic
177D269—42no—
178D269—81no—
179D269—81no—
180C269#311911yescharacteristic, complemented, Sylow
181#3119—2691nomaximal, Sylow
182#540—2691no—
183#520—2691no—
184#481—2691no—
185#480—2691no—
186#479—2691no—
187#478—2691no—
188#460—2691no—
189#459—2691no—
190#449—2691no—
191#449—2691no—
192#442—2691no—
193#440—2691no—
194C4×SD16—2691no—
195C4×D8—2691no—
196#433D26911yescharacteristic, complemented
197C2×#41—2691no—
198C2×SD16—2691no—
199C2×SD16—2691no—
200C2×D8—2691no—
201C2×D8—2691no—
202#127—2691no—
203#125—2691no—
204#123—5381no—
205#123—5381no—
206#121—2691no—
207#121—2691no—
208#121—5381no—
209#121—5381no—
210C4×Q8—2691no—
211C4×Q8—2691no—
212C4×D4—2691no—
213C4×D4—2691no—
214C4×D4—2691no—
215C4×D4—2691no—
216C4×D4—5381no—
217C4×D4—5381no—
218#117—5381no—
219#117C2×D26911yescharacteristic
220C2×C4⋊C4—2691no—
221C2×C4⋊C4—5381no—
222#107—2691no—
223#107—2691no—
224#106—2691no—
225#106—2691no—
226C4⋊C8C2×D26911yescharacteristic
227C4⋊C8C2×D26911yescharacteristic
228#103—2691no—
229#103—2691no—
230#102—2691no—
231#102—2691no—
232#102—2691no—
233#102—2691no—
234#102—2691no—
235#102—2691no—
236C22⋊C8C2×D26911yescharacteristic
237C22⋊C8C2×D26911yescharacteristic
238#97C2×D26911yescharacteristic
239C4×C8C2×D26911yescharacteristic
240#41—5382no—
241#41—5382no—
242C2×Q8—2691no—
243C2×D4—2691no—
244C2×D4—2691no—
245C2×D4—2691no—
246C2×D4—5381no—
247C2×D4—5381no—
248C2×D4—5381no—
249C2×D4—5381no—
250C2×D4—5381no—
251C22×C4—5381no—
252C22×C4—5381no—
253C22×C4—5381no—
254C22×C4—5381no—
255C22×C4—5381no—
256C22×C4—5381no—
257C22×C4C22×D26911yescharacteristic
258SD16—5382no—
259SD16—5382no—
260D8—5382no—
261D8—5382no—
262C2×C8C22×D26911yescharacteristic
263C2×C8C22×D26911yescharacteristic
264C2×C8C22×D26911yescharacteristic
265C2×C8C22×D26911yescharacteristic
266C4⋊C4—2691no—
267C4⋊C4—2691no—
268C4⋊C4—2691no—
269C4⋊C4—2691no—
270C4⋊C4—5381no—
271C4⋊C4—5381no—
272C4⋊C4—5381no—
273C4⋊C4—5381no—
274C4⋊C4—5381no—
275C4⋊C4D107611yescharacteristic
276C4⋊C4D107611yescharacteristic
277C22⋊C4—5381no—
278C22⋊C4—5381no—
279C22⋊C4—5381no—
280C22⋊C4—5381no—
281C22⋊C4—5381no—
282C22⋊C4—5381no—
283C22⋊C4D107611yescharacteristic
284C22⋊C4D107611yescharacteristic
285C42—5381no—
286C42—5381no—
287C42C22×D26911yescharacteristic
288C42C22×D26911yescharacteristic
289C23—5381no—
290C23—5381no—
291C23—5381no—
292C23C2×D107611yescharacteristic
293Q8—2692no—
294Q8—5381no—
295D4—2692no—
296D4—5384no—
297D4—5381no—
298D4—5381no—
299D4—5381no—
300D4—5381no—
301D4—5381no—
302D4—21521no—
303D4—21521no—
304D4—21521no—
305D4—21521no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—5384no—
309C2×C4—5381no—
310C2×C4—5381no—
311C2×C4—5381no—
312C2×C4—5381no—
313C2×C4—5381no—
314C2×C4—21521no—
315C2×C4—21521no—
316C2×C4—21521no—
317C2×C4—21521no—
318C2×C4—21521no—
319C2×C4C2×D107611yescharacteristic
320C2×C4C2×D107611yescharacteristic
321C2×C4C2×D107611yescharacteristic
322C2×C4C2×D107611yescharacteristic
323C2×C4C2×D107611yescharacteristic
324C2×C4C23×D26911yescharacteristic
325C8—21no—
326C8—21no—
327C8—21no—
328C8—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—5382no—
333C22—10761no—
334C22—10761no—
335C22—10761no—
336C22—10761no—
337C22—10761no—
338C22—10761no—
339C22—10761no—
340C22—10761no—
341C22C22×D107611yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—5382no—
348C4—10761no—
349C4—10761no—
350C4—10761no—
351C4—10761no—
352C4#41×D26911yescharacteristic
353C4#41×D26911yescharacteristic
354C2—41no—
355C2—10762no—
356C2—21521no—
357C2—21521no—
358C2#3177111711yescharacteristic
359C2#3177141011yescharacteristic
360C2#3177141711yescharacteristic
subgroupG/H
centerC22C22×D1076
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#433×C269C2
socleC22×C269C22×D4
hypercenter#433D269
hypocenterC269#3119
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #31771210C2semidirect
2. #31771085C2semidirect
3. #31770924C2semidirect
4. #31770919C2semidirect
5. #31770913C2semidirect
6. #31770906C2semidirect
7. #31770806C2semidirect
8. #31770801C2semidirect
9. #31770752C2semidirect
10. #31770752C2semidirect
11. #31770718C2semidirect
12. #31770707C2semidirect
13. C4×#16864391C2semidirect
14. C4×D2152C2semidirect
15. #433×C269C2semidirect
180. C269#3119semidirect
196. #433D269semidirect

Maximal subgroups

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

subgroupindex
#317712102
#317710852
#317709242
#317709192
#317709132
#317709062
#317708062
#317708012
#317707522
#317707182
#317707072
C4×#168643912
C4×D21522
#433×C2692
#3119269