Finite Group Databasebeta

← #46822298

Subgroups — #46822298

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#31771226C211yesmaximal, characteristic, complemented
2#31771210C211yesmaximal, characteristic, complemented
3#31770913C211yesmaximal, characteristic, complemented
4#31770906C211yesmaximal, characteristic, complemented
5#31770896C211yesmaximal, characteristic, complemented
6#31770886C211yesmaximal, characteristic, complemented
7#31770858C211yesmaximal, characteristic, complemented
8#31770851C211yesmaximal, characteristic, complemented
9#31770841C211yesmaximal, characteristic, complemented
10#31770834C211yesmaximal, characteristic, complemented
11#31770821C211yesmaximal, characteristic, complemented
12#31770821C211yesmaximal, characteristic, complemented
13#31770806C211yesmaximal, characteristic, complemented
14#31770801C211yesmaximal, characteristic, complemented
15#424×C269C211yesmaximal, characteristic, complemented
16C2×#16864391C2211yescharacteristic
17C2×#16864391C2211yescharacteristic
18C2×D2152C2211yescharacteristic
19C2×D2152C2211yescharacteristic
20#22575453C2211yescharacteristic
21#22575450C2211yescharacteristic
22#22575448—21no—
23#22575445C2211yescharacteristic
24#22575441C2211yescharacteristic
25#22575439—21no—
26#22575438—21no—
27#22575438—21no—
28#22575435—21no—
29#22575432C2211yescharacteristic
30#22575431—21no—
31#22575427C2211yescharacteristic
32#22575427C2211yescharacteristic
33#22575427C2211yescharacteristic
34#22575426—21no—
35#22575426—21no—
36C4×Dic538C2211yescharacteristic
37C4×D1076C2211yescharacteristic
38C4×D1076C2211yescharacteristic
39C4×D1076C2211yescharacteristic
40#22575387C2211yescharacteristic
41#22575387C2211yescharacteristic
42#22575385C2211yescharacteristic
43#22575385C2211yescharacteristic
44#22575378C2211yescharacteristic
45#22575378C2211yescharacteristic
46#22575375C2211yescharacteristic
47#22575375C2211yescharacteristic
48#22575375C2211yescharacteristic
49#22575375C2211yescharacteristic
50#22575375C2211yescharacteristic
51#22575375C2211yescharacteristic
52C2×M16×C269C2211yescharacteristic
53C22×C8×C269C2211yescharacteristic
54#117×C269C2211yescharacteristic
55C4⋊C8×C269C2211yescharacteristic
56C4⋊C8×C269C2211yescharacteristic
57C4⋊C8×C269C2211yescharacteristic
58C4⋊C8×C269C2211yescharacteristic
59C2×Dic538—21no—
60C2×Dic538C2311yescharacteristic
61C2×D1076—21no—
62C2×D1076—21no—
63C2×D1076C2311yescharacteristic
64C2×D1076C2311yescharacteristic
65C2×D1076C2311yescharacteristic
66C2×C22⋊D269—21no—
67C2×C22⋊D269—21no—
68C2×C22⋊D269—21no—
69C2×C4×D269—21no—
70C2×C4×D269—21no—
71C2×C4×D269—21no—
72#16864391—41no—
73#16864391—41no—
74D2152—41no—
75D2152—41no—
76C4⋊Dic269—21no—
77C4⋊Dic269C2311yescharacteristic
78C4⋊Dic269C2311yescharacteristic
79C4⋊Dic269C2311yescharacteristic
80C4⋊Dic269C2311yescharacteristic
81#16864381—21no—
82#16864381—21no—
83#16864381—21no—
84#16864381—21no—
85C22⋊Dic269—21no—
86#16864379—21no—
87#16864379—21no—
88#16864379—21no—
89#16864379—21no—
90#16864379—21no—
91#16864379—21no—
92#16864379—21no—
93#16864379—21no—
94C4×Dic269—21no—
95C22×C4×C269C2311yescharacteristic
96M16×C269—41no—
97C2×C8×C269—41no—
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—21no—
113Dic538—81no—
114D1076—21no—
115D1076—21no—
116D1076—21no—
117D1076—21no—
118D1076—21no—
119D1076—21no—
120D1076—81no—
121D1076—81no—
122C22⋊D269—81no—
123C22⋊D269—81no—
124C22⋊D269—81no—
125C2×Dic269—21no—
126C2×Dic269—21no—
127C2×Dic269—21no—
128C2×Dic269—21no—
129C2×Dic269—21no—
130C4×D269—81no—
131C4×D269—81no—
132C4×D269—81no—
133C23×C269C2×D411yescharacteristic
134C2×C4×C269—21no—
135C2×C4×C269—21no—
136C2×C4×C269C2×D411yescharacteristic
137C2×C4×C269C2×D411yescharacteristic
138C2×C4×C269C2×D411yescharacteristic
139C2×C4×C269C2×D411yescharacteristic
140C2×C4×C269C2×D411yescharacteristic
141C2×C4×C269C2411yescharacteristic
142C8×C269—21no—
143C8×C269—21no—
144C8×C269—21no—
145C8×C269—21no—
146C22×C269—21no—
147C22×C269—21no—
148C22×C269—21no—
149C22×C269C22×D411yescharacteristic
150C2×D269—41no—
151C2×D269—41no—
152C2×D269—41no—
153C2×D269—41no—
154C2×D269—41no—
155C2×D269—41no—
156C2×D269—41no—
157C2×D269—41no—
158C2×D269—41no—
159C4×C269—21no—
160C4×C269—21no—
161C4×C269—21no—
162C4×C269—21no—
163C4×C269—21no—
164C4×C269H(5,𝔽2)11yescharacteristic
165C4×C2692−1+411yescharacteristic
166Dic269—41no—
167Dic269—41no—
168Dic269—41no—
169Dic269—41no—
170Dic269—41no—
171C2×C269—41no—
172C2×C269#53711yescharacteristic
173C2×C269#57611yescharacteristic
174C2×C269#57711yescharacteristic
175D269—81no—
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#465—2691no—
190#463—2691no—
191#463—2691no—
192#460—2691no—
193#459—2691no—
194#424D26911yescharacteristic, complemented
195C2×SD16—2691no—
196C2×SD16—2691no—
197C2×D8—2691no—
198C2×D8—2691no—
199C2×M16C2×D26911yescharacteristic
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—2691no—
211C22⋊Q8—5381no—
212#121—2691no—
213#121—2691no—
214#121—2691no—
215#121—5381no—
216#121—5381no—
217C4×Q8—2691no—
218C4×D4—2691no—
219C4×D4—2691no—
220C4×D4—2691no—
221#117C2×D26911yescharacteristic
222#107—2691no—
223#107—2691no—
224#106—2691no—
225#106—2691no—
226C4⋊C8C2×D26911yescharacteristic
227C4⋊C8C2×D26911yescharacteristic
228C4⋊C8C2×D26911yescharacteristic
229C4⋊C8C2×D26911yescharacteristic
230#103—2691no—
231#103—2691no—
232#102—2691no—
233#102—2691no—
234#102—2691no—
235#102—2691no—
236#102—2691no—
237#102—2691no—
238C2×Q8—2691no—
239C2×Q8—5381no—
240C2×D4—2691no—
241C2×D4—2691no—
242C2×D4—2691no—
243C2×D4—5381no—
244C2×D4—5381no—
245C2×D4—5381no—
246C2×D4—5381no—
247C2×D4—5381no—
248C22×C4—5381no—
249C22×C4—5381no—
250C22×C4—5381no—
251C22×C4C22×D26911yescharacteristic
252SD16—10761no—
253SD16—10761no—
254D8—10761no—
255D8—10761no—
256M16—41no—
257C2×C8—41no—
258C2×C8C22×D26911yescharacteristic
259C2×C8C22×D26911yescharacteristic
260C2×C8C22×D26911yescharacteristic
261C2×C8C22×D26911yescharacteristic
262C4⋊C4—2691no—
263C4⋊C4—2691no—
264C4⋊C4—2691no—
265C4⋊C4—2691no—
266C4⋊C4—5381no—
267C4⋊C4—5381no—
268C4⋊C4—5381no—
269C4⋊C4—5381no—
270C4⋊C4—5381no—
271C4⋊C4D107611yescharacteristic
272C4⋊C4D107611yescharacteristic
273C22⋊C4—5381no—
274C22⋊C4—5381no—
275C22⋊C4—5381no—
276C22⋊C4—5381no—
277C22⋊C4—5381no—
278C22⋊C4—5381no—
279C22⋊C4—5381no—
280C22⋊C4—5381no—
281C22⋊C4—5381no—
282C22⋊C4D107611yescharacteristic
283C22⋊C4D107611yescharacteristic
284C42—5381no—
285C42C22×D26911yescharacteristic
286C42C22×D26911yescharacteristic
287C23—5381no—
288C23—5381no—
289C23—5381no—
290C23C2×D107611yescharacteristic
291Q8—5381no—
292Q8—5381no—
293Q8—21521no—
294D4—5381no—
295D4—5381no—
296D4—5381no—
297D4—5381no—
298D4—5381no—
299D4—5381no—
300D4—21521no—
301D4—21521no—
302D4—21521no—
303D4—21521no—
304D4—21521no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—5381no—
308C2×C4—5381no—
309C2×C4—5381no—
310C2×C4—5381no—
311C2×C4—5381no—
312C2×C4—21521no—
313C2×C4—21521no—
314C2×C4—21521no—
315C2×C4C2×D107611yescharacteristic
316C2×C4C2×D107611yescharacteristic
317C2×C4C2×D107611yescharacteristic
318C2×C4C2×D107611yescharacteristic
319C2×C4C2×D107611yescharacteristic
320C2×C4C23×D26911yescharacteristic
321C8—21no—
322C8—21no—
323C8—21no—
324C8—21no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—10761no—
329C22—10761no—
330C22—10761no—
331C22—10761no—
332C22—10761no—
333C22—10761no—
334C22—10761no—
335C22—10761no—
336C22—10761no—
337C22C22×D107611yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—10761no—
344C4—10761no—
345C4—10761no—
346C4—10761no—
347C4—10761no—
348C4#2257549811yescharacteristic
349C4#2257550111yescharacteristic
350C2—41no—
351C2—21521no—
352C2—21521no—
353C2—21521no—
354C2#3177118611yescharacteristic
355C2#3177141011yescharacteristic
356C2#3177141711yescharacteristic
subgroupG/H
centerC22C22×D1076
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#424×C269C2
socleC22×C269C22×D4
hypercenter#424D269
hypocenterC269#3257
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ #117 ◁ #424

Complements

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

NH ≅ G/Ntype
1. #31771226C2semidirect
2. #31771210C2semidirect
3. #31770913C2semidirect
4. #31770906C2semidirect
5. #31770896C2semidirect
6. #31770886C2semidirect
7. #31770858C2semidirect
8. #31770851C2semidirect
9. #31770841C2semidirect
10. #31770834C2semidirect
11. #31770821C2semidirect
12. #31770821C2semidirect
13. #31770806C2semidirect
14. #31770801C2semidirect
15. #424×C269C2semidirect
178. C269#3257semidirect
194. #424D269semidirect

Maximal subgroups

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

subgroupindex
#317712262
#317712102
#317709132
#317709062
#317708962
#317708862
#317708582
#317708512
#317708412
#317708342
#317708212
#317708062
#317708012
#424×C2692
#3257269