Finite Group Databasebeta

← #46822296

Subgroups — #46822296

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#31771210C211yesmaximal, characteristic, complemented
2#31770912C211yesmaximal, characteristic, complemented
3#31770905C211yesmaximal, characteristic, complemented
4#31770892C211yesmaximal, characteristic, complemented
5#31770882C211yesmaximal, characteristic, complemented
6#31770856C211yesmaximal, characteristic, complemented
7#31770853C211yesmaximal, characteristic, complemented
8#31770839C211yesmaximal, characteristic, complemented
9#31770836C211yesmaximal, characteristic, complemented
10#31770817C211yesmaximal, characteristic, complemented
11#31770817C211yesmaximal, characteristic, complemented
12#31770805C211yesmaximal, characteristic, complemented
13#31770800C211yesmaximal, characteristic, complemented
14#31770632C211yesmaximal, characteristic, complemented
15#542×C269C211yesmaximal, characteristic, complemented
16C2×#16864389C2211yescharacteristic
17C2×#16864389C2211yescharacteristic
18C2×#16864387C2211yescharacteristic
19C2×#16864387C2211yescharacteristic
20C2×#16864386C2211yescharacteristic
21C22×#14524130C2211yescharacteristic
22#22575450C2211yescharacteristic
23#22575445C2211yescharacteristic
24#22575438—21no—
25#22575438—21no—
26#22575427C2211yescharacteristic
27#22575427C2211yescharacteristic
28#22575426—21no—
29#22575426—21no—
30C4×D1076C2211yescharacteristic
31C4×D1076C2211yescharacteristic
32#22575386C2211yescharacteristic
33#22575386C2211yescharacteristic
34#22575384C2211yescharacteristic
35#22575384C2211yescharacteristic
36C4⋊#14524130C2211yescharacteristic
37C4⋊#14524130C2211yescharacteristic
38C4⋊#14524130C2211yescharacteristic
39C4⋊#14524130C2211yescharacteristic
40#22575377C2211yescharacteristic
41#22575377C2211yescharacteristic
42#22575374C2211yescharacteristic
43#22575374C2211yescharacteristic
44#22575373C2211yescharacteristic
45#22575373C2211yescharacteristic
46#22575373C2211yescharacteristic
47#22575373C2211yescharacteristic
48C4⋊Q8×C269C2211yescharacteristic
49#126×C269—21no—
50#124×C269—21no—
51#124×C269C2211yescharacteristic
52#123×C269—21no—
53C22⋊Q8×C269—21no—
54C22⋊Q8×C269C2211yescharacteristic
55#121×C269C2211yescharacteristic
56C4×Q8×C269C2211yescharacteristic
57C4×D4×C269C2211yescharacteristic
58#117×C269C2211yescharacteristic
59C2×D1076—21no—
60C2×D1076—21no—
61C2×D1076C2311yescharacteristic
62C2×D1076C2311yescharacteristic
63C2×C22⋊D269—21no—
64C2×C22⋊D269—21no—
65C2×C4×D269—21no—
66C2×C4×D269—21no—
67#16864389—41no—
68#16864389—41no—
69#16864387—41no—
70#16864387—41no—
71#16864386—41no—
72C2×#14524130—41no—
73C2×#14524130C2311yescharacteristic
74C2×#14524130C2311yescharacteristic
75C2×#14524130C2311yescharacteristic
76C2×#14524130C2311yescharacteristic
77C4⋊Dic269C2311yescharacteristic
78C4⋊Dic269C2311yescharacteristic
79#16864381—21no—
80#16864381—21no—
81#16864379—21no—
82#16864379—21no—
83#16864379—21no—
84#16864379—21no—
85C2×Q8×C269—21no—
86C2×Q8×C269C2311yescharacteristic
87C2×D4×C269—21no—
88C2×D4×C269C2311yescharacteristic
89C22×C4×C269—21no—
90C22×C4×C269C2311yescharacteristic
91C4⋊C4×C269—21no—
92C4⋊C4×C269—21no—
93C4⋊C4×C269—21no—
94C4⋊C4×C269D411yescharacteristic
95C4⋊C4×C269D411yescharacteristic
96C4⋊C4×C269C2311yescharacteristic
97C4⋊C4×C269C2311yescharacteristic
98C22⋊C4×C269—21no—
99C22⋊C4×C269—21no—
100C22⋊C4×C269—21no—
101C22⋊C4×C269—21no—
102C22⋊C4×C269—21no—
103C22⋊C4×C269D411yescharacteristic
104C22⋊C4×C269D411yescharacteristic
105C42×C269—21no—
106C42×C269C2311yescharacteristic
107C42×C269C2311yescharacteristic
108C22×D269—21no—
109C22×D269—21no—
110D1076—21no—
111D1076—21no—
112D1076—21no—
113D1076—21no—
114D1076—81no—
115D1076—81no—
116C22⋊D269—81no—
117C22⋊D269—81no—
118C2×Dic269—21no—
119C2×Dic269—21no—
120C4×D269—81no—
121C4×D269—81no—
122#14524130—21no—
123#14524130—21no—
124#14524130—21no—
125#14524130—21no—
126C23×C269—21no—
127C23×C269C2×D411yescharacteristic
128Q8×C269—21no—
129Q8×C269—21no—
130Q8×C269—81no—
131D4×C269—21no—
132D4×C269—21no—
133D4×C269—81no—
134C2×C4×C269—21no—
135C2×C4×C269—21no—
136C2×C4×C269—21no—
137C2×C4×C269—21no—
138C2×C4×C269—21no—
139C2×C4×C269—81no—
140C2×C4×C269C2×D411yescharacteristic
141C2×C4×C269C2×D411yescharacteristic
142C2×C4×C269C2×D411yescharacteristic
143C2×C4×C269C2×D411yescharacteristic
144C2×C4×C269C2×D411yescharacteristic
145C2×C4×C269C2411yescharacteristic
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—21no—
161C4×C269—21no—
162C4×C269—21no—
163C4×C269—21no—
164C4×C269—41no—
165C4×C269—41no—
166C4×C269—41no—
167C4×C269H(5,𝔽2)11yescharacteristic
168C4×C2692−1+411yescharacteristic
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#542D26911yescharacteristic, complemented
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#424—2691no—
195C2×SD16—2691no—
196C2×SD16—2691no—
197C2×D8—2691no—
198C2×D8—2691no—
199C2×M16—2691no—
200C22×C8—2691no—
201C4⋊Q8C2×D26911yescharacteristic
202#127—2691no—
203#126—21no—
204#125—2691no—
205#124—21no—
206#124C2×D26911yescharacteristic
207#123—21no—
208#123—5381no—
209#123—5381no—
210C22⋊Q8—21no—
211C22⋊Q8C2×D26911yescharacteristic
212#121—2691no—
213#121—2691no—
214#121—5381no—
215#121—5381no—
216#121C2×D26911yescharacteristic
217C4×Q8C2×D26911yescharacteristic
218C4×D4—2691no—
219C4×D4—2691no—
220C4×D4C2×D26911yescharacteristic
221#117C2×D26911yescharacteristic
222#107—2691no—
223#107—2691no—
224#106—2691no—
225#106—2691no—
226C4⋊C8—2691no—
227C4⋊C8—2691no—
228C4⋊C8—2691no—
229C4⋊C8—2691no—
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—21no—
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—21no—
249C22×C4—5381no—
250C22×C4—5381no—
251C22×C4C22×D26911yescharacteristic
252SD16—10761no—
253SD16—10761no—
254D8—10761no—
255D8—10761no—
256M16—10761no—
257C2×C8—2691no—
258C2×C8—2691no—
259C2×C8—2691no—
260C2×C8—2691no—
261C2×C8—10761no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—2691no—
266C4⋊C4—2691no—
267C4⋊C4—5381no—
268C4⋊C4—5381no—
269C4⋊C4C22⋊D26911yescharacteristic
270C4⋊C4C22⋊D26911yescharacteristic
271C4⋊C4C22×D26911yescharacteristic
272C4⋊C4C22×D26911yescharacteristic
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—5381no—
279C22⋊C4—5381no—
280C22⋊C4—5381no—
281C22⋊C4—5381no—
282C22⋊C4C22⋊D26911yescharacteristic
283C22⋊C4C22⋊D26911yescharacteristic
284C42—21no—
285C42C22×D26911yescharacteristic
286C42C22×D26911yescharacteristic
287C23—21no—
288C23—5381no—
289C23—5381no—
290C23C2×C22⋊D26911yescharacteristic
291Q8—21no—
292Q8—21no—
293Q8—81no—
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—81no—
311C2×C4—5381no—
312C2×C4—5381no—
313C2×C4—21521no—
314C2×C4—21521no—
315C2×C4C2×C22⋊D26911yescharacteristic
316C2×C4C2×C22⋊D26911yescharacteristic
317C2×C4C2×C22⋊D26911yescharacteristic
318C2×C4C2×C22⋊D26911yescharacteristic
319C2×C4C2×C22⋊D26911yescharacteristic
320C2×C4C23×D26911yescharacteristic
321C8—5381no—
322C8—5381no—
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—
337C22C22×C22⋊D26911yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—10761no—
347C4—10761no—
348C4#2257549911yescharacteristic
349C4#2257550011yescharacteristic
350C2—41no—
351C2—81no—
352C2—21521no—
353C2—21521no—
354C2#3177118311yescharacteristic
355C2#3177140811yescharacteristic
356C2#3177141311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#542×C269C2
socleC22×C269C22×D4
hypercenter#542D269
hypocenterC269#3257
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #31771210C2semidirect
2. #31770912C2semidirect
3. #31770905C2semidirect
4. #31770892C2semidirect
5. #31770882C2semidirect
6. #31770856C2semidirect
7. #31770853C2semidirect
8. #31770839C2semidirect
9. #31770836C2semidirect
10. #31770817C2semidirect
11. #31770817C2semidirect
12. #31770805C2semidirect
13. #31770800C2semidirect
14. #31770632C2semidirect
15. #542×C269C2semidirect
178. C269#3257semidirect
180. #542D269semidirect

Maximal subgroups

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

subgroupindex
#317712102
#317709122
#317709052
#317708922
#317708822
#317708562
#317708532
#317708392
#317708362
#317708172
#317708052
#317708002
#317706322
#542×C2692
#3257269