Finite Group Databasebeta

← #46822951

Subgroups — #46822951

Order 34432.

380 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#31771325C211yesmaximal, characteristic, complemented
2#31770964C211yesmaximal, characteristic, complemented
3#31770943C211yesmaximal, characteristic, complemented
4#31770926C211yesmaximal, characteristic, complemented
5#31770900C211yesmaximal, characteristic, complemented
6#31770849C211yesmaximal, characteristic, complemented
7#31770844C211yesmaximal, characteristic, complemented
8#31770824C211yesmaximal, characteristic, complemented
9#31770767C211yesmaximal, characteristic, complemented
10#31770761C211yesmaximal, characteristic, complemented
11#31770710C211yesmaximal, characteristic, complemented
12#31770677C211yesmaximal, characteristic, complemented
13#31770614C211yesmaximal, characteristic, complemented
14#31770601C211yesmaximal, characteristic, complemented
15#548×C269C211yesmaximal, characteristic
16C2×#16864392C2211yescharacteristic
17C2×#16864392C2211yescharacteristic
18C2×#16864390C2211yescharacteristic
19C2×#16864386C2211yescharacteristic
20C22×#14524130C2211yescharacteristic
21#22575453C2211yescharacteristic
22#22575446—21no—
23#22575446—21no—
24#22575440—21no—
25#22575432C2211yescharacteristic
26#22575432C2211yescharacteristic
27C4×Dic538C2211yescharacteristic
28#22575418—21no—
29#22575412C2211yescharacteristic
30#22575412C2211yescharacteristic
31#22575386C2211yescharacteristic
32#22575386C2211yescharacteristic
33#22575384C2211yescharacteristic
34C4⋊#14524130C2211yescharacteristic
35#22575377C2211yescharacteristic
36#22575377C2211yescharacteristic
37#22575377C2211yescharacteristic
38#22575377C2211yescharacteristic
39#22575377C2211yescharacteristic
40#22575377C2211yescharacteristic
41#22575376C2211yescharacteristic
42#22575374C2211yescharacteristic
43#22575374C2211yescharacteristic
44#22575374C2211yescharacteristic
45C22⋊#14524130C2211yescharacteristic
46C22⋊#14524130C2211yescharacteristic
47#22575364C2211yescharacteristic
48C2×#41×C269C2211yescharacteristic
49C22×Q8×C269C2211yescharacteristic
50#124×C269—21no—
51#124×C269C2211yescharacteristic
52C22⋊Q8×C269—21no—
53C22⋊Q8×C269C2211yescharacteristic
54#121×C269—21no—
55#121×C269C2211yescharacteristic
56C4×Q8×C269C2211yescharacteristic
57C4×D4×C269—21no—
58C4×D4×C269C2211yescharacteristic
59C2×Dic538—21no—
60C2×Dic538C2311yescharacteristic
61#16864392—22no—
62#16864392—41no—
63#16864390—41no—
64#16864386—41no—
65C2×#14524130—41no—
66C2×#14524130C2311yescharacteristic
67C2×#14524130C2311yescharacteristic
68C2×#14524130C2311yescharacteristic
69C2×#14524130C2311yescharacteristic
70C4⋊Dic269—21no—
71C4⋊Dic269C2311yescharacteristic
72C4⋊Dic269C2311yescharacteristic
73C4⋊Dic269C2311yescharacteristic
74#16864381—21no—
75#16864381—21no—
76#16864381—21no—
77C22⋊Dic269—21no—
78C22⋊Dic269—21no—
79C22⋊Dic269—21no—
80C22⋊Dic269—21no—
81C4×Dic269—21no—
82C4×Dic269—21no—
83C4×Dic269—21no—
84#41×C269—22no—
85#41×C269—41no—
86C2×Q8×C269—21no—
87C2×Q8×C269—22no—
88C2×Q8×C269—41no—
89C2×Q8×C269C2311yescharacteristic
90C2×Q8×C269C2311yescharacteristic
91C2×D4×C269—21no—
92C2×D4×C269—21no—
93C2×D4×C269D411yescharacteristic
94C2×D4×C269C2311yescharacteristic
95C22×C4×C269—21no—
96C22×C4×C269—21no—
97C22×C4×C269C2311yescharacteristic
98C22×C4×C269C2311yescharacteristic
99C4⋊C4×C269—21no—
100C4⋊C4×C269—21no—
101C4⋊C4×C269D411yescharacteristic
102C4⋊C4×C269C2311yescharacteristic
103C22⋊C4×C269—21no—
104C22⋊C4×C269—21no—
105C22⋊C4×C269—21no—
106C22⋊C4×C269—21no—
107C22⋊C4×C269D411yescharacteristic
108C22⋊C4×C269D411yescharacteristic
109C42×C269—21no—
110C42×C269C2311yescharacteristic
111Dic538—21no—
112Dic538—21no—
113Dic538—42no—
114C2×Dic269—21no—
115C2×Dic269—21no—
116C2×Dic269—21no—
117C2×Dic269—21no—
118#14524130—21no—
119#14524130—21no—
120#14524130—21no—
121#14524130—21no—
122C23×C269—21no—
123C23×C269C2×D411yescharacteristic
124C23×C269C2×D411yescharacteristic
125Q8×C269—21no—
126Q8×C269—21no—
127Q8×C269—21no—
128Q8×C269—42no—
129Q8×C269#4112yes—
130D4×C269—21no—
131D4×C269—21no—
132D4×C269—41no—
133D4×C269—42no—
134D4×C269—42no—
135C2×C4×C269—21no—
136C2×C4×C269—21no—
137C2×C4×C269—21no—
138C2×C4×C269—21no—
139C2×C4×C269—21no—
140C2×C4×C269—21no—
141C2×C4×C269—21no—
142C2×C4×C269—42no—
143C2×C4×C269—42no—
144C2×C4×C269C2×D411yescharacteristic
145C2×C4×C269C2×D411yescharacteristic
146C2×C4×C269C2×D411yescharacteristic
147C2×C4×C269C2×D411yescharacteristic
148C2×C4×C269C2411yescharacteristic
149C22×C269—21no—
150C22×C269—21no—
151C22×C269—21no—
152C22×C269—21no—
153C22×C269—21no—
154C22×C269—21no—
155C22×C269—41no—
156C22×C269—41no—
157C22×C269—41no—
158C22×C269C22×D411yescharacteristic
159C4×C269—21no—
160C4×C269—21no—
161C4×C269—22no—
162C4×C269—21no—
163C4×C269—21no—
164C4×C269—41no—
165C4×C269—41no—
166C4×C269C2×#4111yescharacteristic
167C4×C269H(5,𝔽2)11yescharacteristic
168Dic269—41no—
169Dic269—41no—
170Dic269—41no—
171Dic269—41no—
172C2×C269—41no—
173C2×C269—41no—
174C2×C269—81no—
175C2×C269#54611yescharacteristic
176C2×C269#57511yescharacteristic
177C2×C269#57811yescharacteristic
178C269#331311yescharacteristic, complemented, Sylow
179#3313—2691nomaximal, Sylow
180#556—2691no—
181#548D26911yescharacteristic
182#489—2691no—
183#485—2691no—
184#482—2691no—
185#477—2691no—
186#468—2691no—
187#467—2691no—
188#464—2691no—
189#452—2691no—
190#451—2691no—
191#441—2691no—
192#435—2691no—
193#419—2691no—
194#416—2691no—
195C2×#41C2×D26911yescharacteristic
196C22×Q8C2×D26911yescharacteristic
197C2×Q16—2691no—
198C2×Q16—2691no—
199C2×SD16—2691no—
200C2×M16—2691no—
201C22×C8—2691no—
202C4⋊Q8—2691no—
203#126—5381no—
204#126—5381no—
205#124—21no—
206#124—5381no—
207#124C2×D26911yescharacteristic
208C22⋊Q8—21no—
209C22⋊Q8—2691no—
210C22⋊Q8—2691no—
211C22⋊Q8C2×D26911yescharacteristic
212#121—21no—
213#121C2×D26911yescharacteristic
214C4×Q8—2691no—
215C4×Q8—5381no—
216C4×Q8C2×D26911yescharacteristic
217C4×D4—21no—
218C4×D4C2×D26911yescharacteristic
219#117—2691no—
220#117—2691no—
221#107—2691no—
222#107—2691no—
223#106—2691no—
224C4⋊C8—2691no—
225#103—2691no—
226#103—2691no—
227#103—2691no—
228#103—2691no—
229#103—2691no—
230#103—2691no—
231#103—2691no—
232#102—2691no—
233#102—2691no—
234#102—2691no—
235C22⋊C8—2691no—
236C22⋊C8—2691no—
237#97—2691no—
238#41—22no—
239#41—41no—
240C2×Q8—21no—
241C2×Q8—22no—
242C2×Q8—41no—
243C2×Q8—2691no—
244C2×Q8—5381no—
245C2×Q8C22×D26911yescharacteristic
246C2×Q8C22×D26911yescharacteristic
247C2×D4—21no—
248C2×D4—21no—
249C2×D4C22⋊D26911yescharacteristic
250C2×D4C22×D26911yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4C22×D26911yescharacteristic
254C22×C4C22×D26911yescharacteristic
255Q16—5382no—
256Q16—10761no—
257SD16—10761no—
258M16—10761no—
259C2×C8—2691no—
260C2×C8—2691no—
261C2×C8—2691no—
262C2×C8—2691no—
263C2×C8—10761no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—2691no—
267C4⋊C4—2691no—
268C4⋊C4—2691no—
269C4⋊C4—5381no—
270C4⋊C4—5381no—
271C4⋊C4—5381no—
272C4⋊C4—5381no—
273C4⋊C4C22⋊D26911yescharacteristic
274C4⋊C4C22×D26911yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—5381no—
280C22⋊C4—5381no—
281C22⋊C4—5381no—
282C22⋊C4—5381no—
283C22⋊C4C22⋊D26911yescharacteristic
284C22⋊C4C22⋊D26911yescharacteristic
285C42—21no—
286C42—5381no—
287C42—5381no—
288C42—5381no—
289C42C22×D26911yescharacteristic
290C23—21no—
291C23C2×C22⋊D26911yescharacteristic
292C23C2×C22⋊D26911yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—42no—
297Q8—5381no—
298Q8—5381no—
299Q8—10762no—
300Q8#1686440112yes—
301D4—21no—
302D4—21no—
303D4—41no—
304D4—42no—
305D4—42no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—5381no—
316C2×C4—5381no—
317C2×C4—5381no—
318C2×C4—5381no—
319C2×C4C2×C22⋊D26911yescharacteristic
320C2×C4C2×C22⋊D26911yescharacteristic
321C2×C4C2×C22⋊D26911yescharacteristic
322C2×C4C2×C22⋊D26911yescharacteristic
323C2×C4C23×D26911yescharacteristic
324C8—5381no—
325C8—5381no—
326C8—5381no—
327C8—5381no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22C22×C22⋊D26911yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—22no—
343C4—41no—
344C4—41no—
345C4—10761no—
346C4—10761no—
347C4—10761no—
348C4—10761no—
349C4C2×#1686440111yescharacteristic
350C4#2257549811yescharacteristic
351C2—41no—
352C2—41no—
353C2—81no—
354C2#3177124911yescharacteristic
355C2#3177140311yescharacteristic
356C2#3177142011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting, prime radical#548×C269C2
socleC22×C269C22×D4
hypercenter#548D269
hypocenterC269#3313
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. #31771325C2semidirect
2. #31770964C2semidirect
3. #31770943C2semidirect
4. #31770926C2semidirect
5. #31770900C2semidirect
6. #31770849C2semidirect
7. #31770844C2semidirect
8. #31770824C2semidirect
9. #31770767C2semidirect
10. #31770761C2semidirect
11. #31770710C2semidirect
12. #31770677C2semidirect
13. #31770614C2semidirect
14. #31770601C2semidirect
178. C269#3313semidirect

Maximal subgroups

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

subgroupindex
#317713252
#317709642
#317709432
#317709262
#317709002
#317708492
#317708442
#317708242
#317707672
#317707612
#317707102
#317706772
#317706142
#317706012
#548×C2692
#3313269