Finite Group Databasebeta

← #46822870

Subgroups — #46822870

Order 34432.

420 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771264C211yesmaximal, characteristic, complemented
2#31770967C211yesmaximal, characteristic, complemented
3#31770940C211yesmaximal, characteristic, complemented
4#31770918C211yesmaximal, characteristic, complemented
5#31770897C211yesmaximal, characteristic, complemented
6#31770849C211yesmaximal, characteristic, complemented
7#31770839C211yesmaximal, characteristic, complemented
8#31770820C211yesmaximal, characteristic, complemented
9#31770748C211yesmaximal, characteristic, complemented
10#31770743C211yesmaximal, characteristic, complemented
11#31770705C211yesmaximal, characteristic, complemented
12#31770677C211yesmaximal, characteristic, complemented
13#31770604C211yesmaximal, characteristic, complemented
14C2×#22575376C211yesmaximal, characteristic, complemented
15#547×C269C211yesmaximal, characteristic, complemented
16C2×#16864402C2211yescharacteristic
17C22×Dic538C2211yescharacteristic
18C2×#16864390C2211yescharacteristic
19C2×#16864390C2211yescharacteristic
20C2×#16864387C2211yescharacteristic
21C2×#16864386C2211yescharacteristic
22C22×#14524130C2211yescharacteristic
23#22575441C2211yescharacteristic
24#22575439—21no—
25#22575432C2211yescharacteristic
26#22575431—21no—
27#22575427C2211yescharacteristic
28#22575425—21no—
29C4×Dic538C2211yescharacteristic
30#22575413—21no—
31#22575386C2211yescharacteristic
32#22575386C2211yescharacteristic
33#22575386C2211yescharacteristic
34C4⋊#14524130C2211yescharacteristic
35#22575376C2211yescharacteristic
36#22575376C2211yescharacteristic
37#22575376C2211yescharacteristic
38#22575376C2211yescharacteristic
39#22575376C2211yescharacteristic
40#22575376C2211yescharacteristic
41#22575374C2211yescharacteristic
42#22575373C2211yescharacteristic
43#22575373C2211yescharacteristic
44#22575373C2211yescharacteristic
45C22⋊#14524130C2211yescharacteristic
46C22⋊#14524130C2211yescharacteristic
47#22575364C2211yescharacteristic
48C2×#41×C269—21no—
49C4⋊Q8×C269C2211yescharacteristic
50#123×C269—21no—
51#123×C269—21no—
52C22⋊Q8×C269—21no—
53#121×C269C2211yescharacteristic
54#121×C269C2211yescharacteristic
55C4×D4×C269C2211yescharacteristic
56C4×D4×C269C2211yescharacteristic
57C2×C4⋊C4×C269C2211yescharacteristic
58C2×C4⋊C4×C269C2211yescharacteristic
59#16864402—22no—
60#16864402—41no—
61C2×Dic538—22no—
62C2×Dic538—21no—
63C2×Dic538—41no—
64C2×Dic538C2311yescharacteristic
65C2×Dic538C2311yescharacteristic
66C2×D1076C2311yescharacteristic
67C2×C22⋊D269—21no—
68C2×C22⋊D269—21no—
69C22×Dic269—21no—
70C2×C4×D269—21no—
71#16864390—22no—
72#16864390—41no—
73#16864387—41no—
74#16864386—41no—
75C2×#14524130—41no—
76C2×#14524130C2311yescharacteristic
77C2×#14524130C2311yescharacteristic
78C2×#14524130C2311yescharacteristic
79C2×#14524130C2311yescharacteristic
80C4⋊Dic269C2311yescharacteristic
81#16864381—21no—
82#16864381—21no—
83C22⋊Dic269—21no—
84#16864379—21no—
85#16864379—21no—
86#16864379—21no—
87C4×Dic269—21no—
88#41×C269—44no—
89C2×Q8×C269—21no—
90C2×D4×C269—21no—
91C2×D4×C269—21no—
92C2×D4×C269D411yescharacteristic
93C2×D4×C269C2311yescharacteristic
94C22×C4×C269—21no—
95C22×C4×C269—21no—
96C22×C4×C269—21no—
97C22×C4×C269C2311yescharacteristic
98C22×C4×C269C2311yescharacteristic
99C4⋊C4×C269—21no—
100C4⋊C4×C269—21no—
101C4⋊C4×C269—21no—
102C4⋊C4×C269D411yescharacteristic
103C4⋊C4×C269C2311yescharacteristic
104C4⋊C4×C269C2311yescharacteristic
105C4⋊C4×C269C2311yescharacteristic
106C22⋊C4×C269—21no—
107C22⋊C4×C269—21no—
108C22⋊C4×C269—21no—
109C22⋊C4×C269D411yescharacteristic
110C22⋊C4×C269D411yescharacteristic
111C42×C269C2311yescharacteristic
112C22×D269—21no—
113Dic538—21no—
114Dic538—21no—
115Dic538—21no—
116Dic538—42no—
117Dic538#4112yescomplemented
118D1076—21no—
119D1076—21no—
120C22⋊D269—42no—
121C22⋊D269—42no—
122C2×Dic269—21no—
123C2×Dic269—21no—
124C2×Dic269—21no—
125C2×Dic269—42no—
126C4×D269—42no—
127#14524130—21no—
128#14524130—21no—
129#14524130—21no—
130#14524130—21no—
131C23×C269—21no—
132C23×C269C2×D411yescharacteristic
133C23×C269C2×D411yescharacteristic
134Q8×C269—42no—
135D4×C269—22no—
136D4×C269—21no—
137D4×C269—21no—
138D4×C269—42no—
139D4×C269—42no—
140C2×C4×C269—21no—
141C2×C4×C269—21no—
142C2×C4×C269—21no—
143C2×C4×C269—21no—
144C2×C4×C269—21no—
145C2×C4×C269—21no—
146C2×C4×C269—21no—
147C2×C4×C269—42no—
148C2×C4×C269—42no—
149C2×C4×C269—42no—
150C2×C4×C269C2×D411yescharacteristic
151C2×C4×C269C2×D411yescharacteristic
152C2×C4×C269C2×D411yescharacteristic
153C2×C4×C269C2×D411yescharacteristic
154C2×C4×C269C2411yescharacteristic
155C22×C269—21no—
156C22×C269—21no—
157C22×C269—21no—
158C22×C269—21no—
159C22×C269—21no—
160C22×C269—41no—
161C22×C269—41no—
162C22×C269—41no—
163C22×C269AGL(1,ℤ/8)12yes—
164C22×C269C22×D411yescharacteristic
165C2×D269—41no—
166C2×D269—41no—
167C2×D269—41no—
168C4×C269—21no—
169C4×C269—21no—
170C4×C269—21no—
171C4×C269—21no—
172C4×C269—41no—
173C4×C269—41no—
174C4×C269—41no—
175C4×C269C2×#4111yescharacteristic
176C4×C269H(5,𝔽2)11yescharacteristic
177Dic269—22no—
178Dic269—41no—
179Dic269—41no—
180C2×C269—22no—
181C2×C269—41no—
182C2×C269—81no—
183C2×C269#54611yescharacteristic
184C2×C269C2×AGL(1,ℤ/8)11yescharacteristic
185C2×C269#57811yescharacteristic
186D269—81no—
187C269#330811yescharacteristic, complemented, Sylow
188#3308—2691nomaximal, Sylow
189#548—2691no—
190#547D26911yescharacteristic, complemented
191#489—2691no—
192#484—2691no—
193#480—2691no—
194#477—2691no—
195#468—2691no—
196#466—2691no—
197#463—2691no—
198#449—2691no—
199#448—2691no—
200#440—2691no—
201#435—2691no—
202#417—2691no—
203C2×#103—2691no—
204C2×#41—21no—
205C2×#41—2691no—
206C22×Q8—2691no—
207C2×SD16—2691no—
208C2×SD16—2691no—
209C2×D8—2691no—
210C2×M16—2691no—
211C22×C8—2691no—
212C4⋊Q8C2×D26911yescharacteristic
213#124—2691no—
214#124—5381no—
215#123—21no—
216#123—21no—
217C22⋊Q8—21no—
218C22⋊Q8—2691no—
219C22⋊Q8—5381no—
220#121—2691no—
221#121—5381no—
222#121C2×D26911yescharacteristic
223#121C2×D26911yescharacteristic
224C4×Q8—2691no—
225C4×D4—5381no—
226C4×D4C2×D26911yescharacteristic
227C4×D4C2×D26911yescharacteristic
228C2×C4⋊C4C2×D26911yescharacteristic
229C2×C4⋊C4C2×D26911yescharacteristic
230#107—2691no—
231#107—2691no—
232#107—2691no—
233C4⋊C8—2691no—
234#103—2691no—
235#103—2691no—
236#103—2691no—
237#103—2691no—
238#103—2691no—
239#103—2691no—
240#102—2691no—
241#102—2691no—
242#102—2691no—
243#102—2691no—
244C22⋊C8—2691no—
245C22⋊C8—2691no—
246#97—2691no—
247#41—44no—
248#41—5382no—
249#41—10761no—
250C2×Q8—21no—
251C2×Q8—2691no—
252C2×Q8—2691no—
253C2×Q8—5382no—
254C2×Q8—5381no—
255C2×Q8—10761no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—2691no—
259C2×D4—5381no—
260C2×D4—5381no—
261C2×D4C22⋊D26911yescharacteristic
262C2×D4C22×D26911yescharacteristic
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—5381no—
267C22×C4—5381no—
268C22×C4C22×D26911yescharacteristic
269C22×C4C22×D26911yescharacteristic
270SD16—5382no—
271SD16—10761no—
272D8—10761no—
273M16—10761no—
274C2×C8—2691no—
275C2×C8—2691no—
276C2×C8—2691no—
277C2×C8—2691no—
278C2×C8—10761no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—2691no—
283C4⋊C4—5381no—
284C4⋊C4—5381no—
285C4⋊C4C22⋊D26911yescharacteristic
286C4⋊C4C22×D26911yescharacteristic
287C4⋊C4C22×D26911yescharacteristic
288C4⋊C4C22×D26911yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—5381no—
293C22⋊C4—5381no—
294C22⋊C4—5381no—
295C22⋊C4—5381no—
296C22⋊C4C22⋊D26911yescharacteristic
297C22⋊C4C22⋊D26911yescharacteristic
298C42—5381no—
299C42C22×D26911yescharacteristic
300C23—21no—
301C23—5381no—
302C23C2×C22⋊D26911yescharacteristic
303C23C2×C22⋊D26911yescharacteristic
304Q8—42no—
305Q8—2692no—
306Q8—5381no—
307Q8—5381no—
308Q8—5381no—
309Q8—10762no—
310D4—22no—
311D4—21no—
312D4—21no—
313D4—42no—
314D4—42no—
315D4—5381no—
316D4—5381no—
317D4—10762no—
318D4—10762no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—5381no—
330C2×C4—5381no—
331C2×C4—5381no—
332C2×C4—10762no—
333C2×C4—10762no—
334C2×C4C2×C22⋊D26911yescharacteristic
335C2×C4C2×C22⋊D26911yescharacteristic
336C2×C4C2×C22⋊D26911yescharacteristic
337C2×C4C2×C22⋊D26911yescharacteristic
338C2×C4C23×D26911yescharacteristic
339C8—5381no—
340C8—5381no—
341C8—5381no—
342C8—5381no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—10761no—
352C22—10761no—
353C22—10761no—
354C22#2257547912yes—
355C22C22×C22⋊D26911yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—41no—
361C4—41no—
362C4—41no—
363C4—5382no—
364C4—10761no—
365C4—10761no—
366C4#41×D26911yescharacteristic
367C4#2257549911yescharacteristic
368C2—22no—
369C2—41no—
370C2—81no—
371C2—21521no—
372C2#3177124311yescharacteristic
373C2C2×#2257547911yescharacteristic
374C2#3177142011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#547×C269C2
socleC22×C269C22×D4
hypercenter#547D269
hypocenterC269#3308
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. #31771264C2semidirect
2. #31770967C2semidirect
3. #31770940C2semidirect
4. #31770918C2semidirect
5. #31770897C2semidirect
6. #31770849C2semidirect
7. #31770839C2semidirect
8. #31770820C2semidirect
9. #31770748C2semidirect
10. #31770743C2semidirect
11. #31770705C2semidirect
12. #31770677C2semidirect
13. #31770604C2semidirect
14. C2×#22575376C2semidirect
15. #547×C269C2semidirect
117. Dic538#41semidirect
187. C269#3308semidirect
190. #547D269semidirect

Maximal subgroups

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

subgroupindex
#317712642
#317709672
#317709402
#317709182
#317708972
#317708492
#317708392
#317708202
#317707482
#317707432
#317707052
#317706772
#317706042
C2×#225753762
#547×C2692
#3308269