Finite Group Databasebeta

← #46822866

Subgroups — #46822866

Order 34432.

394 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771305C211yesmaximal, characteristic, complemented
2#31771259C211yesmaximal, characteristic, complemented
3#31770974C211yesmaximal, characteristic, complemented
4#31770949C211yesmaximal, characteristic, complemented
5#31770937C211yesmaximal, characteristic, complemented
6#31770905C211yesmaximal, characteristic, complemented
7#31770850C211yesmaximal, characteristic, complemented
8#31770833C211yesmaximal, characteristic, complemented
9#31770810C211yesmaximal, characteristic, complemented
10#31770747C211yesmaximal, characteristic, complemented
11#31770747C211yesmaximal, characteristic, complemented
12#31770678C211yesmaximal, characteristic, complemented
13#31770603C211yesmaximal, characteristic, complemented
14#31770598C211yesmaximal, characteristic, complemented
15#442×C269C211yesmaximal, characteristic, complemented
16C2×#16864401C2211yescharacteristic
17C2×#16864401C2211yescharacteristic
18C2×#16864390C2211yescharacteristic
19C2×#16864390C2211yescharacteristic
20C2×#16864385C2211yescharacteristic
21C2×C8×D269C2211yescharacteristic
22#22575453C2211yescharacteristic
23#22575446—21no—
24#22575445C2211yescharacteristic
25#22575437—21no—
26#22575437—21no—
27#22575436—21no—
28#22575433C2211yescharacteristic
29#22575433C2211yescharacteristic
30#22575427—21no—
31#22575426—21no—
32#22575424C2211yescharacteristic
33#22575424C2211yescharacteristic
34C4×D1076C2211yescharacteristic
35C4×C22⋊D269—21no—
36#22575411C2211yescharacteristic
37C2×C4⋊Dic269—21no—
38C4⋊C4×D269C2211yescharacteristic
39#22575386C2211yescharacteristic
40#22575384C2211yescharacteristic
41C4⋊#14524130C2211yescharacteristic
42#22575378C2211yescharacteristic
43#22575378C2211yescharacteristic
44#22575378C2211yescharacteristic
45#22575378C2211yescharacteristic
46#22575376C2211yescharacteristic
47#22575376C2211yescharacteristic
48#22575374C2211yescharacteristic
49#22575374C2211yescharacteristic
50#22575365C2211yescharacteristic
51#22575365C2211yescharacteristic
52C2×D8×C269C2211yescharacteristic
53C4×D4×C269C2211yescharacteristic
54C4×D4×C269C2211yescharacteristic
55#106×C269C2211yescharacteristic
56#102×C269C2211yescharacteristic
57#102×C269C2211yescharacteristic
58#97×C269C2211yescharacteristic
59#16864401—22no—
60#16864401—22no—
61#16864401—41no—
62#16864401—41no—
63C2×Dic538C2311yescharacteristic
64C2×Dic538C2311yescharacteristic
65C2×D1076D411yescharacteristic
66C2×C22⋊D269—21no—
67C2×C22⋊D269—21no—
68C2×C22⋊D269—21no—
69C2×C22⋊D269—21no—
70C22×Dic269—21no—
71C22×Dic269—21no—
72C2×C4×D269—21no—
73C2×C4×D269C2311yescharacteristic
74C2×C4×D269C2311yescharacteristic
75#16864390—41no—
76#16864390—41no—
77#16864385—41no—
78C2×#14524130C2311yescharacteristic
79C2×#14524130C2311yescharacteristic
80C8×D269—41no—
81C4⋊Dic269—21no—
82C4⋊Dic269—21no—
83C4⋊Dic269—21no—
84C4⋊Dic269—21no—
85C4⋊Dic269D411yescharacteristic
86C4⋊Dic269C2311yescharacteristic
87C4⋊Dic269C2311yescharacteristic
88#16864381—21no—
89#16864381—21no—
90#16864381—21no—
91C22⋊Dic269—21no—
92C22⋊Dic269—21no—
93#16864379—21no—
94#16864379—21no—
95#16864379—21no—
96#16864379D411yescharacteristic
97#16864379D411yescharacteristic
98C4×Dic269—21no—
99C2×D4×C269C2311yescharacteristic
100C2×D4×C269C2311yescharacteristic
101C22×C4×C269—21no—
102C22×C4×C269—21no—
103D8×C269—22no—
104C2×C8×C269C2311yescharacteristic
105C2×C8×C269C2311yescharacteristic
106C4⋊C4×C269C2311yescharacteristic
107C4⋊C4×C269C2311yescharacteristic
108C22⋊C4×C269—21no—
109C22⋊C4×C269—21no—
110C42×C269C2311yescharacteristic
111C22×D269C2×D411yescharacteristic
112C22×D269C2×D411yescharacteristic
113Dic538—21no—
114Dic538—21no—
115Dic538—21no—
116Dic538—21no—
117D1076—41no—
118C22⋊D269—42no—
119C22⋊D269—42no—
120C22⋊D269—42no—
121C22⋊D269—81no—
122C2×Dic269—21no—
123C2×Dic269—21no—
124C2×Dic269—21no—
125C2×Dic269—21no—
126C2×Dic269—42no—
127C2×Dic269—42no—
128C2×Dic269C2×D411yescharacteristic
129C2×Dic269C2×D411yescharacteristic
130C4×D269—21no—
131C4×D269—21no—
132C4×D269—21no—
133C4×D269—21no—
134C4×D269—81no—
135#14524130—21no—
136#14524130—21no—
137C23×C269—21no—
138C23×C269—21no—
139D4×C269—21no—
140D4×C269—21no—
141D4×C269—21no—
142D4×C269#4112yes—
143C2×C4×C269—21no—
144C2×C4×C269—21no—
145C2×C4×C269—42no—
146C2×C4×C269—81no—
147C2×C4×C269C2×D411yescharacteristic
148C2×C4×C269C2×D411yescharacteristic
149C2×C4×C269C2411yescharacteristic
150C8×C269—21no—
151C8×C269—21no—
152C22×C269—22no—
153C22×C269—41no—
154C22×C269—41no—
155C22×C269—41no—
156C22×C269—41no—
157C22×C269—41no—
158C22×C269C22×D411yescharacteristic
159C2×D269—21no—
160C2×D269—21no—
161C2×D269—21no—
162C2×D269—21no—
163C2×D269—21no—
164C2×D269—21no—
165C4×C269—21no—
166C4×C269—21no—
167C4×C269—41no—
168C4×C269—41no—
169C4×C269C2×#4111yescharacteristic
170C4×C269H(5,𝔽2)11yescharacteristic
171Dic269—21no—
172Dic269—21no—
173Dic269—41no—
174Dic269—41no—
175Dic269—41no—
176Dic269—41no—
177C2×C269—42no—
178C2×C269—81no—
179C2×C269#54611yescharacteristic
180C2×C269#57511yescharacteristic
181C2×C269#57711yescharacteristic
182D269—41no—
183D269—41no—
184C269#330711yescharacteristic, complemented, Sylow
185#3307—2691nomaximal, Sylow
186#553—2691no—
187#547—2691no—
188#491—2691no—
189#485—2691no—
190#483—2691no—
191#478—2691no—
192#468—2691no—
193#465—2691no—
194#461—2691no—
195#449—2691no—
196#449—2691no—
197#442D26911yescharacteristic, complemented
198#435—2691no—
199#417—2691no—
200#416—2691no—
201C2×#41—2691no—
202C2×#41—2691no—
203C2×SD16—2691no—
204C2×SD16—2691no—
205C2×D8C2×D26911yescharacteristic
206C2×M16—2691no—
207C22×C8—2691no—
208C4⋊Q8—2691no—
209#126—5381no—
210#125—2691no—
211#123—5381no—
212#123—5381no—
213#123—5381no—
214C22⋊Q8—2691no—
215C22⋊Q8—2691no—
216#121—2691no—
217#121—2691no—
218#121—5381no—
219#121—5381no—
220C4×D4—2691no—
221C4×D4—5381no—
222C4×D4C2×D26911yescharacteristic
223C4×D4C2×D26911yescharacteristic
224#117—2691no—
225C2×C4⋊C4—2691no—
226C2×C4⋊C4—5381no—
227#107—2691no—
228#106—2691no—
229#106C2×D26911yescharacteristic
230C4⋊C8—2691no—
231#103—2691no—
232#103—2691no—
233#103—2691no—
234#103—2691no—
235#103—2691no—
236#103—2691no—
237#102—2691no—
238#102—2691no—
239#102C2×D26911yescharacteristic
240#102C2×D26911yescharacteristic
241C22⋊C8—2691no—
242C22⋊C8—2691no—
243#97C2×D26911yescharacteristic
244#41—5382no—
245#41—5382no—
246#41—10761no—
247#41—10761no—
248C2×Q8—2691no—
249C2×Q8—2691no—
250C2×D4—2691no—
251C2×D4—5381no—
252C2×D4—5381no—
253C2×D4—5381no—
254C2×D4—5381no—
255C2×D4C22×D26911yescharacteristic
256C2×D4C22×D26911yescharacteristic
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—2691no—
260C22×C4—2691no—
261C22×C4—5381no—
262C22×C4—5381no—
263C22×C4—5381no—
264SD16—10761no—
265SD16—10761no—
266D8—22no—
267M16—10761no—
268C2×C8—2691no—
269C2×C8—2691no—
270C2×C8—10761no—
271C2×C8C22×D26911yescharacteristic
272C2×C8C22×D26911yescharacteristic
273C4⋊C4—2691no—
274C4⋊C4—2691no—
275C4⋊C4—2691no—
276C4⋊C4—5381no—
277C4⋊C4—5381no—
278C4⋊C4—5381no—
279C4⋊C4—5381no—
280C4⋊C4—5381no—
281C4⋊C4—5381no—
282C4⋊C4—5381no—
283C4⋊C4C22×D26911yescharacteristic
284C4⋊C4C22×D26911yescharacteristic
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—2691no—
288C22⋊C4—2691no—
289C22⋊C4—5381no—
290C22⋊C4—5381no—
291C22⋊C4—5381no—
292C22⋊C4—5381no—
293C22⋊C4—5381no—
294C42—5381no—
295C42C22×D26911yescharacteristic
296C23—21no—
297C23—21no—
298C23—2691no—
299C23—2691no—
300Q8—5381no—
301Q8—5381no—
302Q8—5381no—
303Q8—5381no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—10761no—
308D4—10762no—
309D4—10762no—
310D4—10762no—
311D4—21521no—
312D4#1686440212yes—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—42no—
316C2×C4—81no—
317C2×C4—2691no—
318C2×C4—2691no—
319C2×C4—5381no—
320C2×C4—5381no—
321C2×C4—5381no—
322C2×C4—5381no—
323C2×C4—5381no—
324C2×C4—5381no—
325C2×C4—5381no—
326C2×C4—5381no—
327C2×C4—10762no—
328C2×C4—10762no—
329C2×C4—21521no—
330C2×C4D4×D26911yescharacteristic
331C2×C4D4×D26911yescharacteristic
332C2×C4C23×D26911yescharacteristic
333C8—21no—
334C8—21no—
335C8—5381no—
336C8—5381no—
337C22—22no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—5381no—
344C22—5381no—
345C22—5381no—
346C22—5381no—
347C22—5381no—
348C22—5381no—
349C22C2×D4×D26911yescharacteristic
350C4—21no—
351C4—21no—
352C4—41no—
353C4—41no—
354C4—5381no—
355C4—5381no—
356C4—10761no—
357C4—10761no—
358C4—10761no—
359C4—10761no—
360C4C2×#1686440211yescharacteristic
361C4#2257549911yescharacteristic
362C2—42no—
363C2—81no—
364C2—10761no—
365C2—10761no—
366C2#3177125111yescharacteristic
367C2#3177140111yescharacteristic
368C2#3177141511yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#442×C269C2
socleC22×C269C22×D4
hypercenter#442D269
hypocenterC269#3307
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #31771305C2semidirect
2. #31771259C2semidirect
3. #31770974C2semidirect
4. #31770949C2semidirect
5. #31770937C2semidirect
6. #31770905C2semidirect
7. #31770850C2semidirect
8. #31770833C2semidirect
9. #31770810C2semidirect
10. #31770747C2semidirect
11. #31770747C2semidirect
12. #31770678C2semidirect
13. #31770603C2semidirect
14. #31770598C2semidirect
15. #442×C269C2semidirect
184. C269#3307semidirect
197. #442D269semidirect

Maximal subgroups

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

subgroupindex
#317713052
#317712592
#317709742
#317709492
#317709372
#317709052
#317708502
#317708332
#317708102
#317707472
#317706782
#317706032
#317705982
#442×C2692
#3307269