Finite Group Databasebeta

← #46821104

Subgroups — #46821104

Order 34432.

372 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771218C211yesmaximal, characteristic, complemented
2#31771084C211yesmaximal, characteristic
3#31770942C211yesmaximal, characteristic, complemented
4#31770937C211yesmaximal, characteristic, complemented
5#31770909C211yesmaximal, characteristic, complemented
6#31770816C211yesmaximal, characteristic, complemented
7#31770810C211yesmaximal, characteristic, complemented
8#31770768C211yesmaximal, characteristic
9#31770768C211yesmaximal, characteristic
10#31770711C211yesmaximal, characteristic, complemented
11#31770702C211yesmaximal, characteristic, complemented
12#31770699C211yesmaximal, characteristic, complemented
13#31770696C211yesmaximal, characteristic, complemented
14#31770665C211yesmaximal, characteristic, complemented
15#478×C269C211yesmaximal, characteristic, complemented
16C2×#16864401C2211yescharacteristic
17C2×Dic1076C2211yescharacteristic
18C2×Dic1076C2211yescharacteristic
19C2×#16864390C2211yescharacteristic
20C2×#16864390C2211yescharacteristic
21#22575453C2211yescharacteristic
22#22575448—21no—
23#22575448—21no—
24#22575444—21no—
25#22575444—21no—
26#22575433C2211yescharacteristic
27#22575433C2211yescharacteristic
28C4×Dic538C2211yescharacteristic
29#22575418C2211yescharacteristic
30#22575418C2211yescharacteristic
31#22575418C2211yescharacteristic
32D4×Dic269C2211yescharacteristic
33C4×C22⋊D269—21no—
34#22575413—21no—
35#22575410C2211yescharacteristic
36#22575409—21no—
37C2×#16864381—21no—
38C4⋊C4×D269C2211yescharacteristic
39#22575386C2211yescharacteristic
40#22575384C2211yescharacteristic
41C4⋊#14524130C2211yescharacteristic
42#22575378C2211yescharacteristic
43#22575378C2211yescharacteristic
44#22575376C2211yescharacteristic
45#22575376C2211yescharacteristic
46#22575376C2211yescharacteristic
47#22575376C2211yescharacteristic
48#22575365C2211yescharacteristic
49#22575365C2211yescharacteristic
50#22575363C2211yescharacteristic
51C8×Dic269C2211yescharacteristic
52#125×C269C2211yescharacteristic
53C4×D4×C269C2211yescharacteristic
54#107×C269C2211yescharacteristic
55#106×C269C2211yescharacteristic
56C4⋊C8×C269C2211yescharacteristic
57#102×C269C2211yescharacteristic
58#102×C269C2211yescharacteristic
59#16864401—22no—
60#16864401—22no—
61C2×Dic538C2311yescharacteristic
62C2×Dic538C2311yescharacteristic
63C2×Dic538C2311yescharacteristic
64C2×C22⋊D269—21no—
65C22×Dic269—21no—
66C22×Dic269—21no—
67C2×C4×D269—21no—
68C2×C4×D269C2311yescharacteristic
69Dic1076—22no—
70Dic1076—22no—
71#16864390—22no—
72#16864390—22no—
73C2×#14524130C2311yescharacteristic
74C2×#14524130C2311yescharacteristic
75C4⋊Dic269—21no—
76C4⋊Dic269—21no—
77C4⋊Dic269—21no—
78C4⋊Dic269—21no—
79C4⋊Dic269C2311yescharacteristic
80#16864381—21no—
81#16864381—21no—
82#16864381—21no—
83#16864381—21no—
84#16864381—21no—
85#16864381D411yescharacteristic
86#16864381D411yescharacteristic
87C22⋊Dic269—21no—
88#16864379—21no—
89#16864379—21no—
90#16864379D411yescharacteristic
91#16864379D411yescharacteristic
92C4×Dic269—21no—
93C4×Dic269—21no—
94C4×Dic269—21no—
95C4×Dic269—21no—
96C4×Dic269C2311yescharacteristic
97C2×D4×C269C2311yescharacteristic
98C22×C4×C269—21no—
99C2×C8×C269C2311yescharacteristic
100C2×C8×C269C2311yescharacteristic
101C4⋊C4×C269—21no—
102C4⋊C4×C269—21no—
103C4⋊C4×C269C2311yescharacteristic
104C4⋊C4×C269C2311yescharacteristic
105C4⋊C4×C269C2311yescharacteristic
106C22⋊C4×C269—21no—
107C42×C269C2311yescharacteristic
108C22×D269C2×D411yescharacteristic
109Dic538—21no—
110Dic538—21no—
111Dic538—21no—
112Dic538—21no—
113Dic538—21no—
114Dic538#4112yes—
115C22⋊D269—24no—
116C2×Dic269—24no—
117C2×Dic269—21no—
118C2×Dic269—21no—
119C2×Dic269—21no—
120C2×Dic269—21no—
121C2×Dic269—81no—
122C2×Dic269C2×D411yescharacteristic
123C2×Dic269C2×D411yescharacteristic
124C2×Dic269C2×D411yescharacteristic
125C4×D269—21no—
126C4×D269—21no—
127C4×D269—81no—
128#14524130—21no—
129#14524130—21no—
130C23×C269—21no—
131D4×C269—21no—
132D4×C269#4112yes—
133C2×C4×C269—21no—
134C2×C4×C269—21no—
135C2×C4×C269—21no—
136C2×C4×C269—81no—
137C2×C4×C269C2×D411yescharacteristic
138C2×C4×C269C2×D411yescharacteristic
139C2×C4×C269C2411yescharacteristic
140C8×C269—21no—
141C8×C269—21no—
142C22×C269—22no—
143C22×C269—41no—
144C22×C269—41no—
145C22×C269C22×D411yescharacteristic
146C2×D269—21no—
147C2×D269—21no—
148C2×D269—21no—
149C4×C269—21no—
150C4×C269—21no—
151C4×C269—41no—
152C4×C269—41no—
153C4×C269—41no—
154C4×C269C2×#4111yescharacteristic
155C4×C269C2×#4111yescharacteristic
156Dic269—21no—
157Dic269—22no—
158Dic269—21no—
159Dic269—21no—
160Dic269—41no—
161Dic269—41no—
162Dic269—41no—
163C2×C269—42no—
164C2×C269#52511yescharacteristic
165C2×C269#57711yescharacteristic
166C2×C269#57811yescharacteristic
167D269—41no—
168C269#312011yescharacteristic, complemented, Sylow
169#3120—2691nomaximal, Sylow
170#541—2691no—
171#520—2691no—
172#484—2691no—
173#483—2691no—
174#479—2691no—
175#478D26911yescharacteristic, complemented
176#462—2691no—
177#461—2691no—
178#452—2691no—
179#452—2691no—
180#441—2691no—
181#440—2691no—
182C4×Q16—2691no—
183C4×SD16—2691no—
184#433—2691no—
185C2×#41—2691no—
186C2×Q16—2691no—
187C2×Q16—2691no—
188C2×SD16—2691no—
189C2×SD16—2691no—
190C4⋊Q8—2691no—
191#126—5381no—
192#126—5381no—
193#125—5381no—
194#125—5381no—
195#125C2×D26911yescharacteristic
196C22⋊Q8—2691no—
197C22⋊Q8—2691no—
198C4×Q8—2691no—
199C4×Q8—2691no—
200C4×Q8—2691no—
201C4×Q8—2691no—
202C4×D4—2691no—
203C4×D4—5381no—
204C4×D4—5381no—
205C4×D4C2×D26911yescharacteristic
206#117—2691no—
207#117—5381no—
208C2×C4⋊C4—2691no—
209C2×C4⋊C4—5381no—
210#107—2691no—
211#107C2×D26911yescharacteristic
212#106—2691no—
213#106C2×D26911yescharacteristic
214C4⋊C8—2691no—
215C4⋊C8C2×D26911yescharacteristic
216#103—2691no—
217#103—2691no—
218#103—2691no—
219#103—2691no—
220#103—2691no—
221#103—2691no—
222#102C2×D26911yescharacteristic
223#102C2×D26911yescharacteristic
224C22⋊C8—2691no—
225C22⋊C8—2691no—
226#97—2691no—
227C4×C8—2691no—
228#41—5382no—
229#41—5382no—
230C2×Q8—2691no—
231C2×Q8—2691no—
232C2×Q8—2691no—
233C2×D4—5381no—
234C2×D4C22×D26911yescharacteristic
235C22×C4—21no—
236C22×C4—2691no—
237C22×C4—5381no—
238C22×C4—5381no—
239C22×C4—5381no—
240Q16—5382no—
241Q16—5382no—
242SD16—5382no—
243SD16—5382no—
244C2×C8—2691no—
245C2×C8—2691no—
246C2×C8C22×D26911yescharacteristic
247C2×C8C22×D26911yescharacteristic
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—2691no—
251C4⋊C4—2691no—
252C4⋊C4—2691no—
253C4⋊C4—5381no—
254C4⋊C4—5381no—
255C4⋊C4—5381no—
256C4⋊C4—5381no—
257C4⋊C4—5381no—
258C4⋊C4—5381no—
259C4⋊C4—5381no—
260C4⋊C4—5381no—
261C4⋊C4—5381no—
262C4⋊C4C22×D26911yescharacteristic
263C4⋊C4C22×D26911yescharacteristic
264C4⋊C4C22×D26911yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—2691no—
267C22⋊C4—2691no—
268C22⋊C4—5381no—
269C22⋊C4—5381no—
270C22⋊C4—5381no—
271C42—2691no—
272C42—5381no—
273C42—5381no—
274C42—5381no—
275C42—5381no—
276C42C22×D26911yescharacteristic
277C23—21no—
278C23—2691no—
279Q8—2692no—
280Q8—5381no—
281Q8—5381no—
282Q8—5381no—
283Q8—5381no—
284Q8—5381no—
285D4—21no—
286D4—5384no—
287D4#1686440312yes—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—81no—
292C2×C4—2691no—
293C2×C4—2691no—
294C2×C4—2691no—
295C2×C4—5384no—
296C2×C4—5381no—
297C2×C4—5381no—
298C2×C4—5381no—
299C2×C4—5381no—
300C2×C4—5381no—
301C2×C4—5381no—
302C2×C4—21521no—
303C2×C4—21521no—
304C2×C4D4×D26911yescharacteristic
305C2×C4D4×D26911yescharacteristic
306C2×C4C23×D26911yescharacteristic
307C8—21no—
308C8—21no—
309C8—5381no—
310C8—5381no—
311C22—22no—
312C22—41no—
313C22—41no—
314C22—5381no—
315C22—5381no—
316C22—5381no—
317C22C2×D4×D26911yescharacteristic
318C4—21no—
319C4—21no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—5381no—
324C4—5381no—
325C4—5381no—
326C4—5382no—
327C4—10761no—
328C4—10761no—
329C4—10761no—
330C4#41×D26911yescharacteristic
331C4C2×#1686440311yescharacteristic
332C2—42no—
333C2—10761no—
334C2#3177111811yescharacteristic
335C2#3177141511yescharacteristic
336C2#3177141911yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#478×C269C2
socleC22×C269C22×D4
prime radicalC2×#16864401C22
hypercenter#478D269
hypocenterC269#3120
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #31771218C2semidirect
3. #31770942C2semidirect
4. #31770937C2semidirect
5. #31770909C2semidirect
6. #31770816C2semidirect
7. #31770810C2semidirect
10. #31770711C2semidirect
11. #31770702C2semidirect
12. #31770699C2semidirect
13. #31770696C2semidirect
14. #31770665C2semidirect
15. #478×C269C2semidirect
168. C269#3120semidirect
175. #478D269semidirect

Maximal subgroups

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

subgroupindex
#317712182
#317710842
#317709422
#317709372
#317709092
#317708162
#317708102
#317707682
#317707112
#317707022
#317706992
#317706962
#317706652
#478×C2692
#3120269