Finite Group Databasebeta

← #46821139

Subgroups — #46821139

Order 34432.

394 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771218C211yesmaximal, characteristic, complemented
2#31771077C211yesmaximal, characteristic
3#31770949C211yesmaximal, characteristic, complemented
4#31770948C211yesmaximal, characteristic, complemented
5#31770902C211yesmaximal, characteristic, complemented
6#31770811C211yesmaximal, characteristic, complemented
7#31770810C211yesmaximal, characteristic, complemented
8#31770757C211yesmaximal, characteristic
9#31770757C211yesmaximal, characteristic
10#31770704C211yesmaximal, characteristic, complemented
11#31770702C211yesmaximal, characteristic, complemented
12#31770696C211yesmaximal, characteristic, complemented
13#31770692C211yesmaximal, characteristic, complemented
14#31770665C211yesmaximal, characteristic, complemented
15#478×C269C211yesmaximal, characteristic, complemented
16C2×D4×D269C2211yescharacteristic
17C2×#16864391C2211yescharacteristic
18C2×#16864391C2211yescharacteristic
19C2×#16864390C2211yescharacteristic
20C2×#16864390C2211yescharacteristic
21#22575453C2211yescharacteristic, complemented
22#22575448—21no—
23#22575448—21no—
24#22575444—21no—
25#22575444—21no—
26#22575433C2211yescharacteristic
27#22575433C2211yescharacteristic
28#22575418C2211yescharacteristic, complemented
29#22575418C2211yescharacteristic, complemented
30C4×D1076C2211yescharacteristic
31D4×Dic269C2211yescharacteristic
32#22575415C2211yescharacteristic
33C4×C22⋊D269—21no—
34#22575413—21no—
35#22575411C2211yescharacteristic
36#22575410C2211yescharacteristic
37C2×#16864379—21no—
38C22⋊C4×D269—21no—
39#22575386C2211yescharacteristic, complemented
40#22575384C2211yescharacteristic, complemented
41C4⋊#14524130C2211yescharacteristic, complemented
42#22575378C2211yescharacteristic, complemented
43#22575378C2211yescharacteristic, complemented
44#22575376C2211yescharacteristic, complemented
45#22575376C2211yescharacteristic, complemented
46#22575373C2211yescharacteristic
47#22575373C2211yescharacteristic
48#22575365C2211yescharacteristic
49#22575365C2211yescharacteristic
50#22575363C2211yescharacteristic, complemented
51C8×Dic269C2211yescharacteristic, complemented
52#125×C269C2211yescharacteristic, complemented
53C4×D4×C269C2211yescharacteristic
54#107×C269C2211yescharacteristic, complemented
55#106×C269C2211yescharacteristic, complemented
56C4⋊C8×C269C2211yescharacteristic, complemented
57#102×C269C2211yescharacteristic
58#102×C269C2211yescharacteristic
59C23×D269—21no—
60C2×Dic538C2311yescharacteristic
61C2×Dic538C2311yescharacteristic
62C2×D1076C2311yescharacteristic
63C2×C22⋊D269—21no—
64D4×D269—22no—
65D4×D269—22no—
66C22×Dic269—21no—
67C2×C4×D269—21no—
68C2×C4×D269—21no—
69C2×C4×D269C2311yescharacteristic
70#16864391—22no—
71#16864391—22no—
72#16864390—22no—
73#16864390—22no—
74C2×#14524130C2311yescharacteristic
75C2×#14524130C2311yescharacteristic
76C4⋊Dic269—21no—
77C4⋊Dic269—21no—
78C4⋊Dic269—21no—
79C4⋊Dic269—21no—
80C4⋊Dic269C2311yescharacteristic
81#16864381—21no—
82#16864381—21no—
83#16864381D411yescharacteristic
84#16864381D411yescharacteristic
85C22⋊Dic269—21no—
86#16864379—21no—
87#16864379—21no—
88#16864379—21no—
89#16864379—21no—
90#16864379—21no—
91#16864379D411yescharacteristic
92#16864379D411yescharacteristic
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×D269—21no—
109C22×D269—24no—
110C22×D269—81no—
111C22×D269—81no—
112C22×D269C2×D411yescharacteristic
113Dic538—21no—
114Dic538—21no—
115Dic538—21no—
116Dic538—21no—
117D1076—21no—
118D1076#4112yes—
119C22⋊D269—24no—
120C2×Dic269—21no—
121C2×Dic269—21no—
122C2×Dic269—21no—
123C2×Dic269—81no—
124C2×Dic269C2×D411yescharacteristic
125C2×Dic269C2×D411yescharacteristic
126C2×Dic269C2×D411yescharacteristic
127C4×D269—21no—
128C4×D269—21no—
129C4×D269—81no—
130C4×D269—81no—
131#14524130—21no—
132#14524130—21no—
133C23×C269—21no—
134D4×C269—21no—
135D4×C269#4112yes—
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×C269C2411yescharacteristic
143C8×C269—21no—
144C8×C269—21no—
145C22×C269—22no—
146C22×C269—41no—
147C22×C269—41no—
148C22×C269C22×D411yescharacteristic
149C2×D269—21no—
150C2×D269—22no—
151C2×D269—21no—
152C2×D269—21no—
153C2×D269—41no—
154C2×D269—41no—
155C2×D269—84no—
156C4×C269—21no—
157C4×C269—21no—
158C4×C269—41no—
159C4×C269—41no—
160C4×C269—41no—
161C4×C269C2×#4111yescharacteristic
162C4×C269C2×#4111yescharacteristic
163Dic269—21no—
164Dic269—21no—
165Dic269—21no—
166Dic269—41no—
167Dic269—41no—
168Dic269—41no—
169C2×C269—42no—
170C2×C269#52511yescharacteristic
171C2×C269#57711yescharacteristic
172C2×C269#57711yescharacteristic
173D269—41no—
174D269—42no—
175C269#312311yescharacteristic, complemented, Sylow
176#3123—2691nomaximal, Sylow
177#541—2691no—
178#518—2691no—
179#485—2691no—
180#485—2691no—
181#478—2691no—
182#478D26911yescharacteristic, complemented
183#461—2691no—
184#461—2691no—
185#450—2691no—
186#450—2691no—
187#440—2691no—
188#440—2691no—
189C4×SD16—2691no—
190C4×SD16—2691no—
191#433—2691no—
192C22×D4—2691no—
193C2×SD16—2691no—
194C2×SD16—2691no—
195C2×SD16—2691no—
196C2×SD16—2691no—
197C4⋊Q8—2691no—
198#126—5381no—
199#126—5381no—
200#125—5381no—
201#125—5381no—
202#125C2×D26911yescharacteristic, complemented
203C22⋊Q8—2691no—
204C22⋊Q8—2691no—
205C4×Q8—2691no—
206C4×Q8—2691no—
207C4×D4—2691no—
208C4×D4—2691no—
209C4×D4—2691no—
210C4×D4—5381no—
211C4×D4—5381no—
212C4×D4C2×D26911yescharacteristic
213#117—2691no—
214#117—2691no—
215C2×C22⋊C4—5381no—
216C2×C22⋊C4—5381no—
217#107—2691no—
218#107C2×D26911yescharacteristic, complemented
219#106—2691no—
220#106C2×D26911yescharacteristic, complemented
221C4⋊C8—2691no—
222C4⋊C8C2×D26911yescharacteristic, complemented
223#103—2691no—
224#103—2691no—
225#103—2691no—
226#103—2691no—
227#102—2691no—
228#102—2691no—
229#102C2×D26911yescharacteristic
230#102C2×D26911yescharacteristic
231C22⋊C8—2691no—
232C22⋊C8—2691no—
233#97—2691no—
234C4×C8—2691no—
235C24—5381no—
236C2×Q8—2691no—
237C2×Q8—2691no—
238C2×D4—2691no—
239C2×D4—5381no—
240C2×D4—5382no—
241C2×D4—5382no—
242C2×D4C22×D26911yescharacteristic
243C22×C4—21no—
244C22×C4—2691no—
245C22×C4—5381no—
246C22×C4—5381no—
247C22×C4—5381no—
248SD16—5382no—
249SD16—5382no—
250SD16—5382no—
251SD16—5382no—
252C2×C8—2691no—
253C2×C8—2691no—
254C2×C8C22×D26911yescharacteristic
255C2×C8C22×D26911yescharacteristic
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—2691no—
259C4⋊C4—2691no—
260C4⋊C4—2691no—
261C4⋊C4—5381no—
262C4⋊C4—5381no—
263C4⋊C4—5381no—
264C4⋊C4—5381no—
265C4⋊C4—5381no—
266C4⋊C4—5381no—
267C4⋊C4C22×D26911yescharacteristic
268C4⋊C4C22×D26911yescharacteristic
269C4⋊C4C22×D26911yescharacteristic
270C22⋊C4—21no—
271C22⋊C4—2691no—
272C22⋊C4—2691no—
273C22⋊C4—5381no—
274C22⋊C4—5381no—
275C22⋊C4—5381no—
276C22⋊C4—5381no—
277C22⋊C4—5381no—
278C22⋊C4—5381no—
279C42—2691no—
280C42—5381no—
281C42—5381no—
282C42—5381no—
283C42C22×D26911yescharacteristic
284C23—21no—
285C23—2691no—
286C23—5384no—
287C23—5381no—
288C23—21521no—
289C23—21521no—
290Q8—5381no—
291Q8—5381no—
292Q8—5381no—
293Q8—5381no—
294D4—21no—
295D4—2692no—
296D4—5384no—
297D4—5381no—
298D4#1686440312yes—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—81no—
303C2×C4—2691no—
304C2×C4—2691no—
305C2×C4—2691no—
306C2×C4—5381no—
307C2×C4—5381no—
308C2×C4—5381no—
309C2×C4—5381no—
310C2×C4—5381no—
311C2×C4—21521no—
312C2×C4—21521no—
313C2×C4—21521no—
314C2×C4D4×D26911yescharacteristic
315C2×C4D4×D26911yescharacteristic
316C2×C4C23×D26911yescharacteristic
317C8—21no—
318C8—21no—
319C8—5381no—
320C8—5381no—
321C22—22no—
322C22—41no—
323C22—41no—
324C22—5381no—
325C22—5381no—
326C22—5381no—
327C22—5382no—
328C22—10761no—
329C22—10761no—
330C22—21524no—
331C22C2×D4×D26911yescharacteristic
332C4—21no—
333C4—21no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—5381no—
338C4—5381no—
339C4—5381no—
340C4—10761no—
341C4—10761no—
342C4—10761no—
343C4#41×D26911yescharacteristic
344C4C2×#1686440311yescharacteristic
345C2—42no—
346C2—10761no—
347C2—10762no—
348C2#3177111811yescharacteristic
349C2#3177141211yescharacteristic
350C2#3177141511yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#478×C269C2
socleC22×C269C22×D4
prime radicalC2×D4×D269C22
hypercenter#478D269
hypocenterC269#3123
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. #31770949C2semidirect
4. #31770948C2semidirect
5. #31770902C2semidirect
6. #31770811C2semidirect
7. #31770810C2semidirect
10. #31770704C2semidirect
11. #31770702C2semidirect
12. #31770696C2semidirect
13. #31770692C2semidirect
14. #31770665C2semidirect
15. #478×C269C2semidirect
21. #22575453C22semidirect
28. #22575418C22semidirect
29. #22575418C22semidirect
39. #22575386C22semidirect
40. #22575384C22semidirect
41. C4⋊#14524130C22semidirect
42. #22575378C22semidirect
43. #22575378C22semidirect
44. #22575376C22semidirect
45. #22575376C22semidirect
50. #22575363C22semidirect
51. C8×Dic269C22semidirect
52. #125×C269C22semidirect
54. #107×C269C22semidirect
55. #106×C269C22semidirect
56. C4⋊C8×C269C22semidirect
175. C269#3123semidirect
182. #478D269semidirect
202. #125C2×D269semidirect
218. #107C2×D269semidirect
220. #106C2×D269semidirect
222. C4⋊C8C2×D269semidirect

Maximal subgroups

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

subgroupindex
#317712182
#317710772
#317709492
#317709482
#317709022
#317708112
#317708102
#317707572
#317707042
#317707022
#317706962
#317706922
#317706652
#478×C2692
#3123269