Finite Group Databasebeta

← #46821135

Subgroups — #46821135

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#31771216C211yesmaximal, characteristic, complemented
2#31771077C211yesmaximal, characteristic
3#31770945C211yesmaximal, characteristic, complemented
4#31770944C211yesmaximal, characteristic, complemented
5#31770906C211yesmaximal, characteristic, complemented
6#31770905C211yesmaximal, characteristic, complemented
7#31770807C211yesmaximal, characteristic, complemented
8#31770754C211yesmaximal, characteristic
9#31770754C211yesmaximal, characteristic
10#31770708C211yesmaximal, characteristic, complemented
11#31770706C211yesmaximal, characteristic, complemented
12SD16×Dic269C211yesmaximal, characteristic, complemented
13#31770690C211yesmaximal, characteristic, complemented
14#31770665C211yesmaximal, characteristic, complemented
15#461×C269C211yesmaximal, characteristic, complemented
16C2×D4×D269C2211yescharacteristic
17C2×#16864389C2211yescharacteristic
18C2×#16864389C2211yescharacteristic
19#22575448—21no—
20#22575448—21no—
21#22575445C2211yescharacteristic, complemented
22#22575443—21no—
23#22575443—21no—
24#22575429C2211yescharacteristic
25#22575429C2211yescharacteristic
26Q8×Dic269C2211yescharacteristic, complemented
27Q8×Dic269C2211yescharacteristic, complemented
28C4×D1076C2211yescharacteristic
29D4×Dic269C2211yescharacteristic
30#22575415C2211yescharacteristic
31C4×C22⋊D269—21no—
32#22575413—21no—
33#22575411C2211yescharacteristic
34#22575410C2211yescharacteristic
35C2×#16864379—21no—
36C22⋊C4×D269—21no—
37#22575387C2211yescharacteristic, complemented
38#22575386C2211yescharacteristic, complemented
39#22575385C2211yescharacteristic, complemented
40#22575384C2211yescharacteristic, complemented
41C4⋊#14524130C2211yescharacteristic, complemented
42#22575377C2211yescharacteristic, complemented
43#22575377C2211yescharacteristic, complemented
44#22575375C2211yescharacteristic
45#22575375C2211yescharacteristic
46#22575374C2211yescharacteristic
47#22575374C2211yescharacteristic
48#22575365C2211yescharacteristic
49#22575365C2211yescharacteristic
50#22575363C2211yescharacteristic, complemented
51C8×Dic269C2211yescharacteristic, complemented
52C2×SD16×C269C2211yescharacteristic
53C2×SD16×C269C2211yescharacteristic
54C4⋊Q8×C269C2211yescharacteristic, complemented
55C4×D4×C269C2211yescharacteristic
56C4⋊C8×C269C2211yescharacteristic, complemented
57#103×C269C2211yescharacteristic, complemented
58#103×C269C2211yescharacteristic, complemented
59C23×D269—21no—
60C2×D1076C2311yescharacteristic
61C2×C22⋊D269—21no—
62D4×D269—22no—
63D4×D269—22no—
64C22×Dic269—21no—
65C2×C4×D269—21no—
66C2×C4×D269—21no—
67C2×C4×D269C2311yescharacteristic
68#16864389—22no—
69#16864389—22no—
70C2×#14524130C2311yescharacteristic
71C2×#14524130C2311yescharacteristic
72C4⋊Dic269—21no—
73C4⋊Dic269—21no—
74C4⋊Dic269C2311yescharacteristic
75C4⋊Dic269C2311yescharacteristic
76C4⋊Dic269C2311yescharacteristic
77#16864381—21no—
78#16864381—21no—
79#16864381—21no—
80#16864381—21no—
81#16864381D411yescharacteristic
82#16864381D411yescharacteristic
83C22⋊Dic269—21no—
84#16864379—21no—
85#16864379—21no—
86#16864379—21no—
87#16864379—21no—
88#16864379—21no—
89#16864379D411yescharacteristic
90#16864379D411yescharacteristic
91C4×Dic269—21no—
92C4×Dic269—21no—
93C4×Dic269—21no—
94C4×Dic269C2311yescharacteristic
95C2×Q8×C269C2311yescharacteristic
96C2×Q8×C269C2311yescharacteristic
97C2×D4×C269C2311yescharacteristic
98C22×C4×C269—21no—
99SD16×C269—22no—
100SD16×C269—22no—
101C2×C8×C269C2311yescharacteristic
102C2×C8×C269C2311yescharacteristic
103C4⋊C4×C269—21no—
104C4⋊C4×C269—21no—
105C4⋊C4×C269C2311yescharacteristic
106C22⋊C4×C269—21no—
107C42×C269C2311yescharacteristic
108C22×D269—21no—
109C22×D269—24no—
110C22×D269—81no—
111C22×D269—81no—
112C22×D269C2×D411yescharacteristic
113D1076—21no—
114D1076#4112yes—
115C22⋊D269—24no—
116C2×Dic269—21no—
117C2×Dic269—21no—
118C2×Dic269—21no—
119C2×Dic269—81no—
120C2×Dic269C2×D411yescharacteristic
121C2×Dic269C2×D411yescharacteristic
122C2×Dic269C2×D411yescharacteristic
123C4×D269—21no—
124C4×D269—21no—
125C4×D269—81no—
126C4×D269—81no—
127#14524130—21no—
128#14524130—21no—
129C23×C269—21no—
130Q8×C269—21no—
131Q8×C269—21no—
132Q8×C269—21no—
133Q8×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#478—2691no—
183#461—2691no—
184#461D26911yescharacteristic, complemented
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×SD16C2×D26911yescharacteristic
196C2×SD16C2×D26911yescharacteristic
197C4⋊Q8C2×D26911yescharacteristic, complemented
198#126—5381no—
199#126—5381no—
200#125—2691no—
201#125—5381no—
202#125—5381no—
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#107—2691no—
219#106—2691no—
220#106—2691no—
221C4⋊C8—2691no—
222C4⋊C8C2×D26911yescharacteristic, complemented
223#103—2691no—
224#103—2691no—
225#103C2×D26911yescharacteristic, complemented
226#103C2×D26911yescharacteristic, complemented
227#102—2691no—
228#102—2691no—
229#102—2691no—
230#102—2691no—
231C22⋊C8—2691no—
232C22⋊C8—2691no—
233#97—2691no—
234C4×C8—2691no—
235C24—5381no—
236C2×Q8C22×D26911yescharacteristic
237C2×Q8C22×D26911yescharacteristic
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—22no—
249SD16—22no—
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—2691no—
262C4⋊C4—2691no—
263C4⋊C4—5381no—
264C4⋊C4—5381no—
265C4⋊C4—5381no—
266C4⋊C4—5381no—
267C4⋊C4—5381no—
268C4⋊C4—5381no—
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—21no—
291Q8—21no—
292Q8—21no—
293Q8—21no—
294D4—21no—
295D4—2692no—
296D4—5384no—
297D4—5381no—
298D4#1686440112yes—
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×#1686440111yescharacteristic
345C2—42no—
346C2—10761no—
347C2—10762no—
348C2#3177111511yescharacteristic
349C2#3177141111yescharacteristic
350C2#3177141411yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#461×C269C2
socleC22×C269C22×D4
prime radicalC2×D4×D269C22
hypercenter#461D269
hypocenterC269#3123
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. #31771216C2semidirect
3. #31770945C2semidirect
4. #31770944C2semidirect
5. #31770906C2semidirect
6. #31770905C2semidirect
7. #31770807C2semidirect
10. #31770708C2semidirect
11. #31770706C2semidirect
12. SD16×Dic269C2semidirect
13. #31770690C2semidirect
14. #31770665C2semidirect
15. #461×C269C2semidirect
21. #22575445C22semidirect
26. Q8×Dic269C22semidirect
27. Q8×Dic269C22semidirect
37. #22575387C22semidirect
38. #22575386C22semidirect
39. #22575385C22semidirect
40. #22575384C22semidirect
41. C4⋊#14524130C22semidirect
42. #22575377C22semidirect
43. #22575377C22semidirect
50. #22575363C22semidirect
51. C8×Dic269C22semidirect
54. C4⋊Q8×C269C22semidirect
56. C4⋊C8×C269C22semidirect
57. #103×C269C22semidirect
58. #103×C269C22semidirect
175. C269#3123semidirect
184. #461D269semidirect
197. C4⋊Q8C2×D269semidirect
222. C4⋊C8C2×D269semidirect
225. #103C2×D269semidirect
226. #103C2×D269semidirect

Maximal subgroups

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

subgroupindex
#317712162
#317710772
#317709452
#317709442
#317709062
#317709052
#317708072
#317707542
#317707082
#317707062
SD16×Dic2692
#317706902
#317706652
#461×C2692
#3123269