Finite Group Databasebeta

← #46819712

Subgroups — #46819712

Order 34432.

506 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22575480C211yesmaximal, characteristic
2#31771087C211yesmaximal, characteristic, complemented
3#31771077C211yesmaximal, characteristic, complemented
4#31770716C211yesmaximal, characteristic, complemented
5#31770715C211yesmaximal, characteristic, complemented
6#31770706C211yesmaximal, characteristic, complemented
7#31770703C211yesmaximal, characteristic, complemented
8#31770690C211yesmaximal, characteristic, complemented
9C4×D2152C211yesmaximal, characteristic, complemented
10#31770685C211yesmaximal, characteristic, complemented
11#31770644C211yesmaximal, characteristic, complemented
12#31770600C211yesmaximal, characteristic, complemented
13#102×D269C211yesmaximal, characteristic, complemented
14#31770559C211yesmaximal, characteristic, complemented
15C4×SD16×C269C211yesmaximal, characteristic, complemented
16C2×#16864403C2211yescharacteristic
17C2×D4×D269C2211yescharacteristic
18#22575480C418yescomplemented
19C2×#16864389C2211yescharacteristic
20C2×D2152C2211yescharacteristic
21C2×#16864387C2211yescharacteristic
22C2×#16864385C2211yescharacteristic
23C2×C8×D269C2211yescharacteristic
24Q8×Dic269C2211yescharacteristic, complemented
25C4×D1076—21no—
26C4×D1076C2211yescharacteristic
27C4×D1076C2211yescharacteristic, complemented
28D4×Dic269C2211yescharacteristic
29#22575415—21no—
30#22575415C2211yescharacteristic
31#22575415C2211yescharacteristic, complemented
32C4×C22⋊D269—21no—
33#22575413—21no—
34#22575411C2211yescharacteristic
35#22575410—21no—
36#22575410C2211yescharacteristic
37C4⋊C4×D269—21no—
38C4⋊C4×D269C2211yescharacteristic
39C2×#16864379—21no—
40C22⋊C4×D269—21no—
41#22575387C2211yescharacteristic, complemented
42#22575386C2211yescharacteristic, complemented
43#22575384C2211yescharacteristic, complemented
44#22575377C2211yescharacteristic, complemented
45#22575375C2211yescharacteristic
46#22575375C2211yescharacteristic, complemented
47#22575374C2211yescharacteristic
48#22575373C2211yescharacteristic
49#22575373C2211yescharacteristic, complemented
50#22575364C2211yescharacteristic, complemented
51#22575363C2211yescharacteristic, complemented
52C8×Dic269C2211yescharacteristic, complemented
53C2×SD16×C269C2211yescharacteristic
54C4×Q8×C269C2211yescharacteristic, complemented
55C4×D4×C269C2211yescharacteristic
56#106×C269C2211yescharacteristic, complemented
57#103×C269C2211yescharacteristic, complemented
58#102×C269C2211yescharacteristic
59C4×C8×C269C2211yescharacteristic, complemented
60C23×D269—21no—
61#16864403—22no—
62#16864403C2×C414yescomplemented
63C2×D1076—21no—
64C2×D1076C2311yescharacteristic
65C2×D1076C2311yescharacteristic
66C2×C22⋊D269—21no—
67D4×D269—22no—
68D4×D269C2×C414yescomplemented
69C22×Dic269—21no—
70C2×C4×D269—21no—
71C2×C4×D269—21no—
72C2×C4×D269—21no—
73C2×C4×D269—21no—
74C2×C4×D269—21no—
75C2×C4×D269—21no—
76C2×C4×D269C2311yescharacteristic
77#16864389C2×C414yescomplemented
78D2152C2×C414yescomplemented
79#16864387C2×C414yescomplemented
80#16864385C2×C414yescomplemented
81C2×#14524130C2311yescharacteristic
82C2×#14524130C2311yescharacteristic
83C8×D269—22no—
84C4⋊Dic269—21no—
85C4⋊Dic269C2311yescharacteristic
86C4⋊Dic269C2311yescharacteristic
87#16864381—21no—
88#16864381D411yescharacteristic
89#16864381D411yescharacteristic
90C22⋊Dic269—21no—
91#16864379—21no—
92#16864379—21no—
93#16864379—21no—
94#16864379—21no—
95#16864379—21no—
96#16864379D411yescharacteristic
97#16864379D411yescharacteristic
98C4×Dic269—21no—
99C4×Dic269—21no—
100C4×Dic269C2311yescharacteristic
101C2×Q8×C269C2311yescharacteristic
102C2×D4×C269C2311yescharacteristic
103C22×C4×C269—21no—
104SD16×C269C2×C414yescomplemented
105C2×C8×C269C2311yescharacteristic
106C2×C8×C269C2311yescharacteristic
107C4⋊C4×C269—21no—
108C4⋊C4×C269C2311yescharacteristic
109C4⋊C4×C269C2311yescharacteristic
110C22⋊C4×C269—21no—
111C42×C269—21no—
112C42×C269C2311yescharacteristic
113C22×D269—21no—
114C22×D269—21no—
115C22×D269—24no—
116C22×D269—81no—
117C22×D269—81no—
118C22×D269C2×D411yescharacteristic
119D1076—24no—
120D1076—21no—
121D1076—21no—
122D1076C22×C412yes—
123D1076C22×C412yes—
124C22⋊D269—24no—
125C2×Dic269—21no—
126C2×Dic269—21no—
127C2×Dic269—81no—
128C2×Dic269C2×D411yescharacteristic
129C2×Dic269C2×D411yescharacteristic
130C2×Dic269C2×D411yescharacteristic
131C4×D269—24no—
132C4×D269—81no—
133C4×D269—81no—
134C4×D269—81no—
135C4×D269—81no—
136C4×D269—81no—
137C4×D269C22×C412yes—
138C4×D269#4112yes—
139#14524130—21no—
140#14524130C22×C412yes—
141C23×C269—21no—
142Q8×C269—21no—
143Q8×C269C22×C412yes—
144D4×C269—21no—
145D4×C269C22×C412yes—
146C2×C4×C269—21no—
147C2×C4×C269—21no—
148C2×C4×C269—21no—
149C2×C4×C269—81no—
150C2×C4×C269C2×D411yescharacteristic
151C2×C4×C269C2×D411yescharacteristic
152C2×C4×C269C2411yescharacteristic
153C8×C269—21no—
154C8×C269C22×C412yes—
155C22×C269—22no—
156C22×C269—41no—
157C22×C269—41no—
158C22×C269C22×D411yescharacteristic
159C2×D269—21no—
160C2×D269—21no—
161C2×D269—22no—
162C2×D269—22no—
163C2×D269—41no—
164C2×D269—41no—
165C2×D269—41no—
166C2×D269—41no—
167C2×D269—84no—
168C2×D269C4×D412yes—
169C4×C269—22no—
170C4×C269—21no—
171C4×C269—21no—
172C4×C269—41no—
173C4×C269—41no—
174C4×C269C23×C411yescharacteristic
175C4×C269C2×#4111yescharacteristic
176Dic269—21no—
177Dic269—21no—
178Dic269—41no—
179Dic269—41no—
180Dic269C4×D412yes—
181C2×C269—42no—
182C2×C269C2×C4×D411yescharacteristic
183C2×C269#57611yescharacteristic
184C2×C269#57711yescharacteristic
185D269—22no—
186D269—42no—
187D269—42no—
188C269#294611yescharacteristic, complemented, Sylow
189#2946—2691nomaximal, Sylow
190C2×AGL(1,ℤ/8)—2691no—
191#520—2691no—
192#518—2691no—
193#442—2691no—
194#442—2691no—
195#440—2691no—
196#440—2691no—
197C4×SD16—2691no—
198C4×SD16D26911yescharacteristic, complemented
199C4×D8—2691no—
200C4×D8—2691no—
201#428—2691no—
202#416—2691no—
203C2×#102—2691no—
204#405—2691no—
205C2×#41—2691no—
206C22×D4—2691no—
207AGL(1,ℤ/8)—2698no—
208C2×SD16—2691no—
209C2×SD16C2×D26911yescharacteristic
210C2×D8—2691no—
211C2×D8—2691no—
212C2×M16—2691no—
213C22×C8—2691no—
214C4×Q8—2691no—
215C4×Q8C2×D26911yescharacteristic, complemented
216C4×D4—2691no—
217C4×D4—2691no—
218C4×D4—2691no—
219C4×D4—2691no—
220C4×D4—2691no—
221C4×D4—5381no—
222C4×D4—5381no—
223C4×D4—5381no—
224C4×D4—5381no—
225C4×D4C2×D26911yescharacteristic
226#117—2691no—
227#117—2691no—
228#117—5381no—
229C2×C4⋊C4—2691no—
230C2×C4⋊C4—5381no—
231C2×C22⋊C4—5381no—
232C2×C22⋊C4—5381no—
233#107—2691no—
234#107—2691no—
235#106—2691no—
236#106C2×D26911yescharacteristic, complemented
237#103—2691no—
238#103C2×D26911yescharacteristic, complemented
239#102—2691no—
240#102—2691no—
241#102—2691no—
242#102—2691no—
243#102—2691no—
244#102C2×D26911yescharacteristic
245#97—2691no—
246#97—2691no—
247C4×C8—2691no—
248C4×C8C2×D26911yescharacteristic, complemented
249C24—5381no—
250#41—2694no—
251#41—5382no—
252C2×Q8C22×D26911yescharacteristic
253C2×D4—2694no—
254C2×D4—2691no—
255C2×D4—2691no—
256C2×D4—5381no—
257C2×D4—5382no—
258C2×D4—5381no—
259C2×D4C22×D26911yescharacteristic
260C22×C4—21no—
261C22×C4—2691no—
262C22×C4—5381no—
263C22×C4—5381no—
264C22×C4—5381no—
265C22×C4—5381no—
266C22×C4—5381no—
267C22×C4—5381no—
268C22×C4—5381no—
269SD16—2694no—
270SD16C4×D26914yescomplemented
271D8—2694no—
272D8—2694no—
273M16—2694no—
274C2×C8—2691no—
275C2×C8—2691no—
276C2×C8—5382no—
277C2×C8C22×D26911yescharacteristic
278C2×C8C22×D26911yescharacteristic
279C4⋊C4—21no—
280C4⋊C4—2691no—
281C4⋊C4—2691no—
282C4⋊C4—2691no—
283C4⋊C4—2691no—
284C4⋊C4—5381no—
285C4⋊C4—5381no—
286C4⋊C4C22×D26911yescharacteristic
287C4⋊C4C22×D26911yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—2691no—
290C22⋊C4—2691no—
291C22⋊C4—5381no—
292C22⋊C4—5381no—
293C22⋊C4—5381no—
294C22⋊C4—5381no—
295C22⋊C4—5381no—
296C22⋊C4—5381no—
297C42—21no—
298C42—2691no—
299C42—5381no—
300C42—5381no—
301C42C22×D26911yescharacteristic
302C23—21no—
303C23—2691no—
304C23—5384no—
305C23—5381no—
306C23—5381no—
307C23—21521no—
308C23—21521no—
309Q8—21no—
310Q8C2×C4×D26912yes—
311D4—21no—
312D4—2692no—
313D4—2692no—
314D4—5384no—
315D4—5384no—
316D4—5381no—
317D4—5381no—
318D4C2×C4×D26912yes—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—81no—
323C2×C4—2691no—
324C2×C4—2692no—
325C2×C4—2692no—
326C2×C4—2691no—
327C2×C4—2691no—
328C2×C4—5384no—
329C2×C4—5381no—
330C2×C4—5381no—
331C2×C4—21521no—
332C2×C4—21521no—
333C2×C4—21521no—
334C2×C4—21521no—
335C2×C4—21521no—
336C2×C4—21521no—
337C2×C4D4×D26911yescharacteristic
338C2×C4D4×D26911yescharacteristic
339C2×C4C23×D26911yescharacteristic
340C8—21no—
341C8—2692no—
342C8—5381no—
343C8C2×C4×D26912yes—
344C22—22no—
345C22—41no—
346C22—41no—
347C22—2692no—
348C22—5381no—
349C22—5381no—
350C22—5382no—
351C22—5382no—
352C22—10761no—
353C22—10761no—
354C22—10761no—
355C22—10761no—
356C22—21524no—
357C22C2×D4×D26911yescharacteristic
358C4—21no—
359C4—21no—
360C4—22no—
361C4—41no—
362C4—41no—
363C4—2692no—
364C4—5381no—
365C4—5381no—
366C4—10761no—
367C4—10761no—
368C4C22×C4×D26911yescharacteristic
369C4#41×D26911yescharacteristic
370C2—42no—
371C2—5382no—
372C2—10762no—
373C2—10762no—
374C2C4×D4×D26911yescharacteristic
375C2#3177140711yescharacteristic
376C2#3177141111yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutatorC4×C269C23×C4
FrattiniC2×C4C23×D269
FittingC4×SD16×C269C2
socleC22×C269C22×D4
prime radicalC2×#22575480C2
cosocleC2×C4×C269C24
hypercenterC4×SD16D269
hypocenterC269#2946
LCSG ▷ C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
2. #31771087C2semidirect
3. #31771077C2semidirect
4. #31770716C2semidirect
5. #31770715C2semidirect
6. #31770706C2semidirect
7. #31770703C2semidirect
8. #31770690C2semidirect
9. C4×D2152C2semidirect
10. #31770685C2semidirect
11. #31770644C2semidirect
12. #31770600C2semidirect
13. #102×D269C2semidirect
14. #31770559C2semidirect
15. C4×SD16×C269C2semidirect
18. #22575480C4semidirect
24. Q8×Dic269C22semidirect
27. C4×D1076C22semidirect
31. #22575415C22semidirect
41. #22575387C22semidirect
42. #22575386C22semidirect
43. #22575384C22semidirect
44. #22575377C22semidirect
46. #22575375C22semidirect
49. #22575373C22semidirect
50. #22575364C22semidirect
51. #22575363C22semidirect
52. C8×Dic269C22semidirect
54. C4×Q8×C269C22semidirect
56. #106×C269C22semidirect
57. #103×C269C22semidirect
59. C4×C8×C269C22semidirect
62. #16864403C2×C4semidirect
68. D4×D269C2×C4semidirect
77. #16864389C2×C4semidirect
78. D2152C2×C4semidirect
79. #16864387C2×C4semidirect
80. #16864385C2×C4semidirect
104. SD16×C269C2×C4semidirect
188. C269#2946semidirect
198. C4×SD16D269semidirect
215. C4×Q8C2×D269semidirect
236. #106C2×D269semidirect
238. #103C2×D269semidirect
248. C4×C8C2×D269semidirect
270. SD16C4×D269semidirect

Maximal subgroups

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

subgroupindex
C2×#225754802
#317710872
#317710772
#317707162
#317707152
#317707062
#317707032
#317706902
C4×D21522
#317706852
#317706442
#317706002
#102×D2692
#317705592
C4×SD16×C2692
#2946269