Finite Group Databasebeta

← #46819701

Subgroups — #46819701

Order 34432.

484 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22575485C211yesmaximal, characteristic
2C4×#16864403C211yesmaximal, characteristic
3C4×Q8×D269C211yesmaximal, characteristic, complemented
4#31770710C211yesmaximal, characteristic, complemented
5#31770707C211yesmaximal, characteristic, complemented
6#31770703C211yesmaximal, characteristic, complemented
7Q16×Dic269C211yesmaximal, characteristic, complemented
8#31770697C211yesmaximal, characteristic, complemented
9#31770692C211yesmaximal, characteristic, complemented
10#31770690C211yesmaximal, characteristic, complemented
11#31770644C211yesmaximal, characteristic, complemented
12#31770612C211yesmaximal, characteristic, complemented
13#31770605C211yesmaximal, characteristic
14#31770557C211yesmaximal, characteristic, complemented
15#441×C269C211yesmaximal, characteristic, complemented
16C2×#16864403C2211yescharacteristic
17C2×Q8×D269C2211yescharacteristic
18#22575485C418yescomplemented
19C2×#16864392C2211yescharacteristic
20C2×#16864391C2211yescharacteristic
21C2×#16864389C2211yescharacteristic
22C2×#16864385C2211yescharacteristic
23C2×#16864385C2211yescharacteristic
24Q8×Dic269C2211yescharacteristic
25Q8×Dic269C2211yescharacteristic
26C4×Dic538—21no—
27C4×Dic538C2211yescharacteristic
28#22575418—21no—
29#22575418C2211yescharacteristic
30C4×D1076—21no—
31C4×D1076C2211yescharacteristic
32#22575415—21no—
33#22575415C2211yescharacteristic
34#22575411—21no—
35#22575411C2211yescharacteristic
36C4⋊C4×D269—21no—
37C4⋊C4×D269C2211yescharacteristic
38C42×D269—21no—
39C42×D269—21no—
40C42×D269C2211yescharacteristic
41#22575387C2211yescharacteristic
42#22575386C2211yescharacteristic
43#22575384C2211yescharacteristic
44#22575378C2211yescharacteristic
45#22575377C2211yescharacteristic
46#22575377C2211yescharacteristic
47#22575376C2211yescharacteristic
48#22575375C2211yescharacteristic
49#22575373C2211yescharacteristic
50#22575364C2211yescharacteristic
51C8×Dic269C2211yescharacteristic
52C8×Dic269C2211yescharacteristic
53C2×Q16×C269C2211yescharacteristic
54C4×Q8×C269C2211yescharacteristic
55C4×Q8×C269C2211yescharacteristic
56#106×C269C2211yescharacteristic
57#103×C269C2211yescharacteristic
58#103×C269C2211yescharacteristic
59#97×C269C2211yescharacteristic
60#16864403—22no—
61#16864403C2×C414yes—
62C2×Dic538—21no—
63C2×Dic538C2311yescharacteristic
64Q8×D269—22no—
65Q8×D269C2×C414yescomplemented
66C2×D1076—21no—
67C2×D1076C2311yescharacteristic
68C2×C4×D269—21no—
69C2×C4×D269—21no—
70C2×C4×D269—21no—
71C2×C4×D269—21no—
72C2×C4×D269—21no—
73C2×C4×D269D411yescharacteristic
74C2×C4×D269D411yescharacteristic
75C2×C4×D269C2311yescharacteristic
76#16864392C2×C414yescomplemented
77#16864391C2×C414yescomplemented
78#16864389C2×C414yescomplemented
79#16864385—22no—
80#16864385C2×C414yescomplemented
81C2×#14524130C2311yescharacteristic
82C2×#14524130C2311yescharacteristic
83C4⋊Dic269—21no—
84C4⋊Dic269—21no—
85C4⋊Dic269C2311yescharacteristic
86C4⋊Dic269C2311yescharacteristic
87#16864381—21no—
88#16864381—21no—
89#16864381—21no—
90#16864379—21no—
91#16864379—21no—
92#16864379—21no—
93C4×Dic269—21no—
94C4×Dic269—21no—
95C4×Dic269—21no—
96C4×Dic269—21no—
97C4×Dic269—21no—
98C4×Dic269D411yescharacteristic
99C4×Dic269D411yescharacteristic
100C4×Dic269C2311yescharacteristic
101C2×Q8×C269C2311yescharacteristic
102C2×Q8×C269C2311yescharacteristic
103Q16×C269C2×C414yescomplemented
104C2×C8×C269C2311yescharacteristic
105C2×C8×C269C2311yescharacteristic
106C4⋊C4×C269—21no—
107C4⋊C4×C269—21no—
108C4⋊C4×C269C2311yescharacteristic
109C4⋊C4×C269C2311yescharacteristic
110C42×C269—21no—
111C42×C269—21no—
112C42×C269C2311yescharacteristic
113C22×D269—21no—
114C22×D269C2×D411yescharacteristic
115Dic538—21no—
116Dic538—24no—
117Dic538C22×C412yes—
118D1076—24no—
119D1076—21no—
120D1076C22×C412yes—
121C2×Dic269—21no—
122C2×Dic269—21no—
123C2×Dic269—21no—
124C2×Dic269C2×D411yescharacteristic
125C2×Dic269C2×D411yescharacteristic
126C2×Dic269C2×D411yescharacteristic
127C4×D269—24no—
128C4×D269—24no—
129C4×D269—22no—
130C4×D269—41no—
131C4×D269—42no—
132C4×D269—42no—
133C4×D269—42no—
134C4×D269C22×C412yes—
135C4×D269#4112yes—
136#14524130—21no—
137#14524130C22×C412yes—
138Q8×C269—21no—
139Q8×C269—21no—
140Q8×C269C22×C412yes—
141Q8×C269C22×C412yes—
142C2×C4×C269—21no—
143C2×C4×C269—21no—
144C2×C4×C269—21no—
145C2×C4×C269—21no—
146C2×C4×C269C2×D411yescharacteristic
147C2×C4×C269C2×D411yescharacteristic
148C2×C4×C269C2411yescharacteristic
149C8×C269—21no—
150C8×C269C22×C412yes—
151C22×C269C22×D411yescharacteristic
152C2×D269—21no—
153C2×D269—21no—
154C2×D269—22no—
155C2×D269—41no—
156C2×D269—41no—
157C2×D269C4×D412yes—
158C4×C269—22no—
159C4×C269—22no—
160C4×C269—21no—
161C4×C269—21no—
162C4×C269—41no—
163C4×C269—41no—
164C4×C269C23×C411yescharacteristic
165C4×C269C2×#4111yescharacteristic
166Dic269—22no—
167Dic269—21no—
168Dic269—41no—
169Dic269—41no—
170Dic269C4×D412yes—
171Dic269#13712yescomplemented
172C2×C269C2×C4×D411yescharacteristic
173C2×C269C2×#13711yescharacteristic
174C2×C269#57511yescharacteristic
175D269—22no—
176D269—42no—
177C269C4×#13711yescharacteristic, complemented, Sylow
178C4×#137—2691nomaximal, Sylow
179C2×#137—2691no—
180C4×#41—2691no—
181C2×C4×Q8—2691no—
182#441—2691no—
183#441D26911yescharacteristic, complemented
184#440—2691no—
185#440—2691no—
186C4×Q16—2691no—
187C4×Q16—2691no—
188C4×SD16—2691no—
189C4×SD16—2691no—
190#428—2691no—
191#419—2691no—
192#417—2691no—
193C4×M16—2691no—
194C2×#41—2691no—
195C22×Q8—2691no—
196#137—2698no—
197C2×Q16—2691no—
198C2×Q16C2×D26911yescharacteristic
199C2×SD16—2691no—
200C2×SD16—2691no—
201C2×M16—2691no—
202C2×M16—2691no—
203C4×Q8—2691no—
204C4×Q8—2691no—
205C4×Q8—2691no—
206C4×Q8—2691no—
207C4×Q8—5381no—
208C4×Q8—5381no—
209C4×Q8C2×D26911yescharacteristic
210C4×Q8C2×D26911yescharacteristic
211C4×D4—2691no—
212C4×D4—2691no—
213C4×D4—5381no—
214C4×D4—5381no—
215#117—2691no—
216#117—5381no—
217C2×C4⋊C4—2691no—
218C2×C4⋊C4—5381no—
219C2×C42—2691no—
220C2×C42—5381no—
221C2×C42—5381no—
222#107—2691no—
223#107—2691no—
224#106—2691no—
225#106C2×D26911yescharacteristic
226#103—2691no—
227#103—2691no—
228#103—2691no—
229#103—2691no—
230#103C2×D26911yescharacteristic
231#103C2×D26911yescharacteristic
232#102—2691no—
233#102—2691no—
234#97—2691no—
235#97C2×D26911yescharacteristic
236C4×C8—2691no—
237C4×C8—2691no—
238#41—2694no—
239#41—5382no—
240C2×Q8—2694no—
241C2×Q8—2691no—
242C2×Q8—5381no—
243C2×Q8—5382no—
244C2×Q8C22×D26911yescharacteristic
245C2×Q8C22×D26911yescharacteristic
246C2×D4—2691no—
247C2×D4—5381no—
248C22×C4—2691no—
249C22×C4—2691no—
250C22×C4—2691no—
251C22×C4—5381no—
252C22×C4—5381no—
253C22×C4—5381no—
254C22×C4—5381no—
255C22×C4—5381no—
256Q16—2694no—
257Q16C4×D26914yescomplemented
258SD16—2694no—
259SD16—2694no—
260M16—2694no—
261M16—5382no—
262C2×C8—2691no—
263C2×C8—2691no—
264C2×C8C22×D26911yescharacteristic
265C2×C8C22×D26911yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—2691no—
269C4⋊C4—2691no—
270C4⋊C4—5381no—
271C4⋊C4—5381no—
272C4⋊C4—5381no—
273C4⋊C4—5381no—
274C4⋊C4—5381no—
275C4⋊C4C22×D26911yescharacteristic
276C4⋊C4C22×D26911yescharacteristic
277C22⋊C4—5381no—
278C22⋊C4—5381no—
279C22⋊C4—5381no—
280C42—21no—
281C42—21no—
282C42—2691no—
283C42—2691no—
284C42—2691no—
285C42—5381no—
286C42—5381no—
287C42—5381no—
288C42—5381no—
289C42—5381no—
290C42C22×D26911yescharacteristic
291C23—2691no—
292C23—5381no—
293Q8—21no—
294Q8—21no—
295Q8—2692no—
296Q8—5384no—
297Q8—5381no—
298Q8C2×C4×D26912yes—
299Q8C2×C4×D26912yes—
300D4—2692no—
301D4—5384no—
302D4—5381no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—2691no—
308C2×C4—2691no—
309C2×C4—2692no—
310C2×C4—2692no—
311C2×C4—2691no—
312C2×C4—5382no—
313C2×C4—5384no—
314C2×C4—5384no—
315C2×C4—5381no—
316C2×C4—5381no—
317C2×C4—5381no—
318C2×C4—10761no—
319C2×C4—10762no—
320C2×C4—10762no—
321C2×C4—10762no—
322C2×C4D4×D26911yescharacteristic
323C2×C4D4×D26911yescharacteristic
324C2×C4C23×D26911yescharacteristic
325C8—21no—
326C8—2692no—
327C8—5381no—
328C8C2×C4×D26912yes—
329C22—2692no—
330C22—5381no—
331C22—5381no—
332C22—5382no—
333C22—10761no—
334C22—10761no—
335C22C2×D4×D26911yescharacteristic
336C4—21no—
337C4—21no—
338C4—22no—
339C4—22no—
340C4—41no—
341C4—41no—
342C4—2692no—
343C4—2692no—
344C4—5381no—
345C4—5382no—
346C4—10761no—
347C4—10761no—
348C4C22×C4×D26911yescharacteristic
349C4#41×D26911yescharacteristic
350C2—5382no—
351C2—10762no—
352C2C4×D4×D26911yescharacteristic
353C2#137×D26911yescharacteristic
354C2#3177140411yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutatorC4×C269C23×C4
FrattiniC2×C4C23×D269
Fitting#441×C269C2
socleC22×C269C22×D4
prime radicalC2×#16864403C22
cosocleC2×C4×C269C24
hypercenter#441D269
hypocenterC269C4×#137
LCSG ▷ C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
3. C4×Q8×D269C2semidirect
4. #31770710C2semidirect
5. #31770707C2semidirect
6. #31770703C2semidirect
7. Q16×Dic269C2semidirect
8. #31770697C2semidirect
9. #31770692C2semidirect
10. #31770690C2semidirect
11. #31770644C2semidirect
12. #31770612C2semidirect
14. #31770557C2semidirect
15. #441×C269C2semidirect
18. #22575485C4semidirect
65. Q8×D269C2×C4semidirect
76. #16864392C2×C4semidirect
77. #16864391C2×C4semidirect
78. #16864389C2×C4semidirect
80. #16864385C2×C4semidirect
103. Q16×C269C2×C4semidirect
171. Dic269#137semidirect
177. C269C4×#137semidirect
183. #441D269semidirect
257. Q16C4×D269semidirect

Maximal subgroups

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

subgroupindex
C2×#225754852
C4×#168644032
C4×Q8×D2692
#317707102
#317707072
#317707032
Q16×Dic2692
#317706972
#317706922
#317706902
#317706442
#317706122
#317706052
#317705572
#441×C2692
C4×#137269