Finite Group Databasebeta

← #46822595

Subgroups — #46822595

Order 34432.

504 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22575473C211yesmaximal, characteristic, complemented
2C2×SD16×D269C211yesmaximal, characteristic, complemented
3#31771262C211yesmaximal, characteristic, complemented
4#31771252C211yesmaximal, characteristic, complemented
5#31770988C211yesmaximal, characteristic, complemented
6#31770833C211yesmaximal, characteristic, complemented
7#31770832C211yesmaximal, characteristic, complemented
8#31770825C211yesmaximal, characteristic, complemented
9#31770819C211yesmaximal, characteristic, complemented
10#31770769C211yesmaximal, characteristic, complemented
11#31770762C211yesmaximal, characteristic, complemented
12#31770737C211yesmaximal, characteristic, complemented
13#31770690C211yesmaximal, characteristic, complemented
14#31770668C211yesmaximal, characteristic, complemented
15#449×C269C211yesmaximal, characteristic, complemented
16C2×#16864402C2211yescharacteristic
17C2×Q8×D269C2211yescharacteristic
18C2×D4×D269C2211yescharacteristic
19#22575473—24no—
20C2×Dic1076C2211yescharacteristic, complemented
21C2×#16864392C2211yescharacteristic, complemented
22C2×#16864391C2211yescharacteristic
23C2×#16864390C2211yescharacteristic
24C2×#16864390C2211yescharacteristic, complemented
25C2×#16864389C2211yescharacteristic
26SD16×D269—24no—
27C2×#16864387C2211yescharacteristic
28C22×#14524130C2211yescharacteristic, complemented
29C2×C8×D269C2211yescharacteristic
30#22575440—21no—
31#22575440C2211yescharacteristic
32#22575440C2211yescharacteristic, complemented
33#22575435—21no—
34#22575433C2211yescharacteristic
35#22575432—21no—
36#22575432C2211yescharacteristic, complemented
37#22575424—21no—
38#22575424—21no—
39#22575424C2211yescharacteristic
40#22575421—21no—
41Q8×Dic269C2211yescharacteristic, complemented
42#22575415C2211yescharacteristic
43C4×C22⋊D269—21no—
44C4×C22⋊D269C2211yescharacteristic
45C22⋊C4×D269—21no—
46#22575384C2211yescharacteristic, complemented
47#22575382C2211yescharacteristic, complemented
48#22575378C2211yescharacteristic, complemented
49#22575376C2211yescharacteristic, complemented
50#22575375C2211yescharacteristic
51#22575374C2211yescharacteristic
52#22575365C2211yescharacteristic
53C8×Dic269C2211yescharacteristic, complemented
54C2×#41×C269C2211yescharacteristic, complemented
55C2×SD16×C269C2211yescharacteristic
56C2×D8×C269C2211yescharacteristic
57#121×C269C2211yescharacteristic
58#103×C269C2211yescharacteristic, complemented
59#102×C269C2211yescharacteristic, complemented
60C22⋊C8×C269C2211yescharacteristic, complemented
61C23×D269—21no—
62#16864402—22no—
63#16864402—41no—
64C2×Dic538—21no—
65C2×Dic538C2311yescharacteristic
66C2×Dic538C2311yescharacteristic
67Q8×D269—22no—
68Q8×D269—41no—
69C2×D1076C2311yescharacteristic
70C2×C22⋊D269—21no—
71C2×C22⋊D269—21no—
72C2×C22⋊D269—21no—
73C2×C22⋊D269D411yescharacteristic
74D4×D269—22no—
75D4×D269—41no—
76C2×C4×D269—21no—
77C2×C4×D269—21no—
78C2×C4×D269—21no—
79C2×C4×D269C2311yescharacteristic
80Dic1076—41no—
81#16864392—22no—
82#16864391—22no—
83#16864390—22no—
84#16864390—22no—
85#16864389D414yescomplemented
86#16864387—22no—
87C2×#14524130—22no—
88C2×#14524130C2311yescharacteristic
89C2×#14524130C2311yescharacteristic
90C8×D269—22no—
91C4⋊Dic269—21no—
92C4⋊Dic269—21no—
93C4⋊Dic269C2311yescharacteristic
94#16864381—21no—
95#16864381D411yescharacteristic
96C22⋊Dic269—21no—
97C22⋊Dic269—21no—
98C22⋊Dic269—21no—
99C22⋊Dic269—21no—
100C22⋊Dic269—21no—
101C22⋊Dic269—21no—
102C22⋊Dic269D411yescharacteristic
103#16864379—21no—
104#16864379—21no—
105#16864379D411yescharacteristic
106C4×Dic269—21no—
107C4×Dic269C2311yescharacteristic
108#41×C269—22no—
109#41×C269—41no—
110C2×Q8×C269C2311yescharacteristic
111C2×D4×C269—21no—
112C2×D4×C269—21no—
113C2×D4×C269C2311yescharacteristic
114C2×D4×C269C2311yescharacteristic
115C22×C4×C269—21no—
116C22×C4×C269C2311yescharacteristic
117SD16×C269—22no—
118D8×C269—41no—
119C2×C8×C269C2311yescharacteristic
120C2×C8×C269C2311yescharacteristic
121C4⋊C4×C269C2311yescharacteristic
122C22⋊C4×C269—21no—
123C22×D269—21no—
124C22×D269—42no—
125C22×D269—42no—
126C22×D269—81no—
127C22×D269C2×D411yescharacteristic
128Dic538—21no—
129Dic538—21no—
130Dic538—21no—
131Dic538—21no—
132Dic538—42no—
133D1076—21no—
134D1076C2×D412yes—
135C22⋊D269—22no—
136C22⋊D269—42no—
137C22⋊D269—42no—
138C22⋊D269—42no—
139C2×Dic269—21no—
140C2×Dic269—21no—
141C2×Dic269—21no—
142C2×Dic269C2×D411yescharacteristic
143C2×Dic269C2×D411yescharacteristic
144C2×Dic269C2×D411yescharacteristic
145C4×D269—21no—
146C4×D269—21no—
147C4×D269—42no—
148C4×D269—42no—
149C4×D269—81no—
150#14524130—21no—
151#14524130C2×D412yes—
152C23×C269—21no—
153C23×C269—21no—
154C23×C269C2×D411yescharacteristic
155Q8×C269—21no—
156Q8×C269C2×D412yes—
157D4×C269—21no—
158D4×C269—21no—
159D4×C269—21no—
160D4×C269—21no—
161D4×C269—42no—
162D4×C269—81no—
163C2×C4×C269—21no—
164C2×C4×C269—21no—
165C2×C4×C269—21no—
166C2×C4×C269—21no—
167C2×C4×C269—42no—
168C2×C4×C269C2×D411yescharacteristic
169C2×C4×C269C2411yescharacteristic
170C8×C269—21no—
171C8×C269—21no—
172C22×C269—21no—
173C22×C269—21no—
174C22×C269—21no—
175C22×C269—41no—
176C22×C269—41no—
177C22×C269—41no—
178C22×C269—41no—
179C22×C269—41no—
180C22×C269—41no—
181C22×C269C22×D411yescharacteristic
182C2×D269—21no—
183C2×D269—21no—
184C2×D269—22no—
185C2×D269—41no—
186C2×D269—41no—
187C2×D269—84no—
188C2×D269#13512yescomplemented
189C4×C269—21no—
190C4×C269—22no—
191C4×C269—41no—
192C4×C269C22×D411yescharacteristic
193C4×C269H(5,𝔽2)11yescharacteristic
194Dic269—21no—
195Dic269—21no—
196Dic269—21no—
197Dic269—41no—
198Dic269—41no—
199Dic269—41no—
200C2×C269—41no—
201C2×C269—81no—
202C2×C269—81no—
203C2×C269D4211yescharacteristic
204C2×C269C2×#13511yescharacteristic
205C2×C269#57711yescharacteristic
206D269—22no—
207D269—42no—
208C269#328211yescharacteristic, complemented, Sylow
209#3282—2691nomaximal, Sylow
210C2×#135—2691no—
211C22×SD16—2691no—
212#548—2691no—
213#546—2691no—
214#495—2691no—
215#465—2691no—
216#465—2691no—
217#464—2691no—
218#463—2691no—
219#452—2691no—
220#451—2691no—
221#449D26911yescharacteristic, complemented
222#447—2691no—
223C4×SD16—2691no—
224C8×D4—2691no—
225C2×#41—2691no—
226C2×#41C2×D26911yescharacteristic, complemented
227C22×Q8—2691no—
228C22×D4—2691no—
229#135—5384no—
230C2×Q16—2691no—
231C2×Q16—2691no—
232C2×SD16—2691no—
233C2×SD16—2691no—
234C2×SD16—2691no—
235C2×SD16—2691no—
236C2×SD16—5384no—
237C2×SD16C2×D26911yescharacteristic
238C2×D8—2691no—
239C2×D8C2×D26911yescharacteristic
240C22×C8—2691no—
241C22×C8—2691no—
242#124—2691no—
243#124—2691no—
244#124—5381no—
245#123—5381no—
246C22⋊Q8—2691no—
247C22⋊Q8—2691no—
248C22⋊Q8—5381no—
249#121—2691no—
250#121—5381no—
251#121—5381no—
252#121C2×D26911yescharacteristic
253#120—5381no—
254C4×Q8—2691no—
255C4×D4—2691no—
256C4×D4—2691no—
257C4×D4—5381no—
258C2×C22⋊C4—5381no—
259#106—2691no—
260C4⋊C8—2691no—
261#103—2691no—
262#103—2691no—
263#103C2×D26911yescharacteristic, complemented
264#102—2691no—
265#102—2691no—
266#102C2×D26911yescharacteristic, complemented
267C22⋊C8—2691no—
268C22⋊C8C2×D26911yescharacteristic, complemented
269C4×C8—2691no—
270C24—5381no—
271#41—22no—
272#41—41no—
273#41—5382no—
274#41—10761no—
275C2×Q8—2691no—
276C2×Q8—2691no—
277C2×Q8—5381no—
278C2×Q8—5382no—
279C2×Q8—10761no—
280C2×Q8C22×D26911yescharacteristic
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—2691no—
284C2×D4—2691no—
285C2×D4—5381no—
286C2×D4—5382no—
287C2×D4—5381no—
288C2×D4—5381no—
289C2×D4—10761no—
290C2×D4C22×D26911yescharacteristic
291C2×D4C22×D26911yescharacteristic
292C22×C4—21no—
293C22×C4—2691no—
294C22×C4—5381no—
295C22×C4—5381no—
296C22×C4—5381no—
297C22×C4C22×D26911yescharacteristic
298Q16—5382no—
299Q16—10761no—
300SD16—22no—
301SD16—2694no—
302SD16—5382no—
303SD16—5382no—
304SD16—5382no—
305D8—41no—
306D8—5382no—
307C2×C8—2691no—
308C2×C8—2691no—
309C2×C8—5382no—
310C2×C8—5382no—
311C2×C8C22×D26911yescharacteristic
312C2×C8C22×D26911yescharacteristic
313C4⋊C4—2691no—
314C4⋊C4—2691no—
315C4⋊C4—5381no—
316C4⋊C4—5381no—
317C4⋊C4—5381no—
318C4⋊C4C22×D26911yescharacteristic
319C22⋊C4—21no—
320C22⋊C4—2691no—
321C22⋊C4—2691no—
322C22⋊C4—5381no—
323C22⋊C4—5381no—
324C22⋊C4—5381no—
325C22⋊C4—5381no—
326C22⋊C4—5381no—
327C22⋊C4—5381no—
328C22⋊C4—5381no—
329C22⋊C4—5381no—
330C42—2691no—
331C42—5381no—
332C23—21no—
333C23—21no—
334C23—2691no—
335C23—5381no—
336C23—10762no—
337C23—10762no—
338C23—21521no—
339C23D4×D26911yescharacteristic
340Q8—21no—
341Q8—5381no—
342Q8—5381no—
343Q8—5381no—
344Q8—5381no—
345Q8—10762no—
346Q8D4×D26912yes—
347D4—21no—
348D4—21no—
349D4—21no—
350D4—21no—
351D4—42no—
352D4—81no—
353D4—2692no—
354D4—5382no—
355D4—5381no—
356D4—10762no—
357D4—10762no—
358D4—10762no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—42no—
364C2×C4—2691no—
365C2×C4—2691no—
366C2×C4—2691no—
367C2×C4—5381no—
368C2×C4—5381no—
369C2×C4—5381no—
370C2×C4—5381no—
371C2×C4—5381no—
372C2×C4—10762no—
373C2×C4—10762no—
374C2×C4—21521no—
375C2×C4D4×D26911yescharacteristic
376C2×C4C23×D26911yescharacteristic
377C8—21no—
378C8—21no—
379C8—2692no—
380C8—5381no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—2692no—
391C22—5381no—
392C22—5381no—
393C22—5382no—
394C22—10761no—
395C22—10761no—
396C22—21524no—
397C22C2×D4×D26911yescharacteristic
398C4—21no—
399C4—22no—
400C4—41no—
401C4—5381no—
402C4—5381no—
403C4—5381no—
404C4—10761no—
405C4—10761no—
406C4—10761no—
407C4C2×D4×D26911yescharacteristic
408C4#2257549811yescharacteristic
409C2—41no—
410C2—81no—
411C2—81no—
412C2—5382no—
413C2—10762no—
414C2#3177123711yescharacteristic
415C2#135×D26911yescharacteristic
416C2#3177141511yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#449×C269C2
socleC22×C269C22×D4
hypercenter#449D269
hypocenterC269#3282
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. C2×#22575473C2semidirect
2. C2×SD16×D269C2semidirect
3. #31771262C2semidirect
4. #31771252C2semidirect
5. #31770988C2semidirect
6. #31770833C2semidirect
7. #31770832C2semidirect
8. #31770825C2semidirect
9. #31770819C2semidirect
10. #31770769C2semidirect
11. #31770762C2semidirect
12. #31770737C2semidirect
13. #31770690C2semidirect
14. #31770668C2semidirect
15. #449×C269C2semidirect
20. C2×Dic1076C22semidirect
21. C2×#16864392C22semidirect
24. C2×#16864390C22semidirect
28. C22×#14524130C22semidirect
32. #22575440C22semidirect
36. #22575432C22semidirect
41. Q8×Dic269C22semidirect
46. #22575384C22semidirect
47. #22575382C22semidirect
48. #22575378C22semidirect
49. #22575376C22semidirect
53. C8×Dic269C22semidirect
54. C2×#41×C269C22semidirect
58. #103×C269C22semidirect
59. #102×C269C22semidirect
60. C22⋊C8×C269C22semidirect
85. #16864389D4semidirect
188. C2×D269#135semidirect
208. C269#3282semidirect
221. #449D269semidirect
226. C2×#41C2×D269semidirect
263. #103C2×D269semidirect
266. #102C2×D269semidirect
268. C22⋊C8C2×D269semidirect

Maximal subgroups

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

subgroupindex
C2×#225754732
C2×SD16×D2692
#317712622
#317712522
#317709882
#317708332
#317708322
#317708252
#317708192
#317707692
#317707622
#317707372
#317706902
#317706682
#449×C2692
#3282269