Finite Group Databasebeta

← #46820419

Subgroups — #46820419

Order 34432.

504 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22575477C211yesmaximal, characteristic, complemented
2C2×#22575472C211yesmaximal, characteristic, complemented
3#31771168C211yesmaximal, characteristic, complemented
4#31771084C211yesmaximal, characteristic, complemented
5#31770828C211yesmaximal, characteristic, complemented
6#31770826C211yesmaximal, characteristic, complemented
7#31770820C211yesmaximal, characteristic, complemented
8#31770818C211yesmaximal, characteristic, complemented
9#31770804C211yesmaximal, characteristic, complemented
10#31770802C211yesmaximal, characteristic, complemented
11#31770798C211yesmaximal, characteristic, complemented
12#31770630C211yesmaximal, characteristic, complemented
13#31770603C211yesmaximal, characteristic, complemented
14#102×D269C211yesmaximal, characteristic, complemented
15#459×C269C211yesmaximal, characteristic, complemented
16C2×#16864401C2211yescharacteristic
17C2×#16864401C2211yescharacteristic
18C2×D4×D269C2211yescharacteristic
19#22575477—24no—
20#22575472—24no—
21C2×Dic1076C2211yescharacteristic, complemented
22C2×#16864391C2211yescharacteristic
23C2×#16864390C2211yescharacteristic
24C2×#16864390C2211yescharacteristic, complemented
25C2×#16864390C2211yescharacteristic, complemented
26C2×#16864387C2211yescharacteristic
27C2×#16864385C2211yescharacteristic
28C2×C8×D269C2211yescharacteristic
29#22575449C2211yescharacteristic
30#22575441C2211yescharacteristic
31#22575440C2211yescharacteristic
32#22575425—21no—
33#22575425—21no—
34#22575421—21no—
35#22575421—21no—
36C4×Dic538C2211yescharacteristic, complemented
37#22575418C2211yescharacteristic, complemented
38D4×Dic269C2211yescharacteristic, complemented
39C4×C22⋊D269—21no—
40#22575413—21no—
41#22575410C2211yescharacteristic
42#22575409—21no—
43C2×#16864381—21no—
44C4⋊C4×D269C2211yescharacteristic
45C4⋊#14524130C2211yescharacteristic, complemented
46#22575382C2211yescharacteristic, complemented
47#22575382C2211yescharacteristic, complemented
48#22575378C2211yescharacteristic, complemented
49#22575376C2211yescharacteristic, complemented
50#22575375C2211yescharacteristic
51#22575374C2211yescharacteristic
52#22575374C2211yescharacteristic, complemented
53#22575373C2211yescharacteristic
54C2×D8×C269C2211yescharacteristic
55C2×D8×C269C2211yescharacteristic, complemented
56#127×C269C2211yescharacteristic
57C4×D4×C269C2211yescharacteristic, complemented
58C4⋊C8×C269C2211yescharacteristic, complemented
59#102×C269C2211yescharacteristic
60#102×C269C2211yescharacteristic, complemented
61C23×D269—21no—
62#16864401—22no—
63#16864401—22no—
64#16864401—22no—
65#16864401D414yescomplemented
66C2×Dic538C2311yescharacteristic
67C2×Dic538C2311yescharacteristic
68C2×D1076C2311yescharacteristic
69C2×C22⋊D269—21no—
70C2×C22⋊D269—21no—
71C2×C22⋊D269—21no—
72C2×C22⋊D269—21no—
73C2×C22⋊D269—21no—
74D4×D269—22no—
75D4×D269—22no—
76C22×Dic269—21no—
77C22×Dic269—21no—
78C22×Dic269—21no—
79C2×C4×D269—21no—
80C2×C4×D269C2311yescharacteristic
81Dic1076—22no—
82#16864391—22no—
83#16864390—22no—
84#16864390—22no—
85#16864390—22no—
86#16864387—22no—
87#16864385—22no—
88C2×#14524130C2311yescharacteristic
89C2×#14524130C2311yescharacteristic
90C8×D269—22no—
91C4⋊Dic269C2311yescharacteristic
92#16864381—21no—
93#16864381—21no—
94#16864381—21no—
95#16864381D411yescharacteristic
96#16864381D411yescharacteristic
97C22⋊Dic269—21no—
98C22⋊Dic269—21no—
99C22⋊Dic269—21no—
100#16864379—21no—
101#16864379—21no—
102#16864379D411yescharacteristic
103#16864379D411yescharacteristic
104C4×Dic269—21no—
105C4×Dic269—21no—
106C4×Dic269C2311yescharacteristic
107C2×D4×C269—21no—
108C2×D4×C269—21no—
109C2×D4×C269C2311yescharacteristic
110C2×D4×C269C2311yescharacteristic
111C2×D4×C269C2311yescharacteristic
112C22×C4×C269—21no—
113D8×C269—22no—
114D8×C269—22no—
115C2×C8×C269C2311yescharacteristic
116C2×C8×C269C2311yescharacteristic
117C4⋊C4×C269C2311yescharacteristic
118C22⋊C4×C269—21no—
119C42×C269C2311yescharacteristic
120C22×D269—21no—
121C22×D269—42no—
122C22×D269—81no—
123C22×D269—81no—
124C22×D269C2×D411yescharacteristic
125Dic538—21no—
126Dic538—21no—
127Dic538—21no—
128Dic538C2×D412yes—
129D1076—21no—
130D1076—21no—
131C22⋊D269—24no—
132C22⋊D269—42no—
133C22⋊D269—42no—
134C22⋊D269—81no—
135C22⋊D269—81no—
136C2×Dic269—21no—
137C2×Dic269—24no—
138C2×Dic269—21no—
139C2×Dic269—21no—
140C2×Dic269—42no—
141C2×Dic269—81no—
142C2×Dic269C2×D411yescharacteristic
143C2×Dic269C2×D411yescharacteristic
144C2×Dic269C2×D411yescharacteristic
145C4×D269—81no—
146C4×D269C2×D412yes—
147C4×D269#4112yes—
148#14524130—21no—
149#14524130—21no—
150C23×C269—21no—
151C23×C269—21no—
152C23×C269—21no—
153D4×C269—21no—
154D4×C269—21no—
155D4×C269—21no—
156D4×C269—21no—
157D4×C269—21no—
158D4×C269—81no—
159D4×C269—81no—
160D4×C269C2×D412yes—
161C2×C4×C269—21no—
162C2×C4×C269—81no—
163C2×C4×C269C2×D411yescharacteristic
164C2×C4×C269C2×D411yescharacteristic
165C2×C4×C269C2411yescharacteristic
166C8×C269—21no—
167C8×C269—21no—
168C22×C269—22no—
169C22×C269—41no—
170C22×C269—41no—
171C22×C269—41no—
172C22×C269—41no—
173C22×C269—41no—
174C22×C269—41no—
175C22×C269—41no—
176C22×C269—41no—
177C22×C269C22×D411yescharacteristic
178C2×D269—21no—
179C2×D269—21no—
180C2×D269—41no—
181C2×D269—41no—
182C2×D269—41no—
183C2×D269—84no—
184C2×D269#12112yes—
185C4×C269—21no—
186C4×C269—21no—
187C4×C269—41no—
188C4×C269C22×D411yescharacteristic
189C4×C269C2×#4111yescharacteristic
190Dic269—22no—
191Dic269—21no—
192Dic269—21no—
193Dic269—41no—
194Dic269—41no—
195Dic269#12112yes—
196C2×C269—42no—
197C2×C269—81no—
198C2×C269—81no—
199C2×C269C2×#12111yescharacteristic
200C2×C269#57611yescharacteristic
201C2×C269#57711yescharacteristic
202D269—22no—
203D269—81no—
204C269#304511yescharacteristic, complemented, Sylow
205#3045—2691nomaximal, Sylow
206C2×AGL(1,ℤ/8)—2691no—
207C2×#135—2691no—
208#535—2691no—
209#520—2691no—
210#464—2691no—
211#464—2691no—
212#463—2691no—
213#463—2691no—
214#460—2691no—
215#460—2691no—
216#459—2691no—
217#459D26911yescharacteristic, complemented
218#424—2691no—
219#417—2691no—
220C2×#102—2691no—
221C2×#41—2691no—
222C2×#41—2691no—
223C22×D4—2691no—
224AGL(1,ℤ/8)—5384no—
225#135—5384no—
226C2×Q16—2691no—
227C2×SD16—2691no—
228C2×SD16—2691no—
229C2×SD16—2691no—
230C2×SD16—2691no—
231C2×D8—2691no—
232C2×D8C2×D26911yescharacteristic
233C2×D8C2×D26911yescharacteristic, complemented
234C2×M16—2691no—
235C22×C8—2691no—
236#127—2691no—
237#127C2×D26911yescharacteristic
238#124—2691no—
239#124—2691no—
240#121—5381no—
241#121—5381no—
242#120—5381no—
243#120—5381no—
244C4×Q8—2691no—
245C4×Q8—2691no—
246C4×D4—2691no—
247C4×D4—5381no—
248C4×D4—5381no—
249C4×D4C2×D26911yescharacteristic, complemented
250#117—2691no—
251#117—5381no—
252C2×C4⋊C4—2691no—
253C2×C4⋊C4—5381no—
254C4⋊C8—2691no—
255C4⋊C8—2691no—
256C4⋊C8—2691no—
257C4⋊C8C2×D26911yescharacteristic, complemented
258#103—2691no—
259#103—2691no—
260#102—2691no—
261#102—2691no—
262#102—2691no—
263#102—2691no—
264#102C2×D26911yescharacteristic
265#102C2×D26911yescharacteristic, complemented
266C24—5381no—
267#41—2694no—
268#41—5382no—
269#41—5382no—
270#41—5382no—
271C2×Q8—2691no—
272C2×Q8—2691no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4—2691no—
276C2×D4—5382no—
277C2×D4—5382no—
278C2×D4—5381no—
279C2×D4—5381no—
280C2×D4—5381no—
281C2×D4—5381no—
282C2×D4—5381no—
283C2×D4C22×D26911yescharacteristic
284C2×D4C22×D26911yescharacteristic
285C2×D4C22×D26911yescharacteristic
286C22×C4—21no—
287C22×C4—2691no—
288C22×C4—5381no—
289C22×C4—5381no—
290C22×C4—5381no—
291C22×C4—5381no—
292Q16—5382no—
293SD16—5382no—
294SD16—5382no—
295SD16—5382no—
296SD16—5382no—
297D8—22no—
298D8—22no—
299D8—5382no—
300M16—5382no—
301C2×C8—2691no—
302C2×C8—2691no—
303C2×C8—5382no—
304C2×C8C22×D26911yescharacteristic
305C2×C8C22×D26911yescharacteristic
306C4⋊C4—2691no—
307C4⋊C4—2691no—
308C4⋊C4—2691no—
309C4⋊C4—5381no—
310C4⋊C4—5381no—
311C4⋊C4—5381no—
312C4⋊C4C22×D26911yescharacteristic
313C22⋊C4—21no—
314C22⋊C4—2691no—
315C22⋊C4—2691no—
316C22⋊C4—5381no—
317C22⋊C4—5381no—
318C22⋊C4—5381no—
319C22⋊C4—5381no—
320C22⋊C4—5381no—
321C42—2691no—
322C42—5381no—
323C42—5381no—
324C42C22×D26911yescharacteristic
325C23—21no—
326C23—21no—
327C23—21no—
328C23—2691no—
329C23—5381no—
330C23—10762no—
331C23—21521no—
332C23—21521no—
333Q8—2692no—
334Q8—5381no—
335Q8—5381no—
336Q8—5381no—
337D4—21no—
338D4—21no—
339D4—21no—
340D4—21no—
341D4—21no—
342D4—81no—
343D4—81no—
344D4—5384no—
345D4—5381no—
346D4—5381no—
347D4—10762no—
348D4—10762no—
349D4—21521no—
350D4—21521no—
351D4D4×D26912yes—
352C2×C4—21no—
353C2×C4—81no—
354C2×C4—2691no—
355C2×C4—2692no—
356C2×C4—2692no—
357C2×C4—2691no—
358C2×C4—2691no—
359C2×C4—5384no—
360C2×C4—5381no—
361C2×C4—5381no—
362C2×C4—5381no—
363C2×C4—10762no—
364C2×C4—21521no—
365C2×C4—21521no—
366C2×C4D4×D26911yescharacteristic
367C2×C4D4×D26911yescharacteristic
368C2×C4C23×D26911yescharacteristic
369C8—21no—
370C8—21no—
371C8—5381no—
372C8—5381no—
373C22—22no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—2692no—
383C22—5381no—
384C22—5381no—
385C22—10761no—
386C22—10761no—
387C22—10761no—
388C22—21524no—
389C22C2×D4×D26911yescharacteristic
390C4—21no—
391C4—21no—
392C4—41no—
393C4—2692no—
394C4—5381no—
395C4—5381no—
396C4—5382no—
397C4—10761no—
398C4—10761no—
399C4C2×D4×D26911yescharacteristic
400C4#41×D26911yescharacteristic
401C2—42no—
402C2—81no—
403C2—81no—
404C2—5382no—
405C2—21521no—
406C2#121×D26911yescharacteristic
407C2#3177140611yescharacteristic
408C2#3177141511yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#459×C269C2
socleC22×C269C22×D4
hypercenter#459D269
hypocenterC269#3045
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. C2×#22575477C2semidirect
2. C2×#22575472C2semidirect
3. #31771168C2semidirect
4. #31771084C2semidirect
5. #31770828C2semidirect
6. #31770826C2semidirect
7. #31770820C2semidirect
8. #31770818C2semidirect
9. #31770804C2semidirect
10. #31770802C2semidirect
11. #31770798C2semidirect
12. #31770630C2semidirect
13. #31770603C2semidirect
14. #102×D269C2semidirect
15. #459×C269C2semidirect
21. C2×Dic1076C22semidirect
24. C2×#16864390C22semidirect
25. C2×#16864390C22semidirect
36. C4×Dic538C22semidirect
37. #22575418C22semidirect
38. D4×Dic269C22semidirect
45. C4⋊#14524130C22semidirect
46. #22575382C22semidirect
47. #22575382C22semidirect
48. #22575378C22semidirect
49. #22575376C22semidirect
52. #22575374C22semidirect
55. C2×D8×C269C22semidirect
57. C4×D4×C269C22semidirect
58. C4⋊C8×C269C22semidirect
60. #102×C269C22semidirect
65. #16864401D4semidirect
204. C269#3045semidirect
217. #459D269semidirect
233. C2×D8C2×D269semidirect
249. C4×D4C2×D269semidirect
257. C4⋊C8C2×D269semidirect
265. #102C2×D269semidirect

Maximal subgroups

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

subgroupindex
C2×#225754772
C2×#225754722
#317711682
#317710842
#317708282
#317708262
#317708202
#317708182
#317708042
#317708022
#317707982
#317706302
#317706032
#102×D2692
#459×C2692
#3045269