Finite Group Databasebeta

← #46820436

Subgroups — #46820436

Order 34432.

472 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22575482C211yesmaximal, characteristic, complemented
2C2×#22575472C211yesmaximal, characteristic
3#31771175C211yesmaximal, characteristic, complemented
4#31771084C211yesmaximal, characteristic, complemented
5#31770826C211yesmaximal, characteristic, complemented
6#31770824C211yesmaximal, characteristic, complemented
7#31770818C211yesmaximal, characteristic, complemented
8#31770816C211yesmaximal, characteristic, complemented
9#31770814C211yesmaximal, characteristic, complemented
10#31770810C211yesmaximal, characteristic, complemented
11#31770808C211yesmaximal, characteristic, complemented
12#31770630C211yesmaximal, characteristic, complemented
13#31770603C211yesmaximal, characteristic, complemented
14#103×D269C211yesmaximal, characteristic, complemented
15#463×C269C211yesmaximal, characteristic, complemented
16C2×#16864401C2211yescharacteristic
17C2×#16864401C2211yescharacteristic
18C2×Q8×D269C2211yescharacteristic
19#22575482—24no—
20#22575472—24no—
21C2×Dic1076C2211yescharacteristic
22C2×Dic1076C2211yescharacteristic
23C2×#16864392C2211yescharacteristic
24C2×#16864390C2211yescharacteristic
25C2×#16864390C2211yescharacteristic
26C2×#16864390C2211yescharacteristic
27C2×#16864385C2211yescharacteristic
28C2×C8×D269C2211yescharacteristic
29#22575453C2211yescharacteristic
30#22575451C2211yescharacteristic
31#22575440C2211yescharacteristic
32#22575435—21no—
33#22575435—21no—
34#22575430—21no—
35#22575430—21no—
36C4×Dic538C2211yescharacteristic
37#22575418C2211yescharacteristic
38D4×Dic269C2211yescharacteristic
39C4×C22⋊D269—21no—
40#22575413—21no—
41#22575410C2211yescharacteristic
42#22575409—21no—
43C2×#16864381—21no—
44C4⋊C4×D269C2211yescharacteristic
45C4⋊#14524130C2211yescharacteristic
46#22575382C2211yescharacteristic
47#22575382C2211yescharacteristic
48#22575378C2211yescharacteristic
49#22575378C2211yescharacteristic
50#22575377C2211yescharacteristic
51#22575376C2211yescharacteristic
52#22575376C2211yescharacteristic
53#22575374C2211yescharacteristic
54C2×SD16×C269C2211yescharacteristic
55C2×D8×C269C2211yescharacteristic
56#124×C269C2211yescharacteristic
57C4×D4×C269C2211yescharacteristic
58C4⋊C8×C269C2211yescharacteristic
59#103×C269C2211yescharacteristic
60#102×C269C2211yescharacteristic
61#16864401—22no—
62#16864401—22no—
63#16864401—22no—
64#16864401D414yes—
65C2×Dic538—21no—
66C2×Dic538C2311yescharacteristic
67C2×Dic538C2311yescharacteristic
68C2×Dic538C2311yescharacteristic
69Q8×D269—22no—
70Q8×D269—22no—
71C2×C22⋊D269—21no—
72C2×C22⋊D269—21no—
73C22×Dic269—21no—
74C22×Dic269—21no—
75C22×Dic269—21no—
76C2×C4×D269—21no—
77C2×C4×D269—21no—
78C2×C4×D269C2311yescharacteristic
79Dic1076—22no—
80Dic1076—22no—
81#16864392—22no—
82#16864390—22no—
83#16864390—22no—
84#16864390—22no—
85#16864385—22no—
86C2×#14524130C2311yescharacteristic
87C2×#14524130C2311yescharacteristic
88C8×D269—22no—
89C4⋊Dic269—21no—
90C4⋊Dic269—21no—
91C4⋊Dic269C2311yescharacteristic
92#16864381—21no—
93#16864381—21no—
94#16864381—21no—
95#16864381—21no—
96#16864381—21no—
97#16864381D411yescharacteristic
98#16864381D411yescharacteristic
99C22⋊Dic269—21no—
100C22⋊Dic269—21no—
101C22⋊Dic269—21no—
102#16864379D411yescharacteristic
103#16864379D411yescharacteristic
104C4×Dic269—21no—
105C4×Dic269—21no—
106C4×Dic269C2311yescharacteristic
107C2×Q8×C269C2311yescharacteristic
108C2×D4×C269C2311yescharacteristic
109C2×D4×C269C2311yescharacteristic
110C22×C4×C269—21no—
111SD16×C269—22no—
112D8×C269—22no—
113C2×C8×C269C2311yescharacteristic
114C2×C8×C269C2311yescharacteristic
115C4⋊C4×C269C2311yescharacteristic
116C22⋊C4×C269—21no—
117C22⋊C4×C269—21no—
118C22⋊C4×C269—21no—
119C42×C269C2311yescharacteristic
120C22×D269C2×D411yescharacteristic
121Dic538—21no—
122Dic538—21no—
123Dic538—21no—
124Dic538—21no—
125Dic538—21no—
126Dic538—42no—
127Dic538C2×D412yes—
128C22⋊D269—24no—
129C22⋊D269—42no—
130C2×Dic269—21no—
131C2×Dic269—24no—
132C2×Dic269—21no—
133C2×Dic269—21no—
134C2×Dic269—21no—
135C2×Dic269—42no—
136C2×Dic269—81no—
137C2×Dic269C2×D411yescharacteristic
138C2×Dic269C2×D411yescharacteristic
139C2×Dic269C2×D411yescharacteristic
140C4×D269—42no—
141C4×D269—81no—
142C4×D269C2×D412yes—
143C4×D269#4112yes—
144#14524130—21no—
145#14524130—21no—
146C23×C269—21no—
147C23×C269—21no—
148Q8×C269—21no—
149Q8×C269—21no—
150D4×C269—21no—
151D4×C269—21no—
152D4×C269—21no—
153D4×C269C2×D412yes—
154C2×C4×C269—21no—
155C2×C4×C269—21no—
156C2×C4×C269—81no—
157C2×C4×C269C2×D411yescharacteristic
158C2×C4×C269C2×D411yescharacteristic
159C2×C4×C269C2411yescharacteristic
160C8×C269—21no—
161C8×C269—21no—
162C22×C269—22no—
163C22×C269—41no—
164C22×C269—41no—
165C22×C269—41no—
166C22×C269—41no—
167C22×C269—41no—
168C22×C269C22×D411yescharacteristic
169C2×D269—21no—
170C2×D269—21no—
171C2×D269#12112yes—
172C4×C269—21no—
173C4×C269—21no—
174C4×C269—41no—
175C4×C269—41no—
176C4×C269C22×D411yescharacteristic
177C4×C269C2×#4111yescharacteristic
178Dic269—22no—
179Dic269—21no—
180Dic269—21no—
181Dic269—41no—
182Dic269—41no—
183Dic269—41no—
184Dic269#12112yes—
185C2×C269—42no—
186C2×C269—81no—
187C2×C269C2×#12111yescharacteristic
188C2×C269#57711yescharacteristic
189C2×C269#57811yescharacteristic
190D269—22no—
191C269#304611yescharacteristic, complemented, Sylow
192#3046—2691nomaximal, Sylow
193C2×#137—2691no—
194C2×#135—2691no—
195#536—2691no—
196#520—2691no—
197#464—2691no—
198#464—2691no—
199#463—2691no—
200#463D26911yescharacteristic, complemented
201#462—2691no—
202#462—2691no—
203#461—2691no—
204#461—2691no—
205#424—2691no—
206#417—2691no—
207C2×#103—2691no—
208C2×#41—2691no—
209C2×#41—2691no—
210C22×Q8—2691no—
211#137—5384no—
212#135—5384no—
213C2×Q16—2691no—
214C2×Q16—2691no—
215C2×Q16—2691no—
216C2×SD16—2691no—
217C2×SD16—2691no—
218C2×SD16—2691no—
219C2×SD16C2×D26911yescharacteristic
220C2×D8C2×D26911yescharacteristic
221C2×M16—2691no—
222C22×C8—2691no—
223C4⋊Q8—2691no—
224C4⋊Q8—2691no—
225#124—2691no—
226#124C2×D26911yescharacteristic
227#123—5381no—
228#123—5381no—
229C22⋊Q8—5381no—
230C22⋊Q8—5381no—
231C4×Q8—2691no—
232C4×Q8—2691no—
233C4×D4—2691no—
234C4×D4—5381no—
235C4×D4—5381no—
236C4×D4C2×D26911yescharacteristic
237#117—2691no—
238#117—5381no—
239C2×C4⋊C4—2691no—
240C2×C4⋊C4—5381no—
241C4⋊C8—2691no—
242C4⋊C8—2691no—
243C4⋊C8—2691no—
244C4⋊C8C2×D26911yescharacteristic
245#103—2691no—
246#103—2691no—
247#103—2691no—
248#103—2691no—
249#103—2691no—
250#103C2×D26911yescharacteristic
251#102—2691no—
252#102C2×D26911yescharacteristic
253#41—2694no—
254#41—5382no—
255#41—5382no—
256#41—5382no—
257C2×Q8—2691no—
258C2×Q8—2691no—
259C2×Q8—2691no—
260C2×Q8—5381no—
261C2×Q8—5382no—
262C2×Q8—5382no—
263C2×Q8C22×D26911yescharacteristic
264C2×D4—5381no—
265C2×D4—5381no—
266C2×D4C22×D26911yescharacteristic
267C2×D4C22×D26911yescharacteristic
268C22×C4—21no—
269C22×C4—2691no—
270C22×C4—5381no—
271C22×C4—5381no—
272C22×C4—5381no—
273C22×C4—5381no—
274C22×C4—5381no—
275Q16—5382no—
276Q16—5382no—
277Q16—5382no—
278SD16—22no—
279SD16—5382no—
280SD16—5382no—
281SD16—5382no—
282D8—22no—
283M16—5382no—
284C2×C8—2691no—
285C2×C8—2691no—
286C2×C8—5382no—
287C2×C8C22×D26911yescharacteristic
288C2×C8C22×D26911yescharacteristic
289C4⋊C4—2691no—
290C4⋊C4—2691no—
291C4⋊C4—2691no—
292C4⋊C4—5381no—
293C4⋊C4—5381no—
294C4⋊C4—5381no—
295C4⋊C4—5381no—
296C4⋊C4—5381no—
297C4⋊C4—5381no—
298C4⋊C4—5381no—
299C4⋊C4C22×D26911yescharacteristic
300C22⋊C4—21no—
301C22⋊C4—21no—
302C22⋊C4—21no—
303C22⋊C4—2691no—
304C22⋊C4—2691no—
305C22⋊C4—5381no—
306C22⋊C4—5381no—
307C22⋊C4—5381no—
308C42—2691no—
309C42—5381no—
310C42—5381no—
311C42C22×D26911yescharacteristic
312C23—21no—
313C23—21no—
314C23—2691no—
315Q8—21no—
316Q8—21no—
317Q8—2692no—
318Q8—5381no—
319Q8—5381no—
320Q8—5381no—
321Q8—5381no—
322Q8—5381no—
323Q8—10762no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—5384no—
328D4—10762no—
329D4D4×D26912yes—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—81no—
333C2×C4—2691no—
334C2×C4—2692no—
335C2×C4—2692no—
336C2×C4—2691no—
337C2×C4—2691no—
338C2×C4—5384no—
339C2×C4—5381no—
340C2×C4—5381no—
341C2×C4—5381no—
342C2×C4—5381no—
343C2×C4—10762no—
344C2×C4—10762no—
345C2×C4—21521no—
346C2×C4—21521no—
347C2×C4D4×D26911yescharacteristic
348C2×C4D4×D26911yescharacteristic
349C2×C4C23×D26911yescharacteristic
350C8—21no—
351C8—21no—
352C8—5381no—
353C8—5381no—
354C22—22no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—2692no—
361C22—5381no—
362C22—5381no—
363C22C2×D4×D26911yescharacteristic
364C4—21no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—2692no—
369C4—5381no—
370C4—5381no—
371C4—5382no—
372C4—10761no—
373C4—10761no—
374C4—10761no—
375C4C2×D4×D26911yescharacteristic
376C4#41×D26911yescharacteristic
377C2—42no—
378C2—81no—
379C2—5382no—
380C2#121×D26911yescharacteristic
381C2#3177141511yescharacteristic
382C2#3177141911yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#463×C269C2
socleC22×C269C22×D4
prime radicalC2×#22575472C2
hypercenter#463D269
hypocenterC269#3046
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×#22575482C2semidirect
3. #31771175C2semidirect
4. #31771084C2semidirect
5. #31770826C2semidirect
6. #31770824C2semidirect
7. #31770818C2semidirect
8. #31770816C2semidirect
9. #31770814C2semidirect
10. #31770810C2semidirect
11. #31770808C2semidirect
12. #31770630C2semidirect
13. #31770603C2semidirect
14. #103×D269C2semidirect
15. #463×C269C2semidirect
191. C269#3046semidirect
200. #463D269semidirect

Maximal subgroups

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

subgroupindex
C2×#225754822
C2×#225754722
#317711752
#317710842
#317708262
#317708242
#317708182
#317708162
#317708142
#317708102
#317708082
#317706302
#317706032
#103×D2692
#463×C2692
#3046269