Finite Group Databasebeta

← #46819721

Subgroups — #46819721

Order 34432.

470 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22575482C211yesmaximal, characteristic
2#31771084C211yesmaximal, characteristic
3#31771081C211yesmaximal, characteristic, complemented
4#31770711C211yesmaximal, characteristic, complemented
5#31770710C211yesmaximal, characteristic, complemented
6#31770706C211yesmaximal, characteristic, complemented
7#31770705C211yesmaximal, characteristic, complemented
8C4×Dic1076C211yesmaximal, characteristic, complemented
9#31770697C211yesmaximal, characteristic, complemented
10#31770696C211yesmaximal, characteristic, complemented
11#31770644C211yesmaximal, characteristic, complemented
12#31770598C211yesmaximal, characteristic
13#103×D269C211yesmaximal, characteristic, complemented
14#31770559C211yesmaximal, characteristic, complemented
15C4×SD16×C269C211yesmaximal, characteristic, complemented
16C2×#16864401C2211yescharacteristic
17C2×Q8×D269C2211yescharacteristic
18#22575482C418yescomplemented
19C2×Dic1076C2211yescharacteristic
20C2×#16864392C2211yescharacteristic
21C2×#16864390C2211yescharacteristic
22C2×#16864385C2211yescharacteristic
23C2×C8×D269C2211yescharacteristic
24Q8×Dic269C2211yescharacteristic
25C4×Dic538—21no—
26C4×Dic538C2211yescharacteristic
27C4×Dic538C2211yescharacteristic
28#22575418—21no—
29#22575418C2211yescharacteristic
30#22575418C2211yescharacteristic
31D4×Dic269C2211yescharacteristic
32C4×C22⋊D269—21no—
33#22575413—21no—
34#22575411—21no—
35#22575411C2211yescharacteristic
36#22575410—21no—
37#22575410C2211yescharacteristic
38#22575409—21no—
39C2×#16864381—21no—
40C4⋊C4×D269C2211yescharacteristic
41#22575387C2211yescharacteristic
42#22575386C2211yescharacteristic
43#22575384C2211yescharacteristic
44#22575378C2211yescharacteristic
45#22575378C2211yescharacteristic
46#22575377C2211yescharacteristic
47#22575376C2211yescharacteristic
48#22575376C2211yescharacteristic
49#22575374C2211yescharacteristic
50#22575364C2211yescharacteristic
51#22575363C2211yescharacteristic
52C8×Dic269C2211yescharacteristic
53C2×SD16×C269C2211yescharacteristic
54C4×Q8×C269C2211yescharacteristic
55C4×D4×C269C2211yescharacteristic
56#106×C269C2211yescharacteristic
57#103×C269C2211yescharacteristic
58#102×C269C2211yescharacteristic
59C4×C8×C269C2211yescharacteristic
60#16864401—22no—
61#16864401C2×C414yes—
62C2×Dic538—21no—
63C2×Dic538C2311yescharacteristic
64C2×Dic538C2311yescharacteristic
65Q8×D269—22no—
66Q8×D269C2×C414yescomplemented
67C2×C22⋊D269—21no—
68C22×Dic269—21no—
69C22×Dic269—21no—
70C2×C4×D269—21no—
71C2×C4×D269—21no—
72C2×C4×D269C2311yescharacteristic
73Dic1076C2×C414yescomplemented
74#16864392C2×C414yescomplemented
75#16864390C2×C414yescomplemented
76#16864385C2×C414yescomplemented
77C2×#14524130C2311yescharacteristic
78C2×#14524130C2311yescharacteristic
79C8×D269—22no—
80C4⋊Dic269—21no—
81C4⋊Dic269C2311yescharacteristic
82C4⋊Dic269C2311yescharacteristic
83#16864381—21no—
84#16864381—21no—
85#16864381—21no—
86#16864381—21no—
87#16864381—21no—
88#16864381D411yescharacteristic
89#16864381D411yescharacteristic
90C22⋊Dic269—21no—
91#16864379—21no—
92#16864379D411yescharacteristic
93#16864379D411yescharacteristic
94C4×Dic269—21no—
95C4×Dic269—21no—
96C4×Dic269—21no—
97C4×Dic269—21no—
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×D269C2×D411yescharacteristic
114Dic538—21no—
115Dic538—21no—
116Dic538—24no—
117Dic538C22×C412yes—
118Dic538C22×C412yes—
119C22⋊D269—24no—
120C2×Dic269—21no—
121C2×Dic269—21no—
122C2×Dic269—24no—
123C2×Dic269—21no—
124C2×Dic269—21no—
125C2×Dic269—81no—
126C2×Dic269C2×D411yescharacteristic
127C2×Dic269C2×D411yescharacteristic
128C2×Dic269C2×D411yescharacteristic
129C4×D269—24no—
130C4×D269—81no—
131C4×D269C22×C412yes—
132C4×D269#4112yes—
133#14524130—21no—
134#14524130C22×C412yes—
135C23×C269—21no—
136Q8×C269—21no—
137Q8×C269C22×C412yes—
138D4×C269—21no—
139D4×C269C22×C412yes—
140C2×C4×C269—21no—
141C2×C4×C269—21no—
142C2×C4×C269—21no—
143C2×C4×C269—81no—
144C2×C4×C269C2×D411yescharacteristic
145C2×C4×C269C2×D411yescharacteristic
146C2×C4×C269C2411yescharacteristic
147C8×C269—21no—
148C8×C269C22×C412yes—
149C22×C269—22no—
150C22×C269—41no—
151C22×C269—41no—
152C22×C269C22×D411yescharacteristic
153C2×D269—21no—
154C2×D269—21no—
155C2×D269C4×D412yes—
156C4×C269—22no—
157C4×C269—21no—
158C4×C269—21no—
159C4×C269—41no—
160C4×C269—41no—
161C4×C269C23×C411yescharacteristic
162C4×C269C2×#4111yescharacteristic
163Dic269—22no—
164Dic269—22no—
165Dic269—21no—
166Dic269—21no—
167Dic269—41no—
168Dic269—41no—
169Dic269C4×D412yes—
170C2×C269—42no—
171C2×C269C2×C4×D411yescharacteristic
172C2×C269#57711yescharacteristic
173C2×C269#57811yescharacteristic
174D269—22no—
175C269#294711yescharacteristic, complemented, Sylow
176#2947—2691nomaximal, Sylow
177C2×#137—2691no—
178#520—2691no—
179#519—2691no—
180#441—2691no—
181#441—2691no—
182#440—2691no—
183#440—2691no—
184C4×Q16—2691no—
185C4×Q16—2691no—
186C4×SD16—2691no—
187C4×SD16D26911yescharacteristic, complemented
188#428—2691no—
189#416—2691no—
190C2×#103—2691no—
191#405—2691no—
192C2×#41—2691no—
193C22×Q8—2691no—
194#137—2698no—
195C2×Q16—2691no—
196C2×Q16—2691no—
197C2×SD16—2691no—
198C2×SD16C2×D26911yescharacteristic
199C2×M16—2691no—
200C22×C8—2691no—
201C4×Q8—2691no—
202C4×Q8—2691no—
203C4×Q8—2691no—
204C4×Q8—2691no—
205C4×Q8—2691no—
206C4×Q8—5381no—
207C4×Q8—5381no—
208C4×Q8C2×D26911yescharacteristic
209C4×D4—2691no—
210C4×D4—5381no—
211C4×D4—5381no—
212C4×D4C2×D26911yescharacteristic
213#117—2691no—
214#117—2691no—
215#117—5381no—
216#117—5381no—
217#117—5381no—
218C2×C4⋊C4—2691no—
219C2×C4⋊C4—5381no—
220#107—2691no—
221#107—2691no—
222#106—2691no—
223#106C2×D26911yescharacteristic
224#103—2691no—
225#103—2691no—
226#103—2691no—
227#103—2691no—
228#103—2691no—
229#103C2×D26911yescharacteristic
230#102—2691no—
231#102C2×D26911yescharacteristic
232#97—2691no—
233#97—2691no—
234C4×C8—2691no—
235C4×C8C2×D26911yescharacteristic
236#41—2694no—
237#41—5382no—
238C2×Q8—2694no—
239C2×Q8—2691no—
240C2×Q8—2691no—
241C2×Q8—5381no—
242C2×Q8—5382no—
243C2×Q8C22×D26911yescharacteristic
244C2×D4—5381no—
245C2×D4C22×D26911yescharacteristic
246C22×C4—21no—
247C22×C4—2691no—
248C22×C4—5381no—
249C22×C4—5381no—
250C22×C4—5381no—
251C22×C4—5381no—
252Q16—2694no—
253Q16—2694no—
254SD16—2694no—
255SD16C4×D26914yescomplemented
256M16—2694no—
257C2×C8—2691no—
258C2×C8—2691no—
259C2×C8—5382no—
260C2×C8C22×D26911yescharacteristic
261C2×C8C22×D26911yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—2691no—
264C4⋊C4—2691no—
265C4⋊C4—2691no—
266C4⋊C4—2691no—
267C4⋊C4—5381no—
268C4⋊C4—5381no—
269C4⋊C4—5381no—
270C4⋊C4—5381no—
271C4⋊C4—5381no—
272C4⋊C4—5381no—
273C4⋊C4C22×D26911yescharacteristic
274C4⋊C4C22×D26911yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—2691no—
277C22⋊C4—2691no—
278C22⋊C4—5381no—
279C22⋊C4—5381no—
280C42—21no—
281C42—2691no—
282C42—5381no—
283C42—5381no—
284C42—5381no—
285C42—5381no—
286C42—5381no—
287C42—5381no—
288C42C22×D26911yescharacteristic
289C23—21no—
290C23—2691no—
291Q8—21no—
292Q8—2692no—
293Q8—2692no—
294Q8—5384no—
295Q8—5381no—
296Q8—5381no—
297Q8C2×C4×D26912yes—
298D4—21no—
299D4—5384no—
300D4C2×C4×D26912yes—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—81no—
305C2×C4—2691no—
306C2×C4—2692no—
307C2×C4—2692no—
308C2×C4—2691no—
309C2×C4—2691no—
310C2×C4—5384no—
311C2×C4—5384no—
312C2×C4—5381no—
313C2×C4—5381no—
314C2×C4—5381no—
315C2×C4—5381no—
316C2×C4—21521no—
317C2×C4—21521no—
318C2×C4D4×D26911yescharacteristic
319C2×C4D4×D26911yescharacteristic
320C2×C4C23×D26911yescharacteristic
321C8—21no—
322C8—2692no—
323C8—5381no—
324C8C2×C4×D26912yes—
325C22—22no—
326C22—41no—
327C22—41no—
328C22—2692no—
329C22—5381no—
330C22—5381no—
331C22C2×D4×D26911yescharacteristic
332C4—21no—
333C4—21no—
334C4—22no—
335C4—41no—
336C4—41no—
337C4—2692no—
338C4—5381no—
339C4—5381no—
340C4—5382no—
341C4—5382no—
342C4—10761no—
343C4—10761no—
344C4C22×C4×D26911yescharacteristic
345C4#41×D26911yescharacteristic
346C2—42no—
347C2—5382no—
348C2C4×D4×D26911yescharacteristic
349C2#3177141111yescharacteristic
350C2#3177141911yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutatorC4×C269C23×C4
FrattiniC2×C4C23×D269
FittingC4×SD16×C269C2
socleC22×C269C22×D4
prime radicalC2×#16864401C22
cosocleC2×C4×C269C24
hypercenterC4×SD16D269
hypocenterC269#2947
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
3. #31771081C2semidirect
4. #31770711C2semidirect
5. #31770710C2semidirect
6. #31770706C2semidirect
7. #31770705C2semidirect
8. C4×Dic1076C2semidirect
9. #31770697C2semidirect
10. #31770696C2semidirect
11. #31770644C2semidirect
13. #103×D269C2semidirect
14. #31770559C2semidirect
15. C4×SD16×C269C2semidirect
18. #22575482C4semidirect
66. Q8×D269C2×C4semidirect
73. Dic1076C2×C4semidirect
74. #16864392C2×C4semidirect
75. #16864390C2×C4semidirect
76. #16864385C2×C4semidirect
104. SD16×C269C2×C4semidirect
175. C269#2947semidirect
187. C4×SD16D269semidirect
255. SD16C4×D269semidirect

Maximal subgroups

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

subgroupindex
C2×#225754822
#317710842
#317710812
#317707112
#317707102
#317707062
#317707052
C4×Dic10762
#317706972
#317706962
#317706442
#317705982
#103×D2692
#317705592
C4×SD16×C2692
#2947269