Finite Group Databasebeta

← #46820604

Subgroups — #46820604

Order 34432.

452 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
1#31771405C211yesmaximal, characteristic, complemented
2#31771403C211yesmaximal, characteristic, complemented
3C2×#22575473C211yesmaximal, characteristic, complemented
4C2×#22575461C211yesmaximal, characteristic, complemented
5#31770879C212yesmaximal, complemented
6#31770874C212yesmaximal, complemented
7#31770871C212yesmaximal, complemented
8#31770867C212yesmaximal, complemented
9C2×#22575388C211yesmaximal, characteristic, complemented
10#31770587C211yesmaximal, characteristic, complemented
11#413×C269C211yesmaximal, characteristic, complemented
12C2×#16864402C2211yescharacteristic
13C2×#16864402C2211yescharacteristic
14#22575486—21no—
15#22575486C2212yes—
16#22575484C2212yes—
17#22575483—21no—
18#22575481—21no—
19#22575481C2212yes—
20#22575479C2212yes—
21#22575478—21no—
22#22575475—22no—
23#22575473—22no—
24#22575473—21no—
25#22575473—21no—
26#22575473—21no—
27#22575473—21no—
28C2×#16864392C2211yescharacteristic, complemented
29C2×#16864390C2211yescharacteristic, complemented
30C2×#16864389C2211yescharacteristic, complemented
31C2×#16864387C2211yescharacteristic, complemented
32#22575461—21no—
33#22575461—21no—
34#22575461C2212yes—
35#22575461C2212yes—
36C2×#16864386C2211yescharacteristic
37C2×#16864385—21no—
38C22×#14524130C2211yescharacteristic
39C2×C8×D269—21no—
40#22575388C2212yescomplemented
41#22575388C2212yescomplemented
42#22575371C2212yescomplemented
43#22575369C2212yescomplemented
44C2×#41×C269C2211yescharacteristic
45C2×M16×C269C2211yescharacteristic
46C2×M16×C269C2211yescharacteristic
47#101×C269C2212yescomplemented
48#100×C269C2212yescomplemented
49#16864402—21no—
50#16864402—21no—
51#16864402—21no—
52#16864402—21no—
53#16864402—21no—
54#16864402—21no—
55#16864402D412yes—
56#16864402C2312yes—
57C2×Dic538D411yescharacteristic
58C2×Dic538C2311yescharacteristic
59C2×D1076D411yescharacteristic
60C2×D1076C2311yescharacteristic
61C2×C22⋊D269—21no—
62C2×C22⋊D269—21no—
63C2×C4×D269—21no—
64C2×C4×D269—21no—
65Dic1076—22no—
66#16864392—22no—
67#16864392—21no—
68#16864392—21no—
69#16864391—22no—
70#16864391—22no—
71#16864390—22no—
72#16864390—21no—
73#16864390—21no—
74#16864389—22no—
75#16864389—21no—
76#16864389—21no—
77D2152—22no—
78#16864387—22no—
79#16864387—21no—
80#16864387—21no—
81#16864386—21no—
82#16864386C2312yes—
83#16864385—22no—
84#16864385—22no—
85C2×#14524130—21no—
86C2×#14524130D411yescharacteristic
87C2×#14524130D411yescharacteristic
88C2×#14524130D411yescharacteristic
89C2×#14524130D411yescharacteristic
90C2×#14524130C2311yescharacteristic
91C2×#14524130C2311yescharacteristic
92C8×D269—22no—
93C8×D269—22no—
94#41×C269—21no—
95#41×C269—21no—
96#41×C269—21no—
97#41×C269—21no—
98C2×Q8×C269C2311yescharacteristic
99C2×D4×C269—21no—
100C2×D4×C269C2311yescharacteristic
101C22×C4×C269—21no—
102C22×C4×C269C2311yescharacteristic
103M16×C269—21no—
104M16×C269—21no—
105M16×C269C2312yes—
106M16×C269C2312yes—
107C2×C8×C269—21no—
108C2×C8×C269—21no—
109C22×D269—21no—
110C22×D269—21no—
111Dic538—21no—
112Dic538—21no—
113Dic538—21no—
114Dic538C2×D412yes—
115D1076—21no—
116D1076—21no—
117D1076—21no—
118D1076C2×D412yes—
119C22⋊D269—22no—
120C22⋊D269—22no—
121C22⋊D269—41no—
122C22⋊D269—41no—
123C2×Dic269—21no—
124C2×Dic269—21no—
125C4×D269—22no—
126C4×D269—22no—
127C4×D269—41no—
128C4×D269—41no—
129#14524130—22no—
130#14524130C2×D411yescharacteristic
131#14524130C2×D411yescharacteristic
132#14524130C2×D411yescharacteristic
133#14524130C2×D411yescharacteristic
134C23×C269—21no—
135C23×C269#4111yescharacteristic
136Q8×C269—21no—
137Q8×C269—21no—
138D4×C269—21no—
139D4×C269—21no—
140D4×C269—41no—
141D4×C269—41no—
142C2×C4×C269—21no—
143C2×C4×C269—41no—
144C2×C4×C269—41no—
145C2×C4×C269C2×D411yescharacteristic
146C2×C4×C269C2×D411yescharacteristic
147C2×C4×C269C2×D411yescharacteristic
148C2×C4×C269C2×D411yescharacteristic
149C2×C4×C269#4111yescharacteristic
150C2×C4×C269C2411yescharacteristic
151C8×C269—22no—
152C8×C269—22no—
153C22×C269—41no—
154C22×C269—41no—
155C22×C269—81no—
156C22×C269#12111yescharacteristic
157C22×C269#12111yescharacteristic
158C22×C269C2×#4111yescharacteristic
159C2×D269—22no—
160C2×D269—42no—
161C2×D269—41no—
162C2×D269—81no—
163C4×C269—41no—
164C4×C269#12111yescharacteristic
165C4×C269#12111yescharacteristic
166C4×C269C22×D411yescharacteristic
167C4×C269C22×D411yescharacteristic
168Dic269—22no—
169Dic269—41no—
170C2×C269—21no—
171C2×C269—21no—
172C2×C269—21no—
173C2×C269—81no—
174C2×C269C2×#12111yescharacteristic
175D269—42no—
176D269—81no—
177C269#306711yescharacteristic, complemented, Sylow
178#3067—2691nomaximal, Sylow
179#575—2691no—
180#575—2691no—
181C2×#135—2691no—
182C2×#131—2691no—
183#473—2692no—
184#472—2692no—
185#471—2692no—
186#471—2692no—
187C2×#108—2691no—
188#413—2691no—
189#413D26911yescharacteristic, complemented
190C2×#41—2691no—
191C2×#41—2691no—
192C2×#41C2×D26911yescharacteristic
193#137—2692no—
194#137—2692no—
195#137—5381no—
196#137—5381no—
197AGL(1,ℤ/8)—2692no—
198AGL(1,ℤ/8)—2692no—
199AGL(1,ℤ/8)—5381no—
200AGL(1,ℤ/8)—5381no—
201#135—5382no—
202#135—5381no—
203#135—5381no—
204#135—5381no—
205#135—5381no—
206#135—5382no—
207C2×Q16—2691no—
208C2×SD16—2691no—
209C2×SD16—2691no—
210C2×D8—2691no—
211#131—2692no—
212#131—2692no—
213#131—5381no—
214#131—5381no—
215C2×M16—2691no—
216C2×M16—5381no—
217C2×M16C2×D26911yescharacteristic
218C2×M16C2×D26911yescharacteristic
219C22×C8—2691no—
220C22×C8—5381no—
221#108—2692no—
222#108—2692no—
223#101—2692no—
224#101C2×D26912yescomplemented
225#100—2692no—
226#100C2×D26912yescomplemented
227#41—21no—
228#41—21no—
229#41—21no—
230#41—21no—
231#41—2692no—
232#41—2692no—
233#41—5381no—
234#41—5381no—
235#41—5381no—
236#41—5381no—
237#41—5381no—
238#41—5381no—
239C2×Q8—2691no—
240C2×Q8—2691no—
241C2×Q8C22×D26911yescharacteristic
242C2×D4—21no—
243C2×D4—2691no—
244C2×D4—2691no—
245C2×D4—5381no—
246C2×D4—5381no—
247C2×D4C22×D26911yescharacteristic
248C22×C4—21no—
249C22×C4—5381no—
250C22×C4—5381no—
251C22×C4C22×D26911yescharacteristic
252Q16—5382no—
253Q16—5381no—
254Q16—5381no—
255Q16—5382no—
256SD16—5382no—
257SD16—5382no—
258SD16—5381no—
259SD16—5381no—
260SD16—5381no—
261SD16—5381no—
262SD16—5382no—
263SD16—5382no—
264D8—5382no—
265D8—5381no—
266D8—5381no—
267D8—5382no—
268M16—21no—
269M16—21no—
270M16—2692no—
271M16—5382no—
272M16—5382no—
273M16—5381no—
274M16C22×D26912yes—
275M16C22×D26912yes—
276C2×C8—21no—
277C2×C8—21no—
278C2×C8—2691no—
279C2×C8—2691no—
280C2×C8—2691no—
281C2×C8—2691no—
282C2×C8—2691no—
283C2×C8—2691no—
284C2×C8—5382no—
285C2×C8—5382no—
286C2×C8—5381no—
287C23—21no—
288C23—5381no—
289C23—5381no—
290C23#1686440211yescharacteristic
291Q8—21no—
292Q8—21no—
293Q8—2692no—
294Q8—5381no—
295Q8—5381no—
296Q8—5381no—
297D4—21no—
298D4—21no—
299D4—41no—
300D4—41no—
301D4—2692no—
302D4—5382no—
303D4—5382no—
304D4—5381no—
305D4—5381no—
306D4—5381no—
307D4—10761no—
308D4—10761no—
309C2×C4—21no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—5381no—
313C2×C4—5382no—
314C2×C4—5382no—
315C2×C4—5381no—
316C2×C4—10761no—
317C2×C4—10761no—
318C2×C4D4×D26911yescharacteristic
319C2×C4D4×D26911yescharacteristic
320C2×C4D4×D26911yescharacteristic
321C2×C4D4×D26911yescharacteristic
322C2×C4#1686440211yescharacteristic
323C2×C4C23×D26911yescharacteristic
324C8—22no—
325C8—22no—
326C8—2691no—
327C8—2691no—
328C8—2691no—
329C8—2691no—
330C8—5382no—
331C22—41no—
332C22—41no—
333C22—81no—
334C22—5382no—
335C22—10762no—
336C22—10761no—
337C22—21521no—
338C22#2257542611yescharacteristic
339C22#2257542611yescharacteristic
340C22C2×#1686440211yescharacteristic
341C4—41no—
342C4—5382no—
343C4—10761no—
344C4#2257542611yescharacteristic
345C4#2257542611yescharacteristic
346C4C2×D4×D26911yescharacteristic
347C4C2×D4×D26911yescharacteristic
348C2—21no—
349C2—21no—
350C2—21no—
351C2—81no—
352C2—10762no—
353C2—21521no—
354C2C2×#2257542611yescharacteristic
subgroupG/H
centerC4#22575426
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#413×C269C2
socleC2×C269C2×#121
hypercenter#413D269
hypocenterC269#3067
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C4 ◁ C22×C4 ◁ #413

Complements

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

NH ≅ G/Ntype
1. #31771405C2semidirect
2. #31771403C2semidirect
3. C2×#22575473C2semidirect
4. C2×#22575461C2semidirect
5. #31770879C2semidirect
6. #31770874C2semidirect
7. #31770871C2semidirect
8. #31770867C2semidirect
9. C2×#22575388C2semidirect
10. #31770587C2semidirect
11. #413×C269C2semidirect
28. C2×#16864392C22semidirect
29. C2×#16864390C22semidirect
30. C2×#16864389C22semidirect
31. C2×#16864387C22semidirect
40. #22575388C22semidirect
41. #22575388C22semidirect
42. #22575371C22semidirect
43. #22575369C22semidirect
47. #101×C269C22semidirect
48. #100×C269C22semidirect
177. C269#3067semidirect
189. #413D269semidirect
224. #101C2×D269semidirect
226. #100C2×D269semidirect

Maximal subgroups

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

subgroupindex
#317714052
#317714032
C2×#225754732
C2×#225754612
#317708792
#317708742
#317708712
#317708672
C2×#225753882
#317705872
#413×C2692
#3067269