Finite Group Databasebeta

← #24993971

Subgroups — #24993971

Order 11008.

594 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 594 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143618C211yesmaximal, characteristic
2#19139544C211yesmaximal, characteristic
3#19134584C211yesmaximal, characteristic
4#19133281C211yesmaximal, characteristic, complemented
5#19133279C211yesmaximal, characteristic, complemented
6#19132498C211yesmaximal, characteristic, complemented
7C43×#1303C211yesmaximal, characteristic, complemented
8C2×#13063325C2211yescharacteristic
9C2×#13063305—22no—
10C2×C4×D172C2211yescharacteristic
11C8×D172—22no—
12#14582964—22no—
13#14582952C2211yescharacteristic
14#14582923C2211yescharacteristic
15C2×#13063241—21no—
16C22⋊C8×D43—22no—
17#14582836C414yes—
18#14582801—21no—
19#14582769—21no—
20#14582667—21no—
21#14582646—22no—
22#14582644—22no—
23C43×#431C2211yescharacteristic
24C43×#423C2211yescharacteristic
25C4×C4⋊C4×C43C2211yescharacteristic
26C22×Dic86—21no—
27C22×D172D411yescharacteristic
28C22×C4×D43D412yes—
29C2×#10621877—21no—
30C2×C8×D43—24no—
31#13063325—21no—
32#13063325—21no—
33#13063325—21no—
34#13063325—21no—
35#13063305—48no—
36C4×D172—21no—
37C4×D172—21no—
38C4×D172—21no—
39C4×D172—21no—
40C2×C4⋊Dic43—21no—
41C2×C4⋊Dic43—24no—
42C2×C4⋊Dic43C2×C412yes—
43C2×C4⋊Dic43D411yescharacteristic
44C2×(C2×D43)⋊C4—24no—
45C2×(C2×D43)⋊C4C2×C412yes—
46C4⋊(C43⋊C8)—21no—
47C4⋊(C43⋊C8)—21no—
48C4⋊(C43⋊C8)D412yes—
49#13063241—42no—
50C22⋊(C43⋊C8)—21no—
51(C2×D43)⋊C8—24no—
52C4×C43⋊C8—21no—
53C2×M16×C43—21no—
54C2×C4⋊C4×C43—21no—
55C2×C42×C43—21no—
56C2×C42×C43C2311yescharacteristic
57C4⋊C8×C43—21no—
58C4⋊C8×C43—21no—
59C4⋊C8×C43D412yes—
60C22⋊C8×C43—21no—
61C4×C8×C43—21no—
62#95×C43C2×C412yes—
63C23×D43C22⋊C412yes—
64C22×C4×C43—22no—
65C22×C4×C43C22×C411yescharacteristic
66C22×C4×C43C2×D411yescharacteristic
67C22×C4×C43C2×D411yescharacteristic
68C22×Dic43—22no—
69C22×Dic43C22⋊C412yes—
70C2×D172—21no—
71C2×D172—21no—
72C2×D172—21no—
73C2×D172—21no—
74C2×D172SD1612yes—
75C2×D172Q1612yes—
76C2×C4×D43—22no—
77C2×C4×D43—22no—
78C2×C4×D43—44no—
79C2×Dic86—44no—
80C2×Dic86—41no—
81C2×Dic86—41no—
82M16×C43—41no—
83M16×C43—41no—
84C2×C8×C43—22no—
85C2×C8×C43—41no—
86C4⋊C4×C43—24no—
87C42×C43—41no—
88C42×C43—41no—
89C42×C43C2×D411yescharacteristic
90C42×C43C2×D411yescharacteristic
91C42×C43#4111yescharacteristic
92C42×C43#4111yescharacteristic
93(C2×D43)⋊C4—22no—
94(C2×D43)⋊C4—22no—
95(C2×D43)⋊C4—48no—
96C4⋊Dic43—21no—
97C4⋊Dic43—21no—
98C4⋊Dic43—22no—
99C4⋊Dic43—22no—
100C4⋊Dic43—48no—
101C4⋊Dic43—41no—
102C4⋊Dic43—41no—
103#10621877—41no—
104#10621877—41no—
105C2×C43⋊C8—22no—
106C2×C43⋊C8—41no—
107C8×D43—84no—
108C23×C43C2×C22⋊C411yescharacteristic
109C22×D43—22no—
110C22×D43—22no—
111C22×D43—42no—
112C22×D43—42no—
113C22×D43#10314yes—
114C2×C4×C43—22no—
115C2×C4×C43—24no—
116C2×C4×C43—41no—
117C2×C4×C43—42no—
118C2×C4×C43—42no—
119C2×C4×C43C4×D411yescharacteristic
120C2×C4×C43C4×D411yescharacteristic
121C2×C4×C43#12011yescharacteristic
122C2×C4×C43#12111yescharacteristic
123C2×C4×C43#12111yescharacteristic
124C2×C4×C43#12311yescharacteristic
125C2×C4×C43C2×SD1611yescharacteristic
126C2×C4×C43C2×Q1611yescharacteristic
127C2×C4×C43#13511yescharacteristic
128C2×C4×C43#13511yescharacteristic
129C2×Dic43—22no—
130C2×Dic43—42no—
131C2×Dic43—44no—
132C2×Dic43—42no—
133D172—22no—
134D172—22no—
135D172—22no—
136D172—22no—
137C4×D43—44no—
138C4×D43—82no—
139Dic86—82no—
140Dic86—82no—
141C8×C43—42no—
142C8×C43—81no—
143C43⋊C8—42no—
144C43⋊C8—81no—
145#9395—431nomaximal, Sylow
146C22×C43—21no—
147C22×C43—21no—
148C22×C43#38611yescharacteristic
149C22×C43C2×#10311yescharacteristic
150C22×C43#41611yescharacteristic
151C2×D43—24no—
152C2×D43—42no—
153C2×D43—42no—
154C2×D43—44no—
155C2×D43—82no—
156C4×C43—21no—
157C4×C43—21no—
158C4×C43—21no—
159C4×C43—44no—
160C4×C43#45312yes—
161C4×C43#46511yescharacteristic
162C4×C43#46511yescharacteristic
163C4×C43#46711yescharacteristic
164C4×C43#46711yescharacteristic
165Dic43—42no—
166Dic43—82no—
167#2972—431no—
168#2542—431no—
169#1800—431no—
170#1549—431no—
171#1549—431no—
172#1303—431no—
173#1303D4311yescharacteristic, complemented
174C2×C43—21no—
175C2×C43—21no—
176C2×C43#188711yescharacteristic
177C2×C43#189211yescharacteristic
178C2×C43#191511yescharacteristic
179D43—44no—
180C2×C4⋊Q8—431no—
181C2×C22⋊Q8—862no—
182C2×C4×D4—431no—
183C8×D4—862no—
184C8×D4—862no—
185#431—431no—
186#431C2×D4311yescharacteristic
187#423—431no—
188#423C2×D4311yescharacteristic
189C2×#100—861no—
190C2×C22⋊C8—862no—
191#399—434no—
192#390—861no—
193#384—861no—
194C4×C4⋊C4C2×D4311yescharacteristic
195#343—861no—
196#332—862no—
197#332—862no—
198C43#939511yescharacteristic, complemented, Sylow
199C22×Q8—861no—
200C22×D4—431no—
201C23×C4—432no—
202C2×M16—21no—
203C2×M16—861no—
204C22×C8—864no—
205C4⋊Q8—861no—
206C4⋊Q8—861no—
207C4⋊Q8—861no—
208C4⋊Q8—861no—
209C22⋊Q8—1728no—
210C4×D4—861no—
211C4×D4—861no—
212C4×D4—861no—
213C4×D4—861no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—431no—
216C2×C4⋊C4—432no—
217C2×C4⋊C4—864no—
218C2×C4⋊C4—861no—
219C2×C22⋊C4—432no—
220C2×C22⋊C4—864no—
221C2×C42—21no—
222C2×C42C22×D4311yescharacteristic
223C4⋊C8—21no—
224C4⋊C8—21no—
225C4⋊C8—432no—
226C4⋊C8—861no—
227C4⋊C8—861no—
228C4⋊C8D17212yes—
229#100—1722no—
230C22⋊C8—21no—
231C22⋊C8—864no—
232C22⋊C8—861no—
233C4×C8—21no—
234C4×C8—861no—
235#95C4×D4312yes—
236C24—432no—
237C2×Q8—1724no—
238C2×Q8—1721no—
239C2×Q8—1721no—
240C2×D4—432no—
241C2×D4—432no—
242C2×D4—861no—
243C2×D4—861no—
244C2×D4—861no—
245C2×D4—861no—
246C22×C4—22no—
247C22×C4—432no—
248C22×C4—862no—
249C22×C4—862no—
250C22×C4—862no—
251C22×C4—1724no—
252C22×C4C2×C4×D4311yescharacteristic
253C22×C4D4×D4311yescharacteristic
254C22×C4D4×D4311yescharacteristic
255M16—41no—
256M16—41no—
257M16—1721no—
258M16—1721no—
259C2×C8—22no—
260C2×C8—41no—
261C2×C8—862no—
262C2×C8—3444no—
263C2×C8—1721no—
264C4⋊C4—24no—
265C4⋊C4—861no—
266C4⋊C4—861no—
267C4⋊C4—862no—
268C4⋊C4—862no—
269C4⋊C4—1728no—
270C4⋊C4—1721no—
271C4⋊C4—1721no—
272C22⋊C4—862no—
273C22⋊C4—862no—
274C22⋊C4—1728no—
275C42—41no—
276C42—41no—
277C42C2×D17211yescharacteristic
278C42#1062189811yescharacteristic
279C42D4×D4311yescharacteristic
280C42#1062190211yescharacteristic
281C23—434no—
282C23—862no—
283C23—862no—
284C23—1722no—
285C23—1722no—
286C23C22⋊C4×D4311yescharacteristic
287Q8—3442no—
288Q8—3442no—
289D4—862no—
290D4—862no—
291D4—862no—
292D4—862no—
293C2×C4—22no—
294C2×C4—24no—
295C2×C4—41no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—862no—
299C2×C4—3442no—
300C2×C4—1724no—
301C2×C4—1722no—
302C2×C4—1724no—
303C2×C4—1722no—
304C2×C4#1306328711yescharacteristic
305C2×C4C4×D17211yescharacteristic
306C2×C4#1306329511yescharacteristic
307C2×C4#1306329811yescharacteristic
308C2×C4#1306330011yescharacteristic
309C2×C4#1306331011yescharacteristic
310C2×C4SD16×D4311yescharacteristic
311C2×C4Q16×D4311yescharacteristic
312C2×C4#1306334411yescharacteristic
313C2×C4#1306334611yescharacteristic
314C8—42no—
315C8—81no—
316C8—3441no—
317C8—1722no—
318C22—21no—
319C22—21no—
320C22—864no—
321C22—3442no—
322C22—1724no—
323C22—1722no—
324C22—1722no—
325C22#1458277711yescharacteristic
326C22#103×D4311yescharacteristic
327C22#1458289211yescharacteristic
328C4—21no—
329C4—21no—
330C4—21no—
331C4—44no—
332C4—3442no—
333C4—1722no—
334C4#1458306812yes—
335C4#1458312711yescharacteristic
336C4#1458312911yescharacteristic
337C4#1458313911yescharacteristic
338C4#1458314111yescharacteristic
339C2—21no—
340C2—21no—
341C2—1724no—
342C2#1913499211yescharacteristic
343C2#1913501711yescharacteristic
344C2#1913514611yescharacteristic
subgroupG/H
centerC22#14582777
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1303C2
socleC22×C43#386
prime radicalC22×D172D4
cosocleC2×C42×C43C23
hypercenter#1303D43
hypocenterC43#9395
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1303

Complements

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

NH ≅ G/Ntype
4. #19133281C2semidirect
5. #19133279C2semidirect
6. #19132498C2semidirect
7. C43×#1303C2semidirect
173. #1303D43semidirect
198. C43#9395semidirect

Maximal subgroups

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

subgroupindex
#191436182
#191395442
#191345842
#191332812
#191332792
#191324982
C43×#13032
#939543