Finite Group Databasebeta

← #25101301

Subgroups — #25101301

Order 11008.

646 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19137069C211yesmaximal, characteristic
2#19135535C211yesmaximal, characteristic
3#19135534C211yesmaximal, characteristic
4#19135319C211yesmaximal, characteristic
5#19135162C212yesmaximal
6#19135156C212yesmaximal
7#19134454C212yesmaximal
8#19134450C211yesmaximal, characteristic
9#19134345C212yesmaximal
10#97×Dic43C211yesmaximal, characteristic
11C43×#1940C211yesmaximal, characteristic
12C2×C4×Dic86C2211yescharacteristic
13C2×C4⋊(C43⋊C8)C2211yescharacteristic
14C2×C4⋊(C43⋊C8)C2212yes—
15C2×#13063236C2211yescharacteristic
16C2×#13063235C2211yescharacteristic
17C2×#13063235C2211yescharacteristic
18C2×#13063235C2212yes—
19C2×C8×Dic43C2211yescharacteristic
20C2×C8×Dic43C2211yescharacteristic
21#14582804C412yes—
22#14582795C412yes—
23#14582781C414yes—
24C4×Dic43⋊C4C2212yes—
25#14582745C2212yes—
26C42×Dic43C2211yescharacteristic
27#14582654C2212yes—
28#14582653C2212yes—
29#14582653C2212yes—
30#14582653C2212yes—
31#14582653C2212yes—
32#14582653C2212yes—
33C2×C4⋊C8×C43C2211yescharacteristic
34C2×C4⋊C8×C43C2212yes—
35C2×#97×C43C2211yescharacteristic
36C4×C4⋊C4×C43C2211yescharacteristic
37C43×#336C2212yes—
38C22×Dic86C2×C411yescharacteristic
39C22×C43⋊C8C2312yes—
40C22×C43⋊C8C2311yescharacteristic
41C22×C43⋊C8C2311yescharacteristic
42C4×Dic86—22no—
43C4×Dic86—22no—
44C2×C4⋊Dic43C2×C411yescharacteristic
45C2×Dic43⋊C4C2×C412yes—
46C2×Dic43⋊C4C2×C414yes—
47C2×C4×Dic43C2×C412yes—
48C2×C4×Dic43C2×C412yes—
49C2×C4×Dic43C2311yescharacteristic
50C2×C4×Dic43C2312yes—
51C2×C4×Dic43C2311yescharacteristic
52C4⋊(C43⋊C8)—22no—
53C4⋊(C43⋊C8)—24no—
54#13063236—22no—
55#13063235—22no—
56#13063235—24no—
57#13063235—22no—
58C8×Dic43—22no—
59C8×Dic43Q814yescomplemented
60C43⋊#95C2×C414yes—
61C43⋊#95C2×C414yes—
62C43⋊#95C2×C414yes—
63C22×C8×C43C2312yes—
64C22×C8×C43C2311yescharacteristic
65C22×C8×C43C2311yescharacteristic
66C2×C4⋊C4×C43C2×C412yes—
67C2×C42×C43C2312yes—
68C2×C42×C43C2311yescharacteristic
69C4⋊C8×C43—24no—
70C4⋊C8×C43—22no—
71#97×C43—22no—
72#95×C43C2×C412yes—
73C22×C4×C43C22×C414yes—
74C22×C4×C43C22×C411yescharacteristic
75C22×C4×C43C22×C411yescharacteristic
76C22×C4×C43C2411yescharacteristic
77C22×Dic43C22×C412yes—
78C22×Dic43C22×C412yes—
79C22×Dic43C22×C412yes—
80C22×Dic43C22×C412yes—
81C2×Dic86—22no—
82C2×Dic86—42no—
83C2×C8×C43—21no—
84C2×C8×C43—21no—
85C2×C8×C43—21no—
86C2×C8×C43—21no—
87C2×C8×C43—22no—
88C2×C8×C43—22no—
89C2×C8×C43—22no—
90C2×C8×C43C2×Q812yes—
91C2×C8×C43#4112yes—
92C4⋊C4×C43—42no—
93C42×C43—22no—
94C42×C43—22no—
95C42×C43#4112yes—
96C42×C43#4112yes—
97C4⋊Dic43—22no—
98Dic43⋊C4—24no—
99Dic43⋊C4—44no—
100C4×Dic43—21no—
101C4×Dic43—21no—
102C4×Dic43—22no—
103C4×Dic43—22no—
104C4×Dic43—42no—
105C4×Dic43—42no—
106C4×Dic43C2×Q812yes—
107C4×Dic43#4112yes—
108C2×C43⋊C8—21no—
109C2×C43⋊C8—21no—
110C2×C43⋊C8—21no—
111C2×C43⋊C8—21no—
112C2×C43⋊C8—22no—
113C2×C43⋊C8—22no—
114C2×C43⋊C8—22no—
115C2×C43⋊C8C2×Q812yes—
116C2×C43⋊C8#4112yes—
117C23×C43C23×C411yescharacteristic
118C2×C4×C43—22no—
119C2×C4×C43—22no—
120C2×C4×C43—24no—
121C2×C4×C43—24no—
122C2×C4×C43—24no—
123C2×C4×C43#11712yes—
124C2×C4×C43#11712yes—
125C2×C4×C43C22×Q811yescharacteristic
126C2×C4×C43C2×#4111yescharacteristic
127C2×C4×C43C2×#4111yescharacteristic
128C2×C4×C43C2×#4111yescharacteristic
129C2×C4×C43C2×#4111yescharacteristic
130C2×C4×C43C2×#4111yescharacteristic
131C2×Dic43—22no—
132C2×Dic43—22no—
133C2×Dic43—22no—
134C2×Dic43—22no—
135C2×Dic43—22no—
136C2×Dic43—22no—
137C2×Dic43—22no—
138C2×Dic43—24no—
139C2×Dic43—24no—
140C2×Dic43C4×Q814yes—
141Dic86—44no—
142C8×C43—22no—
143C8×C43—22no—
144C8×C43—42no—
145C43⋊C8—22no—
146C43⋊C8—22no—
147C43⋊C8—42no—
148#21342—431nomaximal, Sylow
149C22×C43C2×#11711yescharacteristic
150C22×C43C2×C4×Q811yescharacteristic
151C22×C43C4×#4111yescharacteristic
152C22×C43#56812yes—
153C22×C43#56812yes—
154C4×C43—22no—
155C4×C43—22no—
156C4×C43—44no—
157C4×C43#52911yescharacteristic
158C4×C43#52911yescharacteristic
159C4×C43#53311yescharacteristic
160C4×C43#53311yescharacteristic
161Dic43—24no—
162Dic43—42no—
163Dic43—42no—
164Dic43—42no—
165#2295—431no—
166#1985—431no—
167#1985—431no—
168#1940—431no—
169#1940D4311yescharacteristic
170#1917—432no—
171#1917—432no—
172#1768—432no—
173#1767—431no—
174#1746—432no—
175C4×#97—431no—
176C2×C43#229511yescharacteristic
177C2×C43#292111yescharacteristic
178C2×C43#292311yescharacteristic
179C2×C43#296112yes—
180C2×C43#296712yes—
181C2×C4×Q8—431no—
182C2×C4⋊C8—432no—
183C2×C4⋊C8—431no—
184C2×C4⋊C8C2×D4312yes—
185C2×C4⋊C8C2×D4311yescharacteristic
186C2×#97—431no—
187C2×#97—431no—
188C2×#97—432no—
189C2×#97—431no—
190C2×#97C2×D4311yescharacteristic
191C2×C4×C8—431no—
192C2×C4×C8—431no—
193#391—432no—
194#389—432no—
195#387—434no—
196C4×C4⋊C4—432no—
197C4×C4⋊C4C2×D4311yescharacteristic
198#376—432no—
199C43—431no—
200#336—432no—
201#336—432no—
202#336—432no—
203#336—432no—
204#336—432no—
205#336—432no—
206#336C2×D4312yes—
207C43#2134211yescharacteristic, complemented, Sylow
208C22×Q8—431no—
209C22×C8—431no—
210C22×C8—431no—
211C22×C8—432no—
212C22×C8C22×D4312yes—
213C22×C8C22×D4311yescharacteristic
214C22×C8C22×D4311yescharacteristic
215C4×Q8—862no—
216C4×Q8—862no—
217C2×C4⋊C4—432no—
218C2×C4⋊C4—431no—
219C2×C4⋊C4—434no—
220C2×C4⋊C4C4×D4312yes—
221C2×C42—431no—
222C2×C42—432no—
223C2×C42—431no—
224C2×C42—432no—
225C2×C42—432no—
226C2×C42C22×D4312yes—
227C2×C42C22×D4311yescharacteristic
228C4⋊C8—24no—
229C4⋊C8—22no—
230C4⋊C8—864no—
231C4⋊C8—862no—
232#97—22no—
233#97—864no—
234#97—862no—
235#97—862no—
236#97—862no—
237C4×C8—434no—
238C4×C8—862no—
239#95—434no—
240#95—434no—
241#95—434no—
242#95C4×D4312yes—
243C2×Q8—862no—
244C2×Q8—1722no—
245C22×C4—432no—
246C22×C4—432no—
247C22×C4—432no—
248C22×C4—432no—
249C22×C4C2×C4×D4314yes—
250C22×C4C2×C4×D4311yescharacteristic
251C22×C4C2×C4×D4311yescharacteristic
252C22×C4C23×D4311yescharacteristic
253C2×C8—21no—
254C2×C8—21no—
255C2×C8—21no—
256C2×C8—21no—
257C2×C8—22no—
258C2×C8—22no—
259C2×C8—22no—
260C2×C8—432no—
261C2×C8—432no—
262C2×C8—861no—
263C2×C8—861no—
264C2×C8—861no—
265C2×C8—861no—
266C2×C8—862no—
267C2×C8—862no—
268C2×C8—862no—
269C2×C8#1062190012yes—
270C2×C8Q8×D4312yes—
271C4⋊C4—42no—
272C4⋊C4—864no—
273C4⋊C4—862no—
274C4⋊C4—1724no—
275C42—22no—
276C42—22no—
277C42—432no—
278C42—432no—
279C42—861no—
280C42—861no—
281C42—862no—
282C42—862no—
283C42—1722no—
284C42—1722no—
285C42#1062190012yes—
286C42#1062190212yes—
287C23C22×C4×D4311yescharacteristic
288Q8—1724no—
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—24no—
292C2×C4—24no—
293C2×C4—24no—
294C2×C4—434no—
295C2×C4—862no—
296C2×C4—862no—
297C2×C4—862no—
298C2×C4—862no—
299C2×C4—862no—
300C2×C4—862no—
301C2×C4—864no—
302C2×C4—862no—
303C2×C4—864no—
304C2×C4#1306328312yes—
305C2×C4#1306328312yes—
306C2×C4C2×Q8×D4311yescharacteristic
307C2×C4#41×D4311yescharacteristic
308C2×C4#41×D4311yescharacteristic
309C2×C4C2×#1062190011yescharacteristic
310C2×C4C2×#1062190011yescharacteristic
311C2×C4C2×#1062190211yescharacteristic
312C8—22no—
313C8—22no—
314C8—42no—
315C8—862no—
316C8—862no—
317C8—1722no—
318C22C2×#1306328311yescharacteristic
319C22C4×Q8×D4311yescharacteristic
320C22C4×#1062190011yescharacteristic
321C22#1458366412yes—
322C22#1458366512yes—
323C4—22no—
324C4—22no—
325C4—44no—
326C4—864no—
327C4—1722no—
328C4—1722no—
329C4—1722no—
330C4#1458343011yescharacteristic
331C4#1458343411yescharacteristic
332C4#1458345111yescharacteristic
333C4#1458345411yescharacteristic
334C2#1913706611yescharacteristic
335C2#1914323211yescharacteristic
336C2#1914324511yescharacteristic
337C2#1914353112yes—
338C2#1914357712yes—
subgroupG/H
center, FrattiniC22×C4C23×D43
commutator, socle, prime radicalC23×C43C23×C4
FittingC43×#1940C2
cosocleC22×C4×C43C24
hypercenter#1940D43
hypocenterC43#21342
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ #1940

Complements

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

NH ≅ G/Ntype
59. C8×Dic43Q8semidirect
207. C43#21342semidirect

Maximal subgroups

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

subgroupindex
#191370692
#191355352
#191355342
#191353192
#191351622
#191351562
#191344542
#191344502
#191343452
#97×Dic432
C43×#19402
#2134243