Finite Group Databasebeta

← #24994834

Subgroups — #24994834

Order 11008.

378 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#13063241C211yesmaximal, characteristic
2#19133347C211yesmaximal, characteristic, complemented
3#19132987C211yesmaximal, characteristic
4C2×#14582628C211yesmaximal, characteristic
5C8×#10621877C211yesmaximal, characteristic, complemented
6#19132444C211yesmaximal, characteristic, complemented
7C43×#1278C211yesmaximal, characteristic, complemented
8C2×C4×D172C2211yescharacteristic
9#14582952C2211yescharacteristic
10C2×C4⋊(C43⋊C8)C2211yescharacteristic
11C2×#13063241C411yescharacteristic
12C2×#13063241C411yescharacteristic
13C4×#10621877C2211yescharacteristic
14#14582667C411yescharacteristic
15#14582667C411yescharacteristic
16#14582652—21no—
17#14582650—21no—
18#14582628—21no—
19#14582628—21no—
20#14582628—21no—
21#14582628—21no—
22#14582621—21no—
23C8×C43⋊C8—21no—
24C43×#431C2211yescharacteristic
25C4×M16×C43C2211yescharacteristic
26C2×C4×C8×C43C2211yescharacteristic
27C22×D172C2×C411yescharacteristic
28C22×C4×D43—21no—
29C2×#10621877C2×C411yescharacteristic
30C2×#10621877C2×C411yescharacteristic
31C22×C43⋊C8—21no—
32C4×D172—21no—
33C4×D172—21no—
34C4×D172—21no—
35C4×D172—21no—
36C2×C4⋊Dic43C2×C411yescharacteristic
37C2×(C2×D43)⋊C4—21no—
38C4⋊(C43⋊C8)—21no—
39C4⋊(C43⋊C8)—21no—
40C4⋊(C43⋊C8)D411yescharacteristic
41C4⋊(C43⋊C8)D411yescharacteristic
42#13063241—22no—
43#13063241C814yescomplemented
44C22⋊(C43⋊C8)—21no—
45#13063236—21no—
46C4×C43⋊C8—21no—
47C4×C43⋊C8—21no—
48C2×M16×C43C2×C411yescharacteristic
49C2×M16×C43C2×C411yescharacteristic
50C22×C8×C43—21no—
51C2×C42×C43C2311yescharacteristic
52C4⋊C8×C43—21no—
53C22⋊C8×C43—21no—
54#97×C43—21no—
55C4×C8×C43—21no—
56C4×C8×C43—21no—
57C4×C8×C43—21no—
58C4×C8×C43D411yescharacteristic
59C4×C8×C43D411yescharacteristic
60C23×D43—21no—
61C22×C4×C43C22×C411yescharacteristic
62C22×C4×C43#4111yescharacteristic
63C22×C4×C43#4111yescharacteristic
64C22×Dic43—21no—
65C2×D172—21no—
66C2×D172—21no—
67C2×D172—21no—
68C2×D172—21no—
69C2×D172—21no—
70C2×D172C2×C812yes—
71C2×C4×D43—41no—
72C2×C4×D43—41no—
73C2×C4×D43—81no—
74C2×C4×D43—81no—
75M16×C43—21no—
76M16×C43—21no—
77M16×C43—21no—
78M16×C43C2×C812yes—
79C2×C8×C43—21no—
80C2×C8×C43—21no—
81C2×C8×C43—21no—
82C2×C8×C43—21no—
83C2×C8×C43—42no—
84C2×C8×C43—41no—
85C42×C43C2×D411yescharacteristic
86C42×C43C2×D411yescharacteristic
87C42×C43#4111yescharacteristic
88C42×C43#4111yescharacteristic
89(C2×D43)⋊C4—41no—
90(C2×D43)⋊C4—41no—
91C4⋊Dic43—21no—
92C4⋊Dic43—21no—
93#10621877—21no—
94#10621877—21no—
95#10621877C2×C812yes—
96#10621877M1612yes—
97C2×C43⋊C8—21no—
98C2×C43⋊C8—21no—
99C2×C43⋊C8—21no—
100C2×C43⋊C8—21no—
101C2×C43⋊C8—41no—
102C2×C43⋊C8—81no—
103C23×C43#11711yescharacteristic
104C22×D43—22no—
105C22×D43—41no—
106C22×D43—41no—
107C22×D43—81no—
108C22×D43—81no—
109C2×C4×C43—21no—
110C2×C4×C43—21no—
111C2×C4×C43—41no—
112C2×C4×C43C4×D411yescharacteristic
113C2×C4×C43C4×D411yescharacteristic
114C2×C4×C43#12111yescharacteristic
115C2×C4×C43#12311yescharacteristic
116C2×C4×C43#12411yescharacteristic
117C2×C4×C43#12611yescharacteristic
118C2×C4×C43C22×C811yescharacteristic
119C2×C4×C43C2×M1611yescharacteristic
120C2×C4×C43#13111yescharacteristic
121C2×C4×C43#13111yescharacteristic
122C2×Dic43—41no—
123C2×Dic43—81no—
124D172—22no—
125D172—22no—
126D172—41no—
127D172—41no—
128C4×D43—82no—
129C4×D43—81no—
130C4×D43—81no—
131C8×C43—22no—
132C8×C43—22no—
133C8×C43—41no—
134C8×C43—41no—
135C8×C43—81no—
136C43⋊C8—22no—
137C43⋊C8—22no—
138C43⋊C8—41no—
139C43⋊C8—41no—
140C43⋊C8—81no—
141#9550—431nomaximal, Sylow
142C22×C43—21no—
143C22×C43—21no—
144C22×C43#38811yescharacteristic
145C22×C43#43111yescharacteristic
146C22×C43#43311yescharacteristic
147C2×D43—42no—
148C2×D43—82no—
149C2×D43—81no—
150C2×D43—81no—
151C2×D43—82no—
152C4×C43—21no—
153C4×C43—21no—
154C4×C43—21no—
155C4×C43C8×D411yescharacteristic
156C4×C43C8×D411yescharacteristic
157C4×C43#43511yescharacteristic
158C4×C43#43611yescharacteristic
159C4×C43#47111yescharacteristic
160C4×C43#47211yescharacteristic
161Dic43—81no—
162C4×#100—431no—
163#1565—431no—
164#1478—431no—
165C2×D4⋊C8—431no—
166C8×M16—431no—
167#1283—431no—
168#1278D4311yescharacteristic, complemented
169C2×C43—21no—
170C2×C43—21no—
171C2×C43#192311yescharacteristic
172C2×C43#193111yescharacteristic
173C2×C43#193211yescharacteristic
174D43—82no—
175C2×C4×D4—431no—
176#431—431no—
177#431C2×D4311yescharacteristic
178C2×C4⋊C8—431no—
179C2×#100—431no—
180C2×#100—431no—
181C4×M16—431no—
182C4×M16C2×D4311yescharacteristic
183C2×C4×C8C2×D4311yescharacteristic
184#343—431no—
185#343—431no—
186#335—861no—
187#334—861no—
188D4⋊C8—861no—
189D4⋊C8—861no—
190D4⋊C8—861no—
191D4⋊C8—861no—
192#322—861no—
193C82—861no—
194C43#955011yescharacteristic, complemented, Sylow
195C22×D4—431no—
196C23×C4—861no—
197C2×M16—431no—
198C2×M16—431no—
199C2×M16C4×D4311yescharacteristic
200C2×M16C4×D4311yescharacteristic
201C22×C8—21no—
202C22×C8—861no—
203C4×D4—861no—
204C4×D4—861no—
205C4×D4—861no—
206C4×D4—861no—
207C2×C4⋊C4—431no—
208C2×C22⋊C4—861no—
209C2×C42C22×D4311yescharacteristic
210C4⋊C8—21no—
211C4⋊C8—431no—
212C4⋊C8—431no—
213C4⋊C8—861no—
214C4⋊C8—861no—
215#100—434no—
216#100—862no—
217C22⋊C8—21no—
218C22⋊C8—861no—
219#97—21no—
220#97—861no—
221C4×C8—21no—
222C4×C8—21no—
223C4×C8—21no—
224C4×C8—861no—
225C4×C8—861no—
226C4×C8D17211yescharacteristic
227C4×C8D17211yescharacteristic
228C24—861no—
229C2×D4—432no—
230C2×D4—861no—
231C2×D4—861no—
232C2×D4—861no—
233C2×D4—861no—
234C2×D4—861no—
235C22×C4—861no—
236C22×C4—3441no—
237C22×C4—3441no—
238C22×C4—1721no—
239C22×C4—1721no—
240C22×C4C2×C4×D4311yescharacteristic
241C22×C4#1062190011yescharacteristic
242C22×C4#1062190211yescharacteristic
243M16—21no—
244M16—21no—
245M16—21no—
246M16—432no—
247M16—432no—
248M16—861no—
249M16—861no—
250M16C8×D4312yes—
251C2×C8—21no—
252C2×C8—21no—
253C2×C8—21no—
254C2×C8—21no—
255C2×C8—42no—
256C2×C8—41no—
257C2×C8—861no—
258C2×C8—861no—
259C2×C8—861no—
260C2×C8—861no—
261C2×C8—3441no—
262C2×C8—1721no—
263C4⋊C4—861no—
264C4⋊C4—861no—
265C22⋊C4—1721no—
266C22⋊C4—1721no—
267C42C2×D17211yescharacteristic
268C42#1062189811yescharacteristic
269C42D4×D4311yescharacteristic
270C42#1062190011yescharacteristic
271C23—862no—
272C23—3441no—
273C23—3441no—
274C23—1721no—
275C23—1721no—
276C23#1306328311yescharacteristic
277D4—862no—
278D4—862no—
279D4—1721no—
280D4—1721no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—41no—
284C2×C4—3442no—
285C2×C4—3441no—
286C2×C4—3441no—
287C2×C4—3441no—
288C2×C4—1721no—
289C2×C4(C22⋊D43)⋊C411yescharacteristic
290C2×C4C4×D17211yescharacteristic
291C2×C4#1306330011yescharacteristic
292C2×C4#1306330911yescharacteristic
293C2×C4#1306331111yescharacteristic
294C2×C4#1306332011yescharacteristic
295C2×C4C2×C8×D4311yescharacteristic
296C2×C4M16×D4311yescharacteristic
297C2×C4#1306333111yescharacteristic
298C2×C4#1306333311yescharacteristic
299C8—22no—
300C8—22no—
301C8—41no—
302C8—41no—
303C8—81no—
304C8—862no—
305C8—862no—
306C8—3441no—
307C8—1721no—
308C8—1721no—
309C22—21no—
310C22—21no—
311C22—3442no—
312C22—3442no—
313C22—3441no—
314C22—3441no—
315C22—1722no—
316C22#1458279111yescharacteristic
317C22#1458295111yescharacteristic
318C22#1458295911yescharacteristic
319C4—21no—
320C4—21no—
321C4—21no—
322C4—3441no—
323C4(C22⋊D43)⋊C811yescharacteristic
324C4C8×D17211yescharacteristic
325C4#1458297211yescharacteristic
326C4#1458297411yescharacteristic
327C4#1458316311yescharacteristic
328C4#1458317011yescharacteristic
329C2—21no—
330C2—21no—
331C2—3442no—
332C2#1913520211yescharacteristic
333C2#1913525811yescharacteristic
334C2#1913526511yescharacteristic
subgroupG/H
centerC2×C4#13063300
commutatorC2×C4×C43C22×C8
FrattiniC2×C42C22×D43
FittingC43×#1278C2
socleC22×C43#388
prime radicalC22×D172C2×C4
cosocleC2×C42×C43C23
hypercenter#1278D43
hypocenterC43#9550
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1278

Complements

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

NH ≅ G/Ntype
2. #19133347C2semidirect
5. C8×#10621877C2semidirect
6. #19132444C2semidirect
7. C43×#1278C2semidirect
43. #13063241C8semidirect
168. #1278D43semidirect
194. C43#9550semidirect

Maximal subgroups

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

subgroupindex
C4×#130632412
#191333472
#191329872
C2×#145826282
C8×#106218772
#191324442
C43×#12782
#955043