Finite Group Databasebeta

← #25013106

Subgroups — #25013106

Order 11008.

442 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582936C211yesmaximal, characteristic
2C2×#14582724C211yesmaximal, characteristic, complemented
3C2×(C2×D43)⋊C16C211yesmaximal, characteristic
4#19134621C211yesmaximal, characteristic
5#19132687C211yesmaximal, characteristic, complemented
6#19132686C211yesmaximal, characteristic, complemented
7C2×C43×#367C211yesmaximal, characteristic, complemented
8C22×C8×D43C2211yescharacteristic
9C2×#13063283—21no—
10C22×C43⋊C16C2211yescharacteristic
11#14582936—22no—
12#14582936—22no—
13C2×#13063259C2211yescharacteristic
14C2×#13063259C2211yescharacteristic
15C2×#13063256—21no—
16#14582756—21no—
17#14582724—22no—
18(C2×D43)⋊C16C414yescomplemented
19#14582661—21no—
20C22×C16×C43C2211yescharacteristic
21C2×#107×C43C2211yescharacteristic
22C2×#107×C43C2211yescharacteristic
23C43×#367—22no—
24C22×C4×D43D411yescharacteristic
25C22×C43⋊C8D411yescharacteristic
26C2×C8×D43—21no—
27C2×C8×D43—21no—
28C2×C8×D43—21no—
29C2×C8×D43—21no—
30C2×C8×D43C2×C412yes—
31C2×C8×D43Q812yes—
32#13063283—24no—
33#13063283—42no—
34C2×C4⋊Dic43—21no—
35C2×C4⋊Dic43—21no—
36C2×(C2×D43)⋊C4—41no—
37C2×(C2×D43)⋊C4—41no—
38C2×C4×Dic43—41no—
39C2×C43⋊C16—21no—
40C2×C43⋊C16—21no—
41C2×C43⋊C16C2×C412yes—
42#13063259—21no—
43#13063259—21no—
44#13063259—21no—
45#13063259D412yes—
46#13063256—24no—
47C43⋊#95—41no—
48C22×C8×C43C2311yescharacteristic
49C2×C4⋊C4×C43—21no—
50C2×C4⋊C4×C43—21no—
51C2×C16×C43—21no—
52C2×C16×C43—21no—
53C2×C16×C43C2×C412yes—
54#107×C43—21no—
55#107×C43—21no—
56#107×C43—21no—
57#107×C43D412yes—
58C23×D43D811yescharacteristic
59C22×C4×C43—41no—
60C22×C4×C43—41no—
61C22×C4×C43C2×D411yescharacteristic
62C22×Dic43—41no—
63C22×Dic43—41no—
64C22×Dic43D811yescharacteristic
65C2×C4×D43—21no—
66C2×C4×D43—21no—
67C2×C4×D43—21no—
68C2×C4×D43—21no—
69C2×C4×D43C4⋊C412yes—
70C2×C4×D43Q1612yes—
71C2×C8×C43C22×C411yescharacteristic
72C2×C8×C43C2×D411yescharacteristic
73C2×C8×C43C2×D411yescharacteristic
74C2×C8×C43C2×Q811yescharacteristic
75C2×C8×C43#4111yescharacteristic
76C2×C8×C43#4111yescharacteristic
77C4⋊C4×C43—22no—
78C4⋊C4×C43—41no—
79C4⋊C4×C43—41no—
80C4⋊C4×C43—41no—
81(C2×D43)⋊C4—44no—
82(C2×D43)⋊C4—82no—
83C4⋊Dic43—22no—
84C4⋊Dic43—41no—
85C4⋊Dic43—41no—
86C4⋊Dic43—41no—
87C4×Dic43—44no—
88C2×C43⋊C8—21no—
89C2×C43⋊C8—21no—
90C2×C43⋊C8C4⋊C412yes—
91C8×D43—22no—
92C8×D43—22no—
93C8×D43—22no—
94C8×D43—22no—
95C16×C43—22no—
96C43⋊C16—22no—
97C23×C43C2×D811yescharacteristic
98C22×D43—21no—
99C22×D43—21no—
100C22×D43—21no—
101C22×D43—21no—
102C22×D43—21no—
103C22×D43—21no—
104C22×D43#10712yes—
105C2×C4×C43—42no—
106C2×C4×C43—81no—
107C2×C4×C43—81no—
108C2×C4×C43—81no—
109C2×C4×C43—81no—
110C2×C4×C43—81no—
111C2×C4×C43C2×C4⋊C411yescharacteristic
112C2×C4×C43#12011yescharacteristic
113C2×C4×C43#12311yescharacteristic
114C2×C4×C43C2×Q1611yescharacteristic
115C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
116C2×C4×C43#13711yescharacteristic
117C2×Dic43—21no—
118C2×Dic43—21no—
119C2×Dic43—42no—
120C2×Dic43—81no—
121C2×Dic43—81no—
122C2×Dic43—81no—
123C2×Dic43—81no—
124C2×Dic43—81no—
125C2×Dic43#10712yes—
126C4×D43—22no—
127C4×D43—22no—
128C4×D43—22no—
129C4×D43—22no—
130C8×C43C4×D411yescharacteristic
131C8×C43C4×D411yescharacteristic
132C8×C43C22⋊Q811yescharacteristic
133C8×C43C22⋊Q811yescharacteristic
134C43⋊C8—22no—
135#12921—431nomaximal, Sylow
136C22×C43C2×#10711yescharacteristic
137C22×C43#44711yescharacteristic
138C22×C43#48011yescharacteristic
139C22×C43#50811yescharacteristic
140C22×C43#50811yescharacteristic
141C22×C43#50911yescharacteristic
142C22×C43#51011yescharacteristic
143C2×D43—22no—
144C2×D43—22no—
145C2×D43—22no—
146C2×D43—41no—
147C2×D43—41no—
148C2×D43—41no—
149C2×D43—41no—
150C4×C43—82no—
151C4×C43—161no—
152C4×C43#38511yescharacteristic
153C4×C43#42811yescharacteristic
154C4×C43#45111yescharacteristic
155C4×C43#48411yescharacteristic
156Dic43—22no—
157Dic43—82no—
158Dic43—161no—
159C2×#427—431no—
160C2×#367D4311yescharacteristic, complemented
161C2×#366—431no—
162C2×C22⋊C16—431no—
163#1808—431no—
164#1380—431no—
165#1380—431no—
166C2×C43#185211yescharacteristic
167C2×C43#215811yescharacteristic
168C2×C43#215911yescharacteristic
169C2×C43#218611yescharacteristic
170C2×C43#218911yescharacteristic
171C2×C43#223411yescharacteristic
172C2×C43#223711yescharacteristic
173D43—42no—
174C23×C8—431no—
175C2×#117—861no—
176C22×C16—431no—
177C22×C16C2×D4311yescharacteristic
178#427—862no—
179#427—862no—
180C2×#107—431no—
181C2×#107—431no—
182C2×#107C2×D4311yescharacteristic
183C2×#107C2×D4311yescharacteristic
184C2×#106—861no—
185#380—861no—
186#367—22no—
187#366—862no—
188C22⋊C16—434no—
189#340—861no—
190C43#1292111yescharacteristic, complemented, Sylow
191C23×C4—431no—
192C22×C8—431no—
193C22×C8—432no—
194C22×C8—432no—
195C22×C8—861no—
196C22×C8—861no—
197C22×C8—861no—
198C22×C8—861no—
199C22×C8C22×D4311yescharacteristic
200#117—864no—
201#117—1722no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—861no—
205C2×C4⋊C4—861no—
206C2×C22⋊C4—1721no—
207C2×C22⋊C4—1721no—
208C2×C42—1721no—
209C2×C16—21no—
210C2×C16—21no—
211C2×C16—432no—
212C2×C16—861no—
213C2×C16—861no—
214C2×C16C4×D4312yes—
215#107—21no—
216#107—21no—
217#107—21no—
218#107—432no—
219#107—861no—
220#107—861no—
221#107—861no—
222#107C22⋊D4312yes—
223#106—864no—
224#95—1721no—
225C24—431no—
226C22×C4—41no—
227C22×C4—41no—
228C22×C4—431no—
229C22×C4—432no—
230C22×C4—432no—
231C22×C4—861no—
232C22×C4—861no—
233C22×C4—861no—
234C22×C4—861no—
235C22×C4—1721no—
236C22×C4—1721no—
237C22×C4D4×D4311yescharacteristic
238C2×C8—432no—
239C2×C8—861no—
240C2×C8—861no—
241C2×C8—862no—
242C2×C8—862no—
243C2×C8—862no—
244C2×C8—862no—
245C2×C8C2×C4×D4311yescharacteristic
246C2×C8#1062189811yescharacteristic
247C2×C8D4×D4311yescharacteristic
248C2×C8Q8×D4311yescharacteristic
249C2×C8#1062190211yescharacteristic
250C2×C8C2×C22⋊D4311yescharacteristic
251C4⋊C4—22no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—862no—
256C4⋊C4—1721no—
257C4⋊C4—1721no—
258C4⋊C4—1721no—
259C22⋊C4—3442no—
260C22⋊C4—1724no—
261C42—1724no—
262C16—22no—
263C16—862no—
264C23—432no—
265C23—861no—
266C23—861no—
267C23—861no—
268C23—861no—
269C23—861no—
270C23—861no—
271C23D8×D4311yescharacteristic
272C2×C4—42no—
273C2×C4—81no—
274C2×C4—81no—
275C2×C4—81no—
276C2×C4—81no—
277C2×C4—81no—
278C2×C4—432no—
279C2×C4—861no—
280C2×C4—861no—
281C2×C4—862no—
282C2×C4—862no—
283C2×C4—862no—
284C2×C4—862no—
285C2×C4—3441no—
286C2×C4—3441no—
287C2×C4—3441no—
288C2×C4—3441no—
289C2×C4—3441no—
290C2×C4—1722no—
291C2×C4C4⋊C4×D4311yescharacteristic
292C2×C4#1306329311yescharacteristic
293C2×C4#1306331011yescharacteristic
294C2×C4Q16×D4311yescharacteristic
295C2×C4#1306334911yescharacteristic
296C2×C4#1306335711yescharacteristic
297C8—862no—
298C8C4×C22⋊D4311yescharacteristic
299C8#1306328711yescharacteristic
300C8#1306330111yescharacteristic
301C8#1306330311yescharacteristic
302C22—862no—
303C22—862no—
304C22—862no—
305C22—1721no—
306C22—1721no—
307C22—1721no—
308C22—1721no—
309C22#107×D4311yescharacteristic
310C22#1458303111yescharacteristic
311C22#1458321411yescharacteristic
312C22#1458333011yescharacteristic
313C22#1458333011yescharacteristic
314C22#1458333611yescharacteristic
315C22#1458333811yescharacteristic
316C4—82no—
317C4—161no—
318C4—862no—
319C4—3442no—
320C4—6881no—
321C4#1458277011yescharacteristic
322C4#1458294011yescharacteristic
323C4#1458305311yescharacteristic
324C4#1458323611yescharacteristic
325C2—1722no—
326C2#1913478111yescharacteristic
327C2#1913637811yescharacteristic
328C2#1913638211yescharacteristic
329C2#1913651711yescharacteristic
330C2#1913653211yescharacteristic
331C2#1913678811yescharacteristic
332C2#1913680611yescharacteristic
subgroupG/H
centerC23D8×D43
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
FittingC2×C43×#367C2
socleC23×C43C2×D8
prime radicalC23×D43D8
cosocleC22×C8×C43C23
hypercenterC2×#367D43
hypocenterC43#12921
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#367

Complements

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

NH ≅ G/Ntype
2. C2×#14582724C2semidirect
5. #19132687C2semidirect
6. #19132686C2semidirect
7. C2×C43×#367C2semidirect
18. (C2×D43)⋊C16C4semidirect
160. C2×#367D43semidirect
190. C43#12921semidirect

Maximal subgroups

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

subgroupindex
C2×#145829362
C2×#145827242
C2×(C2×D43)⋊C162
#191346212
#191326872
#191326862
C2×C43×#3672
#1292143