Finite Group Databasebeta

← #25015944

Subgroups — #25015944

Order 11008.

482 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583284C211yesmaximal, characteristic
2C2×#14582703C211yesmaximal, characteristic, complemented
3C2×#14582701C211yesmaximal, characteristic
4C2×#14582699C211yesmaximal, characteristic
5#19135326C211yesmaximal, characteristic, complemented
6#19132672C211yesmaximal, characteristic, complemented
7C2×C43×#358C211yesmaximal, characteristic, complemented
8C22×#10621884—21no—
9C22×D344C2211yescharacteristic
10C2×#13063314—21no—
11C22×C43⋊C16C2211yescharacteristic
12#14583284—22no—
13#14583284—22no—
14C2×#13063259C2211yescharacteristic
15C2×C8×Dic43C2211yescharacteristic
16#14582795—21no—
17#14582703—22no—
18#14582701—22no—
19#14582699—22no—
20#14582661—21no—
21C22×Q16×C43C2211yescharacteristic
22C22×C16×C43C2211yescharacteristic
23C2×#107×C43C2211yescharacteristic
24C43×#358—22no—
25C22×D172—21no—
26C2×#10621884—24no—
27C2×#10621884—42no—
28C2×#10621884—42no—
29C2×D344—21no—
30C2×D344—21no—
31C2×D344—21no—
32C2×D344—21no—
33C2×D344—21no—
34C2×D344D412yes—
35C22×C43⋊C8D411yescharacteristic
36#13063314—24no—
37#13063314—42no—
38C2×C4⋊Dic43—21no—
39C2×Dic43⋊C4—41no—
40C2×(C2×D43)⋊C4—41no—
41C2×(C2×D43)⋊C4—41no—
42C2×C4×Dic43D411yescharacteristic
43C2×C43⋊C16—21no—
44C2×C43⋊C16—21no—
45C2×C43⋊C16—21no—
46#13063259—21no—
47#13063259D412yes—
48C8×Dic43—21no—
49C8×Dic43—21no—
50C43⋊#95—41no—
51C22×Q8×C43—21no—
52C2×Q16×C43—21no—
53C2×Q16×C43—21no—
54C2×Q16×C43—21no—
55C2×Q16×C43—21no—
56C2×Q16×C43—21no—
57C2×Q16×C43D412yes—
58C22×C8×C43C2311yescharacteristic
59C2×C4⋊C4×C43—21no—
60C2×C16×C43—21no—
61C2×C16×C43—21no—
62C2×C16×C43—21no—
63#107×C43—21no—
64#107×C43—21no—
65C23×D43—41no—
66C2×Q8×C43—22no—
67C2×Q8×C43—41no—
68C2×Q8×C43—41no—
69C2×Q8×C43—41no—
70C2×Q8×C43—41no—
71C2×Q8×C43—41no—
72C22×C4×C43—41no—
73C22×C4×C43—41no—
74C22×C4×C43C2×D411yescharacteristic
75C22×Dic43—41no—
76C22×Dic43D811yescharacteristic
77C22×Dic43D811yescharacteristic
78C2×D172—22no—
79C2×D172—41no—
80C2×D172—41no—
81C2×D172—41no—
82C2×D172—41no—
83C2×D172—41no—
84Q16×C43—22no—
85Q16×C43—22no—
86Q16×C43—41no—
87Q16×C43—41no—
88C2×C8×C43C2×D411yescharacteristic
89C2×C8×C43C2×D411yescharacteristic
90C2×C8×C43C2×D411yescharacteristic
91C2×C8×C43#4111yescharacteristic
92C2×C8×C43#4111yescharacteristic
93C2×C8×C43#4111yescharacteristic
94C4⋊C4×C43—41no—
95C4⋊C4×C43—41no—
96#10621884—48no—
97(C2×D43)⋊C4—44no—
98(C2×D43)⋊C4—44no—
99C4⋊Dic43—22no—
100C4⋊Dic43—41no—
101Dic43⋊C4—82no—
102C4×Dic43—21no—
103C4×Dic43—21no—
104C2×C43⋊C8—21no—
105C2×C43⋊C8—21no—
106C2×C43⋊C8SD1612yes—
107D344—22no—
108D344—22no—
109D344—41no—
110D344—41no—
111C16×C43—41no—
112C43⋊C16—41no—
113C23×C43C2×D811yescharacteristic
114C22×D43—42no—
115C22×D43—81no—
116C22×D43—81no—
117C22×D43—81no—
118C22×D43—81no—
119C22×D43—81no—
120C22×D43—81no—
121Q8×C43—42no—
122Q8×C43—42no—
123Q8×C43—81no—
124Q8×C43—81no—
125C2×C4×C43—42no—
126C2×C4×C43—81no—
127C2×C4×C43—81no—
128C2×C4×C43—81no—
129C2×C4×C43—81no—
130C2×C4×C43—81no—
131C2×C4×C43#12011yescharacteristic
132C2×C4×C43#12111yescharacteristic
133C2×C4×C43#12411yescharacteristic
134C2×C4×C43C2×SD1611yescharacteristic
135C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
137C2×Dic43—21no—
138C2×Dic43—21no—
139C2×Dic43—21no—
140C2×Dic43—21no—
141C2×Dic43—21no—
142C2×Dic43—21no—
143C2×Dic43—42no—
144C2×Dic43—81no—
145C2×Dic43—81no—
146D172—42no—
147D172—42no—
148D172—81no—
149D172—81no—
150C8×C43#12111yescharacteristic
151C8×C43#12111yescharacteristic
152C8×C43#12311yescharacteristic
153C8×C43#12311yescharacteristic
154C43⋊C8—22no—
155#13408—431nomaximal, Sylow
156C22×C43#44711yescharacteristic
157C22×C43#45911yescharacteristic
158C22×C43#48611yescharacteristic
159C22×C43#50811yescharacteristic
160C22×C43#50811yescharacteristic
161C22×C43#50911yescharacteristic
162C22×C43#51011yescharacteristic
163C2×D43—82no—
164C2×D43—82no—
165C2×D43—82no—
166C2×D43—161no—
167C2×D43—161no—
168C2×D43—161no—
169C2×D43—161no—
170C4×C43—82no—
171C4×C43—161no—
172C4×C43#39411yescharacteristic
173C4×C43#45011yescharacteristic
174C4×C43#46011yescharacteristic
175C4×C43#49011yescharacteristic
176Dic43—41no—
177Dic43—41no—
178Dic43—82no—
179C2×#495—431no—
180C2×#358—431no—
181C2×#358D4311yescharacteristic, complemented
182C2×#357—431no—
183C2×#357—431no—
184#1942—431no—
185#1374—431no—
186C2×C43#204111yescharacteristic
187C2×C43#218611yescharacteristic
188C2×C43#218911yescharacteristic
189C2×C43#221011yescharacteristic
190C2×C43#221111yescharacteristic
191C2×C43#224211yescharacteristic
192C2×C43#224311yescharacteristic
193D43—162no—
194C22×Q16C2×D4311yescharacteristic
195C22×SD16—861no—
196C22×D8—431no—
197C2×#124—861no—
198C22×C16—431no—
199C22×C16C2×D4311yescharacteristic
200#495—862no—
201#495—862no—
202C2×#107—431no—
203C2×#107C2×D4311yescharacteristic
204C2×C4×C8—431no—
205#389—861no—
206#358—22no—
207#358—862no—
208#357—862no—
209#357—862no—
210#340—861no—
211C43#1340811yescharacteristic, complemented, Sylow
212C22×Q8—21no—
213C22×D4—861no—
214C2×Q16—21no—
215C2×Q16—21no—
216C2×Q16—21no—
217C2×Q16—21no—
218C2×Q16—21no—
219C2×Q16C22⋊D4312yes—
220C2×SD16—864no—
221C2×SD16—1722no—
222C2×SD16—1722no—
223C2×D8—432no—
224C2×D8—861no—
225C2×D8—861no—
226C2×D8—861no—
227C2×D8—861no—
228C2×D8—861no—
229C22×C8—431no—
230C22×C8C22×D4311yescharacteristic
231#124—864no—
232#124—1722no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—861no—
235C2×C4⋊C4—1721no—
236C2×C22⋊C4—1721no—
237C2×C22⋊C4—1721no—
238C2×C42—431no—
239C2×C16—21no—
240C2×C16—21no—
241C2×C16—21no—
242C2×C16—861no—
243C2×C16—861no—
244C2×C16—861no—
245#107—21no—
246#107—21no—
247#107—432no—
248#107—861no—
249C4×C8—861no—
250C4×C8—861no—
251#95—1721no—
252C24—1721no—
253C2×Q8—22no—
254C2×Q8—41no—
255C2×Q8—41no—
256C2×Q8—41no—
257C2×Q8—41no—
258C2×Q8—41no—
259C2×D4—862no—
260C2×D4—1721no—
261C2×D4—1721no—
262C2×D4—1721no—
263C2×D4—1721no—
264C2×D4—1721no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—431no—
268C22×C4—431no—
269C22×C4—1721no—
270C22×C4D4×D4311yescharacteristic
271Q16—22no—
272Q16—22no—
273Q16—41no—
274Q16—41no—
275SD16—1728no—
276D8—862no—
277D8—862no—
278D8—1721no—
279D8—1721no—
280C2×C8—432no—
281C2×C8—861no—
282C2×C8—861no—
283C2×C8#1062189811yescharacteristic
284C2×C8#1062189811yescharacteristic
285C2×C8D4×D4311yescharacteristic
286C2×C8D4×D4311yescharacteristic
287C2×C8#1062190011yescharacteristic
288C2×C8C2×C22⋊D4311yescharacteristic
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4—862no—
292C4⋊C4—3442no—
293C4⋊C4—1721no—
294C22⋊C4—1724no—
295C22⋊C4—1724no—
296C42—861no—
297C42—861no—
298C16—41no—
299C16—1721no—
300C23—3441no—
301C23—3441no—
302C23—3441no—
303C23—3441no—
304C23—3441no—
305C23—3441no—
306C23—1722no—
307C23D8×D4311yescharacteristic
308Q8—42no—
309Q8—42no—
310Q8—81no—
311Q8—81no—
312D4—3441no—
313D4—3441no—
314D4—1722no—
315D4—1722no—
316C2×C4—42no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—861no—
323C2×C4—861no—
324C2×C4—861no—
325C2×C4—861no—
326C2×C4—861no—
327C2×C4—861no—
328C2×C4—3441no—
329C2×C4—3441no—
330C2×C4—1722no—
331C2×C4#1306329311yescharacteristic
332C2×C4#1306329811yescharacteristic
333C2×C4#1306331111yescharacteristic
334C2×C4SD16×D4311yescharacteristic
335C2×C4#1306334911yescharacteristic
336C2×C4#1306335211yescharacteristic
337C8—862no—
338C8#1306329711yescharacteristic
339C8#1306329811yescharacteristic
340C8#1306330711yescharacteristic
341C8#1306330811yescharacteristic
342C22—3442no—
343C22—3442no—
344C22—3442no—
345C22—6881no—
346C22—6881no—
347C22—6881no—
348C22—6881no—
349C22#1458303111yescharacteristic
350C22#1458309311yescharacteristic
351C22#1458324411yescharacteristic
352C22#1458333011yescharacteristic
353C22#1458333211yescharacteristic
354C22#1458333611yescharacteristic
355C22#1458334111yescharacteristic
356C4—82no—
357C4—161no—
358C4—3442no—
359C4—1721no—
360C4—1721no—
361C4#1458281411yescharacteristic
362C4#1458304811yescharacteristic
363C4#1458309811yescharacteristic
364C4#1458326211yescharacteristic
365C2—6882no—
366C2#1913582711yescharacteristic
367C2#1913651711yescharacteristic
368C2#1913653411yescharacteristic
369C2#1913665311yescharacteristic
370C2#1913666011yescharacteristic
371C2#1913682811yescharacteristic
372C2#1913683311yescharacteristic
subgroupG/H
centerC23D8×D43
commutator, cosocleC22×C8×C43C23
FrattiniC22×C8C22×D43
FittingC2×C43×#358C2
socleC23×C43C2×D8
prime radicalC22×D344C22
hypercenterC2×#358D43
hypocenterC43#13408
LCSG ▷ C22×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#358

Complements

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

NH ≅ G/Ntype
2. C2×#14582703C2semidirect
5. #19135326C2semidirect
6. #19132672C2semidirect
7. C2×C43×#358C2semidirect
181. C2×#358D43semidirect
211. C43#13408semidirect

Maximal subgroups

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

subgroupindex
C2×#145832842
C2×#145827032
C2×#145827012
C2×#145826992
#191353262
#191326722
C2×C43×#3582
#1340843