Finite Group Databasebeta

← #25014851

Subgroups — #25014851

Order 11008.

470 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
1C2×#14583277C211yesmaximal, characteristic
2C2×#14582716C211yesmaximal, characteristic
3C2×#14582715C211yesmaximal, characteristic
4C2×#14582714C211yesmaximal, characteristic
5M32×Dic43C211yesmaximal, characteristic
6#19134765C211yesmaximal, characteristic
7C2×C43×#362C211yesmaximal, characteristic
8C22×Dic172C2211yescharacteristic
9C22×#10621885—21no—
10C2×#13063323—21no—
11C2×#13063265C2211yescharacteristic
12#14583277—21no—
13#14583277—21no—
14#14583277C412yes—
15#14583277C412yes—
16C2×#13063261C2211yescharacteristic
17C2×#13063260—21no—
18#14582922—21no—
19C2×C8×Dic43C2211yescharacteristic
20#14582716—22no—
21#14582715—22no—
22#14582714—22no—
23#14582674—21no—
24C16×Dic43—21no—
25C22×Q16×C43C2211yescharacteristic
26C2×M32×C43C2211yescharacteristic
27C2×#108×C43C2211yescharacteristic
28C43×#362—22no—
29C22×Dic86—21no—
30C2×Dic172—21no—
31C2×Dic172—21no—
32C2×Dic172—21no—
33C2×Dic172—21no—
34C2×Dic172—21no—
35C2×Dic172C2×C412yes—
36C2×#10621885—22no—
37C2×#10621885—22no—
38C2×#10621885—42no—
39C2×#10621885—42no—
40C2×#10621877—21no—
41C22×C43⋊C8D411yescharacteristic
42#13063323—22no—
43#13063323—22no—
44#13063323—42no—
45C2×Dic43⋊C4—42no—
46C2×C4×Dic43D411yescharacteristic
47#13063265—21no—
48#13063265D412yes—
49C2×C43⋊C16—21no—
50#13063261—21no—
51#13063261—21no—
52#13063260—42no—
53Dic43⋊C8—42no—
54C8×Dic43C2×C411yescharacteristic
55C8×Dic43C2×C411yescharacteristic
56C8×Dic43D411yescharacteristic
57C8×Dic43D411yescharacteristic
58C22×Q8×C43—21no—
59C2×Q16×C43—21no—
60C2×Q16×C43—21no—
61C2×Q16×C43—21no—
62C2×Q16×C43—21no—
63C2×Q16×C43—21no—
64C2×Q16×C43C2×C412yes—
65C2×M16×C43—21no—
66C22×C8×C43C2311yescharacteristic
67M32×C43—21no—
68M32×C43D412yes—
69C2×C16×C43—21no—
70#108×C43—21no—
71#108×C43—21no—
72C2×Q8×C43—22no—
73C2×Q8×C43—41no—
74C2×Q8×C43—41no—
75C2×Q8×C43—41no—
76C2×Q8×C43—41no—
77C2×Q8×C43—41no—
78C22×C4×C43—41no—
79C22×C4×C43C2×D411yescharacteristic
80C22×Dic43—41no—
81C22×Dic43SD1612yes—
82C2×Dic86—22no—
83C2×Dic86—41no—
84C2×Dic86—41no—
85C2×Dic86—41no—
86C2×Dic86—41no—
87C2×Dic86—41no—
88Q16×C43—22no—
89Q16×C43—22no—
90Q16×C43—41no—
91Q16×C43—41no—
92M16×C43—41no—
93M16×C43—41no—
94C2×C8×C43—41no—
95C2×C8×C43C22×C411yescharacteristic
96C2×C8×C43C2×D411yescharacteristic
97C2×C8×C43C2×D411yescharacteristic
98C2×C8×C43C2×D411yescharacteristic
99C2×C8×C43#4111yescharacteristic
100C2×C8×C43#4111yescharacteristic
101#10621885—44no—
102#10621885—44no—
103Dic43⋊C4—44no—
104Dic43⋊C4—44no—
105C4×Dic43C22⋊C411yescharacteristic
106C4×Dic43C22⋊C411yescharacteristic
107C4×Dic43D812yes—
108#10621877—41no—
109#10621877—41no—
110C2×C43⋊C8—41no—
111C2×C43⋊C8C22⋊C411yescharacteristic
112C2×C43⋊C8C22⋊C411yescharacteristic
113C2×C43⋊C8D812yes—
114C2×C43⋊C8SD1612yes—
115Dic172—22no—
116Dic172—22no—
117Dic172—41no—
118Dic172—41no—
119C16×C43—22no—
120C43⋊C16—22no—
121C23×C43C2×SD1611yescharacteristic
122Q8×C43—42no—
123Q8×C43—42no—
124Q8×C43—81no—
125Q8×C43—81no—
126C2×C4×C43—42no—
127C2×C4×C43—81no—
128C2×C4×C43—81no—
129C2×C4×C43C2×C22⋊C411yescharacteristic
130C2×C4×C43#12411yescharacteristic
131C2×C4×C43#12711yescharacteristic
132C2×C4×C43C2×D811yescharacteristic
133C2×C4×C43C2×D811yescharacteristic
134C2×C4×C43C2×SD1611yescharacteristic
135C2×Dic43—24no—
136C2×Dic43—42no—
137C2×Dic43—81no—
138C2×Dic43—81no—
139C2×Dic43#10212yes—
140C2×Dic43#10212yes—
141Dic86—42no—
142Dic86—42no—
143Dic86—81no—
144Dic86—81no—
145C8×C43—81no—
146C8×C43C4×D411yescharacteristic
147C8×C43C4×D411yescharacteristic
148C8×C43#12111yescharacteristic
149C8×C43#12111yescharacteristic
150C43⋊C8—81no—
151C43⋊C8#10212yes—
152C43⋊C8#10212yes—
153#13212—431nomaximal, Sylow
154C22×C43—22no—
155C22×C43C2×#10211yescharacteristic
156C22×C43#48611yescharacteristic
157C22×C43#49211yescharacteristic
158C4×C43—82no—
159C4×C43#39011yescharacteristic
160C4×C43C2×#10211yescharacteristic
161C4×C43#48611yescharacteristic
162C4×C43#49311yescharacteristic
163Dic43—22no—
164Dic43—82no—
165Dic43#36214yescomplemented
166C2×#494—431no—
167C2×#362—431no—
168C2×#362—431no—
169C2×#362—431no—
170C2×#362D4311yescharacteristic
171C4×M32—431no—
172#1848—431no—
173C2×C43—21no—
174C2×C43—21no—
175C2×C43#195711yescharacteristic
176C2×C43C2×#36212yes—
177C22×Q16—431no—
178C22×Q16—861no—
179C22×Q16C2×D4311yescharacteristic
180C2×C4⋊Q8—861no—
181C2×M32—431no—
182C2×M32C2×D4311yescharacteristic
183#494—432no—
184#494—432no—
185#494—861no—
186#494—861no—
187C2×#108—431no—
188C2×#108—861no—
189C2×#108C2×D4311yescharacteristic
190#423—861no—
191C2×C4×C8—431no—
192#362—22no—
193#362—862no—
194#362—862no—
195#362—862no—
196#346—861no—
197C4×C16—861no—
198C43#1321211yescharacteristic, complemented, Sylow
199C22×Q8—21no—
200C22×Q8—861no—
201C2×Q16—21no—
202C2×Q16—21no—
203C2×Q16—21no—
204C2×Q16—21no—
205C2×Q16—21no—
206C2×Q16—432no—
207C2×Q16—862no—
208C2×Q16—862no—
209C2×Q16—861no—
210C2×Q16—861no—
211C2×Q16—861no—
212C2×Q16—861no—
213C2×Q16—861no—
214C2×Q16—1722no—
215C2×Q16—1722no—
216C2×Q16C4×D4312yes—
217C2×M16—21no—
218C2×M16—861no—
219C22×C8—431no—
220C22×C8C22×D4311yescharacteristic
221C4⋊Q8—862no—
222C4⋊Q8—862no—
223C4⋊Q8—1722no—
224C2×C4⋊C4—1722no—
225C2×C42—431no—
226M32—21no—
227M32—432no—
228M32—861no—
229M32C22⋊D4312yes—
230C2×C16—21no—
231C2×C16—861no—
232#108—21no—
233#108—21no—
234#108—861no—
235#108—861no—
236#108—1722no—
237C4⋊C8—1722no—
238C4×C8—431no—
239C4×C8—431no—
240C4×C8—431no—
241C4×C8—431no—
242C2×Q8—22no—
243C2×Q8—41no—
244C2×Q8—41no—
245C2×Q8—41no—
246C2×Q8—41no—
247C2×Q8—41no—
248C2×Q8—862no—
249C2×Q8—1721no—
250C2×Q8—1721no—
251C2×Q8—1721no—
252C2×Q8—1721no—
253C2×Q8—1721no—
254C22×C4—41no—
255C22×C4—432no—
256C22×C4—1721no—
257C22×C4D4×D4311yescharacteristic
258Q16—22no—
259Q16—22no—
260Q16—41no—
261Q16—41no—
262Q16—862no—
263Q16—862no—
264Q16—1724no—
265Q16—1724no—
266Q16—1721no—
267Q16—1721no—
268M16—41no—
269M16—41no—
270M16—1721no—
271M16—1721no—
272C2×C8—41no—
273C2×C8—431no—
274C2×C8—431no—
275C2×C8—432no—
276C2×C8—432no—
277C2×C8—1721no—
278C2×C8C2×C4×D4311yescharacteristic
279C2×C8#1062189811yescharacteristic
280C2×C8D4×D4311yescharacteristic
281C2×C8D4×D4311yescharacteristic
282C2×C8#1062190011yescharacteristic
283C2×C8C2×C22⋊D4311yescharacteristic
284C4⋊C4—1724no—
285C4⋊C4—1724no—
286C42—431no—
287C42—431no—
288C42—432no—
289C16—22no—
290C16—862no—
291C23SD16×D4311yescharacteristic
292Q8—42no—
293Q8—42no—
294Q8—81no—
295Q8—81no—
296Q8—3441no—
297Q8—3441no—
298Q8—1722no—
299Q8—1722no—
300C2×C4—42no—
301C2×C4—81no—
302C2×C4—81no—
303C2×C4—432no—
304C2×C4—432no—
305C2×C4—864no—
306C2×C4—3441no—
307C2×C4—3441no—
308C2×C4—1722no—
309C2×C4C22⋊C4×D4311yescharacteristic
310C2×C4#1306331111yescharacteristic
311C2×C4#1306332111yescharacteristic
312C2×C4D8×D4311yescharacteristic
313C2×C4D8×D4311yescharacteristic
314C2×C4SD16×D4311yescharacteristic
315C8—81no—
316C8—432no—
317C8—432no—
318C8—3441no—
319C8(C22⋊D43)⋊C411yescharacteristic
320C8C4×C22⋊D4311yescharacteristic
321C8#1306329711yescharacteristic
322C8#1306329811yescharacteristic
323C22—22no—
324C22#102×D4311yescharacteristic
325C22#1458324411yescharacteristic
326C22#1458327011yescharacteristic
327C4—82no—
328C4—434no—
329C4—862no—
330C4—3442no—
331C4#1458279911yescharacteristic
332C4#102×D4311yescharacteristic
333C4#1458324411yescharacteristic
334C4#1458327411yescharacteristic
335C2—21no—
336C2—21no—
337C2#1913539911yescharacteristic
338C2#362×D4312yes—
subgroupG/H
centerC22#102×D43
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
FittingC2×C43×#362C2
socleC22×C43C2×#102
prime radicalC23×C43C2×SD16
cosocleC22×C8×C43C23
hypercenterC2×#362D43
hypocenterC43#13212
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#362

Complements

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

NH ≅ G/Ntype
165. Dic43#362semidirect
198. C43#13212semidirect

Maximal subgroups

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

subgroupindex
C2×#145832772
C2×#145827162
C2×#145827152
C2×#145827142
M32×Dic432
#191347652
C2×C43×#3622
#1321243