Finite Group Databasebeta

← #24990876

Subgroups — #24990876

Order 11008.

388 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
1#19134766C211yesmaximal, characteristic, complemented
2#19133383C211yesmaximal, characteristic, complemented
3#19133034C211yesmaximal, characteristic
4#19132977C211yesmaximal, characteristic
5#19132484C211yesmaximal, characteristic, complemented
6#19132431C211yesmaximal, characteristic, complemented
7C43×#2991C211yesmaximal, characteristic
8#14582952C2211yescharacteristic
9C2×#13063260—22no—
10#14582923C2211yescharacteristic
11C4×#10621877C2211yescharacteristic
12C2×C4×C43⋊C8C2211yescharacteristic
13#14582651—21no—
14#14582649—21no—
15Q8⋊(C43⋊C8)—21no—
16Q8⋊(C43⋊C8)C411yescharacteristic
17Q8⋊(C43⋊C8)C411yescharacteristic
18D4⋊(C43⋊C8)—21no—
19D4⋊(C43⋊C8)C411yescharacteristic
20D4⋊(C43⋊C8)C411yescharacteristic
21C4×#41×C43C2211yescharacteristic
22C8×Q8×C43—21no—
23C43×#436—22no—
24C43×#436—21no—
25C43×#431—21no—
26C43×#431C2211yescharacteristic
27C43×#423—21no—
28C43×#423C2211yescharacteristic
29C2×#10621877—21no—
30C2×#10621877—21no—
31C22×C43⋊C8—21no—
32#13063260—44no—
33C4⋊(C43⋊C8)—21no—
34C4⋊(C43⋊C8)—21no—
35C4⋊(C43⋊C8)C2×C411yescharacteristic
36C4⋊(C43⋊C8)C2×C411yescharacteristic
37C22⋊(C43⋊C8)—21no—
38#13063236—21no—
39C4×C43⋊C8—21no—
40C4×C43⋊C8—21no—
41C4×C43⋊C8—21no—
42C4×C43⋊C8C2×C411yescharacteristic
43C4×C43⋊C8C2×C411yescharacteristic
44C2×#41×C43Q811yescharacteristic
45C2×M16×C43—22no—
46C2×M16×C43D412yes—
47C4×Q8×C43C2×C411yescharacteristic
48C4×Q8×C43D411yescharacteristic
49C4×D4×C43—21no—
50C4×D4×C43—21no—
51C4×D4×C43C2×C411yescharacteristic
52C4×D4×C43D411yescharacteristic
53#117×C43—21no—
54#117×C43Q811yescharacteristic
55C2×C42×C43—21no—
56C2×C42×C43C2311yescharacteristic
57C4⋊C8×C43—22no—
58C4⋊C8×C43—21no—
59C4⋊C8×C43—21no—
60C4⋊C8×C43D411yescharacteristic
61C4⋊C8×C43D411yescharacteristic
62C22⋊C8×C43—22no—
63C22⋊C8×C43—21no—
64C4×C8×C43—22no—
65C4×C8×C43—21no—
66#41×C43—22no—
67#41×C43—41no—
68C2×Q8×C43C4⋊C411yescharacteristic
69C2×D4×C43—21no—
70C2×D4×C43C4⋊C411yescharacteristic
71C22×C4×C43—21no—
72C22×C4×C43—21no—
73C22×C4×C43—21no—
74C22×C4×C43C2×D411yescharacteristic
75C22×C4×C43C2×Q811yescharacteristic
76C22×C4×C43#4111yescharacteristic
77M16×C43—42no—
78M16×C43—82no—
79C2×C8×C43—21no—
80C2×C8×C43—22no—
81C2×C8×C43—21no—
82C4⋊C4×C43—21no—
83C4⋊C4×C43—21no—
84C4⋊C4×C43C4⋊C411yescharacteristic
85C4⋊C4×C43C4⋊C411yescharacteristic
86C22⋊C4×C43—21no—
87C22⋊C4×C43—21no—
88C22⋊C4×C43—21no—
89C42×C43—21no—
90C42×C43—21no—
91C42×C43—21no—
92C42×C43C22×C411yescharacteristic
93C42×C43C2×D411yescharacteristic
94C42×C43C2×D411yescharacteristic
95C42×C43#4111yescharacteristic
96#10621877—22no—
97#10621877—41no—
98#10621877—42no—
99C2×C43⋊C8—22no—
100C2×C43⋊C8—22no—
101C2×C43⋊C8—21no—
102C2×C43⋊C8—21no—
103C2×C43⋊C8—21no—
104C2×C43⋊C8—21no—
105C2×C43⋊C8—41no—
106C2×C43⋊C8—41no—
107C23×C43—21no—
108C23×C43C22⋊Q811yescharacteristic
109Q8×C43—21no—
110Q8×C43#10812yescomplemented
111D4×C43—21no—
112D4×C43—21no—
113D4×C43—42no—
114C2×C4×C43—21no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—42no—
124C2×C4×C43—41no—
125C2×C4×C43—41no—
126C2×C4×C43—41no—
127C2×C4×C43—41no—
128C2×C4×C43C2×C4⋊C411yescharacteristic
129C2×C4×C43C4×D411yescharacteristic
130C2×C4×C43C4×D411yescharacteristic
131C2×C4×C43#12011yescharacteristic
132C2×C4×C43C22⋊Q811yescharacteristic
133C2×C4×C43#12311yescharacteristic
134C8×C43—42no—
135C8×C43—41no—
136C8×C43—41no—
137C43⋊C8—22no—
138C43⋊C8—22no—
139C43⋊C8—42no—
140C43⋊C8—41no—
141C43⋊C8—41no—
142C43⋊C8—81no—
143#8899—431nomaximal, Sylow
144C22×C43—21no—
145C22×C43—21no—
146C22×C43—21no—
147C22×C43—41no—
148C22×C43—41no—
149C22×C43—41no—
150C22×C43#38511yescharacteristic
151C4×C43—21no—
152C4×C43—22no—
153C4×C43—21no—
154C4×C43—21no—
155C4×C43—41no—
156C4×C43—41no—
157C4×C43C2×#10811yescharacteristic
158C4×C43#43011yescharacteristic
159C4×C43#44311yescharacteristic
160C4×C43#44411yescharacteristic
161C4×C43#45311yescharacteristic
162C4×C43#45611yescharacteristic
163#2991D4311yescharacteristic
164#1848—431no—
165#1574—431no—
166#1489—431no—
167#1476—431no—
168#1299—431no—
169#1278—431no—
170C2×C43—41no—
171C2×C43—81no—
172C2×C43#185511yescharacteristic
173C2×C43#185911yescharacteristic
174C2×C43#186611yescharacteristic
175C4×#41C2×D4311yescharacteristic
176C8×Q8—21no—
177#436—22no—
178#436—21no—
179#431—21no—
180#431—431no—
181#431C2×D4311yescharacteristic
182C2×#108—862no—
183#423—21no—
184#423—431no—
185#423C2×D4311yescharacteristic
186C4×M16—431no—
187C2×C4×C8—431no—
188#335—861no—
189#334—861no—
190Q8⋊C8—431no—
191Q8⋊C8—431no—
192Q8⋊C8—861no—
193D4⋊C8—431no—
194D4⋊C8—431no—
195D4⋊C8—861no—
196C43#889911yescharacteristic, complemented, Sylow
197C2×#41Dic8611yescharacteristic
198C2×M16—22no—
199C2×M16—861no—
200C2×M16—861no—
201C2×M16C22⋊D4312yes—
202C22×C8—861no—
203C4×Q8C4×D4311yescharacteristic
204C4×Q8C22⋊D4311yescharacteristic
205C4×D4—21no—
206C4×D4—21no—
207C4×D4C4×D4311yescharacteristic
208C4×D4C22⋊D4311yescharacteristic
209#117—21no—
210#117Dic8611yescharacteristic
211C2×C42—21no—
212C2×C42C22×D4311yescharacteristic
213#108—1724no—
214C4⋊C8—22no—
215C4⋊C8—21no—
216C4⋊C8—21no—
217C4⋊C8—431no—
218C4⋊C8—431no—
219C4⋊C8—861no—
220C4⋊C8—861no—
221C4⋊C8C22⋊D4311yescharacteristic
222C4⋊C8C22⋊D4311yescharacteristic
223C22⋊C8—22no—
224C22⋊C8—21no—
225C22⋊C8—861no—
226#97—861no—
227C4×C8—22no—
228C4×C8—21no—
229C4×C8—431no—
230C4×C8—431no—
231C4×C8—861no—
232C4×C8—861no—
233C4×C8—861no—
234#41—22no—
235#41—41no—
236C2×Q8Dic43⋊C411yescharacteristic
237C2×D4—21no—
238C2×D4Dic43⋊C411yescharacteristic
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4C2×Dic8611yescharacteristic
243C22×C4#1062189811yescharacteristic
244C22×C4C2×C22⋊D4311yescharacteristic
245M16—42no—
246M16—82no—
247M16—862no—
248M16—1722no—
249M16—1721no—
250C2×C8—21no—
251C2×C8—22no—
252C2×C8—21no—
253C2×C8—862no—
254C2×C8—862no—
255C2×C8—861no—
256C2×C8—861no—
257C2×C8—861no—
258C2×C8—861no—
259C2×C8—1721no—
260C2×C8—1721no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4Dic43⋊C411yescharacteristic
264C4⋊C4Dic43⋊C411yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C42—21no—
269C42—21no—
270C42—21no—
271C42C2×C4×D4311yescharacteristic
272C42#1062189811yescharacteristic
273C42C2×C22⋊D4311yescharacteristic
274C42C2×C22⋊D4311yescharacteristic
275C23—21no—
276C23#1306330411yescharacteristic
277Q8—21no—
278Q8#1306326012yescomplemented
279D4—21no—
280D4—21no—
281D4—42no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—42no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4C2×Dic43⋊C411yescharacteristic
297C2×C4C4×C22⋊D4311yescharacteristic
298C2×C4C4×C22⋊D4311yescharacteristic
299C2×C4#1306329411yescharacteristic
300C2×C4#1306330411yescharacteristic
301C2×C4#1306330811yescharacteristic
302C8—42no—
303C8—41no—
304C8—41no—
305C8—862no—
306C8—862no—
307C8—3441no—
308C8—1722no—
309C8—1721no—
310C8—1721no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22#1458277211yescharacteristic
318C4—21no—
319C4—22no—
320C4—21no—
321C4—21no—
322C4—41no—
323C4—41no—
324C4C2×#1306326011yescharacteristic
325C4#1458294711yescharacteristic
326C4#1458301411yescharacteristic
327C4#1458301911yescharacteristic
328C4#1458306711yescharacteristic
329C4#1458308211yescharacteristic
330C2—41no—
331C2—81no—
332C2#1913480011yescharacteristic
333C2#1913482111yescharacteristic
334C2#1913487011yescharacteristic
subgroupG/H
centerC2×C4#13063294
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2991C2
socleC22×C43#385
prime radicalC2×#41×C43Q8
cosocleC2×C42×C43C23
hypercenter#2991D43
hypocenterC43#8899
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2991

Complements

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

NH ≅ G/Ntype
1. #19134766C2semidirect
2. #19133383C2semidirect
5. #19132484C2semidirect
6. #19132431C2semidirect
110. Q8×C43#108semidirect
196. C43#8899semidirect
278. Q8#13063260semidirect

Maximal subgroups

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

subgroupindex
#191347662
#191333832
#191330342
#191329772
#191324842
#191324312
C43×#29912
#889943