Finite Group Databasebeta

← #24990871

Subgroups — #24990871

Order 11008.

390 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#19143720C211yesmaximal, characteristic
2#19134767C211yesmaximal, characteristic, complemented
3#19133384C211yesmaximal, characteristic, complemented
4#19133034C211yesmaximal, characteristic
5#19132486C211yesmaximal, characteristic, complemented
6#19132432C211yesmaximal, characteristic, complemented
7C43×#1476C211yesmaximal, characteristic
8#14583030—21no—
9#14582971—22no—
10D4×C43⋊C8—21no—
11#14582956—21no—
12#14582952C2211yescharacteristic
13C2×#13063261—22no—
14#14582923C2211yescharacteristic
15#14582923C2211yescharacteristic
16C2×C4⋊(C43⋊C8)—21no—
17C4×#10621877C2211yescharacteristic
18#14582652—21no—
19#14582650—21no—
20Q8⋊(C43⋊C8)—21no—
21D4⋊(C43⋊C8)—21no—
22C4×#41×C43C2211yescharacteristic
23C43×#431C2211yescharacteristic
24C2×C4×C8×C43C2211yescharacteristic
25C43×Q8⋊C8C411yescharacteristic
26C43×Q8⋊C8C411yescharacteristic
27C43×D4⋊C8C411yescharacteristic
28C43×D4⋊C8C411yescharacteristic
29C2×#10621877—21no—
30C2×#10621877—21no—
31C2×#10621877D412yes—
32C22×C43⋊C8—22no—
33#13063261—44no—
34C4⋊(C43⋊C8)—22no—
35C4⋊(C43⋊C8)—21no—
36C4⋊(C43⋊C8)—21no—
37C4⋊(C43⋊C8)—21no—
38C4⋊(C43⋊C8)—21no—
39C4⋊(C43⋊C8)D411yescharacteristic
40C4⋊(C43⋊C8)D411yescharacteristic
41C22⋊(C43⋊C8)—22no—
42C22⋊(C43⋊C8)—21no—
43#13063236—22no—
44#13063236—21no—
45C4×C43⋊C8—21no—
46C4×C43⋊C8—21no—
47C2×#41×C43Q811yescharacteristic
48C22×C8×C43—21no—
49C4×Q8×C43C2×C411yescharacteristic
50C4×Q8×C43D411yescharacteristic
51C4×D4×C43—21no—
52C4×D4×C43—21no—
53C4×D4×C43C2×C411yescharacteristic
54C4×D4×C43D411yescharacteristic
55#117×C43—21no—
56#117×C43Q811yescharacteristic
57C2×C42×C43—21no—
58C2×C42×C43C2311yescharacteristic
59C4⋊C8×C43C2×C411yescharacteristic
60C4⋊C8×C43C2×C411yescharacteristic
61C22⋊C8×C43—21no—
62C4×C8×C43—21no—
63C4×C8×C43—21no—
64C4×C8×C43C2×C411yescharacteristic
65C4×C8×C43C2×C411yescharacteristic
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
77C2×C8×C43—22no—
78C2×C8×C43—22no—
79C2×C8×C43—21no—
80C2×C8×C43—21no—
81C2×C8×C43—21no—
82C2×C8×C43—21no—
83C4⋊C4×C43—21no—
84C4⋊C4×C43—21no—
85C4⋊C4×C43C4⋊C411yescharacteristic
86C4⋊C4×C43C4⋊C411yescharacteristic
87C22⋊C4×C43—21no—
88C22⋊C4×C43—21no—
89C22⋊C4×C43—21no—
90C42×C43—21no—
91C42×C43—21no—
92C42×C43—21no—
93C42×C43C22×C411yescharacteristic
94C42×C43C2×D411yescharacteristic
95C42×C43C2×D411yescharacteristic
96C42×C43#4111yescharacteristic
97#10621877—22no—
98#10621877—41no—
99#10621877—42no—
100#10621877—42no—
101C2×C43⋊C8—21no—
102C2×C43⋊C8—21no—
103C2×C43⋊C8—22no—
104C2×C43⋊C8—41no—
105C2×C43⋊C8—41no—
106C2×C43⋊C8—82no—
107C23×C43—21no—
108C23×C43C22⋊Q811yescharacteristic
109Q8×C43—21no—
110Q8×C43—21no—
111D4×C43—21no—
112D4×C43—42no—
113D4×C43#10812yescomplemented
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—22no—
135C8×C43—22no—
136C8×C43—41no—
137C8×C43—41no—
138C43⋊C8—42no—
139C43⋊C8—41no—
140C43⋊C8—42no—
141C43⋊C8—41no—
142C43⋊C8—81no—
143#8898—431nomaximal, Sylow
144C22×C43—22no—
145C22×C43—21no—
146C22×C43—21no—
147C22×C43—21no—
148C22×C43—41no—
149C22×C43—41no—
150C22×C43#38511yescharacteristic
151C4×C43—21no—
152C4×C43—21no—
153C4×C43—21no—
154C4×C43—41no—
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#2990—431no—
164#1848—431no—
165#1574—431no—
166#1489—431no—
167#1476D4311yescharacteristic
168#1299—431no—
169#1278—431no—
170C2×C43—41no—
171C2×C43—42no—
172C2×C43#185511yescharacteristic
173C2×C43#185911yescharacteristic
174C2×C43#186611yescharacteristic
175C4×#41C2×D4311yescharacteristic
176#446—861no—
177#435—862no—
178C8×D4—861no—
179#432—861no—
180#431—431no—
181#431C2×D4311yescharacteristic
182C2×#108—862no—
183#423—431no—
184#423—431no—
185C2×C4⋊C8—861no—
186C4×M16—431no—
187C2×C4×C8C2×D4311yescharacteristic
188#335—861no—
189#334—861no—
190Q8⋊C8—861no—
191Q8⋊C8Dic4311yescharacteristic
192Q8⋊C8Dic4311yescharacteristic
193D4⋊C8—861no—
194D4⋊C8Dic4311yescharacteristic
195D4⋊C8Dic4311yescharacteristic
196C43#889811yescharacteristic, complemented, Sylow
197C2×#41Dic8611yescharacteristic
198C2×M16—432no—
199C2×M16—861no—
200C2×M16—861no—
201C22×C8—21no—
202C22×C8—862no—
203C4×Q8D17211yescharacteristic
204C4×Q8C2×Dic4311yescharacteristic
205C4×D4—21no—
206C4×D4—21no—
207C4×D4D17211yescharacteristic
208C4×D4C2×Dic4311yescharacteristic
209#117—21no—
210#117Dic8611yescharacteristic
211C2×C42—21no—
212C2×C42C22×D4311yescharacteristic
213#108—1724no—
214C4⋊C8—431no—
215C4⋊C8—431no—
216C4⋊C8—862no—
217C4⋊C8—861no—
218C4⋊C8—861no—
219C4⋊C8—861no—
220C4⋊C8—861no—
221C4⋊C8C2×Dic4311yescharacteristic
222C4⋊C8C2×Dic4311yescharacteristic
223C22⋊C8—21no—
224C22⋊C8—862no—
225C22⋊C8—861no—
226#97—862no—
227#97—861no—
228C4×C8—21no—
229C4×C8—21no—
230C4×C8—861no—
231C4×C8—861no—
232C4×C8C2×Dic4311yescharacteristic
233C4×C8C2×Dic4311yescharacteristic
234#41—22no—
235#41—41no—
236C2×Q8C4⋊Dic4311yescharacteristic
237C2×D4—21no—
238C2×D4C4⋊Dic4311yescharacteristic
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4C2×Dic8611yescharacteristic
243C22×C4D4×D4311yescharacteristic
244C22×C4#1062190011yescharacteristic
245M16—862no—
246M16—1722no—
247M16—1721no—
248M16—1722no—
249C2×C8—22no—
250C2×C8—22no—
251C2×C8—21no—
252C2×C8—21no—
253C2×C8—21no—
254C2×C8—21no—
255C2×C8—861no—
256C2×C8—861no—
257C2×C8—862no—
258C2×C8—3442no—
259C2×C8—1721no—
260C2×C8—1721no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4C4⋊Dic4311yescharacteristic
264C4⋊C4C4⋊Dic4311yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C42—21no—
269C42—21no—
270C42—21no—
271C42C2×D17211yescharacteristic
272C42D4×D4311yescharacteristic
273C42#1062190011yescharacteristic
274C42C22×Dic4311yescharacteristic
275C23—21no—
276C23#1306330211yescharacteristic
277Q8—21no—
278Q8—21no—
279D4—21no—
280D4—42no—
281D4#1306326112yescomplemented
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×C4⋊Dic4311yescharacteristic
297C2×C4D4×Dic4311yescharacteristic
298C2×C4D4×Dic4311yescharacteristic
299C2×C4#1306329511yescharacteristic
300C2×C4#1306330211yescharacteristic
301C2×C4#1306330911yescharacteristic
302C8—22no—
303C8—22no—
304C8—41no—
305C8—41no—
306C8—3441no—
307C8—1722no—
308C8—1721no—
309C8—1722no—
310C8—1721no—
311C22—21no—
312C22—22no—
313C22—21no—
314C22—21no—
315C22—41no—
316C22—41no—
317C22#1458277411yescharacteristic
318C4—21no—
319C4—21no—
320C4—21no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4C2×#1306326111yescharacteristic
325C4#1458294811yescharacteristic
326C4#1458301611yescharacteristic
327C4#1458302111yescharacteristic
328C4#1458306811yescharacteristic
329C4#1458308311yescharacteristic
330C2—41no—
331C2—42no—
332C2#1913480211yescharacteristic
333C2#1913482311yescharacteristic
334C2#1913487211yescharacteristic
subgroupG/H
centerC2×C4#13063295
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1476C2
socleC22×C43#385
prime radicalC2×#41×C43Q8
cosocleC2×C42×C43C23
hypercenter#1476D43
hypocenterC43#8898
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1476

Complements

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

NH ≅ G/Ntype
2. #19134767C2semidirect
3. #19133384C2semidirect
5. #19132486C2semidirect
6. #19132432C2semidirect
113. D4×C43#108semidirect
196. C43#8898semidirect
281. D4#13063261semidirect

Maximal subgroups

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

subgroupindex
#191437202
#191347672
#191333842
#191330342
#191324862
#191324322
C43×#14762
#889843