Finite Group Databasebeta

← #24987662

Subgroups — #24987662

Order 11008.

482 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C8×C4⋊Dic43C211yesmaximal, characteristic, complemented
2#19133244C211yesmaximal, characteristic
3#19133090C211yesmaximal, characteristic
4#19132878C211yesmaximal, characteristic, complemented
5#19132496C211yesmaximal, characteristic, complemented
6#19132490C211yesmaximal, characteristic, complemented
7C43×#2931C211yesmaximal, characteristic
8#14582952C2211yescharacteristic
9#14582952C2211yescharacteristic
10C2×C4⋊(C43⋊C8)C2211yescharacteristic
11C2×C8×Dic43—21no—
12C4×C4⋊Dic43C2211yescharacteristic
13#14582653—21no—
14#14582645C412yescomplemented
15#14582643C412yescomplemented
16#14582633C414yes—
17#14582620—21no—
18C8×C43⋊C8—21no—
19C2×#131×C43—21no—
20C43×#532C2211yescharacteristic
21C43×#436—21no—
22C43×#436C412yescomplemented
23C8×D4×C43—21no—
24C8×D4×C43C412yescomplemented
25C43×#423C2211yescharacteristic
26C43×#408—21no—
27C2×C4×C8×C43C2211yescharacteristic
28C22×C43⋊C8—21no—
29C2×C4⋊Dic43—21no—
30C2×C4×Dic43—21no—
31C4⋊(C43⋊C8)—21no—
32C4⋊(C43⋊C8)—21no—
33C4⋊(C43⋊C8)C2×C412yes—
34C4⋊(C43⋊C8)C2×C412yes—
35C22⋊(C43⋊C8)—21no—
36C22⋊(C43⋊C8)C2×C412yes—
37C4×C43⋊C8—21no—
38C4×C43⋊C8—21no—
39C8×Dic43—42no—
40C43⋊#95C2×C412yes—
41C2×#41×C43—21no—
42#131×C43—42no—
43#131×C43—42no—
44C2×M16×C43—21no—
45C2×M16×C43—22no—
46C22×C8×C43—22no—
47C22×C8×C43D411yescharacteristic
48C22×C8×C43D411yescharacteristic
49C4⋊Q8×C43C2×C411yescharacteristic
50#127×C43C2×C411yescharacteristic
51#124×C43—21no—
52#121×C43—21no—
53#121×C43C2×C412yes—
54C4×D4×C43—21no—
55C4×D4×C43C2×C412yes—
56C2×C42×C43C2311yescharacteristic
57C4⋊C8×C43—21no—
58C4⋊C8×C43C2×C412yes—
59C22⋊C8×C43—22no—
60C22⋊C8×C43—22no—
61C4×C8×C43C2×C411yescharacteristic
62C4×C8×C43C2×C411yescharacteristic
63C4×C8×C43D411yescharacteristic
64C4×C8×C43D411yescharacteristic
65#41×C43—41no—
66#41×C43—41no—
67#41×C43—41no—
68#41×C43—41no—
69C2×Q8×C43—21no—
70C2×D4×C43—21no—
71C2×D4×C43—21no—
72C2×D4×C43—22no—
73C2×D4×C43C4212yes—
74C22×C4×C43—22no—
75C22×C4×C43C22×C411yescharacteristic
76C22×C4×C43C2×D411yescharacteristic
77C22×C4×C43#4111yescharacteristic
78C22×Dic43—22no—
79M16×C43—41no—
80M16×C43—41no—
81M16×C43—44no—
82C2×C8×C43—21no—
83C2×C8×C43—21no—
84C2×C8×C43—22no—
85C2×C8×C43—44no—
86C2×C8×C43C22⋊C411yescharacteristic
87C2×C8×C43C22⋊C411yescharacteristic
88C2×C8×C43C22⋊C411yescharacteristic
89C2×C8×C43C22⋊C411yescharacteristic
90C2×C8×C43D812yes—
91C2×C8×C43SD1612yes—
92C4⋊C4×C43—21no—
93C4⋊C4×C43C4212yes—
94C22⋊C4×C43—22no—
95C22⋊C4×C43—22no—
96C42×C43C22×C411yescharacteristic
97C42×C43C22×C411yescharacteristic
98C42×C43C2×D411yescharacteristic
99C42×C43#4111yescharacteristic
100C4⋊Dic43—24no—
101C4×Dic43—41no—
102C4×Dic43—41no—
103C2×C43⋊C8—22no—
104C2×C43⋊C8—22no—
105C2×C43⋊C8—22no—
106C2×C43⋊C8—41no—
107C2×C43⋊C8—41no—
108C23×C43—22no—
109C23×C43C4×D411yescharacteristic
110Q8×C43—41no—
111Q8×C43—41no—
112D4×C43—42no—
113D4×C43—42no—
114D4×C43—42no—
115D4×C43—41no—
116D4×C43—41no—
117D4×C43—42no—
118C2×C4×C43—22no—
119C2×C4×C43—22no—
120C2×C4×C43—41no—
121C2×C4×C43—42no—
122C2×C4×C43—42no—
123C2×C4×C43C2×C4211yescharacteristic
124C2×C4×C43C2×C22⋊C411yescharacteristic
125C2×C4×C43#11711yescharacteristic
126C2×C4×C43C4×D411yescharacteristic
127C2×C4×C43C4×D411yescharacteristic
128C2×C4×C43C4×D411yescharacteristic
129C2×C4×C43C2×D811yescharacteristic
130C2×C4×C43C2×SD1611yescharacteristic
131C2×C4×C43#13511yescharacteristic
132C2×C4×C43#13511yescharacteristic
133C2×Dic43—24no—
134C2×Dic43—42no—
135C2×Dic43—42no—
136C8×C43—21no—
137C8×C43—21no—
138C8×C43—42no—
139C8×C43#10212yes—
140C8×C43#10212yes—
141C43⋊C8—42no—
142C43⋊C8—42no—
143C43⋊C8—42no—
144#8251—431nomaximal, Sylow
145C22×C43—21no—
146C22×C43—21no—
147C22×C43—42no—
148C22×C43—42no—
149C22×C43—42no—
150C22×C43C4×C22⋊C411yescharacteristic
151C22×C43C4×D811yescharacteristic
152C22×C43C4×SD1611yescharacteristic
153C4×C43—21no—
154C4×C43—21no—
155C4×C43—21no—
156C4×C43—42no—
157C4×C43C2×#10211yescharacteristic
158C4×C43#41611yescharacteristic
159C4×C43C4×D811yescharacteristic
160C4×C43C4×SD1611yescharacteristic
161C4×C43#44312yes—
162Dic43—44no—
163#2931D4311yescharacteristic
164C8×C4⋊C4—431no—
165#1540—431no—
166#1502—431no—
167#1450—431no—
168#1303—431no—
169#1301—431no—
170C2×C43—21no—
171C2×C43—21no—
172C2×C43—82no—
173C2×C43#175711yescharacteristic
174C2×C43C4×#10211yescharacteristic
175C2×C43#176411yescharacteristic
176C2×#131—21no—
177#532C2×D4311yescharacteristic
178#436—21no—
179#436Dic4312yescomplemented
180C8×D4—21no—
181C8×D4Dic4312yescomplemented
182#431—431no—
183#431—431no—
184#423C2×D4311yescharacteristic
185C2×C4⋊C8—431no—
186#408—21no—
187C2×C4×C8—861no—
188C2×C4×C8C2×D4311yescharacteristic
189C4×C4⋊C4—431no—
190#336—861no—
191#332—432no—
192#331—432no—
193#327—434no—
194#322—861no—
195C82—861no—
196C43#825111yescharacteristic, complemented, Sylow
197C2×#41—21no—
198#131—42no—
199#131—42no—
200C2×M16—21no—
201C2×M16—22no—
202C22×C8—22no—
203C22×C8—861no—
204C22×C8C22⋊D4311yescharacteristic
205C22×C8C22⋊D4311yescharacteristic
206C4⋊Q8C4×D4311yescharacteristic
207#127C4×D4311yescharacteristic
208#124—21no—
209#121—21no—
210#121C4×D4312yes—
211C4×D4—21no—
212C4×D4C2×Dic4312yes—
213C2×C4⋊C4—861no—
214C2×C42—861no—
215C2×C42C22×D4311yescharacteristic
216C4⋊C8—21no—
217C4⋊C8—432no—
218C4⋊C8—432no—
219C4⋊C8—861no—
220C4⋊C8—861no—
221C4⋊C8C2×Dic4312yes—
222C22⋊C8—22no—
223C22⋊C8—22no—
224C22⋊C8—432no—
225C22⋊C8—861no—
226C4×C8—861no—
227C4×C8—861no—
228C4×C8—1722no—
229C4×C8C2×Dic4311yescharacteristic
230C4×C8C2×Dic4311yescharacteristic
231C4×C8C22⋊D4311yescharacteristic
232C4×C8C22⋊D4311yescharacteristic
233#95—432no—
234#41—41no—
235#41—41no—
236#41—41no—
237#41—41no—
238C2×Q8—21no—
239C2×D4—22no—
240C2×D4—21no—
241C2×D4—21no—
242C2×D4C4×Dic4312yes—
243C22×C4—22no—
244C22×C4—862no—
245C22×C4C2×C4×D4311yescharacteristic
246C22×C4#1062189811yescharacteristic
247C22×C4C2×C22⋊D4311yescharacteristic
248M16—41no—
249M16—41no—
250M16—44no—
251C2×C8—21no—
252C2×C8—21no—
253C2×C8—22no—
254C2×C8—44no—
255C2×C8—862no—
256C2×C8—862no—
257C2×C8—862no—
258C2×C8—1721no—
259C2×C8—1721no—
260C2×C8#1062188212yes—
261C2×C8#1062188312yes—
262C2×C8C22⋊Dic4311yescharacteristic
263C2×C8C22⋊Dic4311yescharacteristic
264C2×C8C22⋊Dic4311yescharacteristic
265C2×C8C22⋊Dic4311yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—864no—
268C4⋊C4C4×Dic4312yes—
269C22⋊C4—22no—
270C22⋊C4—22no—
271C42—1721no—
272C42—1721no—
273C42C2×C4×D4311yescharacteristic
274C42#1062189811yescharacteristic
275C42C22×Dic4311yescharacteristic
276C42C2×C22⋊D4311yescharacteristic
277C23—22no—
278C23C4×C22⋊D4311yescharacteristic
279Q8—41no—
280Q8—41no—
281D4—42no—
282D4—42no—
283D4—42no—
284D4—41no—
285D4—41no—
286D4—42no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—41no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—864no—
293C2×C4—1722no—
294C2×C4—1722no—
295C2×C4C2×C4×Dic4311yescharacteristic
296C2×C4C2×C22⋊Dic4311yescharacteristic
297C2×C4#1306328411yescharacteristic
298C2×C4C4×C22⋊D4311yescharacteristic
299C2×C4C4×C22⋊D4311yescharacteristic
300C2×C4C4×C22⋊D4311yescharacteristic
301C2×C4C2×#1062188211yescharacteristic
302C2×C4C2×#1062188311yescharacteristic
303C2×C4#1306334511yescharacteristic
304C2×C4#1306334511yescharacteristic
305C8—21no—
306C8—21no—
307C8—42no—
308C8—1722no—
309C8—1722no—
310C8—1722no—
311C8#1306324612yes—
312C8#1306324612yes—
313C22—21no—
314C22—21no—
315C22—42no—
316C22—42no—
317C22—42no—
318C22C4×C22⋊Dic4311yescharacteristic
319C22C4×#1062188211yescharacteristic
320C22C4×#1062188311yescharacteristic
321C4—21no—
322C4—21no—
323C4—21no—
324C4—42no—
325C4—1724no—
326C4C2×#1306324611yescharacteristic
327C4#1458289511yescharacteristic
328C4C4×#1062188211yescharacteristic
329C4C4×#1062188311yescharacteristic
330C4#1458301412yes—
331C2—21no—
332C2—21no—
333C2—82no—
334C2#1913439511yescharacteristic
335C2C4×#1306324611yescharacteristic
336C2#1913443011yescharacteristic
subgroupG/H
centerC2×C8C22⋊Dic43
commutatorC2×C4×C43C2×C42
FrattiniC2×C42C22×D43
FittingC43×#2931C2
socleC22×C43C4×C22⋊C4
prime radicalC43×#532C22
cosocleC2×C42×C43C23
hypercenter#2931D43
hypocenterC43#8251
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C8 ◁ C2×C4×C8 ◁ #2931

Complements

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

NH ≅ G/Ntype
1. C8×C4⋊Dic43C2semidirect
4. #19132878C2semidirect
5. #19132496C2semidirect
6. #19132490C2semidirect
14. #14582645C4semidirect
15. #14582643C4semidirect
22. C43×#436C4semidirect
24. C8×D4×C43C4semidirect
179. #436Dic43semidirect
181. C8×D4Dic43semidirect
196. C43#8251semidirect

Maximal subgroups

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

subgroupindex
C8×C4⋊Dic432
#191332442
#191330902
#191328782
#191324962
#191324902
C43×#29312
#825143