Finite Group Databasebeta

← #24987213

Subgroups — #24987213

Order 11008.

610 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#13063290C211yesmaximal, characteristic
2#19134450C211yesmaximal, characteristic
3C4×#13063235C211yesmaximal, characteristic
4C2×#14582631C211yesmaximal, characteristic
5C2×#14582629C211yesmaximal, characteristic
6#19132436C211yesmaximal, characteristic
7C43×#1279C211yesmaximal, characteristic
8C2×C4×Dic86C2211yescharacteristic
9C2×#13063290C412yes—
10C2×C4⋊(C43⋊C8)C2211yescharacteristic
11C2×#13063235—22no—
12C2×#13063235—21no—
13C2×C4×C43⋊C8C2211yescharacteristic
14C4⋊C4×Dic43C412yes—
15C4×Dic43⋊C4—21no—
16#14582750—22no—
17C42×Dic43—21no—
18C42×Dic43C2211yescharacteristic
19#14582653—21no—
20#14582631C414yescomplemented
21#14582629C414yescomplemented
22C2×C4⋊C8×C43C2211yescharacteristic
23C2×C4×C8×C43C2211yescharacteristic
24C4×C4⋊C4×C43C2211yescharacteristic
25C22×Dic86C2×C411yescharacteristic
26C22×C43⋊C8—21no—
27C22×C43⋊C8—21no—
28C4×Dic86—21no—
29C4×Dic86—21no—
30C4×Dic86C2×C412yes—
31C4×Dic86C2×C412yes—
32#13063290—24no—
33#13063290—24no—
34C2×C4⋊Dic43C2×C411yescharacteristic
35C2×Dic43⋊C4—21no—
36C2×Dic43⋊C4—22no—
37C2×C4×Dic43—21no—
38C2×C4×Dic43—22no—
39C2×C4×Dic43—22no—
40C2×C4×Dic43C2×C412yes—
41C2×C4×Dic43D412yes—
42C2×C4×Dic43D411yescharacteristic
43C2×C4×Dic43D411yescharacteristic
44C4⋊(C43⋊C8)—21no—
45C4⋊(C43⋊C8)C2×C412yes—
46#13063235—28no—
47#13063235—42no—
48C4×C43⋊C8—21no—
49C4×C43⋊C8C2×C412yes—
50C43⋊#95—22no—
51C22×C8×C43—21no—
52C22×C8×C43—21no—
53C2×C4⋊C4×C43C2×C412yes—
54C2×C42×C43—21no—
55C2×C42×C43C2311yescharacteristic
56C4⋊C8×C43—21no—
57C4⋊C8×C43C2×C412yes—
58C4×C8×C43—21no—
59C4×C8×C43C2×C412yes—
60#95×C43—21no—
61C22×C4×C43—22no—
62C22×C4×C43C22×C411yescharacteristic
63C22×C4×C43C2×D411yescharacteristic
64C22×C4×C43C2×D411yescharacteristic
65C22×Dic43—21no—
66C22×Dic43—21no—
67C22×Dic43C22⋊C412yes—
68C22×Dic43C22⋊C412yes—
69C2×Dic86—21no—
70C2×Dic86—22no—
71C2×Dic86C4212yes—
72C2×Dic86M1614yes—
73C2×C8×C43—24no—
74C2×C8×C43—22no—
75C2×C8×C43—22no—
76C2×C8×C43—41no—
77C2×C8×C43—41no—
78C4⋊C4×C43—22no—
79C4⋊C4×C43M1614yes—
80C42×C43—41no—
81C42×C43—41no—
82C42×C43C22×C411yescharacteristic
83C42×C43C22×C411yescharacteristic
84C42×C43#4111yescharacteristic
85C42×C43#4111yescharacteristic
86C4⋊Dic43—21no—
87C4⋊Dic43C4212yes—
88Dic43⋊C4—28no—
89Dic43⋊C4—22no—
90Dic43⋊C4—22no—
91C4×Dic43—28no—
92C4×Dic43—22no—
93C4×Dic43—22no—
94C4×Dic43—22no—
95C4×Dic43—22no—
96C4×Dic43—21no—
97C4×Dic43—21no—
98C4×Dic43—21no—
99C4×Dic43—21no—
100C4×Dic43—24no—
101C4×Dic43—44no—
102C2×C43⋊C8—24no—
103C2×C43⋊C8—22no—
104C2×C43⋊C8—22no—
105C2×C43⋊C8—41no—
106C2×C43⋊C8—41no—
107C23×C43C2×C22⋊C411yescharacteristic
108C2×C4×C43—22no—
109C2×C4×C43—24no—
110C2×C4×C43—42no—
111C2×C4×C43—42no—
112C2×C4×C43C2×C4211yescharacteristic
113C2×C4×C43#11711yescharacteristic
114C2×C4×C43C4×D411yescharacteristic
115C2×C4×C43C4×D411yescharacteristic
116C2×C4×C43C4×D411yescharacteristic
117C2×C4×C43C4×D411yescharacteristic
118C2×C4×C43C2×M1612yes—
119C2×C4×C43C2×M1612yes—
120C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
121C2×C4×C43#13711yescharacteristic
122C2×C4×C43#13711yescharacteristic
123C2×C4×C43#13711yescharacteristic
124C2×Dic43—22no—
125C2×Dic43—22no—
126C2×Dic43—24no—
127C2×Dic43—22no—
128C2×Dic43—22no—
129C2×Dic43—22no—
130C2×Dic43—22no—
131C2×Dic43—22no—
132C2×Dic43—42no—
133C2×Dic43#10414yes—
134Dic86—22no—
135Dic86—24no—
136Dic86#9714yescomplemented
137C8×C43—24no—
138C8×C43—42no—
139C43⋊C8—24no—
140C43⋊C8—42no—
141#8173—431nomaximal, Sylow
142C22×C43C4×C22⋊C411yescharacteristic
143C22×C43#40712yes—
144C22×C43#41711yescharacteristic
145C22×C43#41911yescharacteristic
146C22×C43C2×#10412yes—
147C4×C43—21no—
148C4×C43—21no—
149C4×C43—44no—
150C4×C43C2×#9711yescharacteristic
151C4×C43C4×M1611yescharacteristic
152C4×C43#43212yes—
153C4×C43#44011yescharacteristic
154C4×C43#44011yescharacteristic
155C4×C43#44111yescharacteristic
156C4×C43#44111yescharacteristic
157Dic43—24no—
158Dic43—24no—
159Dic43—42no—
160Dic43—42no—
161C42×Q8—431no—
162#1767—431no—
163C4×#97—431no—
164C2×Q8⋊C8—431no—
165C2×Q8⋊C8—431no—
166#1279—431no—
167#1279D4311yescharacteristic
168C2×C43#148912yes—
169C2×C43#149112yes—
170C2×C43#174911yescharacteristic
171C2×C43C4×#10411yescharacteristic
172C2×C43#176311yescharacteristic
173C2×C4×Q8—432no—
174C2×C4×Q8—431no—
175C2×C4⋊C8—431no—
176C2×C4⋊C8C2×D4311yescharacteristic
177C2×#97—862no—
178C2×#97—861no—
179C2×C4×C8—431no—
180C2×C4×C8C2×D4311yescharacteristic
181C4×C4⋊C4—432no—
182C4×C4⋊C4—862no—
183C4×C4⋊C4—861no—
184C4×C4⋊C4C2×D4311yescharacteristic
185C43—431no—
186C43—861no—
187#336—861no—
188Q8⋊C8—434no—
189Q8⋊C8—434no—
190C43#817311yescharacteristic, complemented, Sylow
191C22×Q8—431no—
192C22×C8—21no—
193C22×C8—21no—
194C22×C8—861no—
195C22×C8—861no—
196C4×Q8—432no—
197C4×Q8—432no—
198C4×Q8—864no—
199C4×Q8—864no—
200C4×Q8—861no—
201C4×Q8—861no—
202C2×C4⋊C4—431no—
203C2×C4⋊C4—862no—
204C2×C4⋊C4—861no—
205C2×C4⋊C4C4×D4312yes—
206C2×C42—21no—
207C2×C42—432no—
208C2×C42—432no—
209C2×C42—431no—
210C2×C42—431no—
211C2×C42—862no—
212C2×C42—861no—
213C2×C42—862no—
214C2×C42C22×D4311yescharacteristic
215C4⋊C8—21no—
216C4⋊C8—432no—
217C4⋊C8—861no—
218C4⋊C8C4×D4312yes—
219#97—868no—
220#97—1722no—
221C4×C8—21no—
222C4×C8—432no—
223C4×C8—861no—
224C4×C8C4×D4312yes—
225#95—21no—
226#95—862no—
227C2×Q8—432no—
228C2×Q8—434no—
229C2×Q8—861no—
230C2×Q8—862no—
231C22×C4—22no—
232C22×C4—432no—
233C22×C4—432no—
234C22×C4—861no—
235C22×C4—861no—
236C22×C4C2×C4×D4311yescharacteristic
237C22×C4D4×D4311yescharacteristic
238C22×C4D4×D4311yescharacteristic
239C2×C8—24no—
240C2×C8—22no—
241C2×C8—22no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—864no—
245C2×C8—862no—
246C2×C8—862no—
247C2×C8—1721no—
248C2×C8—1721no—
249C4⋊C4—22no—
250C4⋊C4—432no—
251C4⋊C4—868no—
252C4⋊C4—861no—
253C4⋊C4—862no—
254C4⋊C4—862no—
255C4⋊C4#1062187214yes—
256C42—41no—
257C42—41no—
258C42—864no—
259C42—868no—
260C42—862no—
261C42—862no—
262C42—862no—
263C42—862no—
264C42—861no—
265C42—861no—
266C42—861no—
267C42—861no—
268C42—1724no—
269C42C2×C4×D4311yescharacteristic
270C42C2×C4×D4311yescharacteristic
271C42#1062190011yescharacteristic
272C42#1062190211yescharacteristic
273C23C22⋊C4×D4311yescharacteristic
274Q8—434no—
275Q8—862no—
276Q8—864no—
277C2×C4—22no—
278C2×C4—24no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—434no—
282C2×C4—862no—
283C2×C4—864no—
284C2×C4—862no—
285C2×C4—862no—
286C2×C4—862no—
287C2×C4—862no—
288C2×C4—862no—
289C2×C4—862no—
290C2×C4—1722no—
291C2×C4C42×D4311yescharacteristic
292C2×C4#1306328311yescharacteristic
293C2×C4(C22⋊D43)⋊C411yescharacteristic
294C2×C4(C22⋊D43)⋊C411yescharacteristic
295C2×C4#1306328711yescharacteristic
296C2×C4#1306328711yescharacteristic
297C2×C4M16×D4312yes—
298C2×C4C2×#1062187212yes—
299C2×C4#1306334911yescharacteristic
300C2×C4#1306335411yescharacteristic
301C2×C4#1306335411yescharacteristic
302C2×C4#1306335711yescharacteristic
303C8—24no—
304C8—42no—
305C8—864no—
306C8—1722no—
307C22#1458274611yescharacteristic
308C22#1458286112yes—
309C22#1458289711yescharacteristic
310C22#1458290611yescharacteristic
311C22#104×D4312yes—
312C4—21no—
313C4—21no—
314C4—44no—
315C4—864no—
316C4—864no—
317C4—1722no—
318C4—1722no—
319C4#97×D4311yescharacteristic
320C4C4×#1062187211yescharacteristic
321C4#1458295512yes—
322C4#1458299611yescharacteristic
323C4#1458299811yescharacteristic
324C4#1458300311yescharacteristic
325C4#1458300511yescharacteristic
326C2#1913303112yes—
327C2#1913304012yes—
328C2#1913435611yescharacteristic
329C2#1913439911yescharacteristic
330C2#1913442411yescharacteristic
subgroupG/H
centerC22×C4D4×D43
commutatorC2×C4×C43C2×C42
FrattiniC2×C42C22×D43
FittingC43×#1279C2
socle, prime radicalC23×C43C2×C22⋊C4
cosocleC2×C42×C43C23
hypercenter#1279D43
hypocenterC43#8173
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
20. #14582631C4semidirect
21. #14582629C4semidirect
136. Dic86#97semidirect
190. C43#8173semidirect

Maximal subgroups

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

subgroupindex
C4×#130632902
#191344502
C4×#130632352
C2×#145826312
C2×#145826292
#191324362
C43×#12792
#817343