Finite Group Databasebeta

← #25014824

Subgroups — #25014824

Order 11008.

522 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583284C211yesmaximal, characteristic
2C2×#14582703C211yesmaximal, characteristic, complemented
3C2×#14582701C211yesmaximal, characteristic
4C2×#14582699C211yesmaximal, characteristic
5C2×#14582674C211yesmaximal, characteristic, complemented
6#19134753C211yesmaximal, characteristic, complemented
7C2×C43×#358C211yesmaximal, characteristic, complemented
8C22×#10621884—21no—
9C22×D344C2211yescharacteristic
10C2×#13063314—21no—
11C22×C43⋊C16C2211yescharacteristic
12#14583284—22no—
13#14583284C414yescomplemented
14C2×#13063259C2211yescharacteristic
15C2×#13063258—21no—
16C2×C8×Dic43C2211yescharacteristic
17#14582768—21no—
18#14582703—22no—
19#14582701—22no—
20#14582699—22no—
21#14582674—22no—
22C22×Q16×C43C2211yescharacteristic
23C22×C16×C43C2211yescharacteristic
24C2×#107×C43C2211yescharacteristic
25C43×#358—22no—
26C22×D172—21no—
27C2×#10621884—24no—
28C2×#10621884—42no—
29C2×#10621884—42no—
30C2×D344—21no—
31C2×D344—21no—
32C2×D344—21no—
33C2×D344—21no—
34C2×D344—21no—
35C2×D344C2×C412yes—
36C22×C43⋊C8D411yescharacteristic
37#13063314—24no—
38#13063314—42no—
39C2×C4⋊Dic43—21no—
40C2×Dic43⋊C4—42no—
41C2×(C2×D43)⋊C4—42no—
42C2×C4×Dic43D411yescharacteristic
43C2×C43⋊C16—21no—
44C2×C43⋊C16—21no—
45C2×C43⋊C16D412yes—
46#13063259—21no—
47#13063259—21no—
48#13063258—42no—
49C8×Dic43C2×C412yes—
50C8×Dic43D412yes—
51C22×Q8×C43—21no—
52C2×Q16×C43—21no—
53C2×Q16×C43—21no—
54C2×Q16×C43—21no—
55C2×Q16×C43—21no—
56C2×Q16×C43—21no—
57C2×Q16×C43C2×C412yes—
58C22×C8×C43C2311yescharacteristic
59C2×C4⋊C4×C43—21no—
60C2×C16×C43—21no—
61C2×C16×C43—21no—
62C2×C16×C43D412yes—
63#107×C43—21no—
64#107×C43—21no—
65C23×D43—41no—
66C2×Q8×C43—22no—
67C2×Q8×C43—41no—
68C2×Q8×C43—41no—
69C2×Q8×C43—41no—
70C2×Q8×C43—41no—
71C2×Q8×C43—41no—
72C22×C4×C43—41no—
73C22×C4×C43—41no—
74C22×C4×C43C2×D411yescharacteristic
75C22×Dic43—41no—
76C22×Dic43D812yes—
77C2×D172—22no—
78C2×D172—41no—
79C2×D172—41no—
80C2×D172—41no—
81C2×D172—41no—
82C2×D172—41no—
83Q16×C43—22no—
84Q16×C43—22no—
85Q16×C43—41no—
86Q16×C43—41no—
87C2×C8×C43C22×C411yescharacteristic
88C2×C8×C43C2×D411yescharacteristic
89C2×C8×C43C2×D411yescharacteristic
90C2×C8×C43C2×D411yescharacteristic
91C2×C8×C43#4111yescharacteristic
92C2×C8×C43#4111yescharacteristic
93C4⋊C4×C43—41no—
94C4⋊C4×C43—41no—
95#10621884—48no—
96(C2×D43)⋊C4—48no—
97C4⋊Dic43—41no—
98C4⋊Dic43—41no—
99Dic43⋊C4—84no—
100C4×Dic43C22⋊C412yes—
101C4×Dic43SD1612yes—
102C2×C43⋊C8C22⋊C412yes—
103C2×C43⋊C8D812yes—
104C2×C43⋊C8SD1612yes—
105D344—22no—
106D344—22no—
107D344—41no—
108D344—41no—
109C16×C43—22no—
110C43⋊C16—22no—
111C23×C43C2×D811yescharacteristic
112C22×D43—42no—
113C22×D43—81no—
114C22×D43—81no—
115C22×D43—82no—
116C22×D43—82no—
117Q8×C43—42no—
118Q8×C43—42no—
119Q8×C43—81no—
120Q8×C43—81no—
121C2×C4×C43—42no—
122C2×C4×C43—81no—
123C2×C4×C43—81no—
124C2×C4×C43—81no—
125C2×C4×C43—82no—
126C2×C4×C43C2×C22⋊C411yescharacteristic
127C2×C4×C43#12411yescharacteristic
128C2×C4×C43#12711yescharacteristic
129C2×C4×C43C2×D811yescharacteristic
130C2×C4×C43C2×SD1611yescharacteristic
131C2×C4×C43C2×SD1611yescharacteristic
132C2×Dic43—22no—
133C2×Dic43—22no—
134C2×Dic43—81no—
135C2×Dic43—82no—
136C2×Dic43#10214yes—
137D172—42no—
138D172—42no—
139D172—81no—
140D172—81no—
141C8×C43C4×D411yescharacteristic
142C8×C43C4×D411yescharacteristic
143C8×C43#12111yescharacteristic
144C8×C43#12111yescharacteristic
145C43⋊C8#10214yes—
146#13205—431nomaximal, Sylow
147C22×C43C2×#10211yescharacteristic
148C22×C43#48611yescharacteristic
149C22×C43#49311yescharacteristic
150C22×C43#50912yes—
151C22×C43#51012yes—
152C2×D43—84no—
153C2×D43—82no—
154C2×D43—162no—
155C2×D43—161no—
156C2×D43—161no—
157C4×C43—82no—
158C4×C43—161no—
159C4×C43#39011yescharacteristic
160C4×C43C2×#10211yescharacteristic
161C4×C43#48611yescharacteristic
162C4×C43#49211yescharacteristic
163Dic43—24no—
164Dic43—161no—
165C2×#495—431no—
166C2×#358—431no—
167C2×#358D4311yescharacteristic, complemented
168C2×#357—431no—
169C2×#357—431no—
170C2×#346—431no—
171#1845—431no—
172C2×C43#195711yescharacteristic
173C2×C43#213912yes—
174C2×C43#224312yes—
175C2×C43#225011yescharacteristic
176C2×C43#225111yescharacteristic
177D43—162no—
178C22×Q16C2×D4311yescharacteristic
179C22×SD16—861no—
180C22×D8—431no—
181C2×#124—861no—
182C22×C16—431no—
183C22×C16C2×D4311yescharacteristic
184#495—434no—
185#495—862no—
186C2×#107—431no—
187C2×#107—861no—
188C2×#107C2×D4311yescharacteristic
189C2×C4×C8—431no—
190#384—861no—
191#358—22no—
192#358—862no—
193#357—862no—
194#357—862no—
195#346—862no—
196C43#1320511yescharacteristic, complemented, Sylow
197C22×Q8—21no—
198C22×D4—861no—
199C2×Q16—21no—
200C2×Q16—21no—
201C2×Q16—21no—
202C2×Q16—21no—
203C2×Q16—21no—
204C2×Q16C4×D4312yes—
205C2×SD16—864no—
206C2×SD16—1722no—
207C2×SD16—1722no—
208C2×D8—432no—
209C2×D8—861no—
210C2×D8—861no—
211C2×D8—861no—
212C2×D8—861no—
213C2×D8—861no—
214C22×C8—431no—
215C22×C8C22×D4311yescharacteristic
216#124—864no—
217#124—1722no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—861no—
220C2×C4⋊C4—1722no—
221C2×C22⋊C4—1722no—
222C2×C42—431no—
223C2×C16—21no—
224C2×C16—21no—
225C2×C16—432no—
226C2×C16—861no—
227C2×C16—861no—
228C2×C16C22⋊D4312yes—
229#107—21no—
230#107—21no—
231#107—861no—
232#107—861no—
233#107—1722no—
234C4×C8—432no—
235C4×C8—432no—
236C24—1721no—
237C2×Q8—22no—
238C2×Q8—41no—
239C2×Q8—41no—
240C2×Q8—41no—
241C2×Q8—41no—
242C2×Q8—41no—
243C2×D4—862no—
244C2×D4—1721no—
245C2×D4—1721no—
246C2×D4—1721no—
247C2×D4—1721no—
248C2×D4—1721no—
249C22×C4—41no—
250C22×C4—41no—
251C22×C4—432no—
252C22×C4—1721no—
253C22×C4D4×D4311yescharacteristic
254Q16—22no—
255Q16—22no—
256Q16—41no—
257Q16—41no—
258SD16—1728no—
259D8—862no—
260D8—862no—
261D8—1721no—
262D8—1721no—
263C2×C8—432no—
264C2×C8—432no—
265C2×C8—432no—
266C2×C8C2×C4×D4311yescharacteristic
267C2×C8#1062189811yescharacteristic
268C2×C8D4×D4311yescharacteristic
269C2×C8D4×D4311yescharacteristic
270C2×C8#1062190011yescharacteristic
271C2×C8C2×C22⋊D4311yescharacteristic
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—3444no—
275C4⋊C4—1721no—
276C4⋊C4—1721no—
277C22⋊C4—1728no—
278C42—432no—
279C42—432no—
280C16—22no—
281C16—862no—
282C23—3442no—
283C23—3442no—
284C23—3441no—
285C23—3441no—
286C23—1722no—
287C23D8×D4311yescharacteristic
288Q8—42no—
289Q8—42no—
290Q8—81no—
291Q8—81no—
292D4—3441no—
293D4—3441no—
294D4—1722no—
295D4—1722no—
296C2×C4—42no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4—82no—
300C2×C4—81no—
301C2×C4—434no—
302C2×C4—862no—
303C2×C4—862no—
304C2×C4—3442no—
305C2×C4—3441no—
306C2×C4C22⋊C4×D4311yescharacteristic
307C2×C4#1306331111yescharacteristic
308C2×C4#1306332111yescharacteristic
309C2×C4D8×D4311yescharacteristic
310C2×C4SD16×D4311yescharacteristic
311C2×C4SD16×D4311yescharacteristic
312C8—434no—
313C8(C22⋊D43)⋊C411yescharacteristic
314C8C4×C22⋊D4311yescharacteristic
315C8#1306329711yescharacteristic
316C8#1306329811yescharacteristic
317C22—3444no—
318C22—3442no—
319C22—6882no—
320C22—6881no—
321C22—6881no—
322C22#102×D4311yescharacteristic
323C22#1458324411yescharacteristic
324C22#1458327411yescharacteristic
325C22#1458333612yes—
326C22#1458334112yes—
327C4—82no—
328C4—161no—
329C4—864no—
330C4—6881no—
331C4#1458279911yescharacteristic
332C4#102×D4311yescharacteristic
333C4#1458324411yescharacteristic
334C4#1458327011yescharacteristic
335C2—6882no—
336C2#1913539911yescharacteristic
337C2#1913630612yes—
338C2#1913683312yes—
339C2#1913686011yescharacteristic
340C2#1913686311yescharacteristic
subgroupG/H
centerC23D8×D43
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
FittingC2×C43×#358C2
socleC23×C43C2×D8
prime radicalC22×D344C22
cosocleC22×C8×C43C23
hypercenterC2×#358D43
hypocenterC43#13205
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#358

Complements

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

NH ≅ G/Ntype
2. C2×#14582703C2semidirect
5. C2×#14582674C2semidirect
6. #19134753C2semidirect
7. C2×C43×#358C2semidirect
13. #14583284C4semidirect
167. C2×#358D43semidirect
196. C43#13205semidirect

Maximal subgroups

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

subgroupindex
C2×#145832842
C2×#145827032
C2×#145827012
C2×#145826992
C2×#145826742
#191347532
C2×C43×#3582
#1320543