Finite Group Databasebeta

← #25016203

Subgroups — #25016203

Order 11008.

410 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063271C211yesmaximal, characteristic
2C2×C4⋊(C43⋊C16)C211yesmaximal, characteristic
3C2×#14582703C211yesmaximal, characteristic
4C2×#14582702C211yesmaximal, characteristic
5#19135456C211yesmaximal, characteristic
6#19132686C211yesmaximal, characteristic
7C43×#1969C211yesmaximal, characteristic
8C22×Dic172C2211yescharacteristic
9C2×#13063271—22no—
10C2×#13063271—22no—
11C2×#13063271—22no—
12C22×C43⋊C16C2211yescharacteristic
13C22×C43⋊C16C2211yescharacteristic
14C2×#13063259C2211yescharacteristic
15C2×#13063250—21no—
16#14582805—21no—
17C4⋊(C43⋊C16)—22no—
18#14582703—22no—
19#14582702—22no—
20C22×Q16×C43C2211yescharacteristic
21C2×#107×C43C2211yescharacteristic
22C2×#103×C43—21no—
23C2×C4×C8×C43C2211yescharacteristic
24C43×#391—21no—
25C22×Dic86—21no—
26C2×Dic172—21no—
27C2×Dic172—21no—
28C2×Dic172—21no—
29C2×Dic172—21no—
30C2×Dic172—21no—
31C2×Dic172D412yes—
32C2×C4⋊Dic43—21no—
33#13063271—28no—
34C2×C43⋊C16—21no—
35C2×C43⋊C16—21no—
36C2×C43⋊C16—21no—
37C2×C43⋊C16—21no—
38C2×C43⋊C16—21no—
39C2×C43⋊C16D412yes—
40#13063259—21no—
41#13063259—21no—
42#13063250—42no—
43C43⋊#95—41no—
44C43⋊#95—41no—
45C22×Q8×C43—21no—
46C2×Q16×C43—21no—
47C2×Q16×C43—21no—
48C2×Q16×C43—21no—
49C2×Q16×C43—21no—
50C2×Q16×C43—21no—
51C2×Q16×C43D412yes—
52C22×C8×C43D411yescharacteristic
53C22×C8×C43C2311yescharacteristic
54C2×C4⋊C4×C43—21no—
55C2×C42×C43D411yescharacteristic
56#107×C43—21no—
57#107×C43—21no—
58#103×C43—42no—
59C4×C8×C43—21no—
60C4×C8×C43—21no—
61#95×C43—41no—
62#95×C43—41no—
63C2×Q8×C43—22no—
64C2×Q8×C43—41no—
65C2×Q8×C43—41no—
66C2×Q8×C43—41no—
67C2×Q8×C43—41no—
68C2×Q8×C43—41no—
69C22×C4×C43—41no—
70C22×C4×C43—41no—
71C22×C4×C43D811yescharacteristic
72C22×C4×C43D811yescharacteristic
73C22×C4×C43C2×D411yescharacteristic
74C22×Dic43—41no—
75C22×Dic43—41no—
76C2×Dic86—22no—
77C2×Dic86—41no—
78C2×Dic86—41no—
79C2×Dic86—41no—
80C2×Dic86—41no—
81C2×Dic86—41no—
82Q16×C43—22no—
83Q16×C43—22no—
84Q16×C43—41no—
85Q16×C43—41no—
86C2×C8×C43—21no—
87C2×C8×C43—21no—
88C2×C8×C43—21no—
89C2×C8×C43C2×D411yescharacteristic
90C2×C8×C43C2×D411yescharacteristic
91C2×C8×C43C2×D411yescharacteristic
92C2×C8×C43#4111yescharacteristic
93C2×C8×C43#4111yescharacteristic
94C2×C8×C43#4111yescharacteristic
95C4⋊C4×C43—41no—
96C4⋊C4×C43—41no—
97C42×C43—21no—
98C42×C43—21no—
99C4⋊Dic43—41no—
100C4⋊Dic43—41no—
101Dic172—22no—
102Dic172—22no—
103Dic172—41no—
104Dic172—41no—
105C43⋊C16—22no—
106C43⋊C16—41no—
107C23×C43C2×D811yescharacteristic
108Q8×C43—42no—
109Q8×C43—42no—
110Q8×C43—81no—
111Q8×C43—81no—
112C2×C4×C43—21no—
113C2×C4×C43—21no—
114C2×C4×C43—21no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—42no—
118C2×C4×C43—81no—
119C2×C4×C43—81no—
120C2×C4×C43—81no—
121C2×C4×C43—81no—
122C2×C4×C43—81no—
123C2×C4×C43Q3212yescomplemented
124C2×C4×C43#12111yescharacteristic
125C2×C4×C43#12111yescharacteristic
126C2×C4×C43#12111yescharacteristic
127C2×C4×C43#13511yescharacteristic
128C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
129C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
130C2×Dic43—42no—
131C2×Dic43—81no—
132C2×Dic43—81no—
133C2×Dic43—81no—
134C2×Dic43—81no—
135C2×Dic43—81no—
136Dic86—42no—
137Dic86—42no—
138Dic86—81no—
139Dic86—81no—
140C8×C43—41no—
141C8×C43#12011yescharacteristic
142C8×C43#12311yescharacteristic
143C8×C43#12311yescharacteristic
144C8×C43#12411yescharacteristic
145#13450—431nomaximal, Sylow
146C22×C43#45911yescharacteristic
147C22×C43#45911yescharacteristic
148C22×C43#46611yescharacteristic
149C22×C43C2×Q3211yescharacteristic
150C22×C43#50811yescharacteristic
151C22×C43#51011yescharacteristic
152C22×C43#51011yescharacteristic
153C4×C43—22no—
154C4×C43—41no—
155C4×C43—82no—
156C4×C43—161no—
157C4×C43#39411yescharacteristic
158C4×C43#46311yescharacteristic
159C4×C43#46311yescharacteristic
160C4×C43#46911yescharacteristic
161Dic43—82no—
162Dic43—161no—
163C22×Q32—431no—
164C2×C4⋊C16—431no—
165C2×#358—431no—
166C2×#358—431no—
167#1969—431no—
168#1969D4311yescharacteristic
169#1380—431no—
170C2×C43#205411yescharacteristic
171C2×C43#220911yescharacteristic
172C2×C43#220911yescharacteristic
173C2×C43#221111yescharacteristic
174C2×C43#221111yescharacteristic
175C2×C43#221611yescharacteristic
176C2×C43#221911yescharacteristic
177C22×Q16—431no—
178C22×Q16C2×D4311yescharacteristic
179C2×Q32—862no—
180C2×Q32—862no—
181C2×Q32—862no—
182C22×C16—431no—
183C22×C16—431no—
184C2×#107—431no—
185C2×#107C2×D4311yescharacteristic
186C2×#103—21no—
187C2×#103—861no—
188C2×C4×C8C2×D4311yescharacteristic
189#391—21no—
190#391—861no—
191C4⋊C16—862no—
192#358—862no—
193#358—862no—
194C43#1345011yescharacteristic, complemented, Sylow
195C22×Q8—21no—
196C22×Q8—861no—
197C2×Q16—21no—
198C2×Q16—21no—
199C2×Q16—21no—
200C2×Q16—21no—
201C2×Q16—21no—
202C2×Q16—432no—
203C2×Q16—861no—
204C2×Q16—861no—
205C2×Q16—861no—
206C2×Q16—861no—
207C2×Q16—861no—
208C2×Q16D17212yes—
209C22×C8C22⋊D4311yescharacteristic
210C22×C8C22×D4311yescharacteristic
211C2×C4⋊C4—21no—
212C2×C4⋊C4—861no—
213C2×C42C22⋊D4311yescharacteristic
214Q32—868no—
215C2×C16—432no—
216C2×C16—861no—
217C2×C16—861no—
218C2×C16—861no—
219C2×C16—861no—
220C2×C16—861no—
221#107—21no—
222#107—21no—
223#107—861no—
224#107—861no—
225#103—42no—
226#103—1722no—
227C4×C8—21no—
228C4×C8—21no—
229#95—41no—
230#95—41no—
231#95—1721no—
232#95—1721no—
233C2×Q8—22no—
234C2×Q8—41no—
235C2×Q8—41no—
236C2×Q8—41no—
237C2×Q8—41no—
238C2×Q8—41no—
239C2×Q8—862no—
240C2×Q8—1721no—
241C2×Q8—1721no—
242C2×Q8—1721no—
243C2×Q8—1721no—
244C2×Q8—1721no—
245C22×C4—41no—
246C22×C4—41no—
247C22×C4—1721no—
248C22×C4—1721no—
249C22×C4#1062188211yescharacteristic
250C22×C4#1062188211yescharacteristic
251C22×C4C2×C22⋊D4311yescharacteristic
252Q16—22no—
253Q16—22no—
254Q16—41no—
255Q16—41no—
256Q16—862no—
257Q16—862no—
258Q16—1721no—
259Q16—1721no—
260C2×C8—21no—
261C2×C8—21no—
262C2×C8—21no—
263C2×C8C2×D17211yescharacteristic
264C2×C8#1062189811yescharacteristic
265C2×C8D4×D4311yescharacteristic
266C2×C8D4×D4311yescharacteristic
267C2×C8#1062190011yescharacteristic
268C2×C8#1062190011yescharacteristic
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—1721no—
272C4⋊C4—1721no—
273C42—21no—
274C42—21no—
275C16—862no—
276C16—1721no—
277C23C2×#1062188211yescharacteristic
278Q8—42no—
279Q8—42no—
280Q8—81no—
281Q8—81no—
282Q8—3441no—
283Q8—3441no—
284Q8—1722no—
285Q8—1722no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—42no—
292C2×C4—81no—
293C2×C4—81no—
294C2×C4—81no—
295C2×C4—81no—
296C2×C4—81no—
297C2×C4—3441no—
298C2×C4—3441no—
299C2×C4—3441no—
300C2×C4—3441no—
301C2×C4—3441no—
302C2×C4—1722no—
303C2×C4#1306327112yescomplemented
304C2×C4#1306329611yescharacteristic
305C2×C4#1306329711yescharacteristic
306C2×C4#1306329911yescharacteristic
307C2×C4#1306334511yescharacteristic
308C2×C4#1306335011yescharacteristic
309C2×C4#1306335111yescharacteristic
310C8—41no—
311C8#1306329511yescharacteristic
312C8#1306330711yescharacteristic
313C8#1306330911yescharacteristic
314C8#1306331111yescharacteristic
315C22#1458309111yescharacteristic
316C22#1458309411yescharacteristic
317C22#1458313311yescharacteristic
318C22C2×#1306327111yescharacteristic
319C22#1458332911yescharacteristic
320C22#1458333911yescharacteristic
321C22#1458334011yescharacteristic
322C4—22no—
323C4—41no—
324C4—82no—
325C4—161no—
326C4—3442no—
327C4—6881no—
328C4#1458281511yescharacteristic
329C4#1458311111yescharacteristic
330C4#1458311411yescharacteristic
331C4#1458315011yescharacteristic
332C2#1913590511yescharacteristic
333C2#1913664211yescharacteristic
334C2#1913664511yescharacteristic
335C2#1913665411yescharacteristic
336C2#1913665711yescharacteristic
337C2#1913668411yescharacteristic
338C2#1913670111yescharacteristic
subgroupG/H
centerC23C2×#10621882
commutator, cosocleC22×C8×C43C23
FrattiniC22×C8C22×D43
FittingC43×#1969C2
socle, prime radicalC23×C43C2×D8
hypercenter#1969D43
hypocenterC43#13450
LCSG ▷ C22×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ #1969

Complements

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

NH ≅ G/Ntype
123. C2×C4×C43Q32semidirect
194. C43#13450semidirect
303. C2×C4#13063271semidirect

Maximal subgroups

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

subgroupindex
C22×#130632712
C2×C4⋊(C43⋊C16)2
C2×#145827032
C2×#145827022
#191354562
#191326862
C43×#19692
#1345043