Finite Group Databasebeta

← #25016199

Subgroups — #25016199

Order 11008.

446 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063270C211yesmaximal, characteristic
2C2×#14582704C211yesmaximal, characteristic, complemented
3C2×#14582701C211yesmaximal, characteristic
4#19135461C211yesmaximal, characteristic
5#19135456C211yesmaximal, characteristic, complemented
6#19132687C211yesmaximal, characteristic, complemented
7C2×C43×C4⋊C16C211yesmaximal, characteristic, complemented
8C22×Dic172C2211yescharacteristic
9C22×D344C2211yescharacteristic
10C2×#13063270—22no—
11C2×#13063270—22no—
12C2×#13063270—22no—
13C2×#13063259C2211yescharacteristic
14C2×#13063259C2211yescharacteristic
15C2×#13063250—21no—
16C2×#13063247—21no—
17#14582805—21no—
18#14582801—21no—
19#14582704—22no—
20#14582701—22no—
21C22×C16×C43C2211yescharacteristic
22C22×C16×C43C2211yescharacteristic
23C2×C4×C8×C43C2211yescharacteristic
24C43×C4⋊C16—22no—
25C22×Dic86—21no—
26C22×D172—21no—
27C2×Dic172—21no—
28C2×Dic172—21no—
29C2×Dic172—21no—
30C2×Dic172—21no—
31C2×Dic172—21no—
32C2×Dic172D412yes—
33C2×D344—21no—
34C2×D344—21no—
35C2×D344—21no—
36C2×D344—21no—
37C2×D344—21no—
38C2×D344D412yes—
39C2×C4⋊Dic43—21no—
40C2×C4⋊Dic43—21no—
41C2×(C2×D43)⋊C4—41no—
42C2×(C2×D43)⋊C4—41no—
43#13063270—28no—
44#13063259—21no—
45#13063259—21no—
46#13063259—21no—
47#13063259—21no—
48#13063250—42no—
49#13063247—42no—
50C43⋊#95—41no—
51C43⋊#95—41no—
52C22×C8×C43D411yescharacteristic
53C22×C8×C43C2311yescharacteristic
54C2×C42×C43D411yescharacteristic
55C2×C16×C43—21no—
56C2×C16×C43—21no—
57C2×C16×C43—21no—
58C2×C16×C43—21no—
59C2×C16×C43—21no—
60C2×C16×C43D412yes—
61C4×C8×C43—21no—
62C4×C8×C43—21no—
63C23×D43—41no—
64C22×C4×C43D811yescharacteristic
65C22×C4×C43D811yescharacteristic
66C22×C4×C43C2×D411yescharacteristic
67C22×Dic43—41no—
68C22×Dic43—41no—
69C22×Dic43—41no—
70C2×D172—22no—
71C2×D172—41no—
72C2×D172—41no—
73C2×D172—41no—
74C2×D172—41no—
75C2×D172—41no—
76C2×Dic86—22no—
77C2×Dic86—41no—
78C2×Dic86—41no—
79C2×Dic86—41no—
80C2×Dic86—41no—
81C2×Dic86—41no—
82C2×C8×C43—21no—
83C2×C8×C43—21no—
84C2×C8×C43—21no—
85C2×C8×C43C2×D411yescharacteristic
86C2×C8×C43C2×D411yescharacteristic
87C2×C8×C43C2×D411yescharacteristic
88C2×C8×C43#4111yescharacteristic
89C2×C8×C43#4111yescharacteristic
90C2×C8×C43#4111yescharacteristic
91C42×C43—21no—
92C42×C43—21no—
93(C2×D43)⋊C4—82no—
94(C2×D43)⋊C4—82no—
95C4⋊Dic43—41no—
96C4⋊Dic43—41no—
97C4⋊Dic43—41no—
98C4⋊Dic43—41no—
99Dic172—22no—
100Dic172—22no—
101Dic172—41no—
102Dic172—41no—
103D344—22no—
104D344—22no—
105D344—41no—
106D344—41no—
107C16×C43—22no—
108C16×C43—41no—
109C23×C43C2×D811yescharacteristic
110C22×D43—42no—
111C22×D43—81no—
112C22×D43—81no—
113C22×D43—81no—
114C22×D43—81no—
115C22×D43—81no—
116C22×D43—81no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43SD3212yescomplemented
123C2×C4×C43#12111yescharacteristic
124C2×C4×C43#12111yescharacteristic
125C2×C4×C43#12111yescharacteristic
126C2×C4×C43#13511yescharacteristic
127C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
128C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
129C2×Dic43—42no—
130C2×Dic43—81no—
131C2×Dic43—81no—
132C2×Dic43—81no—
133C2×Dic43—81no—
134C2×Dic43—81no—
135C2×Dic43—81no—
136C2×Dic43—81no—
137C2×Dic43—81no—
138D172—42no—
139D172—42no—
140D172—81no—
141D172—81no—
142Dic86—42no—
143Dic86—42no—
144Dic86—81no—
145Dic86—81no—
146C8×C43—41no—
147C8×C43#12011yescharacteristic
148C8×C43#12311yescharacteristic
149C8×C43#12311yescharacteristic
150C8×C43#12411yescharacteristic
151#13449—431nomaximal, Sylow
152C22×C43#45911yescharacteristic
153C22×C43#45911yescharacteristic
154C22×C43#46611yescharacteristic
155C22×C43C2×SD3211yescharacteristic
156C22×C43#50811yescharacteristic
157C22×C43#50911yescharacteristic
158C22×C43#51011yescharacteristic
159C2×D43—82no—
160C2×D43—82no—
161C2×D43—82no—
162C2×D43—161no—
163C2×D43—161no—
164C2×D43—161no—
165C2×D43—161no—
166C4×C43—22no—
167C4×C43—41no—
168C4×C43#39411yescharacteristic
169C4×C43#46311yescharacteristic
170C4×C43#46311yescharacteristic
171C4×C43#46911yescharacteristic
172Dic43—82no—
173Dic43—161no—
174Dic43—161no—
175C22×SD32—431no—
176C2×C4⋊C16D4311yescharacteristic, complemented
177C2×#358—431no—
178C2×#357—431no—
179#1970—431no—
180#1969—431no—
181#1380—431no—
182C2×C43#205411yescharacteristic
183C2×C43#220711yescharacteristic
184C2×C43#220811yescharacteristic
185C2×C43#221011yescharacteristic
186C2×C43#221111yescharacteristic
187C2×C43#221711yescharacteristic
188C2×C43#222011yescharacteristic
189D43—162no—
190C22×Q16—431no—
191C22×D8—431no—
192C2×SD32—862no—
193C2×SD32—862no—
194C2×SD32—862no—
195C22×C16C2×D4311yescharacteristic
196C22×C16C2×D4311yescharacteristic
197C2×#107—431no—
198C2×#107—431no—
199C2×#103—861no—
200C2×#102—861no—
201C2×C4×C8C2×D4311yescharacteristic
202#391—861no—
203#390—861no—
204C4⋊C16—22no—
205#358—862no—
206#357—862no—
207C43#1344911yescharacteristic, complemented, Sylow
208C22×Q8—861no—
209C22×D4—861no—
210C2×Q16—432no—
211C2×Q16—861no—
212C2×Q16—861no—
213C2×Q16—861no—
214C2×Q16—861no—
215C2×Q16—861no—
216C2×D8—432no—
217C2×D8—861no—
218C2×D8—861no—
219C2×D8—861no—
220C2×D8—861no—
221C2×D8—861no—
222C22×C8D17211yescharacteristic
223C22×C8C22×D4311yescharacteristic
224C2×C4⋊C4—861no—
225C2×C4⋊C4—861no—
226C2×C22⋊C4—1721no—
227C2×C22⋊C4—1721no—
228C2×C42D17211yescharacteristic
229SD32—868no—
230C2×C16—21no—
231C2×C16—21no—
232C2×C16—21no—
233C2×C16—21no—
234C2×C16—21no—
235C2×C16C22⋊D4312yes—
236#107—861no—
237#107—861no—
238#107—861no—
239#107—861no—
240#103—1722no—
241#102—1722no—
242C4×C8—21no—
243C4×C8—21no—
244#95—1721no—
245#95—1721no—
246C24—1721no—
247C2×Q8—862no—
248C2×Q8—1721no—
249C2×Q8—1721no—
250C2×Q8—1721no—
251C2×Q8—1721no—
252C2×Q8—1721no—
253C2×D4—862no—
254C2×D4—1721no—
255C2×D4—1721no—
256C2×D4—1721no—
257C2×D4—1721no—
258C2×D4—1721no—
259C22×C4—1721no—
260C22×C4—1721no—
261C22×C4—1721no—
262C22×C4D34411yescharacteristic
263C22×C4D34411yescharacteristic
264C22×C4C2×D17211yescharacteristic
265Q16—862no—
266Q16—862no—
267Q16—1721no—
268Q16—1721no—
269D8—862no—
270D8—862no—
271D8—1721no—
272D8—1721no—
273C2×C8—21no—
274C2×C8—21no—
275C2×C8—21no—
276C2×C8#1062189811yescharacteristic
277C2×C8D4×D4311yescharacteristic
278C2×C8D4×D4311yescharacteristic
279C2×C8#1062190211yescharacteristic
280C2×C8#1062190211yescharacteristic
281C2×C8C2×C22⋊D4311yescharacteristic
282C4⋊C4—1721no—
283C4⋊C4—1721no—
284C4⋊C4—1721no—
285C4⋊C4—1721no—
286C22⋊C4—3442no—
287C22⋊C4—3442no—
288C42—21no—
289C42—21no—
290C16—22no—
291C16—41no—
292C23—3441no—
293C23—3441no—
294C23—3441no—
295C23—3441no—
296C23—3441no—
297C23—3441no—
298C23—1722no—
299C23C2×D34411yescharacteristic
300Q8—3441no—
301Q8—3441no—
302Q8—1722no—
303Q8—1722no—
304D4—3441no—
305D4—3441no—
306D4—1722no—
307D4—1722no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—3441no—
314C2×C4—3441no—
315C2×C4—3441no—
316C2×C4—3441no—
317C2×C4—3441no—
318C2×C4—3441no—
319C2×C4—3441no—
320C2×C4—3441no—
321C2×C4—1722no—
322C2×C4#1306327012yescomplemented
323C2×C4#1306329911yescharacteristic
324C2×C4#1306330011yescharacteristic
325C2×C4#1306330011yescharacteristic
326C2×C4#1306334711yescharacteristic
327C2×C4#1306335311yescharacteristic
328C2×C4#1306335311yescharacteristic
329C8—41no—
330C8#1306329311yescharacteristic
331C8#1306331011yescharacteristic
332C8#1306331011yescharacteristic
333C8#1306331411yescharacteristic
334C22—3442no—
335C22—3442no—
336C22—3442no—
337C22—6881no—
338C22—6881no—
339C22—6881no—
340C22—6881no—
341C22#1458309511yescharacteristic
342C22#1458309511yescharacteristic
343C22#1458313511yescharacteristic
344C22C2×#1306327011yescharacteristic
345C22#1458333111yescharacteristic
346C22#1458333711yescharacteristic
347C22#1458334211yescharacteristic
348C4—22no—
349C4—41no—
350C4—3442no—
351C4—6881no—
352C4—6881no—
353C4#1458281611yescharacteristic
354C4#1458311511yescharacteristic
355C4#1458311511yescharacteristic
356C4#1458315211yescharacteristic
357C2—6882no—
358C2#1913590611yescharacteristic
359C2#1913663611yescharacteristic
360C2#1913664111yescharacteristic
361C2#1913665111yescharacteristic
362C2#1913665811yescharacteristic
363C2#1913669111yescharacteristic
364C2#1913670811yescharacteristic
subgroupG/H
centerC23C2×D344
commutator, cosocleC22×C8×C43C23
FrattiniC22×C8C22×D43
FittingC2×C43×C4⋊C16C2
socleC23×C43C2×D8
prime radicalC22×D344C22
hypercenterC2×C4⋊C16D43
hypocenterC43#13449
LCSG ▷ C22×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×C4⋊C16

Complements

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

NH ≅ G/Ntype
2. C2×#14582704C2semidirect
5. #19135456C2semidirect
6. #19132687C2semidirect
7. C2×C43×C4⋊C16C2semidirect
122. C2×C4×C43SD32semidirect
176. C2×C4⋊C16D43semidirect
207. C43#13449semidirect
322. C2×C4#13063270semidirect

Maximal subgroups

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

subgroupindex
C22×#130632702
C2×#145827042
C2×#145827012
#191354612
#191354562
#191326872
C2×C43×C4⋊C162
#1344943