Finite Group Databasebeta

← #25016196

Subgroups — #25016196

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×#13063268C211yesmaximal, characteristic
2C2×C4⋊(C43⋊C16)C211yesmaximal, characteristic, complemented
3C2×#14582703C211yesmaximal, characteristic, complemented
4C2×#14582699C211yesmaximal, characteristic
5#19135461C211yesmaximal, characteristic
6#19132686C211yesmaximal, characteristic, complemented
7C43×#1969C211yesmaximal, characteristic, complemented
8C22×D344C2211yescharacteristic
9C2×#13063268—22no—
10C2×#13063268—22no—
11C2×#13063268—22no—
12C22×C43⋊C16C2211yescharacteristic
13C22×C43⋊C16C2211yescharacteristic
14C2×#13063259C2211yescharacteristic
15C2×#13063247—21no—
16#14582801—21no—
17C4⋊(C43⋊C16)—22no—
18#14582703—22no—
19#14582699—22no—
20C22×Q16×C43C2211yescharacteristic
21C2×#107×C43C2211yescharacteristic
22C2×#103×C43—21no—
23C2×C4×C8×C43C2211yescharacteristic
24C43×#391—21no—
25C22×D172—21no—
26C2×D344—21no—
27C2×D344—21no—
28C2×D344—21no—
29C2×D344—21no—
30C2×D344—21no—
31C2×D344D412yes—
32C2×C4⋊Dic43—21no—
33C2×(C2×D43)⋊C4—41no—
34C2×(C2×D43)⋊C4—41no—
35#13063268—28no—
36C2×C43⋊C16—21no—
37C2×C43⋊C16—21no—
38C2×C43⋊C16—21no—
39C2×C43⋊C16—21no—
40C2×C43⋊C16—21no—
41C2×C43⋊C16D412yes—
42#13063259—21no—
43#13063259—21no—
44#13063247—42no—
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—
63C23×D43—41no—
64C2×Q8×C43—22no—
65C2×Q8×C43—41no—
66C2×Q8×C43—41no—
67C2×Q8×C43—41no—
68C2×Q8×C43—41no—
69C2×Q8×C43—41no—
70C22×C4×C43—41no—
71C22×C4×C43—41no—
72C22×C4×C43D811yescharacteristic
73C22×C4×C43D811yescharacteristic
74C22×C4×C43C2×D411yescharacteristic
75C22×Dic43—41no—
76C2×D172—22no—
77C2×D172—41no—
78C2×D172—41no—
79C2×D172—41no—
80C2×D172—41no—
81C2×D172—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—
99(C2×D43)⋊C4—82no—
100(C2×D43)⋊C4—82no—
101C4⋊Dic43—41no—
102C4⋊Dic43—41no—
103D344—22no—
104D344—22no—
105D344—41no—
106D344—41no—
107C43⋊C16—22no—
108C43⋊C16—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—
117Q8×C43—42no—
118Q8×C43—42no—
119Q8×C43—81no—
120Q8×C43—81no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—42no—
127C2×C4×C43—81no—
128C2×C4×C43—81no—
129C2×C4×C43—81no—
130C2×C4×C43—81no—
131C2×C4×C43—81no—
132C2×C4×C43SD3212yescomplemented
133C2×C4×C43#12111yescharacteristic
134C2×C4×C43#12111yescharacteristic
135C2×C4×C43#12111yescharacteristic
136C2×C4×C43#13511yescharacteristic
137C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
139C2×Dic43—81no—
140C2×Dic43—81no—
141C2×Dic43—81no—
142D172—42no—
143D172—42no—
144D172—81no—
145D172—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—82no—
169C4×C43—161no—
170C4×C43#39411yescharacteristic
171C4×C43#46311yescharacteristic
172C4×C43#46311yescharacteristic
173C4×C43#46911yescharacteristic
174Dic43—161no—
175C22×SD32—431no—
176C2×C4⋊C16—431no—
177C2×#358—431no—
178C2×#357—431no—
179#1970—431no—
180#1969D4311yescharacteristic, complemented
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×Q16C2×D4311yescharacteristic
191C22×D8—431no—
192C2×SD32—862no—
193C2×SD32—862no—
194C2×SD32—862no—
195C22×C16—431no—
196C22×C16—431no—
197C2×#107—431no—
198C2×#107C2×D4311yescharacteristic
199C2×#103—21no—
200C2×#102—861no—
201C2×C4×C8C2×D4311yescharacteristic
202#391—21no—
203#390—861no—
204C4⋊C16—862no—
205#358—862no—
206#357—862no—
207C43#1344911yescharacteristic, complemented, Sylow
208C22×Q8—21no—
209C22×D4—861no—
210C2×Q16—21no—
211C2×Q16—21no—
212C2×Q16—21no—
213C2×Q16—21no—
214C2×Q16—21no—
215C2×Q16D17212yes—
216C2×D8—432no—
217C2×D8—861no—
218C2×D8—861no—
219C2×D8—861no—
220C2×D8—861no—
221C2×D8—861no—
222C22×C8C22⋊D4311yescharacteristic
223C22×C8C22×D4311yescharacteristic
224C2×C4⋊C4—21no—
225C2×C4⋊C4—861no—
226C2×C22⋊C4—1721no—
227C2×C22⋊C4—1721no—
228C2×C42C22⋊D4311yescharacteristic
229SD32—868no—
230C2×C16—432no—
231C2×C16—861no—
232C2×C16—861no—
233C2×C16—861no—
234C2×C16—861no—
235C2×C16—861no—
236#107—21no—
237#107—21no—
238#107—861no—
239#107—861no—
240#103—42no—
241#102—1722no—
242C4×C8—21no—
243C4×C8—21no—
244#95—41no—
245#95—41no—
246C24—1721no—
247C2×Q8—22no—
248C2×Q8—41no—
249C2×Q8—41no—
250C2×Q8—41no—
251C2×Q8—41no—
252C2×Q8—41no—
253C2×D4—862no—
254C2×D4—1721no—
255C2×D4—1721no—
256C2×D4—1721no—
257C2×D4—1721no—
258C2×D4—1721no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—1721no—
262C22×C4#1062188211yescharacteristic
263C22×C4#1062188211yescharacteristic
264C22×C4C2×C22⋊D4311yescharacteristic
265Q16—22no—
266Q16—22no—
267Q16—41no—
268Q16—41no—
269D8—862no—
270D8—862no—
271D8—1721no—
272D8—1721no—
273C2×C8—21no—
274C2×C8—21no—
275C2×C8—21no—
276C2×C8C2×D17211yescharacteristic
277C2×C8#1062189811yescharacteristic
278C2×C8D4×D4311yescharacteristic
279C2×C8D4×D4311yescharacteristic
280C2×C8#1062190011yescharacteristic
281C2×C8#1062190011yescharacteristic
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—1721no—
285C4⋊C4—1721no—
286C22⋊C4—3442no—
287C22⋊C4—3442no—
288C42—21no—
289C42—21no—
290C16—862no—
291C16—1721no—
292C23—3441no—
293C23—3441no—
294C23—3441no—
295C23—3441no—
296C23—3441no—
297C23—3441no—
298C23—1722no—
299C23C2×#1062188211yescharacteristic
300Q8—42no—
301Q8—42no—
302Q8—81no—
303Q8—81no—
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—42no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4—3441no—
320C2×C4—3441no—
321C2×C4—3441no—
322C2×C4#1306326812yescomplemented
323C2×C4#1306329611yescharacteristic
324C2×C4#1306329711yescharacteristic
325C2×C4#1306329911yescharacteristic
326C2×C4#1306334511yescharacteristic
327C2×C4#1306335011yescharacteristic
328C2×C4#1306335111yescharacteristic
329C8—41no—
330C8#1306329511yescharacteristic
331C8#1306330711yescharacteristic
332C8#1306330911yescharacteristic
333C8#1306331111yescharacteristic
334C22—3442no—
335C22—3442no—
336C22—3442no—
337C22—6881no—
338C22—6881no—
339C22—6881no—
340C22—6881no—
341C22#1458309111yescharacteristic
342C22#1458309411yescharacteristic
343C22#1458313311yescharacteristic
344C22C2×#1306326811yescharacteristic
345C22#1458332911yescharacteristic
346C22#1458333411yescharacteristic
347C22#1458334011yescharacteristic
348C4—22no—
349C4—41no—
350C4—82no—
351C4—161no—
352C4—6881no—
353C4#1458281511yescharacteristic
354C4#1458311111yescharacteristic
355C4#1458311411yescharacteristic
356C4#1458315011yescharacteristic
357C2—6882no—
358C2#1913590511yescharacteristic
359C2#1913663511yescharacteristic
360C2#1913663711yescharacteristic
361C2#1913664711yescharacteristic
362C2#1913665711yescharacteristic
363C2#1913669311yescharacteristic
364C2#1913671011yescharacteristic
subgroupG/H
centerC23C2×#10621882
commutator, cosocleC22×C8×C43C23
FrattiniC22×C8C22×D43
FittingC43×#1969C2
socleC23×C43C2×D8
prime radicalC22×D344C22
hypercenter#1969D43
hypocenterC43#13449
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
2. C2×C4⋊(C43⋊C16)C2semidirect
3. C2×#14582703C2semidirect
6. #19132686C2semidirect
7. C43×#1969C2semidirect
132. C2×C4×C43SD32semidirect
180. #1969D43semidirect
207. C43#13449semidirect
322. C2×C4#13063268semidirect

Maximal subgroups

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

subgroupindex
C22×#130632682
C2×C4⋊(C43⋊C16)2
C2×#145827032
C2×#145826992
#191354612
#191326862
C43×#19692
#1344943