Finite Group Databasebeta

← #25013665

Subgroups — #25013665

Order 11008.

554 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063268C211yesmaximal, characteristic
2C2×#14582981C211yesmaximal, characteristic
3C2×#14582701C211yesmaximal, characteristic
4#19135457C211yesmaximal, characteristic, complemented
5#19132686C211yesmaximal, characteristic, complemented
6#19132672C211yesmaximal, characteristic, complemented
7C2×C43×#358C211yesmaximal, characteristic, complemented
8C22×D344C2211yescharacteristic
9C2×#13063287—21no—
10C2×#13063268—22no—
11C2×#13063268—22no—
12C2×#13063268C414yescomplemented
13C22×C43⋊C16C2211yescharacteristic
14#14582981—22no—
15#14582981—22no—
16C2×#13063259C2211yescharacteristic
17C2×#13063249—21no—
18C2×#13063245—21no—
19C2×C8×Dic43C2211yescharacteristic
20#14582806—21no—
21#14582701—22no—
22C22×Q16×C43C2211yescharacteristic
23C22×C16×C43C2211yescharacteristic
24C2×#107×C43C2211yescharacteristic
25C43×#358—22no—
26C22×D172—21no—
27C22×C4×D43—41no—
28C2×D344—21no—
29C2×D344—21no—
30C2×D344—21no—
31C2×D344C2×C412yes—
32C2×D344D412yes—
33C2×D344D412yes—
34C22×C43⋊C8D411yescharacteristic
35#13063287—24no—
36#13063287—42no—
37C2×C4⋊Dic43—21no—
38C2×(C2×D43)⋊C4—41no—
39C2×C4×Dic43D411yescharacteristic
40#13063268—28no—
41C2×C43⋊C16—21no—
42C2×C43⋊C16—21no—
43C2×C43⋊C16C2×C412yescomplemented
44#13063259—21no—
45#13063259—21no—
46#13063249—42no—
47#13063245—24no—
48C8×Dic43—21no—
49C8×Dic43—21no—
50C43⋊#95—41no—
51C43⋊#95—41no—
52C22×Q8×C43—21no—
53C2×Q16×C43—21no—
54C2×Q16×C43—21no—
55C2×Q16×C43—21no—
56C2×Q16×C43—21no—
57C2×Q16×C43—21no—
58C2×Q16×C43C2×C412yescomplemented
59C22×C8×C43C2311yescharacteristic
60C2×C4⋊C4×C43—21no—
61C2×C16×C43—21no—
62C2×C16×C43—21no—
63C2×C16×C43—21no—
64#107×C43—21no—
65#107×C43D412yes—
66C23×D43—41no—
67C2×Q8×C43—22no—
68C2×Q8×C43—41no—
69C2×Q8×C43—41no—
70C2×Q8×C43—41no—
71C2×Q8×C43—41no—
72C2×Q8×C43—41no—
73C22×C4×C43—41no—
74C22×C4×C43—41no—
75C22×C4×C43C2×D411yescharacteristic
76C22×Dic43—41no—
77C22×Dic43D811yescharacteristic
78C22×Dic43D811yescharacteristic
79C2×D172—22no—
80C2×D172—22no—
81C2×D172—22no—
82C2×D172—41no—
83C2×D172—41no—
84C2×D172—41no—
85C2×C4×D43—44no—
86C2×C4×D43—82no—
87C2×C4×D43—82no—
88Q16×C43—22no—
89Q16×C43—22no—
90Q16×C43—41no—
91Q16×C43—41no—
92C2×C8×C43C22×C411yescharacteristic
93C2×C8×C43C2×D411yescharacteristic
94C2×C8×C43C2×D411yescharacteristic
95C2×C8×C43C2×D411yescharacteristic
96C2×C8×C43#4111yescharacteristic
97C2×C8×C43#4111yescharacteristic
98C4⋊C4×C43—22no—
99C4⋊C4×C43—41no—
100(C2×D43)⋊C4—44no—
101C4⋊Dic43—41no—
102C4⋊Dic43—41no—
103C4×Dic43—21no—
104C4×Dic43—21no—
105C2×C43⋊C8—21no—
106C2×C43⋊C8—21no—
107C2×C43⋊C8—21no—
108D344—22no—
109D344—22no—
110D344—22no—
111D344C22⋊C414yes—
112C16×C43—41no—
113C43⋊C16—22no—
114C23×C43C2×D811yescharacteristic
115C22×D43—42no—
116C22×D43—42no—
117C22×D43—42no—
118C22×D43—81no—
119C22×D43—81no—
120C22×D43—81no—
121C22×D43—81no—
122Q8×C43—42no—
123Q8×C43—42no—
124Q8×C43—81no—
125Q8×C43—81no—
126C2×C4×C43—42no—
127C2×C4×C43—42no—
128C2×C4×C43—81no—
129C2×C4×C43—81no—
130C2×C4×C43—81no—
131C2×C4×C43—81no—
132C2×C4×C43C4×D411yescharacteristic
133C2×C4×C43#12011yescharacteristic
134C2×C4×C43#12111yescharacteristic
135C2×C4×C43#13511yescharacteristic
136C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
138C2×Dic43—21no—
139C2×Dic43—21no—
140C2×Dic43—21no—
141C2×Dic43—21no—
142C2×Dic43—21no—
143C2×Dic43—81no—
144C2×Dic43—81no—
145C2×Dic43—81no—
146C2×Dic43SD3212yescomplemented
147D172—24no—
148D172—42no—
149D172—42no—
150D172—42no—
151C4×D43—88no—
152C8×C43C2×C22⋊C411yescharacteristic
153C8×C43C4×D411yescharacteristic
154C8×C43#12111yescharacteristic
155C8×C43#12311yescharacteristic
156C43⋊C8—41no—
157#13014—431nomaximal, Sylow
158C22×C43C4×D811yescharacteristic
159C22×C43#44711yescharacteristic
160C22×C43#45911yescharacteristic
161C22×C43C2×SD3211yescharacteristic
162C22×C43#50811yescharacteristic
163C22×C43#50911yescharacteristic
164C22×C43#51011yescharacteristic
165C2×D43—44no—
166C2×D43—82no—
167C2×D43—82no—
168C2×D43—82no—
169C2×D43—82no—
170C2×D43—82no—
171C2×D43—82no—
172C4×C43—82no—
173C4×C43—82no—
174C4×C43#38611yescharacteristic
175C4×C43#44211yescharacteristic
176C4×C43#44911yescharacteristic
177C4×C43#46311yescharacteristic
178Dic43—22no—
179Dic43—41no—
180Dic43—161no—
181C22×SD32—431no—
182C2×C4×D8—431no—
183C2×#358D4311yescharacteristic, complemented
184C2×#357—431no—
185#1969—431no—
186#1380—431no—
187#1374—431no—
188C2×C43#187911yescharacteristic
189C2×C43C4×SD3211yescharacteristic
190C2×C43#217511yescharacteristic
191C2×C43#218711yescharacteristic
192C2×C43#218911yescharacteristic
193C2×C43#220811yescharacteristic
194C2×C43#221011yescharacteristic
195D43—84no—
196C22×Q16C2×D4311yescharacteristic
197C22×D8—431no—
198C2×C4×D4—861no—
199C2×SD32—434no—
200C2×SD32—862no—
201C2×SD32—862no—
202C22×C16—431no—
203C22×C16C2×D4311yescharacteristic
204C4×D8—862no—
205C4×D8—862no—
206C2×#107—431no—
207C2×#107C2×D4311yescharacteristic
208C2×#103—861no—
209C2×#102—861no—
210C2×C4×C8—431no—
211#391—861no—
212#358—22no—
213#357—862no—
214C43#1301411yescharacteristic, complemented, Sylow
215C22×Q8—21no—
216C22×D4—861no—
217C23×C4—1721no—
218C2×Q16—21no—
219C2×Q16—21no—
220C2×Q16—21no—
221C2×Q16—21no—
222C2×Q16—21no—
223C2×Q16C4×D4312yescomplemented
224C2×D8—432no—
225C2×D8—432no—
226C2×D8—432no—
227C2×D8—861no—
228C2×D8—861no—
229C2×D8—861no—
230C22×C8—431no—
231C22×C8C22×D4311yescharacteristic
232C4×D4—864no—
233C4×D4—1722no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—861no—
236C2×C22⋊C4—1721no—
237C2×C42—431no—
238SD32—868no—
239C2×C16—21no—
240C2×C16—21no—
241C2×C16—21no—
242C2×C16—432no—
243C2×C16—861no—
244C2×C16—861no—
245#107—21no—
246#107—861no—
247#107—861no—
248#107C22⋊D4312yes—
249#103—1722no—
250#102—864no—
251C4×C8—861no—
252C4×C8—861no—
253#95—1721no—
254#95—1721no—
255C24—1721no—
256C2×Q8—22no—
257C2×Q8—41no—
258C2×Q8—41no—
259C2×Q8—41no—
260C2×Q8—41no—
261C2×Q8—41no—
262C2×D4—862no—
263C2×D4—862no—
264C2×D4—862no—
265C2×D4—1721no—
266C2×D4—1721no—
267C2×D4—1721no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—431no—
271C22×C4—431no—
272C22×C4—3442no—
273C22×C4—3442no—
274C22×C4—1724no—
275C22×C4—1721no—
276C22×C4D4×D4311yescharacteristic
277Q16—22no—
278Q16—22no—
279Q16—41no—
280Q16—41no—
281D8—434no—
282D8—862no—
283D8—862no—
284D8—862no—
285C2×C8—861no—
286C2×C8—861no—
287C2×C8—861no—
288C2×C8C2×C4×D4311yescharacteristic
289C2×C8#1062189811yescharacteristic
290C2×C8D4×D4311yescharacteristic
291C2×C8D4×D4311yescharacteristic
292C2×C8#1062190011yescharacteristic
293C2×C8C2×C22⋊D4311yescharacteristic
294C4⋊C4—22no—
295C4⋊C4—41no—
296C4⋊C4—1721no—
297C4⋊C4—1721no—
298C22⋊C4—1724no—
299C42—861no—
300C42—861no—
301C16—41no—
302C16—862no—
303C23—3441no—
304C23—3441no—
305C23—3441no—
306C23—3441no—
307C23—1722no—
308C23—1722no—
309C23—1722no—
310C23D8×D4311yescharacteristic
311Q8—42no—
312Q8—42no—
313Q8—81no—
314Q8—81no—
315D4—864no—
316D4—1722no—
317D4—1722no—
318D4—1722no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4—432no—
326C2×C4—861no—
327C2×C4—861no—
328C2×C4—861no—
329C2×C4—861no—
330C2×C4—861no—
331C2×C4—3448no—
332C2×C4—3441no—
333C2×C4—3441no—
334C2×C4—3441no—
335C2×C4(C22⋊D43)⋊C411yescharacteristic
336C2×C4#1306329311yescharacteristic
337C2×C4#1306329811yescharacteristic
338C2×C4#1306334611yescharacteristic
339C2×C4#1306334911yescharacteristic
340C2×C4#1306335211yescharacteristic
341C8—1721no—
342C8C22⋊C4×D4311yescharacteristic
343C8C4×C22⋊D4311yescharacteristic
344C8#1306329611yescharacteristic
345C8#1306330711yescharacteristic
346C22—3442no—
347C22—3442no—
348C22—3442no—
349C22—3442no—
350C22—3442no—
351C22—3442no—
352C22—1724no—
353C22#1458297911yescharacteristic
354C22#1458303111yescharacteristic
355C22#1458309311yescharacteristic
356C22SD32×D4311yescharacteristic
357C22#1458333211yescharacteristic
358C22#1458333611yescharacteristic
359C22#1458334111yescharacteristic
360C4—82no—
361C4—82no—
362C4—862no—
363C4—1721no—
364C4—6881no—
365C4#1458277511yescharacteristic
366C4#1458300811yescharacteristic
367C4#1458304311yescharacteristic
368C4#1458311311yescharacteristic
369C2—3444no—
370C2#1913494011yescharacteristic
371C2#1913644411yescharacteristic
372C2#1913646211yescharacteristic
373C2#1913652211yescharacteristic
374C2#1913653411yescharacteristic
375C2#1913663911yescharacteristic
376C2#1913665311yescharacteristic
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#13014
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
4. #19135457C2semidirect
5. #19132686C2semidirect
6. #19132672C2semidirect
7. C2×C43×#358C2semidirect
12. C2×#13063268C4semidirect
43. C2×C43⋊C16C2×C4semidirect
58. C2×Q16×C43C2×C4semidirect
146. C2×Dic43SD32semidirect
183. C2×#358D43semidirect
214. C43#13014semidirect
223. C2×Q16C4×D43semidirect

Maximal subgroups

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

subgroupindex
C22×#130632682
C2×#145829812
C2×#145827012
#191354572
#191326862
#191326722
C2×C43×#3582
#1301443