Finite Group Databasebeta

← #25013669

Subgroups — #25013669

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×#13063270C211yesmaximal, characteristic
2C2×#14582981C211yesmaximal, characteristic
3C2×#14582702C211yesmaximal, characteristic, complemented
4C2×#14582699C211yesmaximal, characteristic
5#19135454C211yesmaximal, characteristic, complemented
6#19132672C211yesmaximal, characteristic, complemented
7C43×#1380C211yesmaximal, characteristic, complemented
8C22×Dic172C2211yescharacteristic
9C22×D344C2211yescharacteristic
10C2×#13063287—21no—
11C2×#13063270—22no—
12C2×#13063270—22no—
13C2×#13063270C414yescomplemented
14C22×C43⋊C16C2211yescharacteristic
15#14582981—22no—
16#14582981—22no—
17C2×#13063248—21no—
18C2×#13063245—21no—
19C2×C8×Dic43C2211yescharacteristic
20#14582804—21no—
21#14582702—22no—
22#14582699—22no—
23C22×C16×C43C2211yescharacteristic
24C2×#107×C43C2211yescharacteristic
25C2×#107×C43C2211yescharacteristic
26C22×Dic86—21no—
27C22×D172—21no—
28C22×C4×D43—41no—
29C2×Dic172—21no—
30C2×Dic172—21no—
31C2×Dic172—21no—
32C2×Dic172—21no—
33C2×Dic172—21no—
34C2×Dic172C2×C412yescomplemented
35C2×D344—21no—
36C2×D344—21no—
37C2×D344—21no—
38C2×D344C2×C412yes—
39C2×D344D412yes—
40C2×D344D412yes—
41C22×C43⋊C8D411yescharacteristic
42#13063287—24no—
43#13063287—42no—
44C2×(C2×D43)⋊C4—41no—
45C2×C4×Dic43D411yescharacteristic
46#13063270—28no—
47C2×C43⋊C16—21no—
48C2×C43⋊C16—21no—
49C2×C43⋊C16—21no—
50#13063248—42no—
51#13063245—24no—
52C8×Dic43—21no—
53C8×Dic43—21no—
54C43⋊#95—41no—
55C43⋊#95—41no—
56C22×C8×C43C2311yescharacteristic
57C2×C4⋊C4×C43—21no—
58C2×C4⋊C4×C43—21no—
59C2×C16×C43—21no—
60C2×C16×C43—21no—
61C2×C16×C43C2×C412yescomplemented
62#107×C43—21no—
63#107×C43—21no—
64#107×C43—21no—
65#107×C43D412yes—
66C23×D43—41no—
67C22×C4×C43—41no—
68C22×C4×C43—41no—
69C22×C4×C43C2×D411yescharacteristic
70C22×Dic43—41no—
71C22×Dic43D811yescharacteristic
72C22×Dic43D811yescharacteristic
73C2×D172—22no—
74C2×D172—22no—
75C2×D172—22no—
76C2×D172—41no—
77C2×D172—41no—
78C2×D172—41no—
79C2×C4×D43—44no—
80C2×C4×D43—82no—
81C2×C4×D43—82no—
82C2×Dic86—22no—
83C2×Dic86—41no—
84C2×Dic86—41no—
85C2×Dic86—41no—
86C2×Dic86—41no—
87C2×Dic86—41no—
88C2×C8×C43C22×C411yescharacteristic
89C2×C8×C43C2×D411yescharacteristic
90C2×C8×C43C2×D411yescharacteristic
91C2×C8×C43C2×D411yescharacteristic
92C2×C8×C43#4111yescharacteristic
93C2×C8×C43#4111yescharacteristic
94C4⋊C4×C43—22no—
95C4⋊C4×C43—41no—
96C4⋊C4×C43—41no—
97C4⋊C4×C43—41no—
98(C2×D43)⋊C4—44no—
99C4×Dic43—21no—
100C4×Dic43—21no—
101C2×C43⋊C8—21no—
102C2×C43⋊C8—21no—
103C2×C43⋊C8—21no—
104Dic172—22no—
105Dic172—22no—
106Dic172—41no—
107Dic172—41no—
108D344—22no—
109D344—22no—
110D344—22no—
111D344C22⋊C414yes—
112C16×C43—22no—
113C43⋊C16—41no—
114C23×C43C2×D811yescharacteristic
115C22×D43—42no—
116C22×D43—42no—
117C22×D43—42no—
118C22×D43—81no—
119C22×D43—81no—
120C22×D43—81no—
121C22×D43—81no—
122C2×C4×C43—42no—
123C2×C4×C43—81no—
124C2×C4×C43—81no—
125C2×C4×C43—81no—
126C2×C4×C43—81no—
127C2×C4×C43—81no—
128C2×C4×C43C4×D411yescharacteristic
129C2×C4×C43#12011yescharacteristic
130C2×C4×C43#12111yescharacteristic
131C2×C4×C43#13511yescharacteristic
132C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
134C2×Dic43—21no—
135C2×Dic43—21no—
136C2×Dic43—21no—
137C2×Dic43—21no—
138C2×Dic43—21no—
139C2×Dic43—42no—
140C2×Dic43—81no—
141C2×Dic43—81no—
142C2×Dic43SD3212yescomplemented
143D172—24no—
144D172—42no—
145D172—42no—
146D172—42no—
147C4×D43—88no—
148Dic86—42no—
149Dic86—42no—
150Dic86—81no—
151Dic86—81no—
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—161no—
174C4×C43#38611yescharacteristic
175C4×C43#44211yescharacteristic
176C4×C43#44911yescharacteristic
177C4×C43#46311yescharacteristic
178Dic43—22no—
179Dic43—41no—
180Dic43—82no—
181C22×SD32—431no—
182C2×C4×D8—431no—
183C2×#358—431no—
184C2×#357—431no—
185#1969—431no—
186#1380D4311yescharacteristic, complemented
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×Q16—431no—
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×#107C2×D4311yescharacteristic
207C2×#107C2×D4311yescharacteristic
208C2×#103—861no—
209C2×#102—861no—
210C2×C4×C8—431no—
211#391—861no—
212#358—862no—
213#357—862no—
214C43#1301411yescharacteristic, complemented, Sylow
215C22×Q8—861no—
216C22×D4—861no—
217C23×C4—1721no—
218C2×Q16—432no—
219C2×Q16—861no—
220C2×Q16—861no—
221C2×Q16—861no—
222C2×Q16—861no—
223C2×Q16—861no—
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—21no—
236C2×C22⋊C4—1721no—
237C2×C42—431no—
238SD32—868no—
239C2×C16—21no—
240C2×C16—21no—
241C2×C16—861no—
242C2×C16—861no—
243C2×C16—861no—
244C2×C16C4×D4312yescomplemented
245#107—21no—
246#107—21no—
247#107—21no—
248#107D17212yes—
249#103—1722no—
250#102—864no—
251C4×C8—861no—
252C4×C8—861no—
253#95—1721no—
254#95—1721no—
255C24—1721no—
256C2×Q8—862no—
257C2×Q8—1721no—
258C2×Q8—1721no—
259C2×Q8—1721no—
260C2×Q8—1721no—
261C2×Q8—1721no—
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—862no—
278Q16—862no—
279Q16—1721no—
280Q16—1721no—
281D8—434no—
282D8—862no—
283D8—862no—
284D8—862no—
285C2×C8—861no—
286C2×C8—861no—
287C2×C8—861no—
288C2×C8C2×C4×D4311yescharacteristic
289C2×C8C2×D17211yescharacteristic
290C2×C8#1062189811yescharacteristic
291C2×C8D4×D4311yescharacteristic
292C2×C8D4×D4311yescharacteristic
293C2×C8#1062190211yescharacteristic
294C4⋊C4—22no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C22⋊C4—1724no—
299C42—861no—
300C42—861no—
301C16—22no—
302C16—1721no—
303C23—3441no—
304C23—3441no—
305C23—3441no—
306C23—3441no—
307C23—1722no—
308C23—1722no—
309C23—1722no—
310C23D8×D4311yescharacteristic
311Q8—3441no—
312Q8—3441no—
313Q8—1722no—
314Q8—1722no—
315D4—864no—
316D4—1722no—
317D4—1722no—
318D4—1722no—
319C2×C4—42no—
320C2×C4—81no—
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—1722no—
335C2×C4#1306328711yescharacteristic
336C2×C4#1306329511yescharacteristic
337C2×C4#1306329811yescharacteristic
338C2×C4#1306334811yescharacteristic
339C2×C4#1306335211yescharacteristic
340C2×C4#1306335211yescharacteristic
341C8—1721no—
342C8C22⋊C4×D4311yescharacteristic
343C8C4×D17211yescharacteristic
344C8#1306330011yescharacteristic
345C8#1306331011yescharacteristic
346C22—3442no—
347C22—3442no—
348C22—3442no—
349C22—3442no—
350C22—3442no—
351C22—3442no—
352C22—1724no—
353C22#1458298111yescharacteristic
354C22#1458303411yescharacteristic
355C22#1458309311yescharacteristic
356C22SD32×D4311yescharacteristic
357C22#1458333011yescharacteristic
358C22#1458333311yescharacteristic
359C22#1458334111yescharacteristic
360C4—82no—
361C4—161no—
362C4—862no—
363C4—3442no—
364C4—1721no—
365C4#1458277711yescharacteristic
366C4#1458301011yescharacteristic
367C4#1458304711yescharacteristic
368C4#1458311711yescharacteristic
369C2—3444no—
370C2#1913494411yescharacteristic
371C2#1913644611yescharacteristic
372C2#1913645811yescharacteristic
373C2#1913652511yescharacteristic
374C2#1913653811yescharacteristic
375C2#1913663911yescharacteristic
376C2#1913664911yescharacteristic
subgroupG/H
centerC23D8×D43
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
FittingC43×#1380C2
socleC23×C43C2×D8
prime radicalC22×D344C22
cosocleC22×C8×C43C23
hypercenter#1380D43
hypocenterC43#13014
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ #1380

Complements

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

NH ≅ G/Ntype
3. C2×#14582702C2semidirect
5. #19135454C2semidirect
6. #19132672C2semidirect
7. C43×#1380C2semidirect
13. C2×#13063270C4semidirect
34. C2×Dic172C2×C4semidirect
61. C2×C16×C43C2×C4semidirect
142. C2×Dic43SD32semidirect
186. #1380D43semidirect
214. C43#13014semidirect
244. C2×C16C4×D43semidirect

Maximal subgroups

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

subgroupindex
C22×#130632702
C2×#145829812
C2×#145827022
C2×#145826992
#191354542
#191326722
C43×#13802
#1301443