Finite Group Databasebeta

← #25015072

Subgroups — #25015072

Order 11008.

514 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583284C211yesmaximal, characteristic
2C2×Dic43⋊C16C211yesmaximal, characteristic, complemented
3C2×#14582703C211yesmaximal, characteristic, complemented
4C2×#14582701C211yesmaximal, characteristic
5C2×#14582699C211yesmaximal, characteristic
6#107×Dic43C211yesmaximal, characteristic, complemented
7C2×C43×#358C211yesmaximal, characteristic, complemented
8C22×#10621884—21no—
9C22×D344C2211yescharacteristic
10C2×#13063314—21no—
11C22×C43⋊C16C2211yescharacteristic
12#14583284—22no—
13#14583284C414yescomplemented
14C2×#13063259C2211yescharacteristic
15C2×C8×Dic43C2211yescharacteristic
16C4⋊C4×Dic43—21no—
17Dic43⋊C16—22no—
18#14582703—22no—
19#14582701—22no—
20#14582699—22no—
21#14582661—21no—
22C22×Q16×C43C2211yescharacteristic
23C22×C16×C43C2211yescharacteristic
24C2×#107×C43C2211yescharacteristic
25C43×#358—22no—
26C22×D172—21no—
27C2×#10621884—24no—
28C2×#10621884—42no—
29C2×#10621884—42no—
30C2×D344—21no—
31C2×D344—21no—
32C2×D344—21no—
33C2×D344—21no—
34C2×D344—21no—
35C2×D344C2×C412yes—
36C22×C43⋊C8D411yescharacteristic
37#13063314—24no—
38#13063314—42no—
39C2×C4⋊Dic43—21no—
40C2×(C2×D43)⋊C4—41no—
41C2×(C2×D43)⋊C4—41no—
42C2×C4×Dic43—41no—
43C2×C4×Dic43D411yescharacteristic
44C2×C43⋊C16—21no—
45C2×C43⋊C16—21no—
46C2×C43⋊C16—21no—
47#13063259—21no—
48#13063259D412yes—
49C8×Dic43C2×C412yes—
50C8×Dic43D412yes—
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×C412yes—
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—41no—
81C2×D172—41no—
82C2×D172—41no—
83C2×D172—41no—
84C2×D172—41no—
85Q16×C43—22no—
86Q16×C43—22no—
87Q16×C43—41no—
88Q16×C43—41no—
89C2×C8×C43C22×C411yescharacteristic
90C2×C8×C43C2×D411yescharacteristic
91C2×C8×C43C2×D411yescharacteristic
92C2×C8×C43C2×D411yescharacteristic
93C2×C8×C43#4111yescharacteristic
94C2×C8×C43#4111yescharacteristic
95C4⋊C4×C43—22no—
96C4⋊C4×C43—41no—
97#10621884—48no—
98(C2×D43)⋊C4—44no—
99(C2×D43)⋊C4—44no—
100C4⋊Dic43—22no—
101C4⋊Dic43—41no—
102C4×Dic43—82no—
103C4×Dic43C22⋊C412yes—
104C4×Dic43SD1612yes—
105C2×C43⋊C8—21no—
106C2×C43⋊C8—21no—
107C2×C43⋊C8C22⋊C412yes—
108D344—22no—
109D344—22no—
110D344—41no—
111D344—41no—
112C16×C43—41no—
113C43⋊C16—41no—
114C23×C43C2×D811yescharacteristic
115C22×D43—42no—
116C22×D43—81no—
117C22×D43—81no—
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×C43C2×C22⋊C411yescharacteristic
133C2×C4×C43#12111yescharacteristic
134C2×C4×C43#12111yescharacteristic
135C2×C4×C43C2×SD1611yescharacteristic
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—42no—
143C2×Dic43—81no—
144C2×Dic43—81no—
145C2×Dic43#10212yes—
146C2×Dic43#10212yes—
147D172—42no—
148D172—42no—
149D172—81no—
150D172—81no—
151C8×C43C4×D411yescharacteristic
152C8×C43C4×D411yescharacteristic
153C8×C43#12411yescharacteristic
154C8×C43#12711yescharacteristic
155C43⋊C8—22no—
156#13254—431nomaximal, Sylow
157C22×C43C2×#10211yescharacteristic
158C22×C43#45911yescharacteristic
159C22×C43#45911yescharacteristic
160C22×C43#50811yescharacteristic
161C22×C43#50811yescharacteristic
162C22×C43#50911yescharacteristic
163C22×C43#51011yescharacteristic
164C2×D43—82no—
165C2×D43—82no—
166C2×D43—82no—
167C2×D43—161no—
168C2×D43—161no—
169C2×D43—161no—
170C2×D43—161no—
171C4×C43—82no—
172C4×C43—82no—
173C4×C43#39011yescharacteristic
174C4×C43#41811yescharacteristic
175C4×C43#46011yescharacteristic
176C4×C43#46011yescharacteristic
177Dic43—22no—
178Dic43—22no—
179Dic43—82no—
180C2×#495—431no—
181C2×C4⋊C16—431no—
182C2×#358—431no—
183C2×#358D4311yescharacteristic, complemented
184C2×#357—431no—
185C2×#357—431no—
186C4×#107—431no—
187C2×C43#198211yescharacteristic
188C2×C43#213811yescharacteristic
189C2×C43#213911yescharacteristic
190C2×C43#221011yescharacteristic
191C2×C43#221011yescharacteristic
192C2×C43#221111yescharacteristic
193C2×C43#221111yescharacteristic
194D43—162no—
195C22×Q16C2×D4311yescharacteristic
196C22×SD16—861no—
197C22×D8—431no—
198C2×#124—861no—
199C22×C16—431no—
200C22×C16C2×D4311yescharacteristic
201#495—434no—
202#495—862no—
203C2×#107—431no—
204C2×#107C2×D4311yescharacteristic
205C2×C4×C8—431no—
206C4×C4⋊C4—861no—
207C4⋊C16—862no—
208#358—22no—
209#358—862no—
210#357—862no—
211#357—862no—
212#340—861no—
213C43#1325411yescharacteristic, complemented, Sylow
214C22×Q8—21no—
215C22×D4—861no—
216C2×Q16—21no—
217C2×Q16—21no—
218C2×Q16—21no—
219C2×Q16—21no—
220C2×Q16—21no—
221C2×Q16C4×D4312yes—
222C2×SD16—864no—
223C2×SD16—1722no—
224C2×SD16—1722no—
225C2×D8—432no—
226C2×D8—861no—
227C2×D8—861no—
228C2×D8—861no—
229C2×D8—861no—
230C2×D8—861no—
231C22×C8—431no—
232C22×C8C22×D4311yescharacteristic
233#124—864no—
234#124—1722no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—861no—
237C2×C22⋊C4—1721no—
238C2×C22⋊C4—1721no—
239C2×C42—431no—
240C2×C42—1721no—
241C2×C16—21no—
242C2×C16—21no—
243C2×C16—21no—
244C2×C16—861no—
245C2×C16—861no—
246C2×C16—861no—
247#107—21no—
248#107—432no—
249#107—861no—
250#107C22⋊D4312yes—
251C4×C8—432no—
252C4×C8—432no—
253#95—1721no—
254C24—1721no—
255C2×Q8—22no—
256C2×Q8—41no—
257C2×Q8—41no—
258C2×Q8—41no—
259C2×Q8—41no—
260C2×Q8—41no—
261C2×D4—862no—
262C2×D4—1721no—
263C2×D4—1721no—
264C2×D4—1721no—
265C2×D4—1721no—
266C2×D4—1721no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4—431no—
270C22×C4—431no—
271C22×C4—1721no—
272C22×C4D4×D4311yescharacteristic
273Q16—22no—
274Q16—22no—
275Q16—41no—
276Q16—41no—
277SD16—1728no—
278D8—862no—
279D8—862no—
280D8—1721no—
281D8—1721no—
282C2×C8—432no—
283C2×C8—861no—
284C2×C8—861no—
285C2×C8C2×C4×D4311yescharacteristic
286C2×C8#1062189811yescharacteristic
287C2×C8D4×D4311yescharacteristic
288C2×C8D4×D4311yescharacteristic
289C2×C8#1062190011yescharacteristic
290C2×C8C2×C22⋊D4311yescharacteristic
291C4⋊C4—22no—
292C4⋊C4—41no—
293C4⋊C4—862no—
294C4⋊C4—1721no—
295C22⋊C4—1724no—
296C22⋊C4—1724no—
297C42—432no—
298C42—432no—
299C42—3442no—
300C16—41no—
301C16—1721no—
302C23—3441no—
303C23—3441no—
304C23—3441no—
305C23—3441no—
306C23—3441no—
307C23—3441no—
308C23—1722no—
309C23D8×D4311yescharacteristic
310Q8—42no—
311Q8—42no—
312Q8—81no—
313Q8—81no—
314D4—3441no—
315D4—3441no—
316D4—1722no—
317D4—1722no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4—432no—
325C2×C4—432no—
326C2×C4—861no—
327C2×C4—861no—
328C2×C4—861no—
329C2×C4—861no—
330C2×C4—3441no—
331C2×C4—3441no—
332C2×C4—1722no—
333C2×C4C22⋊C4×D4311yescharacteristic
334C2×C4#1306329711yescharacteristic
335C2×C4#1306329811yescharacteristic
336C2×C4SD16×D4311yescharacteristic
337C2×C4#1306334911yescharacteristic
338C2×C4#1306335211yescharacteristic
339C8—862no—
340C8(C22⋊D43)⋊C411yescharacteristic
341C8C4×C22⋊D4311yescharacteristic
342C8#1306331111yescharacteristic
343C8#1306332111yescharacteristic
344C22—3442no—
345C22—3442no—
346C22—3442no—
347C22—6881no—
348C22—6881no—
349C22—6881no—
350C22—6881no—
351C22#102×D4311yescharacteristic
352C22#1458309211yescharacteristic
353C22#1458309311yescharacteristic
354C22#1458333011yescharacteristic
355C22#1458333211yescharacteristic
356C22#1458333611yescharacteristic
357C22#1458334111yescharacteristic
358C4—82no—
359C4—82no—
360C4—862no—
361C4—862no—
362C4—3442no—
363C4#1458279911yescharacteristic
364C4#1458290211yescharacteristic
365C4#1458309711yescharacteristic
366C4#1458309811yescharacteristic
367C2—6882no—
368C2#1913552011yescharacteristic
369C2#1913630111yescharacteristic
370C2#1913630611yescharacteristic
371C2#1913665211yescharacteristic
372C2#1913665311yescharacteristic
373C2#1913665911yescharacteristic
374C2#1913666011yescharacteristic
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#13254
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
2. C2×Dic43⋊C16C2semidirect
3. C2×#14582703C2semidirect
6. #107×Dic43C2semidirect
7. C2×C43×#358C2semidirect
13. #14583284C4semidirect
183. C2×#358D43semidirect
213. C43#13254semidirect

Maximal subgroups

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

subgroupindex
C2×#145832842
C2×Dic43⋊C162
C2×#145827032
C2×#145827012
C2×#145826992
#107×Dic432
C2×C43×#3582
#1325443