Finite Group Databasebeta

← #25066816

Subgroups — #25066816

Order 11008.

590 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144634C211yesmaximal, characteristic
2#19143529C211yesmaximal, characteristic
3#19133490C214yesmaximal, complemented
4#19133443C214yesmaximal, complemented
5#19133369C211yesmaximal, characteristic
6#19133024C211yesmaximal, characteristic
7#19132997C211yesmaximal, characteristic
8#19132878C211yesmaximal, characteristic
9C2×C43×#446C211yesmaximal, characteristic
10#14583456C2211yescharacteristic
11#14583234C412yes—
12#14583194C412yes—
13#14583109C412yes—
14#14583055C412yes—
15#14583029—21no—
16#14583029C2212yes—
17C8×Dic86—21no—
18C8×Dic86C2212yes—
19C4×#10621885C2214yes—
20#14582952C2211yescharacteristic
21#14582952C2211yescharacteristic
22#14582925—21no—
23#14582923C2211yescharacteristic
24#14582854—21no—
25#14582651C2214yes—
26Q8⋊(C43⋊C8)C2214yes—
27#14582629C2214yes—
28#14582620C2212yes—
29C8×C43⋊C8C2212yes—
30C2×C4×Q8×C43C2211yescharacteristic
31C43×#446—21no—
32C43×#446—21no—
33C43×#446C2212yes—
34C43×#446C2212yes—
35C2×C4⋊C8×C43—21no—
36C2×C4⋊C8×C43C2211yescharacteristic
37C2×#97×C43—21no—
38C2×C4×C8×C43C2211yescharacteristic
39C2×#10621885C2×C414yes—
40C2×#10621877—21no—
41#13063325C2×C411yescharacteristic
42#13063325C2×C411yescharacteristic
43#13063317—21no—
44#13063304—21no—
45#13063304C2×C412yes—
46C4×Dic86—21no—
47C4×Dic86C2312yes—
48#13063284—21no—
49#13063258C2×C414yes—
50C4⋊(C43⋊C8)—21no—
51C4⋊(C43⋊C8)—21no—
52C4⋊(C43⋊C8)C2×C412yes—
53C4⋊(C43⋊C8)C2312yes—
54Dic43⋊C8—22no—
55Dic43⋊C8—22no—
56#13063249C2×C414yes—
57#13063248C2×C414yes—
58C22⋊(C43⋊C8)—21no—
59C22⋊(C43⋊C8)C2×C412yes—
60#13063235—22no—
61C4×C43⋊C8C2312yes—
62C4×C43⋊C8C2312yes—
63C8×Dic43—22no—
64C22×Q8×C43C2×C411yescharacteristic
65C22×C8×C43—21no—
66C22×C8×C43D411yescharacteristic
67C22×C8×C43D411yescharacteristic
68C4×Q8×C43—21no—
69C4×Q8×C43—21no—
70C4×Q8×C43C2×C412yes—
71C4×Q8×C43C2312yes—
72C2×C4⋊C4×C43—21no—
73C2×C4⋊C4×C43C2×C411yescharacteristic
74C2×C42×C43—21no—
75C2×C42×C43C2311yescharacteristic
76C4⋊C8×C43—22no—
77C4⋊C8×C43—22no—
78C4⋊C8×C43—21no—
79C4⋊C8×C43C2312yes—
80#97×C43—22no—
81#97×C43—22no—
82C4×C8×C43D411yescharacteristic
83C4×C8×C43D411yescharacteristic
84C4×C8×C43C2311yescharacteristic
85C4×C8×C43C2311yescharacteristic
86C2×Q8×C43—21no—
87C2×Q8×C43—42no—
88C2×Q8×C43C22×C412yes—
89C22×C4×C43—21no—
90C22×C4×C43—21no—
91C22×C4×C43C22×C411yescharacteristic
92C22×C4×C43C2×D411yescharacteristic
93C22×C4×C43#4111yescharacteristic
94C2×Dic86—21no—
95C2×Dic86C22×C412yes—
96C2×C8×C43—22no—
97C2×C8×C43—22no—
98C2×C8×C43—42no—
99C2×C8×C43Q1614yescomplemented
100C2×C8×C43C2×D411yescharacteristic
101C2×C8×C43C2×D411yescharacteristic
102C2×C8×C43C2×D411yescharacteristic
103C2×C8×C43C2×D411yescharacteristic
104C4⋊C4×C43—22no—
105C4⋊C4×C43—21no—
106C4⋊C4×C43—22no—
107C4⋊C4×C43C22×C412yes—
108C42×C43—22no—
109C42×C43—22no—
110C42×C43C22×C411yescharacteristic
111C42×C43C2×D411yescharacteristic
112C42×C43#4111yescharacteristic
113C42×C43C2411yescharacteristic
114C22⋊Dic43—22no—
115#10621885—44no—
116C4⋊Dic43—21no—
117C4⋊Dic43—21no—
118C4⋊Dic43—21no—
119C4⋊Dic43C22×C412yes—
120Dic43⋊C4—22no—
121Dic43⋊C4—22no—
122C4×Dic43—22no—
123#10621877—42no—
124C2×C43⋊C8—22no—
125C2×C43⋊C8—22no—
126C2×C43⋊C8C22×C414yes—
127C23×C43C4×D411yescharacteristic
128Q8×C43—22no—
129Q8×C43—22no—
130Q8×C43—42no—
131C2×C4×C43—22no—
132C2×C4×C43—22no—
133C2×C4×C43—22no—
134C2×C4×C43—41no—
135C2×C4×C43—42no—
136C2×C4×C43—42no—
137C2×C4×C43C4×D411yescharacteristic
138C2×C4×C43C4×D411yescharacteristic
139C2×C4×C43C4×D411yescharacteristic
140C2×C4×C43C2×Q1612yes—
141C2×C4×C43#13512yes—
142C2×C4×C43C23×C411yescharacteristic
143C2×C4×C43C22×D411yescharacteristic
144C2×C4×C43C2×#4111yescharacteristic
145C2×Dic43—22no—
146C2×Dic43—22no—
147Dic86—24no—
148Dic86—42no—
149C8×C43—21no—
150C8×C43—21no—
151C8×C43—42no—
152C8×C43C2×Q1612yes—
153C8×C43C2×Q1612yes—
154C43⋊C8—24no—
155C43⋊C8—42no—
156C43⋊C8—42no—
157#17931—431nomaximal, Sylow
158C22×C43—21no—
159C22×C43—21no—
160C22×C43C4×Q1612yes—
161C22×C43C2×C4×D411yescharacteristic
162C4×C43—21no—
163C4×C43—21no—
164C4×C43—21no—
165C4×C43—42no—
166C4×C43—42no—
167C4×C43C4×Q1612yes—
168C4×C43#56812yes—
169C4×C43C22×Q1611yescharacteristic
170C4×C43C2×#13511yescharacteristic
171Dic43—42no—
172Dic43—42no—
173#3104—431no—
174#2960—431no—
175C2×#446D4311yescharacteristic
176#1591—434no—
177#1584—434no—
178#1571—431no—
179#1487—431no—
180#1481—431no—
181#1450—431no—
182C2×C43—22no—
183C2×C43#293011yescharacteristic
184C2×C43C2×C4×Q1611yescharacteristic
185C2×C43#295511yescharacteristic
186#533—431no—
187C2×C4×Q8C2×D4311yescharacteristic
188#484—432no—
189#477—432no—
190#462—432no—
191#451—432no—
192#446—21no—
193#446—21no—
194#446—432no—
195#446—861no—
196#446C2×D4312yes—
197#446C2×D4312yes—
198C8×Q8—432no—
199C8×Q8—861no—
200C4×Q16—434no—
201#431—431no—
202#431—431no—
203#424—861no—
204#423—431no—
205C2×C4⋊C8—21no—
206C2×C4⋊C8C2×D4311yescharacteristic
207#405—861no—
208C2×#97—21no—
209C2×C4×C8C2×D4311yescharacteristic
210#335—434no—
211Q8⋊C8—434no—
212Q8⋊C8—434no—
213#322—432no—
214C82—432no—
215C43#1793111yescharacteristic, complemented, Sylow
216C22×Q8C4×D4311yescharacteristic
217C2×Q16—434no—
218C2×M16—861no—
219C22×C8—21no—
220C22×C8C22⋊D4311yescharacteristic
221C22×C8C22⋊D4311yescharacteristic
222C4⋊Q8—431no—
223C4⋊Q8—431no—
224#125—861no—
225C22⋊Q8—432no—
226C22⋊Q8—861no—
227C4×Q8—21no—
228C4×Q8—21no—
229C4×Q8—432no—
230C4×Q8—861no—
231C4×Q8C4×D4312yes—
232C4×Q8C22×D4312yes—
233#117—861no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4C4×D4311yescharacteristic
236C2×C42—21no—
237C2×C42C22×D4311yescharacteristic
238#107—434no—
239C4⋊C8—22no—
240C4⋊C8—22no—
241C4⋊C8—21no—
242C4⋊C8—432no—
243C4⋊C8—432no—
244C4⋊C8—862no—
245C4⋊C8—862no—
246C4⋊C8—861no—
247C4⋊C8—861no—
248C4⋊C8C22×D4312yes—
249#103—434no—
250#103—434no—
251C22⋊C8—432no—
252C22⋊C8—861no—
253#97—22no—
254#97—22no—
255#97—862no—
256C4×C8—432no—
257C4×C8—432no—
258C4×C8—862no—
259C4×C8C22⋊D4311yescharacteristic
260C4×C8C22⋊D4311yescharacteristic
261C4×C8C22×D4311yescharacteristic
262C4×C8C22×D4311yescharacteristic
263C2×Q8—21no—
264C2×Q8—42no—
265C2×Q8—432no—
266C2×Q8—861no—
267C2×Q8C2×C4×D4312yes—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4C2×C4×D4311yescharacteristic
271C22×C4#1062189811yescharacteristic
272C22×C4C2×C22⋊D4311yescharacteristic
273Q16—1724no—
274M16—1722no—
275C2×C8—22no—
276C2×C8—22no—
277C2×C8—42no—
278C2×C8—434no—
279C2×C8—862no—
280C2×C8—862no—
281C2×C8#1062188514yescomplemented
282C2×C8C2×C22⋊D4311yescharacteristic
283C2×C8C2×C22⋊D4311yescharacteristic
284C2×C8C2×C22⋊D4311yescharacteristic
285C2×C8C2×C22⋊D4311yescharacteristic
286C4⋊C4—22no—
287C4⋊C4—21no—
288C4⋊C4—22no—
289C4⋊C4—432no—
290C4⋊C4—861no—
291C4⋊C4—861no—
292C4⋊C4—862no—
293C4⋊C4—861no—
294C4⋊C4—862no—
295C4⋊C4C2×C4×D4312yes—
296C22⋊C4—862no—
297C42—22no—
298C42—22no—
299C42—862no—
300C42C2×C4×D4311yescharacteristic
301C42#1062189811yescharacteristic
302C42C2×C22⋊D4311yescharacteristic
303C42C23×D4311yescharacteristic
304C23C4×C22⋊D4311yescharacteristic
305Q8—22no—
306Q8—22no—
307Q8—42no—
308Q8—864no—
309Q8—1722no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—41no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—862no—
317C2×C4—862no—
318C2×C4C4×C22⋊D4311yescharacteristic
319C2×C4C4×C22⋊D4311yescharacteristic
320C2×C4C4×C22⋊D4311yescharacteristic
321C2×C4C2×#1062188512yes—
322C2×C4#1306334512yes—
323C2×C4C22×C4×D4311yescharacteristic
324C2×C4C22×C22⋊D4311yescharacteristic
325C2×C4C2×#1062189811yescharacteristic
326C8—21no—
327C8—21no—
328C8—42no—
329C8—864no—
330C8—1722no—
331C8—1722no—
332C8C2×#1062188512yes—
333C8C2×#1062188512yes—
334C22—21no—
335C22—21no—
336C22C4×#1062188512yes—
337C22C2×C4×C22⋊D4311yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—42no—
342C4—42no—
343C4—1722no—
344C4—1722no—
345C4C4×#1062188512yes—
346C4#1458366512yes—
347C4C22×#1062188511yescharacteristic
348C4C2×#1306334511yescharacteristic
349C2—22no—
350C2#1914329811yescharacteristic
351C2C2×C4×#1062188511yescharacteristic
352C2#1914349611yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC2×C43×#446C2
socleC22×C43C2×C4×D4
prime radicalC23×C43C4×D4
cosocleC42×C43C24
hypercenterC2×#446D43
hypocenterC43#17931
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C4×C8 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
3. #19133490C2semidirect
4. #19133443C2semidirect
99. C2×C8×C43Q16semidirect
215. C43#17931semidirect
281. C2×C8#10621885semidirect

Maximal subgroups

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

subgroupindex
#191446342
#191435292
#191334902
#191334432
#191333692
#191330242
#191329972
#191328782
C2×C43×#4462
#1793143