Finite Group Databasebeta

← #25023370

Subgroups — #25023370

Order 11008.

1830 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q8×Dic43C211yesmaximal, characteristic, complemented
2C2×#14582810C211yesmaximal, characteristic
3C2×#14582788C213yesmaximal
4#19132859C213yesmaximal, complemented
5#19132841C213yesmaximal
6#19132820C213yesmaximal, complemented
7C43×#1446C211yesmaximal, characteristic, complemented
8C2×Q8×Dic43—212no—
9C22×C4⋊Dic43C2213yes—
10C22×Dic43⋊C4C2213yes—
11C22×(C2×D43)⋊C4C2211yescharacteristic
12C22×(C2×D43)⋊C4C2213yes—
13C22×(C2×D43)⋊C4C2213yes—
14C22×C4×Dic43C2213yes—
15#14582810C418yescomplemented
16#14582788—212no—
17C2×C43⋊#95C2213yes—
18C2×C43⋊#95C2216yes—
19C2×C43⋊#95C2213yes—
20C23×Q8×C43C2211yescharacteristic
21C2×#95×C43C2213yes—
22C2×#95×C43C2213yes—
23C24×D43C2311yescharacteristic
24C23×Dic43C2313yes—
25C23×Dic43C2313yes—
26C23×Dic43C2311yescharacteristic
27Q8×Dic43—232no—
28C2×C4⋊Dic43—26no—
29C2×C4⋊Dic43—212no—
30C2×Dic43⋊C4—26no—
31C2×Dic43⋊C4—46no—
32C2×(C2×D43)⋊C4—26no—
33C2×(C2×D43)⋊C4—26no—
34C2×(C2×D43)⋊C4—26no—
35C2×(C2×D43)⋊C4—26no—
36C2×(C2×D43)⋊C4—46no—
37C2×(C2×D43)⋊C4C2×C4112yes—
38C2×C4×Dic43—212no—
39C2×C4×Dic43D4112yes—
40C43⋊#95—26no—
41C43⋊#95—46no—
42C43⋊#95C2×C4112yes—
43C22×Q8×C43—26no—
44C22×Q8×C43—26no—
45C22×Q8×C43C2×C414yes—
46C23×C4×C43C2311yescharacteristic
47C23×C4×C43C2313yes—
48C23×C4×C43C2313yes—
49#95×C43—26no—
50#95×C43—26no—
51C24×C43C2411yescharacteristic
52C23×D43—23no—
53C23×D43—23no—
54C23×D43—23no—
55C23×D43—21no—
56C23×D43—21no—
57C23×D43—23no—
58C23×D43C22×C412yes—
59C2×Q8×C43—224no—
60C2×Q8×C43—28no—
61C2×Q8×C43—224no—
62C22×C4×C43—26no—
63C22×C4×C43—23no—
64C22×C4×C43—23no—
65C22×C4×C43—26no—
66C22×C4×C43—26no—
67C22×C4×C43—26no—
68C22×C4×C43—23no—
69C22×C4×C43—23no—
70C22×C4×C43—21no—
71C22×C4×C43—23no—
72C22×C4×C43C22×C416yes—
73C22×C4×C43C2×D416yes—
74C22×C4×C43#4116yes—
75C22×Dic43—23no—
76C22×Dic43—26no—
77C22×Dic43—23no—
78C22×Dic43—23no—
79C22×Dic43—26no—
80C22×Dic43—26no—
81C22×Dic43—21no—
82C22×Dic43—23no—
83C22×Dic43—23no—
84C22×Dic43—26no—
85C22×Dic43C22×C416yes—
86C22×Dic43C2×D416yes—
87C22×Dic43C2×D416yes—
88(C2×D43)⋊C4—224no—
89(C2×D43)⋊C4—412no—
90(C2×D43)⋊C4—44no—
91C4⋊Dic43—224no—
92Dic43⋊C4—412no—
93C4×Dic43—224no—
94C23×C43C23×C411yescharacteristic
95C23×C43C22×D413yes—
96C23×C43C2×#4113yes—
97C23×C43H(5,𝔽2)13yes—
98C23×C432−1+411yescharacteristic
99C23×C432−1+411yescharacteristic
100C23×C432−1+413yes—
101C22×D43—26no—
102C22×D43—22no—
103C22×D43—26no—
104C22×D43—41no—
105C22×D43—43no—
106C22×D43—43no—
107C22×D43—43no—
108C22×D43—43no—
109C22×D43—43no—
110C22×D43—43no—
111C22×D43—43no—
112C22×D43—46no—
113Q8×C43—232no—
114C2×C4×C43—212no—
115C2×C4×C43—26no—
116C2×C4×C43—26no—
117C2×C4×C43—212no—
118C2×C4×C43—41no—
119C2×C4×C43—43no—
120C2×C4×C43—43no—
121C2×C4×C43—43no—
122C2×C4×C43—43no—
123C2×C4×C43—43no—
124C2×C4×C43—46no—
125C2×C4×C43—46no—
126C2×C4×C43C4×D4112yes—
127C2×Dic43—26no—
128C2×Dic43—26no—
129C2×Dic43—26no—
130C2×Dic43—212no—
131C2×Dic43—26no—
132C2×Dic43—26no—
133C2×Dic43—26no—
134C2×Dic43—43no—
135C2×Dic43—46no—
136C2×Dic43—43no—
137C2×Dic43—46no—
138C2×Dic43—46no—
139C2×Dic43#12014yes—
140#14301—431nomaximal, Sylow
141C22×C43C2×C4×D413yes—
142C22×C43#51911yescharacteristic
143C22×C43#52013yes—
144C22×C43C2×#12011yescharacteristic
145C22×C43#52513yes—
146C22×C43#53513yes—
147C22×C43#53613yes—
148C22×C43#53613yes—
149C22×C43#53713yes—
150C22×C43#54113yes—
151C22×C43#54213yes—
152C22×C43#54216yes—
153C2×D43—46no—
154C2×D43—46no—
155C2×D43—42no—
156C2×D43—81no—
157C2×D43—81no—
158C2×D43—83no—
159C2×D43—83no—
160C4×C43—212no—
161C4×C43—81no—
162C4×C43—83no—
163Dic43—24no—
164Dic43—46no—
165Dic43—46no—
166C22×C4×Q8—431no—
167C2×#393—431no—
168C2×#388—433no—
169#1446D4311yescharacteristic, complemented
170#1444—433no—
171#1439—433no—
172#1434—433no—
173C2×C43C4×#12011yescharacteristic
174C2×C43#232313yes—
175C2×C43#232613yes—
176C2×C43#261411yescharacteristic
177C2×C43#261511yescharacteristic
178C2×C43#263213yes—
179C2×C43#263713yes—
180D43—82no—
181C23×Q8C2×D4311yescharacteristic
182C2×C4×Q8—8612no—
183C22×C4⋊C4—433no—
184C22×C4⋊C4—433no—
185C22×C22⋊C4—433no—
186C22×C22⋊C4—431no—
187C22×C22⋊C4—433no—
188C22×C42—433no—
189#393—438no—
190#388—8612no—
191C2×#95—433no—
192C2×#95—433no—
193C2×#95—436no—
194C2×#95C2×D4313yes—
195C2×#95C2×D4313yes—
196C43#1430111yescharacteristic, complemented, Sylow
197C25—431no—
198C22×Q8—26no—
199C22×Q8—26no—
200C22×Q8C4×D4314yes—
201C23×C4—431no—
202C23×C4—433no—
203C23×C4—433no—
204C23×C4C22×D4311yescharacteristic
205C23×C4C22×D4313yes—
206C23×C4C22×D4313yes—
207C4×Q8—8632no—
208C2×C4⋊C4—8612no—
209C2×C4⋊C4—866no—
210C2×C4⋊C4—866no—
211C2×C4⋊C4—1726no—
212C2×C22⋊C4—4312no—
213C2×C22⋊C4—866no—
214C2×C22⋊C4—866no—
215C2×C22⋊C4—866no—
216C2×C22⋊C4—866no—
217C2×C22⋊C4—1726no—
218C2×C42—4312no—
219C2×C42—8612no—
220#95—26no—
221#95—26no—
222#95—4312no—
223#95—866no—
224#95—1726no—
225C24—432no—
226C24—863no—
227C24—863no—
228C24—863no—
229C24—861no—
230C24—861no—
231C24—863no—
232C24C23×D4311yescharacteristic
233C2×Q8—28no—
234C2×Q8—224no—
235C2×Q8—224no—
236C22×C4—26no—
237C22×C4—26no—
238C22×C4—23no—
239C22×C4—23no—
240C22×C4—26no—
241C22×C4—26no—
242C22×C4—23no—
243C22×C4—23no—
244C22×C4—23no—
245C22×C4—21no—
246C22×C4—436no—
247C22×C4—436no—
248C22×C4—436no—
249C22×C4—861no—
250C22×C4—863no—
251C22×C4—863no—
252C22×C4—866no—
253C22×C4—863no—
254C22×C4—863no—
255C22×C4—866no—
256C22×C4—866no—
257C22×C4—866no—
258C22×C4—863no—
259C22×C4C2×C4×D4316yes—
260C22×C4D4×D4316yes—
261C22×C4#1062190016yes—
262C4⋊C4—8624no—
263C4⋊C4—17212no—
264C22⋊C4—8624no—
265C22⋊C4—1724no—
266C22⋊C4—17212no—
267C42—8624no—
268C23—866no—
269C23—862no—
270C23—866no—
271C23—1721no—
272C23—1723no—
273C23—1723no—
274C23—1723no—
275C23—1723no—
276C23—1723no—
277C23—1723no—
278C23—1723no—
279C23—1726no—
280C23C22×C4×D4311yescharacteristic
281C23C2×D4×D4313yes—
282C23C2×#1062190013yes—
283C23#1306337113yes—
284C23#1306337211yescharacteristic
285C23#1306337311yescharacteristic
286C23#1306337313yes—
287Q8—232no—
288C2×C4—212no—
289C2×C4—26no—
290C2×C4—26no—
291C2×C4—212no—
292C2×C4—41no—
293C2×C4—43no—
294C2×C4—43no—
295C2×C4—43no—
296C2×C4—43no—
297C2×C4—43no—
298C2×C4—46no—
299C2×C4—46no—
300C2×C4—434no—
301C2×C4—866no—
302C2×C4—866no—
303C2×C4—866no—
304C2×C4—8612no—
305C2×C4—866no—
306C2×C4—866no—
307C2×C4—866no—
308C2×C4—1723no—
309C2×C4—1726no—
310C2×C4—1723no—
311C2×C4—1726no—
312C2×C4—1726no—
313C2×C4(C22⋊D43)⋊C4112yes—
314C22—3443no—
315C22—3443no—
316C22—3441no—
317C22—3441no—
318C22—1726no—
319C22—1726no—
320C22—1722no—
321C22C2×(C22⋊D43)⋊C413yes—
322C22#1458337511yescharacteristic
323C22#1458338113yes—
324C22#120×D4311yescharacteristic
325C22#1458340513yes—
326C22#1458346713yes—
327C22#1458347213yes—
328C22#1458347413yes—
329C22#1458347913yes—
330C22#1458351013yes—
331C22#1458351813yes—
332C22#1458352216yes—
333C4—212no—
334C4—83no—
335C4—81no—
336C4—864no—
337C4—1726no—
338C4—1726no—
339C2—3442no—
340C2#1913709411yescharacteristic
341C2#1913728013yes—
342C2#1913730913yes—
343C2#1914031511yescharacteristic
344C2#1914032211yescharacteristic
345C2#1914045413yes—
346C2#1914050213yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1446C2
socle, cosocleC24×C43C24
prime radicalC24×D43C23
hypercenter#1446D43
hypocenterC43#14301
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1446

Complements

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

NH ≅ G/Ntype
1. C22×Q8×Dic43C2semidirect
4. #19132859C2semidirect
6. #19132820C2semidirect
7. C43×#1446C2semidirect
15. #14582810C4semidirect
169. #1446D43semidirect
196. C43#14301semidirect

Maximal subgroups

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

subgroupindex
C22×Q8×Dic432
C2×#145828102
C2×#145827882
#191328592
#191328412
#191328202
C43×#14462
#1430143