Finite Group Databasebeta

← #25023369

Subgroups — #25023369

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×#14582792C213yesmaximal
3#19132866C211yesmaximal, characteristic, complemented
4#19132860C213yesmaximal, complemented
5#19132840C213yesmaximal
6#19132820C213yesmaximal, complemented
7C2×C43×#393C211yesmaximal, characteristic
8C2×Q8×Dic43—212no—
9C22×C4⋊Dic43C2213yes—
10C22×C4⋊Dic43C2213yes—
11C22×C22⋊Dic43C2211yescharacteristic
12C22×C22⋊Dic43C2213yes—
13C22×C4×Dic43C2213yes—
14#14582792—212no—
15C2×C43⋊#95C2213yes—
16C2×C43⋊#95C2213yes—
17C2×C43⋊#95C2213yes—
18C2×C43⋊#95C2216yes—
19C23×Q8×C43C2211yescharacteristic
20C22×C22⋊C4×C43C2213yes—
21C43×#393C418yescomplemented
22C2×#95×C43C2213yes—
23C23×Dic43C2311yescharacteristic
24C23×Dic43C2313yes—
25C23×Dic43C2313yes—
26C23×Dic43C2311yescharacteristic
27Q8×Dic43—232no—
28C2×C4⋊Dic43—26no—
29C2×C4⋊Dic43—212no—
30C2×C4⋊Dic43—26no—
31C2×C4⋊Dic43—46no—
32C2×C22⋊Dic43—26no—
33C2×C22⋊Dic43—26no—
34C2×C22⋊Dic43—46no—
35C2×C4×Dic43—212no—
36C2×C4×Dic43D4112yes—
37C43⋊#95—26no—
38C43⋊#95—26no—
39C43⋊#95—26no—
40C43⋊#95—46no—
41C25×C43C2311yescharacteristic
42C22×Q8×C43—26no—
43C22×Q8×C43—26no—
44C22×Q8×C43C2×C414yes—
45C23×C4×C43C2313yes—
46C23×C4×C43C2313yes—
47C2×C22⋊C4×C43—26no—
48C2×C22⋊C4×C43—26no—
49C2×C22⋊C4×C43C2×C4112yes—
50#95×C43C2×C4112yes—
51C24×C43—23no—
52C24×C43—23no—
53C24×C43—23no—
54C24×C43—21no—
55C24×C43—21no—
56C24×C43—23no—
57C24×C43C22×C412yes—
58C24×C43C2411yescharacteristic
59C2×Q8×C43—224no—
60C2×Q8×C43—28no—
61C2×Q8×C43—224no—
62C22×C4×C43—26no—
63C22×C4×C43—23no—
64C22×C4×C43—26no—
65C22×C4×C43—23no—
66C22×C4×C43—26no—
67C22×C4×C43—26no—
68C22×C4×C43C22×C416yes—
69C22×C4×C43C22×C416yes—
70C22×C4×C43C2×D416yes—
71C22×C4×C43#4116yes—
72C22×Dic43—26no—
73C22×Dic43—23no—
74C22×Dic43—23no—
75C22×Dic43—26no—
76C22×Dic43—23no—
77C22×Dic43—26no—
78C22×Dic43—26no—
79C22×Dic43—23no—
80C22×Dic43—23no—
81C22×Dic43—21no—
82C22×Dic43—23no—
83C22×Dic43—23no—
84C22×Dic43—23no—
85C22×Dic43—21no—
86C22×Dic43C2×D416yes—
87C22×Dic43C2×D416yes—
88C22⋊C4×C43—224no—
89C22⋊Dic43—412no—
90C22⋊Dic43—44no—
91C4⋊Dic43—224no—
92C4⋊Dic43—412no—
93C4×Dic43—224no—
94C23×C43—26no—
95C23×C43—22no—
96C23×C43—26no—
97C23×C43—41no—
98C23×C43—43no—
99C23×C43—43no—
100C23×C43—43no—
101C23×C43—43no—
102C23×C43—43no—
103C23×C43—43no—
104C23×C43—46no—
105C23×C43—43no—
106C23×C43C23×C411yescharacteristic
107C23×C43C22×D413yes—
108C23×C43C2×#4113yes—
109C23×C43H(5,𝔽2)13yes—
110C23×C432−1+413yes—
111C23×C432−1+411yescharacteristic
112C23×C432−1+411yescharacteristic
113Q8×C43—232no—
114C2×C4×C43—212no—
115C2×C4×C43—26no—
116C2×C4×C43—26no—
117C2×C4×C43—212no—
118C2×C4×C43—26no—
119C2×C4×C43—212no—
120C2×C4×C43—43no—
121C2×C4×C43—43no—
122C2×C4×C43—46no—
123C2×C4×C43C4×D4112yes—
124C2×Dic43—26no—
125C2×Dic43—26no—
126C2×Dic43—26no—
127C2×Dic43—26no—
128C2×Dic43—26no—
129C2×Dic43—46no—
130C2×Dic43—46no—
131C2×Dic43—41no—
132C2×Dic43—43no—
133C2×Dic43—43no—
134C2×Dic43—43no—
135C2×Dic43—43no—
136C2×Dic43—43no—
137C2×Dic43—46no—
138C2×Dic43—46no—
139C2×Dic43#12014yes—
140#14301—431nomaximal, Sylow
141C22×C43—46no—
142C22×C43—46no—
143C22×C43—42no—
144C22×C43—81no—
145C22×C43—81no—
146C22×C43—83no—
147C22×C43—83no—
148C22×C43C2×C4×D413yes—
149C22×C43#51911yescharacteristic
150C22×C43#52013yes—
151C22×C43C2×#12011yescharacteristic
152C22×C43#52513yes—
153C22×C43#53513yes—
154C22×C43#53613yes—
155C22×C43#53613yes—
156C22×C43#53713yes—
157C22×C43#54113yes—
158C22×C43#54216yes—
159C22×C43#54213yes—
160C4×C43—212no—
161C4×C43—46no—
162Dic43—24no—
163Dic43—46no—
164Dic43—81no—
165Dic43—83no—
166C22×C4×Q8—431no—
167C2×#393D4311yescharacteristic
168C2×#388—433no—
169#1446—431no—
170#1444—433no—
171#1439—433no—
172#1434—433no—
173C2×C43—82no—
174C2×C43C4×#12011yescharacteristic
175C2×C43#232313yes—
176C2×C43#232613yes—
177C2×C43#261411yescharacteristic
178C2×C43#261511yescharacteristic
179C2×C43#263213yes—
180C2×C43#263713yes—
181C23×Q8C2×D4311yescharacteristic
182C2×C4×Q8—8612no—
183C22×C4⋊C4—433no—
184C22×C4⋊C4—433no—
185C22×C22⋊C4—431no—
186C22×C22⋊C4—433no—
187C22×C22⋊C4C2×D4313yes—
188C22×C42—433no—
189#393Dic4318yescomplemented
190#388—8612no—
191C2×#95—433no—
192C2×#95—433no—
193C2×#95—433no—
194C2×#95—436no—
195C2×#95C2×D4313yes—
196C43#1430111yescharacteristic, complemented, Sylow
197C25C22×D4311yescharacteristic
198C22×Q8—26no—
199C22×Q8—26no—
200C22×Q8C2×Dic4314yes—
201C23×C4—431no—
202C23×C4—433no—
203C23×C4—431no—
204C23×C4—433no—
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—26no—
213C2×C22⋊C4—26no—
214C2×C22⋊C4—866no—
215C2×C22⋊C4—866no—
216C2×C22⋊C4—1726no—
217C2×C22⋊C4C2×Dic43112yes—
218C2×C42—4312no—
219C2×C42—8612no—
220#95—866no—
221#95—866no—
222#95—866no—
223#95—1726no—
224#95C2×Dic43112yes—
225C24—23no—
226C24—23no—
227C24—23no—
228C24—23no—
229C24—21no—
230C24—21no—
231C24C22×Dic4312yes—
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—436no—
243C22×C4—436no—
244C22×C4—863no—
245C22×C4—861no—
246C22×C4—866no—
247C22×C4—863no—
248C22×C4—866no—
249C22×C4—863no—
250C22×C4—863no—
251C22×C4—863no—
252C22×C4—866no—
253C22×C4—866no—
254C22×C4—863no—
255C22×C4—863no—
256C22×C4—863no—
257C22×C4—861no—
258C22×C4D4×D4316yes—
259C22×C4#1062190016yes—
260C22×C4C22×Dic4316yes—
261C22×C4C22×Dic4316yes—
262C4⋊C4—8624no—
263C4⋊C4—17212no—
264C22⋊C4—224no—
265C22⋊C4—1724no—
266C22⋊C4—17212no—
267C42—8624no—
268C23—26no—
269C23—22no—
270C23—26no—
271C23—41no—
272C23—43no—
273C23—43no—
274C23—43no—
275C23—43no—
276C23—43no—
277C23—43no—
278C23—46no—
279C23—43no—
280C23C23×Dic4311yescharacteristic
281C23C2×D4×D4313yes—
282C23C2×#1062190013yes—
283C23#1306337113yes—
284C23#1306337213yes—
285C23#1306337311yescharacteristic
286C23#1306337311yescharacteristic
287Q8—232no—
288C2×C4—212no—
289C2×C4—26no—
290C2×C4—26no—
291C2×C4—212no—
292C2×C4—26no—
293C2×C4—212no—
294C2×C4—43no—
295C2×C4—43no—
296C2×C4—46no—
297C2×C4—434no—
298C2×C4—866no—
299C2×C4—866no—
300C2×C4—866no—
301C2×C4—866no—
302C2×C4—866no—
303C2×C4—1721no—
304C2×C4—1723no—
305C2×C4—1723no—
306C2×C4—1723no—
307C2×C4—1723no—
308C2×C4—1723no—
309C2×C4—1726no—
310C2×C4—1726no—
311C2×C4—1726no—
312C2×C4—1726no—
313C2×C4D4×Dic43112yes—
314C22—46no—
315C22—42no—
316C22—46no—
317C22—83no—
318C22—83no—
319C22—81no—
320C22—81no—
321C22C2×D4×Dic4313yes—
322C22#1458337711yescharacteristic
323C22#1458338213yes—
324C22#120×D4311yescharacteristic
325C22#1458340513yes—
326C22#1458346713yes—
327C22#1458346913yes—
328C22#1458347213yes—
329C22#1458347913yes—
330C22#1458350913yes—
331C22#1458351816yes—
332C22#1458352213yes—
333C4—212no—
334C4—46no—
335C4—864no—
336C4—3443no—
337C4—3441no—
338C4—1726no—
339C2—82no—
340C2#120×Dic4311yescharacteristic
341C2#1913727913yes—
342C2#1913730813yes—
343C2#1914031311yescharacteristic
344C2#1914032211yescharacteristic
345C2#1914045413yes—
346C2#1914050013yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC2×C43×#393C2
socle, cosocleC24×C43C24
prime radicalC25×C43C23
hypercenterC2×#393D43
hypocenterC43#14301
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#393

Complements

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

NH ≅ G/Ntype
1. C22×Q8×Dic43C2semidirect
3. #19132866C2semidirect
4. #19132860C2semidirect
6. #19132820C2semidirect
21. C43×#393C4semidirect
189. #393Dic43semidirect
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×#145827922
#191328662
#191328602
#191328402
#191328202
C2×C43×#3932
#1430143