Finite Group Databasebeta

← #25023715

Subgroups — #25023715

Order 11008.

1290 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19132863C213yesmaximal, complemented
2#19132857C211yesmaximal, characteristic, complemented
3#19132844C213yesmaximal
4#19132832C213yesmaximal
5#19132827C213yesmaximal, complemented
6#95×Dic43C211yesmaximal, characteristic, complemented
7C2×C43×#396C211yesmaximal, characteristic
8C22×C22⋊Dic43C2211yescharacteristic
9C22×C22⋊Dic43C2213yes—
10C22×C4×Dic43C2213yes—
11C2×C43⋊#95C2213yes—
12C2×C43⋊#95C2213yes—
13C2×C43⋊#95C2213yes—
14C2×C43⋊#95C2213yes—
15C2×C43⋊#95C2213yes—
16C2×C43⋊#95C2213yes—
17C2×C43⋊#95C2213yes—
18C22×C4⋊C4×C43C2213yes—
19C22×C22⋊C4×C43C2213yes—
20C43×#396C418yescomplemented
21C2×#95×C43C2211yescharacteristic
22C23×Dic43C2313yes—
23C23×Dic43C2311yescharacteristic
24C23×Dic43C2313yes—
25C23×Dic43C2311yescharacteristic
26C2×C22⋊Dic43—26no—
27C2×C22⋊Dic43—26no—
28C2×C22⋊Dic43—43no—
29C2×C22⋊Dic43—43no—
30C2×C4×Dic43—26no—
31C2×C4×Dic43—43no—
32C2×C4×Dic43—43no—
33C43⋊#95—26no—
34C43⋊#95—26no—
35C43⋊#95—26no—
36C43⋊#95—43no—
37C43⋊#95—43no—
38C43⋊#95—43no—
39C43⋊#95—43no—
40C25×C43C2311yescharacteristic
41C23×C4×C43C2313yes—
42C23×C4×C43C2313yes—
43C2×C4⋊C4×C43—43no—
44C2×C4⋊C4×C43—43no—
45C2×C4⋊C4×C43C2×C4112yes—
46C2×C22⋊C4×C43—43no—
47C2×C22⋊C4×C43—43no—
48C2×C22⋊C4×C43C2×C4112yes—
49#95×C43C2×C414yes—
50C24×C43—23no—
51C24×C43—23no—
52C24×C43—23no—
53C24×C43—23no—
54C24×C43—21no—
55C24×C43—21no—
56C24×C43C22×C412yes—
57C24×C43C2411yescharacteristic
58C22×C4×C43—23no—
59C22×C4×C43—23no—
60C22×C4×C43—23no—
61C22×C4×C43—23no—
62C22×C4×C43—23no—
63C22×C4×C43—23no—
64C22×C4×C43—23no—
65C22×C4×C43—23no—
66C22×C4×C43—23no—
67C22×C4×C43—23no—
68C22×C4×C43—23no—
69C22×C4×C43—23no—
70C22×C4×C43C22×C416yes—
71C22×C4×C43C22×C416yes—
72C22×Dic43—23no—
73C22×Dic43—23no—
74C22×Dic43—23no—
75C22×Dic43—23no—
76C22×Dic43—23no—
77C22×Dic43—23no—
78C22×Dic43—23no—
79C22×Dic43—23no—
80C22×Dic43—23no—
81C22×Dic43—23no—
82C22×Dic43—23no—
83C22×Dic43—23no—
84C22×Dic43—23no—
85C22×Dic43—23no—
86C22×Dic43—21no—
87C22×Dic43—23no—
88C22×Dic43—23no—
89C22×Dic43—21no—
90C22×Dic43#4116yes—
91C22×Dic43#4116yes—
92C4⋊C4×C43—412no—
93C22⋊C4×C43—412no—
94C22⋊Dic43—412no—
95C22⋊Dic43—44no—
96C4×Dic43—412no—
97C23×C43—26no—
98C23×C43—26no—
99C23×C43—22no—
100C23×C43—41no—
101C23×C43—43no—
102C23×C43—43no—
103C23×C43—43no—
104C23×C43—43no—
105C23×C43—43no—
106C23×C43—43no—
107C23×C43—43no—
108C23×C43—43no—
109C23×C43—43no—
110C23×C43C23×C411yescharacteristic
111C23×C43C2×#4113yes—
112C23×C43C2×#4113yes—
113C23×C43H(5,𝔽2)13yes—
114C23×C43H(5,𝔽2)13yes—
115C23×C432−1+411yescharacteristic
116C23×C432−1+411yescharacteristic
117C2×C4×C43—26no—
118C2×C4×C43—26no—
119C2×C4×C43—26no—
120C2×C4×C43—26no—
121C2×C4×C43—26no—
122C2×C4×C43—26no—
123C2×C4×C43—43no—
124C2×C4×C43—43no—
125C2×C4×C43—43no—
126C2×C4×C43—43no—
127C2×C4×C43—43no—
128C2×C4×C43—43no—
129C2×C4×C43—43no—
130C2×C4×C43—43no—
131C2×Dic43—26no—
132C2×Dic43—26no—
133C2×Dic43—26no—
134C2×Dic43—26no—
135C2×Dic43—26no—
136C2×Dic43—43no—
137C2×Dic43—43no—
138C2×Dic43—43no—
139C2×Dic43—43no—
140C2×Dic43—41no—
141C2×Dic43—43no—
142C2×Dic43—43no—
143C2×Dic43—43no—
144C2×Dic43—43no—
145C2×Dic43—43no—
146C2×Dic43—43no—
147C2×Dic43—43no—
148C2×Dic43—43no—
149C2×Dic43—43no—
150C2×Dic43#12614yes—
151#14331—431nomaximal, Sylow
152C22×C43—42no—
153C22×C43—46no—
154C22×C43—46no—
155C22×C43—81no—
156C22×C43—81no—
157C22×C43—83no—
158C22×C43—83no—
159C22×C43C4×#4113yes—
160C22×C43#51813yes—
161C22×C43#51911yescharacteristic
162C22×C43C2×#12611yescharacteristic
163C22×C43#52913yes—
164C22×C43#53813yes—
165C22×C43#53813yes—
166C22×C43#53913yes—
167C22×C43#53913yes—
168C22×C43#54013yes—
169C22×C43#54013yes—
170C22×C43#54213yes—
171C22×C43#54213yes—
172C4×C43—46no—
173C4×C43—46no—
174Dic43—24no—
175Dic43—46no—
176Dic43—81no—
177Dic43—83no—
178C2×#396D4311yescharacteristic
179#1445—433no—
180#1443—431no—
181#1440—433no—
182#1437—433no—
183#1436—433no—
184C4×#95—431no—
185C2×C43—82no—
186C2×C43C4×#12611yescharacteristic
187C2×C43#233213yes—
188C2×C43#233313yes—
189C2×C43#264311yescharacteristic
190C2×C43#264411yescharacteristic
191C2×C43#264913yes—
192C2×C43#265113yes—
193C22×C4⋊C4C2×D4313yes—
194C22×C22⋊C4—431no—
195C22×C22⋊C4—433no—
196C22×C22⋊C4C2×D4313yes—
197C22×C42—433no—
198#396Dic4318yescomplemented
199C2×#95—433no—
200C2×#95—433no—
201C2×#95—433no—
202C2×#95—433no—
203C2×#95—433no—
204C2×#95—433no—
205C2×#95—433no—
206C2×#95C2×D4311yescharacteristic
207C43#1433111yescharacteristic, complemented, Sylow
208C25C22×D4311yescharacteristic
209C23×C4—431no—
210C23×C4—433no—
211C23×C4—433no—
212C23×C4—431no—
213C23×C4C22×D4313yes—
214C23×C4C22×D4313yes—
215C2×C4⋊C4—43no—
216C2×C4⋊C4—43no—
217C2×C4⋊C4C2×Dic43112yes—
218C2×C22⋊C4—43no—
219C2×C22⋊C4—43no—
220C2×C22⋊C4—866no—
221C2×C22⋊C4—866no—
222C2×C22⋊C4—1723no—
223C2×C22⋊C4—1723no—
224C2×C22⋊C4C2×Dic43112yes—
225C2×C42—866no—
226C2×C42—1723no—
227C2×C42—1723no—
228#95—866no—
229#95—866no—
230#95—866no—
231#95—1723no—
232#95—1723no—
233#95—1723no—
234#95—1723no—
235#95C2×Dic4314yes—
236C24—23no—
237C24—23no—
238C24—23no—
239C24—23no—
240C24—21no—
241C24—21no—
242C24C22×Dic4312yes—
243C24C23×D4311yescharacteristic
244C22×C4—23no—
245C22×C4—23no—
246C22×C4—23no—
247C22×C4—23no—
248C22×C4—23no—
249C22×C4—23no—
250C22×C4—23no—
251C22×C4—23no—
252C22×C4—23no—
253C22×C4—23no—
254C22×C4—23no—
255C22×C4—23no—
256C22×C4—436no—
257C22×C4—436no—
258C22×C4—863no—
259C22×C4—861no—
260C22×C4—863no—
261C22×C4—863no—
262C22×C4—863no—
263C22×C4—863no—
264C22×C4—863no—
265C22×C4—863no—
266C22×C4—863no—
267C22×C4—863no—
268C22×C4—863no—
269C22×C4—863no—
270C22×C4—863no—
271C22×C4—863no—
272C22×C4—863no—
273C22×C4—863no—
274C22×C4—863no—
275C22×C4—861no—
276C22×C4C22×Dic4316yes—
277C22×C4C22×Dic4316yes—
278C4⋊C4—412no—
279C22⋊C4—412no—
280C22⋊C4—1724no—
281C22⋊C4—17212no—
282C42—17212no—
283C23—26no—
284C23—26no—
285C23—22no—
286C23—41no—
287C23—43no—
288C23—43no—
289C23—43no—
290C23—43no—
291C23—43no—
292C23—43no—
293C23—43no—
294C23—43no—
295C23—43no—
296C23C23×Dic4311yescharacteristic
297C23#41×D4313yes—
298C23#41×D4313yes—
299C23#1306337013yes—
300C23#1306337013yes—
301C23#1306337311yescharacteristic
302C23#1306337311yescharacteristic
303C2×C4—26no—
304C2×C4—26no—
305C2×C4—26no—
306C2×C4—26no—
307C2×C4—26no—
308C2×C4—26no—
309C2×C4—43no—
310C2×C4—43no—
311C2×C4—43no—
312C2×C4—43no—
313C2×C4—43no—
314C2×C4—43no—
315C2×C4—43no—
316C2×C4—43no—
317C2×C4—434no—
318C2×C4—866no—
319C2×C4—866no—
320C2×C4—866no—
321C2×C4—866no—
322C2×C4—866no—
323C2×C4—1721no—
324C2×C4—1723no—
325C2×C4—1723no—
326C2×C4—1723no—
327C2×C4—1723no—
328C2×C4—1723no—
329C2×C4—1723no—
330C2×C4—1723no—
331C2×C4—1723no—
332C2×C4—1723no—
333C2×C4—1723no—
334C2×C4—1723no—
335C2×C4—1723no—
336C2×C4—1723no—
337C22—46no—
338C22—46no—
339C22—42no—
340C22—83no—
341C22—81no—
342C22—81no—
343C22—83no—
344C22#41×Dic4313yes—
345C22#1458337413yes—
346C22#1458337711yescharacteristic
347C22#126×D4311yescharacteristic
348C22#1458343213yes—
349C22#1458348113yes—
350C22#1458348113yes—
351C22#1458349513yes—
352C22#1458349513yes—
353C22#1458349913yes—
354C22#1458349913yes—
355C22#1458351913yes—
356C22#1458351913yes—
357C4—46no—
358C4—46no—
359C4—864no—
360C4—3443no—
361C4—3441no—
362C4—1726no—
363C2—82no—
364C2#126×Dic4311yescharacteristic
365C2#1913735313yes—
366C2#1913736213yes—
367C2#1914055211yescharacteristic
368C2#1914055711yescharacteristic
369C2#1914060313yes—
370C2#1914063513yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC2×C43×#396C2
socle, cosocleC24×C43C24
prime radicalC25×C43C23
hypercenterC2×#396D43
hypocenterC43#14331
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. #19132863C2semidirect
2. #19132857C2semidirect
5. #19132827C2semidirect
6. #95×Dic43C2semidirect
20. C43×#396C4semidirect
198. #396Dic43semidirect
207. C43#14331semidirect

Maximal subgroups

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

subgroupindex
#191328632
#191328572
#191328442
#191328322
#191328272
#95×Dic432
C2×C43×#3962
#1433143