Finite Group Databasebeta

← #25017810

Subgroups — #25017810

Order 11008.

2606 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4×Dic43C211yesmaximal, characteristic
2C2×#14582760C212yesmaximal
3C2×C22⋊C4×Dic43C212yesmaximal
4#19132821C214yesmaximal, complemented
5#19132818C211yesmaximal, characteristic
6#95×Dic43C214yesmaximal, complemented
7C43×C22⋊#95C211yesmaximal, characteristic
8C24×Dic43C2211yescharacteristic
9C24×Dic43C2211yescharacteristic
10C22×C22⋊Dic43C2212yes—
11C22×C4×Dic43—28no—
12C22×C4×Dic43C418yescomplemented
13C22×C4×Dic43C2214yes—
14C22×C4×Dic43C2212yes—
15C22×C4×Dic43C2212yes—
16#14582760C4116yescomplemented
17C22⋊C4×Dic43—28no—
18C2×C43⋊#95C2214yes—
19C2×C43⋊#95C2214yes—
20C2×C43⋊#95C2218yes—
21C24×C4×C43C2211yescharacteristic
22C22×C22⋊C4×C43C2212yes—
23C2×#95×C43C2214yes—
24C23×Dic43—24no—
25C23×Dic43—22no—
26C23×Dic43—22no—
27C23×Dic43—28no—
28C23×Dic43C2×C414yes—
29C23×Dic43C2×C418yes—
30C23×Dic43C2×C414yes—
31C23×Dic43D418yes—
32C23×Dic43C2314yes—
33C23×Dic43C2312yes—
34C23×Dic43C2311yescharacteristic
35C23×Dic43C2311yescharacteristic
36C2×C22⋊Dic43—24no—
37C2×C22⋊Dic43—24no—
38C2×C22⋊Dic43C2×C418yes—
39C2×C4×Dic43—232no—
40C2×C4×Dic43—28no—
41C2×C4×Dic43—28no—
42C2×C4×Dic43—28no—
43C2×C4×Dic43—216no—
44C2×C4×Dic43C2×C418yes—
45C2×C4×Dic43C2×C418yes—
46C43⋊#95—28no—
47C43⋊#95—28no—
48C43⋊#95C2×C4132yescomplemented
49C25×C43C2311yescharacteristic
50C23×C4×C43—24no—
51C23×C4×C43—28no—
52C23×C4×C43C2×C414yes—
53C23×C4×C43C2314yes—
54C23×C4×C43C2312yes—
55C2×C22⋊C4×C43—24no—
56C2×C22⋊C4×C43—24no—
57C2×C22⋊C4×C43C2×C418yes—
58#95×C43—28no—
59C24×C43—24no—
60C24×C43—24no—
61C24×C43C22×C412yes—
62C24×C43C22×C414yes—
63C24×C43C2×D414yes—
64C24×C43#4112yes—
65C24×C43#4112yes—
66C24×C43C2411yescharacteristic
67C22×C4×C43—232no—
68C22×C4×C43—216no—
69C22×C4×C43—28no—
70C22×C4×C43—24no—
71C22×C4×C43—24no—
72C22×C4×C43—24no—
73C22×C4×C43—28no—
74C22×C4×C43—24no—
75C22×C4×C43—28no—
76C22×C4×C43C22×C418yes—
77C22×C4×C43C22×C414yes—
78C22×C4×C43#4118yes—
79C22×Dic43—216no—
80C22×Dic43—232no—
81C22×Dic43—28no—
82C22×Dic43—28no—
83C22×Dic43—216no—
84C22×Dic43—216no—
85C22×Dic43—24no—
86C22×Dic43—24no—
87C22×Dic43—24no—
88C22×Dic43—22no—
89C22×Dic43—22no—
90C22×Dic43—28no—
91C22×Dic43—28no—
92C22×Dic43—24no—
93C22×Dic43C42116yescomplemented
94C22×Dic43C22⋊C4116yes—
95C22×Dic43C22×C418yes—
96C22×Dic43C22×C418yes—
97C22×Dic43C22×C414yes—
98C22×Dic43C22×C412yes—
99C22×Dic43C22×C412yes—
100C22×Dic43C2×D414yes—
101C22×Dic43C2×D414yes—
102C22×Dic43#4118yes—
103C22⋊C4×C43—216no—
104C22⋊Dic43—216no—
105C4×Dic43—216no—
106C4×Dic43—216no—
107C4×Dic43—416no—
108C23×C43—24no—
109C23×C43—24no—
110C23×C43—216no—
111C23×C43—28no—
112C23×C43—28no—
113C23×C43—28no—
114C23×C43—28no—
115C23×C43C2×C4214yes—
116C23×C43C2×C22⋊C414yes—
117C23×C43#11714yes—
118C23×C43C4×D418yes—
119C23×C43C4×D418yes—
120C23×C43C23×C411yescharacteristic
121C23×C43C23×C412yes—
122C23×C43C22×D412yes—
123C23×C43C2×#4114yes—
124C23×C43C2×#4111yescharacteristic
125C23×C43C2×#4114yes—
126C23×C43C2×#4111yescharacteristic
127C2×C4×C43—232no—
128C2×C4×C43—24no—
129C2×C4×C43—24no—
130C2×C4×C43—216no—
131C2×C4×C43—28no—
132C2×C4×C43—216no—
133C2×C4×C43—44no—
134C2×C4×C43—44no—
135C2×C4×C43—48no—
136C2×C4×C43#11718yes—
137C2×Dic43—24no—
138C2×Dic43—24no—
139C2×Dic43—24no—
140C2×Dic43—28no—
141C2×Dic43—28no—
142C2×Dic43—28no—
143C2×Dic43—232no—
144C2×Dic43—232no—
145C2×Dic43—28no—
146C2×Dic43—216no—
147C2×Dic43—44no—
148C2×Dic43—44no—
149C2×Dic43—48no—
150C2×Dic43C2×C4218yes—
151C2×Dic43C2×C22⋊C414yes—
152C2×Dic43C2×C22⋊C414yes—
153C2×Dic43#11718yes—
154C2×Dic43#123116yes—
155C4×#381—431nomaximal, Sylow
156C22×C43—28no—
157C22×C43—24no—
158C22×C43—24no—
159C22×C43—28no—
160C22×C43—216no—
161C22×C43—216no—
162C22×C43C4×C22⋊C418yes—
163C22×C43C22×C4211yescharacteristic
164C22×C43C22×C22⋊C411yescharacteristic
165C22×C43C2×#11712yes—
166C22×C43C2×#11712yes—
167C22×C43C2×#11711yescharacteristic
168C22×C43C2×C4×D412yes—
169C22×C43C2×C4×D412yes—
170C22×C43C4×#4118yes—
171C22×C43C2×#12314yes—
172C22×C43#52514yes—
173C22×C43#52914yes—
174C22×C43#52914yes—
175C4×C43—28no—
176C4×C43—48no—
177Dic43—28no—
178Dic43—24no—
179Dic43—48no—
180Dic43#38118yescomplemented
181C23×C42—431no—
182C2×#381—432no—
183C2×C4×C22⋊C4—432no—
184#1434—434no—
185C22⋊#95—431no—
186C22⋊#95D4311yescharacteristic
187C4×#95—434no—
188C2×C43—28no—
189C2×C43C2×C4×C22⋊C411yescharacteristic
190C2×C43C4×#11712yes—
191C2×C43C2×#38111yescharacteristic
192C2×C43#228011yescharacteristic
193C2×C43#228312yes—
194C2×C43C4×#12314yes—
195C2×C43C4×#12314yes—
196C24×C4—431no—
197C24×C4—431no—
198C24×C4C2×D4311yescharacteristic
199C22×C22⋊C4—432no—
200C22×C22⋊C4C2×D4312yes—
201C22×C42—432no—
202C22×C42—432no—
203C22×C42—438no—
204C22×C42—434no—
205C22×C42—868no—
206#381—4316no—
207C4×C22⋊C4—868no—
208C2×#95—438no—
209C2×#95—434no—
210C2×#95—434no—
211C2×#95C2×D4314yes—
212C43C4×#38111yescharacteristic, complemented, Sylow
213C25C22×D4311yescharacteristic
214C23×C4—24no—
215C23×C4—28no—
216C23×C4—431no—
217C23×C4—438no—
218C23×C4—434no—
219C23×C4—434no—
220C23×C4—438no—
221C23×C4—432no—
222C23×C4—431no—
223C23×C4—434no—
224C23×C4—868no—
225C23×C4—864no—
226C23×C4—862no—
227C23×C4—862no—
228C23×C4C4×D4314yes—
229C23×C4C22×D4314yes—
230C23×C4C22×D4312yes—
231C2×C22⋊C4—24no—
232C2×C22⋊C4—24no—
233C2×C22⋊C4—438no—
234C2×C22⋊C4—864no—
235C2×C22⋊C4—864no—
236C2×C22⋊C4C4×D4318yes—
237C2×C42—438no—
238C2×C42—438no—
239C2×C42—8632no—
240C2×C42—868no—
241C2×C42—868no—
242C2×C42—868no—
243C2×C42—8616no—
244#95—28no—
245#95—4332no—
246#95—868no—
247#95—868no—
248C24—24no—
249C24—24no—
250C24C2×C4×D4312yes—
251C24C2×C4×D4314yes—
252C24D4×D4314yes—
253C24#1062190012yes—
254C24#1062190212yes—
255C24C23×D4311yescharacteristic
256C22×C4—232no—
257C22×C4—28no—
258C22×C4—24no—
259C22×C4—24no—
260C22×C4—216no—
261C22×C4—24no—
262C22×C4—28no—
263C22×C4—28no—
264C22×C4—24no—
265C22×C4—432no—
266C22×C4—434no—
267C22×C4—438no—
268C22×C4—4316no—
269C22×C4—4316no—
270C22×C4—438no—
271C22×C4—434no—
272C22×C4—432no—
273C22×C4—434no—
274C22×C4—438no—
275C22×C4—8616no—
276C22×C4—8632no—
277C22×C4—868no—
278C22×C4—868no—
279C22×C4—8616no—
280C22×C4—8616no—
281C22×C4—864no—
282C22×C4—864no—
283C22×C4—862no—
284C22×C4—862no—
285C22×C4—864no—
286C22×C4—868no—
287C22×C4—868no—
288C22×C4—864no—
289C22×C4C2×C4×D4318yes—
290C22×C4C2×C4×D4314yes—
291C22×C4#1062190018yes—
292C22⋊C4—216no—
293C22⋊C4—8616no—
294C42—8616no—
295C42—8616no—
296C42—17216no—
297C23—24no—
298C23—24no—
299C23—216no—
300C23—28no—
301C23—28no—
302C23—28no—
303C23—28no—
304C23C42×D4314yes—
305C23C22⋊C4×D4314yes—
306C23#1306328314yes—
307C23(C22⋊D43)⋊C418yes—
308C23#1306328718yes—
309C23C22×C4×D4311yescharacteristic
310C23C22×C4×D4312yes—
311C23C2×D4×D4312yes—
312C23#41×D4314yes—
313C23C2×#1062190014yes—
314C23C2×#1062190011yescharacteristic
315C23C2×#1062190211yescharacteristic
316C2×C4—232no—
317C2×C4—24no—
318C2×C4—24no—
319C2×C4—216no—
320C2×C4—28no—
321C2×C4—216no—
322C2×C4—44no—
323C2×C4—44no—
324C2×C4—48no—
325C2×C4—434no—
326C2×C4—438no—
327C2×C4—4316no—
328C2×C4—438no—
329C2×C4—434no—
330C2×C4—8632no—
331C2×C4—864no—
332C2×C4—864no—
333C2×C4—864no—
334C2×C4—868no—
335C2×C4—868no—
336C2×C4—868no—
337C2×C4—8632no—
338C2×C4—868no—
339C2×C4—8616no—
340C2×C4—1724no—
341C2×C4—1724no—
342C2×C4—1728no—
343C2×C4#1306328118yes—
344C22—216no—
345C22—216no—
346C22—28no—
347C22—24no—
348C22—24no—
349C22—28no—
350C22#1458274618yes—
351C22C2×C42×D4311yescharacteristic
352C22C2×C22⋊C4×D4311yescharacteristic
353C22#117×D4312yes—
354C22C2×#1306328112yes—
355C22C2×#1306328311yescharacteristic
356C22C2×(C22⋊D43)⋊C412yes—
357C22C2×#1306328712yes—
358C22C4×#1062190018yes—
359C22#123×D4314yes—
360C22#1458340514yes—
361C22#1458343014yes—
362C22#1458343514yes—
363C4—28no—
364C4—48no—
365C4—438no—
366C4—868no—
367C4—864no—
368C4—1728no—
369C2—28no—
370C2C2×#1458274611yescharacteristic
371C2C4×#1306328112yes—
372C2#381×D4311yescharacteristic
373C2#1913697311yescharacteristic
374C2#1913699012yes—
375C2#1913711414yes—
376C2#1913712014yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC22×C43C22×C42
FittingC43×C22⋊#95C2
socle, cosocleC24×C43C24
prime radicalC25×C43C23
hypercenterC22⋊#95D43
hypocenterC43C4×#381
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
4. #19132821C2semidirect
6. #95×Dic43C2semidirect
12. C22×C4×Dic43C4semidirect
16. #14582760C4semidirect
48. C43⋊#95C2×C4semidirect
93. C22×Dic43C42semidirect
180. Dic43#381semidirect
212. C43C4×#381semidirect

Maximal subgroups

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

subgroupindex
C23×C4×Dic432
C2×#145827602
C2×C22⋊C4×Dic432
#191328212
#191328182
#95×Dic432
C43×C22⋊#952
C4×#38143