Finite Group Databasebeta

← #25097084

Subgroups — #25097084

Order 11008.

1110 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
1C2×#14582955C212yesmaximal
2C43×D43C211yesmaximal, characteristic
3#19134747C211yesmaximal, characteristic, complemented
4#19134711C212yesmaximal, complemented
5#19134572C214yesmaximal
6#19134450C214yesmaximal, complemented
7C43×#1842C211yesmaximal, characteristic, complemented
8C2×C42×D43C412yes—
9C2×C42×D43C411yescharacteristic
10C2×C42×D43C411yescharacteristic
11C2×C42×D43C2212yes—
12C2×C42×D43C2211yescharacteristic
13#14582955—28no—
14C2×C4⋊(C43⋊C8)C2212yes—
15C2×C4⋊(C43⋊C8)C2214yes—
16C2×(C2×D43)⋊C8C2214yes—
17C2×#13063235C2214yes—
18C42×Dic43C412yes—
19C42×Dic43C411yescharacteristic
20C42×Dic43C411yescharacteristic
21C42×Dic43C2212yes—
22C42×Dic43C2211yescharacteristic
23#14582653C2218yes—
24C2×C4⋊C8×C43C2212yes—
25C2×C4⋊C8×C43C2214yes—
26C43×C43C2211yescharacteristic
27C22×C4×D43C2×C412yes—
28C22×C4×D43C2×C411yescharacteristic
29C22×C4×D43C2×C411yescharacteristic
30C22×C4×D43C2×C412yes—
31C22×C4×D43C2311yescharacteristic
32C22×C43⋊C8C2314yes—
33C2×C4×Dic43C2×C412yes—
34C2×C4×Dic43C2×C412yes—
35C2×C4×Dic43C2×C411yescharacteristic
36C2×C4×Dic43C2×C412yes—
37C2×C4×Dic43C2×C412yes—
38C2×C4×Dic43C2×C412yes—
39C2×C4×Dic43C2×C412yes—
40C2×C4×Dic43C2×C412yes—
41C2×C4×Dic43C2×C411yescharacteristic
42C2×C4×Dic43C2×C411yescharacteristic
43C2×C4×Dic43C2×C411yescharacteristic
44C2×C4×Dic43C2312yes—
45C2×C4×Dic43C2311yescharacteristic
46C42×D43—28no—
47C42×D43—24no—
48C42×D43—24no—
49C42×D43—24no—
50C42×D43—24no—
51C42×D43D414yes—
52C42×D43Q814yes—
53C4⋊(C43⋊C8)—24no—
54C4⋊(C43⋊C8)—28no—
55(C2×D43)⋊C8—28no—
56#13063235—28no—
57C22×C8×C43C2314yes—
58C2×C42×C43C2×C412yes—
59C2×C42×C43C2×C411yescharacteristic
60C2×C42×C43C2×C411yescharacteristic
61C2×C42×C43C2311yescharacteristic
62C2×C42×C43C2312yes—
63C4⋊C8×C43—24no—
64C4⋊C8×C43—28no—
65C23×D43C22×C411yescharacteristic
66C22×C4×C43C22×C411yescharacteristic
67C22×C4×C43C22×C412yes—
68C22×C4×C43C22×C411yescharacteristic
69C22×C4×C43C22×C412yes—
70C22×C4×C43C2411yescharacteristic
71C22×Dic43C22×C411yescharacteristic
72C22×Dic43C22×C411yescharacteristic
73C22×Dic43C22×C411yescharacteristic
74C22×Dic43C22×C412yes—
75C22×Dic43C22×C412yes—
76C2×C4×D43—24no—
77C2×C4×D43—24no—
78C2×C4×D43—22no—
79C2×C4×D43—22no—
80C2×C4×D43—24no—
81C2×C4×D43—22no—
82C2×C4×D43—22no—
83C2×C4×D43—24no—
84C2×C4×D43—24no—
85C2×C4×D43—24no—
86C2×C4×D43C4⋊C414yes—
87C2×C4×D43C4⋊C414yes—
88C2×C4×D43M1618yes—
89C2×C4×D43C2×D412yes—
90C2×C4×D43C2×Q812yes—
91C2×C8×C43—24no—
92C2×C8×C43—28no—
93C42×C43—22no—
94C42×C43—24no—
95C42×C43M1614yes—
96C42×C43C2×D412yes—
97C42×C43C2×Q812yes—
98C42×C43#4114yes—
99C42×C43#4114yes—
100C4×Dic43—24no—
101C4×Dic43—24no—
102C4×Dic43—24no—
103C4×Dic43—22no—
104C4×Dic43—24no—
105C4×Dic43—22no—
106C4×Dic43—22no—
107C4×Dic43—24no—
108C4×Dic43—24no—
109C4×Dic43—24no—
110C4×Dic43C4⋊C414yes—
111C4×Dic43C4⋊C414yes—
112C4×Dic43M1614yes—
113C4×Dic43C2×D412yes—
114C4×Dic43C2×Q812yes—
115C2×C43⋊C8—24no—
116C2×C43⋊C8—28no—
117C23×C43C23×C411yescharacteristic
118C22×D43—22no—
119C22×D43—21no—
120C22×D43—21no—
121C22×D43C2×C4⋊C412yes—
122C22×D43C2×M1614yes—
123C2×C4×C43—22no—
124C2×C4×C43—22no—
125C2×C4×C43—22no—
126C2×C4×C43C2×C4⋊C412yes—
127C2×C4×C43C2×C4⋊C412yes—
128C2×C4×C43#11714yes—
129C2×C4×C43#11714yes—
130C2×C4×C43C2×M1612yes—
131C2×C4×C43C2×M1614yes—
132C2×C4×C43C2×M1612yes—
133C2×C4×C43C2×M1614yes—
134C2×C4×C43C22×D411yescharacteristic
135C2×C4×C43C22×Q811yescharacteristic
136C2×C4×C43C2×#4112yes—
137C2×C4×C43C2×#4112yes—
138C2×Dic43—22no—
139C2×Dic43—22no—
140C2×Dic43—22no—
141C2×Dic43—22no—
142C2×Dic43—21no—
143C2×Dic43—22no—
144C2×Dic43—21no—
145C2×Dic43—22no—
146C2×Dic43C2×C4⋊C412yes—
147C2×Dic43C2×C4⋊C412yes—
148C2×Dic43C2×C4⋊C412yes—
149C2×Dic43C2×M1614yes—
150C2×Dic43C2×M1614yes—
151C4×D43—216no—
152C4×D43—28no—
153C4×D43—22no—
154C4×D43—22no—
155C4×D43—24no—
156C4×D43—28no—
157C4×D43—216no—
158C8×C43—44no—
159C43⋊C8—44no—
160#20810—431nomaximal, Sylow
161C22×C43C22×C4⋊C411yescharacteristic
162C22×C43C2×#11712yes—
163C22×C43C22×M1612yes—
164C22×C43C22×M1611yescharacteristic
165C22×C43C22×M1611yescharacteristic
166C2×D43—22no—
167C2×D43—24no—
168C2×D43—24no—
169C2×D43—22no—
170C2×D43#42314yes—
171C4×C43—22no—
172C4×C43—24no—
173C4×C43#42314yes—
174C4×C43#43218yescomplemented
175C4×C43#53211yescharacteristic
176C4×C43#53211yescharacteristic
177C4×C43#53312yes—
178Dic43—22no—
179Dic43—22no—
180Dic43—24no—
181Dic43—24no—
182Dic43—22no—
183C2×#432—432no—
184C2×C43—431no—
185#1842—431no—
186#1842D4311yescharacteristic, complemented
187#1831—432no—
188#1797—434no—
189#1767—434no—
190C2×C43#228511yescharacteristic
191C2×C43C2×#42311yescharacteristic
192C2×C43C2×#42311yescharacteristic
193C2×C43C2×#43212yes—
194C2×C43#292012yes—
195D43—24no—
196C22×C42—431no—
197C22×C42—432no—
198C22×C42—431no—
199C22×C42—432no—
200C22×C42—431no—
201#432—868no—
202C2×C4⋊C8—434no—
203C2×C4⋊C8—432no—
204C2×C4⋊C8C2×D4314yes—
205C2×C4⋊C8C2×D4312yes—
206C2×C22⋊C8—434no—
207C2×#97—434no—
208C43—431no—
209C43—432no—
210C43—431no—
211C43—432no—
212C43—431no—
213C43C2×D4311yescharacteristic
214#336—438no—
215C43#2081011yescharacteristic, complemented, Sylow
216C23×C4—431no—
217C23×C4—431no—
218C23×C4—432no—
219C23×C4—431no—
220C23×C4—432no—
221C22×C8—434no—
222C22×C8C22×D4314yes—
223C2×C42—431no—
224C2×C42—431no—
225C2×C42—431no—
226C2×C42—431no—
227C2×C42—434no—
228C2×C42—434no—
229C2×C42—432no—
230C2×C42—432no—
231C2×C42—432no—
232C2×C42—432no—
233C2×C42—432no—
234C2×C42—432no—
235C2×C42—431no—
236C2×C42—432no—
237C2×C42—432no—
238C2×C42—864no—
239C2×C42—868no—
240C2×C42—864no—
241C2×C42—864no—
242C2×C42—864no—
243C2×C42C4×D4312yes—
244C2×C42C4×D4311yescharacteristic
245C2×C42C4×D4311yescharacteristic
246C2×C42C22×D4311yescharacteristic
247C2×C42C22×D4312yes—
248C4⋊C8—24no—
249C4⋊C8—28no—
250C4⋊C8—864no—
251C4⋊C8—868no—
252C22⋊C8—868no—
253#97—868no—
254C24—431no—
255C22×C4—431no—
256C22×C4—431no—
257C22×C4—431no—
258C22×C4—432no—
259C22×C4—432no—
260C22×C4—434no—
261C22×C4—434no—
262C22×C4—438no—
263C22×C4—432no—
264C22×C4—432no—
265C22×C4—864no—
266C22×C4—864no—
267C22×C4—864no—
268C22×C4—864no—
269C22×C4—864no—
270C22×C4—862no—
271C22×C4—862no—
272C22×C4—864no—
273C22×C4—862no—
274C22×C4—862no—
275C22×C4C2×C4×D4311yescharacteristic
276C22×C4C2×C4×D4312yes—
277C22×C4C2×C4×D4311yescharacteristic
278C22×C4C2×C4×D4312yes—
279C22×C4C23×D4311yescharacteristic
280C2×C8—24no—
281C2×C8—28no—
282C2×C8—864no—
283C2×C8—868no—
284C42—22no—
285C42—24no—
286C42—434no—
287C42—434no—
288C42—434no—
289C42—432no—
290C42—432no—
291C42—864no—
292C42—864no—
293C42—864no—
294C42—864no—
295C42—864no—
296C42—864no—
297C42—862no—
298C42—864no—
299C42—862no—
300C42—862no—
301C42#1062187214yes—
302C42D4×D4312yes—
303C42#1062190014yes—
304C42Q8×D4312yes—
305C42#1062190214yes—
306C23—432no—
307C23—434no—
308C23—862no—
309C23—861no—
310C23—861no—
311C23C22×C4×D4311yescharacteristic
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—432no—
316C2×C4—432no—
317C2×C4—432no—
318C2×C4—434no—
319C2×C4—434no—
320C2×C4—868no—
321C2×C4—8616no—
322C2×C4—862no—
323C2×C4—862no—
324C2×C4—862no—
325C2×C4—862no—
326C2×C4—862no—
327C2×C4—861no—
328C2×C4—862no—
329C2×C4—861no—
330C2×C4—868no—
331C2×C4—862no—
332C2×C4—862no—
333C2×C4—864no—
334C2×C4—8616no—
335C2×C4C4⋊C4×D4312yes—
336C2×C4C4⋊C4×D4312yes—
337C2×C4#1306328314yes—
338C2×C4#1306328314yes—
339C2×C4M16×D4312yes—
340C2×C4M16×D4314yes—
341C2×C4C2×#1062187212yes—
342C2×C4C2×#1062187214yes—
343C2×C4C2×D4×D4311yescharacteristic
344C2×C4C2×Q8×D4311yescharacteristic
345C2×C4C2×#1062190012yes—
346C2×C4C2×#1062190212yes—
347C8—44no—
348C8—1724no—
349C22—434no—
350C22—864no—
351C22—864no—
352C22—862no—
353C22—862no—
354C22C2×C4⋊C4×D4311yescharacteristic
355C22C2×#1306328312yes—
356C22C2×M16×D4312yes—
357C22C2×M16×D4311yescharacteristic
358C22C22×#1062187211yescharacteristic
359C4—24no—
360C4—22no—
361C4—864no—
362C4—864no—
363C4—862no—
364C4—862no—
365C4—862no—
366C4#1458292114yes—
367C4#1458295518yescomplemented
368C4#1458344711yescharacteristic
369C4#1458345011yescharacteristic
370C4#1458345412yes—
371C2—864no—
372C2#1913700011yescharacteristic
373C2#423×D4311yescharacteristic
374C2C2×#1458292111yescharacteristic
375C2C2×#1458295512yes—
376C2#1914322712yes—
subgroupG/H
center, FrattiniC22×C4C23×D43
commutator, socleC23×C43C23×C4
FittingC43×#1842C2
prime radicalC23×D43C22×C4
cosocleC22×C4×C43C24
hypercenter#1842D43
hypocenterC43#20810
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ #1842

Complements

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

NH ≅ G/Ntype
3. #19134747C2semidirect
4. #19134711C2semidirect
6. #19134450C2semidirect
7. C43×#1842C2semidirect
174. C4×C43#432semidirect
186. #1842D43semidirect
215. C43#20810semidirect
367. C4#14582955semidirect

Maximal subgroups

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

subgroupindex
C2×#145829552
C43×D432
#191347472
#191347112
#191345722
#191344502
C43×#18422
#2081043