Finite Group Databasebeta

← #24996671

Subgroups — #24996671

Order 11008.

566 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19142905C211yesmaximal, characteristic
2#19132822C211yesmaximal, characteristic
3#19132475C212yesmaximal
4#19132475C212yesmaximal
5C4×C22⋊C8×C43C211yesmaximal, characteristic
6C2×#13063317C411yescharacteristic, complemented
7#14582797C411yescharacteristic, complemented
8#14582797C411yescharacteristic, complemented
9#14582783—21no—
10#14582783—21no—
11#14582772—21no—
12#14582772—21no—
13#14582765C411yescharacteristic, complemented
14#14582759C2211yescharacteristic
15#14582759C2211yescharacteristic
16C2×C43⋊#95—21no—
17C2×C43⋊#95—21no—
18C2×C43⋊#95C2212yes—
19C22×C42×C43C2211yescharacteristic
20C2×C22⋊C8×C43C2212yes—
21C2×C4×C8×C43—21no—
22C43×#336—21no—
23C23×Dic43—22no—
24#13063317—42no—
25C2×C4⋊Dic43C2×C411yescharacteristic
26C2×C4⋊Dic43C2×C411yescharacteristic
27C2×C4⋊Dic43C2×C411yescharacteristic
28C2×C4⋊Dic43C2×C411yescharacteristic
29C2×Dic43⋊C4—21no—
30C2×Dic43⋊C4—21no—
31C2×Dic43⋊C4—21no—
32C2×Dic43⋊C4—21no—
33C2×C22⋊Dic43—21no—
34C2×C22⋊Dic43—21no—
35C43⋊#95—24no—
36C43⋊#95—21no—
37C43⋊#95—21no—
38C43⋊#95—21no—
39C43⋊#95—21no—
40C43⋊#95—21no—
41C43⋊#95—21no—
42C43⋊#95—24no—
43C43⋊#95—42no—
44C23×C4×C43D411yescharacteristic
45C23×C4×C43D411yescharacteristic
46C23×C4×C43C2311yescharacteristic
47C22×C8×C43—22no—
48C2×C42×C43—42no—
49C2×C42×C43C2×C411yescharacteristic
50C2×C42×C43C2×C411yescharacteristic
51C2×C42×C43D411yescharacteristic
52C2×C42×C43D411yescharacteristic
53C22⋊C8×C43—22no—
54C22⋊C8×C43Q814yes—
55C4×C8×C43—42no—
56C24×C43C2×D411yescharacteristic
57C22×C4×C43—22no—
58C22×C4×C43—22no—
59C22×C4×C43—22no—
60C22×C4×C43—22no—
61C22×C4×C43—41no—
62C22×C4×C43—41no—
63C22×C4×C43—41no—
64C22×C4×C43—41no—
65C22×C4×C43C22⋊C411yescharacteristic
66C22×C4×C43C22⋊C411yescharacteristic
67C22×C4×C43C22⋊C411yescharacteristic
68C22×C4×C43C22⋊C411yescharacteristic
69C22×C4×C43C22×C411yescharacteristic
70C22×C4×C43C2×D411yescharacteristic
71C22×C4×C43C2×Q812yes—
72C22×C4×C43#4112yes—
73C22×Dic43—24no—
74C22×Dic43—21no—
75C22×Dic43—21no—
76C22×Dic43—21no—
77C22×Dic43—21no—
78C22×Dic43—42no—
79C22×Dic43—42no—
80C22×Dic43—42no—
81C22×Dic43—42no—
82C22×Dic43—42no—
83C22×Dic43—42no—
84C2×C8×C43—24no—
85C2×C8×C43—42no—
86C2×C8×C43—42no—
87C42×C43—22no—
88C42×C43—22no—
89C42×C43—41no—
90C42×C43—41no—
91C22⋊Dic43—42no—
92C22⋊Dic43—42no—
93C4⋊Dic43—41no—
94C4⋊Dic43—41no—
95C4⋊Dic43—41no—
96C4⋊Dic43—41no—
97Dic43⋊C4—42no—
98Dic43⋊C4—42no—
99Dic43⋊C4—42no—
100Dic43⋊C4—42no—
101C23×C43—21no—
102C23×C43—21no—
103C23×C43—21no—
104C23×C43—21no—
105C23×C43C2×C22⋊C411yescharacteristic
106C23×C43#12411yescharacteristic
107C23×C43C4⋊Q811yescharacteristic
108C23×C43#13512yes—
109C23×C43#13512yes—
110C2×C4×C43—21no—
111C2×C4×C43—21no—
112C2×C4×C43—21no—
113C2×C4×C43—21no—
114C2×C4×C43—21no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—42no—
125C2×C4×C43—42no—
126C2×C4×C43—44no—
127C2×C4×C43—44no—
128C2×C4×C43#9912yes—
129C2×C4×C43#10412yes—
130C2×C4×C43C4×Q812yes—
131C2×C4×C43C22⋊Q812yes—
132C2×Dic43—44no—
133C2×Dic43—44no—
134C2×Dic43—44no—
135C2×Dic43—41no—
136C2×Dic43—41no—
137C2×Dic43—41no—
138C2×Dic43—41no—
139C2×Dic43—41no—
140C2×Dic43—41no—
141C2×Dic43—41no—
142C2×Dic43—41no—
143C2×Dic43—41no—
144C2×Dic43—41no—
145C2×Dic43—41no—
146C2×Dic43—41no—
147C2×Dic43—82no—
148C2×Dic43—82no—
149C2×Dic43—82no—
150C2×Dic43—82no—
151C8×C43—44no—
152#9886—431nomaximal, Sylow
153C22×C43—21no—
154C22×C43—21no—
155C22×C43—21no—
156C22×C43—21no—
157C22×C43—22no—
158C22×C43—22no—
159C22×C43—22no—
160C22×C43—22no—
161C22×C43#39111yescharacteristic
162C22×C43C2×#9911yescharacteristic
163C22×C43#41011yescharacteristic
164C22×C43#41611yescharacteristic
165C22×C43#41611yescharacteristic
166C22×C43C2×#10411yescharacteristic
167C22×C43#42111yescharacteristic
168C22×C43#48812yes—
169C22×C43#49912yes—
170C4×C43—22no—
171C4×C43—22no—
172C4×C43—22no—
173C4×C43—22no—
174C4×C43—41no—
175C4×C43—41no—
176Dic43—84no—
177Dic43—81no—
178Dic43—81no—
179Dic43—81no—
180Dic43—81no—
181#2851—431no—
182C4×C22⋊C8D4311yescharacteristic
183#1434—431no—
184#1294—432no—
185#1294—432no—
186C2×C43—22no—
187C2×C43—22no—
188C2×C43#150011yescharacteristic
189C2×C43#150111yescharacteristic
190C2×C43#151611yescharacteristic
191C2×C43#152111yescharacteristic
192C2×C43#198611yescharacteristic
193C2×C43#199111yescharacteristic
194C2×C43#199611yescharacteristic
195C2×#125—431no—
196C22×C42C2×D4311yescharacteristic
197C2×C22⋊C8C2×D4312yes—
198C2×C4×C8—21no—
199#389—431no—
200#389—431no—
201#387—861no—
202#387—861no—
203#385—861no—
204#385—861no—
205#382—431no—
206#380—431no—
207#380—431no—
208C2×#95—432no—
209C2×#95—861no—
210C2×#95—861no—
211#336—21no—
212C43#988611yescharacteristic, complemented, Sylow
213C23×C4—862no—
214C23×C4D17211yescharacteristic
215C23×C4D17211yescharacteristic
216C23×C4C22×D4311yescharacteristic
217C22×C8—22no—
218#125—1722no—
219C2×C4⋊C4—431no—
220C2×C4⋊C4—431no—
221C2×C4⋊C4—431no—
222C2×C4⋊C4—431no—
223C2×C4⋊C4—861no—
224C2×C4⋊C4—861no—
225C2×C4⋊C4—861no—
226C2×C4⋊C4—861no—
227C2×C22⋊C4—861no—
228C2×C22⋊C4—861no—
229C2×C42—42no—
230C2×C42C4×D4311yescharacteristic
231C2×C42C4×D4311yescharacteristic
232C2×C42C22⋊D4311yescharacteristic
233C2×C42C22⋊D4311yescharacteristic
234C22⋊C8—22no—
235C22⋊C8Dic8614yes—
236C4×C8—42no—
237#95—864no—
238#95—861no—
239#95—861no—
240#95—861no—
241#95—861no—
242#95—861no—
243#95—861no—
244#95—864no—
245#95—1722no—
246C24C2×D17211yescharacteristic
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—41no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4—864no—
256C22×C4—861no—
257C22×C4—861no—
258C22×C4—861no—
259C22×C4—861no—
260C22×C4—1722no—
261C22×C4—1722no—
262C22×C4—1722no—
263C22×C4—1722no—
264C22×C4—1722no—
265C22×C4—1722no—
266C22×C4(C2×D43)⋊C411yescharacteristic
267C22×C4(C2×D43)⋊C411yescharacteristic
268C22×C4(C2×D43)⋊C411yescharacteristic
269C22×C4(C2×D43)⋊C411yescharacteristic
270C22×C4C2×Dic8612yes—
271C22×C4C2×C4×D4311yescharacteristic
272C22×C4#1062189812yes—
273C22×C4C2×C22⋊D4311yescharacteristic
274C2×C8—24no—
275C2×C8—42no—
276C2×C8—42no—
277C4⋊C4—1721no—
278C4⋊C4—1721no—
279C4⋊C4—1721no—
280C4⋊C4—1721no—
281C4⋊C4—1722no—
282C4⋊C4—1722no—
283C4⋊C4—1722no—
284C4⋊C4—1722no—
285C22⋊C4—1722no—
286C22⋊C4—1722no—
287C42—22no—
288C42—22no—
289C42—41no—
290C42—41no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23C2×(C2×D43)⋊C411yescharacteristic
296C23#1306331311yescharacteristic
297C23#1306332511yescharacteristic
298C23#1306334712yes—
299C23#1306334712yes—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—44no—
317C2×C4—44no—
318C2×C4—3442no—
319C2×C4—3442no—
320C2×C4—3442no—
321C2×C4—3442no—
322C2×C4—1724no—
323C2×C4—1724no—
324C2×C4—1724no—
325C2×C4—1721no—
326C2×C4—1721no—
327C2×C4—1721no—
328C2×C4—1721no—
329C2×C4—1721no—
330C2×C4—1721no—
331C2×C4—1721no—
332C2×C4—1721no—
333C2×C4—1721no—
334C2×C4—1721no—
335C2×C4—1721no—
336C2×C4—1721no—
337C2×C4#1306323912yes—
338C2×C4#1306325112yes—
339C2×C4C4×Dic8612yes—
340C2×C4#1306330412yes—
341C8—44no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—22no—
347C22—22no—
348C22—22no—
349C22—22no—
350C22#1458280511yescharacteristic
351C22C2×#1306323911yescharacteristic
352C22#1458287211yescharacteristic
353C22#1458289611yescharacteristic
354C22#1458289611yescharacteristic
355C22C2×#1306325111yescharacteristic
356C22#1458291511yescharacteristic
357C22#1458325412yes—
358C22#1458330112yes—
359C4—22no—
360C4—22no—
361C4—22no—
362C4—22no—
363C4—41no—
364C4—41no—
365C4—3444no—
366C4—3441no—
367C4—3441no—
368C4—3441no—
369C4—3441no—
370C2—22no—
371C2—22no—
372C2#1913308211yescharacteristic
373C2#1913308711yescharacteristic
374C2#1913315211yescharacteristic
375C2#1913317311yescharacteristic
376C2#1913553911yescharacteristic
377C2#1913556011yescharacteristic
378C2#1913558011yescharacteristic
subgroupG/H
centerC23C2×(C2×D43)⋊C4
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC4×C22⋊C8×C43C2
socleC23×C43C2×C22⋊C4
prime radicalC24×C43C2×D4
cosocleC23×C4×C43C23
hypercenterC4×C22⋊C8D43
hypocenterC43#9886
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×C22⋊C8

Complements

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

NH ≅ G/Ntype
6. C2×#13063317C4semidirect
7. #14582797C4semidirect
8. #14582797C4semidirect
13. #14582765C4semidirect
212. C43#9886semidirect

Maximal subgroups

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

subgroupindex
#191429052
#191328222
#191324752
C4×C22⋊C8×C432
#988643