Finite Group Databasebeta

← #25015248

Subgroups — #25015248

Order 11008.

484 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19139938C211yesmaximal, characteristic
2C4×#13063242C211yesmaximal, characteristic
3#19132712C212yesmaximal
4#19132712C212yesmaximal
5C43×#1799C211yesmaximal, characteristic
6C22×Dic43⋊C4C411yescharacteristic, complemented
7C2×#13063242C2212yes—
8C4×#10621877—21no—
9#14582832—21no—
10#14582822—21no—
11#14582783—21no—
12#14582779C2211yescharacteristic
13#14582779C2211yescharacteristic
14#14582772—21no—
15#14582771C411yescharacteristic, complemented
16#14582771C411yescharacteristic, complemented
17#14582759C411yescharacteristic, complemented
18#14582668—21no—
19C2×C4×D4×C43C2211yescharacteristic
20C2×#99×C43C2212yes—
21C43×#380—21no—
22C43×#342—21no—
23C23×Dic43C2×C411yescharacteristic
24C23×Dic43C2×C411yescharacteristic
25C2×#10621877—22no—
26C2×C4⋊Dic43—21no—
27C2×Dic43⋊C4—21no—
28C2×Dic43⋊C4—21no—
29C2×Dic43⋊C4—21no—
30C2×Dic43⋊C4—21no—
31C2×Dic43⋊C4—41no—
32C2×Dic43⋊C4—41no—
33C2×C22⋊Dic43—21no—
34C2×C22⋊Dic43—21no—
35C2×C22⋊Dic43C2×C411yescharacteristic
36C2×C22⋊Dic43C2×C411yescharacteristic
37#13063242—22no—
38#13063242Q814yes—
39#13063236—41no—
40C4×C43⋊C8—41no—
41C43⋊#95—21no—
42C43⋊#95—21no—
43C43⋊#95—21no—
44C43⋊#95—21no—
45C43⋊#95—21no—
46C22×D4×C43C2311yescharacteristic
47C23×C4×C43C2×C411yescharacteristic
48C23×C4×C43D411yescharacteristic
49C4×D4×C43—41no—
50C4×D4×C43—41no—
51C2×C4⋊C4×C43—41no—
52C2×C4⋊C4×C43D411yescharacteristic
53C2×C22⋊C4×C43—22no—
54C2×C22⋊C4×C43C2×C411yescharacteristic
55C2×C22⋊C4×C43D411yescharacteristic
56C2×C42×C43D411yescharacteristic
57#99×C43—24no—
58#95×C43—41no—
59C24×C43C22×C411yescharacteristic
60C24×C43C2×D411yescharacteristic
61C2×D4×C43—41no—
62C2×D4×C43—41no—
63C2×D4×C43C2×Q812yes—
64C2×D4×C43#4112yes—
65C22×C4×C43—21no—
66C22×C4×C43—21no—
67C22×C4×C43—21no—
68C22×C4×C43—21no—
69C22×C4×C43—42no—
70C22×C4×C43—81no—
71C22×C4×C43—81no—
72C22×C4×C43C22⋊C411yescharacteristic
73C22×C4×C43C22⋊C411yescharacteristic
74C22×C4×C43C22⋊C411yescharacteristic
75C22×C4×C43C22⋊C411yescharacteristic
76C22×C4×C43C2×D411yescharacteristic
77C22×Dic43—21no—
78C22×Dic43—21no—
79C22×Dic43—21no—
80C22×Dic43—21no—
81C22×Dic43—41no—
82C22×Dic43—41no—
83C22×Dic43—42no—
84C22×Dic43—81no—
85C4⋊C4×C43—41no—
86C4⋊C4×C43—82no—
87C22⋊C4×C43—41no—
88C22⋊C4×C43—41no—
89C22⋊C4×C43—42no—
90C22⋊C4×C43—42no—
91C42×C43—21no—
92C42×C43—21no—
93C22⋊Dic43—41no—
94C22⋊Dic43—41no—
95C22⋊Dic43—42no—
96C22⋊Dic43—81no—
97C4⋊Dic43—81no—
98Dic43⋊C4—42no—
99Dic43⋊C4—42no—
100Dic43⋊C4—41no—
101Dic43⋊C4—41no—
102Dic43⋊C4—81no—
103#10621877—24no—
104#10621877—42no—
105C2×C43⋊C8—42no—
106C23×C43—21no—
107C23×C43—21no—
108C23×C43—21no—
109C23×C43—21no—
110C23×C43—41no—
111C23×C43—41no—
112C23×C43—41no—
113C23×C43—41no—
114C23×C43C2×C22⋊C411yescharacteristic
115C23×C43C4×Q812yes—
116C23×C43#12411yescharacteristic
117C23×C43C4⋊Q811yescharacteristic
118D4×C43—42no—
119D4×C43—42no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—41no—
126C2×C4×C43—42no—
127C2×C4×C43—41no—
128C2×C4×C43—41no—
129C2×C4×C43—41no—
130C2×C4×C43—81no—
131C2×C4×C43—81no—
132C2×C4×C43—81no—
133C2×C4×C43—82no—
134C2×C4×C43—82no—
135C2×C4×C43—82no—
136C2×C4×C43#9911yescharacteristic
137C2×C4×C43#9911yescharacteristic
138C2×C4×C43C22⋊Q812yes—
139C2×Dic43—22no—
140C2×Dic43—41no—
141C2×Dic43—42no—
142C2×Dic43—41no—
143C2×Dic43—42no—
144C2×Dic43—41no—
145C2×Dic43—41no—
146C2×Dic43—41no—
147C2×Dic43—41no—
148C2×Dic43—41no—
149C2×Dic43—41no—
150C2×Dic43—41no—
151C2×Dic43—41no—
152C2×Dic43—41no—
153C2×Dic43—82no—
154C43⋊C8—44no—
155#13294—431nomaximal, Sylow
156C22×C43—21no—
157C22×C43—21no—
158C22×C43—22no—
159C22×C43—21no—
160C22×C43—21no—
161C22×C43—42no—
162C22×C43—41no—
163C22×C43—41no—
164C22×C43—42no—
165C22×C43—41no—
166C22×C43—41no—
167C22×C43—41no—
168C22×C43—41no—
169C22×C43—81no—
170C22×C43#39111yescharacteristic
171C22×C43C2×#9911yescharacteristic
172C22×C43#41011yescharacteristic
173C4×C43—21no—
174C4×C43—21no—
175C4×C43—22no—
176C4×C43—41no—
177C4×C43—41no—
178C4×C43—41no—
179C4×C43—162no—
180Dic43—42no—
181Dic43—81no—
182Dic43—81no—
183Dic43—81no—
184#2579—431no—
185#1799D4311yescharacteristic
186C4×#100—431no—
187#1390—432no—
188#1390—432no—
189C2×C43—21no—
190C2×C43—21no—
191C2×C43—41no—
192C2×C43—42no—
193C2×C43—41no—
194C2×C43#199611yescharacteristic
195C2×C43#212011yescharacteristic
196C2×C43#212111yescharacteristic
197C2×C4×D4C2×D4311yescharacteristic
198C22×C4⋊C4—431no—
199C2×#100—432no—
200C2×#99C2×D4312yes—
201C4×M16—861no—
202#398—861no—
203#396—861no—
204#387—861no—
205#386—431no—
206#386—431no—
207#385—431no—
208#385—431no—
209#385—861no—
210#380—21no—
211#380—431no—
212#343—861no—
213#342—21no—
214C43#1329411yescharacteristic, complemented, Sylow
215C22×D4C22×D4311yescharacteristic
216C23×C4—431no—
217C23×C4—431no—
218C23×C4C4×D4311yescharacteristic
219C23×C4C22⋊D4311yescharacteristic
220C2×M16—862no—
221C4×D4—41no—
222C4×D4—41no—
223C2×C4⋊C4—41no—
224C2×C4⋊C4—861no—
225C2×C4⋊C4—861no—
226C2×C4⋊C4—861no—
227C2×C4⋊C4—861no—
228C2×C4⋊C4—861no—
229C2×C4⋊C4—1721no—
230C2×C4⋊C4—1721no—
231C2×C4⋊C4D17211yescharacteristic
232C2×C22⋊C4—22no—
233C2×C22⋊C4—431no—
234C2×C22⋊C4—431no—
235C2×C22⋊C4—861no—
236C2×C22⋊C4—861no—
237C2×C22⋊C4C4×D4311yescharacteristic
238C2×C22⋊C4C22⋊D4311yescharacteristic
239C2×C42D17211yescharacteristic
240#100—434no—
241#100—862no—
242#99—24no—
243#97—1721no—
244C4×C8—1721no—
245#95—41no—
246#95—861no—
247#95—861no—
248#95—861no—
249#95—861no—
250#95—861no—
251C24C2×C4×D4311yescharacteristic
252C24C2×C22⋊D4311yescharacteristic
253C2×D4—41no—
254C2×D4—41no—
255C2×D4#1062190012yes—
256C2×D4Q8×D4312yes—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—42no—
262C22×C4—81no—
263C22×C4—81no—
264C22×C4—861no—
265C22×C4—861no—
266C22×C4—861no—
267C22×C4—861no—
268C22×C4—3441no—
269C22×C4—1722no—
270C22×C4—1721no—
271C22×C4—1721no—
272C22×C4(C2×D43)⋊C411yescharacteristic
273C22×C4(C2×D43)⋊C411yescharacteristic
274C22×C4(C2×D43)⋊C411yescharacteristic
275C22×C4(C2×D43)⋊C411yescharacteristic
276C22×C4C2×D17211yescharacteristic
277M16—864no—
278M16—1722no—
279C2×C8—1722no—
280C4⋊C4—41no—
281C4⋊C4—82no—
282C4⋊C4—3441no—
283C4⋊C4—3441no—
284C4⋊C4—1722no—
285C4⋊C4—1722no—
286C4⋊C4—1721no—
287C4⋊C4—1721no—
288C22⋊C4—41no—
289C22⋊C4—41no—
290C22⋊C4—42no—
291C22⋊C4—42no—
292C22⋊C4—3441no—
293C22⋊C4—1722no—
294C22⋊C4—1721no—
295C22⋊C4—1721no—
296C42—21no—
297C42—21no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—41no—
303C23—41no—
304C23—41no—
305C23—41no—
306C23C2×(C2×D43)⋊C411yescharacteristic
307C23#1306329012yes—
308C23#1306331211yescharacteristic
309C23#1306332311yescharacteristic
310D4—42no—
311D4—42no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—41no—
318C2×C4—42no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4—82no—
326C2×C4—82no—
327C2×C4—82no—
328C2×C4—862no—
329C2×C4—3442no—
330C2×C4—1721no—
331C2×C4—1721no—
332C2×C4—1721no—
333C2×C4—1721no—
334C2×C4—1721no—
335C2×C4—1721no—
336C2×C4—1721no—
337C2×C4—1721no—
338C2×C4—1721no—
339C2×C4—1721no—
340C2×C4—1722no—
341C2×C4—1721no—
342C2×C4—1722no—
343C2×C4#1306323911yescharacteristic
344C2×C4#1306323911yescharacteristic
345C2×C4#1306330512yes—
346C8—1724no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—22no—
351C22—21no—
352C22—42no—
353C22—41no—
354C22—41no—
355C22—42no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—81no—
361C22#1458280411yescharacteristic
362C22C2×#1306323911yescharacteristic
363C22#1458287211yescharacteristic
364C4—22no—
365C4—21no—
366C4—21no—
367C4—41no—
368C4—41no—
369C4—41no—
370C4—162no—
371C4—3441no—
372C4—3441no—
373C4—3441no—
374C4—1722no—
375C2—21no—
376C2—21no—
377C2—41no—
378C2—42no—
379C2—41no—
380C2#1913557911yescharacteristic
381C2#1913623411yescharacteristic
382C2#1913623911yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC24×C43C22×C4
FrattiniC22×D4C22×D43
FittingC43×#1799C2
socleC22×C43C2×#99
prime radical, cosocleC22×D4×C43C23
hypercenter#1799D43
hypocenterC43#13294
LCSG ▷ C24×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1799

Complements

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

NH ≅ G/Ntype
6. C22×Dic43⋊C4C4semidirect
15. #14582771C4semidirect
16. #14582771C4semidirect
17. #14582759C4semidirect
214. C43#13294semidirect

Maximal subgroups

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

subgroupindex
#191399382
C4×#130632422
#191327122
C43×#17992
#1329443