Finite Group Databasebeta

← #25015277

Subgroups — #25015277

Order 11008.

492 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 107 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#19134583C211yesmaximal, characteristic
2C4×#13063240C211yesmaximal, characteristic
3#19132720C212yesmaximal
4#19132720C212yesmaximal
5C43×#2566C211yesmaximal, characteristic
6C2×#13063240C2212yes—
7C2×#13063240C2212yes—
8#14582759—21no—
9C4×C22⋊Dic43—21no—
10#14582666—21no—
11#14582666—21no—
12C2×#125×C43C411yescharacteristic, complemented
13C2×C4×D4×C43C2211yescharacteristic
14C43×#396—21no—
15C43×#396—21no—
16C43×#390C2211yescharacteristic
17C43×#390C2211yescharacteristic
18C43×#385—21no—
19C43×#385—21no—
20C43×#384C411yescharacteristic, complemented
21C43×#382C411yescharacteristic, complemented
22C4×C4⋊C4×C43C411yescharacteristic, complemented
23C2×C4⋊Dic43—41no—
24C2×C22⋊Dic43—22no—
25C2×C22⋊Dic43—22no—
26C2×C4×Dic43—41no—
27#13063240—22no—
28#13063240—24no—
29#13063240Q814yes—
30C43⋊#95—41no—
31C43⋊#95—41no—
32C22×D4×C43C2311yescharacteristic
33C23×C4×C43D411yescharacteristic
34C23×C4×C43D411yescharacteristic
35#125×C43—41no—
36#125×C43—41no—
37C4×D4×C43—41no—
38C4×D4×C43—41no—
39C2×C4⋊C4×C43—21no—
40C2×C4⋊C4×C43—21no—
41C2×C4⋊C4×C43—21no—
42C2×C4⋊C4×C43—21no—
43C2×C4⋊C4×C43—21no—
44C2×C4⋊C4×C43C2×C411yescharacteristic
45C2×C4⋊C4×C43C2×C411yescharacteristic
46C2×C4⋊C4×C43C2×C411yescharacteristic
47C2×C22⋊C4×C43—21no—
48C2×C22⋊C4×C43—21no—
49C2×C22⋊C4×C43—21no—
50C2×C22⋊C4×C43—21no—
51C2×C22⋊C4×C43D411yescharacteristic
52C2×C22⋊C4×C43D411yescharacteristic
53C2×C42×C43C2×C411yescharacteristic
54C2×C42×C43C2×C411yescharacteristic
55C2×C42×C43C2×C411yescharacteristic
56#95×C43—21no—
57#95×C43—21no—
58#95×C43—21no—
59C24×C43C2×D411yescharacteristic
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—21no—
70C22×C4×C43—21no—
71C22×C4×C43—21no—
72C22×C4×C43—21no—
73C22×C4×C43—81no—
74C22×C4×C43—81no—
75C22×C4×C43C22⋊C411yescharacteristic
76C22×C4×C43C22⋊C411yescharacteristic
77C22×C4×C43C22⋊C411yescharacteristic
78C22×C4×C43C22⋊C411yescharacteristic
79C22×C4×C43C22×C411yescharacteristic
80C22×Dic43—42no—
81C22×Dic43—42no—
82C4⋊C4×C43—41no—
83C4⋊C4×C43—41no—
84C4⋊C4×C43—41no—
85C4⋊C4×C43—42no—
86C4⋊C4×C43—42no—
87C4⋊C4×C43—41no—
88C4⋊C4×C43—41no—
89C4⋊C4×C43—81no—
90C4⋊C4×C43—81no—
91C22⋊C4×C43—41no—
92C22⋊C4×C43—41no—
93C22⋊C4×C43—42no—
94C22⋊C4×C43—42no—
95C22⋊C4×C43—81no—
96C22⋊C4×C43—81no—
97C42×C43—21no—
98C42×C43—21no—
99C42×C43—41no—
100C42×C43—41no—
101C22⋊Dic43—24no—
102C22⋊Dic43—42no—
103C22⋊Dic43—42no—
104C22⋊Dic43—42no—
105C4⋊Dic43—82no—
106C4×Dic43—82no—
107C23×C43—21no—
108C23×C43—21no—
109C23×C43—21no—
110C23×C43—21no—
111C23×C43—41no—
112C23×C43—41no—
113C23×C43—41no—
114C23×C43—41no—
115C23×C43C2×C22⋊C411yescharacteristic
116C23×C43C22⋊Q812yes—
117C23×C43#12411yescharacteristic
118C23×C43C4⋊Q811yescharacteristic
119D4×C43—42no—
120D4×C43—42no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—22no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—41no—
128C2×C4×C43—42no—
129C2×C4×C43—42no—
130C2×C4×C43—41no—
131C2×C4×C43—41no—
132C2×C4×C43—41no—
133C2×C4×C43—41no—
134C2×C4×C43—41no—
135C2×C4×C43—41no—
136C2×C4×C43—41no—
137C2×C4×C43—41no—
138C2×C4×C43—41no—
139C2×C4×C43—41no—
140C2×C4×C43—41no—
141C2×C4×C43—41no—
142C2×C4×C43—41no—
143C2×C4×C43—41no—
144C2×C4×C43—81no—
145C2×C4×C43—81no—
146C2×C4×C43#9911yescharacteristic
147C2×C4×C43#9911yescharacteristic
148C2×C4×C43C4×Q812yes—
149C2×Dic43—44no—
150C2×Dic43—82no—
151C2×Dic43—82no—
152C2×Dic43—82no—
153C2×Dic43—82no—
154C2×Dic43—82no—
155#13300—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—41no—
165C22×C43—41no—
166C22×C43—41no—
167C22×C43—41no—
168C22×C43—81no—
169C22×C43—81no—
170C22×C43#39111yescharacteristic
171C22×C43C2×#9911yescharacteristic
172C22×C43#41011yescharacteristic
173C4×C43—21no—
174C4×C43—21no—
175C4×C43—22no—
176C4×C43—42no—
177C4×C43—41no—
178C4×C43—41no—
179C4×C43—41no—
180C4×C43—81no—
181C4×C43—81no—
182C4×C43—81no—
183Dic43—84no—
184Dic43—162no—
185#2566D4311yescharacteristic
186#1799—431no—
187C4×#99—431no—
188#1393—432no—
189#1393—432no—
190C2×C43—21no—
191C2×C43—21no—
192C2×C43—42no—
193C2×C43—41no—
194C2×C43—41no—
195C2×C43#199611yescharacteristic
196C2×C43#212611yescharacteristic
197C2×C43#212711yescharacteristic
198C2×#125Dic4311yescharacteristic, complemented
199C2×C4×D4C2×D4311yescharacteristic
200C2×#99—432no—
201C2×#99—432no—
202#396—21no—
203#396—21no—
204#390C2×D4311yescharacteristic
205#390C2×D4311yescharacteristic
206#385—21no—
207#385—21no—
208#384Dic4311yescharacteristic, complemented
209#382Dic4311yescharacteristic, complemented
210#380—861no—
211C4×C4⋊C4Dic4311yescharacteristic, complemented
212C4×C22⋊C4—861no—
213#342—861no—
214#342—861no—
215C43#1330011yescharacteristic, complemented, Sylow
216C22×D4C22×D4311yescharacteristic
217C23×C4C22⋊D4311yescharacteristic
218C23×C4C22⋊D4311yescharacteristic
219#125—41no—
220#125—41no—
221C4×D4—41no—
222C4×D4—41no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—1721no—
229C2×C4⋊C4C2×Dic4311yescharacteristic
230C2×C4⋊C4C2×Dic4311yescharacteristic
231C2×C4⋊C4C2×Dic4311yescharacteristic
232C2×C22⋊C4—21no—
233C2×C22⋊C4—21no—
234C2×C22⋊C4—21no—
235C2×C22⋊C4—21no—
236C2×C22⋊C4—862no—
237C2×C22⋊C4—862no—
238C2×C22⋊C4C22⋊D4311yescharacteristic
239C2×C22⋊C4C22⋊D4311yescharacteristic
240C2×C42—1721no—
241C2×C42C2×Dic4311yescharacteristic
242C2×C42C2×Dic4311yescharacteristic
243C2×C42C2×Dic4311yescharacteristic
244#99—434no—
245#99—862no—
246#99—864no—
247#95—21no—
248#95—21no—
249#95—21no—
250#95—1721no—
251#95—1721no—
252C24C2×C22⋊D4311yescharacteristic
253C24C2×C22⋊D4311yescharacteristic
254C2×D4—41no—
255C2×D4—41no—
256C2×D4Q8×D4312yes—
257C2×D4#1062190212yes—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—81no—
267C22×C4—81no—
268C22×C4—1722no—
269C22×C4—1722no—
270C22×C4C22⋊Dic4311yescharacteristic
271C22×C4C22⋊Dic4311yescharacteristic
272C22×C4C22⋊Dic4311yescharacteristic
273C22×C4C22⋊Dic4311yescharacteristic
274C22×C4C22×Dic4311yescharacteristic
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—42no—
279C4⋊C4—42no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—81no—
283C4⋊C4—81no—
284C4⋊C4—3442no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C22⋊C4—42no—
288C22⋊C4—42no—
289C22⋊C4—81no—
290C22⋊C4—81no—
291C22⋊C4—864no—
292C22⋊C4—1722no—
293C22⋊C4—1722no—
294C22⋊C4—1722no—
295C42—21no—
296C42—21no—
297C42—41no—
298C42—41no—
299C42—3442no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—41no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23C2×C22⋊Dic4311yescharacteristic
309C23#1306330112yes—
310C23#1306331411yescharacteristic
311C23#1306332311yescharacteristic
312D4—42no—
313D4—42no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—22no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—41no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—3442no—
340C2×C4—3442no—
341C2×C4—3442no—
342C2×C4—3442no—
343C2×C4—3442no—
344C2×C4—1724no—
345C2×C4#1306324011yescharacteristic
346C2×C4#1306324011yescharacteristic
347C2×C4Q8×Dic4312yes—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—22no—
352C22—21no—
353C22—42no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—81no—
361C22—81no—
362C22#1458280611yescharacteristic
363C22C2×#1306324011yescharacteristic
364C22#1458287311yescharacteristic
365C4—21no—
366C4—21no—
367C4—22no—
368C4—42no—
369C4—41no—
370C4—41no—
371C4—41no—
372C4—81no—
373C4—81no—
374C4—81no—
375C4—3444no—
376C4—6882no—
377C2—21no—
378C2—21no—
379C2—42no—
380C2—41no—
381C2—41no—
382C2#1913558111yescharacteristic
383C2#1913626011yescharacteristic
384C2#1913626411yescharacteristic
subgroupG/H
centerC22C2×#13063240
commutatorC22×C4×C43C22×C4
FrattiniC22×D4C22×D43
FittingC43×#2566C2
socleC22×C43C2×#99
prime radical, cosocleC22×D4×C43C23
hypercenter#2566D43
hypocenterC43#13300
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2566

Complements

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

NH ≅ G/Ntype
12. C2×#125×C43C4semidirect
20. C43×#384C4semidirect
21. C43×#382C4semidirect
22. C4×C4⋊C4×C43C4semidirect
198. C2×#125Dic43semidirect
208. #384Dic43semidirect
209. #382Dic43semidirect
211. C4×C4⋊C4Dic43semidirect
215. C43#13300semidirect

Maximal subgroups

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

subgroupindex
#191345832
C4×#130632402
#191327202
C43×#25662
#1330043