Finite Group Databasebeta

← #25012587

Subgroups — #25012587

Order 11008.

588 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 588 conjugacy classes of subgroups — too many to draw. Only its 93 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#19137319C211yesmaximal, characteristic
2C2×#14582691C212yesmaximal
3#19134581C212yesmaximal, complemented
4#19132720C211yesmaximal, characteristic, complemented
5C43×#1393C211yesmaximal, characteristic, complemented
6C2×#13063321C2211yescharacteristic
7C2×D4×Dic43C2211yescharacteristic
8C2×#13063287C411yescharacteristic, complemented
9C2×#13063240C2212yes—
10#14582801C411yescharacteristic, complemented
11#14582776—22no—
12#14582775—22no—
13#14582764C411yescharacteristic, complemented
14#14582757—22no—
15#14582745C411yescharacteristic, complemented
16#14582691—24no—
17#14582665—22no—
18C2×#99×C43C2212yes—
19C43×#390C2211yescharacteristic
20C22×D172C2×C411yescharacteristic
21C22×C22⋊D43—22no—
22C23×Dic43D412yes—
23C22×C4×D43—21no—
24#13063321—22no—
25#13063321D412yes—
26#13063321Q812yes—
27D4×Dic43—42no—
28#13063287—42no—
29C2×C4⋊Dic43C2×C411yescharacteristic
30C2×Dic43⋊C4—42no—
31C2×C22⋊Dic43—22no—
32C2×C22⋊Dic43D412yes—
33C2×(C2×D43)⋊C4—21no—
34C2×(C2×D43)⋊C4—22no—
35C2×C4×Dic43C2×C411yescharacteristic
36C2×C4×Dic43C2×C411yescharacteristic
37#13063240—22no—
38#13063240—22no—
39C43⋊#95—21no—
40C43⋊#95—21no—
41C43⋊#95—22no—
42C43⋊#95—42no—
43C22×D4×C43C2311yescharacteristic
44C2×C4⋊C4×C43C2×C411yescharacteristic
45C2×C22⋊C4×C43—22no—
46C2×C22⋊C4×C43—22no—
47C2×C42×C43C2×C411yescharacteristic
48#99×C43—22no—
49#99×C43—22no—
50C24×C43C2×D412yes—
51C23×D43—21no—
52C2×D4×C43—41no—
53C2×D4×C43—41no—
54C2×D4×C43C2×D411yescharacteristic
55C2×D4×C43C2×Q811yescharacteristic
56C2×D4×C43#4112yes—
57C22×C4×C43—21no—
58C22×C4×C43—21no—
59C22×C4×C43—42no—
60C22×C4×C43C22×C411yescharacteristic
61C2×C22⋊D43—24no—
62C2×C22⋊D43—24no—
63C2×C22⋊D43—82no—
64C2×C22⋊D43—82no—
65C22×Dic43—22no—
66C22×Dic43—22no—
67C22×Dic43—21no—
68C22×Dic43—42no—
69C22×Dic43—82no—
70C22×Dic43C22⋊C411yescharacteristic
71C22×Dic43C22⋊C412yes—
72C22×Dic43C22⋊C411yescharacteristic
73C2×D172—21no—
74C2×D172—41no—
75C2×D172—41no—
76C2×D172C4⋊C412yescomplemented
77C2×C4×D43—42no—
78C2×C4×D43—82no—
79C4⋊C4×C43—41no—
80C22⋊C4×C43—42no—
81C22⋊C4×C43—42no—
82C22⋊C4×C43—82no—
83C42×C43—41no—
84C22⋊Dic43—42no—
85C22⋊Dic43—42no—
86C22⋊Dic43—42no—
87(C2×D43)⋊C4—42no—
88(C2×D43)⋊C4—82no—
89C4⋊Dic43—41no—
90Dic43⋊C4—84no—
91C4×Dic43—21no—
92C4×Dic43—22no—
93C4×Dic43C4⋊C412yescomplemented
94C23×C43—22no—
95C23×C43—22no—
96C23×C43—42no—
97C23×C43—42no—
98C23×C43C2×C22⋊C411yescharacteristic
99C23×C43#12112yes—
100C23×C43C22⋊Q812yes—
101C22×D43—22no—
102C22×D43—42no—
103C22×D43—42no—
104C22×D43—41no—
105C22×D43—41no—
106D4×C43—41no—
107D4×C43—41no—
108D4×C43—42no—
109C2×C4×C43—21no—
110C2×C4×C43—21no—
111C2×C4×C43—41no—
112C2×C4×C43—41no—
113C2×C4×C43—42no—
114C2×C4×C43—41no—
115C2×C4×C43—41no—
116C2×C4×C43—82no—
117C2×C4×C43—82no—
118C2×C4×C43—82no—
119C2×C4×C43C2×C4⋊C411yescharacteristic
120C2×C4×C43#11711yescharacteristic
121C22⋊D43—84no—
122C22⋊D43—84no—
123C2×Dic43—22no—
124C2×Dic43—21no—
125C2×Dic43—22no—
126C2×Dic43—41no—
127C2×Dic43—44no—
128C2×Dic43—41no—
129C2×Dic43—41no—
130C2×Dic43—42no—
131C2×Dic43—41no—
132C2×Dic43—82no—
133C2×Dic43—82no—
134C2×Dic43—82no—
135C2×Dic43—82no—
136C2×Dic43#9912yes—
137D172—42no—
138D172—42no—
139C4×D43—84no—
140#12799—431nomaximal, Sylow
141C22×C43—21no—
142C22×C43—21no—
143C22×C43—22no—
144C22×C43—22no—
145C22×C43—42no—
146C22×C43—42no—
147C22×C43—42no—
148C22×C43—42no—
149C22×C43—82no—
150C22×C43#38011yescharacteristic
151C22×C43C2×#9911yescharacteristic
152C22×C43#41011yescharacteristic
153C2×D43—44no—
154C2×D43—42no—
155C2×D43—82no—
156C2×D43—81no—
157C2×D43—81no—
158C4×C43—21no—
159C4×C43—21no—
160C4×C43—81no—
161C4×C43—81no—
162C4×C43—162no—
163Dic43—22no—
164Dic43—42no—
165Dic43—42no—
166Dic43—41no—
167Dic43—162no—
168#2328—431no—
169C2×#353—432no—
170#1799—432no—
171#1393—431no—
172#1393D4311yescharacteristic, complemented
173C2×C43—21no—
174C2×C43—21no—
175C2×C43—42no—
176C2×C43—42no—
177C2×C43#179911yescharacteristic
178C2×C43#212711yescharacteristic
179C2×C43#212811yescharacteristic
180D43—82no—
181C2×#127—431no—
182C2×C4×D4—431no—
183C2×C4×D4—431no—
184C2×#99—432no—
185C2×#99C2×D4312yes—
186#390—431no—
187#390C2×D4311yescharacteristic
188#386—862no—
189#386—862no—
190#382—431no—
191#380—862no—
192#376—431no—
193#353—864no—
194#342—862no—
195C43#1279911yescharacteristic, complemented, Sylow
196C22×D4—431no—
197C22×D4—862no—
198C22×D4C22×D4311yescharacteristic
199C23×C4—432no—
200C23×C4—861no—
201#127—432no—
202#127—432no—
203#127—862no—
204C4×D4—1722no—
205C4×D4—1722no—
206C2×C4⋊C4—431no—
207C2×C4⋊C4—1722no—
208C2×C4⋊C4C4×D4311yescharacteristic
209C2×C22⋊C4—22no—
210C2×C22⋊C4—22no—
211C2×C22⋊C4—432no—
212C2×C22⋊C4—862no—
213C2×C22⋊C4—861no—
214C2×C22⋊C4—862no—
215C2×C42—431no—
216C2×C42—431no—
217C2×C42C4×D4311yescharacteristic
218#99—22no—
219#99—22no—
220#99—862no—
221#99—862no—
222#95—861no—
223#95—861no—
224#95—862no—
225#95—1722no—
226C24—861no—
227C24D4×D4312yes—
228C2×D4—41no—
229C2×D4—41no—
230C2×D4—432no—
231C2×D4—864no—
232C2×D4—864no—
233C2×D4—861no—
234C2×D4—3442no—
235C2×D4—3442no—
236C2×D4—1721no—
237C2×D4—1721no—
238C2×D4#1062189812yes—
239C2×D4D4×D4311yescharacteristic
240C2×D4Q8×D4311yescharacteristic
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—42no—
244C22×C4—431no—
245C22×C4—431no—
246C22×C4—432no—
247C22×C4—862no—
248C22×C4—862no—
249C22×C4—861no—
250C22×C4—3442no—
251C22×C4—3442no—
252C22×C4—1722no—
253C22×C4—1722no—
254C22×C4C2×C4×D4311yescharacteristic
255C4⋊C4—41no—
256C4⋊C4—3444no—
257C4⋊C4—1721no—
258C22⋊C4—42no—
259C22⋊C4—42no—
260C22⋊C4—82no—
261C22⋊C4—3442no—
262C22⋊C4—1722no—
263C22⋊C4—1722no—
264C22⋊C4—1722no—
265C22⋊C4—1722no—
266C42—41no—
267C42—432no—
268C42—862no—
269C42—861no—
270C23—22no—
271C23—22no—
272C23—42no—
273C23—42no—
274C23—862no—
275C23—1722no—
276C23—1722no—
277C23—1721no—
278C23—1721no—
279C23C22⋊C4×D4311yescharacteristic
280C23#1306329812yes—
281C23#1306330312yes—
282D4—42no—
283D4—41no—
284D4—41no—
285D4—3444no—
286D4—3444no—
287D4—1722no—
288D4—1722no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—41no—
292C2×C4—42no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—82no—
297C2×C4—82no—
298C2×C4—82no—
299C2×C4—432no—
300C2×C4—861no—
301C2×C4—862no—
302C2×C4—862no—
303C2×C4—3444no—
304C2×C4—3442no—
305C2×C4—3442no—
306C2×C4—3442no—
307C2×C4—3442no—
308C2×C4—1721no—
309C2×C4—1724no—
310C2×C4—1721no—
311C2×C4—1721no—
312C2×C4—1722no—
313C2×C4—1721no—
314C2×C4C4⋊C4×D4311yescharacteristic
315C2×C4#1306328211yescharacteristic
316C22—21no—
317C22—21no—
318C22—22no—
319C22—22no—
320C22—42no—
321C22—42no—
322C22—42no—
323C22—42no—
324C22—82no—
325C22—3442no—
326C22—3441no—
327C22—3441no—
328C22—1724no—
329C22—1722no—
330C22#1458275811yescharacteristic
331C22#99×D4311yescharacteristic
332C22#1458287111yescharacteristic
333C4—21no—
334C4—21no—
335C4—81no—
336C4—81no—
337C4—162no—
338C4—862no—
339C4—1722no—
340C4—1722no—
341C4—1721no—
342C4—6882no—
343C2—21no—
344C2—21no—
345C2—42no—
346C2—42no—
347C2—3442no—
348C2#1913458211yescharacteristic
349C2#1913626311yescharacteristic
350C2#1913626511yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC22×C4×C43C22×C4
FrattiniC22×D4C22×D43
FittingC43×#1393C2
socleC22×C43C2×#99
prime radicalC2×#13063321C22
cosocleC22×D4×C43C23
hypercenter#1393D43
hypocenterC43#12799
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #1393

Complements

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

NH ≅ G/Ntype
3. #19134581C2semidirect
4. #19132720C2semidirect
5. C43×#1393C2semidirect
8. C2×#13063287C4semidirect
10. #14582801C4semidirect
13. #14582764C4semidirect
15. #14582745C4semidirect
76. C2×D172C4⋊C4semidirect
93. C4×Dic43C4⋊C4semidirect
172. #1393D43semidirect
195. C43#12799semidirect

Maximal subgroups

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

subgroupindex
#191373192
C2×#145826912
#191345812
#191327202
C43×#13932
#1279943