Finite Group Databasebeta

← #24994325

Subgroups — #24994325

Order 11008.

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

normal subgroups only

This group has 528 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#19139073C211yesmaximal, characteristic
2#19137196C211yesmaximal, characteristic
3#19134673C211yesmaximal, characteristic
4#19133129C211yesmaximal, characteristic
5#19133127C211yesmaximal, characteristic
6#19132448C211yesmaximal, characteristic
7C43×#1284C211yesmaximal, characteristic
8C2×#13063304C2211yescharacteristic
9C22×C4⋊Dic43C2211yescharacteristic
10#14582863C2211yescharacteristic
11#14582831—22no—
12#14582805C412yescomplemented
13#14582784—22no—
14#14582782—22no—
15#14582774—21no—
16#14582774—21no—
17#14582769C412yescomplemented
18#14582762C2211yescharacteristic
19#14582757—21no—
20C22⋊C4×Dic43—21no—
21#14582667—22no—
22#14582637—22no—
23#14582635—22no—
24C43×#407C2211yescharacteristic
25C43×#381C2211yescharacteristic
26C4×C22⋊C4×C43C2211yescharacteristic
27C22×Dic86C2×C411yescharacteristic
28C23×Dic43D411yescharacteristic
29C23×Dic43D411yescharacteristic
30C2×#10621877—21no—
31#13063304—21no—
32#13063304—21no—
33#13063304—21no—
34#13063304—21no—
35C2×C4⋊Dic43—21no—
36C2×C4⋊Dic43—21no—
37C2×C4⋊Dic43—21no—
38C2×C4⋊Dic43—21no—
39C2×C4⋊Dic43—22no—
40C2×C4⋊Dic43—22no—
41C2×C4⋊Dic43C2×C411yescharacteristic
42C2×C4⋊Dic43C2×C412yes—
43C2×C4⋊Dic43D412yes—
44C2×Dic43⋊C4—21no—
45C2×Dic43⋊C4—22no—
46C2×C22⋊Dic43—21no—
47C2×C22⋊Dic43—21no—
48C2×C4×Dic43—22no—
49C22⋊(C43⋊C8)—21no—
50C22⋊(C43⋊C8)—21no—
51C43⋊#95—22no—
52C43⋊#95—22no—
53C43⋊#95—21no—
54C43⋊#95—22no—
55C43⋊#95—22no—
56C43⋊#95D412yes—
57C23×C4×C43C2311yescharacteristic
58C2×M16×C43—21no—
59C2×C22⋊C4×C43—21no—
60C2×C22⋊C4×C43—21no—
61C2×C42×C43C2×C412yes—
62C22⋊C8×C43—21no—
63C22⋊C8×C43—21no—
64#95×C43—21no—
65#95×C43—21no—
66#95×C43D412yes—
67C24×C43C2×D411yescharacteristic
68C22×C4×C43—22no—
69C22×C4×C43—22no—
70C22×C4×C43—42no—
71C22×C4×C43C22×C411yescharacteristic
72C22×C4×C43C2×D411yescharacteristic
73C22×C4×C43C2×D411yescharacteristic
74C22×C4×C43C2×D411yescharacteristic
75C22×C4×C43#4111yescharacteristic
76C22×C4×C43#4111yescharacteristic
77C22×Dic43—21no—
78C22×Dic43—21no—
79C22×Dic43—21no—
80C22×Dic43—21no—
81C22×Dic43—22no—
82C22×Dic43—21no—
83C22×Dic43—21no—
84C22×Dic43—81no—
85C22×Dic43—81no—
86C22×Dic43C22⋊C412yes—
87C22×Dic43C22⋊C412yes—
88C2×Dic86—21no—
89C2×Dic86—21no—
90C2×Dic86—42no—
91M16×C43—42no—
92C2×C8×C43—41no—
93C22⋊C4×C43—24no—
94C22⋊C4×C43—42no—
95C42×C43—42no—
96C22⋊Dic43—42no—
97C22⋊Dic43—41no—
98C22⋊Dic43—41no—
99C4⋊Dic43—22no—
100C4⋊Dic43—22no—
101C4⋊Dic43—22no—
102C4⋊Dic43—22no—
103C4⋊Dic43—21no—
104C4⋊Dic43—21no—
105C4⋊Dic43—82no—
106C4⋊Dic43—82no—
107Dic43⋊C4—41no—
108Dic43⋊C4—41no—
109Dic43⋊C4—82no—
110C4×Dic43—82no—
111#10621877—42no—
112C2×C43⋊C8—41no—
113C23×C43—22no—
114C23×C43—22no—
115C23×C43—41no—
116C23×C43C2×C22⋊C411yescharacteristic
117C23×C43#12011yescharacteristic
118C23×C43#12311yescharacteristic
119C2×C4×C43—22no—
120C2×C4×C43—22no—
121C2×C4×C43—24no—
122C2×C4×C43—41no—
123C2×C4×C43—41no—
124C2×C4×C43—41no—
125C2×C4×C43—41no—
126C2×C4×C43—42no—
127C2×C4×C43—42no—
128C2×C4×C43—42no—
129C2×C4×C43—42no—
130C2×C4×C43—42no—
131C2×C4×C43C4×D411yescharacteristic
132C2×C4×C43C4×D411yescharacteristic
133C2×C4×C43#12111yescharacteristic
134C2×C4×C43#12111yescharacteristic
135C2×Dic43—22no—
136C2×Dic43—22no—
137C2×Dic43—42no—
138C2×Dic43—42no—
139C2×Dic43—42no—
140C2×Dic43—42no—
141C2×Dic43—42no—
142C2×Dic43—42no—
143C2×Dic43—42no—
144C2×Dic43—41no—
145C2×Dic43—41no—
146C2×Dic43—42no—
147C2×Dic43—42no—
148C2×Dic43—81no—
149C2×Dic43—81no—
150Dic86—81no—
151Dic86—81no—
152C8×C43—81no—
153C43⋊C8—81no—
154#9461—431nomaximal, Sylow
155C22×C43—21no—
156C22×C43—21no—
157C22×C43—21no—
158C22×C43—21no—
159C22×C43—21no—
160C22×C43—21no—
161C22×C43—21no—
162C22×C43—44no—
163C22×C43#38611yescharacteristic
164C22×C43#41012yes—
165C22×C43#45612yes—
166C4×C43—21no—
167C4×C43—21no—
168C4×C43—21no—
169C4×C43—21no—
170C4×C43—44no—
171C4×C43—82no—
172Dic43—42no—
173Dic43—42no—
174Dic43—82no—
175Dic43—81no—
176Dic43—81no—
177#2502—431no—
178#2313—431no—
179#1821—431no—
180#1511—431no—
181#1511—431no—
182#1284—431no—
183#1284D4311yescharacteristic
184C2×C43—22no—
185C2×C43—22no—
186C2×C43—41no—
187C2×C43#188611yescharacteristic
188C2×C43#189911yescharacteristic
189C2×C43#191111yescharacteristic
190C2×C22⋊Q8—431no—
191C22×C4⋊C4—431no—
192#407—431no—
193#407C2×D4311yescharacteristic
194#398—862no—
195#391—432no—
196#387—862no—
197#387—862no—
198#385—861no—
199#385—861no—
200#384—432no—
201#381—431no—
202#381C2×D4311yescharacteristic
203#380—861no—
204C4×C22⋊C4—861no—
205C4×C22⋊C4C2×D4311yescharacteristic
206#343—862no—
207#328—862no—
208#328—862no—
209C43#946111yescharacteristic, complemented, Sylow
210C22×Q8—431no—
211C23×C4—431no—
212C23×C4—431no—
213C23×C4C22×D4311yescharacteristic
214C2×M16—21no—
215C2×M16—861no—
216C22⋊Q8—861no—
217C22⋊Q8—861no—
218C22⋊Q8—861no—
219C22⋊Q8—861no—
220C2×C4⋊C4—432no—
221C2×C4⋊C4—432no—
222C2×C4⋊C4—431no—
223C2×C4⋊C4—861no—
224C2×C4⋊C4—861no—
225C2×C4⋊C4—861no—
226C2×C4⋊C4—861no—
227C2×C4⋊C4—862no—
228C2×C4⋊C4—862no—
229C2×C4⋊C4—862no—
230C2×C4⋊C4—861no—
231C2×C22⋊C4—21no—
232C2×C22⋊C4—21no—
233C2×C22⋊C4—861no—
234C2×C22⋊C4—861no—
235C2×C42—862no—
236C2×C42C4×D4312yes—
237C22⋊C8—21no—
238C22⋊C8—21no—
239C22⋊C8—861no—
240C22⋊C8—861no—
241#95—21no—
242#95—21no—
243#95—432no—
244#95—862no—
245#95—862no—
246#95—862no—
247#95—862no—
248#95—861no—
249#95D17212yes—
250C24D4×D4311yescharacteristic
251C2×Q8—861no—
252C2×Q8—861no—
253C2×Q8—1722no—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—42no—
257C22×C4—432no—
258C22×C4—432no—
259C22×C4—861no—
260C22×C4—861no—
261C22×C4—861no—
262C22×C4—861no—
263C22×C4—861no—
264C22×C4—861no—
265C22×C4—862no—
266C22×C4—3441no—
267C22×C4—3441no—
268C22×C4C2×C4×D4311yescharacteristic
269C22×C4C2×D17211yescharacteristic
270C22×C4#1062189811yescharacteristic
271C22×C4D4×D4311yescharacteristic
272C22×C4D4×D4311yescharacteristic
273C22×C4#1062190211yescharacteristic
274M16—42no—
275M16—1722no—
276C2×C8—41no—
277C2×C8—1721no—
278C4⋊C4—862no—
279C4⋊C4—862no—
280C4⋊C4—862no—
281C4⋊C4—862no—
282C4⋊C4—861no—
283C4⋊C4—861no—
284C4⋊C4—3442no—
285C4⋊C4—3442no—
286C4⋊C4—3442no—
287C4⋊C4—1721no—
288C4⋊C4—1721no—
289C22⋊C4—24no—
290C22⋊C4—42no—
291C22⋊C4—1722no—
292C22⋊C4—1721no—
293C22⋊C4—1721no—
294C42—42no—
295C42—3442no—
296C23—22no—
297C23—22no—
298C23—41no—
299C23C22⋊C4×D4311yescharacteristic
300C23#1306329511yescharacteristic
301C23#1306331011yescharacteristic
302Q8—3441no—
303Q8—3441no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—24no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—862no—
317C2×C4—862no—
318C2×C4—3441no—
319C2×C4—3441no—
320C2×C4—1722no—
321C2×C4—1722no—
322C2×C4—1722no—
323C2×C4—1722no—
324C2×C4—1722no—
325C2×C4—1721no—
326C2×C4—1721no—
327C2×C4—1722no—
328C2×C4—1722no—
329C2×C4—1722no—
330C2×C4—1722no—
331C2×C4#1306328711yescharacteristic
332C2×C4C4×D17211yescharacteristic
333C2×C4#1306329811yescharacteristic
334C2×C4#1306330011yescharacteristic
335C8—81no—
336C8—3441no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—44no—
345C22#1458277711yescharacteristic
346C22#1458287112yes—
347C22#1458308312yes—
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—44no—
353C4—82no—
354C4—3442no—
355C4—3441no—
356C4—3441no—
357C4—1722no—
358C4—1722no—
359C2—22no—
360C2—22no—
361C2—41no—
362C2#1913498711yescharacteristic
363C2#1913505211yescharacteristic
364C2#1913512611yescharacteristic
subgroupG/H
centerC22#14582777
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1284C2
socleC22×C43#386
prime radicalC24×C43C2×D4
cosocleC23×C4×C43C23
hypercenter#1284D43
hypocenterC43#9461
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1284

Complements

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

NH ≅ G/Ntype
12. #14582805C4semidirect
17. #14582769C4semidirect
209. C43#9461semidirect

Maximal subgroups

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

subgroupindex
#191390732
#191371962
#191346732
#191331292
#191331272
#191324482
C43×#12842
#946143