Finite Group Databasebeta

← #24994428

Subgroups — #24994428

Order 11008.

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

normal subgroups only

This group has 518 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#19138878C211yesmaximal, characteristic
2#19137195C211yesmaximal, characteristic
3#19134694C211yesmaximal, characteristic
4#19132924C211yesmaximal, characteristic
5#19132449C211yesmaximal, characteristic
6#19132448C211yesmaximal, characteristic
7C43×#1826C211yesmaximal, characteristic
8C22×Dic43⋊C4C2211yescharacteristic
9#14582863C2211yescharacteristic
10#14582837C412yescomplemented
11#14582830C412yescomplemented
12#14582783—22no—
13#14582783—22no—
14#14582781—22no—
15#14582771—21no—
16#14582762C2211yescharacteristic
17#14582760—21no—
18#14582760—21no—
19#14582757—21no—
20C4×C22⋊Dic43C2211yescharacteristic
21#14582658—22no—
22#14582624—22no—
23C2×#117×C43C2211yescharacteristic
24C43×#407C2211yescharacteristic
25C4×C22⋊C4×C43C2211yescharacteristic
26C43×#339—22no—
27C23×Dic43D411yescharacteristic
28C23×Dic43D411yescharacteristic
29C2×#10621877—21no—
30C2×Dic43⋊C4—21no—
31C2×Dic43⋊C4—21no—
32C2×Dic43⋊C4—21no—
33C2×Dic43⋊C4—21no—
34C2×Dic43⋊C4—22no—
35C2×Dic43⋊C4—22no—
36C2×Dic43⋊C4C2×C412yes—
37C2×Dic43⋊C4D412yes—
38C2×C22⋊Dic43—21no—
39C2×C22⋊Dic43—21no—
40C2×C4×Dic43D412yes—
41C22⋊(C43⋊C8)—21no—
42C22⋊(C43⋊C8)—21no—
43C43⋊#95—22no—
44C43⋊#95—24no—
45C43⋊#95—21no—
46C43⋊#95—21no—
47C43⋊#95—22no—
48C43⋊#95—22no—
49C43⋊#95—22no—
50C43⋊#95C2×C412yes—
51C23×C4×C43C2311yescharacteristic
52C2×M16×C43—21no—
53#117×C43—21no—
54#117×C43—21no—
55#117×C43—21no—
56#117×C43—21no—
57C2×C4⋊C4×C43C2×C411yescharacteristic
58C2×C4⋊C4×C43C2×C411yescharacteristic
59C2×C22⋊C4×C43—21no—
60C2×C22⋊C4×C43—21no—
61C2×C42×C43—21no—
62C2×C42×C43D412yes—
63C22⋊C8×C43—21no—
64C22⋊C8×C43—21no—
65#95×C43—21no—
66C24×C43C2×D411yescharacteristic
67C22×C4×C43—21no—
68C22×C4×C43—21no—
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—22no—
78C22×Dic43—21no—
79C22×Dic43—21no—
80C22×Dic43—22no—
81C22×Dic43—21no—
82C22×Dic43—21no—
83C22×Dic43—42no—
84C22×Dic43—42no—
85C22×Dic43C22⋊C412yes—
86C22×Dic43C22⋊C412yes—
87M16×C43—42no—
88C2×C8×C43—41no—
89C4⋊C4×C43—21no—
90C4⋊C4×C43—21no—
91C4⋊C4×C43—21no—
92C4⋊C4×C43—21no—
93C22⋊C4×C43—42no—
94C22⋊C4×C43—41no—
95C22⋊C4×C43—41no—
96C42×C43—42no—
97C42×C43—41no—
98C42×C43—41no—
99C22⋊Dic43—42no—
100C22⋊Dic43—42no—
101Dic43⋊C4—22no—
102Dic43⋊C4—22no—
103Dic43⋊C4—22no—
104Dic43⋊C4—22no—
105Dic43⋊C4—44no—
106Dic43⋊C4—82no—
107C4×Dic43—42no—
108#10621877—42no—
109C2×C43⋊C8—41no—
110C23×C43—22no—
111C23×C43—22no—
112C23×C43—41no—
113C23×C43C2×C22⋊C411yescharacteristic
114C23×C43#12011yescharacteristic
115C23×C43#12311yescharacteristic
116C2×C4×C43—22no—
117C2×C4×C43—22no—
118C2×C4×C43—41no—
119C2×C4×C43—41no—
120C2×C4×C43—41no—
121C2×C4×C43—41no—
122C2×C4×C43—42no—
123C2×C4×C43—42no—
124C2×C4×C43—42no—
125C2×C4×C43—41no—
126C2×C4×C43—41no—
127C2×C4×C43—42no—
128C2×C4×C43—42no—
129C2×C4×C43C4×D411yescharacteristic
130C2×C4×C43C4×D411yescharacteristic
131C2×C4×C43#12111yescharacteristic
132C2×C4×C43#12111yescharacteristic
133C2×Dic43—22no—
134C2×Dic43—22no—
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—42no—
145C2×Dic43—42no—
146C2×Dic43—42no—
147C2×Dic43—81no—
148C8×C43—81no—
149C43⋊C8—81no—
150#9482—431nomaximal, Sylow
151C22×C43—21no—
152C22×C43—21no—
153C22×C43—21no—
154C22×C43—21no—
155C22×C43—21no—
156C22×C43—21no—
157C22×C43—21no—
158C22×C43—44no—
159C22×C43#38611yescharacteristic
160C22×C43#42112yes—
161C22×C43#45812yes—
162C4×C43—21no—
163C4×C43—21no—
164C4×C43—21no—
165C4×C43—21no—
166C4×C43—82no—
167C4×C43—81no—
168C4×C43—81no—
169Dic43—42no—
170Dic43—42no—
171Dic43—82no—
172Dic43—82no—
173#2484—431no—
174#2313—431no—
175#1826—431no—
176#1826D4311yescharacteristic
177#1463—431no—
178#1284—431no—
179#1284—431no—
180C2×C43—22no—
181C2×C43—22no—
182C2×C43—41no—
183C2×C43#189011yescharacteristic
184C2×C43#189711yescharacteristic
185C2×C43#191211yescharacteristic
186C2×#117C2×D4311yescharacteristic
187C22×C4⋊C4—431no—
188#407—431no—
189#407C2×D4311yescharacteristic
190#400—432no—
191#398—432no—
192#387—862no—
193#387—862no—
194#387—862no—
195#385—861no—
196#381—431no—
197#381—861no—
198#381—861no—
199#380—861no—
200C4×C22⋊C4—431no—
201C4×C22⋊C4C2×D4311yescharacteristic
202#339—22no—
203#339—862no—
204#324—862no—
205C43#948211yescharacteristic, complemented, Sylow
206C23×C4—431no—
207C23×C4—431no—
208C23×C4C22×D4311yescharacteristic
209C2×M16—21no—
210C2×M16—861no—
211#117—21no—
212#117—21no—
213#117—21no—
214#117—21no—
215C2×C4⋊C4—432no—
216C2×C4⋊C4—432no—
217C2×C4⋊C4—861no—
218C2×C4⋊C4—861no—
219C2×C4⋊C4—861no—
220C2×C4⋊C4—861no—
221C2×C4⋊C4—862no—
222C2×C4⋊C4—862no—
223C2×C4⋊C4C4×D4311yescharacteristic
224C2×C4⋊C4C4×D4311yescharacteristic
225C2×C22⋊C4—21no—
226C2×C22⋊C4—21no—
227C2×C22⋊C4—861no—
228C2×C22⋊C4—861no—
229C2×C42—21no—
230C2×C42—432no—
231C2×C42C22⋊D4312yes—
232C22⋊C8—21no—
233C22⋊C8—21no—
234C22⋊C8—861no—
235C22⋊C8—861no—
236#95—21no—
237#95—432no—
238#95—862no—
239#95—862no—
240#95—862no—
241#95—862no—
242#95—864no—
243#95—861no—
244#95—861no—
245C24D4×D4311yescharacteristic
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—22no—
249C22×C4—42no—
250C22×C4—432no—
251C22×C4—432no—
252C22×C4—861no—
253C22×C4—861no—
254C22×C4—861no—
255C22×C4—861no—
256C22×C4—862no—
257C22×C4—862no—
258C22×C4—1722no—
259C22×C4—1722no—
260C22×C4C2×C4×D4311yescharacteristic
261C22×C4#1062189811yescharacteristic
262C22×C4D4×D4311yescharacteristic
263C22×C4D4×D4311yescharacteristic
264C22×C4#1062190011yescharacteristic
265C22×C4C2×C22⋊D4311yescharacteristic
266M16—42no—
267M16—1722no—
268C2×C8—41no—
269C2×C8—1721no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—862no—
275C4⋊C4—862no—
276C4⋊C4—862no—
277C4⋊C4—862no—
278C4⋊C4—3442no—
279C4⋊C4—1724no—
280C22⋊C4—42no—
281C22⋊C4—41no—
282C22⋊C4—41no—
283C22⋊C4—1722no—
284C22⋊C4—1722no—
285C42—42no—
286C42—41no—
287C42—41no—
288C42—1722no—
289C23—22no—
290C23—22no—
291C23—41no—
292C23C22⋊C4×D4311yescharacteristic
293C23#1306329311yescharacteristic
294C23#1306330711yescharacteristic
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—862no—
309C2×C4—862no—
310C2×C4—862no—
311C2×C4—862no—
312C2×C4—3441no—
313C2×C4—1722no—
314C2×C4—1722no—
315C2×C4—1722no—
316C2×C4—1722no—
317C2×C4—1722no—
318C2×C4—1722no—
319C2×C4—1722no—
320C2×C4—1722no—
321C2×C4—1722no—
322C2×C4—1722no—
323C2×C4(C22⋊D43)⋊C411yescharacteristic
324C2×C4C4×C22⋊D4311yescharacteristic
325C2×C4#1306329611yescharacteristic
326C2×C4#1306329811yescharacteristic
327C8—81no—
328C8—3441no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—44no—
337C22#1458277511yescharacteristic
338C22#1458291412yes—
339C22#1458308812yes—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—21no—
344C4—82no—
345C4—81no—
346C4—81no—
347C4—3442no—
348C4—3442no—
349C4—1722no—
350C4—1722no—
351C2—22no—
352C2—22no—
353C2—41no—
354C2#1913500511yescharacteristic
355C2#1913504011yescharacteristic
356C2#1913512911yescharacteristic
subgroupG/H
centerC22#14582775
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1826C2
socleC22×C43#386
prime radicalC24×C43C2×D4
cosocleC23×C4×C43C23
hypercenter#1826D43
hypocenterC43#9482
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1826

Complements

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

NH ≅ G/Ntype
10. #14582837C4semidirect
11. #14582830C4semidirect
205. C43#9482semidirect

Maximal subgroups

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

subgroupindex
#191388782
#191371952
#191346942
#191329242
#191324492
#191324482
C43×#18262
#948243