Finite Group Databasebeta

← #24994410

Subgroups — #24994410

Order 11008.

610 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 610 conjugacy classes of subgroups — too many to draw. Only its 97 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#19138884C211yesmaximal, characteristic
2#19136950C211yesmaximal, characteristic
3#19134695C211yesmaximal, characteristic
4#19134692C211yesmaximal, characteristic
5#19132924C211yesmaximal, characteristic
6#19132447C211yesmaximal, characteristic
7C43×#1284C211yesmaximal, characteristic
8C2×#13063284C2211yescharacteristic
9C2×#13063281—21no—
10C22×Dic43⋊C4C2211yescharacteristic
11#14582863C2211yescharacteristic
12#14582839C412yescomplemented
13#14582831C412yescomplemented
14#14582784—22no—
15#14582774—21no—
16#14582760—21no—
17C4×Dic43⋊C4—22no—
18#14582750—22no—
19C22⋊C4×Dic43—21no—
20C4×C22⋊Dic43C2211yescharacteristic
21#14582660—22no—
22#14582659—22no—
23#14582624—22no—
24C43×#407C2211yescharacteristic
25C43×#381C2211yescharacteristic
26C4×C22⋊C4×C43C2211yescharacteristic
27C23×Dic43D411yescharacteristic
28C23×Dic43D411yescharacteristic
29C2×#10621877—21no—
30#13063284—21no—
31#13063284—21no—
32#13063284—21no—
33#13063284—21no—
34#13063281—28no—
35C2×C4⋊Dic43—22no—
36C2×C4⋊Dic43C2×C411yescharacteristic
37C2×C4⋊Dic43C2×C411yescharacteristic
38C2×Dic43⋊C4—22no—
39C2×Dic43⋊C4—21no—
40C2×Dic43⋊C4—21no—
41C2×Dic43⋊C4—21no—
42C2×Dic43⋊C4—21no—
43C2×Dic43⋊C4C2×C412yes—
44C2×Dic43⋊C4D412yes—
45C2×C22⋊Dic43—21no—
46C2×C22⋊Dic43—21no—
47C2×C4×Dic43—22no—
48C2×C4×Dic43—21no—
49C2×C4×Dic43—22no—
50C2×C4×Dic43D412yes—
51C22⋊(C43⋊C8)—21no—
52C22⋊(C43⋊C8)—21no—
53C43⋊#95—22no—
54C43⋊#95—21no—
55C43⋊#95—22no—
56C43⋊#95—22no—
57C43⋊#95—22no—
58C23×C4×C43C2311yescharacteristic
59C2×M16×C43—21no—
60C2×C22⋊C4×C43—21no—
61C2×C22⋊C4×C43—21no—
62C2×C42×C43D412yes—
63C22⋊C8×C43—21no—
64C22⋊C8×C43—21no—
65#95×C43—21no—
66#95×C43—21no—
67#95×C43C2×C412yes—
68C24×C43C2×D411yescharacteristic
69C22×C4×C43—22no—
70C22×C4×C43—22no—
71C22×C4×C43—42no—
72C22×C4×C43C22×C411yescharacteristic
73C22×C4×C43C2×D411yescharacteristic
74C22×C4×C43C2×D411yescharacteristic
75C22×C4×C43C2×D411yescharacteristic
76C22×C4×C43#4111yescharacteristic
77C22×C4×C43#4111yescharacteristic
78C22×Dic43—24no—
79C22×Dic43—21no—
80C22×Dic43—21no—
81C22×Dic43—21no—
82C22×Dic43—22no—
83C22×Dic43—21no—
84C22×Dic43—21no—
85C22×Dic43—21no—
86C22×Dic43—42no—
87C22×Dic43C22⋊C412yes—
88C22×Dic43C22⋊C412yes—
89M16×C43—42no—
90C2×C8×C43—41no—
91C22⋊C4×C43—24no—
92C22⋊C4×C43—42no—
93C42×C43—42no—
94C22⋊Dic43—24no—
95C22⋊Dic43—41no—
96C22⋊Dic43—41no—
97C4⋊Dic43—21no—
98C4⋊Dic43—21no—
99C4⋊Dic43—21no—
100C4⋊Dic43—21no—
101C4⋊Dic43—44no—
102Dic43⋊C4—28no—
103Dic43⋊C4—22no—
104Dic43⋊C4—22no—
105Dic43⋊C4—22no—
106Dic43⋊C4—22no—
107C4×Dic43—28no—
108C4×Dic43—41no—
109C4×Dic43—41no—
110C4×Dic43—42no—
111C4×Dic43—82no—
112#10621877—42no—
113C2×C43⋊C8—41no—
114C23×C43—22no—
115C23×C43—22no—
116C23×C43—41no—
117C23×C43C2×C22⋊C411yescharacteristic
118C23×C43#12011yescharacteristic
119C23×C43#12311yescharacteristic
120C2×C4×C43—22no—
121C2×C4×C43—22no—
122C2×C4×C43—24no—
123C2×C4×C43—41no—
124C2×C4×C43—41no—
125C2×C4×C43—41no—
126C2×C4×C43—41no—
127C2×C4×C43—42no—
128C2×C4×C43—42no—
129C2×C4×C43—42no—
130C2×C4×C43—42no—
131C2×C4×C43—42no—
132C2×C4×C43C4×D411yescharacteristic
133C2×C4×C43C4×D411yescharacteristic
134C2×C4×C43#12111yescharacteristic
135C2×C4×C43#12111yescharacteristic
136C2×Dic43—22no—
137C2×Dic43—22no—
138C2×Dic43—24no—
139C2×Dic43—22no—
140C2×Dic43—22no—
141C2×Dic43—24no—
142C2×Dic43—22no—
143C2×Dic43—42no—
144C2×Dic43—42no—
145C2×Dic43—42no—
146C2×Dic43—42no—
147C2×Dic43—42no—
148C2×Dic43—41no—
149C2×Dic43—41no—
150C2×Dic43—42no—
151C2×Dic43—81no—
152C2×Dic43#10414yes—
153C8×C43—81no—
154C43⋊C8—81no—
155#9478—431nomaximal, Sylow
156C22×C43—21no—
157C22×C43—21no—
158C22×C43—21no—
159C22×C43—21no—
160C22×C43—21no—
161C22×C43—21no—
162C22×C43—21no—
163C22×C43—44no—
164C22×C43#38611yescharacteristic
165C22×C43C2×#10412yes—
166C22×C43#45812yes—
167C4×C43—21no—
168C4×C43—21no—
169C4×C43—21no—
170C4×C43—21no—
171C4×C43—44no—
172C4×C43—82no—
173Dic43—24no—
174Dic43—44no—
175Dic43—42no—
176Dic43—81no—
177Dic43—81no—
178#2484—431no—
179#2274—431no—
180#1826—431no—
181#1826—431no—
182#1463—431no—
183#1284—431no—
184#1284D4311yescharacteristic
185C2×C43—22no—
186C2×C43—22no—
187C2×C43—41no—
188C2×C43#189011yescharacteristic
189C2×C43#189611yescharacteristic
190C2×C43#191211yescharacteristic
191C2×#117—431no—
192C2×#117—861no—
193C22×C4⋊C4—431no—
194#407—431no—
195#407C2×D4311yescharacteristic
196#400—432no—
197#398—432no—
198#387—862no—
199#385—861no—
200#381—861no—
201#381C2×D4311yescharacteristic
202C4×C4⋊C4—862no—
203C4×C4⋊C4—862no—
204C4×C22⋊C4—431no—
205C4×C22⋊C4—861no—
206C4×C22⋊C4C2×D4311yescharacteristic
207#339—862no—
208#339—862no—
209#324—862no—
210C43#947811yescharacteristic, complemented, Sylow
211C23×C4—431no—
212C23×C4—431no—
213C23×C4C22×D4311yescharacteristic
214C2×M16—21no—
215C2×M16—861no—
216#117—868no—
217#117—861no—
218#117—861no—
219#117—861no—
220#117—861no—
221C2×C4⋊C4—432no—
222C2×C4⋊C4—432no—
223C2×C4⋊C4—431no—
224C2×C4⋊C4—431no—
225C2×C4⋊C4—862no—
226C2×C4⋊C4—861no—
227C2×C4⋊C4—861no—
228C2×C4⋊C4—861no—
229C2×C4⋊C4—861no—
230C2×C4⋊C4—862no—
231C2×C22⋊C4—21no—
232C2×C22⋊C4—21no—
233C2×C22⋊C4—861no—
234C2×C22⋊C4—861no—
235C2×C42—432no—
236C2×C42—862no—
237C2×C42—862no—
238C2×C42—861no—
239C2×C42D17212yes—
240C22⋊C8—21no—
241C22⋊C8—21no—
242C22⋊C8—861no—
243C22⋊C8—861no—
244#95—21no—
245#95—21no—
246#95—862no—
247#95—862no—
248#95—862no—
249#95—862no—
250#95—861no—
251#95C4×D4312yes—
252C24D4×D4311yescharacteristic
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—42no—
256C22×C4—432no—
257C22×C4—432no—
258C22×C4—864no—
259C22×C4—861no—
260C22×C4—861no—
261C22×C4—861no—
262C22×C4—862no—
263C22×C4—861no—
264C22×C4—861no—
265C22×C4—861no—
266C22×C4—1722no—
267C22×C4C2×C4×D4311yescharacteristic
268C22×C4C2×D17211yescharacteristic
269C22×C4#1062189811yescharacteristic
270C22×C4D4×D4311yescharacteristic
271C22×C4D4×D4311yescharacteristic
272C22×C4#1062190211yescharacteristic
273M16—42no—
274M16—1722no—
275C2×C8—41no—
276C2×C8—1721no—
277C4⋊C4—868no—
278C4⋊C4—862no—
279C4⋊C4—862no—
280C4⋊C4—862no—
281C4⋊C4—862no—
282C4⋊C4—861no—
283C4⋊C4—861no—
284C4⋊C4—861no—
285C4⋊C4—861no—
286C4⋊C4—1724no—
287C22⋊C4—24no—
288C22⋊C4—42no—
289C22⋊C4—864no—
290C22⋊C4—1721no—
291C22⋊C4—1721no—
292C42—42no—
293C42—868no—
294C42—3442no—
295C42—1722no—
296C42—1721no—
297C42—1721no—
298C23—22no—
299C23—22no—
300C23—41no—
301C23C22⋊C4×D4311yescharacteristic
302C23#1306329511yescharacteristic
303C23#1306331011yescharacteristic
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—434no—
317C2×C4—862no—
318C2×C4—862no—
319C2×C4—864no—
320C2×C4—862no—
321C2×C4—862no—
322C2×C4—864no—
323C2×C4—862no—
324C2×C4—3441no—
325C2×C4—1722no—
326C2×C4—1722no—
327C2×C4—1721no—
328C2×C4—1721no—
329C2×C4—1722no—
330C2×C4—1722no—
331C2×C4—1722no—
332C2×C4—1722no—
333C2×C4#1306328711yescharacteristic
334C2×C4C4×D17211yescharacteristic
335C2×C4#1306329811yescharacteristic
336C2×C4#1306330011yescharacteristic
337C8—81no—
338C8—3441no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—44no—
347C22#1458277711yescharacteristic
348C22#104×D4312yes—
349C22#1458309012yes—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—44no—
355C4—82no—
356C4—864no—
357C4—3441no—
358C4—3441no—
359C4—1724no—
360C4—1722no—
361C2—22no—
362C2—22no—
363C2—41no—
364C2#1913500711yescharacteristic
365C2#1913503711yescharacteristic
366C2#1913513111yescharacteristic
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#9478
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. #14582839C4semidirect
13. #14582831C4semidirect
210. C43#9478semidirect

Maximal subgroups

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

subgroupindex
#191388842
#191369502
#191346952
#191346922
#191329242
#191324472
C43×#12842
#947843