Finite Group Databasebeta

← #25069094

Subgroups — #25069094

Order 11008.

930 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 930 conjugacy classes of subgroups — too many to draw. Only its 167 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
1C2×#14583530C211yesmaximal, characteristic
2#19144544C212yesmaximal
3#19138882C211yesmaximal, characteristic
4#19133639C214yesmaximal, complemented
5#19133605C214yesmaximal, complemented
6#19133129C212yesmaximal
7C43×#1463C211yesmaximal, characteristic
8#14583530—24no—
9#14583530—22no—
10#14583530C2214yes—
11C2×#13063324—22no—
12C2×#13063316—22no—
13C2×#13063304—21no—
14C2×#13063304C2212yes—
15C2×#13063284—21no—
16C2×#13063284C2211yescharacteristic
17#14583241—24no—
18#14583235C2214yes—
19#14583230C2214yes—
20#14582941—22no—
21#14582909—22no—
22#14582838C2212yes—
23#14582829C2212yes—
24#14582780—22no—
25#14582772—21no—
26#14582762—21no—
27#14582762C2211yescharacteristic
28#14582637C2218yes—
29C22×C4⋊C4×C43C2211yescharacteristic
30C43×#407C2212yes—
31C43×#324C2214yes—
32C22×Dic86—21no—
33C22×Dic86D412yes—
34#13063324—28no—
35#13063324—28no—
36#13063316—28no—
37#13063316—28no—
38#13063304—24no—
39#13063304—24no—
40#13063304—22no—
41#13063304—22no—
42#13063304D414yes—
43#13063304C2314yes—
44#13063284—24no—
45#13063284—24no—
46#13063284—22no—
47#13063284—22no—
48C2×C4⋊Dic43—21no—
49C2×C4⋊Dic43—21no—
50C2×C4⋊Dic43—21no—
51C2×C4⋊Dic43D412yes—
52C2×C4⋊Dic43C2311yescharacteristic
53C2×C4⋊Dic43C2311yescharacteristic
54C2×Dic43⋊C4—22no—
55C2×Dic43⋊C4—22no—
56C2×Dic43⋊C4—22no—
57C2×C22⋊Dic43—22no—
58C2×C22⋊Dic43—21no—
59C2×C22⋊Dic43—21no—
60C2×C4×Dic43—22no—
61C2×C4×Dic43—21no—
62#13063259—24no—
63#13063257—24no—
64#13063250—24no—
65#13063250—24no—
66C43⋊#95—22no—
67C43⋊#95—22no—
68C43⋊#95—22no—
69C43⋊#95—21no—
70C43⋊#95C2312yes—
71C23×C4×C43D411yescharacteristic
72C23×C4×C43D411yescharacteristic
73C23×C4×C43C2311yescharacteristic
74C2×M16×C43—22no—
75C2×C4⋊C4×C43—22no—
76C2×C4⋊C4×C43—22no—
77C2×C4⋊C4×C43D412yes—
78C2×C4⋊C4×C43C2312yes—
79C22⋊C8×C43—22no—
80C22⋊C8×C43C2314yes—
81C24×C43C2×D411yescharacteristic
82C22×C4×C43—24no—
83C22×C4×C43—21no—
84C22×C4×C43—21no—
85C22×C4×C43—21no—
86C22×C4×C43—21no—
87C22×C4×C43—42no—
88C22×C4×C43—42no—
89C22×C4×C43C2×D412yes—
90C22×C4×C43C2×D412yes—
91C22×C4×C43C2×D412yes—
92C22×C4×C43C2×D412yes—
93C22×C4×C43C2×D411yescharacteristic
94C22×C4×C43C2411yescharacteristic
95C22×Dic43—22no—
96C22×Dic43—22no—
97C22×Dic43—22no—
98C22×Dic43—21no—
99C22×Dic43—21no—
100C2×Dic86—24no—
101C2×Dic86—22no—
102C2×Dic86—44no—
103C2×Dic86—82no—
104C2×Dic86C2×D414yes—
105M16×C43—44no—
106C2×C8×C43—24no—
107C4⋊C4×C43—24no—
108C4⋊C4×C43—24no—
109C22⋊Dic43—24no—
110C22⋊Dic43—24no—
111C22⋊Dic43—42no—
112C22⋊Dic43—41no—
113C22⋊Dic43—41no—
114C4⋊Dic43—24no—
115C4⋊Dic43—24no—
116C4⋊Dic43—24no—
117C4⋊Dic43—22no—
118C4⋊Dic43—22no—
119C4⋊Dic43—22no—
120C4⋊Dic43C2×D414yes—
121Dic43⋊C4—28no—
122Dic43⋊C4—24no—
123Dic43⋊C4—24no—
124Dic43⋊C4—44no—
125C4×Dic43—28no—
126C4×Dic43—42no—
127C23×C43—22no—
128C23×C43—22no—
129C23×C43—41no—
130C23×C43#12011yescharacteristic
131C23×C43#12011yescharacteristic
132C23×C43C22×D411yescharacteristic
133C2×C4×C43—24no—
134C2×C4×C43—24no—
135C2×C4×C43—22no—
136C2×C4×C43—22no—
137C2×C4×C43—24no—
138C2×C4×C43—22no—
139C2×C4×C43—41no—
140C2×C4×C43—42no—
141C2×C4×C43—41no—
142C2×C4×C43—42no—
143C2×C4×C43—42no—
144C2×C4×C43—81no—
145C2×C4×C43#12012yes—
146C2×C4×C43#13714yes—
147C2×C4×C43C22×D412yes—
148C2×Dic43—24no—
149C2×Dic43—24no—
150C2×Dic43—44no—
151C2×Dic43—44no—
152C2×Dic43—42no—
153C2×Dic43—42no—
154C2×Dic43—42no—
155C2×Dic43—41no—
156C2×Dic43—41no—
157C2×Dic43—42no—
158C2×Dic43—42no—
159Dic86—44no—
160Dic86—82no—
161Dic86—84no—
162C8×C43—44no—
163#18148—431nomaximal, Sylow
164C22×C43—21no—
165C22×C43—21no—
166C22×C43—21no—
167C22×C43—21no—
168C22×C43—21no—
169C22×C43—21no—
170C22×C43—21no—
171C22×C43—44no—
172C22×C43#45812yes—
173C22×C43C2×#12011yescharacteristic
174C22×C43C2×#13712yes—
175C4×C43—24no—
176C4×C43—22no—
177C4×C43—22no—
178C4×C43—42no—
179Dic43—44no—
180Dic43—44no—
181Dic43—82no—
182Dic43—81no—
183Dic43—81no—
184C2×#544—431no—
185#3095—432no—
186#2484—431no—
187#1617—434no—
188#1611—434no—
189#1511—432no—
190#1463D4311yescharacteristic
191C2×C43—22no—
192C2×C43—22no—
193C2×C43—41no—
194C2×C43#300411yescharacteristic
195C2×C43#302011yescharacteristic
196C2×C43C2×#45811yescharacteristic
197#544—434no—
198#544—864no—
199#544—862no—
200C2×C4⋊Q8—862no—
201C2×#125—862no—
202C2×C22⋊Q8—432no—
203C2×C22⋊Q8—861no—
204C2×#117—431no—
205C2×#117—861no—
206C22×C4⋊C4C2×D4311yescharacteristic
207#485—864no—
208#484—434no—
209#483—434no—
210#428—862no—
211#419—862no—
212#407C2×D4312yes—
213#400—432no—
214#398—432no—
215#387—862no—
216#385—861no—
217#381—431no—
218#381—861no—
219#328—438no—
220#324C2×D4314yes—
221C43#1814811yescharacteristic, complemented, Sylow
222C22×Q8—432no—
223C22×Q8—861no—
224C23×C4D17211yescharacteristic
225C23×C4D17211yescharacteristic
226C23×C4C22×D4311yescharacteristic
227C2×M16—22no—
228C4⋊Q8—868no—
229C4⋊Q8—868no—
230#125—868no—
231#125—868no—
232C22⋊Q8—434no—
233C22⋊Q8—434no—
234C22⋊Q8—864no—
235C22⋊Q8—862no—
236C22⋊Q8—864no—
237C22⋊Q8—862no—
238#117—864no—
239#117—864no—
240#117—862no—
241#117—862no—
242C2×C4⋊C4—22no—
243C2×C4⋊C4—22no—
244C2×C4⋊C4—432no—
245C2×C4⋊C4—431no—
246C2×C4⋊C4—431no—
247C2×C4⋊C4—861no—
248C2×C4⋊C4—861no—
249C2×C4⋊C4—861no—
250C2×C4⋊C4—862no—
251C2×C4⋊C4—862no—
252C2×C4⋊C4—862no—
253C2×C4⋊C4D17212yes—
254C2×C4⋊C4C22×D4312yes—
255C2×C22⋊C4—862no—
256C2×C22⋊C4—861no—
257C2×C22⋊C4—861no—
258C2×C42—862no—
259C2×C42—861no—
260#107—864no—
261#106—864no—
262#103—864no—
263#103—864no—
264C22⋊C8—22no—
265C22⋊C8C22×D4314yes—
266#95—432no—
267#95—861no—
268#95—862no—
269#95—862no—
270#95—862no—
271C24C2×D17211yescharacteristic
272C2×Q8—434no—
273C2×Q8—864no—
274C2×Q8—862no—
275C2×Q8—3442no—
276C2×Q8—1724no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—24no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—42no—
283C22×C4—42no—
284C22×C4—862no—
285C22×C4—862no—
286C22×C4—862no—
287C22×C4—861no—
288C22×C4—861no—
289C22×C4C2×D17212yes—
290C22×C4C2×D17212yes—
291C22×C4C2×D17211yescharacteristic
292C22×C4D4×D4312yes—
293C22×C4D4×D4312yes—
294C22×C4C23×D4311yescharacteristic
295M16—44no—
296C2×C8—24no—
297C4⋊C4—24no—
298C4⋊C4—24no—
299C4⋊C4—434no—
300C4⋊C4—864no—
301C4⋊C4—864no—
302C4⋊C4—864no—
303C4⋊C4—868no—
304C4⋊C4—862no—
305C4⋊C4—864no—
306C4⋊C4—864no—
307C4⋊C4—862no—
308C4⋊C4—862no—
309C4⋊C4—1724no—
310C22⋊C4—864no—
311C22⋊C4—864no—
312C22⋊C4—1722no—
313C22⋊C4—1721no—
314C22⋊C4—1721no—
315C42—868no—
316C42—1722no—
317C23—22no—
318C23—22no—
319C23—41no—
320C23#1306329511yescharacteristic
321C23#1306329511yescharacteristic
322C23C22×D17211yescharacteristic
323Q8—3442no—
324Q8—3444no—
325Q8—1724no—
326C2×C4—24no—
327C2×C4—24no—
328C2×C4—24no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—41no—
333C2×C4—42no—
334C2×C4—41no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—81no—
338C2×C4—864no—
339C2×C4—864no—
340C2×C4—1722no—
341C2×C4—1722no—
342C2×C4—1722no—
343C2×C4—1721no—
344C2×C4—1721no—
345C2×C4—1722no—
346C2×C4—1722no—
347C2×C4—1724no—
348C2×C4—1724no—
349C2×C4#1306329512yes—
350C2×C4#1306335814yes—
351C2×C4C2×D4×D4312yes—
352C8—44no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—44no—
361C22#1458309012yes—
362C22C2×#1306329511yescharacteristic
363C22C2×#1306335812yes—
364C4—22no—
365C4—22no—
366C4—24no—
367C4—42no—
368C4—3442no—
369C4—3441no—
370C4—3441no—
371C4—1724no—
372C4—1724no—
373C2—22no—
374C2—22no—
375C2—41no—
376C2#1914383211yescharacteristic
377C2#1914396211yescharacteristic
378C2C2×#1458309011yescharacteristic
subgroupG/H
centerC22C2×#13063295
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1463C2
socleC22×C43C2×#120
prime radicalC24×C43C2×D4
hypercenter#1463D43
hypocenterC43#18148
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1463

Complements

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

NH ≅ G/Ntype
4. #19133639C2semidirect
5. #19133605C2semidirect
221. C43#18148semidirect

Maximal subgroups

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

subgroupindex
C2×#145835302
#191445442
#191388822
#191336392
#191336052
#191331292
C43×#14632
#1814843