Finite Group Databasebeta

← #25069091

Subgroups — #25069091

Order 11008.

930 conjugacy classes of subgroups; only the 183 normal subgroups are shown.

normal subgroups only

This group has 930 conjugacy classes of subgroups — too many to draw. Only its 183 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#19144539C212yesmaximal
2#19138882C211yesmaximal, characteristic
3#19133637C214yesmaximal, complemented
4#19133603C214yesmaximal, complemented
5#19133128C212yesmaximal
6#19132925C211yesmaximal, characteristic
7C2×C43×#544C211yesmaximal, characteristic
8C2×#13063284C2211yescharacteristic
9#14583237—24no—
10#14583232C2214yes—
11#14583227C2214yes—
12#14582939—22no—
13#14582908—22no—
14#14582863C2212yes—
15#14582838C2212yes—
16#14582829C2212yes—
17#14582780—22no—
18#14582772—21no—
19#14582762—21no—
20#14582762C2211yescharacteristic
21#14582636C2218yes—
22#14582625C2214yes—
23C43×#544—24no—
24C43×#544—22no—
25C43×#544C2214yes—
26C2×C4⋊Q8×C43—22no—
27C2×#125×C43—22no—
28C2×C22⋊Q8×C43—21no—
29C2×C22⋊Q8×C43C2212yes—
30C2×#117×C43—21no—
31C22×C4⋊C4×C43C2211yescharacteristic
32C2×#10621877—22no—
33#13063284—22no—
34#13063284—22no—
35C2×C4⋊Dic43C2311yescharacteristic
36C2×C4⋊Dic43C2311yescharacteristic
37C2×Dic43⋊C4—22no—
38C2×C22⋊Dic43—21no—
39C2×C22⋊Dic43—21no—
40C2×C4×Dic43—21no—
41#13063258—24no—
42#13063256—24no—
43#13063249—24no—
44#13063249—24no—
45C22⋊(C43⋊C8)—22no—
46C22⋊(C43⋊C8)C2314yes—
47C43⋊#95—22no—
48C43⋊#95—22no—
49C43⋊#95—22no—
50C43⋊#95—21no—
51C43⋊#95C2312yes—
52C22×Q8×C43—21no—
53C22×Q8×C43D412yes—
54C23×C4×C43D411yescharacteristic
55C23×C4×C43D411yescharacteristic
56C23×C4×C43C2311yescharacteristic
57C4⋊Q8×C43—28no—
58C4⋊Q8×C43—28no—
59#125×C43—28no—
60#125×C43—28no—
61C22⋊Q8×C43—24no—
62C22⋊Q8×C43—24no—
63C22⋊Q8×C43—22no—
64C22⋊Q8×C43—22no—
65C22⋊Q8×C43D414yes—
66C22⋊Q8×C43C2314yes—
67#117×C43—24no—
68#117×C43—24no—
69C2×C4⋊C4×C43—21no—
70C2×C4⋊C4×C43—21no—
71C2×C4⋊C4×C43—21no—
72C2×C4⋊C4×C43—22no—
73C2×C4⋊C4×C43—22no—
74C2×C4⋊C4×C43—22no—
75C2×C4⋊C4×C43—22no—
76C2×C4⋊C4×C43D412yes—
77C2×C4⋊C4×C43D412yes—
78C2×C4⋊C4×C43C2312yes—
79C2×C22⋊C4×C43—22no—
80C2×C42×C43—22no—
81C24×C43C2×D411yescharacteristic
82C2×Q8×C43—24no—
83C2×Q8×C43—22no—
84C2×Q8×C43—44no—
85C2×Q8×C43—82no—
86C2×Q8×C43C2×D414yes—
87C22×C4×C43—24no—
88C22×C4×C43—21no—
89C22×C4×C43—21no—
90C22×C4×C43—22no—
91C22×C4×C43—22no—
92C22×C4×C43—21no—
93C22×C4×C43—21no—
94C22×C4×C43—42no—
95C22×C4×C43—42no—
96C22×C4×C43C2×D412yes—
97C22×C4×C43C2×D412yes—
98C22×C4×C43C2×D412yes—
99C22×C4×C43C2×D412yes—
100C22×C4×C43C2×D411yescharacteristic
101C22×C4×C43C2411yescharacteristic
102C22×Dic43—22no—
103C22×Dic43—21no—
104C22×Dic43—21no—
105C4⋊C4×C43—24no—
106C4⋊C4×C43—24no—
107C4⋊C4×C43—24no—
108C4⋊C4×C43—28no—
109C4⋊C4×C43—24no—
110C4⋊C4×C43—24no—
111C4⋊C4×C43—22no—
112C4⋊C4×C43—24no—
113C4⋊C4×C43—24no—
114C4⋊C4×C43C2×D414yes—
115C22⋊C4×C43—24no—
116C22⋊C4×C43—24no—
117C42×C43—28no—
118C22⋊Dic43—42no—
119C22⋊Dic43—41no—
120C22⋊Dic43—41no—
121C4⋊Dic43—22no—
122C4⋊Dic43—22no—
123Dic43⋊C4—44no—
124C4×Dic43—42no—
125#10621877—44no—
126C2×C43⋊C8—24no—
127C23×C43—22no—
128C23×C43—22no—
129C23×C43—41no—
130C23×C43#12011yescharacteristic
131C23×C43#12011yescharacteristic
132C23×C43C22×D411yescharacteristic
133Q8×C43—44no—
134Q8×C43—82no—
135Q8×C43—84no—
136C2×C4×C43—24no—
137C2×C4×C43—24no—
138C2×C4×C43—22no—
139C2×C4×C43—22no—
140C2×C4×C43—24no—
141C2×C4×C43—24no—
142C2×C4×C43—24no—
143C2×C4×C43—22no—
144C2×C4×C43—42no—
145C2×C4×C43—41no—
146C2×C4×C43—41no—
147C2×C4×C43—44no—
148C2×C4×C43—42no—
149C2×C4×C43—44no—
150C2×C4×C43—42no—
151C2×C4×C43—81no—
152C2×C4×C43#12012yes—
153C2×C4×C43#13714yes—
154C2×C4×C43C22×D412yes—
155C2×Dic43—42no—
156C2×Dic43—42no—
157C2×Dic43—42no—
158C2×Dic43—41no—
159C2×Dic43—41no—
160C2×Dic43—42no—
161C2×Dic43—42no—
162C43⋊C8—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—44no—
179C4×C43—42no—
180C4×C43—44no—
181Dic43—82no—
182Dic43—81no—
183Dic43—81no—
184C2×#544D4311yescharacteristic
185#3095—432no—
186#2484—431no—
187#1617—434no—
188#1611—434no—
189#1511—432no—
190#1463—431no—
191C2×C43—22no—
192C2×C43—22no—
193C2×C43—41no—
194C2×C43#300411yescharacteristic
195C2×C43#302011yescharacteristic
196C2×C43C2×#45811yescharacteristic
197#544—24no—
198#544—22no—
199#544C2×D4314yes—
200C2×C4⋊Q8—22no—
201C2×#125—22no—
202C2×C22⋊Q8—21no—
203C2×C22⋊Q8C2×D4312yes—
204C2×#117—21no—
205C2×#117—431no—
206C22×C4⋊C4C2×D4311yescharacteristic
207#485—864no—
208#484—434no—
209#483—434no—
210#428—862no—
211#419—862no—
212#407—432no—
213#400—432no—
214#398—432no—
215#387—862no—
216#385—861no—
217#381—431no—
218#381—861no—
219#328—438no—
220#324—434no—
221C43#1814811yescharacteristic, complemented, Sylow
222C22×Q8—21no—
223C22×Q8C22⋊D4312yes—
224C23×C4C22⋊D4311yescharacteristic
225C23×C4C22⋊D4311yescharacteristic
226C23×C4C22×D4311yescharacteristic
227C2×M16—862no—
228C4⋊Q8—28no—
229C4⋊Q8—28no—
230#125—28no—
231#125—28no—
232C22⋊Q8—24no—
233C22⋊Q8—24no—
234C22⋊Q8—22no—
235C22⋊Q8—22no—
236C22⋊Q8C22⋊D4314yes—
237C22⋊Q8C22×D4314yes—
238#117—24no—
239#117—24no—
240#117—862no—
241#117—862no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—22no—
246C2×C4⋊C4—22no—
247C2×C4⋊C4—22no—
248C2×C4⋊C4—22no—
249C2×C4⋊C4—431no—
250C2×C4⋊C4—431no—
251C2×C4⋊C4—862no—
252C2×C4⋊C4C22⋊D4312yes—
253C2×C4⋊C4C22⋊D4312yes—
254C2×C4⋊C4C22×D4312yes—
255C2×C22⋊C4—22no—
256C2×C22⋊C4—861no—
257C2×C22⋊C4—861no—
258C2×C42—22no—
259C2×C42—861no—
260#107—864no—
261#106—864no—
262#103—864no—
263#103—864no—
264C22⋊C8—434no—
265C22⋊C8—862no—
266#95—432no—
267#95—861no—
268#95—862no—
269#95—862no—
270#95—862no—
271C24C2×C22⋊D4311yescharacteristic
272C2×Q8—24no—
273C2×Q8—22no—
274C2×Q8—44no—
275C2×Q8—82no—
276C2×Q8C2×C22⋊D4314yes—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—24no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—862no—
287C22×C4—861no—
288C22×C4—861no—
289C22×C4C2×C22⋊D4312yes—
290C22×C4C2×C22⋊D4312yes—
291C22×C4C2×C22⋊D4312yes—
292C22×C4C2×C22⋊D4311yescharacteristic
293C22×C4C2×C22⋊D4312yes—
294C22×C4C23×D4311yescharacteristic
295M16—1724no—
296C2×C8—864no—
297C4⋊C4—24no—
298C4⋊C4—24no—
299C4⋊C4—24no—
300C4⋊C4—28no—
301C4⋊C4—24no—
302C4⋊C4—24no—
303C4⋊C4—22no—
304C4⋊C4—24no—
305C4⋊C4—24no—
306C4⋊C4—862no—
307C4⋊C4—862no—
308C4⋊C4—1724no—
309C4⋊C4C2×C22⋊D4314yes—
310C22⋊C4—24no—
311C22⋊C4—24no—
312C22⋊C4—1722no—
313C22⋊C4—1721no—
314C22⋊C4—1721no—
315C42—28no—
316C42—1722no—
317C23—22no—
318C23—22no—
319C23—41no—
320C23#1306329411yescharacteristic
321C23#1306329411yescharacteristic
322C23C22×C22⋊D4311yescharacteristic
323Q8—44no—
324Q8—82no—
325Q8—84no—
326C2×C4—24no—
327C2×C4—24no—
328C2×C4—24no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—24no—
332C2×C4—24no—
333C2×C4—22no—
334C2×C4—42no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—44no—
338C2×C4—42no—
339C2×C4—44no—
340C2×C4—42no—
341C2×C4—81no—
342C2×C4—1722no—
343C2×C4—1722no—
344C2×C4—1722no—
345C2×C4—1721no—
346C2×C4—1721no—
347C2×C4—1722no—
348C2×C4—1722no—
349C2×C4#1306329412yes—
350C2×C4#1306335614yes—
351C2×C4C22×C22⋊D4312yes—
352C8—1724no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—44no—
361C22#1458308912yes—
362C22C2×#1306329411yescharacteristic
363C22C2×#1306335612yes—
364C4—22no—
365C4—22no—
366C4—24no—
367C4—44no—
368C4—42no—
369C4—44no—
370C4—3442no—
371C4—3441no—
372C4—3441no—
373C2—22no—
374C2—22no—
375C2—41no—
376C2#1914382911yescharacteristic
377C2#1914395911yescharacteristic
378C2C2×#1458308911yescharacteristic
subgroupG/H
centerC22C2×#13063294
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#544C2
socleC22×C43C2×#120
prime radicalC24×C43C2×D4
hypercenterC2×#544D43
hypocenterC43#18148
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
3. #19133637C2semidirect
4. #19133603C2semidirect
221. C43#18148semidirect

Maximal subgroups

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

subgroupindex
#191445392
#191388822
#191336372
#191336032
#191331282
#191329252
C2×C43×#5442
#1814843