Finite Group Databasebeta

← #25070795

Subgroups — #25070795

Order 11008.

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

normal subgroups only

This group has 950 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#19145419C212yesmaximal
3#19139975C211yesmaximal, characteristic
4#19133605C214yesmaximal, complemented
5#19133571C214yesmaximal, complemented
6#19133116C212yesmaximal
7C43×#1463C211yesmaximal, characteristic
8#14583530—24no—
9#14583530—22no—
10#14583530C2214yes—
11C2×#13063324—22no—
12C2×#13063316—22no—
13C2×#13063304—21no—
14C2×#13063304C2212yes—
15C2×#13063304C2211yescharacteristic
16C2×#13063284—21no—
17#14583230—22no—
18#14583230C2214yes—
19#14583157—24no—
20#14583057—22no—
21#14583057C2214yes—
22#14582829C2212yes—
23#14582819C2212yes—
24#14582794—22no—
25#14582772—21no—
26#14582772—21no—
27C4×C22⋊Dic43C2211yescharacteristic
28#14582637C2218yes—
29C22×C4⋊C4×C43C2211yescharacteristic
30C43×#407C2212yes—
31C43×#324C2214yes—
32C22×Dic86—21no—
33C22×Dic86D412yes—
34C22×Dic86C2311yescharacteristic
35C2×Dic172—24no—
36#13063324—28no—
37#13063324—28no—
38#13063316—28no—
39#13063316—28no—
40#13063304—24no—
41#13063304—24no—
42#13063304—22no—
43#13063304—22no—
44#13063304—22no—
45#13063304—22no—
46#13063304D414yes—
47#13063304C2314yes—
48#13063284—24no—
49#13063284—24no—
50C2×C4⋊Dic43—21no—
51C2×C4⋊Dic43—21no—
52C2×C4⋊Dic43—21no—
53C2×C4⋊Dic43D412yes—
54C2×C4⋊Dic43C2311yescharacteristic
55C2×Dic43⋊C4—22no—
56C2×Dic43⋊C4—22no—
57C2×Dic43⋊C4—21no—
58C2×Dic43⋊C4—22no—
59C2×Dic43⋊C4—22no—
60C2×C22⋊Dic43—22no—
61C2×C22⋊Dic43—21no—
62C2×C22⋊Dic43—21no—
63C2×C4×Dic43—22no—
64C2×C4×Dic43—21no—
65#13063257—24no—
66#13063250—24no—
67#13063250—24no—
68C43⋊#95—22no—
69C43⋊#95—22no—
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—81no—
88C22×C4×C43—81no—
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—22no—
101C2×Dic86—24no—
102C2×Dic86—22no—
103C2×Dic86—81no—
104C2×Dic86—82no—
105C2×Dic86—82no—
106C2×Dic86C2×D414yes—
107M16×C43—82no—
108C2×C8×C43—24no—
109C4⋊C4×C43—24no—
110C4⋊C4×C43—24no—
111C22⋊Dic43—24no—
112C22⋊Dic43—24no—
113C22⋊Dic43—24no—
114C22⋊Dic43—41no—
115C22⋊Dic43—41no—
116C4⋊Dic43—24no—
117C4⋊Dic43—24no—
118C4⋊Dic43—24no—
119C4⋊Dic43—22no—
120C4⋊Dic43—22no—
121C4⋊Dic43C2×D414yes—
122Dic43⋊C4—28no—
123Dic43⋊C4—24no—
124Dic43⋊C4—24no—
125Dic43⋊C4—42no—
126Dic43⋊C4—44no—
127Dic43⋊C4—82no—
128C4×Dic43—28no—
129C4×Dic43—81no—
130Dic172—84no—
131C23×C43—22no—
132C23×C43—22no—
133C23×C43—41no—
134C23×C43#12011yescharacteristic
135C23×C43#12011yescharacteristic
136C23×C43C22×D411yescharacteristic
137C2×C4×C43—24no—
138C2×C4×C43—24no—
139C2×C4×C43—22no—
140C2×C4×C43—22no—
141C2×C4×C43—22no—
142C2×C4×C43—41no—
143C2×C4×C43—42no—
144C2×C4×C43—42no—
145C2×C4×C43—41no—
146C2×C4×C43—42no—
147C2×C4×C43—42no—
148C2×C4×C43—81no—
149C2×C4×C43#12012yes—
150C2×C4×C43#13714yes—
151C2×C4×C43C22×D412yes—
152C2×Dic43—24no—
153C2×Dic43—24no—
154C2×Dic43—24no—
155C2×Dic43—42no—
156C2×Dic43—44no—
157C2×Dic43—42no—
158C2×Dic43—44no—
159C2×Dic43—42no—
160C2×Dic43—41no—
161C2×Dic43—41no—
162C2×Dic43—42no—
163Dic86—44no—
164Dic86—44no—
165Dic86—82no—
166Dic86—84no—
167C8×C43—44no—
168#18327—431nomaximal, Sylow
169C22×C43—21no—
170C22×C43—21no—
171C22×C43—21no—
172C22×C43—21no—
173C22×C43—21no—
174C22×C43—21no—
175C22×C43—21no—
176C22×C43—44no—
177C22×C43#45612yes—
178C22×C43C2×#12011yescharacteristic
179C22×C43C2×#13712yes—
180C4×C43—24no—
181C4×C43—22no—
182C4×C43—22no—
183C4×C43—42no—
184Dic43—44no—
185Dic43—44no—
186Dic43—44no—
187Dic43—81no—
188Dic43—81no—
189C2×#544—431no—
190#3195—432no—
191#2583—431no—
192#1611—434no—
193#1605—434no—
194#1508—432no—
195#1463D4311yescharacteristic
196C2×C43—22no—
197C2×C43—22no—
198C2×C43—41no—
199C2×C43#300411yescharacteristic
200C2×C43C2×#45611yescharacteristic
201C2×C43#302611yescharacteristic
202#544—434no—
203#544—864no—
204#544—862no—
205C2×C4⋊Q8—862no—
206C2×#125—862no—
207C2×C22⋊Q8—432no—
208C2×C22⋊Q8—431no—
209C2×C22⋊Q8—861no—
210C2×#117—861no—
211C22×C4⋊C4C2×D4311yescharacteristic
212#483—434no—
213#483—862no—
214#470—864no—
215#451—434no—
216#451—862no—
217#407C2×D4312yes—
218#398—432no—
219#395—432no—
220#389—862no—
221#385—861no—
222#385—861no—
223C4×C22⋊C4—431no—
224#328—438no—
225#324C2×D4314yes—
226C43#1832711yescharacteristic, complemented, Sylow
227C22×Q8—432no—
228C22×Q8—431no—
229C22×Q8—861no—
230C23×C4D17211yescharacteristic
231C23×C4D17211yescharacteristic
232C23×C4C22×D4311yescharacteristic
233C2×Q16—864no—
234C2×M16—22no—
235C4⋊Q8—868no—
236C4⋊Q8—868no—
237#125—868no—
238#125—868no—
239C22⋊Q8—434no—
240C22⋊Q8—434no—
241C22⋊Q8—864no—
242C22⋊Q8—862no—
243C22⋊Q8—864no—
244C22⋊Q8—862no—
245C22⋊Q8—862no—
246C22⋊Q8—862no—
247#117—864no—
248#117—864no—
249C2×C4⋊C4—22no—
250C2×C4⋊C4—22no—
251C2×C4⋊C4—432no—
252C2×C4⋊C4—431no—
253C2×C4⋊C4—861no—
254C2×C4⋊C4—861no—
255C2×C4⋊C4—861no—
256C2×C4⋊C4—862no—
257C2×C4⋊C4—862no—
258C2×C4⋊C4—862no—
259C2×C4⋊C4—861no—
260C2×C4⋊C4—862no—
261C2×C4⋊C4D17212yes—
262C2×C4⋊C4C22×D4312yes—
263C2×C22⋊C4—862no—
264C2×C22⋊C4—861no—
265C2×C22⋊C4—861no—
266C2×C42—862no—
267C2×C42—861no—
268#106—864no—
269#103—864no—
270#103—864no—
271C22⋊C8—22no—
272C22⋊C8C22×D4314yes—
273#95—432no—
274#95—862no—
275#95—862no—
276C24C2×D17211yescharacteristic
277C2×Q8—434no—
278C2×Q8—864no—
279C2×Q8—862no—
280C2×Q8—862no—
281C2×Q8—3442no—
282C2×Q8—3442no—
283C2×Q8—3441no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—24no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—81no—
290C22×C4—81no—
291C22×C4—862no—
292C22×C4—862no—
293C22×C4—862no—
294C22×C4—861no—
295C22×C4—861no—
296C22×C4C2×D17212yes—
297C22×C4C2×D17212yes—
298C22×C4C2×D17211yescharacteristic
299C22×C4D4×D4312yes—
300C22×C4D4×D4312yes—
301C22×C4C23×D4311yescharacteristic
302Q16—3444no—
303M16—82no—
304C2×C8—24no—
305C4⋊C4—24no—
306C4⋊C4—24no—
307C4⋊C4—434no—
308C4⋊C4—864no—
309C4⋊C4—864no—
310C4⋊C4—864no—
311C4⋊C4—868no—
312C4⋊C4—862no—
313C4⋊C4—864no—
314C4⋊C4—864no—
315C4⋊C4—862no—
316C4⋊C4—3442no—
317C4⋊C4—1722no—
318C4⋊C4—1724no—
319C22⋊C4—864no—
320C22⋊C4—864no—
321C22⋊C4—864no—
322C22⋊C4—1721no—
323C22⋊C4—1721no—
324C42—868no—
325C42—3441no—
326C23—22no—
327C23—22no—
328C23—41no—
329C23#1306329511yescharacteristic
330C23#1306329511yescharacteristic
331C23C22×D17211yescharacteristic
332Q8—3442no—
333Q8—3444no—
334Q8—1724no—
335Q8—1724no—
336C2×C4—24no—
337C2×C4—24no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—22no—
341C2×C4—41no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—41no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—81no—
348C2×C4—864no—
349C2×C4—864no—
350C2×C4—864no—
351C2×C4—1722no—
352C2×C4—1721no—
353C2×C4—1721no—
354C2×C4—1722no—
355C2×C4—1722no—
356C2×C4—1724no—
357C2×C4—1724no—
358C2×C4—1722no—
359C2×C4#1306329512yes—
360C2×C4#1306335814yes—
361C2×C4C2×D4×D4312yes—
362C8—44no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—44no—
371C22#1458308412yes—
372C22C2×#1306329511yescharacteristic
373C22C2×#1306335812yes—
374C4—22no—
375C4—22no—
376C4—24no—
377C4—42no—
378C4—3441no—
379C4—3441no—
380C4—1724no—
381C4—1724no—
382C4—1724no—
383C2—22no—
384C2—22no—
385C2—41no—
386C2#1914383211yescharacteristic
387C2C2×#1458308411yescharacteristic
388C2#1914399411yescharacteristic
subgroupG/H
centerC22C2×#13063295
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1463C2
socleC22×C43C2×#120
prime radicalC24×C43C2×D4
hypercenter#1463D43
hypocenterC43#18327
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. #19133605C2semidirect
5. #19133571C2semidirect
226. C43#18327semidirect

Maximal subgroups

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

subgroupindex
C2×#145835302
#191454192
#191399752
#191336052
#191335712
#191331162
C43×#14632
#1832743