Finite Group Databasebeta

← #24994403

Subgroups — #24994403

Order 11008.

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

normal subgroups only

This group has 734 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#19138865C211yesmaximal, characteristic
2#19136947C211yesmaximal, characteristic
3#19134694C211yesmaximal, characteristic, complemented
4#19132921C211yesmaximal, characteristic
5#19132449C211yesmaximal, characteristic, complemented
6#19132448C211yesmaximal, characteristic, complemented
7C43×#1826C211yesmaximal, characteristic, complemented
8C22×(C2×D43)⋊C4C2211yescharacteristic
9C2×C22⋊C4×D43—21no—
10#14582863C2211yescharacteristic
11#14582834C412yescomplemented
12#14582825C412yescomplemented
13#14582790—22no—
14#14582771—21no—
15#14582762C2211yescharacteristic
16#14582754—21no—
17C22⋊C4×Dic43—21no—
18C4×(C2×D43)⋊C4—22no—
19C4×C22⋊Dic43C2211yescharacteristic
20#14582746—22no—
21#14582658—22no—
22#14582622—22no—
23C2×#117×C43C2211yescharacteristic
24C43×#407C2211yescharacteristic
25C4×C22⋊C4×C43C2211yescharacteristic
26C43×#339—22no—
27C24×D43D411yescharacteristic
28C23×Dic43D411yescharacteristic
29C22×C4×D43—22no—
30C2×#10621877—21no—
31C2×Dic43⋊C4—22no—
32C2×C22⋊Dic43—21no—
33C2×C22⋊Dic43—21no—
34C2×(C2×D43)⋊C4—22no—
35C2×(C2×D43)⋊C4—21no—
36C2×(C2×D43)⋊C4—21no—
37C2×(C2×D43)⋊C4—21no—
38C2×(C2×D43)⋊C4—21no—
39C2×(C2×D43)⋊C4—22no—
40C2×(C2×D43)⋊C4—22no—
41C2×(C2×D43)⋊C4C2×C412yes—
42C2×(C2×D43)⋊C4D412yes—
43C22⋊C4×D43—28no—
44C2×C4×Dic43—22no—
45C2×C4×Dic43D412yes—
46C22⋊(C43⋊C8)—21no—
47C22⋊(C43⋊C8)—21no—
48C43⋊#95—22no—
49C43⋊#95—21no—
50C43⋊#95—21no—
51C43⋊#95—22no—
52C43⋊#95C2×C412yescomplemented
53C23×C4×C43C2311yescharacteristic
54C2×M16×C43—21no—
55#117×C43—21no—
56#117×C43—21no—
57#117×C43—21no—
58#117×C43—21no—
59C2×C4⋊C4×C43C2×C411yescharacteristic, complemented
60C2×C4⋊C4×C43C2×C411yescharacteristic, complemented
61C2×C22⋊C4×C43—21no—
62C2×C22⋊C4×C43—21no—
63C2×C42×C43—21no—
64C2×C42×C43D412yes—
65C22⋊C8×C43—21no—
66C22⋊C8×C43—21no—
67#95×C43—21no—
68C24×C43C2×D411yescharacteristic
69C23×D43—21no—
70C23×D43—21no—
71C23×D43—24no—
72C23×D43—42no—
73C23×D43—81no—
74C23×D43C22⋊C412yes—
75C22×C4×C43—21no—
76C22×C4×C43—21no—
77C22×C4×C43—22no—
78C22×C4×C43—42no—
79C22×C4×C43C22×C411yescharacteristic
80C22×C4×C43C2×D411yescharacteristic
81C22×C4×C43C2×D411yescharacteristic
82C22×C4×C43C2×D411yescharacteristic
83C22×C4×C43#4111yescharacteristic
84C22×C4×C43#4111yescharacteristic
85C22×Dic43—22no—
86C22×Dic43—21no—
87C22×Dic43—22no—
88C22×Dic43—21no—
89C22×Dic43—81no—
90C22×Dic43C22⋊C412yes—
91C2×C4×D43—28no—
92C2×C4×D43—82no—
93C2×C4×D43—82no—
94M16×C43—42no—
95C2×C8×C43—41no—
96C4⋊C4×C43—21no—
97C4⋊C4×C43—21no—
98C4⋊C4×C43—21no—
99C4⋊C4×C43—21no—
100C22⋊C4×C43—24no—
101C22⋊C4×C43—41no—
102C22⋊C4×C43—41no—
103C42×C43—42no—
104C42×C43—41no—
105C42×C43—41no—
106C22⋊Dic43—24no—
107C22⋊Dic43—42no—
108(C2×D43)⋊C4—28no—
109(C2×D43)⋊C4—22no—
110(C2×D43)⋊C4—22no—
111(C2×D43)⋊C4—22no—
112(C2×D43)⋊C4—22no—
113(C2×D43)⋊C4—44no—
114(C2×D43)⋊C4—82no—
115Dic43⋊C4—82no—
116C4×Dic43—42no—
117C4×Dic43—82no—
118#10621877—42no—
119C2×C43⋊C8—41no—
120C23×C43—22no—
121C23×C43—22no—
122C23×C43—41no—
123C23×C43C2×C22⋊C411yescharacteristic
124C23×C43#12011yescharacteristic
125C23×C43#12311yescharacteristic
126C22×D43—22no—
127C22×D43—22no—
128C22×D43—22no—
129C22×D43—24no—
130C22×D43—22no—
131C22×D43—42no—
132C22×D43—42no—
133C22×D43—42no—
134C22×D43—42no—
135C22×D43—88no—
136C22×D43—81no—
137C22×D43—81no—
138C22×D43#10414yes—
139C2×C4×C43—22no—
140C2×C4×C43—22no—
141C2×C4×C43—24no—
142C2×C4×C43—41no—
143C2×C4×C43—41no—
144C2×C4×C43—41no—
145C2×C4×C43—41no—
146C2×C4×C43—42no—
147C2×C4×C43—42no—
148C2×C4×C43—42no—
149C2×C4×C43—41no—
150C2×C4×C43—41no—
151C2×C4×C43—42no—
152C2×C4×C43C4×D411yescharacteristic
153C2×C4×C43C4×D411yescharacteristic
154C2×C4×C43#12111yescharacteristic
155C2×C4×C43#12111yescharacteristic
156C2×Dic43—24no—
157C2×Dic43—22no—
158C2×Dic43—42no—
159C2×Dic43—42no—
160C2×Dic43—42no—
161C2×Dic43—42no—
162C2×Dic43—42no—
163C2×Dic43—42no—
164C2×Dic43—42no—
165C2×Dic43—81no—
166C4×D43—88no—
167C8×C43—81no—
168C43⋊C8—81no—
169#9477—431nomaximal, Sylow
170C22×C43—21no—
171C22×C43—21no—
172C22×C43—21no—
173C22×C43—21no—
174C22×C43—21no—
175C22×C43—21no—
176C22×C43—21no—
177C22×C43—44no—
178C22×C43#38611yescharacteristic
179C22×C43C2×#10412yes—
180C22×C43#45812yes—
181C2×D43—24no—
182C2×D43—44no—
183C2×D43—44no—
184C2×D43—42no—
185C2×D43—42no—
186C2×D43—44no—
187C2×D43—82no—
188C2×D43—84no—
189C4×C43—21no—
190C4×C43—21no—
191C4×C43—21no—
192C4×C43—21no—
193C4×C43—44no—
194C4×C43—81no—
195C4×C43—81no—
196Dic43—44no—
197Dic43—42no—
198Dic43—82no—
199#2482—431no—
200#2273—431no—
201#1826—431no—
202#1826D4311yescharacteristic, complemented
203#1462—431no—
204#1284—431no—
205#1284—431no—
206C2×C43—22no—
207C2×C43—22no—
208C2×C43—41no—
209C2×C43#189011yescharacteristic
210C2×C43#189611yescharacteristic
211C2×C43#191111yescharacteristic
212D43—44no—
213C2×#117C2×D4311yescharacteristic
214C22×C22⋊C4—431no—
215C22×C22⋊C4—861no—
216#407—431no—
217#407C2×D4311yescharacteristic
218#399—432no—
219#397—432no—
220#388—862no—
221#385—861no—
222#381—431no—
223#379—861no—
224C4×C22⋊C4—431no—
225C4×C22⋊C4—862no—
226C4×C22⋊C4—861no—
227C4×C22⋊C4—862no—
228C4×C22⋊C4C2×D4311yescharacteristic
229#339—22no—
230#339—862no—
231#323—862no—
232C43#947711yescharacteristic, complemented, Sylow
233C25—431no—
234C23×C4—431no—
235C23×C4—862no—
236C23×C4C22×D4311yescharacteristic
237C2×M16—21no—
238C2×M16—861no—
239#117—21no—
240#117—21no—
241#117—21no—
242#117—21no—
243C2×C4⋊C4—862no—
244C2×C4⋊C4C4×D4311yescharacteristic, complemented
245C2×C4⋊C4C4×D4311yescharacteristic, complemented
246C2×C22⋊C4—21no—
247C2×C22⋊C4—21no—
248C2×C22⋊C4—432no—
249C2×C22⋊C4—432no—
250C2×C22⋊C4—868no—
251C2×C22⋊C4—862no—
252C2×C22⋊C4—861no—
253C2×C22⋊C4—861no—
254C2×C22⋊C4—861no—
255C2×C22⋊C4—861no—
256C2×C22⋊C4—861no—
257C2×C22⋊C4—862no—
258C2×C22⋊C4—862no—
259C2×C22⋊C4—861no—
260C2×C42—21no—
261C2×C42—432no—
262C2×C42—862no—
263C2×C42C22⋊D4312yes—
264C22⋊C8—21no—
265C22⋊C8—21no—
266C22⋊C8—861no—
267C22⋊C8—861no—
268#95—21no—
269#95—432no—
270#95—862no—
271#95—862no—
272#95—861no—
273#95—861no—
274C24—432no—
275C24—864no—
276C24—861no—
277C24—861no—
278C24—3441no—
279C24—1722no—
280C24D4×D4311yescharacteristic
281C22×C4—22no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—42no—
285C22×C4—432no—
286C22×C4—868no—
287C22×C4—861no—
288C22×C4—862no—
289C22×C4—861no—
290C22×C4—862no—
291C22×C4—3442no—
292C22×C4—3442no—
293C22×C4—3441no—
294C22×C4C2×C4×D4311yescharacteristic
295C22×C4#1062189811yescharacteristic
296C22×C4D4×D4311yescharacteristic
297C22×C4D4×D4311yescharacteristic
298C22×C4#1062190011yescharacteristic
299C22×C4C2×C22⋊D4311yescharacteristic
300M16—42no—
301M16—1722no—
302C2×C8—41no—
303C2×C8—1721no—
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—3442no—
309C22⋊C4—24no—
310C22⋊C4—41no—
311C22⋊C4—41no—
312C22⋊C4—868no—
313C22⋊C4—864no—
314C22⋊C4—862no—
315C22⋊C4—862no—
316C22⋊C4—862no—
317C22⋊C4—862no—
318C22⋊C4—3442no—
319C22⋊C4—1724no—
320C22⋊C4—1722no—
321C42—42no—
322C42—41no—
323C42—41no—
324C42—3442no—
325C42—1722no—
326C23—22no—
327C23—22no—
328C23—41no—
329C23—434no—
330C23—864no—
331C23—862no—
332C23—862no—
333C23—862no—
334C23—862no—
335C23—3441no—
336C23—3441no—
337C23—3448no—
338C23—1722no—
339C23—1722no—
340C23—1722no—
341C23—1722no—
342C23C22⋊C4×D4311yescharacteristic
343C23#1306329311yescharacteristic
344C23#1306330711yescharacteristic
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—24no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—864no—
359C2×C4—862no—
360C2×C4—3448no—
361C2×C4—3441no—
362C2×C4—1722no—
363C2×C4—1722no—
364C2×C4—1722no—
365C2×C4—1722no—
366C2×C4—1722no—
367C2×C4—1722no—
368C2×C4—1722no—
369C2×C4(C22⋊D43)⋊C411yescharacteristic
370C2×C4C4×C22⋊D4311yescharacteristic
371C2×C4#1306329611yescharacteristic
372C2×C4#1306329811yescharacteristic
373C8—81no—
374C8—3441no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22—44no—
383C22—864no—
384C22—3442no—
385C22—3444no—
386C22—1724no—
387C22—1724no—
388C22—1724no—
389C22—1722no—
390C22—1722no—
391C22#1458277511yescharacteristic
392C22#104×D4312yes—
393C22#1458308812yes—
394C4—21no—
395C4—21no—
396C4—21no—
397C4—21no—
398C4—44no—
399C4—81no—
400C4—81no—
401C4—3442no—
402C4—1724no—
403C4—1722no—
404C2—22no—
405C2—22no—
406C2—41no—
407C2—1724no—
408C2#1913500511yescharacteristic
409C2#1913503511yescharacteristic
410C2#1913512411yescharacteristic
subgroupG/H
centerC22#14582775
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1826C2
socleC22×C43#386
prime radicalC24×D43D4
cosocleC23×C4×C43C23
hypercenter#1826D43
hypocenterC43#9477
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
3. #19134694C2semidirect
5. #19132449C2semidirect
6. #19132448C2semidirect
7. C43×#1826C2semidirect
11. #14582834C4semidirect
12. #14582825C4semidirect
52. C43⋊#95C2×C4semidirect
59. C2×C4⋊C4×C43C2×C4semidirect
60. C2×C4⋊C4×C43C2×C4semidirect
202. #1826D43semidirect
232. C43#9477semidirect
244. C2×C4⋊C4C4×D43semidirect
245. C2×C4⋊C4C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191388652
#191369472
#191346942
#191329212
#191324492
#191324482
C43×#18262
#947743