Finite Group Databasebeta

← #24994405

Subgroups — #24994405

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#19138871C211yesmaximal, characteristic
2#19136947C211yesmaximal, characteristic
3#19134695C211yesmaximal, characteristic, complemented
4#19134692C211yesmaximal, characteristic, complemented
5#19132921C211yesmaximal, characteristic
6#19132447C211yesmaximal, characteristic, complemented
7C43×#1284C211yesmaximal, characteristic, complemented
8C2×#13063284C2211yescharacteristic
9C22×(C2×D43)⋊C4C2211yescharacteristic
10C2×C22⋊C4×D43—21no—
11#14582863C2211yescharacteristic
12#14582836C412yescomplemented
13#14582826C412yescomplemented
14#14582791—22no—
15#14582774—21no—
16#14582754—21no—
17C22⋊C4×Dic43—21no—
18C4×(C2×D43)⋊C4—22no—
19C4×C22⋊Dic43C2211yescharacteristic
20#14582746—22no—
21#14582660—22no—
22#14582659—22no—
23#14582622—22no—
24C43×#407C2211yescharacteristic
25C43×#381C2211yescharacteristic
26C4×C22⋊C4×C43C2211yescharacteristic
27C24×D43D411yescharacteristic
28C23×Dic43D411yescharacteristic
29C22×C4×D43—22no—
30C2×#10621877—21no—
31#13063284—21no—
32#13063284—21no—
33#13063284—21no—
34#13063284—21no—
35C2×C4⋊Dic43—22no—
36C2×C4⋊Dic43C2×C411yescharacteristic, complemented
37C2×C4⋊Dic43C2×C411yescharacteristic, complemented
38C2×C22⋊Dic43—21no—
39C2×C22⋊Dic43—21no—
40C2×(C2×D43)⋊C4—22no—
41C2×(C2×D43)⋊C4—21no—
42C2×(C2×D43)⋊C4—21no—
43C2×(C2×D43)⋊C4—21no—
44C2×(C2×D43)⋊C4—21no—
45C2×(C2×D43)⋊C4—22no—
46C2×(C2×D43)⋊C4—22no—
47C2×(C2×D43)⋊C4C2×C412yes—
48C2×(C2×D43)⋊C4D412yes—
49C22⋊C4×D43—28no—
50C2×C4×Dic43—21no—
51C2×C4×Dic43—22no—
52C2×C4×Dic43D412yes—
53C22⋊(C43⋊C8)—21no—
54C22⋊(C43⋊C8)—21no—
55C43⋊#95—22no—
56C43⋊#95—21no—
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×C412yescomplemented
68C24×C43C2×D411yescharacteristic
69C23×D43—21no—
70C23×D43—21no—
71C23×D43—24no—
72C23×D43—42no—
73C23×D43—81no—
74C23×D43C22⋊C412yes—
75C22×C4×C43—22no—
76C22×C4×C43—22no—
77C22×C4×C43—42no—
78C22×C4×C43C22×C411yescharacteristic
79C22×C4×C43C2×D411yescharacteristic
80C22×C4×C43C2×D411yescharacteristic
81C22×C4×C43C2×D411yescharacteristic
82C22×C4×C43#4111yescharacteristic
83C22×C4×C43#4111yescharacteristic
84C22×Dic43—21no—
85C22×Dic43—21no—
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—
96C22⋊C4×C43—24no—
97C22⋊C4×C43—42no—
98C42×C43—42no—
99C22⋊Dic43—24no—
100C22⋊Dic43—41no—
101C22⋊Dic43—41no—
102(C2×D43)⋊C4—28no—
103(C2×D43)⋊C4—22no—
104(C2×D43)⋊C4—22no—
105(C2×D43)⋊C4—22no—
106(C2×D43)⋊C4—22no—
107(C2×D43)⋊C4—44no—
108(C2×D43)⋊C4—82no—
109C4⋊Dic43—21no—
110C4⋊Dic43—21no—
111C4⋊Dic43—21no—
112C4⋊Dic43—21no—
113C4⋊Dic43—82no—
114C4×Dic43—41no—
115C4×Dic43—41no—
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—42no—
150C2×C4×C43—42no—
151C2×C4×C43C4×D411yescharacteristic
152C2×C4×C43C4×D411yescharacteristic
153C2×C4×C43#12111yescharacteristic
154C2×C4×C43#12111yescharacteristic
155C2×Dic43—24no—
156C2×Dic43—22no—
157C2×Dic43—42no—
158C2×Dic43—42no—
159C2×Dic43—42no—
160C2×Dic43—42no—
161C2×Dic43—42no—
162C2×Dic43—41no—
163C2×Dic43—41no—
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—82no—
195Dic43—44no—
196Dic43—42no—
197Dic43—81no—
198Dic43—81no—
199#2482—431no—
200#2273—431no—
201#1826—431no—
202#1826—431no—
203#1462—431no—
204#1284—431no—
205#1284D4311yescharacteristic, complemented
206C2×C43—22no—
207C2×C43—22no—
208C2×C43—41no—
209C2×C43#189011yescharacteristic
210C2×C43#189611yescharacteristic
211C2×C43#191111yescharacteristic
212D43—44no—
213C2×#117—431no—
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#381C2×D4311yescharacteristic
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—862no—
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—861no—
240#117—861no—
241#117—861no—
242#117—861no—
243C2×C4⋊C4—431no—
244C2×C4⋊C4—431no—
245C2×C4⋊C4—862no—
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—432no—
261C2×C42—862no—
262C2×C42—861no—
263C2×C42D17212yes—
264C22⋊C8—21no—
265C22⋊C8—21no—
266C22⋊C8—861no—
267C22⋊C8—861no—
268#95—21no—
269#95—21no—
270#95—862no—
271#95—862no—
272#95—861no—
273#95C4×D4312yescomplemented
274C24—432no—
275C24—864no—
276C24—861no—
277C24—861no—
278C24—3441no—
279C24—1722no—
280C24D4×D4311yescharacteristic
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—42no—
284C22×C4—432no—
285C22×C4—868no—
286C22×C4—861no—
287C22×C4—862no—
288C22×C4—861no—
289C22×C4—861no—
290C22×C4—861no—
291C22×C4—3442no—
292C22×C4—3442no—
293C22×C4—3441no—
294C22×C4C2×C4×D4311yescharacteristic
295C22×C4C2×D17211yescharacteristic
296C22×C4#1062189811yescharacteristic
297C22×C4D4×D4311yescharacteristic
298C22×C4D4×D4311yescharacteristic
299C22×C4#1062190211yescharacteristic
300M16—42no—
301M16—1722no—
302C2×C8—41no—
303C2×C8—1721no—
304C4⋊C4—861no—
305C4⋊C4—861no—
306C4⋊C4—861no—
307C4⋊C4—861no—
308C4⋊C4—3442no—
309C22⋊C4—24no—
310C22⋊C4—42no—
311C22⋊C4—868no—
312C22⋊C4—864no—
313C22⋊C4—862no—
314C22⋊C4—862no—
315C22⋊C4—862no—
316C22⋊C4—862no—
317C22⋊C4—3442no—
318C22⋊C4—1724no—
319C22⋊C4—1721no—
320C22⋊C4—1721no—
321C42—42no—
322C42—3442no—
323C42—1722no—
324C42—1721no—
325C42—1721no—
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#1306329511yescharacteristic
344C23#1306331011yescharacteristic
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—42no—
357C2×C4—864no—
358C2×C4—862no—
359C2×C4—3448no—
360C2×C4—3441no—
361C2×C4—1722no—
362C2×C4—1722no—
363C2×C4—1721no—
364C2×C4—1721no—
365C2×C4—1722no—
366C2×C4—1722no—
367C2×C4—1722no—
368C2×C4—1722no—
369C2×C4#1306328711yescharacteristic
370C2×C4C4×D17211yescharacteristic
371C2×C4#1306329811yescharacteristic
372C2×C4#1306330011yescharacteristic
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#1458277711yescharacteristic
392C22#104×D4312yes—
393C22#1458309012yes—
394C4—21no—
395C4—21no—
396C4—21no—
397C4—21no—
398C4—44no—
399C4—82no—
400C4—3441no—
401C4—3441no—
402C4—1724no—
403C4—1722no—
404C2—22no—
405C2—22no—
406C2—41no—
407C2—1724no—
408C2#1913500711yescharacteristic
409C2#1913503711yescharacteristic
410C2#1913512611yescharacteristic
subgroupG/H
centerC22#14582777
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1284C2
socleC22×C43#386
prime radicalC24×D43D4
cosocleC23×C4×C43C23
hypercenter#1284D43
hypocenterC43#9477
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
3. #19134695C2semidirect
4. #19134692C2semidirect
6. #19132447C2semidirect
7. C43×#1284C2semidirect
12. #14582836C4semidirect
13. #14582826C4semidirect
36. C2×C4⋊Dic43C2×C4semidirect
37. C2×C4⋊Dic43C2×C4semidirect
67. #95×C43C2×C4semidirect
205. #1284D43semidirect
232. C43#9477semidirect
273. #95C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191388712
#191369472
#191346952
#191346922
#191329212
#191324472
C43×#12842
#947743