Finite Group Databasebeta

← #25114306

Subgroups — #25114306

Order 11008.

766 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582935C211yesmaximal, characteristic
2#19137482C211yesmaximal, characteristic
3#19137480C211yesmaximal, characteristic
4#19135332C212yesmaximal, complemented
5#19135176C212yesmaximal, complemented
6#19135171C212yesmaximal, complemented
7#19134691C211yesmaximal, characteristic
8#19134618C211yesmaximal, characteristic
9#19134491C212yesmaximal, complemented
10#19134374C211yesmaximal, characteristic
11C43×#1825C211yesmaximal, characteristic
12C23×C43⋊C8C2211yescharacteristic
13C2×#13063284C2211yescharacteristic
14#14582935C418yescomplemented
15C2×#13063258C2211yescharacteristic
16C2×#13063258C2211yescharacteristic
17C2×#13063256C2212yes—
18C2×#13063256C2211yescharacteristic
19C2×#13063256C2211yescharacteristic
20C2×#13063235C2212yes—
21#14582798C2212yes—
22#14582795C2212yes—
23#14582793—22no—
24#14582792—22no—
25#14582765—21no—
26#14582763—21no—
27#14582759C2211yescharacteristic
28C4⋊C4×Dic43C2212yes—
29C4⋊C4×Dic43C2212yes—
30C4×C22⋊Dic43C2211yescharacteristic
31#14582745—21no—
32#14582744—21no—
33#14582662C2212yes—
34#14582662C2212yes—
35#14582661C2212yes—
36#14582653C2212yes—
37C2×#117×C43C2211yescharacteristic
38C2×C22⋊C8×C43C2211yescharacteristic
39C43×#380C2211yescharacteristic
40C43×#340C2212yes—
41C43×#340C2212yes—
42C22×C43⋊C8—24no—
43C22×C43⋊C8C2×C414yes—
44C22×C43⋊C8C2311yescharacteristic
45C22×C43⋊C8C2311yescharacteristic
46#13063284—22no—
47#13063284C2×C414yes—
48C2×C4⋊Dic43—22no—
49C2×C4⋊Dic43C2312yes—
50C2×C4⋊Dic43C2311yescharacteristic
51C2×C4⋊Dic43C2311yescharacteristic
52C2×Dic43⋊C4—22no—
53C2×C22⋊Dic43—21no—
54C2×C22⋊Dic43—21no—
55C2×C22⋊Dic43D412yes—
56C2×C4×Dic43—21no—
57C2×C4×Dic43—22no—
58C2×C4×Dic43—22no—
59C2×C4×Dic43C2312yes—
60#13063258C2×C414yes—
61#13063258C2×C414yes—
62#13063256—24no—
63#13063256C2×C414yes—
64#13063256C2×C414yes—
65#13063235—24no—
66C43⋊#95—21no—
67C43⋊#95—22no—
68C43⋊#95—22no—
69C43⋊#95—22no—
70C43⋊#95—22no—
71C43⋊#95D411yescharacteristic
72C43⋊#95D411yescharacteristic
73C23×C4×C43C2311yescharacteristic
74C22×C8×C43C2312yes—
75#117×C43—22no—
76#117×C43C2×C414yes—
77C2×C4⋊C4×C43C2312yes—
78C2×C4⋊C4×C43C2311yescharacteristic
79C2×C4⋊C4×C43C2311yescharacteristic
80C2×C22⋊C4×C43—21no—
81C2×C22⋊C4×C43—21no—
82C2×C42×C43—21no—
83C22⋊C8×C43—22no—
84#95×C43—21no—
85C24×C43C2×D411yescharacteristic
86C22×C4×C43—22no—
87C22×C4×C43—22no—
88C22×C4×C43—21no—
89C22×C4×C43—21no—
90C22×C4×C43—22no—
91C22×C4×C43C22×C412yes—
92C22×C4×C43C2×D411yescharacteristic
93C22×C4×C43#4112yes—
94C22×C4×C43C2411yescharacteristic
95C22×Dic43—21no—
96C22×Dic43—21no—
97C22×Dic43—22no—
98C22×Dic43C2×D412yes—
99C22×Dic43C2×D412yes—
100C2×C8×C43—22no—
101C2×C8×C43—22no—
102C2×C8×C43—22no—
103C4⋊C4×C43—21no—
104C4⋊C4×C43—21no—
105C4⋊C4×C43—22no—
106C4⋊C4×C43—22no—
107C4⋊C4×C43C22×C412yes—
108C4⋊C4×C43C22×C412yes—
109C22⋊C4×C43—24no—
110C22⋊C4×C43—81no—
111C42×C43—24no—
112C22⋊Dic43—24no—
113C22⋊Dic43—42no—
114C22⋊Dic43—81no—
115C4⋊Dic43—21no—
116C4⋊Dic43—21no—
117C4⋊Dic43—22no—
118C4⋊Dic43—22no—
119C4⋊Dic43—82no—
120C4⋊Dic43C22×C412yes—
121C4⋊Dic43C22×C412yes—
122Dic43⋊C4—82no—
123C4×Dic43—24no—
124C4×Dic43—22no—
125C4×Dic43—22no—
126C4×Dic43—44no—
127C4×Dic43—44no—
128C2×C43⋊C8—22no—
129C2×C43⋊C8—28no—
130C2×C43⋊C8C22×C412yes—
131C2×C43⋊C8C22×C412yes—
132C2×C43⋊C8#4114yes—
133C23×C43—22no—
134C23×C43—22no—
135C23×C43—21no—
136C23×C43—21no—
137C23×C43C4×D412yes—
138C23×C43C22×D411yescharacteristic
139C2×C4×C43—22no—
140C2×C4×C43—22no—
141C2×C4×C43—22no—
142C2×C4×C43—24no—
143C2×C4×C43—22no—
144C2×C4×C43—22no—
145C2×C4×C43—42no—
146C2×C4×C43—41no—
147C2×C4×C43—41no—
148C2×C4×C43—42no—
149C2×C4×C43—42no—
150C2×C4×C43—42no—
151C2×C4×C43C4×D412yes—
152C2×C4×C43C23×C411yescharacteristic
153C2×C4×C43C2×#4112yes—
154C2×C4×C43C2×#4111yescharacteristic
155C2×C4×C432−1+412yes—
156C2×Dic43—22no—
157C2×Dic43—22no—
158C2×Dic43—22no—
159C2×Dic43—22no—
160C2×Dic43—22no—
161C2×Dic43—22no—
162C2×Dic43—22no—
163C2×Dic43—22no—
164C2×Dic43—42no—
165C2×Dic43—41no—
166C2×Dic43—41no—
167C2×Dic43—42no—
168C2×Dic43—42no—
169C2×Dic43—42no—
170C8×C43—42no—
171C43⋊C8—22no—
172C43⋊C8#11714yes—
173#22619—431nomaximal, Sylow
174C22×C43—22no—
175C22×C43—22no—
176C22×C43—22no—
177C22×C43—42no—
178C22×C43—42no—
179C22×C43C2×C4×D411yescharacteristic
180C22×C43#54712yes—
181C22×C43#57512yes—
182C22×C43#57711yescharacteristic
183C22×C43#57711yescharacteristic
184C4×C43—22no—
185C4×C43—42no—
186C4×C43—42no—
187C4×C43—82no—
188C4×C43C2×#11711yescharacteristic
189C4×C43#51911yescharacteristic
190C4×C43#55212yes—
191Dic43—42no—
192Dic43—42no—
193Dic43—42no—
194Dic43—42no—
195Dic43—82no—
196C2×#427—431no—
197#2346—431no—
198#2346—431no—
199#1943—432no—
200#1919—432no—
201#1919—432no—
202#1825—431no—
203#1825D4311yescharacteristic
204#1807—431no—
205#1776—432no—
206#1752—431no—
207C2×C43—42no—
208C2×C43#234411yescharacteristic
209C2×C43#294311yescharacteristic
210C2×C43#295211yescharacteristic
211C2×C43#334812yes—
212C2×C43#334812yes—
213C23×C8—431no—
214C2×#117—431no—
215C2×#117C2×D4311yescharacteristic
216#427—438no—
217C2×#107—431no—
218C2×#107—431no—
219C2×#106—431no—
220C2×#106—431no—
221C2×#106—432no—
222C2×C22⋊C8C2×D4311yescharacteristic
223C2×#97—432no—
224#389—432no—
225#389—432no—
226#388—862no—
227#388—862no—
228#382—861no—
229#382—861no—
230#380—431no—
231#380C2×D4311yescharacteristic
232C4×C4⋊C4—432no—
233C4×C4⋊C4—432no—
234C4×C22⋊C4—431no—
235#376—861no—
236#376—861no—
237#340—432no—
238#340—432no—
239#340—432no—
240#340C2×D4312yes—
241#340C2×D4312yes—
242#336—432no—
243C43#2261911yescharacteristic, complemented, Sylow
244C23×C4C22×D4311yescharacteristic
245C22×C8—431no—
246C22×C8—434no—
247C22×C8—431no—
248C22×C8—864no—
249C22×C8C22×D4312yes—
250#117—22no—
251#117—434no—
252#117—862no—
253#117C4×D4314yes—
254C2×C4⋊C4—431no—
255C2×C4⋊C4—431no—
256C2×C4⋊C4—432no—
257C2×C4⋊C4—862no—
258C2×C4⋊C4—862no—
259C2×C4⋊C4C22×D4312yes—
260C2×C4⋊C4C22×D4311yescharacteristic
261C2×C4⋊C4C22×D4311yescharacteristic
262C2×C22⋊C4—21no—
263C2×C22⋊C4—21no—
264C2×C22⋊C4—432no—
265C2×C22⋊C4—861no—
266C2×C22⋊C4—861no—
267C2×C42—21no—
268C2×C42—432no—
269C2×C42—861no—
270C2×C42—862no—
271C2×C42—862no—
272#107—434no—
273#107—434no—
274#106—434no—
275#106—434no—
276#106—864no—
277C22⋊C8—22no—
278#97—864no—
279#95—21no—
280#95—431no—
281#95—431no—
282#95—862no—
283#95—862no—
284#95—862no—
285#95—862no—
286#95—861no—
287C24D4×D4311yescharacteristic
288C22×C4—22no—
289C22×C4—22no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—22no—
293C22×C4—432no—
294C22×C4—432no—
295C22×C4—861no—
296C22×C4—861no—
297C22×C4—862no—
298C22×C4C2×C4×D4312yes—
299C22×C4D4×D4311yescharacteristic
300C22×C4#1062190012yes—
301C22×C4C23×D4311yescharacteristic
302C2×C8—22no—
303C2×C8—22no—
304C2×C8—22no—
305C2×C8—432no—
306C2×C8—434no—
307C2×C8—432no—
308C2×C8—868no—
309C2×C8—862no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—22no—
313C4⋊C4—22no—
314C4⋊C4—432no—
315C4⋊C4—432no—
316C4⋊C4—861no—
317C4⋊C4—861no—
318C4⋊C4—862no—
319C4⋊C4—862no—
320C4⋊C4—3442no—
321C4⋊C4—3442no—
322C4⋊C4C2×C4×D4312yes—
323C4⋊C4C2×C4×D4312yes—
324C22⋊C4—24no—
325C22⋊C4—81no—
326C22⋊C4—864no—
327C22⋊C4—3441no—
328C22⋊C4—1722no—
329C42—24no—
330C42—864no—
331C42—862no—
332C42—862no—
333C42—1724no—
334C42—1724no—
335C23—22no—
336C23—21no—
337C23—21no—
338C23—22no—
339C23(C22⋊D43)⋊C412yes—
340C23C2×D4×D4311yescharacteristic
341C2×C4—22no—
342C2×C4—24no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—42no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—862no—
354C2×C4—862no—
355C2×C4—862no—
356C2×C4—862no—
357C2×C4—862no—
358C2×C4—862no—
359C2×C4—862no—
360C2×C4—862no—
361C2×C4—1722no—
362C2×C4—1722no—
363C2×C4—1722no—
364C2×C4—1722no—
365C2×C4—1721no—
366C2×C4—1721no—
367C2×C4(C22⋊D43)⋊C412yes—
368C2×C4C22×C4×D4311yescharacteristic
369C2×C4#41×D4312yes—
370C2×C4C2×#1062190011yescharacteristic
371C2×C4#1306337212yes—
372C8—42no—
373C8—434no—
374C8—862no—
375C22—22no—
376C22—22no—
377C22—22no—
378C22—42no—
379C22—42no—
380C22C2×(C22⋊D43)⋊C411yescharacteristic
381C22#1458354712yes—
382C22#1458369612yes—
383C22#1458370811yescharacteristic
384C22#1458370911yescharacteristic
385C4—22no—
386C4—42no—
387C4—42no—
388C4—82no—
389C4—3442no—
390C4—1722no—
391C4—1722no—
392C4—1722no—
393C4—1722no—
394C4#117×D4311yescharacteristic
395C4#1458337611yescharacteristic
396C4#1458358612yes—
397C2—42no—
398C2#1913745911yescharacteristic
399C2#1914339111yescharacteristic
400C2#1914347411yescharacteristic
401C2#1914710812yes—
402C2#1914711412yes—
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1825C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
cosocleC22×C4×C43C24
hypercenter#1825D43
hypocenterC43#22619
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1825

Complements

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

NH ≅ G/Ntype
4. #19135332C2semidirect
5. #19135176C2semidirect
6. #19135171C2semidirect
9. #19134491C2semidirect
14. #14582935C4semidirect
243. C43#22619semidirect

Maximal subgroups

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

subgroupindex
C2×#145829352
#191374822
#191374802
#191353322
#191351762
#191351712
#191346912
#191346182
#191344912
#191343742
C43×#18252
#2261943