Finite Group Databasebeta

← #25114288

Subgroups — #25114288

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×#14582937C211yesmaximal, characteristic
2#19137490C211yesmaximal, characteristic
3#19137482C211yesmaximal, characteristic
4#19135336C212yesmaximal, complemented
5#19135186C212yesmaximal, complemented
6#19135165C212yesmaximal, complemented
7#19134687C211yesmaximal, characteristic
8#19134687C211yesmaximal, characteristic
9#19134494C212yesmaximal, complemented
10#19134371C211yesmaximal, characteristic
11C43×#1808C211yesmaximal, characteristic
12C2×#13063284C2211yescharacteristic
13C2×#13063284C2211yescharacteristic
14#14582937C418yescomplemented
15C2×#13063259C2211yescharacteristic
16C2×#13063259C2211yescharacteristic
17C2×#13063257C2211yescharacteristic
18C2×#13063257C2211yescharacteristic
19C2×C22⋊(C43⋊C8)C2211yescharacteristic
20C2×#13063235C2212yes—
21#14582795C2212yes—
22#14582795C2212yes—
23#14582793—22no—
24#14582787—22no—
25#14582766—21no—
26#14582763—21no—
27C4⋊C4×Dic43C2212yes—
28C4⋊C4×Dic43C2212yes—
29#14582750—21no—
30C4×C22⋊Dic43C2211yescharacteristic
31#14582744—21no—
32#14582661C2212yes—
33#14582661C2212yes—
34#14582661C2212yes—
35#14582661C2212yes—
36#14582653C2212yes—
37C23×C8×C43C2211yescharacteristic
38C2×#107×C43C2212yes—
39C43×#380C2211yescharacteristic
40C43×#380C2211yescharacteristic
41C43×#340C2212yes—
42C22×C43⋊C8C2312yes—
43#13063284—22no—
44#13063284—22no—
45#13063284C2×C414yes—
46#13063284C2×C414yes—
47C2×C4⋊Dic43C2311yescharacteristic
48C2×C4⋊Dic43C2311yescharacteristic
49C2×C4⋊Dic43C2311yescharacteristic
50C2×C4⋊Dic43C2311yescharacteristic
51C2×Dic43⋊C4—22no—
52C2×Dic43⋊C4—22no—
53C2×C22⋊Dic43—21no—
54C2×C22⋊Dic43—21no—
55C2×C22⋊Dic43D412yes—
56C2×C4×Dic43—21no—
57C2×C4×Dic43—21no—
58C2×C4×Dic43—22no—
59C2×C4×Dic43—22no—
60C2×C4×Dic43C2312yes—
61#13063259C2×C414yes—
62#13063259C2×C414yes—
63#13063257C2×C414yes—
64#13063257C2×C414yes—
65C22⋊(C43⋊C8)—22no—
66#13063235—24no—
67C43⋊#95—22no—
68C43⋊#95—22no—
69C43⋊#95—22no—
70C43⋊#95—22no—
71C43⋊#95D411yescharacteristic
72C43⋊#95D411yescharacteristic
73C23×C4×C43C2311yescharacteristic
74C22×C8×C43—24no—
75C22×C8×C43C2×C414yes—
76C22×C8×C43C2311yescharacteristic
77C22×C8×C43C2311yescharacteristic
78C2×C4⋊C4×C43C2312yes—
79C2×C4⋊C4×C43C2312yes—
80C2×C22⋊C4×C43—21no—
81C2×C22⋊C4×C43—21no—
82#107×C43—24no—
83#95×C43—21no—
84#95×C43—21no—
85C24×C43C2×D411yescharacteristic
86C22×C4×C43—22no—
87C22×C4×C43—22no—
88C22×C4×C43—22no—
89C22×C4×C43—22no—
90C22×C4×C43C22×C412yes—
91C22×C4×C43C2×D411yescharacteristic
92C22×C4×C43#4112yes—
93C22×C4×C43C2411yescharacteristic
94C22×Dic43—21no—
95C22×Dic43—21no—
96C22×Dic43—21no—
97C22×Dic43—21no—
98C22×Dic43C2×D412yes—
99C22×Dic43C2×D412yes—
100C2×C8×C43—22no—
101C2×C8×C43—28no—
102C2×C8×C43C22×C412yes—
103C2×C8×C43C22×C412yes—
104C2×C8×C43#4114yes—
105C4⋊C4×C43—22no—
106C4⋊C4×C43—22no—
107C4⋊C4×C43—22no—
108C4⋊C4×C43—22no—
109C22⋊C4×C43—81no—
110C22⋊C4×C43—81no—
111C22⋊Dic43—24no—
112C22⋊Dic43—24no—
113C22⋊Dic43—42no—
114C4⋊Dic43—21no—
115C4⋊Dic43—21no—
116C4⋊Dic43—21no—
117C4⋊Dic43—21no—
118C4⋊Dic43C22×C412yes—
119C4⋊Dic43C22×C412yes—
120C4⋊Dic43C22×C412yes—
121C4⋊Dic43C22×C412yes—
122Dic43⋊C4—44no—
123Dic43⋊C4—82no—
124C4×Dic43—24no—
125C4×Dic43—24no—
126C4×Dic43—22no—
127C4×Dic43—22no—
128C4×Dic43—44no—
129C4×Dic43—82no—
130C2×C43⋊C8—22no—
131C2×C43⋊C8—22no—
132C2×C43⋊C8—22no—
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—42no—
144C2×C4×C43—42no—
145C2×C4×C43—42no—
146C2×C4×C43—42no—
147C2×C4×C43—42no—
148C2×C4×C43—42no—
149C2×C4×C43C4×D412yes—
150C2×C4×C43C23×C411yescharacteristic
151C2×C4×C43C2×#4112yes—
152C2×C4×C43C2×#4111yescharacteristic
153C2×C4×C432−1+412yes—
154C2×Dic43—22no—
155C2×Dic43—22no—
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—42no—
166C2×Dic43—41no—
167C2×Dic43—41no—
168C2×Dic43—41no—
169C2×Dic43—41no—
170C8×C43—22no—
171C8×C43#11714yes—
172C43⋊C8—42no—
173#22616—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#57611yescharacteristic
183C22×C43#57811yescharacteristic
184C4×C43—22no—
185C4×C43—82no—
186C4×C43—82no—
187C4×C43C2×#11711yescharacteristic
188C4×C43#51911yescharacteristic
189C4×C43#55212yes—
190Dic43—42no—
191Dic43—42no—
192Dic43—42no—
193Dic43—42no—
194Dic43—42no—
195Dic43—42no—
196C2×#427—431no—
197#2347—431no—
198#2346—431no—
199#1944—432no—
200#1921—432no—
201#1918—432no—
202#1825—431no—
203#1825—431no—
204#1808D4311yescharacteristic
205#1776—432no—
206#1752—431no—
207C2×C43—42no—
208C2×C43#234411yescharacteristic
209C2×C43#294311yescharacteristic
210C2×C43#295111yescharacteristic
211C2×C43#334712yes—
212C2×C43#334912yes—
213C23×C8C2×D4311yescharacteristic
214C2×#117—431no—
215C2×#117—431no—
216#427—438no—
217C2×#107—431no—
218C2×#107—431no—
219C2×#107C2×D4312yes—
220C2×#106—431no—
221C2×#106—431no—
222C2×C22⋊C8—431no—
223C2×#97—432no—
224#389—432no—
225#389—432no—
226#388—862no—
227#388—862no—
228#383—861no—
229#382—861no—
230#380C2×D4311yescharacteristic
231#380C2×D4311yescharacteristic
232C4×C4⋊C4—432no—
233C4×C4⋊C4—432no—
234C4×C4⋊C4—861no—
235C4×C22⋊C4—431no—
236#376—861no—
237#340—432no—
238#340—432no—
239#340—432no—
240#340—432no—
241#340C2×D4312yes—
242#336—432no—
243C43#2261611yescharacteristic, complemented, Sylow
244C23×C4C22×D4311yescharacteristic
245C22×C8—24no—
246C22×C8—432no—
247C22×C8C4×D4314yes—
248C22×C8C22×D4311yescharacteristic
249C22×C8C22×D4311yescharacteristic
250#117—434no—
251#117—434no—
252#117—862no—
253#117—862no—
254C2×C4⋊C4—431no—
255C2×C4⋊C4—431no—
256C2×C4⋊C4—431no—
257C2×C4⋊C4—431no—
258C2×C4⋊C4—862no—
259C2×C4⋊C4—862no—
260C2×C4⋊C4C22×D4312yes—
261C2×C4⋊C4C22×D4312yes—
262C2×C22⋊C4—21no—
263C2×C22⋊C4—21no—
264C2×C22⋊C4—432no—
265C2×C22⋊C4—861no—
266C2×C22⋊C4—861no—
267C2×C42—432no—
268C2×C42—861no—
269C2×C42—861no—
270C2×C42—862no—
271C2×C42—862no—
272#107—24no—
273#107—434no—
274#107—434no—
275#106—434no—
276#106—434no—
277C22⋊C8—862no—
278#97—864no—
279#95—21no—
280#95—21no—
281#95—431no—
282#95—431no—
283#95—862no—
284#95—862no—
285#95—862no—
286#95—862no—
287C24D4×D4311yescharacteristic
288C22×C4—22no—
289C22×C4—22no—
290C22×C4—22no—
291C22×C4—22no—
292C22×C4—432no—
293C22×C4—432no—
294C22×C4—861no—
295C22×C4—861no—
296C22×C4—861no—
297C22×C4—861no—
298C22×C4C2×C4×D4312yes—
299C22×C4D4×D4311yescharacteristic
300C22×C4#1062190212yes—
301C22×C4C23×D4311yescharacteristic
302C2×C8—22no—
303C2×C8—28no—
304C2×C8—862no—
305C2×C8—862no—
306C2×C8—862no—
307C2×C8C2×C4×D4312yes—
308C2×C8C2×C4×D4312yes—
309C2×C8#1062190014yes—
310C4⋊C4—22no—
311C4⋊C4—22no—
312C4⋊C4—22no—
313C4⋊C4—22no—
314C4⋊C4—432no—
315C4⋊C4—432no—
316C4⋊C4—432no—
317C4⋊C4—432no—
318C4⋊C4—861no—
319C4⋊C4—861no—
320C4⋊C4—861no—
321C4⋊C4—861no—
322C4⋊C4—3442no—
323C4⋊C4—1724no—
324C22⋊C4—81no—
325C22⋊C4—81no—
326C22⋊C4—864no—
327C22⋊C4—864no—
328C22⋊C4—1722no—
329C42—864no—
330C42—864no—
331C42—862no—
332C42—862no—
333C42—3442no—
334C42—1724no—
335C23—22no—
336C23—21no—
337C23—21no—
338C23—22no—
339C23#1306328712yes—
340C23C2×D4×D4311yescharacteristic
341C2×C4—22no—
342C2×C4—24no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—862no—
352C2×C4—862no—
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—1721no—
364C2×C4—1721no—
365C2×C4—1721no—
366C2×C4—1721no—
367C2×C4#1306328712yes—
368C2×C4C22×C4×D4311yescharacteristic
369C2×C4C2×#1062190012yes—
370C2×C4C2×#1062190211yescharacteristic
371C2×C4#1306337212yes—
372C8—22no—
373C8—1722no—
374C8#1306328114yes—
375C22—22no—
376C22—22no—
377C22—22no—
378C22—42no—
379C22—42no—
380C22C2×#1306328711yescharacteristic
381C22#1458354912yes—
382C22#1458369612yes—
383C22#1458370011yescharacteristic
384C22#1458371211yescharacteristic
385C4—22no—
386C4—82no—
387C4—82no—
388C4—1722no—
389C4—1722no—
390C4—1722no—
391C4—1722no—
392C4—1722no—
393C4—1722no—
394C4C2×#1306328111yescharacteristic
395C4#1458337611yescharacteristic
396C4#1458359112yes—
397C2—42no—
398C2#1913746611yescharacteristic
399C2#1914339511yescharacteristic
400C2#1914346911yescharacteristic
401C2#1914710112yes—
402C2#1914713112yes—
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1808C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
cosocleC22×C4×C43C24
hypercenter#1808D43
hypocenterC43#22616
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1808

Complements

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

NH ≅ G/Ntype
4. #19135336C2semidirect
5. #19135186C2semidirect
6. #19135165C2semidirect
9. #19134494C2semidirect
14. #14582937C4semidirect
243. C43#22616semidirect

Maximal subgroups

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

subgroupindex
C2×#145829372
#191374902
#191374822
#191353362
#191351862
#191351652
#191346872
#191344942
#191343712
C43×#18082
#2261643