Finite Group Databasebeta

← #25124003

Subgroups — #25124003

Order 11008.

1378 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148000C211yesmaximal, characteristic, complemented
2#19136974C212yesmaximal
3#19136974C211yesmaximal, characteristic
4#19135763C214yesmaximal, complemented
5#19135760C214yesmaximal
6#19134327C212yesmaximal, complemented
7C43×#1740C211yesmaximal, characteristic, complemented
8C23×C4×D43C2211yescharacteristic
9#14583530—22no—
10#14583527—24no—
11#14583525C2214yes—
12#14583456—22no—
13#14583452—24no—
14C2×#13063284C2211yescharacteristic
15C2×#13063284C2212yes—
16#14582760C2214yes—
17#14582760C2212yes—
18#14582756—24no—
19#14582756—22no—
20#14582754C2214yes—
21#14582754C2212yes—
22C4×(C2×D43)⋊C4—24no—
23C4×(C2×D43)⋊C4—22no—
24#14582665C2218yes—
25C2×#117×C43C2212yes—
26C2×#117×C43C2211yescharacteristic
27C43×#342C2214yes—
28C24×D43C2311yescharacteristic
29C23×Dic43C2311yescharacteristic
30C22×C4×D43—21no—
31C22×C4×D43—22no—
32C22×C4×D43—21no—
33C22×C4×D43—22no—
34C22×C4×D43—24no—
35C22×C4×D43—22no—
36C22×C4×D43Q814yescomplemented
37#13063325—24no—
38#13063324—28no—
39#13063317—24no—
40#13063316—28no—
41#13063304—28no—
42#13063302—216no—
43C4×Dic86—28no—
44#13063284—22no—
45#13063284—22no—
46#13063284—22no—
47#13063284—22no—
48#13063284—24no—
49C2×C4⋊Dic43—21no—
50C2×C4⋊Dic43D414yes—
51C2×C22⋊Dic43C2312yes—
52C2×C22⋊Dic43C2314yes—
53C2×(C2×D43)⋊C4—24no—
54C2×(C2×D43)⋊C4—28no—
55C2×C4×Dic43—21no—
56C2×C4×Dic43D414yes—
57C43⋊#95—24no—
58C43⋊#95—28no—
59C23×C4×C43C2311yescharacteristic
60#117×C43—22no—
61#117×C43—22no—
62#117×C43—24no—
63#117×C43—24no—
64C2×C4⋊C4×C43—22no—
65C2×C4⋊C4×C43D412yes—
66C2×C22⋊C4×C43C2314yes—
67C2×C22⋊C4×C43C2312yes—
68C2×C42×C43—22no—
69C2×C42×C43D412yes—
70C24×C43C2411yescharacteristic
71C23×D43—22no—
72C23×D43—21no—
73C23×D43—21no—
74C23×D43—22no—
75C23×D43—44no—
76C23×D43C2×Q812yes—
77C22×C4×C43—24no—
78C22×C4×C43C2×D414yes—
79C22×C4×C43C2×D411yescharacteristic
80C22×C4×C43C2×D411yescharacteristic
81C22×C4×C43C2×D412yes—
82C22×C4×C43C2×D412yes—
83C22×C4×C43C2×Q812yes—
84C22×C4×C43#4114yes—
85C22×C4×C43#4112yes—
86C22×Dic43—22no—
87C22×Dic43—21no—
88C22×Dic43—22no—
89C22×Dic43—21no—
90C22×Dic43—22no—
91C22×Dic43C2×D418yes—
92C22×Dic43C2×Q812yes—
93C2×C4×D43—28no—
94C2×C4×D43—28no—
95C2×C4×D43—24no—
96C2×C4×D43—24no—
97C2×C4×D43—42no—
98C2×C4×D43—41no—
99C2×C4×D43—41no—
100C2×C4×D43—44no—
101C2×C4×D43—44no—
102C2×C4×D43—42no—
103C2×C4×D43—42no—
104C2×Dic86—28no—
105C4⋊C4×C43—24no—
106C4⋊C4×C43—44no—
107C22⋊C4×C43—24no—
108C22⋊C4×C43—24no—
109C22⋊C4×C43—24no—
110C42×C43—22no—
111C42×C43—22no—
112C42×C43—44no—
113C22⋊Dic43—24no—
114C22⋊Dic43—24no—
115C22⋊Dic43—24no—
116(C2×D43)⋊C4—416no—
117(C2×D43)⋊C4—48no—
118C4⋊Dic43—28no—
119C4⋊Dic43—24no—
120C4⋊Dic43—24no—
121C4⋊Dic43—42no—
122Dic43⋊C4—216no—
123C4×Dic43—24no—
124C4×Dic43—24no—
125C4×Dic43—42no—
126C23×C43—42no—
127C23×C43C22×D412yes—
128C23×C43C22×D411yescharacteristic
129C23×C43C22×Q811yescharacteristic
130C23×C43C2×#4111yescharacteristic
131C23×C43C2×#4112yes—
132C22×D43—28no—
133C22×D43—24no—
134C22×D43—24no—
135C22×D43—22no—
136C22×D43—44no—
137C22×D43—44no—
138C22×D43—48no—
139C22×D43—44no—
140C22×D43—42no—
141C22×D43—41no—
142C22×D43—42no—
143C22×D43—41no—
144C2×C4×C43—24no—
145C2×C4×C43—44no—
146C2×C4×C43—48no—
147C2×C4×C43—44no—
148C2×C4×C43#12012yes—
149C2×C4×C43#12011yescharacteristic
150C2×C4×C43#12011yescharacteristic
151C2×C4×C43C22⋊Q814yes—
152C2×C4×C43C22⋊Q814yes—
153C2×C4×C43C22⋊Q812yes—
154C2×C4×C43C22⋊Q812yes—
155C2×C4×C43#12414yes—
156C2×C4×C43#12414yes—
157C2×C4×C43#12412yes—
158C2×C4×C43#12412yes—
159C2×Dic43—28no—
160C2×Dic43—24no—
161C2×Dic43—22no—
162C2×Dic43—41no—
163C2×Dic43—42no—
164C2×Dic43—41no—
165C2×Dic43—48no—
166C2×Dic43—44no—
167C2×Dic43—42no—
168C4×D43—48no—
169C4×D43—44no—
170C4×D43—44no—
171Dic86—88no—
172#23467—431nomaximal, Sylow
173C22×C43—24no—
174C22×C43—22no—
175C22×C43—41no—
176C22×C43—41no—
177C22×C43—42no—
178C22×C43C2×#12011yescharacteristic
179C22×C43C2×C22⋊Q812yes—
180C22×C43C2×C22⋊Q811yescharacteristic
181C22×C43C2×#12412yes—
182C22×C43C2×#12411yescharacteristic
183C2×D43—28no—
184C2×D43—24no—
185C2×D43—44no—
186C2×D43—48no—
187C2×D43—44no—
188C2×D43—42no—
189C2×D43—42no—
190C2×D43—44no—
191C4×C43—44no—
192C4×C43—84no—
193C4×C43#39314yes—
194C4×C43#39312yes—
195C4×C43#39312yes—
196Dic43—42no—
197Dic43—48no—
198Dic43—82no—
199#3458—431no—
200#2280—432no—
201#2280—431no—
202#2030—434no—
203#2029—434no—
204#1740—432no—
205#1740D4311yescharacteristic, complemented
206C2×C43—21no—
207C2×C43—22no—
208C2×C43—22no—
209C2×C43—21no—
210C2×C43C2×#39311yescharacteristic
211C2×C43#302512yes—
212D43—44no—
213C24×C4—431no—
214#544—864no—
215#544—862no—
216#543—434no—
217#533—864no—
218#533—862no—
219C2×#117—432no—
220C2×#117—431no—
221C2×#117C2×D4312yes—
222C2×#117C2×D4311yescharacteristic
223#381—434no—
224#381—432no—
225#380—864no—
226#380—862no—
227#379—434no—
228#379—432no—
229C4×C22⋊C4—864no—
230C4×C22⋊C4—862no—
231#342—438no—
232#342C2×D4314yes—
233C43#2346711yescharacteristic, complemented, Sylow
234C25—431no—
235C23×C4—431no—
236C23×C4—434no—
237C23×C4—861no—
238C23×C4—861no—
239C23×C4—864no—
240C23×C4—862no—
241C23×C4—862no—
242C23×C4—862no—
243C23×C4C22×D4311yescharacteristic
244C4⋊Q8—864no—
245C4⋊Q8—868no—
246#125—864no—
247#125—868no—
248C22⋊Q8—8616no—
249C22⋊Q8—868no—
250C4×Q8—868no—
251#117—22no—
252#117—22no—
253#117—24no—
254#117—24no—
255#117—862no—
256#117—862no—
257#117—862no—
258#117—862no—
259#117—864no—
260C2×C4⋊C4—22no—
261C2×C4⋊C4—434no—
262C2×C4⋊C4—861no—
263C2×C4⋊C4D17212yes—
264C2×C22⋊C4—434no—
265C2×C22⋊C4—432no—
266C2×C22⋊C4—868no—
267C2×C22⋊C4—864no—
268C2×C22⋊C4C22×D4314yes—
269C2×C22⋊C4C22×D4312yes—
270C2×C42—22no—
271C2×C42—434no—
272C2×C42—861no—
273C2×C42D17212yes—
274#95—868no—
275#95—864no—
276C24—432no—
277C24—862no—
278C24—861no—
279C24—861no—
280C24—862no—
281C24—1724no—
282C24C23×D4311yescharacteristic
283C2×Q8—868no—
284C22×C4—24no—
285C22×C4—432no—
286C22×C4—438no—
287C22×C4—862no—
288C22×C4—861no—
289C22×C4—861no—
290C22×C4—862no—
291C22×C4—868no—
292C22×C4—868no—
293C22×C4—864no—
294C22×C4—864no—
295C22×C4—862no—
296C22×C4—1721no—
297C22×C4—1722no—
298C22×C4—1721no—
299C22×C4—1724no—
300C22×C4—1724no—
301C22×C4—1722no—
302C22×C4—1722no—
303C22×C4C2×D17214yes—
304C22×C4C2×D17211yescharacteristic
305C22×C4C2×D17211yescharacteristic
306C22×C4#1062189814yes—
307C22×C4D4×D4312yes—
308C22×C4D4×D4312yes—
309C22×C4#1062190012yes—
310C22×C4Q8×D4312yes—
311C4⋊C4—24no—
312C4⋊C4—44no—
313C4⋊C4—8616no—
314C4⋊C4—868no—
315C4⋊C4—864no—
316C4⋊C4—864no—
317C4⋊C4—1722no—
318C22⋊C4—24no—
319C22⋊C4—24no—
320C22⋊C4—24no—
321C22⋊C4—864no—
322C22⋊C4—864no—
323C22⋊C4—864no—
324C22⋊C4—1728no—
325C22⋊C4—17216no—
326C42—22no—
327C42—22no—
328C42—44no—
329C42—864no—
330C42—864no—
331C42—1722no—
332C23—42no—
333C23—868no—
334C23—864no—
335C23—864no—
336C23—862no—
337C23—1724no—
338C23—1722no—
339C23—1724no—
340C23—1724no—
341C23—1728no—
342C23—1721no—
343C23—1722no—
344C23—1721no—
345C23C2×D4×D4312yes—
346C23C22×D17211yescharacteristic
347C23C2×Q8×D4311yescharacteristic
348C23C2×#1062190011yescharacteristic
349C23C2×#1062189812yes—
350Q8—3448no—
351C2×C4—24no—
352C2×C4—44no—
353C2×C4—48no—
354C2×C4—44no—
355C2×C4—868no—
356C2×C4—864no—
357C2×C4—862no—
358C2×C4—1724no—
359C2×C4—1722no—
360C2×C4—1721no—
361C2×C4—1722no—
362C2×C4—1721no—
363C2×C4—1724no—
364C2×C4—1728no—
365C2×C4—1724no—
366C2×C4—1728no—
367C2×C4#1306329511yescharacteristic
368C2×C4#1306329512yes—
369C2×C4#1306329511yescharacteristic
370C2×C4#1306330314yes—
371C2×C4#1306330314yes—
372C2×C4#1306330512yes—
373C2×C4#1306330512yes—
374C2×C4#1306331114yes—
375C2×C4#1306331114yes—
376C2×C4#1306331312yes—
377C2×C4#1306331312yes—
378C22—24no—
379C22—22no—
380C22—41no—
381C22—41no—
382C22—42no—
383C22—868no—
384C22—864no—
385C22—1728no—
386C22—1724no—
387C22—1724no—
388C22—1722no—
389C22—1722no—
390C22—1724no—
391C22C2×#1306329511yescharacteristic
392C22C2×#1306330312yes—
393C22C2×#1306330511yescharacteristic
394C22C2×#1306331112yes—
395C22C2×#1306331311yescharacteristic
396C4—44no—
397C4—84no—
398C4—3442no—
399C4—1722no—
400C4—1728no—
401C4#1458281212yes—
402C4#1458281214yes—
403C4#1458281212yes—
404C2—22no—
405C2—21no—
406C2—22no—
407C2—21no—
408C2—1724no—
409C2C2×#1458281211yescharacteristic
410C2#1914398912yes—
subgroupG/H
centerC2×C4#13063295
commutator, cosocleC24×C43C24
FrattiniC24C23×D43
FittingC43×#1740C2
socleC22×C43C2×#120
prime radicalC24×D43C23
hypercenter#1740D43
hypocenterC43#23467
LCSG ▷ C24×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1740

Complements

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

NH ≅ G/Ntype
1. #19148000C2semidirect
4. #19135763C2semidirect
6. #19134327C2semidirect
7. C43×#1740C2semidirect
36. C22×C4×D43Q8semidirect
205. #1740D43semidirect
233. C43#23467semidirect

Maximal subgroups

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

subgroupindex
#191480002
#191369742
#191357632
#191357602
#191343272
C43×#17402
#2346743