Finite Group Databasebeta

← #25125720

Subgroups — #25125720

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
1#19143184C211yesmaximal, characteristic
2C2×#14582935C211yesmaximal, characteristic
3C2×#14582926C211yesmaximal, characteristic
4#19136108C214yesmaximal, complemented
5#19136103C214yesmaximal, complemented
6#19134334C211yesmaximal, characteristic
7#19134333C211yesmaximal, characteristic
8C2×#14582663C211yesmaximal, characteristic
9C43×#2911C211yesmaximal, characteristic
10C22×#10621877C2211yescharacteristic
11C22×#10621877C2211yescharacteristic
12C23×C43⋊C8C2211yescharacteristic
13C2×#13063284C2211yescharacteristic
14#14582942C2214yes—
15#14582939—22no—
16#14582935—22no—
17#14582935—22no—
18#14582935—22no—
19C2×#13063258C2212yes—
20C2×#13063256C2212yes—
21#14582926—22no—
22#14582926C2212yes—
23#14582926C2212yes—
24C2×C4⋊(C43⋊C8)—22no—
25#14582668C2214yes—
26#14582667C2214yes—
27#14582663C2212yes—
28#14582663C2212yes—
29C22×M16×C43C2211yescharacteristic
30C2×#117×C43C2211yescharacteristic
31C2×#117×C43C2211yescharacteristic
32C43×#428—22no—
33C43×#428C2214yes—
34C43×#427—22no—
35C2×#10621877—21no—
36C2×#10621877—22no—
37C2×#10621877—21no—
38C2×#10621877—22no—
39C2×#10621877—22no—
40C2×#10621877Q814yes—
41C2×#10621877C2312yes—
42C2×#10621877C2312yes—
43C22×C43⋊C8—21no—
44C22×C43⋊C8—22no—
45C22×C43⋊C8—22no—
46C22×C43⋊C8—21no—
47C22×C43⋊C8D412yes—
48C22×C43⋊C8D412yes—
49C22×C43⋊C8C2311yescharacteristic
50C22×C43⋊C8C2311yescharacteristic
51#13063284—21no—
52#13063284—21no—
53#13063284—21no—
54#13063284—21no—
55C2×C4⋊Dic43C2312yes—
56C2×C22⋊Dic43—21no—
57C2×C4×Dic43—21no—
58#13063258—24no—
59#13063258—24no—
60#13063256—24no—
61#13063256—24no—
62C4⋊(C43⋊C8)—24no—
63C4⋊(C43⋊C8)—24no—
64C23×C4×C43C2311yescharacteristic
65C2×M16×C43—21no—
66C2×M16×C43—22no—
67C2×M16×C43Q814yes—
68C2×M16×C43C2312yes—
69C22×C8×C43—21no—
70#117×C43—21no—
71#117×C43—21no—
72#117×C43—21no—
73#117×C43—21no—
74#117×C43—21no—
75#117×C43—21no—
76#117×C43D412yes—
77#117×C43C2312yes—
78C2×C4⋊C4×C43D412yes—
79C2×C4⋊C4×C43C2312yes—
80C2×C22⋊C4×C43—21no—
81C2×C22⋊C4×C43—21no—
82C2×C42×C43—21no—
83C2×C42×C43—21no—
84#107×C43—24no—
85#106×C43—24no—
86C24×C43#4111yescharacteristic
87C22×C4×C43—22no—
88C22×C4×C43—22no—
89C22×C4×C43C2×D411yescharacteristic
90C22×C4×C43C2×D411yescharacteristic
91C22×C4×C43C2×D411yescharacteristic
92C22×C4×C43C2×D411yescharacteristic
93C22×C4×C43C2×Q812yes—
94C22×C4×C43C2×Q812yes—
95C22×C4×C43#4112yes—
96C22×C4×C43#4112yes—
97C22×C4×C43#4111yescharacteristic
98C22×C4×C43C2411yescharacteristic
99C22×Dic43—22no—
100M16×C43—24no—
101M16×C43—22no—
102M16×C43C2×Q814yes—
103C2×C8×C43—24no—
104C2×C8×C43—22no—
105C4⋊C4×C43—22no—
106C4⋊C4×C43—22no—
107C4⋊C4×C43—22no—
108C4⋊C4×C43C2×D414yes—
109C22⋊C4×C43—22no—
110C22⋊C4×C43—22no—
111C22⋊C4×C43—41no—
112C22⋊C4×C43—41no—
113C42×C43—22no—
114C42×C43—22no—
115C42×C43—41no—
116C42×C43—41no—
117C22⋊Dic43—41no—
118C22⋊Dic43—41no—
119C4⋊Dic43—22no—
120C4⋊Dic43—22no—
121C4×Dic43—41no—
122C4×Dic43—41no—
123#10621877—24no—
124#10621877—22no—
125#10621877—22no—
126#10621877—22no—
127#10621877—42no—
128#10621877C2×Q814yes—
129C2×C43⋊C8—24no—
130C2×C43⋊C8—24no—
131C2×C43⋊C8—24no—
132C2×C43⋊C8—22no—
133C2×C43⋊C8—21no—
134C2×C43⋊C8—21no—
135C2×C43⋊C8—21no—
136C2×C43⋊C8—21no—
137C2×C43⋊C8—22no—
138C2×C43⋊C8—42no—
139C2×C43⋊C8C2×D412yes—
140C2×C43⋊C8C2×D412yes—
141C23×C43—42no—
142C23×C43#12111yescharacteristic
143C23×C43#12111yescharacteristic
144C23×C43#12512yes—
145C23×C43#12512yes—
146C23×C43C2×#4111yescharacteristic
147C2×C4×C43—24no—
148C2×C4×C43—44no—
149C2×C4×C43—42no—
150C2×C4×C43—82no—
151C2×C4×C43#12111yescharacteristic
152C2×C4×C43#12111yescharacteristic
153C2×C4×C43C22⋊Q812yes—
154C2×C4×C43C22⋊Q812yes—
155C2×C4×C43C22⋊Q812yes—
156C2×C4×C43C22⋊Q812yes—
157C2×C4×C43#12312yes—
158C2×C4×C43#12312yes—
159C2×C4×C43#12512yes—
160C2×C4×C43#12512yes—
161C2×C4×C43C4⋊Q812yes—
162C2×C4×C43C4⋊Q812yes—
163C2×C4×C43C22×D411yescharacteristic
164C2×C4×C43C22×D411yescharacteristic
165C2×C4×C43C22×Q811yescharacteristic
166C2×C4×C43C22×Q811yescharacteristic
167C2×C4×C43C2×#4111yescharacteristic
168C2×C4×C43C2×#4111yescharacteristic
169C2×Dic43—42no—
170C2×Dic43—82no—
171C8×C43—24no—
172C43⋊C8—24no—
173C43⋊C8—22no—
174C43⋊C8—22no—
175C43⋊C8—42no—
176#23674—431nomaximal, Sylow
177C22×C43—22no—
178C22×C43—22no—
179C22×C43—22no—
180C22×C43—42no—
181C22×C43—42no—
182C22×C43#39812yes—
183C22×C43#39812yes—
184C22×C43C2×#12111yescharacteristic
185C22×C43C2×#12511yescharacteristic
186C22×C43C2×#12511yescharacteristic
187C4×C43—44no—
188C4×C43—82no—
189C4×C43#39812yes—
190C4×C43#39812yes—
191C4×C43C2×C22⋊Q811yescharacteristic
192C4×C43C2×C22⋊Q811yescharacteristic
193C4×C43C2×#12311yescharacteristic
194C4×C43C2×C4⋊Q811yescharacteristic
195Dic43—82no—
196#2911—431no—
197#2911D4311yescharacteristic
198C2×#427—431no—
199C2×#424—431no—
200#2090—434no—
201#2089—434no—
202#1742—431no—
203#1742—431no—
204C2×#341—431no—
205C2×C43—21no—
206C2×C43—21no—
207C2×C43—22no—
208C2×C43—22no—
209C2×C43C2×#39811yescharacteristic
210C2×C43#306712yes—
211C22×M16—431no—
212C22×M16—431no—
213C22×M16C2×D4311yescharacteristic
214C23×C8—431no—
215C2×#117—431no—
216C2×#117C2×D4311yescharacteristic
217C2×#117C2×D4311yescharacteristic
218#428—22no—
219#428—434no—
220#428—862no—
221#428C2×D4314yes—
222#427—22no—
223#427—862no—
224#427—862no—
225#427—862no—
226C2×#107—432no—
227C2×#106—432no—
228#424—432no—
229#424—432no—
230#424—862no—
231C2×C4⋊C8—862no—
232#343—434no—
233#343—434no—
234#341—432no—
235#341—432no—
236C43#2367411yescharacteristic, complemented, Sylow
237C23×C4C22×D4311yescharacteristic
238C2×M16—22no—
239C2×M16—21no—
240C2×M16—434no—
241C2×M16—432no—
242C2×M16—432no—
243C2×M16—862no—
244C2×M16—861no—
245C2×M16—861no—
246C2×M16—862no—
247C2×M16—862no—
248C2×M16Dic8614yes—
249C2×M16C22×D4312yes—
250C22×C8—21no—
251C22×C8—432no—
252C22×C8—432no—
253C22×C8—431no—
254C22×C8—431no—
255C22×C8—862no—
256C22×C8—862no—
257C22×C8—861no—
258C22×C8—861no—
259#117—21no—
260#117—21no—
261#117—21no—
262#117—21no—
263#117—21no—
264#117—21no—
265#117—861no—
266#117—861no—
267#117—861no—
268#117—861no—
269#117C22⋊D4312yes—
270#117C22×D4312yes—
271C2×C4⋊C4—432no—
272C2×C4⋊C4C22⋊D4312yes—
273C2×C4⋊C4C22×D4312yes—
274C2×C22⋊C4—21no—
275C2×C22⋊C4—21no—
276C2×C22⋊C4—861no—
277C2×C42—21no—
278C2×C42—21no—
279C2×C42—861no—
280#107—24no—
281#107—864no—
282#107—864no—
283#106—24no—
284#106—864no—
285#106—864no—
286C4⋊C8—864no—
287C4⋊C8—864no—
288C24#1062190011yescharacteristic
289C22×C4—22no—
290C22×C4—22no—
291C22×C4—862no—
292C22×C4C2×Dic8612yes—
293C22×C4#1062189812yes—
294C22×C4D4×D4311yescharacteristic
295C22×C4D4×D4311yescharacteristic
296C22×C4#1062190011yescharacteristic
297C22×C4Q8×D4312yes—
298C22×C4#1062190212yes—
299C22×C4C2×C22⋊D4311yescharacteristic
300C22×C4C2×C22⋊D4311yescharacteristic
301C22×C4C23×D4311yescharacteristic
302M16—24no—
303M16—22no—
304M16—434no—
305M16—864no—
306M16—862no—
307M16—862no—
308M16—862no—
309M16—1722no—
310M16C2×Dic8614yes—
311C2×C8—24no—
312C2×C8—22no—
313C2×C8—432no—
314C2×C8—432no—
315C2×C8—864no—
316C2×C8—864no—
317C2×C8—864no—
318C2×C8—862no—
319C2×C8—861no—
320C2×C8—861no—
321C2×C8—861no—
322C2×C8—861no—
323C2×C8—862no—
324C2×C8—1722no—
325C4⋊C4—22no—
326C4⋊C4—22no—
327C4⋊C4—22no—
328C4⋊C4—862no—
329C4⋊C4—862no—
330C4⋊C4C2×C22⋊D4314yes—
331C22⋊C4—22no—
332C22⋊C4—22no—
333C22⋊C4—41no—
334C22⋊C4—41no—
335C22⋊C4—1721no—
336C22⋊C4—1721no—
337C42—22no—
338C42—22no—
339C42—41no—
340C42—41no—
341C42—1721no—
342C42—1721no—
343C23—42no—
344C23#1306329711yescharacteristic
345C23#1306329711yescharacteristic
346C23#1306331512yes—
347C23#1306331612yes—
348C23C2×#1062190011yescharacteristic
349C2×C4—24no—
350C2×C4—44no—
351C2×C4—42no—
352C2×C4—82no—
353C2×C4—3442no—
354C2×C4—1722no—
355C2×C4#1306329711yescharacteristic
356C2×C4#1306329711yescharacteristic
357C2×C4#1306330112yes—
358C2×C4#1306330112yes—
359C2×C4#1306330412yes—
360C2×C4#1306330412yes—
361C2×C4#1306331012yes—
362C2×C4#1306331012yes—
363C2×C4#1306331512yes—
364C2×C4#1306331612yes—
365C2×C4#1306332412yes—
366C2×C4#1306332412yes—
367C2×C4C2×D4×D4311yescharacteristic
368C2×C4C22×C22⋊D4311yescharacteristic
369C2×C4C2×Q8×D4311yescharacteristic
370C2×C4C22×Dic8611yescharacteristic
371C2×C4C2×#1062189811yescharacteristic
372C2×C4C2×#1062190211yescharacteristic
373C8—24no—
374C8—864no—
375C8—862no—
376C8—862no—
377C8—1722no—
378C22—22no—
379C22—22no—
380C22—22no—
381C22—42no—
382C22—42no—
383C22#1458283212yes—
384C22#1458283212yes—
385C22C2×#1306329711yescharacteristic
386C22C2×#1306331511yescharacteristic
387C22C2×#1306331611yescharacteristic
388C4—44no—
389C4—82no—
390C4—3442no—
391C4#1458283212yes—
392C4#1458283212yes—
393C4C2×#1306330111yescharacteristic
394C4C2×#1306330411yescharacteristic
395C4C2×#1306331011yescharacteristic
396C4C2×#1306332411yescharacteristic
397C2—22no—
398C2—22no—
399C2—21no—
400C2—21no—
401C2C2×#1458283211yescharacteristic
402C2#1914431212yes—
subgroupG/H
centerC2×C4#13063297
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2911C2
socleC22×C43C2×#121
prime radicalC24×C43#41
hypercenter#2911D43
hypocenterC43#23674
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #2911

Complements

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

NH ≅ G/Ntype
4. #19136108C2semidirect
5. #19136103C2semidirect
236. C43#23674semidirect

Maximal subgroups

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

subgroupindex
#191431842
C2×#145829352
C2×#145829262
#191361082
#191361032
#191343342
#191343332
C2×#145826632
C43×#29112
#2367443