Finite Group Databasebeta

← #25065726

Subgroups — #25065726

Order 11008.

602 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143706C211yesmaximal, characteristic
2#19143239C211yesmaximal, characteristic
3#19133386C212yesmaximal, complemented
4#19133381C212yesmaximal, complemented
5#19133376C212yesmaximal, complemented
6#19133367C212yesmaximal, complemented
7#19133348C211yesmaximal, characteristic, complemented
8#19133345C211yesmaximal, characteristic, complemented
9#19133341C211yesmaximal, characteristic, complemented
10C2×#14582649C211yesmaximal, characteristic, complemented
11C43×#2989C211yesmaximal, characteristic
12Q8×C43⋊C8—21no—
13D4×C43⋊C8—22no—
14D4×C43⋊C8—21no—
15#14582960C414yes—
16#14582952C2211yescharacteristic
17#14582952C2212yes—
18#14582952C2212yes—
19#14582952C2212yes—
20#14582926C412yes—
21C2×C4⋊(C43⋊C8)C2211yescharacteristic
22C2×C4⋊(C43⋊C8)C2212yes—
23#14582866C412yes—
24C4×#10621877C2211yescharacteristic
25C2×C4×C43⋊C8C2211yescharacteristic
26#14582651C2211yescharacteristic
27#14582651C2211yescharacteristic
28#14582651C2212yes—
29#14582651C2212yes—
30#14582649C2212yes—
31#14582649C2212yes—
32#14582649C2211yescharacteristic
33#14582649C2211yescharacteristic
34#14582649C2212yes—
35#14582649C2212yes—
36C4×#41×C43C2211yescharacteristic
37C43×#446—21no—
38C43×#436—21no—
39C43×#435—22no—
40C43×#432C2212yes—
41C43×#431C2211yescharacteristic
42C43×#423C2212yes—
43C2×C4⋊C8×C43C2211yescharacteristic
44C2×#10621877C2×C412yes—
45C22×C43⋊C8—21no—
46C22×C43⋊C8—22no—
47C22×C43⋊C8C2×C412yes—
48C4⋊(C43⋊C8)—21no—
49C4⋊(C43⋊C8)—22no—
50C4⋊(C43⋊C8)C2×C414yes—
51C4⋊(C43⋊C8)C2×C414yes—
52C4⋊(C43⋊C8)C2312yes—
53C4⋊(C43⋊C8)C2311yescharacteristic
54C4⋊(C43⋊C8)C2311yescharacteristic
55C22⋊(C43⋊C8)—21no—
56C22⋊(C43⋊C8)—22no—
57C22⋊(C43⋊C8)C2×C414yes—
58C22⋊(C43⋊C8)C2×C414yes—
59#13063236C2×C412yes—
60C4×C43⋊C8—21no—
61C4×C43⋊C8—22no—
62C4×C43⋊C8C2×C412yes—
63C4×C43⋊C8C2311yescharacteristic
64C4×C43⋊C8C2311yescharacteristic
65C4×C43⋊C8C2312yes—
66C2×#41×C43C2×C411yescharacteristic
67C2×M16×C43—22no—
68C22×C8×C43—21no—
69C4×Q8×C43D411yescharacteristic
70C4×Q8×C43Q811yescharacteristic
71C4×D4×C43D412yes—
72C4×D4×C43D411yescharacteristic
73C4×D4×C43Q812yes—
74C4×D4×C43Q811yescharacteristic
75#117×C43C2×C411yescharacteristic
76#117×C43C2×C412yes—
77C2×C42×C43C2311yescharacteristic
78C2×C42×C43C2312yes—
79C4⋊C8×C43—21no—
80C4⋊C8×C43—22no—
81C4⋊C8×C43C2312yes—
82C4⋊C8×C43C2311yescharacteristic
83C4⋊C8×C43C2311yescharacteristic
84C22⋊C8×C43—21no—
85C22⋊C8×C43—22no—
86#97×C43—22no—
87C4×C8×C43—21no—
88#41×C43—24no—
89C2×Q8×C43C4⋊C411yescharacteristic
90C2×D4×C43C4⋊C411yescharacteristic
91C2×D4×C43C4⋊C412yes—
92C22×C4×C43C22×C412yes—
93C22×C4×C43C22×C411yescharacteristic
94C22×C4×C43C2×D411yescharacteristic
95C22×C4×C43C2×D412yes—
96C22×C4×C43C2×Q812yes—
97C22×C4×C43C2×Q811yescharacteristic
98M16×C43—82no—
99C2×C8×C43—21no—
100C2×C8×C43—21no—
101C2×C8×C43—22no—
102C2×C8×C43—81no—
103C4⋊C4×C43C4⋊C412yes—
104C4⋊C4×C43C4⋊C411yescharacteristic
105C4⋊C4×C43C4⋊C412yes—
106C4⋊C4×C43C4⋊C411yescharacteristic
107C22⋊C4×C43C4⋊C412yes—
108C22⋊C4×C43C4⋊C412yes—
109C22⋊C4×C43C4⋊C412yes—
110C42×C43C22×C411yescharacteristic
111C42×C43C22×C412yes—
112C42×C43C2×D411yescharacteristic
113C42×C43C2×D412yes—
114C42×C43C2×Q812yes—
115C42×C43C2×Q811yescharacteristic
116C42×C43C2411yescharacteristic
117#10621877—24no—
118C2×C43⋊C8—24no—
119C2×C43⋊C8—21no—
120C2×C43⋊C8—21no—
121C2×C43⋊C8—22no—
122C2×C43⋊C8—81no—
123C2×C43⋊C8—82no—
124C2×C43⋊C8C22×C412yes—
125C2×C43⋊C8C22×C412yes—
126C2×C43⋊C8C22×C414yes—
127C23×C43C2×C4⋊C412yes—
128C23×C43C2×C4⋊C411yescharacteristic
129Q8×C43—22no—
130D4×C43—24no—
131D4×C43—22no—
132C2×C4×C43—24no—
133C2×C4×C43—21no—
134C2×C4×C43—22no—
135C2×C4×C43—21no—
136C2×C4×C43—22no—
137C2×C4×C43—41no—
138C2×C4×C43—42no—
139C2×C4×C43C2×C4⋊C411yescharacteristic
140C2×C4×C43C2×C4⋊C412yes—
141C2×C4×C43C2×C4⋊C411yescharacteristic
142C2×C4×C43C2×C4⋊C412yes—
143C2×C4×C43C2×C4⋊C412yes—
144C2×C4×C43C2×C4⋊C411yescharacteristic
145C2×C4×C43#13114yes—
146C2×C4×C43C23×C411yescharacteristic
147C2×C4×C43C22×D411yescharacteristic
148C2×C4×C43C22×Q811yescharacteristic
149C8×C43—41no—
150C8×C43—42no—
151C8×C43—41no—
152C43⋊C8—22no—
153C43⋊C8—22no—
154C43⋊C8—24no—
155C43⋊C8—41no—
156C43⋊C8—41no—
157C43⋊C8—42no—
158#17811—431nomaximal, Sylow
159C22×C43—21no—
160C22×C43—21no—
161C22×C43—22no—
162C22×C43—22no—
163C22×C43—22no—
164C22×C43#42412yes—
165C22×C43C22×C4⋊C411yescharacteristic
166C4×C43—22no—
167C4×C43—21no—
168C4×C43—22no—
169C4×C43—21no—
170C4×C43—21no—
171C4×C43—22no—
172C4×C43#42412yes—
173C4×C43C2×#13112yes—
174C4×C43#57711yescharacteristic
175C4×C43#57711yescharacteristic
176#2989D4311yescharacteristic
177#2988—431no—
178#2922—431no—
179#1574—432no—
180#1573—432no—
181#1572—432no—
182#1570—432no—
183#1565—431no—
184#1565—431no—
185#1564—431no—
186C2×#334—431no—
187C2×C43—22no—
188C2×C43—42no—
189C2×C43C2×#42411yescharacteristic
190C2×C43#291211yescharacteristic
191C2×C43#291611yescharacteristic
192C4×#41C2×D4311yescharacteristic
193#446—21no—
194C8×Q8—861no—
195#436—21no—
196#435—22no—
197C8×D4—862no—
198C8×D4—861no—
199#433—434no—
200#432C2×D4312yes—
201#431—432no—
202#431—432no—
203#431—431no—
204#431—432no—
205#431C2×D4311yescharacteristic
206#424—432no—
207#423C2×D4312yes—
208C2×C4⋊C8—431no—
209C2×C4⋊C8—432no—
210C2×C4⋊C8C2×D4311yescharacteristic
211#408—432no—
212C4×M16—431no—
213C2×C4×C8—431no—
214#335—431no—
215#335—431no—
216#335—432no—
217#335—432no—
218#334—432no—
219#334—432no—
220#334—431no—
221#334—431no—
222#334—432no—
223#334—432no—
224C43#1781111yescharacteristic, complemented, Sylow
225C2×#41C4×D4311yescharacteristic
226C2×M16—22no—
227C2×M16—432no—
228C22×C8—21no—
229C22×C8—432no—
230C22×C8—861no—
231C22×C8—862no—
232C4×Q8Dic8611yescharacteristic
233C4×Q8C22⋊D4311yescharacteristic
234C4×D4Dic8612yes—
235C4×D4Dic8611yescharacteristic
236C4×D4C22⋊D4312yes—
237C4×D4C22⋊D4311yescharacteristic
238#117C4×D4311yescharacteristic
239#117C4×D4312yes—
240C2×C42C22×D4311yescharacteristic
241C2×C42C22×D4312yes—
242C4⋊C8—21no—
243C4⋊C8—22no—
244C4⋊C8—434no—
245C4⋊C8—434no—
246C4⋊C8—432no—
247C4⋊C8—431no—
248C4⋊C8—431no—
249C4⋊C8—861no—
250C4⋊C8—862no—
251C4⋊C8C22×D4312yes—
252C4⋊C8C22×D4311yescharacteristic
253C4⋊C8C22×D4311yescharacteristic
254C22⋊C8—21no—
255C22⋊C8—22no—
256C22⋊C8—434no—
257C22⋊C8—434no—
258C22⋊C8—861no—
259C22⋊C8—862no—
260#97—22no—
261#97—432no—
262C4×C8—21no—
263C4×C8—432no—
264C4×C8—431no—
265C4×C8—431no—
266C4×C8—432no—
267C4×C8—861no—
268C4×C8—862no—
269#41—24no—
270C2×Q8Dic43⋊C411yescharacteristic
271C2×D4Dic43⋊C412yes—
272C2×D4Dic43⋊C411yescharacteristic
273C22×C4C2×Dic8612yes—
274C22×C4C2×Dic8611yescharacteristic
275C22×C4C2×C4×D4312yes—
276C22×C4C2×C4×D4311yescharacteristic
277C22×C4C2×C22⋊D4311yescharacteristic
278C22×C4C2×C22⋊D4312yes—
279M16—82no—
280M16—864no—
281C2×C8—21no—
282C2×C8—21no—
283C2×C8—22no—
284C2×C8—81no—
285C2×C8—432no—
286C2×C8—432no—
287C2×C8—434no—
288C2×C8—864no—
289C2×C8—861no—
290C2×C8—861no—
291C2×C8—862no—
292C2×C8—3441no—
293C2×C8—3442no—
294C4⋊C4Dic43⋊C412yes—
295C4⋊C4Dic43⋊C411yescharacteristic
296C4⋊C4Dic43⋊C412yes—
297C4⋊C4Dic43⋊C411yescharacteristic
298C22⋊C4Dic43⋊C412yes—
299C22⋊C4Dic43⋊C412yes—
300C22⋊C4Dic43⋊C412yes—
301C42C2×Dic8612yes—
302C42C2×Dic8611yescharacteristic
303C42C2×C4×D4311yescharacteristic
304C42C2×C4×D4312yes—
305C42C2×C22⋊D4311yescharacteristic
306C42C2×C22⋊D4312yes—
307C42C23×D4311yescharacteristic
308C23C2×Dic43⋊C412yes—
309C23C2×Dic43⋊C411yescharacteristic
310Q8—22no—
311D4—24no—
312D4—22no—
313C2×C4—24no—
314C2×C4—21no—
315C2×C4—22no—
316C2×C4—21no—
317C2×C4—22no—
318C2×C4—41no—
319C2×C4—42no—
320C2×C4C2×Dic43⋊C411yescharacteristic
321C2×C4C2×Dic43⋊C412yes—
322C2×C4C2×Dic43⋊C412yes—
323C2×C4C2×Dic43⋊C411yescharacteristic
324C2×C4C2×Dic43⋊C412yes—
325C2×C4C2×Dic43⋊C411yescharacteristic
326C2×C4#1306333314yes—
327C2×C4C22×C4×D4311yescharacteristic
328C2×C4C22×C22⋊D4311yescharacteristic
329C2×C4C22×Dic8611yescharacteristic
330C8—41no—
331C8—42no—
332C8—41no—
333C8—862no—
334C8—862no—
335C8—864no—
336C8—1721no—
337C8—1722no—
338C8—1721no—
339C22—21no—
340C22—21no—
341C22—22no—
342C22—22no—
343C22—22no—
344C22#1458292712yes—
345C22C22×Dic43⋊C411yescharacteristic
346C4—21no—
347C4—22no—
348C4—21no—
349C4—21no—
350C4—22no—
351C4—22no—
352C4#1458292712yes—
353C4C2×#1306333312yes—
354C4#1458370711yescharacteristic
355C4#1458371011yescharacteristic
356C2—22no—
357C2—42no—
358C2C2×#1458292711yescharacteristic
359C2#1914318811yescharacteristic
360C2#1914320411yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#2989C2
socleC22×C43C22×C4⋊C4
prime radicalC2×#41×C43C2×C4
cosocleC42×C43C24
hypercenter#2989D43
hypocenterC43#17811
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #2989

Complements

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

NH ≅ G/Ntype
3. #19133386C2semidirect
4. #19133381C2semidirect
5. #19133376C2semidirect
6. #19133367C2semidirect
7. #19133348C2semidirect
8. #19133345C2semidirect
9. #19133341C2semidirect
10. C2×#14582649C2semidirect
224. C43#17811semidirect

Maximal subgroups

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

subgroupindex
#191437062
#191432392
#191333862
#191333812
#191333762
#191333672
#191333482
#191333452
#191333412
C2×#145826492
C43×#29892
#1781143