Finite Group Databasebeta

← #24986407

Subgroups — #24986407

Order 11008.

544 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143225C211yesmaximal, characteristic
2#432×D43C211yesmaximal, characteristic
3#431×D43C211yesmaximal, characteristic
4#19132458C211yesmaximal, characteristic, complemented
5#19132457C211yesmaximal, characteristic, complemented
6#19132456C211yesmaximal, characteristic, complemented
7C43×#1287C211yesmaximal, characteristic, complemented
8C2×C42×D43C2211yescharacteristic
9#14582956C2211yescharacteristic
10#14582956C2211yescharacteristic
11#14582955—21no—
12#14582954—21no—
13#14582954C412yes—
14#14582953—21no—
15#14582952C2211yescharacteristic
16#14582951—21no—
17#14582951—21no—
18#14582950C412yes—
19#14582949—21no—
20#14582949C412yes—
21#14582921—21no—
22C4⋊C8×D43—21no—
23C4⋊C8×D43—21no—
24#14582861C412yes—
25C22⋊C8×D43—21no—
26C22⋊C8×D43—21no—
27#14582851—21no—
28#97×D43C412yes—
29C4×C8×D43C412yes—
30C43×#432C2211yescharacteristic
31C43×#432C2211yescharacteristic
32C43×#431C2211yescharacteristic
33C22×C4×D43C2×C411yescharacteristic
34C22×C4×D43D411yescharacteristic
35C22×C4×D43Q811yescharacteristic
36C2×#10621872—22no—
37C2×C8×D43—22no—
38C2×C8×D43—22no—
39C2×C4×Dic43C2×C411yescharacteristic
40C2×C4×Dic43D411yescharacteristic
41C2×C4×Dic43Q811yescharacteristic
42C42×D43C2×C411yescharacteristic
43C42×D43C2×C411yescharacteristic
44C42×D43C2×C411yescharacteristic
45C42×D43C2×C411yescharacteristic
46C42×D43D411yescharacteristic
47C42×D43D411yescharacteristic
48C42×D43D411yescharacteristic
49C42×D43D411yescharacteristic
50C4⋊(C43⋊C8)—21no—
51C4⋊(C43⋊C8)—21no—
52C4⋊(C43⋊C8)—21no—
53Dic43⋊C8—22no—
54Dic43⋊C8—22no—
55Dic43⋊C8—22no—
56C22⋊(C43⋊C8)—21no—
57C22⋊(C43⋊C8)—21no—
58C22⋊(C43⋊C8)C2×C412yes—
59(C2×D43)⋊C8—22no—
60(C2×D43)⋊C8—22no—
61(C2×D43)⋊C8—22no—
62#13063236—21no—
63#13063236C2×C412yes—
64#13063235—22no—
65C4×C43⋊C8C2×C412yes—
66C8×Dic43—22no—
67C8×Dic43—22no—
68C2×C42×C43C2311yescharacteristic
69C4⋊C8×C43—21no—
70C4⋊C8×C43—21no—
71C4⋊C8×C43—21no—
72C22⋊C8×C43—21no—
73C22⋊C8×C43—21no—
74C22⋊C8×C43C2×C412yes—
75#97×C43—21no—
76#97×C43C2×C412yes—
77C4×C8×C43C2×C412yes—
78C23×D43C4⋊C411yescharacteristic
79C22×C4×C43C22×C411yescharacteristic
80C22×C4×C43C2×D411yescharacteristic
81C22×C4×C43C2×Q811yescharacteristic
82C22×Dic43C4⋊C411yescharacteristic
83C22×Dic43C4⋊C411yescharacteristic
84C22×Dic43C4⋊C411yescharacteristic
85C2×C4×D43—24no—
86C2×C4×D43—42no—
87C2×C4×D43—42no—
88C2×C4×D43C4211yescharacteristic
89C2×C4×D43C4211yescharacteristic
90C2×C4×D43C22⋊C411yescharacteristic
91C2×C4×D43C22⋊C411yescharacteristic
92C2×C4×D43C22⋊C411yescharacteristic
93C2×C4×D43C22⋊C411yescharacteristic
94C2×C4×D43C22⋊C411yescharacteristic
95C2×C4×D43C22⋊C411yescharacteristic
96C2×C4×D43C4⋊C411yescharacteristic
97C2×C4×D43C4⋊C411yescharacteristic
98C2×C4×D43C4⋊C411yescharacteristic
99C2×C4×D43C4⋊C411yescharacteristic
100C2×C8×C43—22no—
101C2×C8×C43—22no—
102C2×C8×C43—22no—
103C42×C43C22×C411yescharacteristic
104C42×C43C22×C411yescharacteristic
105C42×C43C2×D411yescharacteristic
106C42×C43C2×D411yescharacteristic
107C4×Dic43C4211yescharacteristic
108C4×Dic43C4211yescharacteristic
109C4×Dic43C22⋊C411yescharacteristic
110C4×Dic43C22⋊C411yescharacteristic
111C4×Dic43C22⋊C411yescharacteristic
112C4×Dic43C22⋊C411yescharacteristic
113C4×Dic43C22⋊C411yescharacteristic
114C4×Dic43C22⋊C411yescharacteristic
115C4×Dic43C4⋊C411yescharacteristic
116C4×Dic43C4⋊C411yescharacteristic
117C4×Dic43C4⋊C411yescharacteristic
118C4×Dic43C4⋊C411yescharacteristic
119C2×C43⋊C8—22no—
120C2×C43⋊C8—22no—
121C2×C43⋊C8—22no—
122#10621872—44no—
123C8×D43—44no—
124C8×D43—44no—
125C23×C43C2×C4⋊C411yescharacteristic
126C22×D43—22no—
127C22×D43—22no—
128C22×D43—41no—
129C22×D43#9511yescharacteristic
130C22×D43#9511yescharacteristic
131C2×C4×C43—22no—
132C2×C4×C43—41no—
133C2×C4×C43—41no—
134C2×C4×C43C2×C4211yescharacteristic
135C2×C4×C43C2×C22⋊C411yescharacteristic
136C2×C4×C43C2×C22⋊C411yescharacteristic
137C2×C4×C43C2×C22⋊C411yescharacteristic
138C2×C4×C43C2×C4⋊C411yescharacteristic
139C2×C4×C43C2×C4⋊C411yescharacteristic
140C2×Dic43—22no—
141C2×Dic43—22no—
142C2×Dic43—41no—
143C2×Dic43#9511yescharacteristic
144C2×Dic43#9511yescharacteristic
145C2×Dic43#9511yescharacteristic
146C2×Dic43#9511yescharacteristic
147C2×Dic43#9511yescharacteristic
148C2×Dic43#9511yescharacteristic
149C4×D43—22no—
150C4×D43—22no—
151C4×D43—22no—
152C4×D43—22no—
153C4×D43—22no—
154C4×D43—22no—
155C4×D43—22no—
156C4×D43—41no—
157C4×D43—41no—
158C4×D43—41no—
159C4×D43—41no—
160C4×D43#10814yes—
161C8×C43—42no—
162C8×C43—42no—
163C8×C43—42no—
164C43⋊C8—42no—
165C43⋊C8—42no—
166C43⋊C8—42no—
167#7964—431nomaximal, Sylow
168C22×C43—21no—
169C22×C43—21no—
170C22×C43—21no—
171C22×C43C2×#9511yescharacteristic
172C2×D43—21no—
173C2×D43—21no—
174C2×D43—21no—
175C2×D43—21no—
176C2×D43—44no—
177C2×D43#34112yes—
178C2×D43#34412yes—
179C4×C43—21no—
180C4×C43—21no—
181C4×C43—21no—
182C4×C43—21no—
183C4×C43—21no—
184C4×C43C2×#10812yes—
185Dic43—21no—
186Dic43—21no—
187Dic43—21no—
188Dic43—21no—
189Dic43H(3,ℤ/4)12yes—
190Dic43#34112yes—
191#2920—431no—
192C2×#432—431no—
193C2×#431—431no—
194#1287—431no—
195#1287—431no—
196#1287—431no—
197#1287D4311yescharacteristic, complemented
198C2×C43—41no—
199C2×C43C2×H(3,ℤ/4)11yescharacteristic
200C2×C43C2×#34111yescharacteristic
201C2×C43C2×#34411yescharacteristic
202D43—22no—
203D43—22no—
204C22×C42—431no—
205#432—431no—
206#432—432no—
207#432—431no—
208#432—861no—
209#432—861no—
210#432—861no—
211#432C2×D4311yescharacteristic
212#432C2×D4311yescharacteristic
213#431—431no—
214#431—432no—
215#431—432no—
216#431—861no—
217#431—861no—
218#431—861no—
219#431C2×D4311yescharacteristic
220#423—861no—
221C2×C4⋊C8—861no—
222C2×C4⋊C8—861no—
223#407—432no—
224C2×C22⋊C8—861no—
225C2×C22⋊C8—861no—
226C4×M16—861no—
227C2×#97—432no—
228C2×C4×C8—432no—
229C43#796411yescharacteristic, complemented, Sylow
230C23×C4—431no—
231C23×C4—431no—
232C23×C4—431no—
233C2×M16—862no—
234C22×C8—862no—
235C22×C8—862no—
236C2×C42—431no—
237C2×C42—431no—
238C2×C42—431no—
239C2×C42—431no—
240C2×C42—431no—
241C2×C42—431no—
242C2×C42—431no—
243C2×C42—431no—
244C2×C42—431no—
245C2×C42—431no—
246C2×C42—431no—
247C2×C42C22×D4311yescharacteristic
248C4⋊C8—21no—
249C4⋊C8—21no—
250C4⋊C8—21no—
251C4⋊C8—862no—
252C4⋊C8—862no—
253C4⋊C8—862no—
254C4⋊C8—861no—
255C4⋊C8—861no—
256C4⋊C8—861no—
257C22⋊C8—21no—
258C22⋊C8—21no—
259C22⋊C8—432no—
260C22⋊C8—862no—
261C22⋊C8—862no—
262C22⋊C8—862no—
263C22⋊C8—861no—
264C22⋊C8—861no—
265C22⋊C8C4×D4312yes—
266#97—21no—
267#97—432no—
268#97—862no—
269#97—861no—
270#97C4×D4312yes—
271C4×C8—432no—
272C4×C8—862no—
273C4×C8—862no—
274C4×C8C4×D4312yes—
275C24—431no—
276C22×C4—431no—
277C22×C4—431no—
278C22×C4—431no—
279C22×C4—431no—
280C22×C4—431no—
281C22×C4—431no—
282C22×C4—431no—
283C22×C4—431no—
284C22×C4—431no—
285C22×C4—431no—
286C22×C4—431no—
287C22×C4—431no—
288C22×C4—431no—
289C22×C4—431no—
290C22×C4—431no—
291C22×C4—864no—
292C22×C4—1722no—
293C22×C4—1722no—
294C22×C4C2×C4×D4311yescharacteristic
295C22×C4D4×D4311yescharacteristic
296C22×C4Q8×D4311yescharacteristic
297M16—1724no—
298C2×C8—22no—
299C2×C8—22no—
300C2×C8—22no—
301C2×C8—862no—
302C2×C8—862no—
303C2×C8—862no—
304C2×C8—1724no—
305C2×C8—1724no—
306C42—431no—
307C42—431no—
308C42—431no—
309C42—431no—
310C42—431no—
311C42—431no—
312C42—431no—
313C42—431no—
314C42—431no—
315C42—431no—
316C42—431no—
317C42—431no—
318C42C2×C4×D4311yescharacteristic
319C42C2×C4×D4311yescharacteristic
320C42D4×D4311yescharacteristic
321C42D4×D4311yescharacteristic
322C23—431no—
323C23—431no—
324C23—862no—
325C23—862no—
326C23—1721no—
327C23C4⋊C4×D4311yescharacteristic
328C2×C4—22no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—431no—
332C2×C4—431no—
333C2×C4—434no—
334C2×C4—431no—
335C2×C4—431no—
336C2×C4—431no—
337C2×C4—431no—
338C2×C4—862no—
339C2×C4—862no—
340C2×C4—862no—
341C2×C4—862no—
342C2×C4—862no—
343C2×C4—862no—
344C2×C4—862no—
345C2×C4—862no—
346C2×C4—862no—
347C2×C4—1721no—
348C2×C4—1721no—
349C2×C4—1721no—
350C2×C4—1721no—
351C2×C4—1721no—
352C2×C4C42×D4311yescharacteristic
353C2×C4C22⋊C4×D4311yescharacteristic
354C2×C4C22⋊C4×D4311yescharacteristic
355C2×C4C22⋊C4×D4311yescharacteristic
356C2×C4C4⋊C4×D4311yescharacteristic
357C2×C4C4⋊C4×D4311yescharacteristic
358C8—42no—
359C8—42no—
360C8—42no—
361C8—1722no—
362C8—1722no—
363C8—1722no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—432no—
368C22—432no—
369C22—861no—
370C22—861no—
371C22—861no—
372C22—861no—
373C22—1724no—
374C22#95×D4311yescharacteristic
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—432no—
381C4—432no—
382C4—861no—
383C4—861no—
384C4—861no—
385C4—861no—
386C4#108×D4312yes—
387C2—41no—
388C2—862no—
389C2—862no—
390C2H(3,ℤ/4)×D4311yescharacteristic
391C2#341×D4311yescharacteristic
392C2#344×D4311yescharacteristic
subgroupG/H
centerC22#95×D43
commutatorC2×C4×C43C2×C42
FrattiniC2×C42C22×D43
FittingC43×#1287C2
socleC22×C43C2×#95
prime radicalC23×D43C4⋊C4
cosocleC2×C42×C43C23
hypercenter#1287D43
hypocenterC43#7964
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1287

Complements

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

NH ≅ G/Ntype
4. #19132458C2semidirect
5. #19132457C2semidirect
6. #19132456C2semidirect
7. C43×#1287C2semidirect
197. #1287D43semidirect
229. C43#7964semidirect

Maximal subgroups

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

subgroupindex
#191432252
#432×D432
#431×D432
#191324582
#191324572
#191324562
C43×#12872
#796443