Finite Group Databasebeta

← #24992452

Subgroups — #24992452

Order 11008.

432 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144404C211yesmaximal, characteristic
2#19143263C211yesmaximal, characteristic
3C2×#14582645C211yesmaximal, characteristic, complemented
4#19132983C211yesmaximal, characteristic
5#19132491C211yesmaximal, characteristic, complemented
6#19132469C211yesmaximal, characteristic, complemented
7C43×#1548C211yesmaximal, characteristic, complemented
8C4×#10621898C2211yescharacteristic
9#14583191C412yes—
10#14583186C412yes—
11#14583181—21no—
12#14583176—21no—
13#14582959—22no—
14#14582955—21no—
15#14582951—21no—
16#14582939—21no—
17#14582923C2211yescharacteristic
18C2×C4⋊(C43⋊C8)C2211yescharacteristic
19C2×C4⋊(C43⋊C8)C2211yescharacteristic
20#14582898—21no—
21#14582867—21no—
22#14582857—21no—
23#14582645—21no—
24#14582645—21no—
25#14582631—21no—
26#14582628—21no—
27C2×C4⋊Q8×C43C2211yescharacteristic
28C43×#431C2211yescharacteristic
29C43×#423C2211yescharacteristic
30C43×#333—22no—
31C2×#10621898D411yescharacteristic
32C2×#10621877—21no—
33C22×C43⋊C8—21no—
34C22×C43⋊C8—21no—
35C4×Dic86C2×C411yescharacteristic
36C4×Dic86D411yescharacteristic
37C4×D172C2×C411yescharacteristic
38C4×D172D411yescharacteristic
39C4×C22⋊D43—21no—
40C4×C22⋊D43—21no—
41#13063284D411yescharacteristic
42#13063282—21no—
43C42×D43—21no—
44#13063258—22no—
45#13063256—22no—
46C4⋊(C43⋊C8)—21no—
47C4⋊(C43⋊C8)—21no—
48C4⋊(C43⋊C8)—21no—
49C4⋊(C43⋊C8)—21no—
50C4⋊(C43⋊C8)C2×C412yes—
51C4⋊(C43⋊C8)D411yescharacteristic
52C4⋊(C43⋊C8)D411yescharacteristic
53#13063248—22no—
54#13063245—22no—
55(C2×D43)⋊C8—22no—
56(C2×D43)⋊C8—22no—
57#13063235—22no—
58C8×Dic43—22no—
59C22×Q8×C43—21no—
60C2×M16×C43—21no—
61C4⋊Q8×C43—21no—
62C4⋊Q8×C43—21no—
63C4⋊Q8×C43—21no—
64C4⋊Q8×C43C2×C412yes—
65C2×C4⋊C4×C43—21no—
66C2×C4⋊C4×C43—21no—
67C2×C42×C43C2311yescharacteristic
68C4⋊C8×C43—21no—
69C4⋊C8×C43—21no—
70C4⋊C8×C43D412yes—
71C22⋊C8×C43—21no—
72C4×C8×C43—21no—
73C2×Q8×C43—22no—
74C2×Q8×C43—41no—
75C2×Q8×C43—81no—
76C2×Q8×C43—81no—
77C22×C4×C43—41no—
78C22×C4×C43C2×D411yescharacteristic
79C22×C4×C43#4111yescharacteristic
80C22×C4×C43#4111yescharacteristic
81C2×C22⋊D43—21no—
82#10621898—21no—
83#10621898—21no—
84#10621898—21no—
85#10621898—21no—
86C2×D172C22⋊C411yescharacteristic
87C2×C4×D43—21no—
88C2×C4×D43—21no—
89C2×C4×D43—21no—
90C2×Dic86C22⋊C411yescharacteristic
91M16×C43—41no—
92M16×C43—41no—
93C2×C8×C43—22no—
94C2×C8×C43—41no—
95C4⋊C4×C43—22no—
96C4⋊C4×C43—22no—
97C4⋊C4×C43—41no—
98C4⋊C4×C43—41no—
99C42×C43C22×C411yescharacteristic
100C42×C43C2×D411yescharacteristic
101C42×C43C2×D411yescharacteristic
102C42×C43C2×D411yescharacteristic
103C22⋊Dic43—21no—
104(C2×D43)⋊C4—21no—
105(C2×D43)⋊C4—21no—
106C4⋊Dic43C22⋊C411yescharacteristic
107C4⋊Dic43C22⋊C411yescharacteristic
108Dic43⋊C4—21no—
109Dic43⋊C4—21no—
110C4×Dic43—21no—
111C4×Dic43—21no—
112C4×Dic43—21no—
113#10621877—41no—
114#10621877—41no—
115C2×C43⋊C8—22no—
116C2×C43⋊C8—21no—
117C2×C43⋊C8—21no—
118C2×C43⋊C8—41no—
119C2×C43⋊C8—41no—
120C2×C43⋊C8—41no—
121C2×C43⋊C8—81no—
122C23×C43#12311yescharacteristic
123C22×D43—21no—
124Q8×C43—82no—
125Q8×C43—81no—
126Q8×C43—81no—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43—41no—
130C2×C4×C43—42no—
131C2×C4×C43—82no—
132C2×C4×C43C2×C22⋊C411yescharacteristic
133C2×C4×C43C4×D411yescharacteristic
134C2×C4×C43C4×D411yescharacteristic
135C2×C4×C43#12011yescharacteristic
136C2×C4×C43#12111yescharacteristic
137C2×C4×C43#12111yescharacteristic
138C2×C4×C43#13511yescharacteristic
139C2×C4×C43#13511yescharacteristic
140C2×C4×C43#13711yescharacteristic
141C2×C4×C43#13711yescharacteristic
142C22⋊D43—41no—
143C22⋊D43—41no—
144C2×Dic43—21no—
145C2×Dic43—21no—
146C2×Dic43—21no—
147D172—21no—
148D172—21no—
149C4×D43—41no—
150C4×D43—41no—
151C4×D43—41no—
152C4×D43—41no—
153C4×D43—81no—
154Dic86—21no—
155Dic86—21no—
156C8×C43—42no—
157C8×C43—81no—
158C43⋊C8—42no—
159C43⋊C8—41no—
160C43⋊C8—41no—
161C43⋊C8—81no—
162#9168—431nomaximal, Sylow
163C22×C43—21no—
164C22×C43—21no—
165C22×C43#38611yescharacteristic
166C22×C43#48511yescharacteristic
167C22×C43#48511yescharacteristic
168C2×D43—41no—
169C2×D43—41no—
170C2×D43—41no—
171C4×C43—21no—
172C4×C43—21no—
173C4×C43—21no—
174C4×C43—82no—
175C4×C43#41611yescharacteristic
176C4×C43#41911yescharacteristic
177C4×C43#45211yescharacteristic
178C4×C43#45211yescharacteristic
179C4×C43#47111yescharacteristic
180C4×C43#47211yescharacteristic
181Dic43—41no—
182Dic43—41no—
183Dic43—41no—
184#3079—431no—
185#2925—431no—
186#1548D4311yescharacteristic, complemented
187C2×#332—431no—
188#1477—431no—
189#1301—431no—
190#1292—431no—
191C2×C43—21no—
192C2×C43—21no—
193C2×C43#187311yescharacteristic
194C2×C43#190211yescharacteristic
195C2×C43#190711yescharacteristic
196D43—81no—
197C2×C4⋊Q8C2×D4311yescharacteristic
198C4×#41—431no—
199#477—432no—
200#476—432no—
201#475—861no—
202#474—861no—
203#433—862no—
204#432—861no—
205#431—861no—
206#431C2×D4311yescharacteristic
207#428—861no—
208#423—431no—
209#423C2×D4311yescharacteristic
210C2×C4⋊C8—431no—
211C2×C4⋊C8—431no—
212#417—861no—
213#408—861no—
214#405—861no—
215#333—22no—
216#332—861no—
217#332—861no—
218Q8⋊C8—861no—
219D4⋊C8—861no—
220C43#916811yescharacteristic, complemented, Sylow
221C2×#41—431no—
222C22×Q8—21no—
223C2×M16—21no—
224C2×M16—861no—
225C22×C8—861no—
226C22×C8—861no—
227C4⋊Q8—21no—
228C4⋊Q8—21no—
229C4⋊Q8—21no—
230C4⋊Q8C4×D4312yes—
231C4×Q8—431no—
232C4×Q8—431no—
233C4×D4—431no—
234C4×D4—431no—
235C4×D4—861no—
236C4×D4—861no—
237#117—431no—
238#117—861no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C42—861no—
242C2×C42C22×D4311yescharacteristic
243#107—862no—
244#106—862no—
245C4⋊C8—21no—
246C4⋊C8—21no—
247C4⋊C8—432no—
248C4⋊C8—431no—
249C4⋊C8—431no—
250C4⋊C8—861no—
251C4⋊C8—861no—
252C4⋊C8—861no—
253C4⋊C8—861no—
254C4⋊C8C22⋊D4312yes—
255#103—862no—
256#102—862no—
257C22⋊C8—21no—
258C22⋊C8—862no—
259C22⋊C8—862no—
260#97—862no—
261C4×C8—21no—
262C4×C8—862no—
263#41—861no—
264#41—861no—
265#41—861no—
266#41—861no—
267C2×Q8—22no—
268C2×Q8—41no—
269C2×Q8—81no—
270C2×Q8—81no—
271C2×Q8—431no—
272C2×D4—431no—
273C2×D4—861no—
274C22×C4—41no—
275C22×C4—861no—
276C22×C4—861no—
277C22×C4—861no—
278C22×C4#1062189811yescharacteristic
279C22×C4D4×D4311yescharacteristic
280C22×C4#1062190011yescharacteristic
281M16—41no—
282M16—41no—
283M16—1721no—
284M16—1721no—
285C2×C8—22no—
286C2×C8—41no—
287C2×C8—862no—
288C2×C8—861no—
289C2×C8—861no—
290C2×C8—3441no—
291C2×C8—1721no—
292C2×C8—1721no—
293C2×C8—1721no—
294C4⋊C4—22no—
295C4⋊C4—22no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—431no—
299C4⋊C4—431no—
300C4⋊C4—861no—
301C4⋊C4—861no—
302C22⋊C4—861no—
303C22⋊C4—861no—
304C22⋊C4—861no—
305C42—861no—
306C42—861no—
307C42—861no—
308C42C2×C4×D4311yescharacteristic
309C42D4×D4311yescharacteristic
310C42D4×D4311yescharacteristic
311C42C2×C22⋊D4311yescharacteristic
312C23—861no—
313C23#1306330711yescharacteristic
314Q8—82no—
315Q8—81no—
316Q8—81no—
317Q8—861no—
318Q8—861no—
319D4—861no—
320D4—861no—
321D4—1721no—
322D4—1721no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—41no—
326C2×C4—42no—
327C2×C4—82no—
328C2×C4—861no—
329C2×C4—861no—
330C2×C4—861no—
331C2×C4—3441no—
332C2×C4—1721no—
333C2×C4—1721no—
334C2×C4—1721no—
335C2×C4—1721no—
336C2×C4C22⋊C4×D4311yescharacteristic
337C2×C4(C22⋊D43)⋊C411yescharacteristic
338C2×C4C4×C22⋊D4311yescharacteristic
339C2×C4#1306329311yescharacteristic
340C2×C4#1306329611yescharacteristic
341C2×C4#1306329811yescharacteristic
342C2×C4#1306334611yescharacteristic
343C2×C4#1306334811yescharacteristic
344C2×C4#1306335411yescharacteristic
345C2×C4#1306335711yescharacteristic
346C8—42no—
347C8—81no—
348C8—3441no—
349C8—1721no—
350C8—1721no—
351C8—1722no—
352C22—21no—
353C22—21no—
354C22—1721no—
355C22—1721no—
356C22—1721no—
357C22#1458277511yescharacteristic
358C22#1458323811yescharacteristic
359C22#1458323911yescharacteristic
360C4—21no—
361C4—21no—
362C4—21no—
363C4—82no—
364C4—1721no—
365C4—1721no—
366C4—1721no—
367C4#1458289411yescharacteristic
368C4#1458290611yescharacteristic
369C4#1458305811yescharacteristic
370C4#1458306011yescharacteristic
371C4#1458316111yescharacteristic
372C4#1458316811yescharacteristic
373C2—21no—
374C2—21no—
375C2—3441no—
376C2#1913490411yescharacteristic
377C2#1913506511yescharacteristic
378C2#1913510011yescharacteristic
subgroupG/H
centerC22#14582775
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1548C2
socleC22×C43#386
prime radicalC2×#10621898D4
cosocleC2×C42×C43C23
hypercenter#1548D43
hypocenterC43#9168
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1548

Complements

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

NH ≅ G/Ntype
3. C2×#14582645C2semidirect
5. #19132491C2semidirect
6. #19132469C2semidirect
7. C43×#1548C2semidirect
186. #1548D43semidirect
220. C43#9168semidirect

Maximal subgroups

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

subgroupindex
#191444042
#191432632
C2×#145826452
#191329832
#191324912
#191324692
C43×#15482
#916843