Finite Group Databasebeta

← #24992454

Subgroups — #24992454

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#19144411C211yesmaximal, characteristic
2#19143260C211yesmaximal, characteristic
3#19133275C211yesmaximal, characteristic, complemented
4C2×#14582644C211yesmaximal, characteristic, complemented
5#19132983C211yesmaximal, characteristic
6#19132469C211yesmaximal, characteristic, complemented
7C43×#1301C211yesmaximal, characteristic, complemented
8C2×#13063325C2211yescharacteristic
9C4×#10621898C2211yescharacteristic
10#14583195C412yes—
11#14583190C412yes—
12#14583185—21no—
13#14583180—21no—
14#14582959—22no—
15#14582955—21no—
16#14582951—21no—
17#14582941—21no—
18#14582923C2211yescharacteristic
19C2×C4⋊(C43⋊C8)C2211yescharacteristic
20#14582901—21no—
21#14582865—21no—
22#14582854—21no—
23#14582647—22no—
24#14582644—21no—
25#14582644—21no—
26#14582631—21no—
27#14582628—21no—
28C43×#431C2211yescharacteristic
29C43×#423C2211yescharacteristic
30C2×C4⋊C8×C43C2211yescharacteristic
31C2×#10621898D411yescharacteristic
32C22×Dic86—21no—
33C2×#10621877—21no—
34C22×C43⋊C8—21no—
35#13063325—21no—
36#13063325—21no—
37#13063325—21no—
38#13063325C2×C412yes—
39C4×Dic86C2×C411yescharacteristic
40C4×Dic86D411yescharacteristic
41C4×D172C2×C411yescharacteristic
42C4×D172D411yescharacteristic
43C4×C22⋊D43—21no—
44C4×C22⋊D43—21no—
45#13063284D411yescharacteristic
46#13063282—21no—
47C2×C4⋊Dic43—21no—
48C2×C4⋊Dic43—21no—
49C42×D43—21no—
50#13063259—22no—
51#13063257—22no—
52C4⋊(C43⋊C8)—21no—
53C4⋊(C43⋊C8)—21no—
54C4⋊(C43⋊C8)—21no—
55C4⋊(C43⋊C8)D412yes—
56#13063250—22no—
57#13063247—22no—
58(C2×D43)⋊C8—22no—
59(C2×D43)⋊C8—22no—
60#13063235—22no—
61C8×Dic43—22no—
62C2×M16×C43—21no—
63C22×C8×C43—21no—
64C2×C42×C43C2311yescharacteristic
65C4⋊C8×C43—21no—
66C4⋊C8×C43—21no—
67C4⋊C8×C43—21no—
68C4⋊C8×C43C2×C412yes—
69C4⋊C8×C43D411yescharacteristic
70C4⋊C8×C43D411yescharacteristic
71C22⋊C8×C43—21no—
72C4×C8×C43—21no—
73C22×C4×C43C2×D411yescharacteristic
74C22×C4×C43#4111yescharacteristic
75C22×C4×C43#4111yescharacteristic
76C2×C22⋊D43—21no—
77C22×Dic43—41no—
78#10621898—21no—
79#10621898—21no—
80#10621898—21no—
81#10621898—21no—
82C2×D172C22⋊C411yescharacteristic
83C2×C4×D43—21no—
84C2×C4×D43—21no—
85C2×C4×D43—21no—
86C2×Dic86—22no—
87C2×Dic86—41no—
88C2×Dic86—81no—
89C2×Dic86—81no—
90C2×Dic86C22⋊C411yescharacteristic
91M16×C43—41no—
92M16×C43—41no—
93C2×C8×C43—22no—
94C2×C8×C43—21no—
95C2×C8×C43—21no—
96C2×C8×C43—41no—
97C2×C8×C43—41no—
98C2×C8×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⋊Dic43—22no—
107C4⋊Dic43—22no—
108C4⋊Dic43—41no—
109C4⋊Dic43—41no—
110C4⋊Dic43C22⋊C411yescharacteristic
111C4⋊Dic43C22⋊C411yescharacteristic
112Dic43⋊C4—21no—
113Dic43⋊C4—21no—
114C4×Dic43—21no—
115C4×Dic43—21no—
116C4×Dic43—21no—
117#10621877—41no—
118#10621877—41no—
119C2×C43⋊C8—22no—
120C2×C43⋊C8—41no—
121C2×C43⋊C8—81no—
122C23×C43#12311yescharacteristic
123C22×D43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—41no—
127C2×C4×C43C2×C22⋊C411yescharacteristic
128C2×C4×C43C4×D411yescharacteristic
129C2×C4×C43C4×D411yescharacteristic
130C2×C4×C43#12011yescharacteristic
131C2×C4×C43#12111yescharacteristic
132C2×C4×C43#12111yescharacteristic
133C2×C4×C43#13511yescharacteristic
134C2×C4×C43#13511yescharacteristic
135C2×C4×C43#13711yescharacteristic
136C2×C4×C43#13711yescharacteristic
137C22⋊D43—41no—
138C22⋊D43—41no—
139C2×Dic43—21no—
140C2×Dic43—21no—
141C2×Dic43—21no—
142C2×Dic43—42no—
143C2×Dic43—82no—
144D172—21no—
145D172—21no—
146C4×D43—41no—
147C4×D43—41no—
148C4×D43—41no—
149C4×D43—41no—
150C4×D43—81no—
151Dic86—21no—
152Dic86—21no—
153Dic86—81no—
154Dic86—81no—
155Dic86—82no—
156C8×C43—42no—
157C8×C43—41no—
158C8×C43—41no—
159C8×C43—81no—
160C43⋊C8—42no—
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#41611yescharacteristic
175C4×C43#41911yescharacteristic
176C4×C43#45211yescharacteristic
177C4×C43#45211yescharacteristic
178C4×C43#47111yescharacteristic
179C4×C43#47211yescharacteristic
180Dic43—41no—
181Dic43—41no—
182Dic43—41no—
183Dic43—82no—
184#3079—431no—
185#2925—431no—
186#1548—431no—
187C2×#332—431no—
188#1477—431no—
189#1301D4311yescharacteristic, complemented
190#1292—431no—
191C2×C43—21no—
192C2×C43—21no—
193C2×C43#187311yescharacteristic
194C2×C43#190211yescharacteristic
195C2×C43#190711yescharacteristic
196D43—81no—
197C2×C4⋊Q8—431no—
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⋊C8C2×D4311yescharacteristic
212#417—861no—
213#408—861no—
214#405—861no—
215#333—862no—
216#332—861no—
217#332—861no—
218Q8⋊C8—861no—
219D4⋊C8—861no—
220C43#916811yescharacteristic, complemented, Sylow
221C2×#41—431no—
222C22×Q8—861no—
223C2×M16—21no—
224C2×M16—861no—
225C22×C8—21no—
226C22×C8—861no—
227C4⋊Q8—432no—
228C4⋊Q8—861no—
229C4⋊Q8—861no—
230C4⋊Q8—861no—
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—861no—
240C2×C4⋊C4—861no—
241C2×C42—861no—
242C2×C42C22×D4311yescharacteristic
243#107—862no—
244#106—862no—
245C4⋊C8—21no—
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8—432no—
249C4⋊C8—861no—
250C4⋊C8—861no—
251C4⋊C8—861no—
252C4⋊C8C4×D4312yes—
253C4⋊C8D17211yescharacteristic
254C4⋊C8D17211yescharacteristic
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—431no—
268C2×Q8—862no—
269C2×Q8—3441no—
270C2×Q8—3441no—
271C2×Q8—1721no—
272C2×D4—431no—
273C2×D4—861no—
274C22×C4—861no—
275C22×C4—861no—
276C22×C4—861no—
277C22×C4—1721no—
278C22×C4#1062189811yescharacteristic
279C22×C4D4×D4311yescharacteristic
280C22×C4#1062190211yescharacteristic
281M16—41no—
282M16—41no—
283M16—1721no—
284M16—1721no—
285C2×C8—22no—
286C2×C8—21no—
287C2×C8—21no—
288C2×C8—41no—
289C2×C8—41no—
290C2×C8—41no—
291C2×C8—862no—
292C2×C8—3441no—
293C2×C8—1721no—
294C4⋊C4—431no—
295C4⋊C4—431no—
296C4⋊C4—861no—
297C4⋊C4—861no—
298C4⋊C4—862no—
299C4⋊C4—862no—
300C4⋊C4—1721no—
301C4⋊C4—1721no—
302C22⋊C4—861no—
303C22⋊C4—861no—
304C22⋊C4—861no—
305C42—861no—
306C42—861no—
307C42—861no—
308C42C2×C4×D4311yescharacteristic
309C42C2×D17211yescharacteristic
310C42D4×D4311yescharacteristic
311C42D4×D4311yescharacteristic
312C23—861no—
313C23#1306331011yescharacteristic
314Q8—861no—
315Q8—861no—
316Q8—3442no—
317Q8—3441no—
318Q8—3441no—
319D4—861no—
320D4—861no—
321D4—1721no—
322D4—1721no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—41no—
326C2×C4—861no—
327C2×C4—861no—
328C2×C4—861no—
329C2×C4—3441no—
330C2×C4—3442no—
331C2×C4—1722no—
332C2×C4—1721no—
333C2×C4—1721no—
334C2×C4—1721no—
335C2×C4—1721no—
336C2×C4C22⋊C4×D4311yescharacteristic
337C2×C4#1306328711yescharacteristic
338C2×C4C4×D17211yescharacteristic
339C2×C4#1306329511yescharacteristic
340C2×C4#1306329811yescharacteristic
341C2×C4#1306330011yescharacteristic
342C2×C4#1306334411yescharacteristic
343C2×C4#1306334611yescharacteristic
344C2×C4#1306335411yescharacteristic
345C2×C4#1306335711yescharacteristic
346C8—41no—
347C8—41no—
348C8—42no—
349C8—81no—
350C8—3441no—
351C8—1722no—
352C22—21no—
353C22—21no—
354C22—1721no—
355C22—1721no—
356C22—1721no—
357C22#1458277711yescharacteristic
358C22#1458324211yescharacteristic
359C22#1458324311yescharacteristic
360C4—21no—
361C4—21no—
362C4—21no—
363C4—3442no—
364C4—1721no—
365C4—1721no—
366C4—1721no—
367C4#1458289211yescharacteristic
368C4#1458290611yescharacteristic
369C4#1458306211yescharacteristic
370C4#1458306411yescharacteristic
371C4#1458316311yescharacteristic
372C4#1458317011yescharacteristic
373C2—21no—
374C2—21no—
375C2—3441no—
376C2#1913490611yescharacteristic
377C2#1913506711yescharacteristic
378C2#1913510211yescharacteristic
subgroupG/H
centerC22#14582777
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1301C2
socleC22×C43#386
prime radicalC2×#10621898D4
cosocleC2×C42×C43C23
hypercenter#1301D43
hypocenterC43#9168
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1301

Complements

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

NH ≅ G/Ntype
3. #19133275C2semidirect
4. C2×#14582644C2semidirect
6. #19132469C2semidirect
7. C43×#1301C2semidirect
189. #1301D43semidirect
220. C43#9168semidirect

Maximal subgroups

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

subgroupindex
#191444112
#191432602
#191332752
C2×#145826442
#191329832
#191324692
C43×#13012
#916843