Finite Group Databasebeta

← #24992449

Subgroups — #24992449

Order 11008.

478 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144411C211yesmaximal, characteristic
2#19143164C211yesmaximal, characteristic
3#19133277C211yesmaximal, characteristic, complemented
4C2×#14582646C211yesmaximal, characteristic, complemented
5#19132980C211yesmaximal, characteristic
6#19132490C211yesmaximal, characteristic, complemented
7C43×#1292C211yesmaximal, characteristic, complemented
8C2×#13063333—21no—
9C2×#13063325C2211yescharacteristic
10C4×#10621898C2211yescharacteristic
11#14583195C412yes—
12#14583190C412yes—
13#14583185—21no—
14#14583180—21no—
15#14582952C2211yescharacteristic
16#14582941—21no—
17#14582927—21no—
18#14582924—22no—
19#14582921—21no—
20C2×C4⋊(C43⋊C8)C2211yescharacteristic
21C4⋊C8×D43—21no—
22#14582901—21no—
23#14582647—22no—
24#14582646—21no—
25#14582646—21no—
26#14582629—21no—
27#14582626—21no—
28C43×#423C2211yescharacteristic
29C43×#423C2211yescharacteristic
30C2×C4⋊C8×C43C2211yescharacteristic
31C2×#10621898D411yescharacteristic
32C22×Dic86—21no—
33#13063333—42no—
34#13063333—42no—
35C2×#10621872—22no—
36C22×C43⋊C8—21no—
37C2×C8×D43—22no—
38#13063325—21no—
39#13063325—21no—
40#13063325—21no—
41#13063325C2×C412yes—
42C4×Dic86C2×C411yescharacteristic
43C4×Dic86D411yescharacteristic
44C4×D172C2×C411yescharacteristic
45C4×D172D411yescharacteristic
46C4×C22⋊D43—21no—
47C4×C22⋊D43—21no—
48#13063284D411yescharacteristic
49#13063282—21no—
50C2×C4⋊Dic43—21no—
51C2×C4⋊Dic43—21no—
52C42×D43—21no—
53#13063259—22no—
54#13063257—22no—
55C4⋊(C43⋊C8)—21no—
56C4⋊(C43⋊C8)—21no—
57C4⋊(C43⋊C8)D411yescharacteristic
58C4⋊(C43⋊C8)D411yescharacteristic
59Dic43⋊C8—22no—
60Dic43⋊C8—22no—
61#13063250—22no—
62#13063247—22no—
63C22⋊(C43⋊C8)—21no—
64C4×C43⋊C8—21no—
65C2×M16×C43—21no—
66C2×M16×C43—21no—
67C22×C8×C43—21no—
68C2×C42×C43C2311yescharacteristic
69C4⋊C8×C43—21no—
70C4⋊C8×C43—21no—
71C4⋊C8×C43—21no—
72C4⋊C8×C43—21no—
73C4⋊C8×C43C2×C412yes—
74C4⋊C8×C43D412yes—
75C22×C4×C43C2×D411yescharacteristic
76C22×C4×C43#4111yescharacteristic
77C22×C4×C43#4111yescharacteristic
78C2×C22⋊D43—21no—
79C22×Dic43—41no—
80#10621898—21no—
81#10621898—21no—
82#10621898SD1612yes—
83#10621898Q1612yes—
84C2×D172C22⋊C411yescharacteristic
85C2×C4×D43—21no—
86C2×C4×D43—21no—
87C2×C4×D43—21no—
88C2×Dic86—22no—
89C2×Dic86—41no—
90C2×Dic86—81no—
91C2×Dic86—81no—
92C2×Dic86C22⋊C411yescharacteristic
93M16×C43—41no—
94M16×C43—41no—
95M16×C43—41no—
96M16×C43—41no—
97C2×C8×C43—22no—
98C2×C8×C43—22no—
99C2×C8×C43—41no—
100C2×C8×C43—81no—
101C42×C43C22×C411yescharacteristic
102C42×C43C2×D411yescharacteristic
103C42×C43C2×D411yescharacteristic
104C42×C43C2×D411yescharacteristic
105C22⋊Dic43—21no—
106(C2×D43)⋊C4—21no—
107(C2×D43)⋊C4—21no—
108C4⋊Dic43—22no—
109C4⋊Dic43—22no—
110C4⋊Dic43—41no—
111C4⋊Dic43—41no—
112C4⋊Dic43C22⋊C411yescharacteristic
113C4⋊Dic43C22⋊C411yescharacteristic
114Dic43⋊C4—21no—
115Dic43⋊C4—21no—
116C4×Dic43—21no—
117C4×Dic43—21no—
118C4×Dic43—21no—
119C2×C43⋊C8—21no—
120C2×C43⋊C8—21no—
121C2×C43⋊C8—41no—
122C2×C43⋊C8—41no—
123C2×C43⋊C8—41no—
124#10621872—44no—
125C8×D43—44no—
126C23×C43#12311yescharacteristic
127C22×D43—21no—
128C2×C4×C43—21no—
129C2×C4×C43—21no—
130C2×C4×C43—41no—
131C2×C4×C43C2×C22⋊C411yescharacteristic
132C2×C4×C43C4×D411yescharacteristic
133C2×C4×C43C4×D411yescharacteristic
134C2×C4×C43#12011yescharacteristic
135C2×C4×C43#12111yescharacteristic
136C2×C4×C43#12111yescharacteristic
137C2×C4×C43C2×SD1611yescharacteristic
138C2×C4×C43C2×Q1611yescharacteristic
139C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C43#13711yescharacteristic
141C22⋊D43—22no—
142C22⋊D43—22no—
143C2×Dic43—21no—
144C2×Dic43—21no—
145C2×Dic43—21no—
146C2×Dic43—42no—
147C2×Dic43—82no—
148D172—21no—
149D172#10312yes—
150C4×D43—22no—
151C4×D43—22no—
152C4×D43—41no—
153C4×D43—41no—
154C4×D43—81no—
155Dic86—21no—
156Dic86—81no—
157Dic86—81no—
158Dic86—82no—
159Dic86#10312yes—
160C8×C43—42no—
161C8×C43—42no—
162C8×C43—81no—
163C43⋊C8—41no—
164C43⋊C8—41no—
165C43⋊C8—81no—
166#9167—431nomaximal, Sylow
167C22×C43—21no—
168C22×C43—21no—
169C22×C43#38611yescharacteristic
170C22×C43#48311yescharacteristic
171C22×C43#48411yescharacteristic
172C2×D43—22no—
173C2×D43—41no—
174C2×D43—41no—
175C4×C43—21no—
176C4×C43—21no—
177C4×C43—21no—
178C4×C43C2×#10311yescharacteristic
179C4×C43#41711yescharacteristic
180C4×C43#45011yescharacteristic
181C4×C43#45111yescharacteristic
182C4×C43#47111yescharacteristic
183C4×C43#47211yescharacteristic
184Dic43—22no—
185Dic43—41no—
186Dic43—41no—
187Dic43—82no—
188#3079—431no—
189#2906—431no—
190#1548—431no—
191C2×#332—431no—
192#1477—431no—
193#1301—431no—
194#1292D4311yescharacteristic, complemented
195C2×C43—21no—
196C2×C43—21no—
197C2×C43#187211yescharacteristic
198C2×C43#190211yescharacteristic
199C2×C43#190711yescharacteristic
200D43—42no—
201C2×#131—861no—
202C2×C4⋊Q8—431no—
203C4×#41—431no—
204#477—432no—
205#476—432no—
206#475—861no—
207#474—861no—
208#431—431no—
209#428—861no—
210#424—861no—
211#424—862no—
212#423—861no—
213#423C2×D4311yescharacteristic
214#423C2×D4311yescharacteristic
215C2×C4⋊C8—431no—
216C2×C4⋊C8—861no—
217C2×C4⋊C8C2×D4311yescharacteristic
218#417—861no—
219#333—862no—
220#332—861no—
221#332—861no—
222Q8⋊C8—861no—
223D4⋊C8—861no—
224C43#916711yescharacteristic, complemented, Sylow
225C2×#41—431no—
226C22×Q8—861no—
227#131—1722no—
228#131—1722no—
229C2×M16—21no—
230C2×M16—21no—
231C2×M16—862no—
232C22×C8—21no—
233C22×C8—862no—
234C22×C8—861no—
235C4⋊Q8—432no—
236C4⋊Q8—861no—
237C4⋊Q8—861no—
238C4⋊Q8—861no—
239C4×Q8—431no—
240C4×Q8—431no—
241C4×D4—431no—
242C4×D4—431no—
243C4×D4—861no—
244C4×D4—861no—
245#117—431no—
246#117—861no—
247C2×C4⋊C4—861no—
248C2×C4⋊C4—861no—
249C2×C42—861no—
250C2×C42C22×D4311yescharacteristic
251#107—862no—
252#106—862no—
253C4⋊C8—21no—
254C4⋊C8—21no—
255C4⋊C8—21no—
256C4⋊C8—21no—
257C4⋊C8—431no—
258C4⋊C8—431no—
259C4⋊C8—862no—
260C4⋊C8—862no—
261C4⋊C8—861no—
262C4⋊C8—861no—
263C4⋊C8C4×D4312yes—
264C4⋊C8D17212yes—
265#103—862no—
266#102—862no—
267C22⋊C8—861no—
268C4×C8—861no—
269#41—432no—
270#41—432no—
271#41—861no—
272#41—861no—
273C2×Q8—431no—
274C2×Q8—862no—
275C2×Q8—3441no—
276C2×Q8—3441no—
277C2×Q8—1721no—
278C2×D4—431no—
279C2×D4—861no—
280C22×C4—861no—
281C22×C4—861no—
282C22×C4—861no—
283C22×C4—1721no—
284C22×C4#1062189811yescharacteristic
285C22×C4D4×D4311yescharacteristic
286C22×C4#1062190211yescharacteristic
287M16—41no—
288M16—41no—
289M16—41no—
290M16—41no—
291M16—1724no—
292C2×C8—22no—
293C2×C8—22no—
294C2×C8—41no—
295C2×C8—81no—
296C2×C8—861no—
297C2×C8—861no—
298C2×C8—1724no—
299C2×C8—1721no—
300C2×C8—1721no—
301C2×C8—1721no—
302C4⋊C4—431no—
303C4⋊C4—431no—
304C4⋊C4—861no—
305C4⋊C4—861no—
306C4⋊C4—862no—
307C4⋊C4—862no—
308C4⋊C4—1721no—
309C4⋊C4—1721no—
310C22⋊C4—861no—
311C22⋊C4—861no—
312C22⋊C4—861no—
313C42—861no—
314C42—861no—
315C42—861no—
316C42C2×C4×D4311yescharacteristic
317C42C2×D17211yescharacteristic
318C42D4×D4311yescharacteristic
319C42D4×D4311yescharacteristic
320C23—861no—
321C23#1306331011yescharacteristic
322Q8—432no—
323Q8—861no—
324Q8—3442no—
325Q8—3441no—
326Q8—3441no—
327D4—432no—
328D4—862no—
329D4—862no—
330D4—861no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—41no—
334C2×C4—861no—
335C2×C4—862no—
336C2×C4—862no—
337C2×C4—861no—
338C2×C4—861no—
339C2×C4—3441no—
340C2×C4—3442no—
341C2×C4—1722no—
342C2×C4—1721no—
343C2×C4—1721no—
344C2×C4C22⋊C4×D4311yescharacteristic
345C2×C4#1306328711yescharacteristic
346C2×C4C4×D17211yescharacteristic
347C2×C4#1306329511yescharacteristic
348C2×C4#1306329811yescharacteristic
349C2×C4#1306330011yescharacteristic
350C2×C4SD16×D4311yescharacteristic
351C2×C4Q16×D4311yescharacteristic
352C2×C4#1306334911yescharacteristic
353C2×C4#1306335411yescharacteristic
354C8—42no—
355C8—42no—
356C8—81no—
357C8—3441no—
358C8—1721no—
359C8—1721no—
360C22—21no—
361C22—21no—
362C22—862no—
363C22—1721no—
364C22—1721no—
365C22#1458277711yescharacteristic
366C22#1458323111yescharacteristic
367C22#1458323611yescharacteristic
368C4—21no—
369C4—21no—
370C4—21no—
371C4—862no—
372C4—3442no—
373C4—1721no—
374C4—1721no—
375C4#103×D4311yescharacteristic
376C4#1458289711yescharacteristic
377C4#1458305111yescharacteristic
378C4#1458305611yescharacteristic
379C4#1458316511yescharacteristic
380C4#1458316811yescharacteristic
381C2—21no—
382C2—21no—
383C2—1722no—
384C2#1913490111yescharacteristic
385C2#1913506911yescharacteristic
386C2#1913510411yescharacteristic
subgroupG/H
centerC22#14582777
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1292C2
socleC22×C43#386
prime radicalC2×#10621898D4
cosocleC2×C42×C43C23
hypercenter#1292D43
hypocenterC43#9167
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1292

Complements

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

NH ≅ G/Ntype
3. #19133277C2semidirect
4. C2×#14582646C2semidirect
6. #19132490C2semidirect
7. C43×#1292C2semidirect
194. #1292D43semidirect
224. C43#9167semidirect

Maximal subgroups

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

subgroupindex
#191444112
#191431642
#191332772
C2×#145826462
#191329802
#191324902
C43×#12922
#916743