Finite Group Databasebeta

← #24992482

Subgroups — #24992482

Order 11008.

464 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144083C211yesmaximal, characteristic
2#19143260C211yesmaximal, characteristic
3#19133266C211yesmaximal, characteristic, complemented
4C2×#14582646C211yesmaximal, characteristic, complemented
5#19132983C211yesmaximal, characteristic
6#19132469C211yesmaximal, characteristic, complemented
7C43×#1301C211yesmaximal, characteristic, complemented
8C2×#13063358—21no—
9C2×#13063325C2211yescharacteristic
10C4×#10621898C2211yescharacteristic
11#14583110—21no—
12#14583110C412yes—
13#14583105—21no—
14#14583105C412yes—
15#14582959—22no—
16#14582955—21no—
17#14582951—21no—
18#14582923C2211yescharacteristic
19C2×C4⋊(C43⋊C8)C2211yescharacteristic
20#14582909—21no—
21#14582865—21no—
22#14582854—21no—
23#14582646—21no—
24#14582646—21no—
25#14582644—22no—
26#14582631—21no—
27#14582628—21no—
28C43×#431C2211yescharacteristic
29C43×#423C2211yescharacteristic
30C2×C4⋊C8×C43C2211yescharacteristic
31C2×#10621898D411yescharacteristic
32C22×Dic86—21no—
33#13063358—42no—
34#13063358—42no—
35C2×Dic172—22no—
36C2×#10621873—22no—
37C2×#10621877—21no—
38C22×C43⋊C8—21no—
39#13063325—21no—
40#13063325—21no—
41#13063325—21no—
42#13063325C2×C412yes—
43C4×Dic86C2×C411yescharacteristic
44C4×Dic86D411yescharacteristic
45C4×D172C2×C411yescharacteristic
46C4×D172D411yescharacteristic
47C4×C22⋊D43—21no—
48C4×C22⋊D43—21no—
49#13063284D411yescharacteristic
50#13063282—21no—
51C2×C4⋊Dic43—21no—
52C2×C4⋊Dic43—21no—
53C42×D43—21no—
54C4⋊(C43⋊C8)—21no—
55C4⋊(C43⋊C8)—21no—
56C4⋊(C43⋊C8)—21no—
57C4⋊(C43⋊C8)D412yes—
58#13063250—22no—
59#13063250—22no—
60(C2×D43)⋊C8—22no—
61(C2×D43)⋊C8—22no—
62#13063235—22no—
63C8×Dic43—22no—
64C2×M16×C43—21no—
65C22×C8×C43—21no—
66C2×C42×C43C2311yescharacteristic
67C4⋊C8×C43—21no—
68C4⋊C8×C43—21no—
69C4⋊C8×C43—21no—
70C4⋊C8×C43C2×C412yes—
71C4⋊C8×C43D411yescharacteristic
72C4⋊C8×C43D411yescharacteristic
73C22⋊C8×C43—21no—
74C4×C8×C43—21no—
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#10621898—21no—
83#10621898—21no—
84C2×D172C22⋊C411yescharacteristic
85C2×C4×D43—21no—
86C2×C4×D43—21no—
87C2×C4×D43—21no—
88C2×Dic86—22no—
89C2×Dic86—41no—
90C2×Dic86—41no—
91C2×Dic86—41no—
92C2×Dic86—41no—
93C2×Dic86—41no—
94C2×Dic86C22⋊C411yescharacteristic
95M16×C43—41no—
96M16×C43—41no—
97C2×C8×C43—22no—
98C2×C8×C43—21no—
99C2×C8×C43—21no—
100C2×C8×C43—41no—
101C2×C8×C43—41no—
102C2×C8×C43—41no—
103C42×C43C22×C411yescharacteristic
104C42×C43C2×D411yescharacteristic
105C42×C43C2×D411yescharacteristic
106C42×C43C2×D411yescharacteristic
107C22⋊Dic43—21no—
108(C2×D43)⋊C4—21no—
109(C2×D43)⋊C4—21no—
110C4⋊Dic43—22no—
111C4⋊Dic43—22no—
112C4⋊Dic43—41no—
113C4⋊Dic43—41no—
114C4⋊Dic43C22⋊C411yescharacteristic
115C4⋊Dic43C22⋊C411yescharacteristic
116Dic43⋊C4—21no—
117Dic43⋊C4—21no—
118C4×Dic43—21no—
119C4×Dic43—21no—
120C4×Dic43—21no—
121#10621877—41no—
122#10621877—41no—
123C2×C43⋊C8—22no—
124C2×C43⋊C8—41no—
125C2×C43⋊C8—81no—
126Dic172—44no—
127#10621873—44no—
128C23×C43#12311yescharacteristic
129C22×D43—21no—
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43—41no—
133C2×C4×C43C2×C22⋊C411yescharacteristic
134C2×C4×C43C4×D411yescharacteristic
135C2×C4×C43C4×D411yescharacteristic
136C2×C4×C43#12011yescharacteristic
137C2×C4×C43#12111yescharacteristic
138C2×C4×C43#12111yescharacteristic
139C2×C4×C43#13511yescharacteristic
140C2×C4×C43#13511yescharacteristic
141C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
143C22⋊D43—41no—
144C22⋊D43—41no—
145C2×Dic43—21no—
146C2×Dic43—21no—
147C2×Dic43—21no—
148C2×Dic43—42no—
149C2×Dic43—81no—
150C2×Dic43—81no—
151D172—21no—
152D172—21no—
153C4×D43—41no—
154C4×D43—41no—
155C4×D43—41no—
156C4×D43—41no—
157C4×D43—81no—
158Dic86—21no—
159Dic86—21no—
160Dic86—42no—
161Dic86—42no—
162Dic86—81no—
163Dic86—81no—
164C8×C43—42no—
165C8×C43—41no—
166C8×C43—41no—
167C8×C43—81no—
168C43⋊C8—42no—
169C43⋊C8—81no—
170#9172—431nomaximal, Sylow
171C22×C43—21no—
172C22×C43—21no—
173C22×C43#38611yescharacteristic
174C22×C43#48211yescharacteristic
175C22×C43#48211yescharacteristic
176C2×D43—41no—
177C2×D43—41no—
178C2×D43—41no—
179C4×C43—21no—
180C4×C43—21no—
181C4×C43—21no—
182C4×C43#41611yescharacteristic
183C4×C43#41811yescharacteristic
184C4×C43#44911yescharacteristic
185C4×C43#44911yescharacteristic
186C4×C43#47111yescharacteristic
187C4×C43#47311yescharacteristic
188Dic43—41no—
189Dic43—41no—
190Dic43—41no—
191Dic43—82no—
192#3039—431no—
193#2925—431no—
194#1546—431no—
195C2×#332—431no—
196#1477—431no—
197#1301D4311yescharacteristic, complemented
198#1292—431no—
199C2×C43—21no—
200C2×C43—21no—
201C2×C43#187511yescharacteristic
202C2×C43#190211yescharacteristic
203C2×C43#190811yescharacteristic
204D43—81no—
205C2×#137—861no—
206C2×C4⋊Q8—431no—
207C4×#41—431no—
208#462—432no—
209#462—861no—
210#461—432no—
211#461—861no—
212#433—862no—
213#432—861no—
214#431—861no—
215#431C2×D4311yescharacteristic
216#423—431no—
217#423C2×D4311yescharacteristic
218C2×C4⋊C8—431no—
219C2×C4⋊C8C2×D4311yescharacteristic
220#419—861no—
221#408—861no—
222#405—861no—
223#332—862no—
224#332—861no—
225#332—861no—
226Q8⋊C8—861no—
227D4⋊C8—861no—
228C43#917211yescharacteristic, complemented, Sylow
229C2×#41—431no—
230C22×Q8—861no—
231#137—1722no—
232#137—1722no—
233C2×Q16—862no—
234C2×SD16—862no—
235C2×M16—21no—
236C2×M16—861no—
237C22×C8—21no—
238C22×C8—861no—
239C4⋊Q8—432no—
240C4⋊Q8—861no—
241C4⋊Q8—861no—
242C4⋊Q8—861no—
243C4×Q8—431no—
244C4×Q8—431no—
245C4×D4—431no—
246C4×D4—431no—
247C4×D4—861no—
248C4×D4—861no—
249#117—431no—
250#117—861no—
251C2×C4⋊C4—861no—
252C2×C4⋊C4—861no—
253C2×C42—861no—
254C2×C42C22×D4311yescharacteristic
255C4⋊C8—21no—
256C4⋊C8—21no—
257C4⋊C8—21no—
258C4⋊C8—432no—
259C4⋊C8—861no—
260C4⋊C8—861no—
261C4⋊C8—861no—
262C4⋊C8C4×D4312yes—
263C4⋊C8D17211yescharacteristic
264C4⋊C8D17211yescharacteristic
265#103—862no—
266#103—862no—
267C22⋊C8—21no—
268C22⋊C8—862no—
269C22⋊C8—862no—
270#97—862no—
271C4×C8—21no—
272C4×C8—862no—
273#41—861no—
274#41—861no—
275#41—861no—
276#41—861no—
277C2×Q8—431no—
278C2×Q8—862no—
279C2×Q8—1721no—
280C2×Q8—1721no—
281C2×Q8—1721no—
282C2×Q8—1721no—
283C2×Q8—1721no—
284C2×D4—431no—
285C2×D4—861no—
286C22×C4—861no—
287C22×C4—861no—
288C22×C4—861no—
289C22×C4—1721no—
290C22×C4#1062189811yescharacteristic
291C22×C4D4×D4311yescharacteristic
292C22×C4#1062190211yescharacteristic
293Q16—1724no—
294SD16—1724no—
295M16—41no—
296M16—41no—
297M16—1721no—
298M16—1721no—
299C2×C8—22no—
300C2×C8—21no—
301C2×C8—21no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—862no—
306C2×C8—3441no—
307C2×C8—1721no—
308C4⋊C4—431no—
309C4⋊C4—431no—
310C4⋊C4—861no—
311C4⋊C4—861no—
312C4⋊C4—862no—
313C4⋊C4—862no—
314C4⋊C4—1721no—
315C4⋊C4—1721no—
316C22⋊C4—861no—
317C22⋊C4—861no—
318C22⋊C4—861no—
319C42—861no—
320C42—861no—
321C42—861no—
322C42C2×C4×D4311yescharacteristic
323C42C2×D17211yescharacteristic
324C42D4×D4311yescharacteristic
325C42D4×D4311yescharacteristic
326C23—861no—
327C23#1306331011yescharacteristic
328Q8—861no—
329Q8—861no—
330Q8—3441no—
331Q8—3441no—
332Q8—1722no—
333Q8—1722no—
334D4—861no—
335D4—861no—
336D4—1721no—
337D4—1721no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—41no—
341C2×C4—861no—
342C2×C4—861no—
343C2×C4—861no—
344C2×C4—3441no—
345C2×C4—3441no—
346C2×C4—3441no—
347C2×C4—1722no—
348C2×C4—1721no—
349C2×C4—1721no—
350C2×C4—1721no—
351C2×C4—1721no—
352C2×C4C22⋊C4×D4311yescharacteristic
353C2×C4#1306328711yescharacteristic
354C2×C4C4×D17211yescharacteristic
355C2×C4#1306329511yescharacteristic
356C2×C4#1306329811yescharacteristic
357C2×C4#1306330011yescharacteristic
358C2×C4#1306334611yescharacteristic
359C2×C4#1306334811yescharacteristic
360C2×C4#1306334911yescharacteristic
361C2×C4#1306335211yescharacteristic
362C8—41no—
363C8—41no—
364C8—42no—
365C8—81no—
366C8—3441no—
367C8—1722no—
368C22—21no—
369C22—21no—
370C22—1721no—
371C22—1721no—
372C22—1721no—
373C22#1458277711yescharacteristic
374C22#1458322511yescharacteristic
375C22#1458322611yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—3442no—
380C4—1721no—
381C4—1721no—
382C4—1721no—
383C4#1458289411yescharacteristic
384C4#1458290211yescharacteristic
385C4#1458304511yescharacteristic
386C4#1458304711yescharacteristic
387C4#1458316311yescharacteristic
388C4#1458317511yescharacteristic
389C2—21no—
390C2—21no—
391C2—3441no—
392C2#1913491611yescharacteristic
393C2#1913506711yescharacteristic
394C2#1913510911yescharacteristic
subgroupG/H
centerC22#14582777
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1301C2
socleC22×C43#386
prime radicalC2×#10621898D4
cosocleC2×C42×C43C23
hypercenter#1301D43
hypocenterC43#9172
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. #19133266C2semidirect
4. C2×#14582646C2semidirect
6. #19132469C2semidirect
7. C43×#1301C2semidirect
197. #1301D43semidirect
228. C43#9172semidirect

Maximal subgroups

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

subgroupindex
#191440832
#191432602
#191332662
C2×#145826462
#191329832
#191324692
C43×#13012
#917243