Finite Group Databasebeta

← #25013609

Subgroups — #25013609

Order 11008.

492 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#19144315C211yesmaximal, characteristic
2#19143190C211yesmaximal, characteristic, complemented
3#19136332C211yesmaximal, characteristic, complemented
4C2×#14582710C211yesmaximal, characteristic, complemented
5#19132710C211yesmaximal, characteristic, complemented
6#19132694C211yesmaximal, characteristic, complemented
7C43×#2117C211yesmaximal, characteristic, complemented
8#14583697—21no—
9C2×#13063347C2211yescharacteristic
10#14583382—21no—
11#14583174C412yescomplemented
12#14583169C412yescomplemented
13#14583162—22no—
14C2×#13063261C2211yescharacteristic
15#14582941—22no—
16#14582941—21no—
17#14582937—21no—
18#14582937C2211yescharacteristic
19C2×#13063257—21no—
20C2×#13063257C2211yescharacteristic
21#14582881—21no—
22#14582710—22no—
23#14582710—21no—
24#14582710—21no—
25C2×#131×C43C2211yescharacteristic
26C2×M32×C43C2211yescharacteristic
27C2×M32×C43C2211yescharacteristic
28C43×#350—22no—
29C2×#10621898—21no—
30#13063356—41no—
31#13063355—22no—
32#13063351—41no—
33#13063350—22no—
34#13063347—21no—
35#13063347—21no—
36#13063347—21no—
37#13063347—21no—
38#13063345—42no—
39C2×Dic172C2×C411yescharacteristic, complemented
40C2×#10621873—21no—
41C2×D344C2×C411yescharacteristic, complemented
42C2×#10621877—21no—
43Q8×Dic43—41no—
44D4×Dic43—42no—
45D4×Dic43—41no—
46#13063284—22no—
47#13063284—21no—
48C2×C4⋊Dic43—22no—
49C2×C4⋊Dic43—21no—
50#13063261—21no—
51#13063261C2×C412yescomplemented
52#13063259—22no—
53#13063259—21no—
54#13063257—22no—
55#13063257—21no—
56#13063257D411yescharacteristic
57#13063257D412yes—
58#13063257D411yescharacteristic
59#13063243—22no—
60#13063241—22no—
61C2×#41×C43D411yescharacteristic
62#131×C43—21no—
63#131×C43—21no—
64#131×C43C2×C412yes—
65#131×C43D412yes—
66C2×M16×C43—21no—
67C2×M16×C43D411yescharacteristic
68C22×C8×C43—21no—
69C22×C8×C43C2311yescharacteristic
70M32×C43—21no—
71M32×C43—21no—
72M32×C43—21no—
73M32×C43—21no—
74C2×C16×C43—21no—
75C2×C16×C43—21no—
76#41×C43—21no—
77#41×C43—21no—
78#41×C43C22⋊C412yes—
79#41×C43SD1612yes—
80C2×Q8×C43D811yescharacteristic
81C2×D4×C43—21no—
82C2×D4×C43D811yescharacteristic
83C22×C4×C43—21no—
84C22×C4×C43C2×D411yescharacteristic
85C2×C22⋊D43—41no—
86C22×Dic43—42no—
87C22×Dic43—41no—
88#10621898—41no—
89#10621898—41no—
90#10621898—41no—
91#10621898—41no—
92C2×D172—21no—
93C2×C4×D43—41no—
94C2×Dic86—21no—
95M16×C43—21no—
96M16×C43—22no—
97M16×C43—22no—
98M16×C43C22⋊C412yes—
99C2×C8×C43—21no—
100C2×C8×C43—22no—
101C2×C8×C43—22no—
102C2×C8×C43C22×C411yescharacteristic
103C2×C8×C43C2×D411yescharacteristic
104C2×C8×C43C2×D411yescharacteristic
105C2×C8×C43C2×D411yescharacteristic
106C2×C8×C43#4111yescharacteristic
107C2×C8×C43#4111yescharacteristic
108C22⋊Dic43—42no—
109C22⋊Dic43—41no—
110#10621885—42no—
111#10621884—42no—
112#10621883—42no—
113#10621882—42no—
114C4⋊Dic43—21no—
115C4⋊Dic43—22no—
116C4⋊Dic43—21no—
117C4⋊Dic43—42no—
118C4⋊Dic43—41no—
119C4×Dic43—42no—
120C4×Dic43—41no—
121#10621877—22no—
122#10621877—41no—
123C2×C43⋊C8—41no—
124Dic172—21no—
125Dic172—21no—
126D344—21no—
127D344—21no—
128#10621873—41no—
129#10621873—41no—
130C16×C43—41no—
131C16×C43—41no—
132C23×C43—21no—
133C23×C43AGL(1,ℤ/8)11yescharacteristic
134C22×D43—41no—
135Q8×C43—21no—
136Q8×C43#10212yes—
137D4×C43—22no—
138D4×C43—22no—
139D4×C43—21no—
140D4×C43#10212yes—
141C2×C4×C43—21no—
142C2×C4×C43—22no—
143C2×C4×C43—22no—
144C2×C4×C43C2×C22⋊C411yescharacteristic
145C2×C4×C43#12011yescharacteristic
146C2×C4×C43#12311yescharacteristic
147C2×C4×C43C2×D811yescharacteristic
148C2×C4×C43C2×SD1611yescharacteristic
149C2×C4×C43#13711yescharacteristic
150C22⋊D43—81no—
151C22⋊D43—81no—
152C2×Dic43—41no—
153C2×Dic43—41no—
154C2×Dic43—42no—
155C2×Dic43—41no—
156C2×Dic43—161no—
157C2×Dic43—162no—
158D172—41no—
159D172—41no—
160C4×D43—81no—
161C4×D43—81no—
162Dic86—41no—
163Dic86—41no—
164C8×C43—22no—
165C8×C43C4×D411yescharacteristic
166C8×C43C4×D411yescharacteristic
167C8×C43#12111yescharacteristic
168C8×C43#12111yescharacteristic
169C43⋊C8—42no—
170#13005—431nomaximal, Sylow
171C22×C43—22no—
172C22×C43—41no—
173C22×C43—42no—
174C22×C43#41711yescharacteristic
175C22×C43#44711yescharacteristic
176C22×C43#48111yescharacteristic
177C2×D43—81no—
178C2×D43—161no—
179C4×C43—22no—
180C4×C43#38611yescharacteristic
181C4×C43C2×#10211yescharacteristic
182C4×C43#44811yescharacteristic
183C4×C43#48011yescharacteristic
184Dic43—81no—
185Dic43—82no—
186Dic43—81no—
187Dic43—81no—
188#3067—431no—
189#2912—431no—
190#2145—431no—
191C2×#360—431no—
192#2117D4311yescharacteristic, complemented
193#1389—431no—
194#1383—431no—
195C2×C43—21no—
196C2×C43—21no—
197C2×C43—21no—
198C2×C43—42no—
199C2×C43#187411yescharacteristic
200D43—161no—
201#575—861no—
202C2×#135—431no—
203C2×#131C2×D4311yescharacteristic
204#520—861no—
205C2×M32C2×D4311yescharacteristic
206C2×M32C2×D4311yescharacteristic
207#473—432no—
208#472—432no—
209#471—862no—
210C2×#108—431no—
211#428—862no—
212#428—861no—
213#427—431no—
214#427—861no—
215C2×#106—431no—
216C2×#106—861no—
217#413—861no—
218#360—862no—
219#360—861no—
220#360—861no—
221#350—22no—
222C43#1300511yescharacteristic, complemented, Sylow
223C2×#41—861no—
224C2×#41D17211yescharacteristic
225#137—862no—
226#137—1721no—
227AGL(1,ℤ/8)—862no—
228AGL(1,ℤ/8)—1721no—
229#135—861no—
230#135—861no—
231#135—861no—
232#135—861no—
233#135—1722no—
234C2×Q16—431no—
235C2×SD16—861no—
236C2×D8—431no—
237#131—21no—
238#131—21no—
239#131C4×D4312yes—
240#131C22⋊D4312yes—
241C2×M16—21no—
242C2×M16—861no—
243C2×M16D17211yescharacteristic
244C22×C8—21no—
245C22×C8C22×D4311yescharacteristic
246C4×Q8—1721no—
247C4×D4—1722no—
248C4×D4—1721no—
249#117—862no—
250#117—861no—
251C2×C4⋊C4—862no—
252C2×C4⋊C4—861no—
253M32—21no—
254M32—21no—
255M32—21no—
256M32—21no—
257C2×C16—21no—
258C2×C16—21no—
259#108—432no—
260#108—861no—
261#107—862no—
262#107—861no—
263#106—432no—
264#106—431no—
265#106—431no—
266#106—862no—
267#106—861no—
268#101—862no—
269#100—862no—
270#41—21no—
271#41—21no—
272#41—1721no—
273#41—1721no—
274#41—1721no—
275#41—1721no—
276#41#1062187312yes—
277#41(C2×D43)⋊C412yes—
278C2×Q8—861no—
279C2×Q8D34411yescharacteristic
280C2×D4—21no—
281C2×D4—861no—
282C2×D4—1721no—
283C2×D4D34411yescharacteristic
284C22×C4—21no—
285C22×C4—1721no—
286C22×C4—1722no—
287C22×C4—1721no—
288C22×C4C2×D17211yescharacteristic
289Q16—861no—
290Q16—861no—
291Q16—1722no—
292SD16—1722no—
293SD16—1722no—
294SD16—1721no—
295SD16—1721no—
296D8—861no—
297D8—861no—
298D8—1722no—
299M16—21no—
300M16—22no—
301M16—22no—
302M16—862no—
303M16—1721no—
304M16(C2×D43)⋊C412yes—
305C2×C8—21no—
306C2×C8—22no—
307C2×C8—22no—
308C2×C8—1721no—
309C2×C8C2×C4×D4311yescharacteristic
310C2×C8D4×D4311yescharacteristic
311C2×C8D4×D4311yescharacteristic
312C2×C8#1062190011yescharacteristic
313C2×C8#1062190011yescharacteristic
314C2×C8C2×C22⋊D4311yescharacteristic
315C4⋊C4—862no—
316C4⋊C4—861no—
317C4⋊C4—861no—
318C4⋊C4—1722no—
319C4⋊C4—1721no—
320C22⋊C4—1722no—
321C22⋊C4—1721no—
322C42—1722no—
323C42—1721no—
324C16—41no—
325C16—41no—
326C23—21no—
327C23—1721no—
328C23#1306335311yescharacteristic
329Q8—21no—
330Q8—1721no—
331Q8—1721no—
332Q8#1306324712yes—
333D4—22no—
334D4—22no—
335D4—21no—
336D4—3441no—
337D4—3441no—
338D4—1721no—
339D4—1721no—
340D4#1306324712yes—
341C2×C4—21no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—3441no—
345C2×C4—3441no—
346C2×C4—1721no—
347C2×C4—1721no—
348C2×C4—1722no—
349C2×C4—1721no—
350C2×C4—6881no—
351C2×C4—6882no—
352C2×C4C2×(C2×D43)⋊C411yescharacteristic
353C2×C4#1306329511yescharacteristic
354C2×C4#1306330911yescharacteristic
355C2×C4C2×D34411yescharacteristic
356C2×C4C2×#1062187311yescharacteristic
357C2×C4#1306335811yescharacteristic
358C8—22no—
359C8—1722no—
360C8(C22⋊D43)⋊C411yescharacteristic
361C8(C22⋊D43)⋊C411yescharacteristic
362C8#1306329711yescharacteristic
363C8#1306329711yescharacteristic
364C22—22no—
365C22—41no—
366C22—42no—
367C22—3441no—
368C22—6881no—
369C22#1458290111yescharacteristic
370C22#1458303511yescharacteristic
371C22#1458321811yescharacteristic
372C4—22no—
373C4—3442no—
374C4—3441no—
375C4—3441no—
376C4—3441no—
377C4#1458277611yescharacteristic
378C4C2×#1306324711yescharacteristic
379C4#1458304011yescharacteristic
380C4#1458321311yescharacteristic
381C2—21no—
382C2—21no—
383C2—21no—
384C2—42no—
385C2—6881no—
386C2#1913491011yescharacteristic
subgroupG/H
centerC2#19134910
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
FittingC43×#2117C2
socleC2×C43#1874
prime radical#19144315C2
cosocleC22×C8×C43C23
hypercenter#2117D43
hypocenterC43#13005
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#131 ◁ #2117

Complements

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

NH ≅ G/Ntype
2. #19143190C2semidirect
3. #19136332C2semidirect
4. C2×#14582710C2semidirect
5. #19132710C2semidirect
6. #19132694C2semidirect
7. C43×#2117C2semidirect
11. #14583174C4semidirect
12. #14583169C4semidirect
39. C2×Dic172C2×C4semidirect
41. C2×D344C2×C4semidirect
51. #13063261C2×C4semidirect
192. #2117D43semidirect
222. C43#13005semidirect

Maximal subgroups

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

subgroupindex
#191443152
#191431902
#191363322
C2×#145827102
#191327102
#191326942
C43×#21172
#1300543