Finite Group Databasebeta

← #25013611

Subgroups — #25013611

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#19136330C211yesmaximal, characteristic, complemented
3C2×#14582708C211yesmaximal, characteristic, complemented
4#19136223C211yesmaximal, characteristic, complemented
5#19132711C211yesmaximal, characteristic, complemented
6#19132693C211yesmaximal, characteristic, complemented
7C43×#2912C211yesmaximal, characteristic, complemented
8#14583697—21no—
9C2×#13063347C2211yescharacteristic
10C2×#13063265C2211yescharacteristic
11C2×#13063265C2211yescharacteristic
12#14583174C412yescomplemented
13#14583169C412yescomplemented
14#14583162—22no—
15C2×#13063261C2211yescharacteristic
16#14582881—21no—
17#14582708—22no—
18#14582708—21no—
19#14582708—21no—
20#14582683—22no—
21C2×#131×C43C2211yescharacteristic
22C43×#520—21no—
23C43×#428—21no—
24C43×#428—22no—
25C43×#427—21no—
26C43×#427C2211yescharacteristic
27C2×#106×C43—21no—
28C2×#106×C43C2211yescharacteristic
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—
43#13063265—21no—
44#13063265—21no—
45#13063265—21no—
46#13063265—21no—
47C2×C43⋊C16—21no—
48C2×C43⋊C16—21no—
49#13063261—21no—
50#13063261C2×C412yescomplemented
51#13063243—22no—
52#13063241—22no—
53C2×#41×C43D411yescharacteristic
54#131×C43—21no—
55#131×C43—21no—
56#131×C43C2×C412yes—
57#131×C43D412yes—
58C2×M16×C43—21no—
59C2×M16×C43D411yescharacteristic
60C22×C8×C43—21no—
61C22×C8×C43C2311yescharacteristic
62C4×Q8×C43—41no—
63C4×D4×C43—42no—
64C4×D4×C43—41no—
65#117×C43—22no—
66#117×C43—21no—
67C2×C4⋊C4×C43—22no—
68C2×C4⋊C4×C43—21no—
69#107×C43—22no—
70#107×C43—21no—
71#106×C43—22no—
72#106×C43—21no—
73#106×C43D411yescharacteristic
74#106×C43D412yes—
75#106×C43D411yescharacteristic
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×C43—42no—
85C22×C4×C43—41no—
86C22×C4×C43C2×D411yescharacteristic
87C2×C22⋊D43—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
108C4⋊C4×C43—21no—
109C4⋊C4×C43—22no—
110C4⋊C4×C43—21no—
111C4⋊C4×C43—42no—
112C4⋊C4×C43—41no—
113C22⋊C4×C43—42no—
114C22⋊C4×C43—41no—
115C42×C43—42no—
116C42×C43—41no—
117#10621885—42no—
118#10621884—42no—
119#10621883—42no—
120#10621882—42no—
121#10621877—22no—
122#10621877—41no—
123C2×C43⋊C8—41no—
124Dic172—21no—
125Dic172—21no—
126D344—21no—
127D344—21no—
128#10621873—41no—
129#10621873—41no—
130C43⋊C16—41no—
131C43⋊C16—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×C43—41no—
145C2×C4×C43—42no—
146C2×C4×C43—41no—
147C2×C4×C43—161no—
148C2×C4×C43—162no—
149C2×C4×C43C2×C22⋊C411yescharacteristic
150C2×C4×C43#12011yescharacteristic
151C2×C4×C43#12311yescharacteristic
152C2×C4×C43C2×D811yescharacteristic
153C2×C4×C43C2×SD1611yescharacteristic
154C2×C4×C43#13711yescharacteristic
155C22⋊D43—81no—
156C22⋊D43—81no—
157C2×Dic43—41no—
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—81no—
181C4×C43—82no—
182C4×C43—81no—
183C4×C43#38611yescharacteristic
184C4×C43C2×#10211yescharacteristic
185C4×C43#44811yescharacteristic
186C4×C43#48011yescharacteristic
187Dic43—81no—
188#3067—431no—
189#2912D4311yescharacteristic, complemented
190#2145—431no—
191C2×#360—431no—
192#2117—431no—
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—21no—
205C2×M32—431no—
206C2×M32—431no—
207#473—432no—
208#472—432no—
209#471—862no—
210C2×#108—431no—
211#428—21no—
212#428—22no—
213#427—21no—
214#427C2×D4311yescharacteristic
215C2×#106—21no—
216C2×#106C2×D4311yescharacteristic
217#413—861no—
218#360—862no—
219#360—861no—
220#360—861no—
221#350—862no—
222C43#1300511yescharacteristic, complemented, Sylow
223C2×#41—861no—
224C2×#41C22⋊D4311yescharacteristic
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#131D17212yes—
241C2×M16—21no—
242C2×M16—861no—
243C2×M16C22⋊D4311yescharacteristic
244C22×C8—21no—
245C22×C8C22×D4311yescharacteristic
246C4×Q8—41no—
247C4×D4—42no—
248C4×D4—41no—
249#117—22no—
250#117—21no—
251C2×C4⋊C4—22no—
252C2×C4⋊C4—21no—
253M32—861no—
254M32—861no—
255M32—861no—
256M32—861no—
257C2×C16—861no—
258C2×C16—861no—
259#108—432no—
260#108—861no—
261#107—22no—
262#107—21no—
263#106—22no—
264#106—21no—
265#106C22⋊D4311yescharacteristic
266#106C22⋊D4312yes—
267#106C22⋊D4311yescharacteristic
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(C2×D43)⋊C412yes—
277#41#1062188412yes—
278C2×Q8—861no—
279C2×Q8#1062188211yescharacteristic
280C2×D4—21no—
281C2×D4—861no—
282C2×D4—1721no—
283C2×D4#1062188211yescharacteristic
284C22×C4—21no—
285C22×C4—42no—
286C22×C4—41no—
287C22×C4—1721no—
288C22×C4C2×C22⋊D4311yescharacteristic
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×C8C2×D17211yescharacteristic
311C2×C8#1062189811yescharacteristic
312C2×C8#1062189811yescharacteristic
313C2×C8C2×C22⋊D4311yescharacteristic
314C2×C8C2×C22⋊D4311yescharacteristic
315C4⋊C4—21no—
316C4⋊C4—22no—
317C4⋊C4—21no—
318C4⋊C4—42no—
319C4⋊C4—41no—
320C22⋊C4—42no—
321C22⋊C4—41no—
322C42—42no—
323C42—41no—
324C16—1721no—
325C16—1721no—
326C23—21no—
327C23—1721no—
328C23#1306335111yescharacteristic
329Q8—21no—
330Q8—1721no—
331Q8—1721no—
332Q8#1306324512yes—
333D4—22no—
334D4—22no—
335D4—21no—
336D4—3441no—
337D4—3441no—
338D4—1721no—
339D4—1721no—
340D4#1306324512yes—
341C2×C4—21no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—41no—
345C2×C4—42no—
346C2×C4—41no—
347C2×C4—161no—
348C2×C4—162no—
349C2×C4—3441no—
350C2×C4—3441no—
351C2×C4—1721no—
352C2×C4C2×(C2×D43)⋊C411yescharacteristic
353C2×C4#1306329411yescharacteristic
354C2×C4#1306330811yescharacteristic
355C2×C4C2×#1062188211yescharacteristic
356C2×C4C2×#1062188411yescharacteristic
357C2×C4#1306335611yescharacteristic
358C8—22no—
359C8—1722no—
360C8C4×C22⋊D4311yescharacteristic
361C8C4×C22⋊D4311yescharacteristic
362C8#1306329911yescharacteristic
363C8#1306329911yescharacteristic
364C22—22no—
365C22—41no—
366C22—42no—
367C22—3441no—
368C22—6881no—
369C22#1458289811yescharacteristic
370C22#1458303311yescharacteristic
371C22#1458321711yescharacteristic
372C4—22no—
373C4—82no—
374C4—81no—
375C4—81no—
376C4—3441no—
377C4#1458277811yescharacteristic
378C4C2×#1306324511yescharacteristic
379C4#1458303811yescharacteristic
380C4#1458321211yescharacteristic
381C2—21no—
382C2—21no—
383C2—21no—
384C2—42no—
385C2—6881no—
386C2#1913491211yescharacteristic
subgroupG/H
centerC2#19134912
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
FittingC43×#2912C2
socleC2×C43#1874
prime radical#19144315C2
cosocleC22×C8×C43C23
hypercenter#2912D43
hypocenterC43#13005
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#131 ◁ #2912

Complements

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

NH ≅ G/Ntype
2. #19136330C2semidirect
3. C2×#14582708C2semidirect
4. #19136223C2semidirect
5. #19132711C2semidirect
6. #19132693C2semidirect
7. C43×#2912C2semidirect
12. #14583174C4semidirect
13. #14583169C4semidirect
39. C2×Dic172C2×C4semidirect
41. C2×D344C2×C4semidirect
50. #13063261C2×C4semidirect
189. #2912D43semidirect
222. C43#13005semidirect

Maximal subgroups

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

subgroupindex
#191443152
#191363302
C2×#145827082
#191362232
#191327112
#191326932
C43×#29122
#1300543