Finite Group Databasebeta

← #25011756

Subgroups — #25011756

Order 11008.

456 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143296C211yesmaximal, characteristic
2#19136237C211yesmaximal, characteristic
3#19136234C211yesmaximal, characteristic
4#19134395C211yesmaximal, characteristic, complemented
5#19132717C211yesmaximal, characteristic, complemented
6#19132715C211yesmaximal, characteristic, complemented
7C43×#1757C211yesmaximal, characteristic, complemented
8C22×#10621872C411yescharacteristic, complemented
9#14583406C2211yescharacteristic
10#14582975—21no—
11#14582975—21no—
12#14582970—21no—
13#14582970—21no—
14#14582927C411yescharacteristic, complemented
15#14582883C2211yescharacteristic
16#14582873C2211yescharacteristic
17#14582866C2211yescharacteristic
18#14582862C411yescharacteristic, complemented
19#14582854—21no—
20#14582854C411yescharacteristic, complemented
21#14582690C412yescomplemented
22#14582688C412yescomplemented
23#14582687C412yescomplemented
24#14582685C412yescomplemented
25#14582670—21no—
26C2×#131×C43C2211yescharacteristic
27C43×#413C2211yescharacteristic
28C43×#410C2211yescharacteristic
29C43×#405—21no—
30C43×#344—21no—
31C22×C4×D43C2×C411yescharacteristic
32C2×#10621877—21no—
33C2×#10621877C2×C411yescharacteristic
34C2×#10621872—21no—
35C2×#10621872—21no—
36C2×#10621872—41no—
37C2×#10621872—41no—
38C22×C43⋊C8C2×C411yescharacteristic
39#13063306C2×C411yescharacteristic
40#13063306C2×C411yescharacteristic
41#13063301—21no—
42#13063296—21no—
43#13063293C2×C411yescharacteristic
44#13063293C2×C411yescharacteristic
45C4×C22⋊D43—21no—
46C4×C22⋊D43—21no—
47#13063284—21no—
48#13063284C2×C411yescharacteristic
49Dic43⋊C8—21no—
50Dic43⋊C8—21no—
51#13063244—21no—
52#13063242C2×C412yes—
53#13063240—21no—
54#13063240C2×C412yes—
55C22⋊(C43⋊C8)—21no—
56C22⋊(C43⋊C8)—21no—
57(C2×D43)⋊C8—21no—
58(C2×D43)⋊C8—21no—
59#13063235—21no—
60#13063235—41no—
61C8×Dic43—21no—
62C8×Dic43—41no—
63C2×#41×C43C2311yescharacteristic
64#131×C43—41no—
65#131×C43—41no—
66C2×M16×C43—21no—
67C2×M16×C43C2×C411yescharacteristic
68C2×M16×C43D411yescharacteristic
69C2×M16×C43D411yescharacteristic
70C22×C8×C43C2×C411yescharacteristic
71C22×C8×C43D411yescharacteristic
72C22×C8×C43D411yescharacteristic
73#117×C43—21no—
74#101×C43—21no—
75#100×C43C2×C412yes—
76#99×C43—21no—
77#99×C43C2×C412yes—
78#97×C43—41no—
79C4×C8×C43—41no—
80C23×D43C4211yescharacteristic
81#41×C43—41no—
82#41×C43—41no—
83C2×Q8×C43#4111yescharacteristic
84C2×D4×C43C22×C411yescharacteristic
85C2×D4×C43C22×C411yescharacteristic
86C2×D4×C43#4111yescharacteristic
87C22×C4×C43C22×C411yescharacteristic
88C22×C4×C43C2×D411yescharacteristic
89C22×C4×C43C2×D411yescharacteristic
90C2×C22⋊D43—21no—
91C2×C22⋊D43—21no—
92C22×Dic43C4211yescharacteristic
93C2×C4×D43—21no—
94C2×C4×D43—21no—
95C2×C4×D43—41no—
96C2×C4×D43—41no—
97M16×C43—22no—
98M16×C43—41no—
99M16×C43—41no—
100M16×C43—41no—
101M16×C43—41no—
102C2×C8×C43—21no—
103C2×C8×C43—21no—
104C2×C8×C43—21no—
105C2×C8×C43—21no—
106C2×C8×C43—21no—
107C2×C8×C43—21no—
108C2×C8×C43—41no—
109C2×C8×C43C22⋊C411yescharacteristic
110C2×C8×C43C22⋊C411yescharacteristic
111C2×C8×C43C22⋊C411yescharacteristic
112C2×C8×C43C22⋊C411yescharacteristic
113C4⋊C4×C43—41no—
114C22⋊C4×C43—22no—
115C42×C43—41no—
116C22⋊Dic43—21no—
117C22⋊Dic43—21no—
118C22⋊Dic43—22no—
119C22⋊Dic43C4211yescharacteristic
120C22⋊Dic43C4211yescharacteristic
121(C2×D43)⋊C4—21no—
122(C2×D43)⋊C4—21no—
123C4⋊Dic43—21no—
124C4⋊Dic43—41no—
125Dic43⋊C4—21no—
126Dic43⋊C4—21no—
127C4×Dic43—21no—
128C4×Dic43—41no—
129#10621877—22no—
130#10621877—41no—
131#10621877—41no—
132C2×C43⋊C8—21no—
133C2×C43⋊C8—21no—
134C2×C43⋊C8—41no—
135C2×C43⋊C8—41no—
136#10621872—42no—
137#10621872—41no—
138#10621872—41no—
139C23×C43C2×C4211yescharacteristic
140C23×C43C4×D411yescharacteristic
141C23×C43C4×D411yescharacteristic
142C22×D43—21no—
143C22×D43—41no—
144C22×D43—81no—
145Q8×C43—41no—
146D4×C43—41no—
147D4×C43—41no—
148D4×C43—41no—
149C2×C4×C43—21no—
150C2×C4×C43—21no—
151C2×C4×C43—21no—
152C2×C4×C43—21no—
153C2×C4×C43—21no—
154C2×C4×C43—21no—
155C2×C4×C43—42no—
156C2×C4×C43C2×C22⋊C411yescharacteristic
157C2×C4×C43#11711yescharacteristic
158C2×C4×C43C4×D411yescharacteristic
159C2×C4×C43C4×D411yescharacteristic
160C22⋊D43—81no—
161C22⋊D43—81no—
162C2×Dic43—21no—
163C2×Dic43—21no—
164C2×Dic43—21no—
165C2×Dic43—41no—
166C2×Dic43—42no—
167C4×D43—42no—
168C4×D43—41no—
169C4×D43—41no—
170C8×C43—21no—
171C8×C43—21no—
172C8×C43—21no—
173C8×C43—42no—
174C8×C43#9911yescharacteristic
175C8×C43#9911yescharacteristic
176C43⋊C8—42no—
177C43⋊C8—41no—
178C43⋊C8—41no—
179#12624—431nomaximal, Sylow
180C22×C43—21no—
181C22×C43—21no—
182C22×C43—21no—
183C22×C43—41no—
184C22×C43—41no—
185C22×C43—41no—
186C22×C43C4×C22⋊C411yescharacteristic
187C2×D43—41no—
188C2×D43—41no—
189C2×D43—41no—
190C2×D43—82no—
191C4×C43—21no—
192C4×C43—21no—
193C4×C43—21no—
194C4×C43—82no—
195C4×C43C2×#9911yescharacteristic
196C4×C43#41011yescharacteristic
197Dic43—41no—
198Dic43—41no—
199Dic43—41no—
200Dic43—82no—
201#2930—431no—
202#2120—431no—
203#2120—431no—
204#1757—431no—
205#1757D4311yescharacteristic, complemented
206#1392—431no—
207#1391—431no—
208C2×C43—21no—
209C2×C43—41no—
210C2×C43—41no—
211C2×C43—41no—
212C2×C43C4×#9911yescharacteristic
213D43—81no—
214C2×#131C2×D4311yescharacteristic
215C22×M16—431no—
216#525—431no—
217#436—861no—
218#436—861no—
219#435—861no—
220#435—861no—
221#424—431no—
222#413—431no—
223#413C2×D4311yescharacteristic
224#410—431no—
225#410C2×D4311yescharacteristic
226#408—431no—
227#407—431no—
228#405—21no—
229#405—431no—
230#405—861no—
231#352—432no—
232#352—432no—
233AΣL(1,𝔽16)—432no—
234AΣL(1,𝔽16)—432no—
235#344—21no—
236#344—861no—
237C43#1262411yescharacteristic, complemented, Sylow
238C2×#41C22×D4311yescharacteristic
239C23×C4—431no—
240#131—41no—
241#131—41no—
242C2×M16—21no—
243C2×M16—431no—
244C2×M16—861no—
245C2×M16—861no—
246C2×M16—861no—
247C2×M16—1721no—
248C2×M16—1721no—
249C2×M16C4×D4311yescharacteristic
250C2×M16D17211yescharacteristic
251C2×M16C22⋊D4311yescharacteristic
252C22×C8—431no—
253C22×C8C4×D4311yescharacteristic
254C22×C8D17211yescharacteristic
255C22×C8C22⋊D4311yescharacteristic
256#123—431no—
257#123—431no—
258C22⋊Q8—861no—
259#121—861no—
260#120—431no—
261#120—431no—
262C4×D4—861no—
263C4×D4—861no—
264#117—21no—
265#117—431no—
266#117—861no—
267C4⋊C8—861no—
268C4⋊C8—861no—
269#101—21no—
270#101—861no—
271#100—432no—
272#100C4×D4312yes—
273#99—21no—
274#99—432no—
275#99—861no—
276#99C4×D4312yes—
277C22⋊C8—861no—
278C22⋊C8—861no—
279C22⋊C8—861no—
280C22⋊C8—861no—
281#97—41no—
282#97—861no—
283#97—1721no—
284C4×C8—41no—
285C4×C8—861no—
286C4×C8—1721no—
287C24—431no—
288#41—41no—
289#41—41no—
290C2×Q8#1062189811yescharacteristic
291C2×D4—861no—
292C2×D4—861no—
293C2×D4C2×C4×D4311yescharacteristic
294C2×D4C2×C4×D4311yescharacteristic
295C2×D4#1062189811yescharacteristic
296C22×C4—431no—
297C22×C4—861no—
298C22×C4—861no—
299C22×C4—1721no—
300C22×C4—1721no—
301C22×C4C2×C4×D4311yescharacteristic
302C22×C4C2×D17211yescharacteristic
303C22×C4C2×C22⋊D4311yescharacteristic
304M16—22no—
305M16—41no—
306M16—41no—
307M16—41no—
308M16—41no—
309M16—862no—
310M16—1722no—
311M16—1721no—
312M16—1721no—
313M16—1721no—
314M16—1721no—
315C2×C8—21no—
316C2×C8—21no—
317C2×C8—21no—
318C2×C8—21no—
319C2×C8—21no—
320C2×C8—21no—
321C2×C8—41no—
322C2×C8—861no—
323C2×C8—861no—
324C2×C8—1721no—
325C2×C8—1721no—
326C2×C8(C2×D43)⋊C411yescharacteristic
327C2×C8(C2×D43)⋊C411yescharacteristic
328C2×C8(C2×D43)⋊C411yescharacteristic
329C2×C8(C2×D43)⋊C411yescharacteristic
330C4⋊C4—41no—
331C4⋊C4—861no—
332C4⋊C4—861no—
333C4⋊C4—861no—
334C4⋊C4—1721no—
335C22⋊C4—22no—
336C22⋊C4—431no—
337C22⋊C4—431no—
338C22⋊C4—861no—
339C22⋊C4—861no—
340C22⋊C4—861no—
341C22⋊C4—861no—
342C22⋊C4—862no—
343C42—41no—
344C42—861no—
345C42—1721no—
346C23—861no—
347C23—3441no—
348C23—1721no—
349C23C42×D4311yescharacteristic
350C23C4×C22⋊D4311yescharacteristic
351C23C4×D17211yescharacteristic
352Q8—41no—
353D4—41no—
354D4—41no—
355D4—41no—
356D4—3441no—
357D4—3441no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—42no—
365C2×C4—861no—
366C2×C4—861no—
367C2×C4—861no—
368C2×C4—1722no—
369C2×C4—1722no—
370C2×C4—1721no—
371C2×C4—1721no—
372C2×C4—1721no—
373C2×C4C2×(C2×D43)⋊C411yescharacteristic
374C2×C4#1306328211yescharacteristic
375C2×C4C4×C22⋊D4311yescharacteristic
376C2×C4C4×D17211yescharacteristic
377C8—21no—
378C8—21no—
379C8—21no—
380C8—42no—
381C8—1722no—
382C8—1721no—
383C8—1721no—
384C8#1306323911yescharacteristic
385C8#1306323911yescharacteristic
386C22—21no—
387C22—21no—
388C22—21no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—3442no—
393C22—1721no—
394C22—1721no—
395C22—1721no—
396C22C4×(C2×D43)⋊C411yescharacteristic
397C4—21no—
398C4—21no—
399C4—21no—
400C4—82no—
401C4—3442no—
402C4—1721no—
403C4—1721no—
404C4—1721no—
405C4C2×#1306323911yescharacteristic
406C4#1458287211yescharacteristic
407C2—21no—
408C2—41no—
409C2—41no—
410C2—41no—
411C2—3441no—
412C2C4×#1306323911yescharacteristic
subgroupG/H
centerC4C2×#13063239
commutatorC23×C43C2×C42
FrattiniC2×#41C22×D43
FittingC43×#1757C2
socleC2×C43C4×#99
prime radical#14583406C22
cosocleC2×#41×C43C23
hypercenter#1757D43
hypocenterC43#12624
LCSG ▷ C23×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C2×C8 ◁ C2×#131 ◁ #1757

Complements

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

NH ≅ G/Ntype
4. #19134395C2semidirect
5. #19132717C2semidirect
6. #19132715C2semidirect
7. C43×#1757C2semidirect
8. C22×#10621872C4semidirect
14. #14582927C4semidirect
18. #14582862C4semidirect
20. #14582854C4semidirect
21. #14582690C4semidirect
22. #14582688C4semidirect
23. #14582687C4semidirect
24. #14582685C4semidirect
205. #1757D43semidirect
237. C43#12624semidirect

Maximal subgroups

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

subgroupindex
#191432962
#191362372
#191362342
#191343952
#191327172
#191327152
C43×#17572
#1262443