Finite Group Databasebeta

← #25011792

Subgroups — #25011792

Order 11008.

460 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143305C211yesmaximal, characteristic
2#19136278C211yesmaximal, characteristic
3#19136258C211yesmaximal, characteristic
4#19134395C211yesmaximal, characteristic, complemented
5#19132725C211yesmaximal, characteristic, complemented
6#19132723C211yesmaximal, characteristic, complemented
7C43×#1757C211yesmaximal, characteristic, complemented
8C2×#13063331C411yescharacteristic, complemented
9#14583445C2211yescharacteristic
10#14582975—21no—
11#14582975—21no—
12C8×C22⋊D43—21no—
13C8×C22⋊D43—21no—
14#14582922C411yescharacteristic, complemented
15#14582883C2211yescharacteristic
16#14582873C2211yescharacteristic
17#14582867C411yescharacteristic, complemented
18#14582866C2211yescharacteristic
19#14582854—21no—
20C2×C8×Dic43C411yescharacteristic, complemented
21#14582697C412yescomplemented
22#14582695C412yescomplemented
23#14582693C412yes—
24#14582691C412yes—
25#14582670—21no—
26C2×#131×C43C2211yescharacteristic
27C43×#413C2211yescharacteristic
28C43×#410C2211yescharacteristic
29C43×#405—21no—
30C43×#344—21no—
31C2×#10621898C2×C411yescharacteristic
32#13063331—41no—
33#13063331—41no—
34C2×#10621877—21no—
35C2×#10621877C2×C411yescharacteristic
36C2×#10621872—21no—
37C22×C43⋊C8C2×C411yescharacteristic
38C2×C8×D43—21no—
39#13063323C2×C411yescharacteristic
40#13063321C2×C411yescharacteristic
41#13063314C2×C411yescharacteristic
42#13063312C2×C411yescharacteristic
43#13063297—21no—
44#13063297—21no—
45C4×C22⋊D43—21no—
46C4×C22⋊D43—21no—
47#13063284—21no—
48C2×C4×Dic43C2×C411yescharacteristic
49Dic43⋊C8—21no—
50Dic43⋊C8—21no—
51#13063244C2×C412yes—
52#13063242—21no—
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—41no—
60C8×Dic43—21no—
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×C43C2×C412yes—
75#100×C43—21no—
76#99×C43—21no—
77#99×C43C2×C412yes—
78#97×C43—41no—
79C4×C8×C43—41no—
80#41×C43—41no—
81#41×C43—41no—
82C2×Q8×C43C22×C411yescharacteristic
83C2×D4×C43C22×C411yescharacteristic
84C2×D4×C43#4111yescharacteristic
85C2×D4×C43#4111yescharacteristic
86C22×C4×C43C22×C411yescharacteristic
87C22×C4×C43C2×D411yescharacteristic
88C22×C4×C43C2×D411yescharacteristic
89C2×C22⋊D43—21no—
90C2×C22⋊D43—21no—
91C2×C22⋊D43—21no—
92C22×Dic43—21no—
93#10621898—41no—
94#10621898—41no—
95C2×D172C4211yescharacteristic
96C2×C4×D43—21no—
97C2×Dic86C4211yescharacteristic
98M16×C43—22no—
99M16×C43—41no—
100M16×C43—41no—
101M16×C43—41no—
102M16×C43—41no—
103C2×C8×C43—21no—
104C2×C8×C43—21no—
105C2×C8×C43—21no—
106C2×C8×C43—21no—
107C2×C8×C43—21no—
108C2×C8×C43—21no—
109C2×C8×C43—41no—
110C2×C8×C43C22⋊C411yescharacteristic
111C2×C8×C43C22⋊C411yescharacteristic
112C2×C8×C43C22⋊C411yescharacteristic
113C2×C8×C43C22⋊C411yescharacteristic
114C4⋊C4×C43—41no—
115C22⋊C4×C43—22no—
116C42×C43—41no—
117C22⋊Dic43—21no—
118C22⋊Dic43—21no—
119C22⋊Dic43—22no—
120(C2×D43)⋊C4—21no—
121(C2×D43)⋊C4—21no—
122C4⋊Dic43—41no—
123Dic43⋊C4—21no—
124Dic43⋊C4—21no—
125C4×Dic43—21no—
126C4×Dic43—41no—
127C4×Dic43C4211yescharacteristic
128C4×Dic43C4211yescharacteristic
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—
137C8×D43—41no—
138C8×D43—41no—
139C23×C43#11711yescharacteristic
140C23×C43C4×D411yescharacteristic
141C23×C43C4×D411yescharacteristic
142C22×D43—21no—
143Q8×C43—41no—
144D4×C43—41no—
145D4×C43—41no—
146D4×C43—41no—
147C2×C4×C43—21no—
148C2×C4×C43—21no—
149C2×C4×C43—21no—
150C2×C4×C43—21no—
151C2×C4×C43—21no—
152C2×C4×C43—21no—
153C2×C4×C43—42no—
154C2×C4×C43C2×C4211yescharacteristic
155C2×C4×C43C2×C22⋊C411yescharacteristic
156C2×C4×C43C4×D411yescharacteristic
157C2×C4×C43C4×D411yescharacteristic
158C22⋊D43—42no—
159C22⋊D43—42no—
160C22⋊D43—42no—
161C2×Dic43—21no—
162C2×Dic43—21no—
163C2×Dic43—21no—
164C2×Dic43—42no—
165C2×Dic43—42no—
166D172—41no—
167C4×D43—41no—
168C4×D43—41no—
169Dic86—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#12633—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—
190C4×C43—21no—
191C4×C43—21no—
192C4×C43—21no—
193C4×C43—82no—
194C4×C43C2×#9911yescharacteristic
195C4×C43#41011yescharacteristic
196Dic43—22no—
197Dic43—41no—
198Dic43—41no—
199Dic43—82no—
200#2931—431no—
201#2132—431no—
202#2126—431no—
203#1757—431no—
204#1757D4311yescharacteristic, complemented
205#1395—431no—
206#1395—431no—
207C2×C43—21no—
208C2×C43—41no—
209C2×C43—41no—
210C2×C43—41no—
211C2×C43C4×#9911yescharacteristic
212D43—81no—
213C2×#131—431no—
214C2×#131C2×D4311yescharacteristic
215#532—431no—
216#436—861no—
217#436—861no—
218C8×D4—861no—
219C8×D4—861no—
220#423—431no—
221#413—431no—
222#413C2×D4311yescharacteristic
223#410—431no—
224#410C2×D4311yescharacteristic
225#408—431no—
226#408—431no—
227#405—21no—
228#405—861no—
229C2×C4×C8—431no—
230#356—432no—
231#355—432no—
232#354—432no—
233#353—432no—
234#344—21no—
235#344—861no—
236C43#1263311yescharacteristic, complemented, Sylow
237C2×#41—431no—
238C2×#41C22×D4311yescharacteristic
239#131—41no—
240#131—41no—
241#131—1721no—
242#131—1721no—
243C2×M16—21no—
244C2×M16—431no—
245C2×M16—861no—
246C2×M16—861no—
247C2×M16C4×D4311yescharacteristic
248C2×M16D17211yescharacteristic
249C2×M16C22⋊D4311yescharacteristic
250C22×C8—431no—
251C22×C8—861no—
252C22×C8C4×D4311yescharacteristic
253C22×C8D17211yescharacteristic
254C22×C8C22⋊D4311yescharacteristic
255C4⋊Q8—431no—
256#127—431no—
257#124—431no—
258#124—431no—
259#121—861no—
260#121—861no—
261C4×D4—861no—
262C4×D4—861no—
263#117—21no—
264#117—861no—
265C2×C42—431no—
266C4⋊C8—861no—
267C4⋊C8—861no—
268#101—432no—
269#101C4×D4312yes—
270#100—21no—
271#100—861no—
272#99—21no—
273#99—432no—
274#99—861no—
275#99C4×D4312yes—
276C22⋊C8—861no—
277C22⋊C8—861no—
278C22⋊C8—861no—
279C22⋊C8—861no—
280#97—41no—
281#97—1721no—
282C4×C8—41no—
283C4×C8—861no—
284C4×C8—861no—
285C4×C8—1721no—
286#41—41no—
287#41—41no—
288#41—1721no—
289#41—1721no—
290C2×Q8—431no—
291C2×Q8C2×C4×D4311yescharacteristic
292C2×D4—431no—
293C2×D4—861no—
294C2×D4—861no—
295C2×D4—861no—
296C2×D4C2×C4×D4311yescharacteristic
297C2×D4#1062189811yescharacteristic
298C2×D4#1062189811yescharacteristic
299C22×C4—861no—
300C22×C4—861no—
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—
313C2×C8—21no—
314C2×C8—21no—
315C2×C8—21no—
316C2×C8—21no—
317C2×C8—21no—
318C2×C8—21no—
319C2×C8—41no—
320C2×C8—861no—
321C2×C8—861no—
322C2×C8—1721no—
323C2×C8—1721no—
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—1721no—
334C22⋊C4—22no—
335C22⋊C4—861no—
336C22⋊C4—861no—
337C22⋊C4—861no—
338C22⋊C4—861no—
339C22⋊C4—862no—
340C42—41no—
341C42—431no—
342C42—431no—
343C42—861no—
344C42—1721no—
345C23—861no—
346C23#1306328211yescharacteristic
347C23C4×C22⋊D4311yescharacteristic
348C23C4×D17211yescharacteristic
349Q8—41no—
350Q8—1721no—
351D4—41no—
352D4—41no—
353D4—41no—
354D4—1721no—
355D4—1722no—
356D4—1722no—
357D4—1722no—
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×C4C42×D4311yescharacteristic
373C2×C4C2×(C2×D43)⋊C411yescharacteristic
374C2×C4C4×C22⋊D4311yescharacteristic
375C2×C4C4×D17211yescharacteristic
376C8—21no—
377C8—21no—
378C8—21no—
379C8—42no—
380C8—1722no—
381C8—1721no—
382C8—1721no—
383C8#1306323911yescharacteristic
384C8#1306323911yescharacteristic
385C22—21no—
386C22—21no—
387C22—21no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—1721no—
392C22—1721no—
393C22—1721no—
394C22C4×(C2×D43)⋊C411yescharacteristic
395C4—21no—
396C4—21no—
397C4—21no—
398C4—82no—
399C4—862no—
400C4—3442no—
401C4—1721no—
402C4—1721no—
403C4C2×#1306323911yescharacteristic
404C4#1458287211yescharacteristic
405C2—21no—
406C2—41no—
407C2—41no—
408C2—41no—
409C2—3441no—
410C2C4×#1306323911yescharacteristic
subgroupG/H
centerC8#13063239
commutatorC2×C4×C43C2×C42
FrattiniC2×#41C22×D43
FittingC43×#1757C2
socleC2×C43C4×#99
prime radical#14583445C22
cosocleC2×#41×C43C23
hypercenter#1757D43
hypocenterC43#12633
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C8 ◁ C2×C8 ◁ C2×#131 ◁ #1757

Complements

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

NH ≅ G/Ntype
4. #19134395C2semidirect
5. #19132725C2semidirect
6. #19132723C2semidirect
7. C43×#1757C2semidirect
8. C2×#13063331C4semidirect
14. #14582922C4semidirect
17. #14582867C4semidirect
20. C2×C8×Dic43C4semidirect
21. #14582697C4semidirect
22. #14582695C4semidirect
204. #1757D43semidirect
236. C43#12633semidirect

Maximal subgroups

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

subgroupindex
#191433052
#191362782
#191362582
#191343952
#191327252
#191327232
C43×#17572
#1263343