Finite Group Databasebeta

← #25068625

Subgroups — #25068625

Order 11008.

564 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#19145177C211yesmaximal, characteristic
2#19143696C211yesmaximal, characteristic
3#19133502C212yesmaximal, complemented
4#19133445C212yesmaximal, complemented
5#19133443C212yesmaximal, complemented
6#19133412C212yesmaximal, complemented
7#19133341C211yesmaximal, characteristic
8#19133016C211yesmaximal, characteristic
9#19133015C211yesmaximal, characteristic
10#19132885C211yesmaximal, characteristic
11C43×#2986C211yesmaximal, characteristic
12#14583456C2211yescharacteristic
13#14583302C411yescharacteristic
14#14583278C411yescharacteristic
15#14583251C411yescharacteristic
16#14583249C411yescharacteristic
17#14583138C412yes—
18#14583138C412yes—
19#14583029C2212yes—
20#14583026—21no—
21C8×Dic86C2212yes—
22#14583023—21no—
23C4×#10621885C2212yes—
24C4×#10621885C2212yes—
25#14582957—22no—
26#14582952C2211yescharacteristic
27C4×#10621877C2211yescharacteristic
28C2×C4×C43⋊C8C2211yescharacteristic
29#14582651C2211yescharacteristic
30#14582651C2211yescharacteristic
31#14582649C2211yescharacteristic
32#14582649C2211yescharacteristic
33Q8⋊(C43⋊C8)C2212yes—
34Q8⋊(C43⋊C8)C2212yes—
35#14582629C2212yes—
36#14582629C2212yes—
37#14582621C2212yes—
38#14582620C2212yes—
39C43×#533C2211yescharacteristic
40C43×#446—21no—
41C43×#446C2212yes—
42C8×Q8×C43—21no—
43C8×Q8×C43C2212yes—
44C43×#433—22no—
45C43×#431C2211yescharacteristic
46C43×#431C2211yescharacteristic
47C2×#10621885C2×C412yes—
48C2×#10621885C2×C412yes—
49C2×#10621877—21no—
50C22×C43⋊C8C2×C411yescharacteristic
51C22×C43⋊C8C2×C411yescharacteristic
52#13063325C2×C411yescharacteristic
53#13063325C2×C411yescharacteristic
54#13063317—21no—
55#13063304—21no—
56#13063304C2×C412yes—
57C4×Dic86—21no—
58C4×Dic86C2312yes—
59#13063284—21no—
60#13063258C2×C412yes—
61#13063258C2×C412yes—
62C4⋊(C43⋊C8)C2311yescharacteristic
63C4⋊(C43⋊C8)C2311yescharacteristic
64Dic43⋊C8—22no—
65Dic43⋊C8—22no—
66#13063249C2×C412yes—
67#13063249C2×C412yes—
68#13063248C2×C412yes—
69#13063248C2×C412yes—
70C22⋊(C43⋊C8)—21no—
71#13063236—21no—
72#13063235—22no—
73C4×C43⋊C8—21no—
74C4×C43⋊C8C2×C411yescharacteristic
75C4×C43⋊C8C2×C411yescharacteristic
76C4×C43⋊C8C2312yes—
77C4×C43⋊C8C2311yescharacteristic
78C4×C43⋊C8C2311yescharacteristic
79C8×Dic43—22no—
80C4⋊Q8×C43C2×C411yescharacteristic
81C4⋊Q8×C43C2×C411yescharacteristic
82#125×C43—21no—
83C22⋊Q8×C43—21no—
84C22⋊Q8×C43C2×C412yes—
85C4×Q8×C43—21no—
86C4×Q8×C43C2312yes—
87#117×C43—21no—
88C2×C42×C43C2311yescharacteristic
89C4⋊C8×C43—22no—
90C4⋊C8×C43—22no—
91C4⋊C8×C43D411yescharacteristic
92C4⋊C8×C43D411yescharacteristic
93C4⋊C8×C43C2311yescharacteristic
94C4⋊C8×C43C2311yescharacteristic
95C22⋊C8×C43—21no—
96C22⋊C8×C43D412yes—
97#97×C43—22no—
98C4×C8×C43—22no—
99C4×C8×C43—21no—
100C4×C8×C43C2312yes—
101C2×Q8×C43—21no—
102C2×Q8×C43C22×C412yes—
103C22×C4×C43C22×C411yescharacteristic
104C22×C4×C43C2×D411yescharacteristic
105C22×C4×C43#4111yescharacteristic
106C2×Dic86—21no—
107C2×Dic86C22×C412yes—
108C2×C8×C43—21no—
109C2×C8×C43—21no—
110C2×C8×C43C2×D412yes—
111C2×C8×C43C2×D412yes—
112C4⋊C4×C43—21no—
113C4⋊C4×C43—21no—
114C4⋊C4×C43—21no—
115C4⋊C4×C43—22no—
116C4⋊C4×C43—22no—
117C4⋊C4×C43C22×C412yes—
118C22⋊C4×C43—22no—
119C42×C43—22no—
120C42×C43C22×C411yescharacteristic
121C42×C43C2×D411yescharacteristic
122C42×C43#4111yescharacteristic
123C42×C43C2411yescharacteristic
124C22⋊Dic43—22no—
125#10621885—24no—
126#10621885—42no—
127C4⋊Dic43—21no—
128C4⋊Dic43—21no—
129C4⋊Dic43—21no—
130C4⋊Dic43C22×C412yes—
131Dic43⋊C4—22no—
132Dic43⋊C4—22no—
133C4×Dic43—22no—
134#10621877—42no—
135C2×C43⋊C8—22no—
136C2×C43⋊C8—21no—
137C2×C43⋊C8—21no—
138C2×C43⋊C8—22no—
139C2×C43⋊C8—41no—
140C2×C43⋊C8C22×C411yescharacteristic
141C2×C43⋊C8C22×C411yescharacteristic
142C2×C43⋊C8C22×C411yescharacteristic
143C2×C43⋊C8C22×C411yescharacteristic
144C23×C43C4×D411yescharacteristic
145Q8×C43—22no—
146Q8×C43—22no—
147Q8×C43—42no—
148C2×C4×C43—21no—
149C2×C4×C43—21no—
150C2×C4×C43—21no—
151C2×C4×C43—21no—
152C2×C4×C43—22no—
153C2×C4×C43—22no—
154C2×C4×C43—22no—
155C2×C4×C43C4×D411yescharacteristic
156C2×C4×C43C4×D411yescharacteristic
157C2×C4×C43C4×D411yescharacteristic
158C2×C4×C43C23×C411yescharacteristic
159C2×C4×C43C22×D411yescharacteristic
160C2×C4×C43C2×#4111yescharacteristic
161C2×Dic43—22no—
162C2×Dic43—22no—
163Dic86—22no—
164Dic86—22no—
165Dic86—42no—
166C8×C43—22no—
167C8×C43—22no—
168C8×C43—41no—
169C8×C43—41no—
170C43⋊C8—21no—
171C43⋊C8—21no—
172C43⋊C8—21no—
173C43⋊C8—42no—
174C43⋊C8—41no—
175C43⋊C8—41no—
176C43⋊C8#13112yes—
177#18090—431nomaximal, Sylow
178C22×C43—21no—
179C22×C43—21no—
180C22×C43—21no—
181C22×C43C2×C4×D411yescharacteristic
182C4×C43—21no—
183C4×C43—21no—
184C4×C43—21no—
185C4×C43—42no—
186C4×C43—42no—
187C4×C43#44412yes—
188C4×C43C2×#13111yescharacteristic
189C4×C43#56811yescharacteristic
190C4×C43#57811yescharacteristic
191C4×C43#57811yescharacteristic
192Dic43—42no—
193Dic43—42no—
194#3170—431no—
195#2986—431no—
196#2986D4311yescharacteristic
197#1593—432no—
198#1584—432no—
199#1584—432no—
200#1579—432no—
201#1564—431no—
202#1485—431no—
203#1485—431no—
204#1451—431no—
205C2×C43—41no—
206C2×C43#293511yescharacteristic
207C2×C43#295011yescharacteristic
208C2×C43C2×#44411yescharacteristic
209#533—431no—
210#533C2×D4311yescharacteristic
211#500—431no—
212#494—431no—
213#487—431no—
214#487—431no—
215#467—432no—
216#467—432no—
217#446—21no—
218#446—432no—
219#446—861no—
220#446C2×D4312yes—
221C8×Q8—21no—
222C8×Q8—432no—
223C8×Q8—861no—
224C8×Q8C2×D4312yes—
225C4×Q16—432no—
226C4×Q16—432no—
227#433—22no—
228#433—862no—
229#431—431no—
230#431C2×D4311yescharacteristic
231#431C2×D4311yescharacteristic
232C4×M16—431no—
233C2×C4×C8—431no—
234#335—431no—
235#335—431no—
236#334—431no—
237#334—431no—
238Q8⋊C8—432no—
239Q8⋊C8—432no—
240Q8⋊C8—432no—
241Q8⋊C8—432no—
242#322—432no—
243#322—432no—
244C43#1809011yescharacteristic, complemented, Sylow
245C2×Q16—432no—
246C2×Q16—432no—
247C2×M16—861no—
248C22×C8—431no—
249C22×C8—431no—
250C4⋊Q8—431no—
251C4⋊Q8—431no—
252C4⋊Q8C4×D4311yescharacteristic
253C4⋊Q8C4×D4311yescharacteristic
254#125—21no—
255#125—861no—
256C22⋊Q8—21no—
257C22⋊Q8—432no—
258C22⋊Q8—861no—
259C22⋊Q8C4×D4312yes—
260C4×Q8—21no—
261C4×Q8—432no—
262C4×Q8—861no—
263C4×Q8C22×D4312yes—
264#117—21no—
265#117—861no—
266C2×C42C22×D4311yescharacteristic
267#107—432no—
268#107—432no—
269C4⋊C8—22no—
270C4⋊C8—22no—
271C4⋊C8—431no—
272C4⋊C8—431no—
273C4⋊C8—862no—
274C4⋊C8—862no—
275C4⋊C8C22⋊D4311yescharacteristic
276C4⋊C8C22⋊D4311yescharacteristic
277C4⋊C8C22×D4311yescharacteristic
278C4⋊C8C22×D4311yescharacteristic
279#103—432no—
280#103—432no—
281#103—432no—
282#103—432no—
283C22⋊C8—21no—
284C22⋊C8—861no—
285C22⋊C8C22⋊D4312yes—
286#97—22no—
287#97—862no—
288#97—861no—
289C4×C8—22no—
290C4×C8—21no—
291C4×C8—431no—
292C4×C8—431no—
293C4×C8—431no—
294C4×C8—431no—
295C4×C8—432no—
296C4×C8—862no—
297C4×C8—861no—
298C4×C8C22×D4312yes—
299C2×Q8—21no—
300C2×Q8—432no—
301C2×Q8—861no—
302C2×Q8C2×C4×D4312yes—
303C22×C4C2×C4×D4311yescharacteristic
304C22×C4#1062189811yescharacteristic
305C22×C4C2×C22⋊D4311yescharacteristic
306Q16—864no—
307Q16—1722no—
308M16—1722no—
309C2×C8—21no—
310C2×C8—21no—
311C2×C8—431no—
312C2×C8—431no—
313C2×C8—431no—
314C2×C8—431no—
315C2×C8—862no—
316C2×C8—861no—
317C2×C8—861no—
318C2×C8—862no—
319C2×C8—1721no—
320C2×C8C2×C22⋊D4312yes—
321C2×C8C2×C22⋊D4312yes—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4—22no—
326C4⋊C4—22no—
327C4⋊C4—432no—
328C4⋊C4—861no—
329C4⋊C4—861no—
330C4⋊C4—862no—
331C4⋊C4—861no—
332C4⋊C4—862no—
333C4⋊C4C2×C4×D4312yes—
334C22⋊C4—22no—
335C22⋊C4—862no—
336C42—22no—
337C42—862no—
338C42C2×C4×D4311yescharacteristic
339C42#1062189811yescharacteristic
340C42C2×C22⋊D4311yescharacteristic
341C42C23×D4311yescharacteristic
342C23C4×C22⋊D4311yescharacteristic
343Q8—22no—
344Q8—22no—
345Q8—42no—
346Q8—862no—
347Q8—862no—
348Q8—1722no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—862no—
357C2×C4—862no—
358C2×C4C4×C22⋊D4311yescharacteristic
359C2×C4C4×C22⋊D4311yescharacteristic
360C2×C4C4×C22⋊D4311yescharacteristic
361C2×C4C22×C4×D4311yescharacteristic
362C2×C4C22×C22⋊D4311yescharacteristic
363C2×C4C2×#1062189811yescharacteristic
364C8—22no—
365C8—22no—
366C8—41no—
367C8—41no—
368C8—432no—
369C8—861no—
370C8—861no—
371C8—861no—
372C8—1722no—
373C8—1721no—
374C8—1721no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22C2×C4×C22⋊D4311yescharacteristic
379C4—21no—
380C4—21no—
381C4—21no—
382C4—42no—
383C4—42no—
384C4—1722no—
385C4—1722no—
386C4#1458301912yes—
387C4#131×D4311yescharacteristic
388C4#1458366411yescharacteristic
389C4#1458371411yescharacteristic
390C4#1458371411yescharacteristic
391C2—41no—
392C2#1914333711yescharacteristic
393C2#1914346111yescharacteristic
394C2C2×#1458301911yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#2986C2
socleC22×C43C2×C4×D4
prime radicalC23×C43C4×D4
cosocleC42×C43C24
hypercenter#2986D43
hypocenterC43#18090
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2986

Complements

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

NH ≅ G/Ntype
3. #19133502C2semidirect
4. #19133445C2semidirect
5. #19133443C2semidirect
6. #19133412C2semidirect
244. C43#18090semidirect

Maximal subgroups

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

subgroupindex
#191451772
#191436962
#191335022
#191334452
#191334432
#191334122
#191333412
#191330162
#191330152
#191328852
C43×#29862
#1809043