Finite Group Databasebeta

← #25106267

Subgroups — #25106267

Order 11008.

1038 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147984C211yesmaximal, characteristic
2#19143157C211yesmaximal, characteristic, complemented
3#19137090C211yesmaximal, characteristic, complemented
4#19135576C211yesmaximal, characteristic, complemented
5#19135571C211yesmaximal, characteristic, complemented
6#19135424C211yesmaximal, characteristic, complemented
7#19134894C214yesmaximal, complemented
8#19134613C214yesmaximal, complemented
9C43×#1963C211yesmaximal, characteristic, complemented
10C2×M16×D43C2212yes—
11#14583518C414yescomplemented
12#14583510C412yescomplemented
13#14583503C412yescomplemented
14#14583494—22no—
15#14583486—22no—
16#14583456C2211yescharacteristic
17#14583429—24no—
18#14583406C2212yes—
19#41×Dic43C2212yes—
20C2×#13063282C2211yescharacteristic
21#14582924—24no—
22#14582923C2211yescharacteristic
23#14582922C2212yes—
24C2×#13063252C2214yes—
25#14582788—22no—
26#14582781—22no—
27C4×Dic43⋊C4C2212yes—
28C4×(C2×D43)⋊C4C2212yes—
29C42×Dic43C2211yescharacteristic
30#14582660C2214yes—
31#14582659C2214yes—
32C43×#532C2211yescharacteristic
33C43×#423C2211yescharacteristic
34C2×#104×C43C2214yes—
35C43×#376C2211yescharacteristic
36C22×C4×D43C2311yescharacteristic
37C2×#10621877C2312yes—
38C2×#10621872—22no—
39M16×D43—44no—
40C2×C8×D43—22no—
41#13063325C2×C412yes—
42#13063320—24no—
43#13063318—24no—
44#13063317C2×C412yes—
45#13063315—24no—
46#13063311—24no—
47#13063309—24no—
48#13063306—22no—
49#13063306—24no—
50#13063304—22no—
51#13063302—24no—
52#13063301C2×C414yes—
53#13063297—24no—
54#13063296C2×C414yes—
55#13063293—22no—
56Q8×Dic43C2×C414yes—
57C4×Dic86—22no—
58D4×Dic43—24no—
59D4×Dic43C2×C414yes—
60C4×C22⋊D43—24no—
61#13063284—22no—
62#13063284C2312yes—
63#13063282C2×C412yes—
64#13063282C2×C412yes—
65#13063282D414yes—
66C2×Dic43⋊C4—22no—
67C2×Dic43⋊C4D412yes—
68C2×(C2×D43)⋊C4—22no—
69C2×(C2×D43)⋊C4D412yes—
70C2×C4×Dic43—22no—
71C2×C4×Dic43—22no—
72C2×C4×Dic43C2312yes—
73C2×C4×Dic43C2311yescharacteristic
74C4⋊(C43⋊C8)—22no—
75Dic43⋊C8—24no—
76#13063252—44no—
77C43⋊#95—22no—
78C43⋊#95—22no—
79C2×#41×C43C2312yes—
80C2×M16×C43C2312yes—
81C4⋊Q8×C43C2×C411yescharacteristic
82#127×C43C2×C411yescharacteristic
83#124×C43C2×C412yes—
84#121×C43—22no—
85C4×D4×C43—22no—
86C2×C42×C43C2312yes—
87C2×C42×C43C2311yescharacteristic
88C4⋊C8×C43—22no—
89#104×C43—44no—
90#95×C43—22no—
91C23×D43C2×D411yescharacteristic
92#41×C43—24no—
93#41×C43—24no—
94C2×Q8×C43C22×C412yes—
95C2×D4×C43—22no—
96C2×D4×C43—22no—
97C2×D4×C43C22×C412yes—
98C22×C4×C43—22no—
99C22×C4×C43—22no—
100C22×C4×C43C2×D412yes—
101C22×C4×C43C2411yescharacteristic
102C2×C22⋊D43—24no—
103C22×Dic43—24no—
104C22×Dic43—22no—
105C22×Dic43C2×D411yescharacteristic
106C22×Dic43C2×D412yes—
107C2×C4×D43—22no—
108C2×C4×D43—22no—
109C2×C4×D43C22×C412yes—
110C2×C4×D43C2×D412yes—
111C2×Dic86—22no—
112M16×C43—24no—
113C2×C8×C43—22no—
114C4⋊C4×C43—22no—
115C22⋊C4×C43—24no—
116C42×C43—22no—
117C42×C43—22no—
118C42×C43C22×C411yescharacteristic
119C42×C43C22×C411yescharacteristic
120C42×C43C2×D412yes—
121C22⋊Dic43—24no—
122C22⋊Dic43—24no—
123C22⋊Dic43—22no—
124(C2×D43)⋊C4—24no—
125(C2×D43)⋊C4—44no—
126(C2×D43)⋊C4C22⋊C414yes—
127(C2×D43)⋊C4C22⋊C414yes—
128C4⋊Dic43—22no—
129C4⋊Dic43—24no—
130C4⋊Dic43C22×C414yes—
131Dic43⋊C4—24no—
132Dic43⋊C4—24no—
133Dic43⋊C4—44no—
134Dic43⋊C4C22⋊C414yes—
135Dic43⋊C4C22⋊C414yes—
136C4×Dic43—22no—
137C4×Dic43—24no—
138C4×Dic43—22no—
139C4×Dic43—22no—
140C4×Dic43—44no—
141C4×Dic43C22×C412yes—
142C4×Dic43C2×D412yes—
143#10621877—24no—
144C2×C43⋊C8—22no—
145#10621872—44no—
146C8×D43—44no—
147C23×C43—22no—
148C23×C43C22×D411yescharacteristic
149C22×D43—22no—
150C22×D43—42no—
151C22×D43C2×C22⋊C412yes—
152Q8×C43—24no—
153D4×C43—24no—
154D4×C43—44no—
155D4×C43—82no—
156C2×C4×C43—22no—
157C2×C4×C43—42no—
158C2×C4×C43—42no—
159C2×C4×C43—42no—
160C2×C4×C43—42no—
161C2×C4×C43—42no—
162C2×C4×C43—42no—
163C2×C4×C43C2×C22⋊C412yes—
164C2×C4×C43C2×C22⋊C412yes—
165C2×C4×C43C23×C411yescharacteristic
166C2×C4×C43C22×D411yescharacteristic
167C2×C4×C43H(5,𝔽2)12yes—
168C2×C4×C432−1+412yes—
169C22⋊D43—84no—
170C2×Dic43—22no—
171C2×Dic43—24no—
172C2×Dic43—24no—
173C2×Dic43—42no—
174C2×Dic43—42no—
175C2×Dic43—42no—
176C2×Dic43—84no—
177C2×Dic43C2×C22⋊C414yes—
178C2×Dic43C2×C22⋊C412yes—
179C4×D43—24no—
180C4×D43—22no—
181C4×D43—22no—
182Dic86—82no—
183C8×C43—42no—
184C43⋊C8—42no—
185#21858—431nomaximal, Sylow
186C22×C43—22no—
187C22×C43—42no—
188C22×C43—44no—
189C22×C43C22×C22⋊C411yescharacteristic
190C22×C43#53712yes—
191C2×D43—22no—
192C2×D43—24no—
193C2×D43—82no—
194C4×C43—22no—
195C4×C43—22no—
196C4×C43—42no—
197C4×C43—82no—
198C4×C43#52012yes—
199C4×C43#53511yescharacteristic
200C4×C43#53611yescharacteristic
201Dic43—22no—
202Dic43—24no—
203Dic43—44no—
204Dic43—44no—
205#3455—431no—
206#2905—431no—
207#2298—431no—
208#1995—431no—
209#1994—431no—
210#1963D4311yescharacteristic, complemented
211#1962—431no—
212#1871—434no—
213#1806—434no—
214C2×C43—22no—
215C2×C43—82no—
216C2×C43#231111yescharacteristic
217C2×C43#290112yes—
218D43—42no—
219C22×M16—432no—
220#542—434no—
221#541—432no—
222#540—432no—
223#539—862no—
224#538—862no—
225#533—431no—
226#532C2×D4311yescharacteristic
227#529—864no—
228#525—432no—
229C4×#41—432no—
230C2×#117—431no—
231#424—864no—
232#423—432no—
233#423—431no—
234#423C2×D4311yescharacteristic
235C2×#104—434no—
236C2×#104C2×D4314yes—
237#388—862no—
238#387—862no—
239C4×C4⋊C4—432no—
240C4×C22⋊C4—432no—
241#376C2×D4311yescharacteristic
242C43—431no—
243#339—434no—
244#339—434no—
245C43#2185811yescharacteristic, complemented, Sylow
246C2×#41C22×D4312yes—
247C23×C4—431no—
248C2×M16—432no—
249C2×M16—862no—
250C2×M16—1724no—
251C2×M16C22×D4312yes—
252C22×C8—862no—
253C4⋊Q8—432no—
254C4⋊Q8C4×D4311yescharacteristic
255#127C4×D4311yescharacteristic
256#126—864no—
257#126—864no—
258#125—432no—
259#125—864no—
260#124—864no—
261#124C4×D4312yes—
262#123—864no—
263#123—864no—
264#123—862no—
265C22⋊Q8—434no—
266C22⋊Q8—864no—
267C22⋊Q8—862no—
268#121—22no—
269#121—434no—
270#121—864no—
271#120—862no—
272C4×Q8—434no—
273C4×Q8—862no—
274C4×D4—22no—
275C4×D4—434no—
276C4×D4—864no—
277C4×D4—864no—
278#117—432no—
279#117—432no—
280#117—434no—
281#117—432no—
282#117—862no—
283C2×C4⋊C4—432no—
284C2×C4⋊C4—862no—
285C2×C22⋊C4—432no—
286C2×C22⋊C4—862no—
287C2×C42—431no—
288C2×C42—432no—
289C2×C42—862no—
290C2×C42—862no—
291C2×C42C22×D4312yes—
292C2×C42C22×D4311yescharacteristic
293C4⋊C8—22no—
294C4⋊C8—864no—
295C4⋊C8—862no—
296#104—44no—
297#104—1724no—
298#95—22no—
299#95—862no—
300#95—862no—
301C24—431no—
302#41—24no—
303#41—24no—
304C2×Q8—862no—
305C2×Q8C2×C4×D4312yes—
306C2×D4—22no—
307C2×D4—22no—
308C2×D4—864no—
309C2×D4C2×C4×D4312yes—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—431no—
313C22×C4—432no—
314C22×C4—432no—
315C22×C4—432no—
316C22×C4—864no—
317C22×C4—862no—
318C22×C4—862no—
319C22×C4—862no—
320C22×C4D4×D4312yes—
321C22×C4C23×D4311yescharacteristic
322M16—24no—
323M16—864no—
324M16—1724no—
325C2×C8—22no—
326C2×C8—862no—
327C2×C8—1724no—
328C4⋊C4—22no—
329C4⋊C4—434no—
330C4⋊C4—434no—
331C4⋊C4—434no—
332C4⋊C4—864no—
333C4⋊C4—864no—
334C4⋊C4—864no—
335C4⋊C4—862no—
336C4⋊C4—1724no—
337C22⋊C4—24no—
338C22⋊C4—434no—
339C22⋊C4—434no—
340C22⋊C4—864no—
341C22⋊C4—864no—
342C22⋊C4—864no—
343C22⋊C4—862no—
344C22⋊C4—1724no—
345C42—22no—
346C42—22no—
347C42—432no—
348C42—432no—
349C42—864no—
350C42—862no—
351C42—862no—
352C42—862no—
353C42—1724no—
354C42C2×C4×D4311yescharacteristic
355C42C2×C4×D4311yescharacteristic
356C42D4×D4312yes—
357C23—22no—
358C23—432no—
359C23—862no—
360C23—1722no—
361C23C2×D4×D4311yescharacteristic
362Q8—24no—
363Q8—3442no—
364D4—24no—
365D4—44no—
366D4—82no—
367D4—3444no—
368C2×C4—22no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—434no—
376C2×C4—432no—
377C2×C4—862no—
378C2×C4—864no—
379C2×C4—862no—
380C2×C4—862no—
381C2×C4—864no—
382C2×C4—864no—
383C2×C4—3444no—
384C2×C4—1722no—
385C2×C4—1722no—
386C2×C4—1722no—
387C2×C4C22⋊C4×D4312yes—
388C2×C4C22⋊C4×D4312yes—
389C2×C4C22×C4×D4311yescharacteristic
390C2×C4C2×D4×D4311yescharacteristic
391C2×C4#1306337012yes—
392C2×C4#1306337212yes—
393C8—42no—
394C8—1722no—
395C22—22no—
396C22—42no—
397C22—44no—
398C22—862no—
399C22—864no—
400C22—3442no—
401C22C2×C22⋊C4×D4311yescharacteristic
402C22#1458347812yes—
403C4—22no—
404C4—22no—
405C4—42no—
406C4—82no—
407C4—862no—
408C4—864no—
409C4—1724no—
410C4—1724no—
411C4#1458337812yes—
412C4#1458346211yescharacteristic
413C4#1458346911yescharacteristic
414C2—22no—
415C2—82no—
416C2—1722no—
417C2#1913718511yescharacteristic
418C2#1914314112yes—
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1963C2
socleC22×C43C22×C22⋊C4
prime radical#19147984C2
cosocleC22×C4×C43C24
hypercenter#1963D43
hypocenterC43#21858
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1963

Complements

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

NH ≅ G/Ntype
2. #19143157C2semidirect
3. #19137090C2semidirect
4. #19135576C2semidirect
5. #19135571C2semidirect
6. #19135424C2semidirect
7. #19134894C2semidirect
8. #19134613C2semidirect
9. C43×#1963C2semidirect
11. #14583518C4semidirect
12. #14583510C4semidirect
13. #14583503C4semidirect
210. #1963D43semidirect
245. C43#21858semidirect

Maximal subgroups

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

subgroupindex
#191479842
#191431572
#191370902
#191355762
#191355712
#191354242
#191348942
#191346132
C43×#19632
#2185843