Finite Group Databasebeta

← #11861223

Subgroups — #11861223

Order 1152.

969 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594684C211yesmaximal, characteristic
2#10594670C212yesmaximal, complemented
3#10592407C211yesmaximal, characteristic, complemented
4C3×#4717C212yesmaximal, complemented
5#10590921C212yesmaximal, complemented
6#10590920C212yesmaximal, complemented
7#10590913C211yesmaximal, characteristic, complemented
8#10590394C212yesmaximal, complemented
9#10590389C212yesmaximal, complemented
10#79899—32nomaximal
11#64306C2212yes—
12C2×#3743C2211yescharacteristic
13C2×C8×C3⋊D3C2211yescharacteristic
14#64081C2211yescharacteristic
15C3×#904C2212yes—
16C3×#901C2214yescomplemented
17#63822C2212yes—
18#63818C2212yes—
19#63815C2214yescomplemented
20#63810C412yescomplemented
21#63809C412yescomplemented
22#63804—24no—
23#63802C411yescharacteristic, complemented
24#63797C411yescharacteristic, complemented
25#63796C412yescomplemented
26D3×ΓL(1,𝔽25)—24no—
27C32×#97C2211yescharacteristic, complemented
28#63642C2211yescharacteristic, complemented
29C8×C3⋊Dic3C2211yescharacteristic, complemented
30C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
31C3×#819C2212yescomplemented
32C3×#805C2214yescomplemented
33#63578C2212yescomplemented
34#63568C2214yescomplemented
35D3×#135—32no—
36#5750—34no—
37C3×#444—32no—
38#5197—32no—
39#5144—34no—
40#4894—32no—
41D3×#108—32no—
42#4824—34no—
43#4821—34no—
44#4717D312yescomplemented
45#4708—32no—
46#4708—61no—
47C2×C4×C3⋊D3C2311yescharacteristic
48C3×#235C2314yes—
49#3811—22no—
50#3805—22no—
51#3802C2×C412yes—
52C4×D32—22no—
53#3798—22no—
54#3797C2×C412yes—
55#3796C2×C414yes—
56C2×C32×C8C2311yescharacteristic
57C2×C32×C8C2311yescharacteristic
58C32×C42C2311yescharacteristic
59#3752—21no—
60#3750—21no—
61C4×C3⋊Dic3C2311yescharacteristic
62C2×C3⋊(C3⋊C8)C2311yescharacteristic
63C2×C3⋊(C3⋊C8)C2311yescharacteristic
64#3743D412yes—
65#3743D412yes—
66C8×C3⋊D3C2×C411yescharacteristic
67C8×C3⋊D3C2×C411yescharacteristic
68C8×C3⋊D3C2×C411yescharacteristic
69C8×C3⋊D3C2×C411yescharacteristic
70C3×#208C2314yes—
71C3×Dic12C2×C412yes—
72C3×D24C2×C412yes—
73C3×#204C2×C414yes—
74C3×ΓL(1,𝔽25)—24no—
75C3×D3×C8—24no—
76#3718C2×C412yes—
77#3715C2×C414yes—
78#3713C2×C412yes—
79#3712—22no—
80#3711—24no—
81#3710—22no—
82D3×C3⋊C8—24no—
83#2957—91noSylow
84D3×#41—34no—
85C3×#135—32no—
86C3×#131—34no—
87#950—34no—
88#948—34no—
89#919—32no—
90D3×Q16—32no—
91#916—34no—
92D3×SD16—34no—
93#912—32no—
94D3×D8—32no—
95#907—34no—
96#907—64no—
97D3×M16—34no—
98D3×M16—64no—
99#904C2×D312yes—
100#901—64no—
101#901C2×D314yescomplemented
102C2×ΓL(1,𝔽25)—32no—
103C2×ΓL(1,𝔽25)—61no—
104C2×ΓL(1,𝔽25)—64no—
105C2×D3×C8—32no—
106C2×D3×C8—61no—
107#872—32no—
108#872—61no—
109C3×#108—32no—
110C3×#104—34no—
111C3×#97—21no—
112C3×#97C2×D312yescomplemented
113#837—34no—
114#825—34no—
115#822—34no—
116#819C2×D312yescomplemented
117#815—32no—
118#815—61no—
119C8×Dic3—32no—
120C8×Dic3—61no—
121#805C2×D314yescomplemented
122C4×C3⋊C8—32no—
123C4×C3⋊C8—61no—
124C22×C3⋊D3#4111yescharacteristic
125C2×D32—22no—
126C2×C32×C4—21no—
127C2×C32×C4C2411yescharacteristic
128C2×C3⋊Dic3—21no—
129C2×C3⋊Dic3#4111yescharacteristic
130C4×C3⋊D3C22×C411yescharacteristic
131C4×C3⋊D3C22×C411yescharacteristic
132C4×C3⋊D3C2×D411yescharacteristic
133C4×C3⋊D3C2×D411yescharacteristic
134C3×#67—24no—
135C3×D12C22×C414yes—
136C3×C4×D3—24no—
137C3×Dic6C22×C414yes—
138#627—22no—
139#626—24no—
140#625—22no—
141#624—22no—
142D3×Dic3—24no—
143C32×C8C22×C411yescharacteristic
144C32×C8C22×C411yescharacteristic
145C32×C8C2×D412yes—
146C3⋊(C3⋊C8)C22×C411yescharacteristic
147C3⋊(C3⋊C8)C22×C411yescharacteristic
148C3⋊(C3⋊C8)C2×D412yes—
149C3×C3⋊C8—24no—
150C2×#135—91no—
151#568—92no—
152#444—32no—
153#444—92no—
154#443—92no—
155#443—92no—
156C2×#108—91no—
157#421—92no—
158#405—91no—
159C3×#41—34no—
160#239—34no—
161D3×Q8—34no—
162#237—34no—
163#237—64no—
164D3×D4—34no—
165D3×D4—64no—
166#235—64no—
167#235C22×D314yes—
168C2×C4×D3—32no—
169C2×C4×D3—61no—
170C2×C4×D3—64no—
171C3×Q16—32no—
172C3×SD16—34no—
173C3×D8—32no—
174C3×M16—34no—
175C3×M16—64no—
176C2×C3×C8—21no—
177C2×C3×C8—21no—
178C2×C3×C8—64no—
179C2×C3×C8C22×D312yes—
180C2×C3×C8C22×D312yes—
181C3×C42—21no—
182C3×C42C22×D312yes—
183#216—34no—
184#215—34no—
185#214—34no—
186#213—34no—
187(C2×D3)⋊C4—62no—
188(C2×D3)⋊C4—62no—
189Dic3⋊C4—62no—
190Dic3⋊C4—62no—
191C4×Dic3—32no—
192C4×Dic3—61no—
193#208—64no—
194#208C22×D314yes—
195C2×C3⋊C8—32no—
196C2×C3⋊C8—32no—
197C2×C3⋊C8—61no—
198C2×C3⋊C8—61no—
199C2×C3⋊C8—64no—
200Dic12C4×D312yes—
201D24C4×D312yes—
202#204C4×D314yes—
203ΓL(1,𝔽25)—24no—
204ΓL(1,𝔽25)—34no—
205ΓL(1,𝔽25)—34no—
206ΓL(1,𝔽25)—62no—
207ΓL(1,𝔽25)—62no—
208ΓL(1,𝔽25)—64no—
209ΓL(1,𝔽25)—64no—
210D3×C8—24no—
211D3×C8—32no—
212D3×C8—32no—
213D3×C8—32no—
214D3×C8—32no—
215D3×C8—61no—
216D3×C8—61no—
217D3×C8—61no—
218D3×C8—61no—
219D3×C8—64no—
220D3×C8—64no—
221C22×C32C2×#4111yescharacteristic
222C2×C3⋊D3—41no—
223C2×C3⋊D3C4×D411yescharacteristic
224C2×C3⋊D3C4×D411yescharacteristic
225C2×C3×D3—24no—
226D32—82no—
227C32×C4—41no—
228C32×C4C23×C411yescharacteristic
229C32×C4C22×D411yescharacteristic
230C3⋊Dic3—41no—
231C3⋊Dic3C4×D411yescharacteristic
232C3⋊Dic3C4×D411yescharacteristic
233C3×Dic3—24no—
234C2×#41—92no—
235#135—32no—
236#135—92no—
237#135—92no—
238#135—92no—
239C2×Q16—91no—
240C2×SD16—92no—
241C2×D8—91no—
242#131—34no—
243#131—94no—
244#131—184no—
245C2×M16—91no—
246C2×M16—92no—
247C2×M16—184no—
248C22×C8—91no—
249#117—91no—
250#108—32no—
251#108—92no—
252#104—34no—
253#104—94no—
254#97—91no—
255#97D3211yescharacteristic, complemented
256C4×C8—91no—
257C4×C8—91no—
258C22×D3—32no—
259C22×D3—61no—
260C22×D3—64no—
261C3×Q8—34no—
262C3×D4—34no—
263C3×D4—64no—
264C2×C3×C4—22no—
265C2×C3×C4—22no—
266C2×C3×C4—21no—
267C2×C3×C4—64no—
268C2×C3×C4C23×D312yes—
269#67—24no—
270#67—64no—
271#67—64no—
272C2×Dic3—32no—
273C2×Dic3—61no—
274C2×Dic3—64no—
275C2×Dic3—62no—
276C2×Dic3—62no—
277D12—64no—
278D12C2×C4×D314yes—
279C4×D3—24no—
280C4×D3—32no—
281C4×D3—32no—
282C4×D3—32no—
283C4×D3—32no—
284C4×D3—61no—
285C4×D3—61no—
286C4×D3—61no—
287C4×D3—61no—
288C4×D3—64no—
289C4×D3—64no—
290Dic6—64no—
291Dic6C2×C4×D314yes—
292C3×C8—21no—
293C3×C8—21no—
294C3×C8—22no—
295C3×C8—64no—
296C3×C8C2×C4×D312yes—
297C3×C8C2×C4×D312yes—
298C3×C8D3×D414yes—
299C3⋊C8—24no—
300C3⋊C8—32no—
301C3⋊C8—32no—
302C3⋊C8—34no—
303C3⋊C8—61no—
304C3⋊C8—61no—
305C3⋊C8—62no—
306C2×C32—21no—
307C2×C32C2×C4×D411yescharacteristic
308C3⋊D3—21no—
309C3⋊D3—21no—
310C3×D3—44no—
311#41—34no—
312#41—94no—
313#41—182no—
314#41—182no—
315C2×Q8—92no—
316C2×D4—92no—
317C2×D4—182no—
318C22×C4—91no—
319C22×C4—182no—
320Q16—32no—
321Q16—92no—
322SD16—34no—
323SD16—94no—
324D8—32no—
325D8—92no—
326M16—34no—
327M16—64no—
328M16—92no—
329M16—92no—
330M16—182no—
331M16—184no—
332C2×C8—64no—
333C2×C8—91no—
334C2×C8—91no—
335C2×C8—91no—
336C2×C8—91no—
337C2×C8—91no—
338C2×C8—91no—
339C2×C8—182no—
340C2×C8—184no—
341C2×C8C2×D3211yescharacteristic
342C2×C8C2×D3211yescharacteristic
343C4⋊C4—181no—
344C22⋊C4—181no—
345C42—91no—
346C42C2×D3211yescharacteristic
347C22×C3—21no—
348C22×C3—64no—
349C22×C3D3×#4112yes—
350C2×D3—24no—
351C2×D3—32no—
352C2×D3—32no—
353C2×D3—61no—
354C2×D3—61no—
355C2×D3—122no—
356C2×D3—122no—
357C2×D3—244no—
358C3×C4—21no—
359C3×C4—21no—
360C3×C4—42no—
361C3×C4—42no—
362C3×C4—64no—
363C3×C4C22×C4×D312yes—
364C3×C4C2×D3×D412yes—
365Dic3—24no—
366Dic3—32no—
367Dic3—32no—
368Dic3—61no—
369Dic3—61no—
370Dic3—122no—
371Dic3—122no—
372C32#295711yescharacteristic, complemented, Sylow
373C23—91no—
374C23—182no—
375Q8—34no—
376Q8—182no—
377D4—34no—
378D4—64no—
379D4—184no—
380D4—182no—
381C2×C4—21no—
382C2×C4—64no—
383C2×C4—91no—
384C2×C4—91no—
385C2×C4—91no—
386C2×C4—91no—
387C2×C4—91no—
388C2×C4—182no—
389C2×C4—184no—
390C2×C4—181no—
391C2×C4C22×D3211yescharacteristic
392C8—64no—
393C8—91no—
394C8—91no—
395C8—92no—
396C8C4×D3211yescharacteristic
397C8C4×D3211yescharacteristic
398C8#380212yes—
399C2×C3—22no—
400C2×C3—22no—
401C2×C3—21no—
402C2×C3—124no—
403C2×C3C4×D3×D412yes—
404D3—44no—
405D3—62no—
406D3—62no—
407D3—121no—
408D3—121no—
409C22—64no—
410C22—91no—
411C22—91no—
412C22—361no—
413C22—722no—
414C22#6430611yescharacteristic
415C4—41no—
416C4—64no—
417C4—91no—
418C4—91no—
419C4—361no—
420C4C2×C4×D3211yescharacteristic
421C4C2×#380211yescharacteristic
422C3—21no—
423C3#7989912yescomplemented
424C2—21no—
425C2—124no—
426C2—181no—
427C2—181no—
428C2C4×#380211yescharacteristic
subgroupG/H
centerC4C2×#3802
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#97C22
socleC2×C32C2×C4×D4
prime radical#10594684C2
cosocleC2×C32×C4C24
hypercenter#97D32
hypocenterC32#2957
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C8 ◁ #97

Complements

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

NH ≅ G/Ntype
2. #10594670C2semidirect
3. #10592407C2semidirect
4. C3×#4717C2semidirect
5. #10590921C2semidirect
6. #10590920C2semidirect
7. #10590913C2semidirect
8. #10590394C2semidirect
9. #10590389C2semidirect
16. C3×#901C22semidirect
19. #63815C22semidirect
20. #63810C4semidirect
21. #63809C4semidirect
23. #63802C4semidirect
24. #63797C4semidirect
25. #63796C4semidirect
27. C32×#97C22semidirect
28. #63642C22semidirect
29. C8×C3⋊Dic3C22semidirect
30. C4×C3⋊(C3⋊C8)C22semidirect
31. C3×#819C22semidirect
32. C3×#805C22semidirect
33. #63578C22semidirect
34. #63568C22semidirect
44. #4717D3semidirect
101. #901C2×D3semidirect
112. C3×#97C2×D3semidirect
116. #819C2×D3semidirect
121. #805C2×D3semidirect
255. #97D32semidirect
372. C32#2957semidirect
423. C3#79899semidirect

Maximal subgroups

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

subgroupindex
#105946842
#105946702
#105924072
C3×#47172
#105909212
#105909202
#105909132
#105903942
#105903892
#798993