Finite Group Databasebeta

← #11858589

Subgroups — #11858589

Order 1152.

1085 conjugacy classes of subgroups.

The subgroup lattice has 429 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64110C211yesmaximal, characteristic
2#10594990C212yesmaximal
3C3×#5106C211yesmaximal, characteristic, complemented
4C2×C3×#818C211yesmaximal, characteristic, complemented
5#10591139C212yesmaximal, complemented
6#10590714C212yesmaximal, complemented
7#10590688C214yesmaximal, complemented
8#10590687C212yesmaximal, complemented
9#79179—31nomaximal
10#79146—31nomaximal
11C2×#3828C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14#64110C418yescomplemented
15C2×#3743C2212yes—
16C2×C8×C3⋊D3C2212yes—
17C3×#926C2212yes—
18C2×C3×C4⋊Dic3C2212yes—
19#63952—24no—
20#63900C2214yes—
21#63894—22no—
22#63849C2214yes—
23#63844—22no—
24C3×#818C2212yes—
25C3×#818C2212yes—
26C3×#818C2211yescharacteristic
27C3×#818C2211yescharacteristic
28C3×#817C2212yes—
29#63576C2214yes—
30#63574C2214yes—
31C2×#901—31no—
32C2×#901—31no—
33C2×#901—61no—
34#5523—32no—
35#5504—32no—
36C3×#427—31no—
37C2×C3×#107—31no—
38#5106D311yescharacteristic, complemented
39C2×#818D311yescharacteristic, complemented
40#4995—32no—
41#4964—32no—
42#4881—34no—
43#4880—32no—
44#4880—32no—
45D3×#107—32no—
46D3×#107—32no—
47#4861—34no—
48C22×C32×C4C2311yescharacteristic
49C2×#638D412yes—
50#3828C2×C414yes—
51#3828Q814yes—
52C2×C4⋊(C3⋊D3)D411yescharacteristic
53C2×C4×C3⋊D3C2312yes—
54C2×#634D411yescharacteristic
55C22×C3×Dic3—22no—
56C2×#624—24no—
57C2×C32×C8C2×C414yescomplemented
58C2×C32×C8C2311yescharacteristic
59C2×C32×C8C2311yescharacteristic
60#3748C2×C414yescomplemented
61C2×C3⋊(C3⋊C8)C2312yes—
62#3743C2×C418yescomplemented
63C8×C3⋊D3C2×C418yescomplemented
64C3×#217—22no—
65C3×C4⋊Dic3—22no—
66C3×C4⋊Dic3C2314yes—
67C3×C4⋊Dic3C2312yes—
68C3×C4⋊Dic3C2312yes—
69C3×C4×Dic3—22no—
70#3724—24no—
71#3722—24no—
72Dic32—24no—
73#2913—91noSylow
74C2×#235—31no—
75C2×#235—31no—
76C2×#235—61no—
77C22×C3×C8—21no—
78C22×C3×C8C2×D311yescharacteristic
79C22×C3×C8C2×D311yescharacteristic
80C3×#117—32no—
81C2×C3×C4⋊C4—32no—
82C4×#67—64no—
83#926C2×D312yes—
84C2×C4⋊Dic3C2×D312yes—
85C2×#208—31no—
86C2×#208—31no—
87C2×#208—61no—
88#901—38no—
89#901—38no—
90#901—68no—
91C2×ΓL(1,𝔽25)—32no—
92C2×ΓL(1,𝔽25)—32no—
93C2×ΓL(1,𝔽25)—62no—
94C2×D3×C8—32no—
95C2×D3×C8—32no—
96C2×D3×C8—62no—
97#893—62no—
98#892—34no—
99#892—34no—
100D3×C4⋊C4—34no—
101D3×C4⋊C4—34no—
102#887—62no—
103#67⋊C4—64no—
104C4×D12—62no—
105C4×Dic6—62no—
106C3×#107—31no—
107C3×#107—32no—
108C3×#107—31no—
109C3×#107—32no—
110C3×#106—32no—
111#818C2×D311yescharacteristic
112#818C2×D312yes—
113#818C2×D311yescharacteristic
114#818C2×D312yes—
115#817C2×D312yes—
116#808—34no—
117#808—34no—
118#807—34no—
119#807—34no—
120C23×C32C2×D411yescharacteristic
121C22×C3⋊D3C2×D412yes—
122C2×C32×C4C22×C412yes—
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×Q812yes—
125C2×C32×C4C2411yescharacteristic
126#638C4⋊C418yes—
127C2×C3⋊Dic3C2×D412yes—
128C4⋊(C3⋊D3)C4⋊C414yes—
129C4×C3⋊D3C22×C414yes—
130C4×C3⋊D3C2×Q814yes—
131#634C4⋊C414yes—
132C2×C3×Dic3—22no—
133C2×C3×Dic3—24no—
134C2×C3×Dic3—22no—
135C2×C3×Dic3—82no—
136#624—84no—
137C32×C8C22×C412yes—
138C32×C8C22×C412yes—
139C3⋊(C3⋊C8)C22×C414yes—
140C2×#131—91no—
141#520—92no—
142#428—94no—
143#428—92no—
144#427—31no—
145#427—92no—
146C2×#107—31no—
147C2×#107—92no—
148C22×C3×C4—21no—
149C22×C3×C4—62no—
150C22×C3×C4C22×D311yescharacteristic
151C22×C3×C4C22×D311yescharacteristic
152C2×#67—32no—
153C2×#67—32no—
154C2×#67—62no—
155C22×Dic3—22no—
156#235—34no—
157#235—34no—
158#235—34no—
159#235—34no—
160#235—64no—
161#235—64no—
162C2×D12—31no—
163C2×D12—31no—
164C2×D12—61no—
165C2×C4×D3—32no—
166C2×C4×D3—32no—
167C2×C4×D3—62no—
168C2×C4×D3—64no—
169C2×C4×D3—64no—
170C2×Dic6—31no—
171C2×Dic6—31no—
172C2×Dic6—61no—
173C2×C3×C8—24no—
174C2×C3×C8—21no—
175C2×C3×C8—21no—
176C2×C3×C8C4×D314yescomplemented
177C2×C3×C8C4×D314yescomplemented
178C2×C3×C8C22×D311yescharacteristic
179C2×C3×C8C22×D311yescharacteristic
180C2×C3×C8C22×D311yescharacteristic
181C2×C3×C8C22×D311yescharacteristic
182C3×C4⋊C4—32no—
183C3×C4⋊C4—34no—
184C3×C4⋊C4—32no—
185C3×C4⋊C4—62no—
186C3×C22⋊C4—62no—
187C3×C42—62no—
188#217—22no—
189(C2×D3)⋊C4—64no—
190(C2×D3)⋊C4—64no—
191C4⋊Dic3—22no—
192C4⋊Dic3C22×D312yes—
193C4⋊Dic3C22×D314yes—
194C4⋊Dic3C22×D312yes—
195Dic3⋊C4—64no—
196Dic3⋊C4—64no—
197C4×Dic3—22no—
198C4×Dic3—64no—
199C4×Dic3—64no—
200#208—34no—
201#208—34no—
202#208—64no—
203C2×C3⋊C8—32no—
204C2×C3⋊C8—32no—
205C2×C3⋊C8—62no—
206ΓL(1,𝔽25)—38no—
207ΓL(1,𝔽25)—38no—
208ΓL(1,𝔽25)—68no—
209D3×C8—38no—
210D3×C8—38no—
211D3×C8—68no—
212C22×C32—21no—
213C22×C32—21no—
214C22×C32C2×C4⋊C412yes—
215C22×C32C22×D411yescharacteristic
216C2×C3⋊D3—22no—
217C2×C3⋊D3—22no—
218C2×C3⋊D3C2×C4⋊C414yes—
219C32×C4C2×C4⋊C412yes—
220C32×C4C23×C411yescharacteristic
221C32×C4C22×Q811yescharacteristic
222C3⋊Dic3C2×C4⋊C414yes—
223C3×Dic3—42no—
224C3×Dic3—44no—
225C3×Dic3—42no—
226C2×#41—91no—
227#131—98no—
228C2×M16—91no—
229C2×M16—92no—
230C22×C8—92no—
231C22×C8D3211yescharacteristic
232C4×Q8—182no—
233C4×D4—182no—
234C4×D4—184no—
235#117—32no—
236#117—94no—
237C2×C4⋊C4—32no—
238C2×C4⋊C4—94no—
239#107—32no—
240#107—32no—
241#107—31no—
242#107—31no—
243#107—94no—
244#106—32no—
245#106—94no—
246C23×C3—21no—
247C23×C3D3×D411yescharacteristic
248C23×C3D3×D411yescharacteristic
249C22×D3—32no—
250C22×D3—32no—
251C22×D3—62no—
252C2×C3×C4—21no—
253C2×C3×C4—22no—
254C2×C3×C4—21no—
255C2×C3×C4—22no—
256C2×C3×C4—62no—
257C2×C3×C4—64no—
258C2×C3×C4—62no—
259C2×C3×C4—242no—
260C2×C3×C4C2×C4×D312yes—
261C2×C3×C4C2×C4×D312yes—
262C2×C3×C4D3×D411yescharacteristic
263C2×C3×C4D3×D411yescharacteristic
264C2×C3×C4D3×Q812yes—
265C2×C3×C4D3×Q812yes—
266C2×C3×C4C23×D311yescharacteristic
267C2×C3×C4C23×D311yescharacteristic
268#67—38no—
269#67—38no—
270#67—68no—
271C2×Dic3—22no—
272C2×Dic3—22no—
273C2×Dic3—24no—
274C2×Dic3—32no—
275C2×Dic3—32no—
276C2×Dic3—62no—
277C2×Dic3—82no—
278D12—34no—
279D12—34no—
280D12—64no—
281C4×D3—34no—
282C4×D3—34no—
283C4×D3—34no—
284C4×D3—34no—
285C4×D3—64no—
286C4×D3—64no—
287C4×D3—244no—
288C4×D3—244no—
289Dic6—34no—
290Dic6—34no—
291Dic6—64no—
292C3×C8—22no—
293C3×C8—22no—
294C3×C8C2×C4×D312yes—
295C3×C8C2×C4×D312yes—
296C3×C8C2×C4×D312yes—
297C3×C8C2×C4×D312yes—
298C3⋊C8—34no—
299C3⋊C8—34no—
300C3⋊C8—64no—
301C2×C32—22no—
302C2×C32C22×C4⋊C411yescharacteristic
303C2×C32#57611yescharacteristic
304C2×C32#57811yescharacteristic
305C3⋊D3—24no—
306#41—94no—
307#41—94no—
308C2×Q8—91no—
309C2×D4—92no—
310C2×D4—91no—
311C22×C4—62no—
312C22×C4—92no—
313C22×C4—184no—
314C22×C4C2×D3211yescharacteristic
315M16—94no—
316M16—98no—
317C2×C8—92no—
318C2×C8—98no—
319C2×C8#62414yescomplemented
320C2×C8C2×D3211yescharacteristic
321C2×C8C2×D3211yescharacteristic
322C4⋊C4—32no—
323C4⋊C4—32no—
324C4⋊C4—34no—
325C4⋊C4—62no—
326C4⋊C4—184no—
327C22⋊C4—62no—
328C22⋊C4—184no—
329C42—62no—
330C42—184no—
331C22×C3—21no—
332C22×C3—21no—
333C22×C3—21no—
334C22×C3—21no—
335C22×C3—21no—
336C22×C3—22no—
337C22×C3—41no—
338C22×C3—41no—
339C22×C3D3×C4⋊C412yes—
340C22×C3D3×C4⋊C412yes—
341C22×C3C2×D3×D411yescharacteristic
342C22×C3C2×D3×D411yescharacteristic
343C2×D3—34no—
344C2×D3—34no—
345C2×D3—64no—
346C2×D3—62no—
347C2×D3—62no—
348C2×D3—62no—
349C2×D3—62no—
350C2×D3—122no—
351C2×D3—122no—
352C3×C4—21no—
353C3×C4—21no—
354C3×C4—22no—
355C3×C4—122no—
356C3×C4—122no—
357C3×C4—124no—
358C3×C4D3×C4⋊C412yes—
359C3×C4D3×C4⋊C412yes—
360C3×C4C22×C4×D311yescharacteristic
361C3×C4C22×C4×D311yescharacteristic
362C3×C4C2×D3×Q811yescharacteristic
363C3×C4C2×D3×Q811yescharacteristic
364Dic3—34no—
365Dic3—34no—
366Dic3—44no—
367Dic3—42no—
368Dic3—42no—
369Dic3—64no—
370C32#291311yescharacteristic, complemented, Sylow
371C23—92no—
372C23#380211yescharacteristic
373Q8—94no—
374D4—98no—
375D4—94no—
376C2×C4—62no—
377C2×C4—62no—
378C2×C4—64no—
379C2×C4—92no—
380C2×C4—94no—
381C2×C4—94no—
382C2×C4—242no—
383C2×C4—724no—
384C2×C4#379712yes—
385C2×C4#380211yescharacteristic
386C2×C4C2×#62412yes—
387C2×C4C22×D3211yescharacteristic
388C8—94no—
389C8C2×#62412yes—
390C8C2×#62412yes—
391C2×C3—22no—
392C2×C3—22no—
393C2×C3—21no—
394C2×C3—21no—
395C2×C3—21no—
396C2×C3—42no—
397C2×C3C2×D3×C4⋊C411yescharacteristic
398C2×C3C2×D3×C4⋊C411yescharacteristic
399C2×C3#575711yescharacteristic
400C2×C3#576611yescharacteristic
401C2×C3#576911yescharacteristic
402C2×C3#577111yescharacteristic
403D3—64no—
404D3—64no—
405D3—124no—
406C22—21no—
407C22—21no—
408C22—94no—
409C22—182no—
410C22—182no—
411C22#6390012yes—
412C22C2×#380211yescharacteristic
413C4—94no—
414C4—124no—
415C4—122no—
416C4—122no—
417C4#6390012yes—
418C4C2×#379711yescharacteristic
419C4C22×#62411yescharacteristic
420C3—21no—
421C3#7914611yescharacteristic, complemented
422C3#7917911yescharacteristic, complemented
423C2—22no—
424C2—184no—
425C2#1059468711yescharacteristic
426C2#1059470311yescharacteristic
427C2C2×#6390011yescharacteristic
subgroupG/H
centerC22C2×#3802
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
prime radicalC2×#3828C22
cosocleC2×C32×C4C24
hypercenterC22×C8D32
hypocenterC32#2913
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
3. C3×#5106C2semidirect
4. C2×C3×#818C2semidirect
5. #10591139C2semidirect
6. #10590714C2semidirect
7. #10590688C2semidirect
8. #10590687C2semidirect
14. #64110C4semidirect
38. #5106D3semidirect
39. C2×#818D3semidirect
57. C2×C32×C8C2×C4semidirect
60. #3748C2×C4semidirect
62. #3743C2×C4semidirect
63. C8×C3⋊D3C2×C4semidirect
176. C2×C3×C8C4×D3semidirect
177. C2×C3×C8C4×D3semidirect
319. C2×C8#624semidirect
370. C32#2913semidirect
421. C3#79146semidirect
422. C3#79179semidirect

Maximal subgroups

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

subgroupindex
C2×#641102
#105949902
C3×#51062
C2×C3×#8182
#105911392
#105907142
#105906882
#105906872
#791793
#791463