Finite Group Databasebeta

← #11876944

Subgroups — #11876944

Order 1152.

811 conjugacy classes of subgroups; only the 152 normal subgroups are shown.

normal subgroups only

This group has 811 conjugacy classes of subgroups — too many to draw. Only its 152 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593943C212yesmaximal, complemented
2C4×#3743C211yesmaximal, characteristic, complemented
3C3×#4697C212yesmaximal, complemented
4#10590856C211yesmaximal, characteristic, complemented
5#10590842C212yesmaximal, complemented
6#10590840C211yesmaximal, characteristic
7#10590791C211yesmaximal, characteristic, complemented
8#10590743C212yesmaximal, complemented
9#10590741C211yesmaximal, characteristic, complemented
10#10590353C211yesmaximal, characteristic, complemented
11#10590314C211yesmaximal, characteristic, complemented
12#81631—32nomaximal
13C2×#3743C2211yescharacteristic
14C2×#3743C2211yescharacteristic
15C42×C3⋊D3C2211yescharacteristic
16C3×#875C2212yes—
17C3×#870C2212yes—
18#63916C2212yes—
19#63898C2212yes—
20#63881—22no—
21#63878—22no—
22#63871C2212yes—
23#63862—22no—
24#63853—22no—
25#63843C2212yes—
26C2×#3718C2211yescharacteristic
27C2×#3715C2212yes—
28C2×#3713C2211yescharacteristic
29C32×C4×C8C2211yescharacteristic
30#63642C2211yescharacteristic
31#63642C2211yescharacteristic
32C4×C3⋊(C3⋊C8)C2211yescharacteristic
33C3×#821C2212yes—
34C3×#821C2212yes—
35C3×#816C2212yes—
36C3×#816C2212yes—
37#63576C2212yes—
38#63574C2211yescharacteristic
39#63574C2211yescharacteristic
40#5691—32no—
41#5680—32no—
42C3×#488—32no—
43#5065—32no—
44#5059—32no—
45#4817—32no—
46#4816—32no—
47#4812—32no—
48#4789—32no—
49#4785—32no—
50#4782—32no—
51#4780—32no—
52#4757—32no—
53#4697D312yescomplemented
54C4×ΓL(1,𝔽25)—32no—
55C4×ΓL(1,𝔽25)—61no—
56C2×C4×C3⋊D3D412yes—
57C2×C4×C3⋊D3C2311yescharacteristic
58C2×C3×D12C2312yes—
59C2×C3×Dic6C2312yes—
60C2×#626—22no—
61C2×D3×Dic3—22no—
62C2×C32×C8C2311yescharacteristic
63C2×C32×C8C2311yescharacteristic
64C32×C42C2311yescharacteristic
65C4×C3⋊Dic3D412yes—
66C4×C3⋊Dic3C2311yescharacteristic
67C2×C3⋊(C3⋊C8)C2311yescharacteristic
68C2×C3⋊(C3⋊C8)C2311yescharacteristic
69#3743—22no—
70#3743—22no—
71C3×(C2×D3)⋊C4—22no—
72C3×(C2×D3)⋊C4—22no—
73C3×C4⋊Dic3C2312yes—
74C3×C4⋊Dic3C2312yes—
75C3×Dic3⋊C4—22no—
76C3×Dic3⋊C4—22no—
77Dic3⋊Dic3—22no—
78Dic3⋊Dic3—22no—
79#3722—22no—
80(C2×D3)⋊Dic3—22no—
81(C2×D3)⋊Dic3—22no—
82Dic32—22no—
83#3718—22no—
84#3715—24no—
85#3713—22no—
86#3183—91noSylow
87C3×#125—32no—
88C3×#124—32no—
89#946—32no—
90Q8×Dic3—32no—
91C2×#216—32no—
92C2×#215—32no—
93#938—32no—
94D4×Dic3—32no—
95C2×#214—32no—
96C2×#213—32no—
97C2×ΓL(1,𝔽25)—32no—
98C2×ΓL(1,𝔽25)—32no—
99C2×ΓL(1,𝔽25)—61no—
100C2×ΓL(1,𝔽25)—61no—
101#898—62no—
102#897—32no—
103#895—32no—
104#894—62no—
105#893—32no—
106#893—62no—
107#892—62no—
108#887—32no—
109#883—62no—
110#67⋊C4—62no—
111#879—62no—
112#877—62no—
113#875C2×D312yes—
114C42×D3—32no—
115C42×D3—61no—
116#870C2×D312yes—
117C3×#103—32no—
118C3×#103—32no—
119C3×#102—32no—
120C3×#102—32no—
121C3×C4×C8—21no—
122C3×C4×C8C2×D312yes—
123#821C2×D312yes—
124#821C2×D312yes—
125#816C2×D312yes—
126#816C2×D312yes—
127#815—32no—
128#815—32no—
129#815—61no—
130#815—61no—
131#808—32no—
132#808—32no—
133#807—32no—
134#807—32no—
135C4×C3⋊C8—32no—
136C4×C3⋊C8—61no—
137C22×C3⋊D3C2×D411yescharacteristic
138C22×C3×D3—22no—
139C2×C32×C4C2×D412yes—
140C2×C32×C4C2411yescharacteristic
141C2×C3⋊Dic3C2×D412yes—
142C2×C3⋊Dic3C2×D411yescharacteristic
143C4×C3⋊D3—21no—
144C4×C3⋊D3—21no—
145C4×C3⋊D3—42no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—22no—
148C2×C3×Dic3—22no—
149C3×D12—22no—
150C3×D12—22no—
151C3×Dic6—22no—
152C3×Dic6—22no—
153#626—44no—
154D3×Dic3—44no—
155C32×C8—21no—
156C32×C8—21no—
157C3⋊(C3⋊C8)#4112yes—
158C3⋊(C3⋊C8)#4112yes—
159#529—92no—
160#499—91no—
161#495—91no—
162#488—32no—
163#470—91no—
164#469—91no—
165#468—92no—
166#442—91no—
167#441—91no—
168#440—92no—
169C4×M16—91no—
170C2×C3×Q8—32no—
171C2×C3×D4—32no—
172C2×#67—62no—
173C22×Dic3—62no—
174C2×D12—62no—
175C2×D12C22×D312yes—
176C2×C4×D3—32no—
177C2×C4×D3—32no—
178C2×C4×D3—32no—
179C2×C4×D3—61no—
180C2×C4×D3—62no—
181C2×C4×D3—62no—
182C2×Dic6C22×D312yes—
183C2×C3×C8—21no—
184C2×C3×C8—21no—
185C2×C3×C8C22×D312yes—
186C2×C3×C8C22×D312yes—
187C3×C4⋊C4—32no—
188C3×C4⋊C4—32no—
189C3×C4⋊C4—62no—
190C3×C4⋊C4—62no—
191C3×C22⋊C4—62no—
192C3×C22⋊C4—62no—
193C3×C42—21no—
194C3×C42C22×D312yes—
195#217—62no—
196#217—62no—
197#216—64no—
198#215—64no—
199#214—64no—
200#213—64no—
201(C2×D3)⋊C4—22no—
202(C2×D3)⋊C4—22no—
203(C2×D3)⋊C4—62no—
204(C2×D3)⋊C4—62no—
205(C2×D3)⋊C4—62no—
206(C2×D3)⋊C4—62no—
207C4⋊Dic3—62no—
208C4⋊Dic3—62no—
209C4⋊Dic3C22×D312yes—
210C4⋊Dic3C22×D312yes—
211Dic3⋊C4—22no—
212Dic3⋊C4—22no—
213Dic3⋊C4—62no—
214Dic3⋊C4—62no—
215C4×Dic3—32no—
216C4×Dic3—32no—
217C4×Dic3—32no—
218C4×Dic3—61no—
219C4×Dic3—62no—
220C4×Dic3—62no—
221C4×Dic3—62no—
222C2×C3⋊C8—32no—
223C2×C3⋊C8—32no—
224C2×C3⋊C8—61no—
225C2×C3⋊C8—61no—
226ΓL(1,𝔽25)—64no—
227ΓL(1,𝔽25)—64no—
228ΓL(1,𝔽25)—64no—
229ΓL(1,𝔽25)—64no—
230C22×C32C22×D411yescharacteristic
231C2×C3⋊D3—21no—
232C2×C3⋊D3—22no—
233C2×C3×D3—42no—
234C2×C3×D3—42no—
235C2×C3×D3—42no—
236C32×C4—22no—
237C32×C4C2×#4111yescharacteristic
238C32×C4C2×#4111yescharacteristic
239C3⋊Dic3—21no—
240C3⋊Dic3—22no—
241C3×Dic3—42no—
242C3×Dic3—42no—
243C3×Dic3—42no—
244C2×Q16—91no—
245C2×SD16—92no—
246C2×D8—91no—
247C2×M16—91no—
248C2×M16—91no—
249#126—182no—
250#125—32no—
251#124—32no—
252#123—182no—
253C22⋊Q8—92no—
254#121—92no—
255C4×Q8—92no—
256C4×D4—92no—
257C4×D4—182no—
258#117—182no—
259C2×C42—91no—
260#107—92no—
261#106—91no—
262#106—91no—
263#103—32no—
264#103—32no—
265#102—32no—
266#102—32no—
267#97—91no—
268#97—91no—
269C4×C8—91no—
270C4×C8D3211yescharacteristic
271C23×C3—62no—
272C22×D3—22no—
273C22×D3—32no—
274C22×D3—61no—
275C3×Q8—62no—
276C3×Q8—62no—
277C3×D4—62no—
278C3×D4—62no—
279C2×C3×C4—21no—
280C2×C3×C4—22no—
281C2×C3×C4—62no—
282C2×C3×C4—62no—
283C2×C3×C4—62no—
284C2×C3×C4D3×D412yes—
285C2×C3×C4D3×D412yes—
286C2×C3×C4C23×D312yes—
287#67—124no—
288C2×Dic3—22no—
289C2×Dic3—22no—
290C2×Dic3—22no—
291C2×Dic3—32no—
292C2×Dic3—32no—
293C2×Dic3—32no—
294C2×Dic3—61no—
295C2×Dic3—62no—
296C2×Dic3—124no—
297D12—22no—
298D12—22no—
299D12—124no—
300C4×D3—62no—
301C4×D3—62no—
302C4×D3—62no—
303C4×D3—62no—
304C4×D3—122no—
305C4×D3—122no—
306C4×D3—124no—
307C4×D3—124no—
308Dic6—22no—
309Dic6—22no—
310C3×C8—22no—
311C3×C8—22no—
312C3×C8—22no—
313C3×C8—22no—
314C3⋊C8—34no—
315C3⋊C8—34no—
316C3⋊C8—62no—
317C3⋊C8—62no—
318C2×C32#53211yescharacteristic
319C2×C32#57512yes—
320C3⋊D3—41no—
321C3×D3—82no—
322C2×Q8—32no—
323C2×D4—32no—
324C2×D4—182no—
325C22×C4—91no—
326C22×C4—92no—
327C22×C4—182no—
328Q16—182no—
329SD16—184no—
330D8—182no—
331M16—182no—
332M16—182no—
333C2×C8—91no—
334C2×C8—91no—
335C2×C8C2×D3211yescharacteristic
336C2×C8C2×D3211yescharacteristic
337C4⋊C4—32no—
338C4⋊C4—32no—
339C4⋊C4—62no—
340C4⋊C4—62no—
341C4⋊C4—182no—
342C4⋊C4—182no—
343C22⋊C4—62no—
344C22⋊C4—62no—
345C22⋊C4—182no—
346C22⋊C4—182no—
347C22⋊C4—182no—
348C42—91no—
349C42—92no—
350C42—182no—
351C42C2×D3211yescharacteristic
352C22×C3—21no—
353C22×C3—122no—
354C22×C3—122no—
355C22×C3—122no—
356C22×C3C2×D3×D412yes—
357C2×D3—42no—
358C2×D3—42no—
359C2×D3—42no—
360C2×D3—62no—
361C2×D3—62no—
362C2×D3—62no—
363C2×D3—62no—
364C2×D3—122no—
365C3×C4—24no—
366C3×C4—22no—
367C3×C4—22no—
368C3×C4—21no—
369C3×C4—21no—
370C3×C4—122no—
371C3×C4—122no—
372C3×C4—122no—
373C3×C4D3×#4112yes—
374C3×C4D3×#4112yes—
375Dic3—42no—
376Dic3—42no—
377Dic3—42no—
378Dic3—62no—
379Dic3—62no—
380Dic3—62no—
381Dic3—62no—
382Dic3—122no—
383C32#318311yescharacteristic, complemented, Sylow
384C23—62no—
385C23—91no—
386Q8—62no—
387Q8—62no—
388D4—62no—
389D4—62no—
390D4—364no—
391C2×C4—62no—
392C2×C4—62no—
393C2×C4—62no—
394C2×C4—92no—
395C2×C4—91no—
396C2×C4—181no—
397C2×C4—181no—
398C2×C4—362no—
399C2×C4—364no—
400C2×C4#380212yes—
401C2×C4C22×D3211yescharacteristic
402C8—21no—
403C8—21no—
404C8—92no—
405C8—92no—
406C2×C3—22no—
407C2×C3—21no—
408C2×C3—242no—
409C2×C3#566812yes—
410C2×C3#576812yes—
411C2×C3#576812yes—
412D3—82no—
413D3—122no—
414D3—122no—
415C22—122no—
416C22—122no—
417C22—122no—
418C22—182no—
419C22—181no—
420C22C2×#380211yescharacteristic
421C4—22no—
422C4—122no—
423C4—122no—
424C4—122no—
425C4—182no—
426C4—181no—
427C4#6430611yescharacteristic
428C4#6430611yescharacteristic
429C3—21no—
430C3#8163112yescomplemented
431C2—242no—
432C2—361no—
433C2#1059397111yescharacteristic
434C2#1059468512yes—
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radical#10590840C2
hypercenterC4×C8D32
hypocenterC32#3183
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
1. #10593943C2semidirect
2. C4×#3743C2semidirect
3. C3×#4697C2semidirect
4. #10590856C2semidirect
5. #10590842C2semidirect
7. #10590791C2semidirect
8. #10590743C2semidirect
9. #10590741C2semidirect
10. #10590353C2semidirect
11. #10590314C2semidirect
53. #4697D3semidirect
383. C32#3183semidirect
430. C3#81631semidirect

Maximal subgroups

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

subgroupindex
#105939432
C4×#37432
C3×#46972
#105908562
#105908422
#105908402
#105907912
#105907432
#105907412
#105903532
#105903142
#816313