Finite Group Databasebeta

← #11876913

Subgroups — #11876913

Order 1152.

811 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5479C212yesmaximal, complemented
2C4×#3748C211yesmaximal, characteristic, complemented
3#10591189C211yesmaximal, characteristic, complemented
4#10591180C212yesmaximal, complemented
5#10591167C211yesmaximal, characteristic
6#10590381C211yesmaximal, characteristic, complemented
7#10590358C212yesmaximal, complemented
8#10590353C211yesmaximal, characteristic, complemented
9#10590344C211yesmaximal, characteristic, complemented
10#10590314C211yesmaximal, characteristic, complemented
11#10590278C212yesmaximal, complemented
12#83139—32nomaximal
13C2×C32×C42C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15C2×#3748C2211yescharacteristic
16C3×#930C2212yes—
17C3×#929—22no—
18C3×C4×#67—22no—
19C3×#924C2212yes—
20C3×#876—22no—
21C3×#875C2212yes—
22C3×C4×D12C2212yes—
23C3×#872—22no—
24C3×#870C2212yes—
25C3×C4×Dic6C2212yes—
26C2×#3718C2211yescharacteristic
27C2×#3715C2212yes—
28C2×#3713C2211yescharacteristic
29#63630C2211yescharacteristic
30#63630C2211yescharacteristic
31C4×C3⋊(C3⋊C8)C2211yescharacteristic
32C4×C3⋊(C3⋊C8)C2211yescharacteristic
33#63576C2212yes—
34#63574C2211yescharacteristic
35#63574C2211yescharacteristic
36#63565C2212yes—
37#63565C2212yes—
38#63562C2212yes—
39#63562C2212yes—
40C3×#529—32no—
41#5479D312yescomplemented
42#5068—32no—
43#5065—32no—
44#5059—32no—
45#5056—32no—
46#5052—32no—
47#5049—32no—
48#5042—32no—
49#5039—32no—
50#5030—32no—
51#5026—32no—
52#5018—32no—
53#5014—32no—
54C4×#208—32no—
55C4×#208—61no—
56C22×C32×C4D412yes—
57C22×C32×C4C2311yescharacteristic
58C2×C3×#67—22no—
59C2×C3×D12C2312yes—
60C2×C3×C4×D3—22no—
61C2×C3×Dic6C2312yes—
62C32×C42D412yes—
63C32×C42C2311yescharacteristic
64C32×C42C2311yescharacteristic
65#3748—22no—
66#3748—22no—
67C2×C3⋊(C3⋊C8)C2311yescharacteristic
68C2×C3⋊(C3⋊C8)C2311yescharacteristic
69C2×C3⋊(C3⋊C8)C2311yescharacteristic
70C2×C3⋊(C3⋊C8)C2311yescharacteristic
71C3×#217—22no—
72C3×(C2×D3)⋊C4—22no—
73C3×(C2×D3)⋊C4—22no—
74C3×(C2×D3)⋊C4—22no—
75C3×(C2×D3)⋊C4—22no—
76C3×C4⋊Dic3C2312yes—
77C3×C4⋊Dic3C2312yes—
78C3×Dic3⋊C4—22no—
79C3×Dic3⋊C4—22no—
80C3×Dic3⋊C4—22no—
81C3×Dic3⋊C4—22no—
82C3×C4×Dic3—22no—
83#3718—22no—
84#3715—24no—
85#3713—22no—
86#3183—91noSylow
87C3×#126—62no—
88C3×#125—32no—
89C3×#124—32no—
90C3×#123—62no—
91C3×C22⋊Q8—32no—
92C3×#121—32no—
93C3×C4×Q8—32no—
94C3×C4×D4—32no—
95C3×C4×D4—62no—
96C3×#117—62no—
97C2×C3×C42—21no—
98C2×C3×C42C2×D312yes—
99C2×#216—32no—
100C2×#215—32no—
101C2×#214—32no—
102C2×#213—32no—
103#930C2×D312yes—
104#929—22no—
105C4×#67—22no—
106#924C2×D312yes—
107C2×#208—32no—
108C2×#208—32no—
109C2×#208—61no—
110C2×#208—61no—
111#876—22no—
112#875C2×D312yes—
113C4×D12C2×D312yes—
114#872—22no—
115#870C2×D312yes—
116C4×Dic6C2×D312yes—
117#835—32no—
118#835—32no—
119#832—32no—
120#832—32no—
121#810—32no—
122#810—32no—
123#809—32no—
124#809—32no—
125#808—32no—
126#808—32no—
127#807—32no—
128#807—32no—
129#803—32no—
130#803—32no—
131#803—61no—
132#803—61no—
133C4×C3⋊C8—32no—
134C4×C3⋊C8—32no—
135C4×C3⋊C8—61no—
136C4×C3⋊C8—61no—
137C23×C32C2×D411yescharacteristic
138C22×C3×D3—22no—
139C2×C32×C4—21no—
140C2×C32×C4—21no—
141C2×C32×C4—42no—
142C2×C32×C4C2×D412yes—
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4C2×D412yes—
145C2×C32×C4C2411yescharacteristic
146C3×#67—44no—
147C2×C3×Dic3—22no—
148C2×C3×Dic3—22no—
149C2×C3×Dic3—22no—
150C3×D12—22no—
151C3×D12—22no—
152C3×C4×D3—44no—
153C3×Dic6—22no—
154C3×Dic6—22no—
155C3⋊(C3⋊C8)—21no—
156C3⋊(C3⋊C8)—21no—
157C3⋊(C3⋊C8)#4112yes—
158C3⋊(C3⋊C8)#4112yes—
159#529—32no—
160#499—91no—
161#495—91no—
162#488—92no—
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×C3×D4—62no—
173C22×C3×C4—22no—
174C22×C3×C4—21no—
175C22×C3×C4—62no—
176C22×C3×C4#6712yes—
177C22×C3×C4#6712yes—
178C22×C3×C4C22×D312yes—
179C2×#67—22no—
180C2×D12C22×D312yes—
181C2×C4×D3—22no—
182C2×Dic6C22×D312yes—
183C3×C4⋊C4—32no—
184C3×C4⋊C4—32no—
185C3×C4⋊C4—62no—
186C3×C4⋊C4—62no—
187C3×C4⋊C4—62no—
188C3×C4⋊C4—62no—
189C3×C22⋊C4—62no—
190C3×C22⋊C4—62no—
191C3×C22⋊C4—62no—
192C3×C22⋊C4—62no—
193C3×C22⋊C4—62no—
194C3×C42—22no—
195C3×C42—21no—
196C3×C42—21no—
197C3×C42—62no—
198C3×C42#6712yes—
199C3×C42#6712yes—
200C3×C42C22×D312yes—
201C3×C42C22×D312yes—
202#217—22no—
203#216—64no—
204#215—64no—
205#214—64no—
206#213—64no—
207(C2×D3)⋊C4—22no—
208(C2×D3)⋊C4—22no—
209(C2×D3)⋊C4—22no—
210(C2×D3)⋊C4—22no—
211C4⋊Dic3C22×D312yes—
212C4⋊Dic3C22×D312yes—
213Dic3⋊C4—22no—
214Dic3⋊C4—22no—
215Dic3⋊C4—22no—
216Dic3⋊C4—22no—
217C4×Dic3—22no—
218#208—64no—
219#208—64no—
220#208—64no—
221#208—64no—
222C2×C3⋊C8—32no—
223C2×C3⋊C8—32no—
224C2×C3⋊C8—32no—
225C2×C3⋊C8—32no—
226C2×C3⋊C8—61no—
227C2×C3⋊C8—61no—
228C2×C3⋊C8—61no—
229C2×C3⋊C8—61no—
230C22×C32—21no—
231C22×C32—22no—
232C22×C32C22×D411yescharacteristic
233C2×C3×D3—42no—
234C2×C3×D3—42no—
235C2×C3×D3—42no—
236C32×C4—21no—
237C32×C4—22no—
238C32×C4—22no—
239C32×C4C2×#4111yescharacteristic
240C32×C4C2×#4111yescharacteristic
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—62no—
250#125—32no—
251#124—32no—
252#123—62no—
253C22⋊Q8—32no—
254#121—32no—
255C4×Q8—32no—
256C4×D4—32no—
257C4×D4—62no—
258#117—62no—
259C2×C42D3211yescharacteristic
260#107—92no—
261#106—91no—
262#106—91no—
263#103—92no—
264#103—92no—
265#102—92no—
266#102—92no—
267#97—91no—
268#97—91no—
269C4×C8—91no—
270C4×C8—91no—
271C23×C3—21no—
272C23×C3—62no—
273C23×C3C2×#6712yes—
274C22×D3—22no—
275C3×Q8—62no—
276C3×Q8—62no—
277C3×D4—62no—
278C3×D4—62no—
279C3×D4—124no—
280C2×C3×C4—22no—
281C2×C3×C4—22no—
282C2×C3×C4—22no—
283C2×C3×C4—22no—
284C2×C3×C4—21no—
285C2×C3×C4—21no—
286C2×C3×C4—22no—
287C2×C3×C4—22no—
288C2×C3×C4—42no—
289C2×C3×C4—42no—
290C2×C3×C4—44no—
291C2×C3×C4—62no—
292C2×C3×C4—62no—
293C2×C3×C4—62no—
294C2×C3×C4—124no—
295C2×C3×C4C2×#6712yes—
296C2×C3×C4C2×#6712yes—
297C2×C3×C4C2×#6712yes—
298C2×C3×C4C2×#6712yes—
299C2×C3×C4C2×#6712yes—
300C2×C3×C4C23×D312yes—
301#67—44no—
302C2×Dic3—22no—
303C2×Dic3—22no—
304C2×Dic3—22no—
305D12—22no—
306D12—22no—
307C4×D3—44no—
308Dic6—22no—
309Dic6—22no—
310C3⋊C8—34no—
311C3⋊C8—34no—
312C3⋊C8—62no—
313C3⋊C8—62no—
314C3⋊C8—62no—
315C3⋊C8—62no—
316C3⋊C8—62no—
317C3⋊C8—62no—
318C2×C32—41no—
319C2×C32#53211yescharacteristic
320C2×C32#57512yes—
321C3×D3—82no—
322C2×Q8—32no—
323C2×D4—32no—
324C2×D4—62no—
325C22×C4—62no—
326C22×C4#62512yes—
327C22×C4C2×D3211yescharacteristic
328Q16—182no—
329SD16—184no—
330D8—182no—
331M16—182no—
332M16—182no—
333C2×C8—91no—
334C2×C8—91no—
335C2×C8—91no—
336C2×C8—91no—
337C4⋊C4—32no—
338C4⋊C4—32no—
339C4⋊C4—62no—
340C4⋊C4—62no—
341C4⋊C4—62no—
342C4⋊C4—62no—
343C22⋊C4—62no—
344C22⋊C4—62no—
345C22⋊C4—62no—
346C22⋊C4—62no—
347C22⋊C4—62no—
348C42—62no—
349C42#62512yes—
350C42C2×D3211yescharacteristic
351C42C2×D3211yescharacteristic
352C22×C3—22no—
353C22×C3—22no—
354C22×C3—22no—
355C22×C3—22no—
356C22×C3—21no—
357C22×C3—42no—
358C22×C3—122no—
359C22×C3—122no—
360C22×C3—122no—
361C22×C3C22×#6712yes—
362C2×D3—42no—
363C2×D3—42no—
364C2×D3—42no—
365C3×C4—22no—
366C3×C4—24no—
367C3×C4—22no—
368C3×C4—22no—
369C3×C4—22no—
370C3×C4—22no—
371C3×C4—22no—
372C3×C4—21no—
373C3×C4—21no—
374C3×C4—42no—
375C3×C4—122no—
376C3×C4—122no—
377C3×C4—122no—
378C3×C4D3×#4112yes—
379C3×C4D3×#4112yes—
380Dic3—42no—
381Dic3—42no—
382Dic3—42no—
383C32#318311yescharacteristic, complemented, Sylow
384C23—62no—
385C23C2×#62511yescharacteristic
386Q8—62no—
387Q8—62no—
388D4—62no—
389D4—62no—
390D4—124no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—42no—
394C2×C4—62no—
395C2×C4—62no—
396C2×C4—62no—
397C2×C4—124no—
398C2×C4C2×#62512yes—
399C2×C4C2×#62511yescharacteristic
400C2×C4C2×#62512yes—
401C2×C4C22×D3211yescharacteristic
402C8—92no—
403C8—92no—
404C8—181no—
405C8—181no—
406C2×C3—21no—
407C2×C3—22no—
408C2×C3—42no—
409C2×C3—42no—
410C2×C3—242no—
411C2×C3#582212yes—
412C2×C3#582212yes—
413C2×C3#583212yes—
414D3—82no—
415C22—21no—
416C22—22no—
417C22—122no—
418C22—122no—
419C22—122no—
420C22C22×#62511yescharacteristic
421C4—21no—
422C4—22no—
423C4—22no—
424C4—122no—
425C4—122no—
426C4—122no—
427C4#6430611yescharacteristic
428C4#6430611yescharacteristic
429C3—21no—
430C3#8313912yescomplemented
431C2—41no—
432C2—242no—
433C2#1059478612yes—
434C2#1059503211yescharacteristic
subgroupG/H
centerC22C22×#625
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C42C22
socleC22×C32C22×D4
prime radical#10591167C2
hypercenterC2×C42D32
hypocenterC32#3183
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C3×#5479C2semidirect
2. C4×#3748C2semidirect
3. #10591189C2semidirect
4. #10591180C2semidirect
6. #10590381C2semidirect
7. #10590358C2semidirect
8. #10590353C2semidirect
9. #10590344C2semidirect
10. #10590314C2semidirect
11. #10590278C2semidirect
41. #5479D3semidirect
383. C32#3183semidirect
430. C3#83139semidirect

Maximal subgroups

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

subgroupindex
C3×#54792
C4×#37482
#105911892
#105911802
#105911672
#105903812
#105903582
#105903532
#105903442
#105903142
#105902782
#831393