Finite Group Databasebeta

← #11876902

Subgroups — #11876902

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
1#10594965C212yesmaximal, complemented
2M16×C3⋊Dic3C211yesmaximal, characteristic, complemented
3C3×#5134C212yesmaximal, complemented
4#10591189C211yesmaximal, characteristic, complemented
5#10591167C211yesmaximal, characteristic
6#10590875C211yesmaximal, characteristic, complemented
7#10590868C212yesmaximal, complemented
8#10590867C211yesmaximal, characteristic, complemented
9#10590791C211yesmaximal, characteristic, complemented
10#10590779C212yesmaximal, complemented
11#10590741C211yesmaximal, characteristic, complemented
12#80791—32nomaximal
13C2×C32×M16C2211yescharacteristic
14C2×C4×C3⋊Dic3C2211yescharacteristic
15C2×#3748C2211yescharacteristic
16C3×#930C2212yes—
17C3×#924C2212yes—
18C2×C3×#204C2212yes—
19#67⋊Dic3—22no—
20#63962—22no—
21#63898C2212yes—
22#63878—22no—
23#63872C2212yes—
24#63863C2212yes—
25#63862—22no—
26#63843C2212yes—
27C2×#3718C2211yescharacteristic
28C2×#3713C2211yescharacteristic
29#63642C2211yescharacteristic
30#63642C2211yescharacteristic
31C8×C3⋊Dic3C2211yescharacteristic
32C8×C3⋊Dic3C2211yescharacteristic
33C3×#821C2212yes—
34C3×#818C2212yes—
35C3×#816C2212yes—
36#63574C2211yescharacteristic
37#63574C2211yescharacteristic
38#63565C2212yes—
39#63562C2212yes—
40#5624—32no—
41#5600—32no—
42C3×#468—32no—
43#5168—32no—
44#5164—32no—
45#5134D312yescomplemented
46Dic3×M16—32no—
47Dic3×M16—61no—
48#5052—32no—
49#5039—32no—
50#4889—32no—
51#4878—32no—
52#4800—32no—
53#4789—32no—
54#4785—32no—
55#4768—32no—
56C22×C32×C4C2311yescharacteristic
57C22×C3⋊Dic3D412yes—
58C2×C3×#67—22no—
59C2×C3×D12C2312yes—
60C2×C3×Dic6C2312yes—
61C2×D3×Dic3—22no—
62C32×M16—22no—
63C2×C32×C8C2311yescharacteristic
64C2×C32×C8C2311yescharacteristic
65C4×C3⋊Dic3D412yes—
66C4×C3⋊Dic3C2311yescharacteristic
67C4×C3⋊Dic3C2311yescharacteristic
68#3748—22no—
69C2×C3⋊(C3⋊C8)C2311yescharacteristic
70C2×C3⋊(C3⋊C8)C2311yescharacteristic
71C3×#217—22no—
72C3×(C2×D3)⋊C4—22no—
73C3×C4⋊Dic3C2312yes—
74C3×C4⋊Dic3C2312yes—
75C3×Dic3⋊C4—22no—
76C3×#204—24no—
77Dic3⋊Dic3—22no—
78Dic3⋊Dic3—22no—
79Dic3⋊Dic3—22no—
80(C2×D3)⋊Dic3—22no—
81(C2×D3)⋊Dic3—22no—
82(C2×D3)⋊Dic3—22no—
83Dic32—22no—
84#3718—22no—
85#3713—22no—
86#3183—91noSylow
87C2×C3×SD16—32no—
88C2×C3×M16—21no—
89C2×C3×M16C2×D312yes—
90C3×C22⋊Q8—32no—
91C3×#121—32no—
92#947—32no—
93Q8×Dic3—32no—
94C2×#216—32no—
95#936—32no—
96#935—62no—
97D4×Dic3—32no—
98D4×Dic3—62no—
99C2×#213—32no—
100#930C2×D312yes—
101#924C2×D312yes—
102C2×C4×Dic3—32no—
103C2×C4×Dic3—61no—
104C2×#208—32no—
105C2×#208—61no—
106C2×#204C2×D312yes—
107#898—62no—
108#893—32no—
109#892—62no—
110#890—32no—
111#890—32no—
112#887—32no—
113#886—62no—
114#67⋊C4—62no—
115#879—62no—
116#877—62no—
117C3×#107—32no—
118C3×#103—32no—
119C3×#102—32no—
120#835—32no—
121#832—32no—
122#821C2×D312yes—
123#818C2×D312yes—
124#816C2×D312yes—
125#815—32no—
126#815—32no—
127#815—61no—
128#815—61no—
129C8×Dic3—32no—
130C8×Dic3—32no—
131C8×Dic3—61no—
132C8×Dic3—61no—
133#810—32no—
134#809—32no—
135#808—32no—
136#808—32no—
137C23×C32C2×D411yescharacteristic
138C22×C3×D3—22no—
139C2×C32×C4—21no—
140C2×C32×C4—21no—
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4C2411yescharacteristic
143C2×C3⋊Dic3—42no—
144C2×C3⋊Dic3C2×D412yes—
145C2×C3⋊Dic3C2×D412yes—
146C3×#67—44no—
147C2×C3×Dic3—22no—
148C2×C3×Dic3—22no—
149C2×C3×Dic3—22no—
150C3×D12—22no—
151C3×D12—22no—
152C3×Dic6—22no—
153C3×Dic6—22no—
154D3×Dic3—44no—
155C32×C8—21no—
156C32×C8#4112yes—
157C3⋊(C3⋊C8)—21no—
158C3⋊(C3⋊C8)#4112yes—
159#529—92no—
160#499—91no—
161#495—91no—
162#488—92no—
163#470—91no—
164#469—91no—
165#468—32no—
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—21no—
174C22×C3×C4C22×D312yes—
175C2×#67—22no—
176C22×Dic3—32no—
177C22×Dic3—32no—
178C22×Dic3—62no—
179C22×Dic3—62no—
180C2×D12C22×D312yes—
181C2×C4×D3—62no—
182C2×Dic6C22×D312yes—
183C3×SD16—64no—
184C3×M16—24no—
185C3×M16—24no—
186C2×C3×C8—21no—
187C2×C3×C8—21no—
188C2×C3×C8C22×D312yes—
189C2×C3×C8C22×D312yes—
190C3×C4⋊C4—32no—
191C3×C4⋊C4—32no—
192C3×C4⋊C4—62no—
193C3×C22⋊C4—62no—
194C3×C22⋊C4—62no—
195#217—22no—
196#217—62no—
197#217—62no—
198#217—62no—
199#216—64no—
200#213—64no—
201(C2×D3)⋊C4—22no—
202(C2×D3)⋊C4—62no—
203(C2×D3)⋊C4—62no—
204(C2×D3)⋊C4—62no—
205C4⋊Dic3—62no—
206C4⋊Dic3—62no—
207C4⋊Dic3—62no—
208C4⋊Dic3C22×D312yes—
209C4⋊Dic3C22×D312yes—
210Dic3⋊C4—22no—
211Dic3⋊C4—62no—
212Dic3⋊C4—62no—
213Dic3⋊C4—62no—
214C4×Dic3—32no—
215C4×Dic3—32no—
216C4×Dic3—32no—
217C4×Dic3—32no—
218C4×Dic3—61no—
219C4×Dic3—61no—
220C4×Dic3—62no—
221C4×Dic3—62no—
222C4×Dic3—62no—
223#208—64no—
224#208—64no—
225C2×C3⋊C8—32no—
226C2×C3⋊C8—32no—
227C2×C3⋊C8—61no—
228C2×C3⋊C8—61no—
229#204—24no—
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×C4C2×#4111yescharacteristic
238C32×C4C2×#4111yescharacteristic
239C3⋊Dic3—22no—
240C3⋊Dic3—22no—
241C3×Dic3—42no—
242C3×Dic3—42no—
243C3×Dic3—42no—
244C2×Q16—91no—
245C2×SD16—32no—
246C2×D8—91no—
247C2×M16—91no—
248C2×M16D3211yescharacteristic
249#126—182no—
250#125—92no—
251#124—92no—
252#123—182no—
253C22⋊Q8—32no—
254#121—32no—
255C4×Q8—92no—
256C4×D4—92no—
257C4×D4—182no—
258#117—182no—
259C2×C42—91no—
260#107—32no—
261#106—91no—
262#106—91no—
263#103—32no—
264#103—92no—
265#102—32no—
266#102—92no—
267#97—91no—
268#97—91no—
269C4×C8—91no—
270C4×C8—91no—
271C23×C3—21no—
272C23×C3—62no—
273C23×C3D3×D412yes—
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—62no—
287C2×C3×C4—62no—
288C2×C3×C4—62no—
289C2×C3×C4D3×D412yes—
290C2×C3×C4C23×D312yes—
291#67—44no—
292C2×Dic3—22no—
293C2×Dic3—22no—
294C2×Dic3—22no—
295C2×Dic3—32no—
296C2×Dic3—32no—
297C2×Dic3—32no—
298C2×Dic3—32no—
299C2×Dic3—62no—
300C2×Dic3—62no—
301C2×Dic3—124no—
302C2×Dic3—122no—
303C2×Dic3—122no—
304C2×Dic3—124no—
305D12—22no—
306D12—22no—
307C4×D3—124no—
308Dic6—22no—
309Dic6—22no—
310C3×C8—22no—
311C3×C8—22no—
312C3×C8—22no—
313C3×C8#23714yes—
314C3⋊C8—34no—
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—92no—
326C22×C4—182no—
327C22×C4C2×D3211yescharacteristic
328Q16—182no—
329SD16—64no—
330D8—182no—
331M16—22no—
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—182no—
341C4⋊C4—182no—
342C4⋊C4—182no—
343C22⋊C4—62no—
344C22⋊C4—62no—
345C22⋊C4—182no—
346C22⋊C4—182no—
347C22⋊C4—182no—
348C42—91no—
349C42—91no—
350C42—92no—
351C42—182no—
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×C3C2×D3×D412yes—
362C2×D3—42no—
363C2×D3—42no—
364C2×D3—42no—
365C3×C4—22no—
366C3×C4—22no—
367C3×C4—21no—
368C3×C4—21no—
369C3×C4—122no—
370C3×C4—122no—
371C3×C4—122no—
372C3×C4C2×#23712yes—
373C3×C4D3×#4112yes—
374Dic3—42no—
375Dic3—42no—
376Dic3—42no—
377Dic3—64no—
378Dic3—62no—
379Dic3—62no—
380Dic3—62no—
381Dic3—62no—
382Dic3—122no—
383C32#318311yescharacteristic, complemented, Sylow
384C23—62no—
385C23#380211yescharacteristic
386Q8—62no—
387Q8—62no—
388D4—62no—
389D4—62no—
390D4—124no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—62no—
394C2×C4—62no—
395C2×C4—62no—
396C2×C4—92no—
397C2×C4—92no—
398C2×C4—364no—
399C2×C4—362no—
400C2×C4#380211yescharacteristic
401C2×C4C22×D3211yescharacteristic
402C8—21no—
403C8—92no—
404C8—181no—
405C8#380512yes—
406C2×C3—21no—
407C2×C3—22no—
408C2×C3—42no—
409C2×C3—42no—
410C2×C3—242no—
411C2×C3#559612yes—
412C2×C3#577312yes—
413C2×C3#577712yes—
414D3—82no—
415C22—21no—
416C22—22no—
417C22—122no—
418C22—122no—
419C22—122no—
420C22C2×#380211yescharacteristic
421C4—21no—
422C4—122no—
423C4—122no—
424C4—122no—
425C4—182no—
426C4—182no—
427C4#6430611yescharacteristic
428C4C2×#380511yescharacteristic
429C3—21no—
430C3#8079112yescomplemented
431C2—41no—
432C2—242no—
433C2#1059471812yes—
434C2#1059492911yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
prime radical#10591167C2
hypercenterC2×M16D32
hypocenterC32#3183
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. #10594965C2semidirect
2. M16×C3⋊Dic3C2semidirect
3. C3×#5134C2semidirect
4. #10591189C2semidirect
6. #10590875C2semidirect
7. #10590868C2semidirect
8. #10590867C2semidirect
9. #10590791C2semidirect
10. #10590779C2semidirect
11. #10590741C2semidirect
45. #5134D3semidirect
383. C32#3183semidirect
430. C3#80791semidirect

Maximal subgroups

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

subgroupindex
#105949652
M16×C3⋊Dic32
C3×#51342
#105911892
#105911672
#105908752
#105908682
#105908672
#105907912
#105907792
#105907412
#807913