Finite Group Databasebeta

← #11865078

Subgroups — #11865078

Order 1152.

2094 conjugacy classes of subgroups; only the 301 normal subgroups are shown.

normal subgroups only

This group has 2094 conjugacy classes of subgroups — too many to draw. Only its 301 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
1C2×#64364C211yesmaximal, characteristic, complemented
2C32×#536C211yesmaximal, characteristic, complemented
3#10596293C212yesmaximal, complemented
4C2×#63663C211yesmaximal, characteristic, complemented
5#10592794C214yesmaximal, complemented
6#10592761C214yesmaximal, complemented
7#10592704C212yesmaximal, complemented
8#83415—34nomaximal
9C2×C32×#41C2211yescharacteristic
10C22×C32×Q8C2211yescharacteristic
11#64364—22no—
12#64364—24no—
13#64364C2214yes—
14C2×#3832—22no—
15C2×Q8×C3⋊D3—22no—
16C2×#3828—22no—
17C2×#3828C2212yes—
18C32×C4⋊Q8C2212yescomplemented
19C32×#124C2212yescomplemented
20C32×#123—22no—
21C32×C22⋊Q8—22no—
22C32×#117C2211yescharacteristic
23#64160—22no—
24#64159—24no—
25#64158—22no—
26#64151C2214yescomplemented
27#64141C2214yescomplemented
28C2×#3748C2212yes—
29#63663C2214yescomplemented
30#63632C2218yescomplemented
31C2×#1007—34no—
32C3×#536D314yescomplemented
33#5822—38no—
34C2×#836—34no—
35#5095—316no—
36#5062—316no—
37#5005—38no—
38C32×#41—22no—
39C32×#41—22no—
40C2×C32×Q8—22no—
41C2×C32×Q8—22no—
42C2×C32×Q8D412yes—
43C2×C32×Q8C2311yescharacteristic
44C2×C32×Q8C2312yes—
45C2×C32×D4—21no—
46C2×C32×D4C2311yescharacteristic
47C22×C32×C4—21no—
48C22×C32×C4D412yes—
49C22×C32×C4C2311yescharacteristic
50C2×#638—22no—
51#3832—28no—
52#3832—28no—
53Q8×C3⋊D3—28no—
54Q8×C3⋊D3—28no—
55#3828—28no—
56#3828—28no—
57#3828—22no—
58#3828—22no—
59#3828D414yes—
60#3828C2314yes—
61C2×C4⋊(C3⋊D3)—22no—
62C2×C4⋊(C3⋊D3)D412yes—
63C2×C4×C3⋊D3—24no—
64C2×C4×C3⋊D3—22no—
65C2×#634—22no—
66C2×#634D412yes—
67C32×C4⋊C4—21no—
68C32×C4⋊C4—24no—
69C32×C22⋊C4—21no—
70C32×C22⋊C4—24no—
71C32×C42C2312yes—
72#3756—24no—
73#3755—24no—
74#3754—24no—
75#3753—24no—
76#3748—22no—
77#3748C2314yes—
78C2×C3⋊(C3⋊C8)—22no—
79#3020—91noSylow
80C2×C3×#41C2×D314yes—
81C22×C3×Q8C2×D314yes—
82#1007—316no—
83#1007—616no—
84#1007—68no—
85C2×#239—68no—
86C2×D3×Q8—68no—
87C2×#235—38no—
88C2×#235—68no—
89C3×C4⋊Q8C2×D318yescomplemented
90C3×#124C2×D318yescomplemented
91C3×#123—28no—
92C3×C22⋊Q8—28no—
93C3×#117C2×D314yes—
94#951—68no—
95#950—616no—
96#949—68no—
97#942—316no—
98#932—316no—
99C2×#208—38no—
100#836—316no—
101#805—332no—
102C23×C32—21no—
103C23×C32C2×D411yescharacteristic
104C22×C3⋊D3—22no—
105C32×Q8—24no—
106C32×Q8—24no—
107C32×Q8—22no—
108C32×D4—22no—
109C32×D4—41no—
110C32×D4—41no—
111C2×C32×C4—22no—
112C2×C32×C4—22no—
113C2×C32×C4—22no—
114C2×C32×C4—21no—
115C2×C32×C4—42no—
116C2×C32×C4C2×D412yes—
117C2×C32×C4C2×D412yes—
118C2×C32×C4C2×D414yes—
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2411yescharacteristic
121#638—24no—
122#638—24no—
123C2×C3⋊Dic3—22no—
124C4⋊(C3⋊D3)—28no—
125C4⋊(C3⋊D3)—22no—
126C4⋊(C3⋊D3)C2×D414yes—
127C4×C3⋊D3—216no—
128C4×C3⋊D3—24no—
129C4×C3⋊D3—24no—
130#634—28no—
131#634—22no—
132#634C2×D414yes—
133C3⋊(C3⋊C8)—24no—
134C2×2−1+4—91no—
135#575—92no—
136#536C3⋊D311yescharacteristic, complemented
137#456—94no—
138#454—94no—
139#421—92no—
140C2×#101—91no—
141C3×#41—28no—
142C3×#41—28no—
143C2×C3×Q8—28no—
144C2×C3×Q8—28no—
145C2×C3×Q8#6718yes—
146C2×C3×Q8C22×D314yes—
147C2×C3×Q8C22×D318yes—
148C2×C3×D4—24no—
149C2×C3×D4C22×D314yes—
150C22×C3×C4—24no—
151C22×C3×C4#6718yes—
152C22×C3×C4C22×D314yes—
153C2×#67—68no—
154#239—632no—
155#239—632no—
156D3×Q8—632no—
157D3×Q8—632no—
158#235—316no—
159#235—316no—
160#235—632no—
161#235—68no—
162#235—68no—
163#235—632no—
164C2×D12—38no—
165C2×D12—68no—
166C2×C4×D3—616no—
167C2×C4×D3—68no—
168C2×Dic6—38no—
169C2×Dic6—68no—
170C3×C4⋊C4—24no—
171C3×C4⋊C4—216no—
172C3×C22⋊C4—24no—
173C3×C22⋊C4—216no—
174C3×C42C22×D318yes—
175#216—616no—
176#215—616no—
177#214—616no—
178#213—616no—
179#208—316no—
180#208—68no—
181C2×C3⋊C8—68no—
182C22×C32—41no—
183C22×C32—42no—
184C22×C32—41no—
185C22×C32#12011yescharacteristic
186C22×C32#12011yescharacteristic
187C22×C32C22×D411yescharacteristic
188C2×C3⋊D3—24no—
189C2×C3⋊D3—44no—
190C32×C4—24no—
191C32×C4—42no—
192C32×C4—41no—
193C32×C4#12012yes—
194C32×C4C22×D412yes—
195C3⋊Dic3—24no—
1962−1+4—94no—
1972−1+4—184no—
1982−1+4—182no—
199C2×#41—92no—
200C2×#41—182no—
201C2×#41—182no—
202C2×#41C2×C3⋊D311yescharacteristic
203C22×Q8—182no—
204C22×Q8C2×C3⋊D311yescharacteristic
205#137—94no—
206#137—182no—
207AGL(1,ℤ/8)—94no—
208AGL(1,ℤ/8)—182no—
209#135—184no—
210C2×M16—92no—
211C4⋊Q8C2×C3⋊D312yescomplemented
212#124C2×C3⋊D312yescomplemented
213#123—22no—
214C22⋊Q8—22no—
215#117C2×C3⋊D311yescharacteristic
216#104—98no—
217#101—94no—
218C23×C3—24no—
219C23×C3C2×#6714yes—
220C22×D3—68no—
221C3×Q8—216no—
222C3×Q8—216no—
223C3×Q8—28no—
224C3×D4—28no—
225C3×D4—44no—
226C3×D4—44no—
227C2×C3×C4—28no—
228C2×C3×C4—28no—
229C2×C3×C4—28no—
230C2×C3×C4—24no—
231C2×C3×C4—48no—
232C2×C3×C4D3×D418yes—
233C2×C3×C4D3×D418yes—
234C2×C3×C4C2×#67116yes—
235C2×C3×C4C2×#6714yes—
236C2×C3×C4C23×D314yes—
237#67—616no—
238#67—616no—
239C2×Dic3—68no—
240D12—316no—
241D12—632no—
242D12—68no—
243C4×D3—664no—
244C4×D3—616no—
245C4×D3—616no—
246Dic6—316no—
247Dic6—632no—
248Dic6—68no—
249C3⋊C8—616no—
250C2×C32—21no—
251C2×C32—21no—
252C2×C32—21no—
253C2×C32—81no—
254C2×C32C2×#12011yescharacteristic
255C3⋊D3—44no—
256#41—22no—
257#41—22no—
258#41—94no—
259#41—94no—
260#41—188no—
261#41—188no—
262#41—188no—
263#41—182no—
264#41—182no—
265#41—188no—
266C2×Q8—22no—
267C2×Q8—22no—
268C2×Q8—92no—
269C2×Q8—182no—
270C2×Q8—188no—
271C2×Q8—188no—
272C2×Q8#63812yes—
273C2×Q8C22×C3⋊D311yescharacteristic
274C2×Q8C22×C3⋊D312yes—
275C2×D4—21no—
276C2×D4—92no—
277C2×D4—182no—
278C2×D4—182no—
279C2×D4C22×C3⋊D311yescharacteristic
280C22×C4—21no—
281C22×C4—184no—
282C22×C4—182no—
283C22×C4#63812yes—
284C22×C4C22×C3⋊D311yescharacteristic
285Q16—184no—
286SD16—184no—
287SD16—184no—
288D8—184no—
289M16—94no—
290M16—182no—
291C2×C8—182no—
292C4⋊C4—21no—
293C4⋊C4—24no—
294C22⋊C4—21no—
295C22⋊C4—24no—
296C42C22×C3⋊D312yes—
297C22×C3—44no—
298C22×C3—48no—
299C22×C3—44no—
300C22×C3#93714yes—
301C22×C3#93714yes—
302C22×C3C22×#6714yes—
303C2×D3—616no—
304C2×D3—1216no—
305C3×C4—216no—
306C3×C4—48no—
307C3×C4—44no—
308C3×C4#93718yes—
309C3×C4C2×D3×D418yes—
310Dic3—616no—
311C32#302011yescharacteristic, complemented, Sylow
312C23—21no—
313C23—182no—
314C23C2×#63811yescharacteristic
315Q8—24no—
316Q8—24no—
317Q8—22no—
318Q8—94no—
319Q8—188no—
320Q8—182no—
321D4—22no—
322D4—41no—
323D4—41no—
324D4—94no—
325D4—188no—
326D4—184no—
327D4—184no—
328D4—182no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—21no—
333C2×C4—42no—
334C2×C4—1816no—
335C2×C4—182no—
336C2×C4—184no—
337C2×C4—184no—
338C2×C4D4×C3⋊D312yes—
339C2×C4D4×C3⋊D312yes—
340C2×C4C2×#63814yes—
341C2×C4C2×#63811yescharacteristic
342C2×C4C23×C3⋊D311yescharacteristic
343C8—184no—
344C2×C3—24no—
345C2×C3—24no—
346C2×C3—24no—
347C2×C3—84no—
348C2×C3C2×#93714yes—
349D3—1216no—
350C22—41no—
351C22—42no—
352C22—41no—
353C22—184no—
354C22—364no—
355C22#6414611yescharacteristic
356C22#6414611yescharacteristic
357C22C22×#63811yescharacteristic
358C4—24no—
359C4—42no—
360C4—41no—
361C4—184no—
362C4#6414612yes—
363C4C2×D4×C3⋊D312yes—
364C3#8341514yescomplemented
365C2—21no—
366C2—21no—
367C2—21no—
368C2—81no—
369C2—364no—
370C2C2×#6414611yescharacteristic
subgroupG/H
centerC2C2×#64146
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#536C2
socleC2×C32C2×#120
hypercenter#536C3⋊D3
hypocenterC32#3020
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ #536

Complements

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

NH ≅ G/Ntype
1. C2×#64364C2semidirect
2. C32×#536C2semidirect
3. #10596293C2semidirect
4. C2×#63663C2semidirect
5. #10592794C2semidirect
6. #10592761C2semidirect
7. #10592704C2semidirect
18. C32×C4⋊Q8C22semidirect
19. C32×#124C22semidirect
26. #64151C22semidirect
27. #64141C22semidirect
29. #63663C22semidirect
30. #63632C22semidirect
32. C3×#536D3semidirect
89. C3×C4⋊Q8C2×D3semidirect
90. C3×#124C2×D3semidirect
136. #536C3⋊D3semidirect
211. C4⋊Q8C2×C3⋊D3semidirect
212. #124C2×C3⋊D3semidirect
311. C32#3020semidirect
364. C3#83415semidirect

Maximal subgroups

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

subgroupindex
C2×#643642
C32×#5362
#105962932
C2×#636632
#105927942
#105927612
#105927042
#834153