Finite Group Databasebeta

← #11793942

Subgroups — #11793942

Order 1152.

786 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 786 conjugacy classes of subgroups — too many to draw. Only its 167 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×#64118C211yesmaximal, characteristic
2C2×#63651C211yesmaximal, characteristic, complemented
3#10592828C211yesmaximal, characteristic
4C2×#63649C211yesmaximal, characteristic, complemented
5C2×#63637C211yesmaximal, characteristic, complemented
6#10592665C211yesmaximal, characteristic
7C32×#343C211yesmaximal, characteristic, complemented
8#68987—34nomaximal
9C2×#3828C2211yescharacteristic
10C22×#634C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15C22×C3⋊(C3⋊C8)C2211yescharacteristic
16#64118—22no—
17#64118—22no—
18C2×#3746—21no—
19C2×#3744—21no—
20#63651—22no—
21#63649—22no—
22#63647—22no—
23#63637—21no—
24#63637—22no—
25#63636—21no—
26C2×#909—34no—
27C2×#824—34no—
28#5129—34no—
29C2×#822—34no—
30C2×#810—34no—
31#4966—34no—
32C3×#343D314yescomplemented
33C22×C32×C4—21no—
34C22×C32×C4C2311yescharacteristic
35C2×#638—21no—
36C22×C3⋊Dic3—21no—
37#3828—21no—
38#3828—21no—
39#3828—21no—
40#3828—21no—
41C2×C4⋊(C3⋊D3)D411yescharacteristic
42C2×C4×C3⋊D3—21no—
43C2×#634—21no—
44C2×#634—21no—
45C2×#634—21no—
46C2×#634—21no—
47C2×#634—21no—
48C2×#634D412yes—
49C2×#634D411yescharacteristic
50C32×M16—21no—
51C32×M16—21no—
52C32×M16—21no—
53C32×M16D412yes—
54C2×C32×C8—21no—
55C2×C32×C8—21no—
56C32×C4⋊C4—21no—
57C32×C4⋊C4—21no—
58#3748—21no—
59#3748—21no—
60C2×C3⋊(C3⋊C8)—21no—
61C2×C3⋊(C3⋊C8)—21no—
62C2×C3⋊(C3⋊C8)—21no—
63C2×C3⋊(C3⋊C8)D412yes—
64#3746—24no—
65#3744—24no—
66#2052—91noSylow
67C2×#235—34no—
68C22×Dic6—34no—
69C2×C3×M16C2×D314yes—
70C2×C3×M16C2×D314yes—
71C2×C3×C4⋊C4C2×D314yes—
72C2×#208—34no—
73C22×C3⋊C8—34no—
74#909—68no—
75#909—68no—
76C2×Dic12—64no—
77C2×#204—64no—
78#824—68no—
79#822—68no—
80(C2×D3)⋊C8—68no—
81#810—68no—
82#810—64no—
83#809—64no—
84C23×C32#4111yescharacteristic
85C22×C3⋊D3—21no—
86C2×C32×C4—41no—
87C2×C32×C4—81no—
88C2×C32×C4C2×D411yescharacteristic
89C2×C32×C4C2×D411yescharacteristic
90C2×C32×C4C2×D411yescharacteristic
91C2×C32×C4C2×D411yescharacteristic
92C2×C32×C4#4111yescharacteristic
93C2×C32×C4#4111yescharacteristic
94#638—41no—
95#638—41no—
96C2×C3⋊Dic3—21no—
97C2×C3⋊Dic3—22no—
98C2×C3⋊Dic3—41no—
99C2×C3⋊Dic3—41no—
100C4⋊(C3⋊D3)—21no—
101C4⋊(C3⋊D3)—21no—
102C4×C3⋊D3—41no—
103C4×C3⋊D3—41no—
104#634—22no—
105#634—21no—
106#634—22no—
107#634—21no—
108#634—41no—
109#634—41no—
110C32×C8—22no—
111C32×C8—41no—
112C3⋊(C3⋊C8)—22no—
113C3⋊(C3⋊C8)—41no—
114C2×#137—91no—
115C2×#108—91no—
116#417—91no—
117C2×#103—91no—
118C2×#101—91no—
119#408—91no—
120#343C3⋊D311yescharacteristic, complemented
121C22×C3×C4—24no—
122C22×C3×C4C22×D314yes—
123C2×#67—64no—
124C22×Dic3—64no—
125#235—64no—
126#235—64no—
127#235—64no—
128#235—64no—
129C2×D12—34no—
130C2×C4×D3—64no—
131C2×Dic6—34no—
132C2×Dic6—38no—
133C2×Dic6—64no—
134C2×Dic6—64no—
135C2×Dic6—64no—
136C2×Dic6—64no—
137C2×Dic6—64no—
138C3×M16—24no—
139C3×M16—24no—
140C3×M16—24no—
141C3×M16D1218yes—
142C2×C3×C8—24no—
143C2×C3×C8—24no—
144C3×C4⋊C4—24no—
145C3×C4⋊C4—24no—
146#208—64no—
147#208—64no—
148C2×C3⋊C8—38no—
149C2×C3⋊C8—64no—
150C2×C3⋊C8—64no—
151C2×C3⋊C8—64no—
152Dic12—616no—
153#204—616no—
154C22×C32—21no—
155C22×C32—21no—
156C22×C32#12111yescharacteristic
157C22×C32#12311yescharacteristic
158C22×C32#12411yescharacteristic
159C2×C3⋊D3—41no—
160C2×C3⋊D3—41no—
161C2×C3⋊D3—41no—
162C32×C4—81no—
163C32×C4#12011yescharacteristic
164C32×C4#12111yescharacteristic
165C32×C4#12111yescharacteristic
166C32×C4#12311yescharacteristic
167C3⋊Dic3—42no—
168C3⋊Dic3—41no—
169C2×#41—91no—
170C22×Q8—91no—
171#137—182no—
172#137—182no—
173C2×Q16—181no—
174C2×SD16—181no—
175C2×M16—91no—
176C2×M16C2×C3⋊D311yescharacteristic
177C2×M16C2×C3⋊D311yescharacteristic
178C22×C8—91no—
179C2×C4⋊C4C2×C3⋊D311yescharacteristic
180#108—182no—
181#103—182no—
182#103—181no—
183#102—181no—
184#101—182no—
185C22⋊C8—182no—
186C23×C3#23514yes—
187C22×D3—64no—
188C2×C3×C4—44no—
189C2×C3×C4—84no—
190C2×C3×C4C2×D1214yes—
191C2×C3×C4#23514yes—
192C2×C3×C4D3×D414yes—
193C2×C3×C4D3×D414yes—
194C2×C3×C4D3×D414yes—
195C2×C3×C4#23914yes—
196#67—124no—
197#67—124no—
198C2×Dic3—64no—
199C2×Dic3—68no—
200C2×Dic3—124no—
201C2×Dic3—124no—
202D12—64no—
203D12—64no—
204C4×D3—124no—
205C4×D3—124no—
206Dic6—68no—
207Dic6—64no—
208Dic6—68no—
209Dic6—64no—
210Dic6—124no—
211Dic6—124no—
212C3×C8—28no—
213C3×C8—44no—
214C3⋊C8—68no—
215C3⋊C8—124no—
216C2×C32—21no—
217C2×C32—21no—
218C2×C32#39411yescharacteristic
219C2×C32#47111yescharacteristic
220C2×C32#47311yescharacteristic
221C3⋊D3—81no—
222#41—181no—
223#41—181no—
224#41—181no—
225#41—181no—
226C2×Q8—92no—
227C2×Q8—91no—
228C2×Q8—181no—
229C2×Q8—181no—
230C2×Q8—181no—
231C2×Q8—181no—
232C2×Q8—181no—
233C2×D4—91no—
234C2×D4—181no—
235C22×C4—21no—
236C22×C4—181no—
237C22×C4—181no—
238C22×C4C22×C3⋊D311yescharacteristic
239Q16—184no—
240SD16—184no—
241M16—21no—
242M16—21no—
243M16—21no—
244M16—181no—
245M16—181no—
246M16C4⋊(C3⋊D3)12yes—
247C2×C8—21no—
248C2×C8—21no—
249C2×C8—92no—
250C2×C8—181no—
251C2×C8—181no—
252C2×C8—181no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C22×C3—24no—
256C22×C3—24no—
257C22×C3#87514yes—
258C22×C3#88414yes—
259C22×C3#89414yes—
260C2×D3—124no—
261C2×D3—124no—
262C2×D3—124no—
263C3×C4—84no—
264C3×C4#88214yes—
265C3×C4#88414yes—
266C3×C4#89414yes—
267C3×C4#89514yes—
268Dic3—128no—
269Dic3—124no—
270C32#205211yescharacteristic, complemented, Sylow
271C23—181no—
272C23#382811yescharacteristic
273Q8—182no—
274Q8—181no—
275Q8—182no—
276Q8—181no—
277Q8—361no—
278Q8—361no—
279D4—181no—
280D4—181no—
281D4—361no—
282D4—361no—
283C2×C4—41no—
284C2×C4—81no—
285C2×C4—181no—
286C2×C4—182no—
287C2×C4—361no—
288C2×C4—361no—
289C2×C4—361no—
290C2×C4—361no—
291C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
292C2×C4#382811yescharacteristic
293C2×C4D4×C3⋊D311yescharacteristic
294C2×C4D4×C3⋊D311yescharacteristic
295C2×C4D4×C3⋊D311yescharacteristic
296C2×C4#383211yescharacteristic
297C8—22no—
298C8—41no—
299C8—182no—
300C8—361no—
301C2×C3—24no—
302C2×C3—24no—
303C2×C3#467214yes—
304C2×C3#474814yes—
305C2×C3#475514yes—
306D3—244no—
307C22—21no—
308C22—21no—
309C22—361no—
310C22—361no—
311C22—361no—
312C22#6408411yescharacteristic
313C22#6409311yescharacteristic
314C22#6410311yescharacteristic
315C4—81no—
316C4—361no—
317C4—362no—
318C4#6409111yescharacteristic
319C4#6409311yescharacteristic
320C4#6410311yescharacteristic
321C4#6410411yescharacteristic
322C3#6898714yescomplemented
323C2—21no—
324C2—21no—
325C2—721no—
326C2#1059237111yescharacteristic
327C2#1059244711yescharacteristic
328C2#1059245411yescharacteristic
subgroupG/H
centerC22#64093
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC32×#343C2
socleC22×C32#121
prime radicalC2×#3828C22
hypercenter#343C3⋊D3
hypocenterC32#2052
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
2. C2×#63651C2semidirect
4. C2×#63649C2semidirect
5. C2×#63637C2semidirect
7. C32×#343C2semidirect
32. C3×#343D3semidirect
120. #343C3⋊D3semidirect
270. C32#2052semidirect
322. C3#68987semidirect

Maximal subgroups

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

subgroupindex
C2×#641182
C2×#636512
#105928282
C2×#636492
C2×#636372
#105926652
C32×#3432
#689873