Finite Group Databasebeta

← #11786620

Subgroups — #11786620

Order 1152.

677 conjugacy classes of subgroups.

The subgroup lattice has 343 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596283C211yesmaximal, characteristic
2C3×#5229C211yesmaximal, characteristic
3C2×C3×#836C211yesmaximal, characteristic
4#10591130C212yesmaximal
5#10589162C212yesmaximal
6#70102—31nomaximal
7#69672—31nomaximal
8C22×C32×Q8C2211yescharacteristic
9Q8×C3⋊Dic3—22no—
10Q8×C3⋊Dic3—22no—
11#64135—22no—
12#64135C2212yes—
13C2×C3×C4⋊Dic3C2211yescharacteristic
14C2×C3×C4×Dic3C2211yescharacteristic
15C2×C3×#208C2212yes—
16C3×#836C414yescomplemented
17C3×C3⋊#95—22no—
18#63575—22no—
19#63573—22no—
20#5812—31no—
21#5812—31no—
22#5812—61no—
23C2×C3×#101—31no—
24C3×#391—31no—
25#5229D311yescharacteristic
26C2×#836D311yescharacteristic
27#5121—32no—
28#4964—32no—
29#4555—32no—
30#4523—32no—
31C2×C32×Q8—22no—
32C2×C32×Q8—22no—
33C2×C32×Q8C2×C412yes—
34C2×C32×Q8Q812yes—
35C22×C32×C4D412yes—
36C22×C32×C4C2311yescharacteristic
37C22×C3×Dic3—21no—
38C22×C3×Dic3—21no—
39#3757—22no—
40C4⋊(C3⋊Dic3)—22no—
41C4⋊(C3⋊Dic3)—22no—
42C4⋊(C3⋊Dic3)D412yes—
43C4⋊(C3⋊Dic3)D412yes—
44C4×C3⋊Dic3—24no—
45C4×C3⋊Dic3—22no—
46C3×C4⋊Dic3—22no—
47C3×C4×Dic3—22no—
48C3×#208—22no—
49C3×#208C2×C414yes—
50C2×C3×C3⋊C8—22no—
51#1857—91noSylow
52C22×C3×Q8—21no—
53C22×C3×Q8C2×D311yescharacteristic
54C22×C3×Q8C2×D311yescharacteristic
55C2×C3×M16—32no—
56C2×C3×C4⋊C4—31no—
57C2×C3×C42—31no—
58Q8×Dic3—62no—
59Q8×Dic3—62no—
60Q8×Dic3—62no—
61Q8×Dic3—62no—
62Q8×Dic3—64no—
63Q8×Dic3—64no—
64#926—32no—
65#926—32no—
66#926—62no—
67#926—64no—
68#926—62no—
69#926—62no—
70C2×C4⋊Dic3C2×D311yescharacteristic
71C2×C4×Dic3C2×D311yescharacteristic
72C2×#208C2×D312yes—
73C3×#101—34no—
74C3×#95—62no—
75#836Dic314yescomplemented
76C3⋊#95—22no—
77#818—62no—
78#817—62no—
79#808—62no—
80#807—62no—
81C23×C32C2×D411yescharacteristic
82C32×Q8—24no—
83C32×Q8—24no—
84C2×C32×C4—22no—
85C2×C32×C4—22no—
86C2×C32×C4C4⋊C414yes—
87C2×C32×C4C22×C411yescharacteristic
88C2×C32×C4C2×D412yes—
89C2×C32×C4C2×Q811yescharacteristic
90C2×C32×C4#4112yes—
91C2×C3⋊Dic3—22no—
92C2×C3⋊Dic3—22no—
93C2×C3×Dic3—22no—
94C2×C3×Dic3—41no—
95C2×C3×Dic3—41no—
96C2×C3×Dic3—42no—
97C2×C3×Dic3—41no—
98C3×C3⋊C8—24no—
99#519—91no—
100#428—92no—
101C2×#101—31no—
102#391—31no—
103#339—92no—
104C2×C3×Q8—24no—
105C2×C3×Q8—24no—
106C2×C3×Q8—22no—
107C2×C3×Q8—22no—
108C2×C3×Q8—22no—
109C2×C3×Q8—22no—
110C2×C3×Q8—22no—
111C2×C3×Q8—22no—
112C2×C3×Q8Dic612yes—
113C2×C3×Q8Dic612yes—
114C2×C3×Q8C4×D312yes—
115C2×C3×Q8C2×Dic312yes—
116C22×C3×C4—22no—
117C22×C3×C4—21no—
118C22×C3×C4—61no—
119C22×C3×C4—61no—
120C22×C3×C4D1212yes—
121C22×C3×C4#6712yes—
122C22×C3×C4C22×D311yescharacteristic
123C22×C3×C4C22×D311yescharacteristic
124C22×Dic3—21no—
125C22×Dic3—21no—
126C3×M16—34no—
127C3×M16—62no—
128C2×C3×C8—62no—
129C3×C4⋊C4—62no—
130C3×C42—62no—
131#217—64no—
132#217—62no—
133#217—62no—
134C4⋊Dic3—22no—
135C4⋊Dic3—32no—
136C4⋊Dic3—32no—
137C4⋊Dic3—32no—
138C4⋊Dic3—32no—
139C4⋊Dic3—62no—
140C4⋊Dic3—62no—
141C4⋊Dic3—64no—
142C4⋊Dic3—64no—
143C4⋊Dic3—62no—
144C4⋊Dic3—62no—
145C4⋊Dic3—62no—
146C4⋊Dic3—62no—
147C4×Dic3—22no—
148C4×Dic3—68no—
149C4×Dic3—64no—
150C4×Dic3—64no—
151C4×Dic3—64no—
152C4×Dic3—62no—
153C4×Dic3—62no—
154#208—22no—
155#208C2×Dic314yes—
156C2×C3⋊C8—22no—
157C22×C32—21no—
158C22×C32—21no—
159C22×C32C2×C4⋊C411yescharacteristic
160C22×C32#12011yescharacteristic
161C22×C32#12311yescharacteristic
162C32×C4—24no—
163C32×C4C4×D412yes—
164C32×C4C22⋊Q812yes—
165C3⋊Dic3—42no—
166C3⋊Dic3—42no—
167C3×Dic3—42no—
168C3×Dic3—81no—
169C22×Q8D3211yescharacteristic
170C2×M16—32no—
171C4×Q8—182no—
172C4×Q8—182no—
173#117—92no—
174#117—182no—
175C2×C4⋊C4—31no—
176C2×C42—31no—
177#107—182no—
178#106—182no—
179#101—34no—
180#95—62no—
181C23×C3—21no—
182C23×C3C2×D1211yescharacteristic
183C23×C3C2×#6711yescharacteristic
184C3×Q8—28no—
185C3×Q8—28no—
186C3×Q8—24no—
187C3×Q8—24no—
188C3×Q8—24no—
189C3×Q8—24no—
190C2×C3×C4—24no—
191C2×C3×C4—24no—
192C2×C3×C4—22no—
193C2×C3×C4—22no—
194C2×C3×C4—22no—
195C2×C3×C4—22no—
196C2×C3×C4—24no—
197C2×C3×C4—21no—
198C2×C3×C4—22no—
199C2×C3×C4—21no—
200C2×C3×C4—22no—
201C2×C3×C4—62no—
202C2×C3×C4—121no—
203C2×C3×C4—121no—
204C2×C3×C4—122no—
205C2×C3×C4—121no—
206C2×C3×C4Dic3⋊C414yes—
207C2×C3×C4C4⋊Dic314yes—
208C2×C3×C4C2×Dic611yescharacteristic
209C2×C3×C4C2×Dic611yescharacteristic
210C2×C3×C4C2×C4×D311yescharacteristic
211C2×C3×C4D3×D412yes—
212C2×C3×C4D3×D412yes—
213C2×C3×C4#23712yes—
214C2×C3×C4#23712yes—
215C2×C3×C4C22×Dic311yescharacteristic
216C2×Dic3—22no—
217C2×Dic3—41no—
218C2×Dic3—41no—
219C2×Dic3—42no—
220C2×Dic3—41no—
221C2×Dic3—64no—
222C2×Dic3—64no—
223C2×Dic3—62no—
224C2×Dic3—62no—
225C2×Dic3—62no—
226C2×Dic3—62no—
227C3×C8—64no—
228C3⋊C8—24no—
229C2×C32—21no—
230C2×C32—21no—
231C2×C32#38511yescharacteristic
232C2×C32#45411yescharacteristic
233C2×C32#45611yescharacteristic
234C2×Q8—22no—
235C2×Q8—22no—
236C2×Q8D3×Dic312yes—
237C2×Q8#62712yes—
238C22×C4—61no—
239C22×C4—61no—
240C22×C4#62612yes—
241C22×C4C2×D3211yescharacteristic
242M16—34no—
243M16—62no—
244C2×C8—62no—
245C4⋊C4—62no—
246C4⋊C4—92no—
247C4⋊C4—92no—
248C4⋊C4—182no—
249C4⋊C4—182no—
250C22⋊C4—182no—
251C42—62no—
252C42—184no—
253C42—182no—
254C22×C3—21no—
255C22×C3—21no—
256C22×C3—21no—
257C22×C3—21no—
258C22×C3—21no—
259C22×C3—21no—
260C22×C3—21no—
261C22×C3—41no—
262C22×C3—41no—
263C22×C3#88211yescharacteristic
264C22×C3#88611yescharacteristic
265C22×C3C2×Dic3⋊C411yescharacteristic
266C22×C3C2×C4⋊Dic311yescharacteristic
267C22×C3#93511yescharacteristic
268C22×C3#93711yescharacteristic
269C3×C4—28no—
270C3×C4—24no—
271C3×C4—24no—
272C3×C4—22no—
273C3×C4—22no—
274C3×C4—122no—
275C3×C4—241no—
276C3×C4#87812yes—
277C3×C4#87812yes—
278C3×C4#67⋊C412yes—
279C3×C4D4×Dic312yes—
280Dic3—42no—
281Dic3—81no—
282Dic3—124no—
283Dic3—124no—
284Dic3—122no—
285Dic3—122no—
286Dic3—122no—
287Dic3—122no—
288C32#185711yescharacteristic, complemented, Sylow
289C23C2×#62611yescharacteristic
290Q8—24no—
291Q8—24no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—62no—
295C2×C4—121no—
296C2×C4—121no—
297C2×C4—122no—
298C2×C4—121no—
299C2×C4—182no—
300C2×C4—182no—
301C2×C4Dic3⋊Dic314yes—
302C2×C4C2×D3×Dic311yescharacteristic
303C2×C4#380512yes—
304C2×C4C2×#62711yescharacteristic
305C2×C4#381112yes—
306C8—64no—
307C2×C3—21no—
308C2×C3—21no—
309C2×C3—21no—
310C2×C3—21no—
311C2×C3—21no—
312C2×C3—21no—
313C2×C3—21no—
314C2×C3—41no—
315C2×C3—41no—
316C2×C3#475211yescharacteristic
317C2×C3#475311yescharacteristic
318C2×C3#494611yescharacteristic
319C2×C3#495011yescharacteristic
320C2×C3#506211yescharacteristic
321C2×C3#509511yescharacteristic
322C22—21no—
323C22—21no—
324C22#6396211yescharacteristic
325C22C2×Dic3⋊Dic311yescharacteristic
326C22#6398111yescharacteristic
327C4—24no—
328C4—122no—
329C4—241no—
330C4—362no—
331C4—362no—
332C4#67⋊Dic312yes—
333C4#6398212yes—
334C3—21no—
335C3#6967211yescharacteristic, complemented
336C3#7010211yescharacteristic, complemented
337C2—21no—
338C2—21no—
339C2#1059164711yescharacteristic
340C2#1059165011yescharacteristic
341C2#1059171911yescharacteristic
subgroupG/H
centerC22#63981
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×Q8C22
socleC22×C32#120
prime radicalC23×C32C2×D4
cosocleC22×C32×C4C23
hypercenterC22×Q8D32
hypocenterC32#1857
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
16. C3×#836C4semidirect
75. #836Dic3semidirect
288. C32#1857semidirect
335. C3#69672semidirect
336. C3#70102semidirect

Maximal subgroups

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

subgroupindex
#105962832
C3×#52292
C2×C3×#8362
#105911302
#105891622
#701023
#696723