Finite Group Databasebeta

← #11786621

Subgroups — #11786621

Order 1152.

617 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5812C211yesmaximal, characteristic
2C2×#63663C211yesmaximal, characteristic
3C3×#5229C211yesmaximal, characteristic
4#10591139C212yesmaximal
5#10589161C212yesmaximal
6#71658—31nomaximal
7#69672—31nomaximal
8C22×C32×Q8C2211yescharacteristic
9C2×#3748C2212yes—
10C3×Q8×Dic3—22no—
11C3×Q8×Dic3—22no—
12C3×#926—22no—
13C3×#926C2212yes—
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16#63663C414yescomplemented
17C3×C3⋊#95—22no—
18#63576—22no—
19#63574—22no—
20C3×#519—31no—
21#5812D311yescharacteristic
22C3×#391—31no—
23#5229D311yescharacteristic
24C2×#836—31no—
25C2×#836—31no—
26C2×#836—61no—
27#4995—32no—
28#4964—32no—
29#4532—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#3748—22no—
40#3748C2×C414yes—
41C2×C3⋊(C3⋊C8)—22no—
42C3×#217—22no—
43C3×C4⋊Dic3—22no—
44C3×C4⋊Dic3—22no—
45C3×C4⋊Dic3—22no—
46C3×C4⋊Dic3D412yes—
47C3×C4⋊Dic3D412yes—
48C3×C4×Dic3—24no—
49C3×C4×Dic3—22no—
50C3×C4×Dic3—22no—
51#1857—91noSylow
52C22×C3×Q8—21no—
53C22×C3×Q8C2×D311yescharacteristic
54C22×C3×Q8C2×D311yescharacteristic
55C3×C4×Q8—62no—
56C3×C4×Q8—62no—
57C3×#117—32no—
58C3×#117—62no—
59C2×C3×C4⋊C4—31no—
60C2×C3×C42—31no—
61Q8×Dic3—22no—
62Q8×Dic3—22no—
63#926—22no—
64#926C2×D312yes—
65C2×C4⋊Dic3C2×D311yescharacteristic
66C2×C4×Dic3C2×D311yescharacteristic
67C2×#208—32no—
68C2×#208—32no—
69C2×#208—62no—
70C3×#95—62no—
71#836—34no—
72#836—34no—
73#836—64no—
74C3⋊#95—22no—
75#808—62no—
76#808—62no—
77#807—62no—
78#807—62no—
79C23×C32C2×D411yescharacteristic
80C32×Q8—24no—
81C32×Q8—24no—
82C2×C32×C4—22no—
83C2×C32×C4—22no—
84C2×C32×C4C4⋊C414yes—
85C2×C32×C4C22×C411yescharacteristic
86C2×C32×C4C2×D412yes—
87C2×C32×C4C2×Q811yescharacteristic
88C2×C32×C4#4112yes—
89C2×C3×Dic3—22no—
90C2×C3×Dic3—22no—
91C2×C3×Dic3—22no—
92C2×C3×Dic3—41no—
93C2×C3×Dic3—41no—
94C2×C3×Dic3—42no—
95C2×C3×Dic3—41no—
96C3⋊(C3⋊C8)—24no—
97#519—31no—
98#428—92no—
99C2×#101—91no—
100#391—31no—
101#339—92no—
102C2×C3×Q8—22no—
103C2×C3×Q8—22no—
104C2×C3×Q8—22no—
105C2×C3×Q8—22no—
106C2×C3×Q8—22no—
107C2×C3×Q8—22no—
108C2×C3×Q8—42no—
109C2×C3×Q8—42no—
110C2×C3×Q8Dic612yes—
111C2×C3×Q8Dic612yes—
112C2×C3×Q8C4×D312yes—
113C2×C3×Q8C4×D312yes—
114C22×C3×C4—22no—
115C22×C3×C4—21no—
116C22×C3×C4—61no—
117C22×C3×C4—61no—
118C22×C3×C4#6712yes—
119C22×C3×C4#6712yes—
120C22×C3×C4C22×D311yescharacteristic
121C22×C3×C4C22×D311yescharacteristic
122C22×Dic3—21no—
123C22×Dic3—21no—
124C3×C4⋊C4—32no—
125C3×C4⋊C4—32no—
126C3×C4⋊C4—62no—
127C3×C4⋊C4—62no—
128C3×C4⋊C4—62no—
129C3×C22⋊C4—62no—
130C3×C42—64no—
131C3×C42—62no—
132C3×C42—62no—
133#217—22no—
134C4⋊Dic3—22no—
135C4⋊Dic3—22no—
136C4⋊Dic3—22no—
137C4⋊Dic3#6712yes—
138C4⋊Dic3#6712yes—
139C4×Dic3—24no—
140C4×Dic3—22no—
141C4×Dic3—22no—
142#208—34no—
143#208—34no—
144#208—64no—
145#208—62no—
146#208—62no—
147#208—122no—
148C2×C3⋊C8—62no—
149C2×C3⋊C8—62no—
150C2×C3⋊C8—122no—
151C22×C32—21no—
152C22×C32—21no—
153C22×C32C2×C4⋊C411yescharacteristic
154C22×C32#12011yescharacteristic
155C22×C32#12311yescharacteristic
156C32×C4—24no—
157C32×C4C4×D412yes—
158C32×C4C22⋊Q812yes—
159C3×Dic3—42no—
160C3×Dic3—42no—
161C3×Dic3—42no—
162C3×Dic3—81no—
163C22×Q8D3211yescharacteristic
164C2×M16—92no—
165C4×Q8—62no—
166C4×Q8—62no—
167#117—32no—
168#117—62no—
169C2×C4⋊C4—31no—
170C2×C42—31no—
171#107—182no—
172#106—182no—
173#101—94no—
174#95—62no—
175C23×C3—21no—
176C23×C3C2×#6711yescharacteristic
177C23×C3C2×#6711yescharacteristic
178C3×Q8—24no—
179C3×Q8—24no—
180C3×Q8—24no—
181C3×Q8—24no—
182C3×Q8—44no—
183C3×Q8—44no—
184C2×C3×C4—22no—
185C2×C3×C4—22no—
186C2×C3×C4—22no—
187C2×C3×C4—22no—
188C2×C3×C4—24no—
189C2×C3×C4—22no—
190C2×C3×C4—21no—
191C2×C3×C4—21no—
192C2×C3×C4—22no—
193C2×C3×C4—42no—
194C2×C3×C4—42no—
195C2×C3×C4—62no—
196C2×C3×C4—62no—
197C2×C3×C4—62no—
198C2×C3×C4—121no—
199C2×C3×C4—121no—
200C2×C3×C4—122no—
201C2×C3×C4—121no—
202C2×C3×C4Dic3⋊C414yes—
203C2×C3×C4Dic3⋊C414yes—
204C2×C3×C4C2×Dic611yescharacteristic
205C2×C3×C4C2×Dic611yescharacteristic
206C2×C3×C4C2×C4×D311yescharacteristic
207C2×C3×C4C2×C4×D311yescharacteristic
208C2×C3×C4#23512yes—
209C2×C3×C4D3×D412yes—
210C2×C3×C4#23712yes—
211C2×C3×C4C2×#6712yes—
212C2×Dic3—22no—
213C2×Dic3—22no—
214C2×Dic3—22no—
215C2×Dic3—41no—
216C2×Dic3—41no—
217C2×Dic3—42no—
218C2×Dic3—41no—
219C3⋊C8—64no—
220C3⋊C8—64no—
221C3⋊C8—124no—
222C2×C32—21no—
223C2×C32—21no—
224C2×C32#38511yescharacteristic
225C2×C32#45411yescharacteristic
226C2×C32#45611yescharacteristic
227C2×Q8—22no—
228C2×Q8—22no—
229C2×Q8#62412yes—
230C2×Q8#62712yes—
231C22×C4—61no—
232C22×C4—61no—
233C22×C4#62512yes—
234C22×C4C2×D3211yescharacteristic
235M16—94no—
236M16—182no—
237C2×C8—182no—
238C4⋊C4—32no—
239C4⋊C4—32no—
240C4⋊C4—62no—
241C4⋊C4—62no—
242C4⋊C4—62no—
243C22⋊C4—62no—
244C42—64no—
245C42—62no—
246C42—62no—
247C22×C3—21no—
248C22×C3—21no—
249C22×C3—21no—
250C22×C3—21no—
251C22×C3—21no—
252C22×C3—21no—
253C22×C3—21no—
254C22×C3—41no—
255C22×C3—41no—
256C22×C3C2×Dic3⋊C411yescharacteristic
257C22×C3C2×Dic3⋊C411yescharacteristic
258C22×C3#92911yescharacteristic
259C22×C3#93511yescharacteristic
260C22×C3#93711yescharacteristic
261C22×C3#95311yescharacteristic
262C3×C4—24no—
263C3×C4—24no—
264C3×C4—22no—
265C3×C4—22no—
266C3×C4—44no—
267C3×C4—122no—
268C3×C4—122no—
269C3×C4—122no—
270C3×C4—241no—
271C3×C4#87812yes—
272C3×C4#67⋊C412yes—
273C3×C4#92412yes—
274C3×C4C4×#6712yes—
275Dic3—42no—
276Dic3—42no—
277Dic3—42no—
278Dic3—81no—
279C32#185711yescharacteristic, complemented, Sylow
280C23C2×#62511yescharacteristic
281Q8—24no—
282Q8—24no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—62no—
286C2×C4—62no—
287C2×C4—62no—
288C2×C4—121no—
289C2×C4—121no—
290C2×C4—122no—
291C2×C4—121no—
292C2×C4#372414yes—
293C2×C4#380412yes—
294C2×C4C2×#62411yescharacteristic
295C2×C4C2×#62711yescharacteristic
296C2×C4D3×#6712yes—
297C8—184no—
298C2×C3—21no—
299C2×C3—21no—
300C2×C3—21no—
301C2×C3—21no—
302C2×C3—21no—
303C2×C3—21no—
304C2×C3—21no—
305C2×C3—41no—
306C2×C3—41no—
307C2×C3#494611yescharacteristic
308C2×C3#506211yescharacteristic
309C2×C3#509511yescharacteristic
310C2×C3#521011yescharacteristic
311C2×C3#524511yescharacteristic
312C2×C3#524611yescharacteristic
313C22—21no—
314C22—21no—
315C22#6396111yescharacteristic
316C22C2×#372411yescharacteristic
317C22#6397611yescharacteristic
318C4—24no—
319C4—122no—
320C4—122no—
321C4—122no—
322C4—241no—
323C4#6395212yes—
324C4#6396412yes—
325C3—21no—
326C3#6967211yescharacteristic, complemented
327C3#7165811yescharacteristic, complemented
328C2—21no—
329C2—21no—
330C2#1059164511yescharacteristic
331C2#1059164811yescharacteristic
332C2#1059169311yescharacteristic
subgroupG/H
centerC22#63976
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. #63663C4semidirect
279. C32#1857semidirect
326. C3#69672semidirect
327. C3#71658semidirect

Maximal subgroups

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

subgroupindex
C3×#58122
C2×#636632
C3×#52292
#105911392
#105891612
#716583
#696723