Finite Group Databasebeta

← #11869030

Subgroups — #11869030

Order 1152.

1086 conjugacy classes of subgroups.

The subgroup lattice has 351 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595987C211yesmaximal, characteristic
2#10595971C211yesmaximal, characteristic
3C32×#428C211yesmaximal, characteristic
4#10592819C211yesmaximal, characteristic
5#10592818C211yesmaximal, characteristic
6#10592697C211yesmaximal, characteristic
7C2×#63637C211yesmaximal, characteristic
8#10592576C212yesmaximal, complemented
9#10592574C212yesmaximal, complemented
10#10592556C212yesmaximal, complemented
11#10592553C212yesmaximal, complemented
12#79246—34nomaximal
13C22×#634C2211yescharacteristic
14C2×C32×M16C2211yescharacteristic
15C32×#117C2211yescharacteristic
16C2×C32×C4⋊C4C2211yescharacteristic
17#64135C2211yescharacteristic
18#64135C2211yescharacteristic
19#64133—22no—
20C22×C3⋊(C3⋊C8)C2211yescharacteristic
21#64099—21no—
22#64099C2212yes—
23#64097—21no—
24#64097C2212yes—
25#64096C2212yes—
26#64096C2212yes—
27#64086—22no—
28C4×#634—21no—
29C4×#634—21no—
30C32×#107C2212yes—
31C32×#106C2212yes—
32#63643C2212yes—
33#63643C2212yes—
34#63641C2212yes—
35#63641C2212yes—
36#63637C2212yes—
37#63637C2212yes—
38#63635C2211yescharacteristic
39#63635C2211yescharacteristic
40#63634C2211yescharacteristic
41#63634C2211yescharacteristic
42#5516—34no—
43#5500—34no—
44C3×#428D314yes—
45#5120—34no—
46#5119—34no—
47#4998—34no—
48C2×#810—34no—
49#4877—38no—
50#4875—38no—
51#4857—38no—
52#4854—38no—
53C22×C32×C4—21no—
54C22×C32×C4C2311yescharacteristic
55C22×C3⋊Dic3—21no—
56C2×#634—21no—
57C2×#634—22no—
58C2×#634—22no—
59C2×#634Q814yescomplemented
60C2×#634C2312yes—
61C32×M16—22no—
62C2×C32×C8C2312yes—
63C32×C4⋊C4—21no—
64C32×C4⋊C4C2311yescharacteristic
65C32×C4⋊C4C2311yescharacteristic
66C32×C4⋊C4C2312yes—
67C32×C22⋊C4—21no—
68C32×C42—21no—
69#3757—21no—
70#3757D412yes—
71C4⋊(C3⋊Dic3)—22no—
72C4⋊(C3⋊Dic3)D411yescharacteristic
73C4⋊(C3⋊Dic3)D411yescharacteristic
74C4⋊(C3⋊Dic3)C2311yescharacteristic
75C4⋊(C3⋊Dic3)C2311yescharacteristic
76#3750—22no—
77#3750—22no—
78#3750—22no—
79#3750—22no—
80C4×C3⋊Dic3—21no—
81C4×C3⋊Dic3—22no—
82C4×C3⋊Dic3—22no—
83C4×C3⋊Dic3C2312yes—
84C2×C3⋊(C3⋊C8)—22no—
85C2×C3⋊(C3⋊C8)C2311yescharacteristic
86C2×C3⋊(C3⋊C8)C2311yescharacteristic
87#3082—91noSylow
88C22×Dic6—34no—
89C2×C3×M16C2×D314yes—
90C3×#117C2×D314yes—
91C2×C3×C4⋊C4C2×D314yes—
92#926—34no—
93#926—34no—
94#924—68no—
95C22×C3⋊C8—34no—
96#890—38no—
97#890—64no—
98#888—38no—
99#888—64no—
100#887—38no—
101#887—38no—
102#877—68no—
103C4×Dic6—64no—
104C4×Dic6—64no—
105C3×#107C2×D318yes—
106C3×#106C2×D318yes—
107#816—38no—
108#816—38no—
109Dic3⋊C8—38no—
110Dic3⋊C8—38no—
111#810—38no—
112#810—38no—
113#808—34no—
114#808—34no—
115#807—34no—
116#807—34no—
117C23×C32C2×D411yescharacteristic
118C2×C32×C4—21no—
119C2×C32×C4—21no—
120C2×C32×C4—22no—
121C2×C32×C4—81no—
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×Q812yes—
124C2×C32×C4#4112yes—
125C2×C32×C4C2411yescharacteristic
126C2×C3⋊Dic3—24no—
127C2×C3⋊Dic3—22no—
128C2×C3⋊Dic3—21no—
129C2×C3⋊Dic3—21no—
130C2×C3⋊Dic3C2×D412yes—
131C2×C3⋊Dic3C2×D412yes—
132#634—24no—
133#634—22no—
134#634—82no—
135#634C2×Q814yes—
136C32×C8—22no—
137C3⋊(C3⋊C8)—21no—
138C3⋊(C3⋊C8)—21no—
139#544—91no—
140#519—91no—
141#479—92no—
142#479—92no—
143#477—92no—
144#475—92no—
145#428C3⋊D311yescharacteristic
146#427—91no—
147#424—91no—
148#419—91no—
149C2×#103—91no—
150C22×C3×C4—24no—
151C22×C3×C4C22×D314yes—
152C22×Dic3—64no—
153C2×Dic6—316no—
154C2×Dic6—38no—
155C2×Dic6—68no—
156C2×Dic6—64no—
157C2×Dic6—68no—
158C3×M16—28no—
159C2×C3×C8C22×D318yes—
160C3×C4⋊C4—24no—
161C3×C4⋊C4C22×D314yes—
162C3×C4⋊C4C22×D314yes—
163C3×C4⋊C4C22×D318yes—
164C3×C22⋊C4—24no—
165C3×C42—24no—
166#217—38no—
167#217—64no—
168C4⋊Dic3—34no—
169C4⋊Dic3—34no—
170C4⋊Dic3—34no—
171C4⋊Dic3—34no—
172C4⋊Dic3—68no—
173Dic3⋊C4—68no—
174Dic3⋊C4—68no—
175Dic3⋊C4—68no—
176Dic3⋊C4—68no—
177C4×Dic3—38no—
178C4×Dic3—68no—
179C4×Dic3—68no—
180C4×Dic3—64no—
181C2×C3⋊C8—34no—
182C2×C3⋊C8—34no—
183C2×C3⋊C8—68no—
184C22×C32—21no—
185C22×C32—21no—
186C22×C32C22⋊Q812yes—
187C22×C32C22×D411yescharacteristic
188C32×C4—42no—
189C32×C4—41no—
190C32×C4—41no—
191C32×C4C22⋊Q812yes—
192C32×C4C22×Q811yescharacteristic
193C32×C4C2×#4111yescharacteristic
194C3⋊Dic3—24no—
195C3⋊Dic3—22no—
196C3⋊Dic3—22no—
197C3⋊Dic3—41no—
198C3⋊Dic3—41no—
199C22×Q8—91no—
200C2×M16C2×C3⋊D311yescharacteristic
201C22×C8—91no—
202C4⋊Q8—92no—
203C4⋊Q8—181no—
204#125—92no—
205#125—181no—
206C22⋊Q8—182no—
207C4×Q8—92no—
208C4×Q8—92no—
209C4×Q8—181no—
210C4×Q8—181no—
211#117—91no—
212#117—91no—
213#117—182no—
214#117C2×C3⋊D311yescharacteristic
215C2×C4⋊C4C2×C3⋊D311yescharacteristic
216#107—91no—
217#107—91no—
218#107C2×C3⋊D312yes—
219#106—91no—
220#106—91no—
221#106C2×C3⋊D312yes—
222C4⋊C8—92no—
223C4⋊C8—92no—
224#103—92no—
225#103—92no—
226#103—92no—
227#103—92no—
228C23×C3D3×D414yes—
229C2×C3×C4—24no—
230C2×C3×C4—24no—
231C2×C3×C4—28no—
232C2×C3×C4—84no—
233C2×C3×C4#23518yes—
234C2×C3×C4D3×D414yes—
235C2×C3×C4D3×Q818yes—
236C2×C3×C4C23×D314yes—
237C2×Dic3—38no—
238C2×Dic3—38no—
239C2×Dic3—616no—
240C2×Dic3—68no—
241C2×Dic3—64no—
242C2×Dic3—64no—
243Dic6—316no—
244Dic6—616no—
245Dic6—68no—
246Dic6—248no—
247C3×C8—28no—
248C3⋊C8—64no—
249C3⋊C8—64no—
250C2×C32—22no—
251C2×C32C2×C22⋊Q811yescharacteristic
252C2×C32#57711yescharacteristic
253C2×C32#57811yescharacteristic
254C2×Q8—92no—
255C2×Q8—94no—
256C2×Q8—182no—
257C2×Q8—182no—
258C2×Q8—181no—
259C22×C4—21no—
260C22×C4—181no—
261C22×C4C22×C3⋊D311yescharacteristic
262M16—22no—
263C2×C8—91no—
264C2×C8—91no—
265C2×C8—182no—
266C2×C8C22×C3⋊D312yes—
267C4⋊C4—21no—
268C4⋊C4—91no—
269C4⋊C4—91no—
270C4⋊C4—91no—
271C4⋊C4—91no—
272C4⋊C4—182no—
273C4⋊C4—182no—
274C4⋊C4—182no—
275C4⋊C4—182no—
276C4⋊C4—182no—
277C4⋊C4C22×C3⋊D312yes—
278C4⋊C4C22×C3⋊D311yescharacteristic
279C4⋊C4C22×C3⋊D311yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—92no—
282C22⋊C4—181no—
283C42—21no—
284C42—92no—
285C42—182no—
286C42—182no—
287C42—181no—
288C22×C3—24no—
289C22×C3—24no—
290C22×C3#89618yes—
291C22×C3C2×D3×D414yes—
292C3×C4—48no—
293C3×C4—44no—
294C3×C4—44no—
295C3×C4#89618yes—
296C3×C4C2×#23514yes—
297C3×C4C2×D3×Q814yes—
298Dic3—616no—
299Dic3—68no—
300Dic3—68no—
301Dic3—124no—
302Dic3—124no—
303C32#308211yescharacteristic, complemented, Sylow
304C23D4×C3⋊D311yescharacteristic
305Q8—94no—
306Q8—182no—
307Q8—184no—
308Q8—722no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—22no—
312C2×C4—81no—
313C2×C4—92no—
314C2×C4—92no—
315C2×C4—182no—
316C2×C4—184no—
317C2×C4—181no—
318C2×C4—181no—
319C2×C4#382812yes—
320C2×C4D4×C3⋊D311yescharacteristic
321C2×C4Q8×C3⋊D312yes—
322C2×C4C23×C3⋊D311yescharacteristic
323C8—22no—
324C8—181no—
325C8—181no—
326C2×C3—28no—
327C2×C3C2×#89614yes—
328C2×C3#577514yes—
329C2×C3#577914yes—
330C22—21no—
331C22—21no—
332C22#6410512yes—
333C22C2×D4×C3⋊D311yescharacteristic
334C4—42no—
335C4—41no—
336C4—41no—
337C4—184no—
338C4—182no—
339C4—182no—
340C4—361no—
341C4—361no—
342C4#6410512yes—
343C4C2×#382811yescharacteristic
344C4C2×Q8×C3⋊D311yescharacteristic
345C3#7924614yescomplemented
346C2—22no—
347C2C2×#6410511yescharacteristic
348C2#1059624611yescharacteristic
349C2#1059625011yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#428C2
socleC22×C32C22×D4
prime radicalC23×C32C2×D4
hypercenter#428C3⋊D3
hypocenterC32#3082
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
8. #10592576C2semidirect
9. #10592574C2semidirect
10. #10592556C2semidirect
11. #10592553C2semidirect
59. C2×#634Q8semidirect
303. C32#3082semidirect
345. C3#79246semidirect

Maximal subgroups

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

subgroupindex
#105959872
#105959712
C32×#4282
#105928192
#105928182
#105926972
C2×#636372
#105925762
#105925742
#105925562
#105925532
#792463