Finite Group Databasebeta

← #11869039

Subgroups — #11869039

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#10595990C211yesmaximal, characteristic
2#10595987C211yesmaximal, characteristic
3C32×#424C211yesmaximal, characteristic
4#10592820C211yesmaximal, characteristic
5#10592819C211yesmaximal, characteristic
6#10592805C211yesmaximal, characteristic
7C2×#63643C211yesmaximal, characteristic
8#10592550C212yesmaximal, complemented
9#10592549C212yesmaximal, complemented
10#10592528C212yesmaximal, complemented
11#10592528C212yesmaximal, complemented
12#79101—34nomaximal
13C22×#634C2211yescharacteristic
14C2×C32×M16C2211yescharacteristic
15C22×C32×C8C2211yescharacteristic
16C32×#117C2211yescharacteristic
17#64135C2211yescharacteristic
18#64135C2211yescharacteristic
19C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
20#64099—21no—
21#64097—21no—
22#64096—21no—
23#64096—21no—
24#64087—22no—
25#64086—22no—
26#64079C2212yes—
27#64078C2212yes—
28C4×#634C2212yes—
29C4×#634C2212yes—
30C32×C4⋊C8C2212yes—
31C32×C4⋊C8C2212yes—
32#63645C2211yescharacteristic
33#63645C2212yes—
34#63645C2211yescharacteristic
35#63644C2211yescharacteristic
36#63644C2212yes—
37#63644C2211yescharacteristic
38#63643C2212yes—
39#63643C2212yes—
40#63643C2212yes—
41#63643C2212yes—
42#5519—34no—
43#5516—34no—
44C3×#424D314yes—
45#5121—34no—
46#5120—34no—
47#5106—34no—
48C2×#816—34no—
49#4851—38no—
50#4850—38no—
51#4829—38no—
52#4829—38no—
53C22×C32×C4C2311yescharacteristic
54C22×C3⋊Dic3—21no—
55C22×C3⋊Dic3—21no—
56C2×#634—21no—
57C2×#634—22no—
58C2×#634—22no—
59C2×#634Q814yescomplemented
60C2×#634C2312yes—
61C32×M16—22no—
62C2×C32×C8—22no—
63C2×C32×C8C2311yescharacteristic
64C2×C32×C8C2312yes—
65C2×C32×C8C2311yescharacteristic
66C32×C4⋊C4D411yescharacteristic
67C32×C4⋊C4D411yescharacteristic
68C32×C22⋊C4D412yes—
69C32×C42C2312yes—
70#3757—21no—
71#3757—21no—
72C4⋊(C3⋊Dic3)—22no—
73C4⋊(C3⋊Dic3)—21no—
74C4⋊(C3⋊Dic3)C2311yescharacteristic
75C4⋊(C3⋊Dic3)C2311yescharacteristic
76C4⋊(C3⋊Dic3)C2311yescharacteristic
77C4⋊(C3⋊Dic3)C2312yes—
78C4⋊(C3⋊Dic3)C2311yescharacteristic
79#3750—22no—
80#3750—22no—
81#3750—22no—
82#3750—22no—
83C4×C3⋊Dic3—22no—
84C4×C3⋊Dic3—22no—
85C4×C3⋊Dic3—21no—
86C4×C3⋊Dic3—21no—
87#3082—91noSylow
88C22×Dic6—34no—
89C2×C3×M16C2×D314yes—
90C22×C3×C8C2×D314yes—
91C3×#117C2×D314yes—
92#926—34no—
93#926—34no—
94C2×C4⋊Dic3—34no—
95#890—64no—
96#888—64no—
97#887—64no—
98#887—64no—
99#878—68no—
100#877—68no—
101#870—38no—
102#869—38no—
103C4×Dic6—38no—
104C4×Dic6—38no—
105C3×C4⋊C8C2×D318yes—
106C3×C4⋊C8C2×D318yes—
107#818—38no—
108#818—34no—
109#818—34no—
110#817—38no—
111#817—34no—
112#817—34no—
113#816—38no—
114#816—38no—
115#816—38no—
116#816—38no—
117C23×C32C2×D411yescharacteristic
118C2×C32×C4C2×D412yes—
119C2×C32×C4C2×D412yes—
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×Q812yes—
122C2×C32×C4#4112yes—
123C2×C32×C4C2411yescharacteristic
124C2×C3⋊Dic3—24no—
125C2×C3⋊Dic3—22no—
126C2×C3⋊Dic3—21no—
127C2×C3⋊Dic3—21no—
128C2×C3⋊Dic3—21no—
129C2×C3⋊Dic3—21no—
130C2×C3⋊Dic3—22no—
131C2×C3⋊Dic3—81no—
132#634—24no—
133#634—22no—
134#634—82no—
135#634C2×Q814yes—
136C32×C8—21no—
137C32×C8—21no—
138C32×C8—22no—
139#544—91no—
140#519—91no—
141#479—92no—
142#479—92no—
143#477—92no—
144#475—92no—
145#428—91no—
146#427—91no—
147#424C3⋊D311yescharacteristic
148#419—91no—
149C2×#103—91no—
150C22×C3×C4C22×D314yes—
151C22×Dic3—64no—
152C22×Dic3—64no—
153C2×Dic6—316no—
154C2×Dic6—38no—
155C2×Dic6—64no—
156C2×Dic6—68no—
157C2×Dic6—68no—
158C3×M16—28no—
159C2×C3×C8—28no—
160C2×C3×C8C22×D314yes—
161C2×C3×C8C22×D318yes—
162C2×C3×C8C22×D314yes—
163C3×C4⋊C4D1214yes—
164C3×C4⋊C4D1214yes—
165C3×C22⋊C4D1218yes—
166C3×C42C22×D318yes—
167#217—64no—
168#217—64no—
169C4⋊Dic3—34no—
170C4⋊Dic3—38no—
171C4⋊Dic3—34no—
172C4⋊Dic3—34no—
173C4⋊Dic3—34no—
174C4⋊Dic3—68no—
175C4⋊Dic3—64no—
176Dic3⋊C4—68no—
177Dic3⋊C4—68no—
178Dic3⋊C4—68no—
179Dic3⋊C4—68no—
180C4×Dic3—68no—
181C4×Dic3—68no—
182C4×Dic3—64no—
183C4×Dic3—64no—
184C22×C32—21no—
185C22×C32—21no—
186C22×C32C22⋊Q812yes—
187C22×C32C22×D411yescharacteristic
188C32×C4—22no—
189C32×C4—22no—
190C32×C4C22⋊Q812yes—
191C32×C4C22×Q811yescharacteristic
192C32×C4C2×#4111yescharacteristic
193C3⋊Dic3—24no—
194C3⋊Dic3—41no—
195C3⋊Dic3—42no—
196C3⋊Dic3—41no—
197C3⋊Dic3—41no—
198C3⋊Dic3—41no—
199C22×Q8—91no—
200C2×M16C2×C3⋊D311yescharacteristic
201C22×C8C2×C3⋊D311yescharacteristic
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⋊C4—91no—
216#107—91no—
217#107—91no—
218#107—92no—
219#106—91no—
220#106—91no—
221#106—92no—
222C4⋊C8C2×C3⋊D312yes—
223C4⋊C8C2×C3⋊D312yes—
224#103—92no—
225#103—92no—
226#103—92no—
227#103—92no—
228C23×C3C2×D1214yes—
229C2×C3×C4C2×D1218yes—
230C2×C3×C4C2×D1218yes—
231C2×C3×C4C2×D1214yes—
232C2×C3×C4#23718yes—
233C2×C3×C4D3×Q818yes—
234C2×C3×C4C23×D314yes—
235C2×Dic3—616no—
236C2×Dic3—68no—
237C2×Dic3—64no—
238C2×Dic3—64no—
239C2×Dic3—64no—
240C2×Dic3—64no—
241C2×Dic3—68no—
242C2×Dic3—244no—
243Dic6—316no—
244Dic6—616no—
245Dic6—68no—
246Dic6—248no—
247C3×C8—24no—
248C3×C8—24no—
249C3×C8—28no—
250C2×C32—22no—
251C2×C32C2×C22⋊Q811yescharacteristic
252C2×C32#57711yescharacteristic
253C2×C32#57811yescharacteristic
254C2×Q8—92no—
255C2×Q8—94no—
256C2×Q8—181no—
257C2×Q8—182no—
258C2×Q8—182no—
259C22×C4—181no—
260C22×C4—181no—
261C22×C4C22×C3⋊D311yescharacteristic
262M16—22no—
263C2×C8—22no—
264C2×C8C22×C3⋊D311yescharacteristic
265C2×C8C22×C3⋊D312yes—
266C2×C8C22×C3⋊D311yescharacteristic
267C4⋊C4—92no—
268C4⋊C4—91no—
269C4⋊C4—91no—
270C4⋊C4—91no—
271C4⋊C4—91no—
272C4⋊C4—181no—
273C4⋊C4—182no—
274C4⋊C4—182no—
275C4⋊C4—182no—
276C4⋊C4—182no—
277C4⋊C4—182no—
278C4⋊C4C4⋊(C3⋊D3)11yescharacteristic
279C4⋊C4C4⋊(C3⋊D3)11yescharacteristic
280C22⋊C4—181no—
281C22⋊C4—181no—
282C22⋊C4C4⋊(C3⋊D3)12yes—
283C42—181no—
284C42—181no—
285C42—182no—
286C42—182no—
287C42C22×C3⋊D312yes—
288C22×C3—24no—
289C22×C3—24no—
290C22×C3#89718yes—
291C22×C3C22×D1214yes—
292C3×C4—28no—
293C3×C4—28no—
294C3×C4#89718yes—
295C3×C4C2×#23714yes—
296C3×C4C2×D3×Q814yes—
297Dic3—616no—
298Dic3—124no—
299Dic3—128no—
300Dic3—124no—
301Dic3—124no—
302Dic3—124no—
303C32#308211yescharacteristic, complemented, Sylow
304C23C2×C4⋊(C3⋊D3)11yescharacteristic
305Q8—94no—
306Q8—182no—
307Q8—184no—
308Q8—722no—
309C2×C4—182no—
310C2×C4—184no—
311C2×C4—181no—
312C2×C4—181no—
313C2×C4—181no—
314C2×C4—181no—
315C2×C4—182no—
316C2×C4—721no—
317C2×C4C2×C4⋊(C3⋊D3)12yes—
318C2×C4C2×C4⋊(C3⋊D3)12yes—
319C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
320C2×C4#383012yes—
321C2×C4Q8×C3⋊D312yes—
322C2×C4C23×C3⋊D311yescharacteristic
323C8—21no—
324C8—21no—
325C8—22no—
326C2×C3—28no—
327C2×C3C2×#89714yes—
328C2×C3#575114yes—
329C2×C3#575314yes—
330C22—21no—
331C22—21no—
332C22#6410612yes—
333C22C22×C4⋊(C3⋊D3)11yescharacteristic
334C4—22no—
335C4—22no—
336C4—184no—
337C4—362no—
338C4—361no—
339C4—361no—
340C4—361no—
341C4—361no—
342C4#6410612yes—
343C4C2×#383011yescharacteristic
344C4C2×Q8×C3⋊D311yescharacteristic
345C3#7910114yescomplemented
346C2—22no—
347C2C2×#6410611yescharacteristic
348C2#1059622211yescharacteristic
349C2#1059622411yescharacteristic
subgroupG/H
centerC22C22×C4⋊(C3⋊D3)
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#424C2
socleC22×C32C22×D4
prime radicalC23×C32C2×D4
hypercenter#424C3⋊D3
hypocenterC32#3082
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117 ◁ #424

Complements

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

NH ≅ G/Ntype
8. #10592550C2semidirect
9. #10592549C2semidirect
10. #10592528C2semidirect
11. #10592528C2semidirect
59. C2×#634Q8semidirect
303. C32#3082semidirect
345. C3#79101semidirect

Maximal subgroups

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

subgroupindex
#105959902
#105959872
C32×#4242
#105928202
#105928192
#105928052
C2×#636432
#105925502
#105925492
#105925282
#791013