Finite Group Databasebeta

← #11895224

Subgroups — #11895224

Order 1152.

1050 conjugacy classes of subgroups.

The subgroup lattice has 363 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596203C211yesmaximal, characteristic, complemented
2#10596201C211yesmaximal, characteristic, complemented
3C32×#487C211yesmaximal, characteristic, complemented
4#10592783C211yesmaximal, characteristic, complemented
5#10592782C211yesmaximal, characteristic, complemented
6#10592518C212yesmaximal
7#10592499C212yesmaximal, complemented
8#10592495C212yesmaximal, complemented
9#10592487C212yesmaximal, complemented
10C4×#3745C211yesmaximal, characteristic
11C8×#634C211yesmaximal, characteristic, complemented
12#81621—34nomaximal
13C32×C4⋊Q8C2211yescharacteristic
14C32×C4⋊Q8C2211yescharacteristic
15#64156C2212yes—
16#64155—22no—
17Q8×C3⋊Dic3C2212yes—
18C2×#3755C2212yes—
19C2×#3745C2211yescharacteristic
20#64107—22no—
21#64106—21no—
22#64106—21no—
23#64102C2212yes—
24#64101—21no—
25C4⋊C4×C3⋊D3—21no—
26#64099C2212yes—
27C4×C4⋊(C3⋊D3)C2211yescharacteristic
28C4×C4⋊(C3⋊D3)C2211yescharacteristic
29C4×#634C2211yescharacteristic
30C32×#103C2212yes—
31C32×#103C2212yes—
32C32×C4×C8C2211yescharacteristic
33#63662C2212yes—
34#63648C2211yescharacteristic
35#63648C2211yescharacteristic
36#63645C2211yescharacteristic
37#63641C2212yes—
38C8×C3⋊Dic3C2212yes—
39#63636C2212yes—
40#63635C2212yes—
41C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
42#5732—34no—
43#5730—34no—
44C3×#487D314yescomplemented
45#5084—34no—
46#5083—34no—
47#4819—38no—
48#4800—38no—
49#4796—38no—
50#4788—38no—
51C4×D24—34no—
52C8×Dic6—34no—
53C2×C32×Q8—21no—
54C2×C32×Q8C2312yes—
55C2×C4⋊(C3⋊D3)C2311yescharacteristic
56C2×C4⋊(C3⋊D3)C2311yescharacteristic
57C2×C4×C3⋊D3—21no—
58C2×C4×C3⋊D3—21no—
59C2×C4×C3⋊D3—22no—
60C2×#634D411yescharacteristic
61C2×C32×C8C2311yescharacteristic
62C2×C32×C8C2311yescharacteristic
63C32×C4⋊C4—21no—
64C32×C4⋊C4—21no—
65C32×C4⋊C4—21no—
66C32×C4⋊C4C2312yes—
67C32×C42C2311yescharacteristic
68#3755—24no—
69#3752—21no—
70#3752—21no—
71#3752—22no—
72#3752—22no—
73#3752—22no—
74C4⋊(C3⋊Dic3)—22no—
75C4⋊(C3⋊Dic3)—22no—
76C4⋊(C3⋊Dic3)D411yescharacteristic
77C4⋊(C3⋊Dic3)C2311yescharacteristic
78C4⋊(C3⋊Dic3)C2311yescharacteristic
79#3750—22no—
80#3750D412yes—
81C4×C3⋊Dic3—22no—
82C4×C3⋊Dic3C2312yes—
83C2×C3⋊(C3⋊C8)C2312yes—
84#3745—22no—
85#3360—91noSylow
86C3×C4⋊Q8C2×D314yes—
87C3×C4⋊Q8C2×D314yes—
88#947—38no—
89#946—68no—
90Q8×Dic3—38no—
91C2×#215—38no—
92C2×D24—34no—
93#898—68no—
94#897—64no—
95#897—64no—
96#893—38no—
97#892—64no—
98D3×C4⋊C4—64no—
99#890—38no—
100C4×D12—34no—
101C4×D12—34no—
102C4×Dic6—34no—
103C3×#103C2×D318yes—
104C3×#103C2×D318yes—
105C3×C4×C8C2×D314yes—
106#835—38no—
107#821—34no—
108#821—34no—
109#818—34no—
110Dic3⋊C8—38no—
111C8×Dic3—38no—
112#809—38no—
113#808—38no—
114C4⋊(C3⋊C8)—34no—
115C22×C3⋊D3—21no—
116C22×C3⋊D3—21no—
117C32×Q8—22no—
118C32×Q8—22no—
119C32×Q8—81no—
120C2×C32×C4—22no—
121C2×C32×C4—22no—
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2411yescharacteristic
125C2×C3⋊Dic3—21no—
126C2×C3⋊Dic3—21no—
127C2×C3⋊Dic3C2×D412yes—
128C2×C3⋊Dic3C2×D412yes—
129C4⋊(C3⋊D3)—21no—
130C4⋊(C3⋊D3)—21no—
131C4⋊(C3⋊D3)—21no—
132C4⋊(C3⋊D3)#4112yes—
133C4×C3⋊D3—42no—
134C4×C3⋊D3—42no—
135C4×C3⋊D3—82no—
136#634—22no—
137C32×C8—21no—
138C32×C8—21no—
139C3⋊(C3⋊C8)—22no—
140#556—91no—
141#554—91no—
142#488—92no—
143#487C3⋊D311yescharacteristic, complemented
144#479—92no—
145#476—91no—
146#463—92no—
147#461—91no—
148C8×Q8—91no—
149C4×SD16—92no—
150C4×D8—91no—
151C2×C3×Q8—24no—
152C2×C3×Q8C22×D318yes—
153C2×D12—34no—
154C2×D12—34no—
155C2×C4×D3—64no—
156C2×C4×D3—64no—
157C2×C4×D3—68no—
158C2×Dic6—34no—
159C2×C3×C8C22×D314yes—
160C2×C3×C8C22×D314yes—
161C3×C4⋊C4—24no—
162C3×C4⋊C4—24no—
163C3×C4⋊C4—24no—
164C3×C4⋊C4C22×D318yes—
165C3×C42C22×D314yes—
166#215—616no—
167(C2×D3)⋊C4—68no—
168(C2×D3)⋊C4—68no—
169(C2×D3)⋊C4—68no—
170(C2×D3)⋊C4—64no—
171(C2×D3)⋊C4—64no—
172C4⋊Dic3—34no—
173C4⋊Dic3—34no—
174C4⋊Dic3—34no—
175C4⋊Dic3—68no—
176C4⋊Dic3—68no—
177Dic3⋊C4—38no—
178Dic3⋊C4—68no—
179C4×Dic3—38no—
180C4×Dic3—68no—
181C2×C3⋊C8—38no—
182D24—68no—
183C22×C32C22×D411yescharacteristic
184C2×C3⋊D3—22no—
185C2×C3⋊D3—41no—
186C2×C3⋊D3—41no—
187C2×C3⋊D3—41no—
188C2×C3⋊D3—41no—
189C2×C3⋊D3—41no—
190C32×C4—21no—
191C32×C4—42no—
192C32×C4—42no—
193C32×C4#13512yes—
194C32×C4C2×#4111yescharacteristic
195C32×C42−1+411yescharacteristic
196C3⋊Dic3—22no—
197C3⋊Dic3—22no—
198C3⋊Dic3—41no—
199C3⋊Dic3—41no—
200C2×SD16—92no—
201C2×D8—91no—
202C4⋊Q8C2×C3⋊D311yescharacteristic
203C4⋊Q8C2×C3⋊D311yescharacteristic
204#126—182no—
205#125—92no—
206#124—92no—
207C22⋊Q8—181no—
208C22⋊Q8—181no—
209C22⋊Q8—182no—
210C4×Q8—91no—
211C4×Q8—92no—
212C4×D4—92no—
213C4×D4—91no—
214C4×D4—91no—
215#117—181no—
216C2×C4⋊C4—181no—
217#107—91no—
218#106—92no—
219C4⋊C8—92no—
220C4⋊C8—91no—
221#103—92no—
222#103C2×C3⋊D312yes—
223#103C2×C3⋊D312yes—
224#102—91no—
225#102—91no—
226#102—92no—
227C4×C8—92no—
228C4×C8C2×C3⋊D311yescharacteristic
229C22×D3—64no—
230C22×D3—64no—
231C3×Q8—28no—
232C3×Q8—28no—
233C3×Q8—84no—
234C2×C3×C4—28no—
235C2×C3×C4—28no—
236C2×C3×C4D3×D414yes—
237C2×C3×C4D3×D414yes—
238C2×C3×C4C23×D314yes—
239C2×Dic3—38no—
240C2×Dic3—38no—
241C2×Dic3—64no—
242C2×Dic3—64no—
243D12—38no—
244D12—64no—
245D12—64no—
246D12—64no—
247C4×D3—128no—
248C4×D3—128no—
249C4×D3—248no—
250Dic6—68no—
251C3×C8—24no—
252C3×C8—24no—
253C3⋊C8—68no—
254C2×C32#54811yescharacteristic
255C2×C32C2×#13511yescharacteristic
256C2×C32#57711yescharacteristic
257C3⋊D3—42no—
258C3⋊D3—81no—
259C2×Q8—21no—
260C2×Q8—91no—
261C2×Q8C22×C3⋊D312yes—
262C2×D4—91no—
263C2×D4—91no—
264C22×C4—182no—
265C22×C4—181no—
266C22×C4—181no—
267SD16—184no—
268D8—182no—
269C2×C8—92no—
270C2×C8C22×C3⋊D311yescharacteristic
271C2×C8C22×C3⋊D311yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—91no—
276C4⋊C4—92no—
277C4⋊C4—91no—
278C4⋊C4—91no—
279C4⋊C4—182no—
280C4⋊C4—182no—
281C4⋊C4—182no—
282C4⋊C4C22×C3⋊D312yes—
283C22⋊C4—182no—
284C22⋊C4—182no—
285C22⋊C4—182no—
286C22⋊C4—181no—
287C22⋊C4—181no—
288C42—92no—
289C42—182no—
290C42C22×C3⋊D311yescharacteristic
291C22×C3C2×D3×D414yes—
292C2×D3—68no—
293C2×D3—124no—
294C2×D3—124no—
295C2×D3—124no—
296C2×D3—124no—
297C2×D3—124no—
298C3×C4—24no—
299C3×C4—48no—
300C3×C4—48no—
301C3×C4#91918yes—
302C3×C4D3×#4114yes—
303C3×C4#101014yes—
304Dic3—68no—
305Dic3—68no—
306Dic3—124no—
307Dic3—124no—
308C32#336011yescharacteristic, complemented, Sylow
309C23—181no—
310C23—181no—
311Q8—22no—
312Q8—22no—
313Q8—81no—
314Q8—182no—
315D4—92no—
316D4—181no—
317D4—181no—
318D4—181no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—92no—
322C2×C4—92no—
323C2×C4—181no—
324C2×C4—181no—
325C2×C4—362no—
326C2×C4—362no—
327C2×C4—722no—
328C2×C4D4×C3⋊D311yescharacteristic
329C2×C4D4×C3⋊D311yescharacteristic
330C2×C4C23×C3⋊D311yescharacteristic
331C8—21no—
332C8—21no—
333C8—182no—
334C2×C3#567714yes—
335C2×C3#576214yes—
336C2×C3C2×#91914yes—
337D3—128no—
338D3—244no—
339C22—182no—
340C22—361no—
341C22—361no—
342C22—361no—
343C22—361no—
344C22—361no—
345C22C2×D4×C3⋊D311yescharacteristic
346C4—21no—
347C4—42no—
348C4—42no—
349C4—182no—
350C4—182no—
351C4—361no—
352C4—361no—
353C4#6412812yes—
354C4#41×C3⋊D311yescharacteristic
355C4#6436711yescharacteristic
356C3#8162114yescomplemented
357C2—362no—
358C2—721no—
359C2#1059614811yescharacteristic
360C2#1059623311yescharacteristic
361C2C2×#6412811yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#487C2
socleC22×C32C22×D4
prime radicalC2×#3745C22
hypercenter#487C3⋊D3
hypocenterC32#3360
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
1. #10596203C2semidirect
2. #10596201C2semidirect
3. C32×#487C2semidirect
4. #10592783C2semidirect
5. #10592782C2semidirect
7. #10592499C2semidirect
8. #10592495C2semidirect
9. #10592487C2semidirect
11. C8×#634C2semidirect
44. C3×#487D3semidirect
143. #487C3⋊D3semidirect
308. C32#3360semidirect
356. C3#81621semidirect

Maximal subgroups

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

subgroupindex
#105962032
#105962012
C32×#4872
#105927832
#105927822
#105925182
#105924992
#105924952
#105924872
C4×#37452
C8×#6342
#816213