Finite Group Databasebeta

← #11895209

Subgroups — #11895209

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
1C32×#554C211yesmaximal, characteristic, complemented
2#10596055C211yesmaximal, characteristic, complemented
3#10592792C211yesmaximal, characteristic, complemented
4#10592783C211yesmaximal, characteristic, complemented
5#10592767C212yesmaximal, complemented
6#10592762C212yesmaximal, complemented
7Q8×C3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8#10592718C211yesmaximal, characteristic, complemented
9C4×#3754C212yesmaximal, complemented
10#10592715C212yesmaximal
11C4×#3753C211yesmaximal, characteristic
12#83637—34nomaximal
13C32×C4⋊Q8C2211yescharacteristic
14C32×#125C2212yes—
15C32×C22⋊Q8—21no—
16C32×C22⋊Q8—22no—
17C32×C4×Q8C2211yescharacteristic
18C32×C4×D4C2211yescharacteristic
19C32×C4×D4C2212yes—
20C2×C32×C4⋊C4—21no—
21#64155—21no—
22C2×#3754C2212yes—
23C2×#3753C2211yescharacteristic
24#64107—22no—
25#64101—21no—
26#64084C2212yes—
27C4×C4⋊(C3⋊D3)C2211yescharacteristic
28#64078C2211yescharacteristic
29C4×#634C2212yes—
30#63659C2211yescharacteristic
31#63637C2212yes—
32#63637C2212yes—
33#63637C2212yes—
34#63636C2212yes—
35#63636C2211yescharacteristic
36#63635C2212yes—
37#63634C2211yescharacteristic
38C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
39C4⋊(C3⋊(C3⋊C8))C2212yes—
40C4×C3⋊(C3⋊C8)C2211yescharacteristic
41C4×C3⋊(C3⋊C8)C2212yes—
42C3×#554D314yescomplemented
43#5584—34no—
44#5093—34no—
45#5084—34no—
46#5068—38no—
47#5063—38no—
48Q8×C3⋊C8—34no—
49#5019—34no—
50C4×#214—38no—
51#5016—38no—
52C4×#213—34no—
53C2×C32×Q8—21no—
54C2×C32×Q8D411yescharacteristic
55C2×C32×D4C2311yescharacteristic
56C22×C32×C4—21no—
57C22×C32×C4—22no—
58C2×C4⋊(C3⋊D3)C2311yescharacteristic
59C2×C4×C3⋊D3—21no—
60C2×#634C2312yes—
61C32×C4⋊C4—22no—
62C32×C4⋊C4—21no—
63C32×C4⋊C4—22no—
64C32×C4⋊C4D411yescharacteristic
65C32×C4⋊C4D412yes—
66C32×C4⋊C4C2311yescharacteristic
67C32×C4⋊C4C2312yes—
68C32×C22⋊C4—21no—
69C32×C22⋊C4—22no—
70C32×C42C2312yes—
71C32×C42C2311yescharacteristic
72#3754—24no—
73#3753—22no—
74#3752—21no—
75#3752—22no—
76#3752—22no—
77C4⋊(C3⋊Dic3)—21no—
78C4⋊(C3⋊Dic3)—21no—
79C4⋊(C3⋊Dic3)C2311yescharacteristic
80#3750—22no—
81C4×C3⋊Dic3—22no—
82C2×C3⋊(C3⋊C8)C2311yescharacteristic
83C2×C3⋊(C3⋊C8)C2311yescharacteristic
84C2×C3⋊(C3⋊C8)C2312yes—
85#3360—91noSylow
86C3×C4⋊Q8C2×D314yes—
87C3×#125C2×D318yes—
88C3×C22⋊Q8—24no—
89C3×C22⋊Q8—28no—
90C3×C4×Q8C2×D314yes—
91C3×C4×D4C2×D314yes—
92C3×C4×D4C2×D318yes—
93C2×C3×C4⋊C4—24no—
94#946—64no—
95C2×#214—38no—
96C2×#213—34no—
97#898—68no—
98#892—64no—
99#875—38no—
100C4×D12—34no—
101#869—34no—
102C4×Dic6—38no—
103#832—34no—
104#810—38no—
105#810—38no—
106#810—38no—
107#809—34no—
108#809—38no—
109#808—38no—
110#807—34no—
111C4⋊(C3⋊C8)—38no—
112C4⋊(C3⋊C8)—34no—
113C4×C3⋊C8—34no—
114C4×C3⋊C8—38no—
115C23×C32—21no—
116C22×C3⋊D3—21no—
117C32×Q8—22no—
118C32×Q8—81no—
119C32×D4—21no—
120C32×D4#4112yes—
121C2×C32×C4—21no—
122C2×C32×C4—22no—
123C2×C32×C4—42no—
124C2×C32×C4—82no—
125C2×C32×C4C2×D412yes—
126C2×C32×C4C2×D412yes—
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2411yescharacteristic
130C2×C3⋊Dic3—21no—
131C2×C3⋊Dic3—22no—
132C4⋊(C3⋊D3)—21no—
133C4⋊(C3⋊D3)—21no—
134C4×C3⋊D3—42no—
135#634—22no—
136#634—22no—
137C3⋊(C3⋊C8)—21no—
138C3⋊(C3⋊C8)—22no—
139C3⋊(C3⋊C8)—21no—
140#556—91no—
141#554C3⋊D311yescharacteristic, complemented
142#488—92no—
143#487—91no—
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×Q8#6714yes—
153C2×C3×D4C22×D314yes—
154C22×C3×C4—24no—
155C22×C3×C4—28no—
156C2×D12—34no—
157C2×C4×D3—64no—
158C2×Dic6—38no—
159C3×C4⋊C4—28no—
160C3×C4⋊C4—24no—
161C3×C4⋊C4—28no—
162C3×C4⋊C4#6714yes—
163C3×C4⋊C4#6718yes—
164C3×C4⋊C4C22×D314yes—
165C3×C4⋊C4C22×D318yes—
166C3×C22⋊C4—24no—
167C3×C22⋊C4—28no—
168C3×C42C22×D318yes—
169C3×C42C22×D314yes—
170#214—616no—
171#213—68no—
172(C2×D3)⋊C4—64no—
173(C2×D3)⋊C4—68no—
174(C2×D3)⋊C4—68no—
175C4⋊Dic3—34no—
176C4⋊Dic3—64no—
177C4⋊Dic3—64no—
178Dic3⋊C4—68no—
179C4×Dic3—68no—
180C2×C3⋊C8—34no—
181C2×C3⋊C8—34no—
182C2×C3⋊C8—38no—
183C22×C32—22no—
184C22×C32—41no—
185C22×C32—41no—
186C22×C32C22×D411yescharacteristic
187C2×C3⋊D3—41no—
188C2×C3⋊D3—41no—
189C2×C3⋊D3—41no—
190C32×C4—22no—
191C32×C4—22no—
192C32×C4—21no—
193C32×C4—41no—
194C32×C4—42no—
195C32×C4#13512yes—
196C32×C4C2×#4111yescharacteristic
197C32×C42−1+411yescharacteristic
198C3⋊Dic3—42no—
199C3⋊Dic3—41no—
200C2×SD16—92no—
201C2×D8—91no—
202C4⋊Q8—91no—
203C4⋊Q8C2×C3⋊D311yescharacteristic
204#126—182no—
205#125C2×C3⋊D312yes—
206#124—92no—
207C22⋊Q8—21no—
208C22⋊Q8—22no—
209C22⋊Q8—181no—
210C4×Q8—92no—
211C4×Q8C2×C3⋊D311yescharacteristic
212C4×D4—91no—
213C4×D4C2×C3⋊D311yescharacteristic
214C4×D4C2×C3⋊D312yes—
215#117—181no—
216C2×C4⋊C4—21no—
217#107—91no—
218#106—92no—
219C4⋊C8—91no—
220C4⋊C8—92no—
221#103—92no—
222#103—92no—
223#103—92no—
224#102—91no—
225#102—91no—
226#102—92no—
227C4×C8—91no—
228C4×C8—92no—
229C23×C3—24no—
230C22×D3—64no—
231C3×Q8—28no—
232C3×Q8—84no—
233C3×D4—24no—
234C3×D4#23918yes—
235C2×C3×C4—24no—
236C2×C3×C4—28no—
237C2×C3×C4—48no—
238C2×C3×C4—88no—
239C2×C3×C4C2×#6718yes—
240C2×C3×C4C2×#6718yes—
241C2×C3×C4C2×#6714yes—
242C2×C3×C4C2×#6714yes—
243C2×C3×C4C23×D314yes—
244C2×Dic3—64no—
245C2×Dic3—68no—
246D12—64no—
247D12—64no—
248C4×D3—128no—
249Dic6—68no—
250Dic6—68no—
251C3⋊C8—64no—
252C3⋊C8—68no—
253C3⋊C8—64no—
254C2×C32—42no—
255C2×C32#54811yescharacteristic
256C2×C32C2×#13511yescharacteristic
257C2×C32#57711yescharacteristic
258C3⋊D3—81no—
259C2×Q8—21no—
260C2×Q8—92no—
261C2×Q8#63811yescharacteristic
262C2×D4—91no—
263C2×D4C22×C3⋊D311yescharacteristic
264C22×C4—21no—
265C22×C4—22no—
266C22×C4—181no—
267SD16—184no—
268D8—182no—
269C2×C8—91no—
270C2×C8—92no—
271C2×C8—91no—
272C4⋊C4—22no—
273C4⋊C4—21no—
274C4⋊C4—22no—
275C4⋊C4—91no—
276C4⋊C4—181no—
277C4⋊C4—182no—
278C4⋊C4—181no—
279C4⋊C4#63811yescharacteristic
280C4⋊C4#63812yes—
281C4⋊C4C22×C3⋊D312yes—
282C4⋊C4C22×C3⋊D311yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—22no—
285C22⋊C4—182no—
286C22⋊C4—181no—
287C22⋊C4—182no—
288C42—182no—
289C42C22×C3⋊D311yescharacteristic
290C42C22×C3⋊D312yes—
291C22×C3—28no—
292C22×C3—44no—
293C22×C3—44no—
294C22×C3C22×#6714yes—
295C2×D3—124no—
296C2×D3—124no—
297C2×D3—124no—
298C3×C4—28no—
299C3×C4—28no—
300C3×C4—24no—
301C3×C4—44no—
302C3×C4—48no—
303C3×C4#95018yes—
304C3×C4C2×#23914yes—
305C3×C4#100714yes—
306Dic3—128no—
307Dic3—124no—
308C32#336011yescharacteristic, complemented, Sylow
309C23—21no—
310C23—181no—
311Q8—22no—
312Q8—81no—
313Q8—182no—
314Q8—182no—
315D4—21no—
316D4—181no—
317D4—181no—
318D4#383212yes—
319C2×C4—21no—
320C2×C4—22no—
321C2×C4—42no—
322C2×C4—82no—
323C2×C4—181no—
324C2×C4—182no—
325C2×C4—362no—
326C2×C4C2×#63812yes—
327C2×C4C2×#63812yes—
328C2×C4C2×#63811yescharacteristic
329C2×C4C2×#63811yescharacteristic
330C2×C4C23×C3⋊D311yescharacteristic
331C8—181no—
332C8—182no—
333C8—181no—
334C2×C3—48no—
335C2×C3#581714yes—
336C2×C3C2×#95014yes—
337C2×C3#583614yes—
338D3—244no—
339C22—22no—
340C22—41no—
341C22—41no—
342C22—361no—
343C22—361no—
344C22—361no—
345C22C22×#63811yescharacteristic
346C4—22no—
347C4—22no—
348C4—21no—
349C4—41no—
350C4—42no—
351C4—362no—
352C4—361no—
353C4#6415912yes—
354C4C2×#383211yescharacteristic
355C4#6436411yescharacteristic
356C3#8363714yescomplemented
357C2—42no—
358C2—721no—
359C2#1059628811yescharacteristic
360C2C2×#6415911yescharacteristic
361C2#1059630711yescharacteristic
subgroupG/H
centerC22C22×#638
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#554C2
socleC22×C32C22×D4
prime radicalC2×#3753C22
hypercenter#554C3⋊D3
hypocenterC32#3360
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #554

Complements

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

NH ≅ G/Ntype
1. C32×#554C2semidirect
2. #10596055C2semidirect
3. #10592792C2semidirect
4. #10592783C2semidirect
5. #10592767C2semidirect
6. #10592762C2semidirect
7. Q8×C3⋊(C3⋊C8)C2semidirect
8. #10592718C2semidirect
9. C4×#3754C2semidirect
42. C3×#554D3semidirect
141. #554C3⋊D3semidirect
308. C32#3360semidirect
356. C3#83637semidirect

Maximal subgroups

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

subgroupindex
C32×#5542
#105960552
#105927922
#105927832
#105927672
#105927622
Q8×C3⋊(C3⋊C8)2
#105927182
C4×#37542
#105927152
C4×#37532
#836373