Finite Group Databasebeta

← #11785125

Subgroups — #11785125

Order 1152.

765 conjugacy classes of subgroups.

The subgroup lattice has 393 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D4×Dic3C211yesmaximal, characteristic
2C2×#63660C211yesmaximal, characteristic
3C2×C3×#833C211yesmaximal, characteristic
4#10591115C212yesmaximal, complemented
5#10589167C212yesmaximal, complemented
6#71617—31nomaximal
7#70063—31nomaximal
8C22×C32×D4C2211yescharacteristic
9C23×C3×Dic3C412yes—
10C2×#3748C2212yes—
11C2×C3×#217C412yes—
12C3×D4×Dic3—22no—
13C3×D4×Dic3—22no—
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C2×C3×#208C2212yes—
17#63660—22no—
18C3×#833—22no—
19Dic3⋊(C3⋊C8)—22no—
20Dic3⋊(C3⋊C8)—22no—
21C2×C3×C4×D4—31no—
22C2×D4×Dic3D311yescharacteristic
23C2×C3×#100—31no—
24C2×#833—31no—
25C2×#833—31no—
26C2×#833—61no—
27C2×#833D311yescharacteristic
28#5118—32no—
29#4924—32no—
30#4554—32no—
31#4530—32no—
32C24×C32C2×C412yes—
33C2×C32×D4—22no—
34C2×C32×D4—22no—
35C2×C32×D4D412yes—
36C2×C32×D4Q812yes—
37C22×C32×C4C2311yescharacteristic
38C22×C3×Dic3—22no—
39C22×C3×Dic3—22no—
40C22×C3×Dic3—44no—
41C22×C3×Dic3C2×C411yescharacteristic
42C22×C3×Dic3C2×C412yes—
43C22×C3×Dic3C2×C411yescharacteristic
44#3748—22no—
45#3748—22no—
46C2×C3⋊(C3⋊C8)—22no—
47C3×#217—24no—
48C3×C4⋊Dic3—22no—
49C3×C4×Dic3D412yes—
50C3×C4×Dic3D412yes—
51C3×#208—22no—
52C3×#208—22no—
53C2×C3×C3⋊C8—22no—
54#1800—91noSylow
55C22×C3×D4—21no—
56C22×C3×D4C2×D311yescharacteristic
57C22×C3×D4C2×D311yescharacteristic
58C23×C3×C4—32no—
59C23×Dic3Dic312yes—
60C2×C3×M16—32no—
61C3×C4×D4—62no—
62C3×C4×D4—62no—
63C2×C3×C4⋊C4—31no—
64C2×C3×C22⋊C4—32no—
65C2×C3×C42—31no—
66C2×#217Dic312yes—
67D4×Dic3—22no—
68D4×Dic3—22no—
69C2×C4⋊Dic3C2×D311yescharacteristic
70C2×C4×Dic3C2×D311yescharacteristic
71C2×#208—32no—
72C2×#208—32no—
73C2×#208—62no—
74C2×#208C2×D312yes—
75C3×#100—62no—
76#833—22no—
77#833—64no—
78#833—62no—
79#833—62no—
80Dic3⋊C8—62no—
81Dic3⋊C8—62no—
82C4⋊(C3⋊C8)—62no—
83C4⋊(C3⋊C8)—62no—
84C23×C32—22no—
85C23×C32—22no—
86C23×C32—42no—
87C23×C32—42no—
88C23×C32C4⋊C414yes—
89C23×C32C22×C411yescharacteristic
90C32×D4—24no—
91C32×D4—24no—
92C2×C32×C4C2×D411yescharacteristic
93C2×C32×C4C2×D412yes—
94C2×C32×C4C2×Q811yescharacteristic
95C2×C32×C4#4112yes—
96C2×C3×Dic3—22no—
97C2×C3×Dic3—22no—
98C2×C3×Dic3—41no—
99C2×C3×Dic3—44no—
100C2×C3×Dic3—44no—
101C2×C3×Dic3—42no—
102C2×C3×Dic3C22⋊C412yes—
103C2×C3×Dic3C22⋊C411yescharacteristic
104C2×C3×Dic3C22⋊C411yescharacteristic
105C3⋊(C3⋊C8)—42no—
106C3×C3⋊C8—42no—
107C2×C4×D4—31no—
108#423—92no—
109C2×#100—31no—
110C2×#100—91no—
111#343—92no—
112C24×C3—22no—
113C24×C3C4×D312yes—
114C24×C3C2×Dic312yes—
115C2×C3×D4—22no—
116C2×C3×D4—22no—
117C2×C3×D4—22no—
118C2×C3×D4—22no—
119C2×C3×D4—22no—
120C2×C3×D4—22no—
121C2×C3×D4—42no—
122C2×C3×D4—42no—
123C2×C3×D4Dic612yes—
124C2×C3×D4Dic612yes—
125C2×C3×D4D1212yes—
126C2×C3×D4#6712yes—
127C22×C3×C4—21no—
128C22×C3×C4—31no—
129C22×C3×C4—31no—
130C22×C3×C4—32no—
131C22×C3×C4—62no—
132C22×C3×C4—62no—
133C22×C3×C4—124no—
134C22×C3×C4C22×D311yescharacteristic
135C22×C3×C4C22×D311yescharacteristic
136C22×Dic3—22no—
137C22×Dic3—22no—
138C22×Dic3—44no—
139C22×Dic3C2×Dic311yescharacteristic
140C22×Dic3C2×Dic312yes—
141C22×Dic3C2×Dic311yescharacteristic
142C3×M16—62no—
143C3×M16—62no—
144C2×C3×C8—62no—
145C3×C4⋊C4—62no—
146C3×C22⋊C4—64no—
147C3×C42—32no—
148C3×C42—32no—
149#217—24no—
150C4⋊Dic3—22no—
151C4×Dic3#6712yes—
152C4×Dic3#6712yes—
153#208—22no—
154#208—22no—
155#208—64no—
156#208—62no—
157#208—62no—
158#208—62no—
159#208—62no—
160#208—122no—
161C2×C3⋊C8—22no—
162C2×C3⋊C8—62no—
163C2×C3⋊C8—62no—
164C2×C3⋊C8—122no—
165C22×C32—21no—
166C22×C32—21no—
167C22×C32—24no—
168C22×C32—44no—
169C22×C32—44no—
170C22×C32—42no—
171C22×C32—42no—
172C22×C32C2×C22⋊C411yescharacteristic
173C22×C32C2×C4⋊C411yescharacteristic
174C22×C32#11711yescharacteristic
175C32×C4#12112yes—
176C32×C4C22⋊Q812yes—
177C3×Dic3—21no—
178C3×Dic3—22no—
179C3×Dic3—42no—
180C3×Dic3#10012yescomplemented
181C22×D4D3211yescharacteristic
182C23×C4—32no—
183C2×M16—32no—
184C2×M16—92no—
185C4×D4—62no—
186C4×D4—62no—
187C2×C4⋊C4—31no—
188C2×C22⋊C4—32no—
189C2×C42—31no—
190C4⋊C8—182no—
191C4⋊C8—182no—
192#100—62no—
193#100—182no—
194C23×C3—22no—
195C23×C3—22no—
196C23×C3—22no—
197C23×C3—22no—
198C23×C3—24no—
199C23×C3—21no—
200C23×C3—42no—
201C23×C3—42no—
202C23×C3—42no—
203C23×C3—42no—
204C23×C3—42no—
205C23×C3—42no—
206C23×C3—82no—
207C23×C3—82no—
208C23×C3Dic3⋊C414yes—
209C23×C3C4⋊Dic314yes—
210C23×C3C2×C4×D311yescharacteristic
211C23×C3C22×Dic311yescharacteristic
212C3×D4—24no—
213C3×D4—24no—
214C3×D4—24no—
215C3×D4—24no—
216C3×D4—44no—
217C3×D4—44no—
218C2×C3×C4—22no—
219C2×C3×C4—21no—
220C2×C3×C4—21no—
221C2×C3×C4—22no—
222C2×C3×C4—31no—
223C2×C3×C4—32no—
224C2×C3×C4—31no—
225C2×C3×C4—62no—
226C2×C3×C4—62no—
227C2×C3×C4—124no—
228C2×C3×C4—121no—
229C2×C3×C4—124no—
230C2×C3×C4—122no—
231C2×C3×C4C2×Dic611yescharacteristic
232C2×C3×C4C2×Dic611yescharacteristic
233C2×C3×C4C2×D1211yescharacteristic
234C2×C3×C4#23512yes—
235C2×C3×C4D3×D412yes—
236C2×C3×C4#23712yes—
237C2×C3×C4C2×#6711yescharacteristic
238C2×C3×C4C2×#6712yes—
239C2×Dic3—22no—
240C2×Dic3—22no—
241C2×Dic3—41no—
242C2×Dic3—44no—
243C2×Dic3—44no—
244C2×Dic3—42no—
245C2×Dic3#21712yes—
246C2×Dic3#21711yescharacteristic
247C2×Dic3#21711yescharacteristic
248C3×C8—122no—
249C3⋊C8—42no—
250C3⋊C8—124no—
251C3⋊C8—122no—
252C3⋊C8—122no—
253C2×C32—21no—
254C2×C32—21no—
255C2×C32—44no—
256C2×C32#38011yescharacteristic
257C2×C32C2×#10011yescharacteristic
258C2×C32#41311yescharacteristic
259C24D3×Dic312yes—
260C2×D4—22no—
261C2×D4—22no—
262C2×D4#62612yes—
263C2×D4#62712yes—
264C22×C4—31no—
265C22×C4—31no—
266C22×C4—32no—
267C22×C4—62no—
268C22×C4—62no—
269C22×C4—124no—
270C22×C4C2×D3211yescharacteristic
271M16—62no—
272M16—62no—
273M16—182no—
274M16—182no—
275C2×C8—62no—
276C2×C8—182no—
277C4⋊C4—62no—
278C22⋊C4—64no—
279C42—32no—
280C42—32no—
281C22×C3—21no—
282C22×C3—21no—
283C22×C3—21no—
284C22×C3—21no—
285C22×C3—24no—
286C22×C3—24no—
287C22×C3—21no—
288C22×C3—21no—
289C22×C3—21no—
290C22×C3—41no—
291C22×C3—41no—
292C22×C3—44no—
293C22×C3—44no—
294C22×C3—44no—
295C22×C3—44no—
296C22×C3—44no—
297C22×C3—42no—
298C22×C3—42no—
299C22×C3—42no—
300C22×C3—42no—
301C22×C3—82no—
302C22×C3—82no—
303C22×C3—84no—
304C22×C3—84no—
305C22×C3#87711yescharacteristic
306C22×C3D3×C22⋊C411yescharacteristic
307C22×C3C2×Dic3⋊C411yescharacteristic
308C22×C3C2×C4⋊Dic311yescharacteristic
309C22×C3#92611yescharacteristic
310C22×C3C2×#21711yescharacteristic
311C3×C4—22no—
312C3×C4—22no—
313C3×C4—32no—
314C3×C4—61no—
315C3×C4—62no—
316C3×C4—122no—
317C3×C4#87812yes—
318C3×C4#92412yes—
319C3×C4#93012yes—
320C3×C4#93912yes—
321Dic3—21no—
322Dic3—22no—
323Dic3—42no—
324Dic3#83312yescomplemented
325C32#180011yescharacteristic, complemented, Sylow
326C23—22no—
327C23—22no—
328C23—42no—
329C23—42no—
330C23Dic3⋊Dic314yes—
331C23C2×D3×Dic311yescharacteristic
332D4—24no—
333D4—24no—
334C2×C4—31no—
335C2×C4—32no—
336C2×C4—31no—
337C2×C4—62no—
338C2×C4—62no—
339C2×C4—124no—
340C2×C4—121no—
341C2×C4—124no—
342C2×C4—122no—
343C2×C4#380412yes—
344C2×C4C2×#62611yescharacteristic
345C2×C4C2×#62711yescharacteristic
346C2×C4D3×#6712yes—
347C8—122no—
348C8—362no—
349C2×C3—21no—
350C2×C3—21no—
351C2×C3—21no—
352C2×C3—21no—
353C2×C3—21no—
354C2×C3—21no—
355C2×C3—21no—
356C2×C3—41no—
357C2×C3—41no—
358C2×C3—44no—
359C2×C3—44no—
360C2×C3—84no—
361C2×C3D3×#10011yescharacteristic
362C2×C3#474511yescharacteristic
363C2×C3#494211yescharacteristic
364C2×C3#521211yescharacteristic
365C2×C3C2×#83311yescharacteristic
366C2×C3#523711yescharacteristic
367C22—21no—
368C22—21no—
369C22—24no—
370C22—44no—
371C22—44no—
372C22—42no—
373C22—42no—
374C22#6395511yescharacteristic
375C22C2×Dic3⋊Dic311yescharacteristic
376C22D3×#21711yescharacteristic
377C4—32no—
378C4—61no—
379C4—62no—
380C4—122no—
381C4#6396412yes—
382C4#6397812yes—
383C3—21no—
384C3#7006311yescharacteristic, complemented
385C3#7161711yescharacteristic, complemented
386C2—21no—
387C2—21no—
388C2—44no—
389C2D3×#83311yescharacteristic
390C2#1059150111yescharacteristic
391C2#1059171611yescharacteristic
subgroupG/H
centerC22D3×#217
commutatorC23×C32C22×C4
FrattiniC22×C4C2×D32
Fitting, prime radicalC22×C32×D4C22
socleC22×C32C2×C22⋊C4
cosocleC22×C32×C4C23
hypercenterC22×D4D32
hypocenterC32#1800
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
4. #10591115C2semidirect
5. #10589167C2semidirect
180. C3×Dic3#100semidirect
324. Dic3#833semidirect
325. C32#1800semidirect
384. C3#70063semidirect
385. C3#71617semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D4×Dic32
C2×#636602
C2×C3×#8332
#105911152
#105891672
#716173
#700633