Finite Group Databasebeta

← #11788922

Subgroups — #11788922

Order 1152.

745 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596290C211yesmaximal, characteristic
2C3×#5825C211yesmaximal, characteristic
3C3×#5237C211yesmaximal, characteristic
4C2×#63560C212yesmaximal, complemented
5#10589169C212yesmaximal, complemented
6#71866—31nomaximal
7#70138—31nomaximal
8C2×C32×#41C2211yescharacteristic
9C22×C3×Dic6C2211yescharacteristic
10#64157—24no—
11C2×#3748—22no—
12C2×#3748C2212yes—
13C3×#944—21no—
14C3×#936—21no—
15C3×#935C414yes—
16C3×#926C2211yescharacteristic
17C3×#924—22no—
18C2×C3×#208C2212yes—
19C3×#836—21no—
20C3×#833—21no—
21#63560—24no—
22C3×#536—31no—
23#5825D311yescharacteristic
24#5819—31no—
25#5819—31no—
26#5819—61no—
27C3×#413—31no—
28#5237D311yescharacteristic
29C2×#836—32no—
30C2×#824—32no—
31#4556—32no—
32#4533—32no—
33C32×#41—22no—
34C32×#41—22no—
35C2×C32×Q8D411yescharacteristic
36C2×C32×D4C2×C412yes—
37C2×C32×D4D411yescharacteristic
38C22×C32×C4D412yes—
39C22×C32×C4C2311yescharacteristic
40C22×C3×Dic3C2×C412yes—
41C2×C3×Dic6—21no—
42C2×C3×Dic6—21no—
43C2×C3×Dic6—22no—
44C2×C3×Dic6—22no—
45#3748—24no—
46#3748—22no—
47#3748D414yes—
48C2×C3⋊(C3⋊C8)—24no—
49C2×C3⋊(C3⋊C8)—22no—
50C3×#217—24no—
51C3×#217C2×C412yes—
52C3×C4⋊Dic3—21no—
53C3×Dic3⋊C4—24no—
54C3×C4×Dic3—21no—
55C3×#208—22no—
56C3×#208—22no—
57C2×C3×C3⋊C8—22no—
58#1915—91noSylow
59C2×C3×#41—21no—
60C2×C3×#41C2×D311yescharacteristic
61C2×C3×#41C2×D311yescharacteristic
62C22×C3×Q8—31no—
63C22×Dic6C2×D311yescharacteristic
64C2×C3×M16—32no—
65C3×C4⋊Q8—61no—
66C3×#124—61no—
67C3×#123—34no—
68C3×C22⋊Q8—62no—
69C3×#117—31no—
70#948—64no—
71#948—64no—
72#948—68no—
73#944—21no—
74#936—21no—
75#935Dic314yes—
76#926C2×D311yescharacteristic
77#924—22no—
78C2×#208—32no—
79C2×#208—32no—
80C2×#208—62no—
81C2×#208—64no—
82C2×#208—62no—
83C2×#208—62no—
84C2×#208C2×D312yes—
85C3×#101—61no—
86C3×#100—61no—
87#836—21no—
88#836—64no—
89#833—21no—
90#824—64no—
91C23×C32C22⋊C412yes—
92C23×C32C22×C411yescharacteristic
93C32×Q8—22no—
94C32×D4—24no—
95C32×D4—22no—
96C2×C32×C4—22no—
97C2×C32×C4—22no—
98C2×C32×C4C22⋊C412yes—
99C2×C32×C4C2×D411yescharacteristic
100C2×C32×C4C2×D412yes—
101C2×C32×C4C2×D411yescharacteristic
102C2×C32×C4#4112yes—
103C2×C3×Dic3—22no—
104C2×C3×Dic3—22no—
105C2×C3×Dic3—24no—
106C3×Dic6—41no—
107C3×Dic6—42no—
108C3×Dic6—41no—
109C3⋊(C3⋊C8)—24no—
110C3×C3⋊C8—42no—
111#568—91no—
112#536—31no—
113#413—31no—
114C2×#101—92no—
115#344—92no—
116C3×#41—24no—
117C3×#41—24no—
118C3×#41—22no—
119C3×#41—22no—
120C3×#41—22no—
121C3×#41—22no—
122C2×C3×Q8—21no—
123C2×C3×Q8—61no—
124C2×C3×Q8—62no—
125C2×C3×Q8—62no—
126C2×C3×Q8—61no—
127C2×C3×Q8#6711yescharacteristic
128C2×C3×Q8#6711yescharacteristic
129C2×C3×D4—22no—
130C2×C3×D4—21no—
131C2×C3×D4C4×D312yes—
132C2×C3×D4C2×Dic312yes—
133C2×C3×D4#6711yescharacteristic
134C2×C3×D4#6711yescharacteristic
135C22×C3×C4—22no—
136C22×C3×C4—21no—
137C22×C3×C4—32no—
138C22×C3×C4D1212yes—
139C22×C3×C4#6712yes—
140C22×C3×C4C22×D311yescharacteristic
141C22×C3×C4C22×D311yescharacteristic
142C22×Dic3C2×Dic312yes—
143C2×Dic6—22no—
144C2×Dic6—22no—
145C2×Dic6—21no—
146C2×Dic6—21no—
147C3×M16—62no—
148C3×M16—62no—
149C2×C3×C8—62no—
150C3×C4⋊C4—64no—
151C3×C4⋊C4—61no—
152C3×C22⋊C4—32no—
153C3×C22⋊C4—64no—
154C3×C42—61no—
155#217—24no—
156#217C2×Dic312yes—
157C4⋊Dic3—21no—
158Dic3⋊C4—24no—
159C4×Dic3—21no—
160#208—22no—
161#208—22no—
162#208—34no—
163#208—34no—
164#208—64no—
165#208—64no—
166#208—68no—
167#208—64no—
168#208—64no—
169#208—62no—
170#208—62no—
171C2×C3⋊C8—22no—
172C2×C3⋊C8—68no—
173C2×C3⋊C8—64no—
174C2×C3⋊C8—64no—
175C2×C3⋊C8—64no—
176C2×C3⋊C8—62no—
177C2×C3⋊C8—62no—
178C22×C32—22no—
179C22×C32—41no—
180C22×C32—42no—
181C22×C32C2×C22⋊C411yescharacteristic
182C22×C32C4×D412yes—
183C32×C4—22no—
184C32×C4#12011yescharacteristic
185C32×C4#12112yes—
186C32×C4#12311yescharacteristic
187C3×Dic3—42no—
188C3×Dic3—42no—
189C2×#41D3211yescharacteristic
190C22×Q8—31no—
191#131—184no—
192C2×M16—32no—
193C2×M16—92no—
194C2×M16—182no—
195C4⋊Q8—61no—
196#124—61no—
197#123—34no—
198C22⋊Q8—62no—
199#117—31no—
200#101—61no—
201#101—184no—
202#100—61no—
203C23×C3—22no—
204C23×C3—21no—
205C23×C3(C2×D3)⋊C412yes—
206C23×C3#21712yes—
207C23×C3C2×C4×D311yescharacteristic
208C23×C3C22×Dic311yescharacteristic
209C3×Q8—24no—
210C3×Q8—22no—
211C3×Q8—22no—
212C3×Q8—121no—
213C3×Q8—121no—
214C3×Q8—122no—
215C3×D4—28no—
216C3×D4—24no—
217C3×D4—24no—
218C3×D4—24no—
219C3×D4—22no—
220C3×D4—22no—
221C2×C3×C4—24no—
222C2×C3×C4—24no—
223C2×C3×C4—22no—
224C2×C3×C4—22no—
225C2×C3×C4—22no—
226C2×C3×C4—22no—
227C2×C3×C4—22no—
228C2×C3×C4—22no—
229C2×C3×C4—21no—
230C2×C3×C4—21no—
231C2×C3×C4—22no—
232C2×C3×C4—64no—
233C2×C3×C4—62no—
234C2×C3×C4—62no—
235C2×C3×C4(C2×D3)⋊C412yes—
236C2×C3×C4#21712yes—
237C2×C3×C4C2×D1211yescharacteristic
238C2×C3×C4D3×D412yes—
239C2×C3×C4D3×D412yes—
240C2×C3×C4#23712yes—
241C2×C3×C4#23712yes—
242C2×C3×C4C2×#6711yescharacteristic
243C2×C3×C4C2×#6711yescharacteristic
244C2×C3×C4C2×#6711yescharacteristic
245C2×Dic3—24no—
246C2×Dic3—22no—
247C2×Dic3—22no—
248Dic6—41no—
249Dic6—41no—
250Dic6—42no—
251C3×C8—122no—
252C3⋊C8—42no—
253C3⋊C8—68no—
254C3⋊C8—64no—
255C3⋊C8—64no—
256C2×C32—21no—
257C2×C32—22no—
258C2×C32—42no—
259C2×C32#38611yescharacteristic
260#41—22no—
261#41—22no—
262C2×Q8—62no—
263C2×Q8—61no—
264C2×Q8—61no—
265C2×Q8—62no—
266C2×Q8#62511yescharacteristic
267C2×D4D3×Dic312yes—
268C2×D4#62511yescharacteristic
269C22×C4—32no—
270C22×C4#62612yes—
271C22×C4C2×D3211yescharacteristic
272M16—62no—
273M16—62no—
274M16—94no—
275M16—184no—
276M16—182no—
277C2×C8—62no—
278C2×C8—184no—
279C2×C8—182no—
280C4⋊C4—64no—
281C4⋊C4—61no—
282C22⋊C4—32no—
283C22⋊C4—64no—
284C42—61no—
285C22×C3—24no—
286C22×C3—22no—
287C22×C3—22no—
288C22×C3—21no—
289C22×C3—22no—
290C22×C3—41no—
291C22×C3—41no—
292C22×C3—42no—
293C22×C3—42no—
294C22×C3—81no—
295C22×C3—82no—
296C22×C3#67⋊C412yes—
297C22×C3C2×(C2×D3)⋊C411yescharacteristic
298C22×C3D4×Dic312yes—
299C22×C3C2×#21711yescharacteristic
300C3×C4—24no—
301C3×C4—22no—
302C3×C4—22no—
303C3×C4—21no—
304C3×C4—22no—
305C3×C4—21no—
306C3×C4—122no—
307C3×C4—122no—
308C3×C4#88211yescharacteristic
309C3×C4#88611yescharacteristic
310C3×C4#93511yescharacteristic
311C3×C4#93711yescharacteristic
312C3×C4#93912yes—
313C3×C4#93912yes—
314Dic3—42no—
315Dic3—42no—
316C32#191511yescharacteristic, complemented, Sylow
317C23(C2×D3)⋊Dic312yes—
318C23C2×D3×Dic311yescharacteristic
319Q8—22no—
320Q8—121no—
321Q8—122no—
322Q8—121no—
323D4—24no—
324D4—22no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—62no—
328C2×C4—62no—
329C2×C4—64no—
330C2×C4(C2×D3)⋊Dic312yes—
331C2×C4#380512yes—
332C2×C4C2×#62511yescharacteristic
333C2×C4C2×#62611yescharacteristic
334C2×C4#381112yes—
335C8—122no—
336C8—184no—
337C2×C3—21no—
338C2×C3—22no—
339C2×C3—21no—
340C2×C3—22no—
341C2×C3—21no—
342C2×C3—41no—
343C2×C3—42no—
344C2×C3—44no—
345C2×C3—42no—
346C2×C3—42no—
347C2×C3#495811yescharacteristic
348C2×C3#522011yescharacteristic
349C22—22no—
350C22—41no—
351C22—42no—
352C22C2×(C2×D3)⋊Dic311yescharacteristic
353C22#67⋊Dic312yes—
354C4—22no—
355C4—122no—
356C4—122no—
357C4#6396211yescharacteristic
358C4#6398012yes—
359C4#6398111yescharacteristic
360C3—21no—
361C3#7013811yescharacteristic, complemented
362C3#7186611yescharacteristic, complemented
363C2—21no—
364C2—22no—
365C2—42no—
366C2#1059171311yescharacteristic
subgroupG/H
centerC2#10591713
commutatorC23×C32C22×C4
FrattiniC22×C4C2×D32
Fitting, prime radicalC2×C32×#41C22
socleC2×C32#386
cosocleC22×C32×C4C23
hypercenterC2×#41D32
hypocenterC32#1915
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
4. C2×#63560C2semidirect
5. #10589169C2semidirect
316. C32#1915semidirect
361. C3#70138semidirect
362. C3#71866semidirect

Maximal subgroups

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

subgroupindex
#105962902
C3×#58252
C3×#52372
C2×#635602
#105891692
#718663
#701383