Finite Group Databasebeta

← #11788195

Subgroups — #11788195

Order 1152.

1074 conjugacy classes of subgroups; only the 191 normal subgroups are shown.

normal subgroups only

This group has 1074 conjugacy classes of subgroups — too many to draw. Only its 191 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595995C211yesmaximal, characteristic
2C2×#64081C211yesmaximal, characteristic, complemented
3C2×#63652C211yesmaximal, characteristic, complemented
4#10592825C211yesmaximal, characteristic, complemented
5C2×#63632C211yesmaximal, characteristic, complemented
6C32×#339C211yesmaximal, characteristic, complemented
7#10589398C211yesmaximal, characteristic, complemented
8#68757—34nomaximal
9C2×#3828C2211yescharacteristic
10C22×C4×C3⋊D3C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C32×#117C2211yescharacteristic
13C2×C32×C42C2211yescharacteristic
14C2×#3752—21no—
15C2×#3750—21no—
16C2×C4×C3⋊Dic3C2211yescharacteristic
17C2×#3748C2211yescharacteristic
18#64106C412yescomplemented
19#64104C412yescomplemented
20#64095—21no—
21#64091—21no—
22C4×C4⋊(C3⋊D3)—22no—
23#64081—22no—
24#64081—22no—
25#63652—22no—
26#63647—22no—
27#63632—22no—
28#5524—34no—
29C2×#872—34no—
30C2×#825—34no—
31#5126—34no—
32C2×#805—34no—
33C3×#339D314yescomplemented
34#4532—34no—
35C23×C3⋊D3D411yescharacteristic
36C22×C32×C4—21no—
37C22×C32×C4C2311yescharacteristic
38C2×#638—21no—
39C22×C3⋊Dic3—21no—
40C22×C3⋊Dic3D411yescharacteristic
41#3828—21no—
42#3828—21no—
43#3828—21no—
44#3828—21no—
45C2×C4⋊(C3⋊D3)—22no—
46C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
47C2×C4×C3⋊D3—21no—
48C2×C4×C3⋊D3—21no—
49C2×C4×C3⋊D3—21no—
50C2×C4×C3⋊D3—21no—
51C2×C4×C3⋊D3—21no—
52C2×C4×C3⋊D3C2×C412yes—
53C2×C4×C3⋊D3D412yes—
54C2×#634C2×C411yescharacteristic
55C32×M16—21no—
56C32×M16—21no—
57C2×C32×C8—21no—
58C32×C4⋊C4C2×C412yes—
59C32×C22⋊C4—21no—
60C32×C42—21no—
61C32×C42—21no—
62C32×C42D412yescomplemented
63#3752—24no—
64#3752—22no—
65#3752—22no—
66C4⋊(C3⋊Dic3)—22no—
67#3750—24no—
68C4×C3⋊Dic3—21no—
69C4×C3⋊Dic3D412yescomplemented
70#3748—21no—
71#3748—21no—
72C2×C3⋊(C3⋊C8)—21no—
73#1897—91noSylow
74C2×#235—34no—
75C22×C4×D3—34no—
76C2×C3×M16C2×D314yes—
77C3×#117C2×D314yes—
78C2×C3×C42C2×D314yes—
79C2×(C2×D3)⋊C4—64no—
80C2×Dic3⋊C4—64no—
81C2×C4×Dic3—34no—
82C2×#208—34no—
83#897—38no—
84#895—38no—
85#886—64no—
86#882—64no—
87C4×D12—68no—
88#872—68no—
89#872—68no—
90#825—68no—
91(C2×D3)⋊C8—68no—
92#805—68no—
93C23×C32C2×D411yescharacteristic
94C22×C3⋊D3—21no—
95C22×C3⋊D3—21no—
96C22×C3⋊D3—21no—
97C22×C3⋊D3—42no—
98C22×C3⋊D3C22⋊C412yes—
99C2×C32×C4—22no—
100C2×C32×C4—22no—
101C2×C32×C4—42no—
102C2×C32×C4C22×C411yescharacteristic
103C2×C32×C4C2×D411yescharacteristic
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4#4111yescharacteristic
107C2×C32×C4#4111yescharacteristic
108#638—41no—
109#638—41no—
110C2×C3⋊Dic3—21no—
111C2×C3⋊Dic3—21no—
112C2×C3⋊Dic3—21no—
113C2×C3⋊Dic3—22no—
114C2×C3⋊Dic3—42no—
115C2×C3⋊Dic3C22⋊C412yes—
116C4⋊(C3⋊D3)—21no—
117C4⋊(C3⋊D3)—21no—
118C4⋊(C3⋊D3)—44no—
119C4×C3⋊D3—22no—
120C4×C3⋊D3—22no—
121C4×C3⋊D3—22no—
122C4×C3⋊D3—22no—
123C4×C3⋊D3—41no—
124C4×C3⋊D3—41no—
125#634—21no—
126#634—21no—
127C32×C8—41no—
128C3⋊(C3⋊C8)—41no—
129#525—91no—
130C2×#117—91no—
131C2×#104—91no—
132C2×#104—91no—
133#407—91no—
134#339—91no—
135#339C3⋊D311yescharacteristic, complemented
136C23×D3—34no—
137C22×C3×C4—24no—
138C22×C3×C4C22×D314yes—
139C2×#67—64no—
140C22×Dic3—34no—
141C22×Dic3—64no—
142#235—64no—
143#235—64no—
144#235—64no—
145#235—64no—
146C2×D12—34no—
147C2×D12—68no—
148C2×C4×D3—38no—
149C2×C4×D3—38no—
150C2×C4×D3—64no—
151C2×C4×D3—64no—
152C2×C4×D3—64no—
153C2×C4×D3—64no—
154C2×C4×D3—64no—
155C2×Dic6—34no—
156C3×M16—24no—
157C3×M16—24no—
158C2×C3×C8—24no—
159C3×C4⋊C4C4×D318yes—
160C3×C22⋊C4—24no—
161C3×C42—24no—
162C3×C42—24no—
163C3×C42D1218yescomplemented
164(C2×D3)⋊C4—68no—
165(C2×D3)⋊C4—68no—
166(C2×D3)⋊C4—616no—
167C4⋊Dic3—68no—
168Dic3⋊C4—616no—
169C4×Dic3—38no—
170C4×Dic3—64no—
171#208—64no—
172#208—64no—
173C2×C3⋊C8—64no—
174C22×C32—22no—
175C22×C32C2×C22⋊C411yescharacteristic
176C22×C32#12011yescharacteristic
177C22×C32#12311yescharacteristic
178C2×C3⋊D3—22no—
179C2×C3⋊D3—22no—
180C2×C3⋊D3—22no—
181C2×C3⋊D3—42no—
182C2×C3⋊D3—42no—
183C2×C3⋊D3—41no—
184C2×C3⋊D3—42no—
185C32×C4—42no—
186C32×C4—42no—
187C32×C4C4×D411yescharacteristic
188C32×C4C4×D411yescharacteristic
189C32×C4#12111yescharacteristic
190C32×C4#12111yescharacteristic
191C3⋊Dic3—22no—
192C3⋊Dic3—42no—
193C3⋊Dic3—41no—
194C2×#41—91no—
195C23×C4—91no—
196C2×M16—91no—
197C2×M16C2×C3⋊D311yescharacteristic
198#123—181no—
199C22⋊Q8—92no—
200#121—92no—
201#120—181no—
202C4×D4—182no—
203#117—182no—
204#117—182no—
205#117C2×C3⋊D311yescharacteristic
206C2×C4⋊C4—181no—
207C2×C22⋊C4—181no—
208C2×C42—91no—
209C2×C42C2×C3⋊D311yescharacteristic
210#104—182no—
211#104—182no—
212C22⋊C8—182no—
213C23×C3D3×D414yes—
214C22×D3—38no—
215C22×D3—64no—
216C22×D3—64no—
217C22×D3—64no—
218C22×D3—128no—
219C2×C3×C4—28no—
220C2×C3×C4—28no—
221C2×C3×C4—48no—
222C2×C3×C4C2×C4×D314yes—
223C2×C3×C4C2×D1214yes—
224C2×C3×C4#23514yes—
225C2×C3×C4D3×D414yes—
226C2×C3×C4D3×D414yes—
227C2×C3×C4#23914yes—
228#67—124no—
229#67—124no—
230C2×Dic3—38no—
231C2×Dic3—64no—
232C2×Dic3—64no—
233C2×Dic3—64no—
234C2×Dic3—68no—
235C2×Dic3—128no—
236D12—64no—
237D12—64no—
238D12—1216no—
239C4×D3—68no—
240C4×D3—68no—
241C4×D3—68no—
242C4×D3—68no—
243C4×D3—124no—
244C4×D3—124no—
245Dic6—64no—
246Dic6—64no—
247C3×C8—44no—
248C3⋊C8—124no—
249C2×C32—21no—
250C2×C32—21no—
251C2×C32#38611yescharacteristic
252C2×C32#42112yes—
253C3⋊D3—42no—
254C3⋊D3—81no—
255C24—91no—
256#41—181no—
257#41—181no—
258#41—181no—
259#41—181no—
260C2×Q8—91no—
261C2×D4—91no—
262C2×D4—182no—
263C2×D4—181no—
264C22×C4—21no—
265C22×C4—91no—
266C22×C4—92no—
267C22×C4—92no—
268C22×C4—181no—
269C22×C4—181no—
270C22×C4—181no—
271C22×C4—181no—
272C22×C4—181no—
273C22×C4—181no—
274C22×C4C22×C3⋊D311yescharacteristic
275M16—21no—
276M16—21no—
277M16—181no—
278M16—181no—
279C2×C8—21no—
280C2×C8—181no—
281C4⋊C4—182no—
282C4⋊C4—184no—
283C4⋊C4C4×C3⋊D312yes—
284C22⋊C4—21no—
285C22⋊C4—182no—
286C22⋊C4—182no—
287C22⋊C4—184no—
288C42—21no—
289C42—21no—
290C42—92no—
291C42—181no—
292C42C4⋊(C3⋊D3)12yescomplemented
293C22×C3—28no—
294C22×C3D3×C22⋊C414yes—
295C22×C3#88214yes—
296C22×C3#89414yes—
297C2×D3—68no—
298C2×D3—68no—
299C2×D3—68no—
300C2×D3—128no—
301C2×D3—128no—
302C2×D3—124no—
303C2×D3—128no—
304C3×C4—48no—
305C3×C4—48no—
306C3×C4C4×D1214yes—
307C3×C4#88414yes—
308C3×C4#89314yes—
309C3×C4#89514yes—
310Dic3—68no—
311Dic3—128no—
312Dic3—124no—
313C32#189711yescharacteristic, complemented, Sylow
314C23—92no—
315C23—181no—
316C23—181no—
317C23—181no—
318C23—362no—
319C23D4×C3⋊D311yescharacteristic
320Q8—181no—
321Q8—181no—
322D4—181no—
323D4—181no—
324D4—364no—
325D4—361no—
326D4—361no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—42no—
330C2×C4—92no—
331C2×C4—181no—
332C2×C4—181no—
333C2×C4—182no—
334C2×C4—182no—
335C2×C4—182no—
336C2×C4—182no—
337C2×C4—181no—
338C2×C4—182no—
339C2×C4—362no—
340C2×C4—361no—
341C2×C4—361no—
342C2×C4C2×C4×C3⋊D311yescharacteristic
343C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
344C2×C4#382811yescharacteristic
345C2×C4D4×C3⋊D311yescharacteristic
346C2×C4D4×C3⋊D311yescharacteristic
347C2×C4#383211yescharacteristic
348C8—41no—
349C8—361no—
350C2×C3—24no—
351C2×C3—24no—
352C2×C3#466514yes—
353C2×C3#482118yes—
354D3—128no—
355D3—244no—
356C22—22no—
357C22—182no—
358C22—182no—
359C22—182no—
360C22—362no—
361C22—362no—
362C22—362no—
363C22—361no—
364C22C22⋊C4×C3⋊D311yescharacteristic
365C22#6409111yescharacteristic
366C22#6410311yescharacteristic
367C4—42no—
368C4—42no—
369C4—182no—
370C4—362no—
371C4—361no—
372C4C4×C4⋊(C3⋊D3)11yescharacteristic
373C4#6409311yescharacteristic
374C4#6410211yescharacteristic
375C4#6410411yescharacteristic
376C3#6875714yescomplemented
377C2—21no—
378C2—21no—
379C2—362no—
380C2—721no—
381C2#1059236411yescharacteristic
382C2#1059252012yes—
subgroupG/H
centerC2×C4D4×C3⋊D3
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#339C2
socleC22×C32C2×C22⋊C4
prime radical#10595995C2
cosocleC22×C32×C4C23
hypercenter#339C3⋊D3
hypocenterC32#1897
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
2. C2×#64081C2semidirect
3. C2×#63652C2semidirect
4. #10592825C2semidirect
5. C2×#63632C2semidirect
6. C32×#339C2semidirect
7. #10589398C2semidirect
18. #64106C4semidirect
19. #64104C4semidirect
33. C3×#339D3semidirect
62. C32×C42D4semidirect
69. C4×C3⋊Dic3D4semidirect
135. #339C3⋊D3semidirect
163. C3×C42D12semidirect
292. C42C4⋊(C3⋊D3)semidirect
313. C32#1897semidirect
376. C3#68757semidirect

Maximal subgroups

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

subgroupindex
#105959952
C2×#640812
C2×#636522
#105928252
C2×#636322
C32×#3392
#105893982
#687573