Finite Group Databasebeta

← #11790798

Subgroups — #11790798

Order 1152.

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

normal subgroups only

This group has 960 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#10596303C211yesmaximal, characteristic
2C2×C32×#104C211yesmaximal, characteristic, complemented
3C2×#63664C211yesmaximal, characteristic, complemented
4C2×#63652C211yesmaximal, characteristic, complemented
5#10592817C211yesmaximal, characteristic, complemented
6#10592631C211yesmaximal, characteristic, complemented
7C2×#63632C211yesmaximal, characteristic, complemented
8#70357—34nomaximal
9C2×C32×#41C2211yescharacteristic
10C2×#3828C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C2×C32×C42C2211yescharacteristic
13#64156C411yescharacteristic, complemented
14#64153C411yescharacteristic, complemented
15#64149C411yescharacteristic, complemented
16#64148—22no—
17#64145C411yescharacteristic, complemented
18C4×#638—22no—
19C2×C4×C3⋊Dic3C2211yescharacteristic
20C2×C4×C3⋊Dic3C2211yescharacteristic
21C2×#3748C2211yescharacteristic
22C32×#104—22no—
23#63664—22no—
24#63658—22no—
25#63652—22no—
26#63641—22no—
27#63632—22no—
28#5832—34no—
29C2×C3×#104D314yescomplemented
30C2×#837—34no—
31C2×#825—34no—
32#5118—34no—
33#4932—34no—
34C2×#805—34no—
35C32×#41—21no—
36C32×#41—21no—
37C32×#41—21no—
38C32×#41—21no—
39C2×C32×Q8C2×C411yescharacteristic
40C2×C32×D4—21no—
41C2×C32×D4C2×C411yescharacteristic
42C22×C32×C4—21no—
43C22×C32×C4—21no—
44C22×C32×C4C2311yescharacteristic
45C2×#638—21no—
46C2×#638—22no—
47C22×C3⋊Dic3—21no—
48C22×C3⋊Dic3D412yes—
49#3828—21no—
50#3828—21no—
51#3828—21no—
52#3828—21no—
53C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
54C2×C4×C3⋊D3—21no—
55C2×#634C2×C411yescharacteristic
56C32×M16—21no—
57C32×M16—21no—
58C2×C32×C8—21no—
59C32×C42—21no—
60C32×C42D412yescomplemented
61#3757—22no—
62#3752—22no—
63#3750—22no—
64C4×C3⋊Dic3—21no—
65C4×C3⋊Dic3C2×C411yescharacteristic
66C4×C3⋊Dic3C2×C411yescharacteristic
67C4×C3⋊Dic3D412yes—
68C4×C3⋊Dic3D412yescomplemented
69#3748—21no—
70#3748—21no—
71C2×C3⋊(C3⋊C8)—21no—
72#1963—91noSylow
73C2×C3×#41C2×D314yes—
74C2×#235—34no—
75C2×C3×M16C2×D314yes—
76C2×C3×C42C2×D314yes—
77#947—34no—
78#944—34no—
79#940—34no—
80#939—68no—
81#936—34no—
82C4×#67—68no—
83C2×C4×Dic3—34no—
84C2×C4×Dic3—34no—
85C2×#208—34no—
86C3×#104—28no—
87#837—68no—
88C3⋊#95—68no—
89#825—68no—
90Dic3⋊C8—68no—
91#805—68no—
92C23×C32—21no—
93C23×C32C2×D411yescharacteristic
94C22×C3⋊D3—21no—
95C32×Q8—21no—
96C32×Q8—21no—
97C32×D4—21no—
98C32×D4—21no—
99C32×D4—41no—
100C32×D4—41no—
101C2×C32×C4—21no—
102C2×C32×C4—22no—
103C2×C32×C4—42no—
104C2×C32×C4—41no—
105C2×C32×C4—41no—
106C2×C32×C4C22×C411yescharacteristic
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4#4111yescharacteristic
111C2×C32×C4#4111yescharacteristic
112#638—44no—
113#638—41no—
114#638—41no—
115C2×C3⋊Dic3—21no—
116C2×C3⋊Dic3—22no—
117C2×C3⋊Dic3—42no—
118C2×C3⋊Dic3—42no—
119C2×C3⋊Dic3C22⋊C412yes—
120C2×C3⋊Dic3C22⋊C412yes—
121C4⋊(C3⋊D3)—21no—
122C4⋊(C3⋊D3)—21no—
123C4×C3⋊D3—41no—
124C4×C3⋊D3—41no—
125#634—21no—
126#634—21no—
127C32×C8—41no—
128C3⋊(C3⋊C8)—41no—
129#532—91no—
130#423—91no—
131C2×#104—91no—
132C2×#104—91no—
133C2×#104—91no—
134C2×#104C3⋊D311yescharacteristic, complemented
135#376—91no—
136C3×#41—24no—
137C3×#41—24no—
138C3×#41—24no—
139C3×#41—24no—
140C2×C3×Q8C4×D314yes—
141C2×C3×D4—24no—
142C2×C3×D4C4×D314yes—
143C22×C3×C4—24no—
144C22×C3×C4—24no—
145C22×C3×C4C22×D314yes—
146C2×#67—68no—
147C2×#67—64no—
148C22×Dic3—38no—
149C22×Dic3—64no—
150#235—64no—
151#235—64no—
152#235—64no—
153#235—64no—
154C2×D12—34no—
155C2×C4×D3—64no—
156C2×Dic6—34no—
157C3×M16—24no—
158C3×M16—24no—
159C2×C3×C8—24no—
160C3×C42—24no—
161C3×C42#6718yescomplemented
162#217—68no—
163(C2×D3)⋊C4—68no—
164Dic3⋊C4—68no—
165C4×Dic3—34no—
166C4×Dic3—34no—
167C4×Dic3—38no—
168C4×Dic3—38no—
169C4×Dic3—64no—
170#208—64no—
171#208—64no—
172C2×C3⋊C8—64no—
173C22×C32—22no—
174C22×C32—41no—
175C22×C32—42no—
176C22×C32C2×C22⋊C411yescharacteristic
177C22×C32#12111yescharacteristic
178C22×C32#12111yescharacteristic
179C2×C3⋊D3—41no—
180C2×C3⋊D3—42no—
181C32×C4—42no—
182C32×C4—41no—
183C32×C4C4×D411yescharacteristic
184C32×C4C4×D411yescharacteristic
185C32×C4#12411yescharacteristic
186C32×C4#12711yescharacteristic
187C3⋊Dic3—22no—
188C3⋊Dic3—22no—
189C3⋊Dic3—42no—
190C3⋊Dic3—41no—
191C2×#41—91no—
192C2×#41C2×C3⋊D311yescharacteristic
193C2×M16—91no—
194C2×M16C2×C3⋊D311yescharacteristic
195C4⋊Q8—91no—
196#127—91no—
197#124—91no—
198#124—91no—
199#121—182no—
200C4×D4—182no—
201C2×C42—91no—
202C2×C42—91no—
203C2×C42C2×C3⋊D311yescharacteristic
204C4⋊C8—182no—
205#104—22no—
206#104—182no—
207#104—182no—
208#104—182no—
209#95—182no—
210C23×C3—24no—
211C23×C3D3×D414yes—
212C22×D3—64no—
213C3×Q8—24no—
214C3×Q8—24no—
215C3×D4—24no—
216C3×D4—24no—
217C3×D4—44no—
218C3×D4—44no—
219C2×C3×C4—24no—
220C2×C3×C4—28no—
221C2×C3×C4—48no—
222C2×C3×C4—44no—
223C2×C3×C4—44no—
224C2×C3×C4C2×C4×D314yes—
225C2×C3×C4#23514yes—
226C2×C3×C4D3×D414yes—
227C2×C3×C4D3×D414yes—
228C2×C3×C4#23714yes—
229C2×C3×C4C2×#6714yes—
230#67—1216no—
231#67—124no—
232#67—124no—
233C2×Dic3—38no—
234C2×Dic3—38no—
235C2×Dic3—64no—
236C2×Dic3—68no—
237C2×Dic3—128no—
238C2×Dic3—128no—
239D12—64no—
240D12—64no—
241C4×D3—124no—
242C4×D3—124no—
243Dic6—64no—
244Dic6—64no—
245C3×C8—44no—
246C3⋊C8—124no—
247C2×C32—21no—
248C2×C32—21no—
249C2×C32—81no—
250C2×C32#39011yescharacteristic
251C2×C32#42112yes—
252C3⋊D3—81no—
253#41—21no—
254#41—21no—
255#41—21no—
256#41—21no—
257#41—181no—
258#41—181no—
259#41—181no—
260#41—181no—
261C2×Q8—91no—
262C2×Q8C4×C3⋊D311yescharacteristic
263C2×D4—21no—
264C2×D4—91no—
265C2×D4—182no—
266C2×D4—181no—
267C2×D4C4×C3⋊D311yescharacteristic
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—92no—
271C22×C4—181no—
272C22×C4—181no—
273C22×C4C22×C3⋊D311yescharacteristic
274M16—21no—
275M16—21no—
276M16—181no—
277M16—181no—
278C2×C8—21no—
279C2×C8—181no—
280C4⋊C4—182no—
281C22⋊C4—182no—
282C22⋊C4—182no—
283C42—21no—
284C42—91no—
285C42—91no—
286C42—92no—
287C42—92no—
288C42—181no—
289C42#63812yescomplemented
290C22×C3—28no—
291C22×C3—44no—
292C22×C3—48no—
293C22×C3D3×C22⋊C414yes—
294C22×C3#88414yes—
295C22×C3#93914yes—
296C2×D3—124no—
297C2×D3—128no—
298C3×C4—48no—
299C3×C4—44no—
300C3×C4#67⋊C414yes—
301C3×C4#88514yes—
302C3×C4C4×#6714yes—
303C3×C4#94014yes—
304Dic3—68no—
305Dic3—68no—
306Dic3—128no—
307Dic3—124no—
308C32#196311yescharacteristic, complemented, Sylow
309C23—21no—
310C23—181no—
311C23D4×C3⋊D311yescharacteristic
312Q8—21no—
313Q8—21no—
314Q8—181no—
315Q8—181no—
316D4—21no—
317D4—21no—
318D4—41no—
319D4—41no—
320D4—181no—
321D4—181no—
322D4—364no—
323D4—361no—
324D4—361no—
325C2×C4—21no—
326C2×C4—22no—
327C2×C4—42no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—92no—
331C2×C4—92no—
332C2×C4—181no—
333C2×C4—182no—
334C2×C4—362no—
335C2×C4—362no—
336C2×C4—361no—
337C2×C4—361no—
338C2×C4C2×C4×C3⋊D311yescharacteristic
339C2×C4#382811yescharacteristic
340C2×C4D4×C3⋊D311yescharacteristic
341C2×C4D4×C3⋊D311yescharacteristic
342C2×C4#383011yescharacteristic
343C2×C4C2×#63811yescharacteristic
344C8—41no—
345C8—361no—
346C2×C3—24no—
347C2×C3—24no—
348C2×C3—84no—
349C2×C3#482118yes—
350C2×C3#495714yes—
351D3—244no—
352C22—22no—
353C22—42no—
354C22—41no—
355C22—362no—
356C22—361no—
357C22C22⋊C4×C3⋊D311yescharacteristic
358C22#6409311yescharacteristic
359C22#6414811yescharacteristic
360C4—42no—
361C4—41no—
362C4—182no—
363C4—182no—
364C4—362no—
365C4—361no—
366C4#6409011yescharacteristic
367C4#6409411yescharacteristic
368C4C4×#63811yescharacteristic
369C4#6414911yescharacteristic
370C3#7035714yescomplemented
371C2—21no—
372C2—21no—
373C2—81no—
374C2—721no—
375C2#1059252012yes—
376C2#1059265611yescharacteristic
subgroupG/H
centerC2×C4D4×C3⋊D3
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC2×C32×#104C2
socleC22×C32C2×C22⋊C4
prime radical#10596303C2
cosocleC22×C32×C4C23
hypercenterC2×#104C3⋊D3
hypocenterC32#1963
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. C2×C32×#104C2semidirect
3. C2×#63664C2semidirect
4. C2×#63652C2semidirect
5. #10592817C2semidirect
6. #10592631C2semidirect
7. C2×#63632C2semidirect
13. #64156C4semidirect
14. #64153C4semidirect
15. #64149C4semidirect
17. #64145C4semidirect
29. C2×C3×#104D3semidirect
60. C32×C42D4semidirect
68. C4×C3⋊Dic3D4semidirect
134. C2×#104C3⋊D3semidirect
161. C3×C42#67semidirect
289. C42#638semidirect
308. C32#1963semidirect
370. C3#70357semidirect

Maximal subgroups

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

subgroupindex
#105963032
C2×C32×#1042
C2×#636642
C2×#636522
#105928172
#105926312
C2×#636322
#703573