Finite Group Databasebeta

← #11777819

Subgroups — #11777819

Order 1152.

393 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 393 conjugacy classes of subgroups — too many to draw. Only its 102 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
1C4×#3754C211yesmaximal, characteristic
2C3×#5012C211yesmaximal, characteristic
3#10590296C211yesmaximal, characteristic, complemented
4C3×D4⋊(C3⋊C8)C211yesmaximal, characteristic
5#10589098C211yesmaximal, characteristic, complemented
6#10589085C211yesmaximal, characteristic, complemented
7C3⋊C82C211yesmaximal, characteristic, complemented
8#70866—31nomaximal
9#68161—31nomaximal
10C32×C4×D4C2211yescharacteristic
11C2×#3754C411yescharacteristic
12C4×#634C2211yescharacteristic
13C2×C3×#208—21no—
14#63659C411yescharacteristic
15#63637C411yescharacteristic
16#63635C411yescharacteristic
17C4×C3⋊(C3⋊C8)C2211yescharacteristic
18C3×#830—21no—
19C3×C4⋊(C3⋊C8)C2211yescharacteristic
20C3×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×C4×C3⋊C8C2211yescharacteristic
22C3×C4×C3⋊C8C2211yescharacteristic
23#63572—21no—
24#63555—21no—
25C3×#436—31no—
26C4×#214—31no—
27C4×#214—31no—
28C4×#214—61no—
29#5012D311yescharacteristic
30#4831—31no—
31#4679—31no—
32C3×D4⋊C8—31no—
33D4⋊(C3⋊C8)D311yescharacteristic
34#4484—31no—
35#4480—31no—
36#4480—31no—
37#4456—31no—
38C8×C3⋊C8—31no—
39C8×C3⋊C8—31no—
40C2×C32×D4C2×C411yescharacteristic
41C22×C32×C4—21no—
42C2×#634C2×C411yescharacteristic
43C32×C4⋊C4C2×C411yescharacteristic
44C32×C22⋊C4—21no—
45C32×C42C2311yescharacteristic
46#3754—22no—
47C4⋊(C3⋊Dic3)C2×C411yescharacteristic
48#3750—21no—
49C4×C3⋊Dic3—21no—
50C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
51C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
52C3×#208—42no—
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8—21no—
56C2×C3×C3⋊C8D411yescharacteristic
57C2×C3×C3⋊C8D411yescharacteristic
58#1590—91noSylow
59C2×C3×M16—61no—
60C3×C4×D4—21no—
61C3×C4×D4C2×D311yescharacteristic
62C3×C4×D4C2×D311yescharacteristic
63C2×#214—31no—
64C2×#214—31no—
65C2×#214—61no—
66C2×#208—21no—
67C4×Dic6—31no—
68C4×Dic6—31no—
69C4×Dic6—61no—
70C3×C4⋊C8—31no—
71C3×C4⋊C8—31no—
72C3×C22⋊C8—61no—
73C3×C4×C8—31no—
74C3×C4×C8—31no—
75#832—31no—
76#832—31no—
77#832—61no—
78#830—21no—
79#815—61no—
80#815—61no—
81Dic3⋊C8—61no—
82Dic3⋊C8—61no—
83#810—31no—
84#810—31no—
85#810—61no—
86#808—31no—
87#808—31no—
88#808—61no—
89C4⋊(C3⋊C8)C2×D311yescharacteristic
90C4⋊(C3⋊C8)C2×D311yescharacteristic
91C4×C3⋊C8—31no—
92C4×C3⋊C8—31no—
93C4×C3⋊C8—61no—
94C4×C3⋊C8C2×D311yescharacteristic
95C4×C3⋊C8C2×D311yescharacteristic
96C23×C32—21no—
97C32×D4—21no—
98C32×D4—21no—
99C2×C32×C4—21no—
100C2×C32×C4—41no—
101C2×C32×C4—41no—
102C2×C32×C4C22×C411yescharacteristic
103C2×C32×C4C2×D411yescharacteristic
104C2×C32×C4#4111yescharacteristic
105C2×C3⋊Dic3—21no—
106C2×C3⋊Dic3—21no—
107#634—21no—
108#634—21no—
109C3⋊(C3⋊C8)—21no—
110C3⋊(C3⋊C8)M1612yescomplemented
111C3×C3⋊C8—22no—
112C3×C3⋊C8—21no—
113C3×C3⋊C8—41no—
114C3×C3⋊C8—41no—
115C3×C3⋊C8SD1612yescomplemented
116#446—91no—
117C4×SD16—91no—
118#436—31no—
119#334—91no—
120Q8⋊C8—91no—
121D4⋊C8—31no—
122C82—91no—
123C2×C3×D4—21no—
124C2×C3×D4C4×D311yescharacteristic
125C2×C3×D4C4×D311yescharacteristic
126C22×C3×C4—21no—
127C22×C3×C4—21no—
128C22×C3×C4—41no—
129C2×Dic6—31no—
130C2×Dic6—31no—
131C2×Dic6—61no—
132C3×M16—122no—
133C2×C3×C8—31no—
134C2×C3×C8—31no—
135C2×C3×C8—61no—
136C2×C3×C8—61no—
137C2×C3×C8—61no—
138C3×C4⋊C4—21no—
139C3×C4⋊C4C4×D311yescharacteristic
140C3×C4⋊C4C4×D311yescharacteristic
141C3×C22⋊C4—21no—
142C3×C22⋊C4—21no—
143C3×C22⋊C4—41no—
144C3×C42—21no—
145C3×C42C22×D311yescharacteristic
146C3×C42C22×D311yescharacteristic
147#214—62no—
148#214—62no—
149#214—64no—
150C4⋊Dic3—31no—
151C4⋊Dic3—31no—
152C4⋊Dic3—61no—
153Dic3⋊C4—61no—
154Dic3⋊C4—61no—
155Dic3⋊C4—121no—
156C4×Dic3—61no—
157C4×Dic3—61no—
158C4×Dic3—121no—
159#208—42no—
160C2×C3⋊C8—21no—
161C2×C3⋊C8—21no—
162C2×C3⋊C8—21no—
163C2×C3⋊C8—31no—
164C2×C3⋊C8—31no—
165C2×C3⋊C8—31no—
166C2×C3⋊C8—31no—
167C2×C3⋊C8—61no—
168C2×C3⋊C8—61no—
169C2×C3⋊C8#6711yescharacteristic
170C2×C3⋊C8#6711yescharacteristic
171C22×C32—41no—
172C22×C32—41no—
173C22×C32—41no—
174C22×C32C4×D411yescharacteristic
175C32×C4—21no—
176C32×C4—41no—
177C32×C4C2×M1611yescharacteristic
178C32×C4#13111yescharacteristic
179C32×C4C2×SD1611yescharacteristic
180C32×C4#13511yescharacteristic
181C3⋊Dic3—41no—
182C3⋊Dic3—41no—
183C2×SD16—91no—
184C2×M16—61no—
185C4×Q8—91no—
186C4×D4D3211yescharacteristic
187#106—91no—
188C4⋊C8—31no—
189C4⋊C8—31no—
190C4⋊C8—181no—
191#103—91no—
192#102—91no—
193C22⋊C8—61no—
194#97—181no—
195C4×C8—31no—
196C4×C8—31no—
197C4×C8—91no—
198C23×C3—21no—
199C23×C3—21no—
200C23×C3—41no—
201C3×D4—22no—
202C3×D4—21no—
203C3×D4—21no—
204C3×D4—21no—
205C3×D4—21no—
206C3×D4—41no—
207C2×C3×C4—21no—
208C2×C3×C4—21no—
209C2×C3×C4—21no—
210C2×C3×C4—21no—
211C2×C3×C4—21no—
212C2×C3×C4—41no—
213C2×C3×C4—41no—
214C2×C3×C4—41no—
215C2×C3×C4—41no—
216C2×C3×C4—41no—
217C2×C3×C4—81no—
218C2×C3×C4—81no—
219C2×C3×C4C2×C4×D311yescharacteristic
220C2×C3×C4C2×C4×D311yescharacteristic
221C2×C3×C4#23511yescharacteristic
222C2×C3×C4D3×D411yescharacteristic
223C2×C3×C4#23711yescharacteristic
224C2×C3×C4C2×#6711yescharacteristic
225C2×Dic3—61no—
226C2×Dic3—61no—
227C2×Dic3—61no—
228C2×Dic3—61no—
229C2×Dic3—121no—
230C2×Dic3—121no—
231Dic6—62no—
232Dic6—61no—
233Dic6—61no—
234Dic6—61no—
235Dic6—61no—
236Dic6—121no—
237C3×C8—32no—
238C3×C8—62no—
239C3×C8—61no—
240C3×C8—121no—
241C3×C8—121no—
242C3⋊C8—22no—
243C3⋊C8—21no—
244C3⋊C8—32no—
245C3⋊C8—32no—
246C3⋊C8—41no—
247C3⋊C8—41no—
248C3⋊C8—62no—
249C3⋊C8—61no—
250C3⋊C8—61no—
251C3⋊C8—121no—
252C3⋊C8#21412yescomplemented
253C2×C32—81no—
254C2×C32#43611yescharacteristic
255C2×C32C4×SD1611yescharacteristic
256C2×C32#44311yescharacteristic
257C2×Q8—91no—
258C2×D4#62411yescharacteristic
259C22×C4—21no—
260SD16—182no—
261M16—122no—
262C2×C8—31no—
263C2×C8—31no—
264C2×C8—61no—
265C2×C8—61no—
266C2×C8—61no—
267C2×C8—91no—
268C2×C8—91no—
269C4⋊C4—91no—
270C4⋊C4—181no—
271C4⋊C4#62411yescharacteristic
272C22⋊C4—21no—
273C42—181no—
274C42C2×D3211yescharacteristic
275C22×C3—21no—
276C22×C3—42no—
277C22×C3—41no—
278C22×C3—41no—
279C22×C3—41no—
280C22×C3—41no—
281C22×C3—41no—
282C22×C3—41no—
283C22×C3—81no—
284C22×C3—81no—
285C22×C3#67⋊C411yescharacteristic
286C22×C3C4×#6711yescharacteristic
287C3×C4—21no—
288C3×C4—21no—
289C3×C4—21no—
290C3×C4—21no—
291C3×C4—21no—
292C3×C4—21no—
293C3×C4—41no—
294C3×C4—41no—
295C3×C4—41no—
296C3×C4—81no—
297C3×C4#90111yescharacteristic
298C3×C4D3×M1611yescharacteristic
299C3×C4D3×M1611yescharacteristic
300C3×C4#90711yescharacteristic
301C3×C4#91211yescharacteristic
302C3×C4D3×SD1611yescharacteristic
303C3×C4C2×#21411yescharacteristic
304C3×C4#95011yescharacteristic
305Dic3—122no—
306Dic3—121no—
307Dic3—121no—
308Dic3—121no—
309Dic3—121no—
310Dic3—241no—
311C32#159011yescharacteristic, complemented, Sylow
312C23—21no—
313Q8—181no—
314Q8—181no—
315D4—21no—
316D4—21no—
317C2×C4—21no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—181no—
321C2×C4—181no—
322C2×C4#380411yescharacteristic
323C2×C4C2×#62411yescharacteristic
324C2×C4D3×#6711yescharacteristic
325C8—32no—
326C8—62no—
327C8—61no—
328C8—92no—
329C8—121no—
330C8—121no—
331C8—181no—
332C2×C3—21no—
333C2×C3—21no—
334C2×C3—21no—
335C2×C3—82no—
336C2×C3—81no—
337C2×C3—81no—
338C2×C3#472911yescharacteristic
339C2×C3#475811yescharacteristic
340C2×C3#482411yescharacteristic
341C2×C3C4×#21411yescharacteristic
342C2×C3#512811yescharacteristic
343C2×C3#514411yescharacteristic
344C22—41no—
345C22—41no—
346C22—41no—
347C22#6395211yescharacteristic
348C4—21no—
349C4—41no—
350C4—361no—
351C4—361no—
352C4#6381711yescharacteristic
353C4#6381811yescharacteristic
354C4D3×#21411yescharacteristic
355C4#6393311yescharacteristic
356C3—21no—
357C3#6816111yescharacteristic, complemented
358C3#7086611yescharacteristic, complemented
359C2—81no—
360C2#1059105111yescharacteristic
361C2#1059140111yescharacteristic
362C2#1059166211yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4×D4C22
socleC22×C32C4×D4
prime radicalC2×C32×D4C2×C4
cosocleC32×C42C23
hypercenterC4×D4D32
hypocenterC32#1590
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
3. #10590296C2semidirect
5. #10589098C2semidirect
6. #10589085C2semidirect
7. C3⋊C82C2semidirect
110. C3⋊(C3⋊C8)M16semidirect
115. C3×C3⋊C8SD16semidirect
252. C3⋊C8#214semidirect
311. C32#1590semidirect
357. C3#68161semidirect
358. C3#70866semidirect

Maximal subgroups

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

subgroupindex
C4×#37542
C3×#50122
#105902962
C3×D4⋊(C3⋊C8)2
#105890982
#105890852
C3⋊C822
#708663
#681613