Finite Group Databasebeta

← #11779473

Subgroups — #11779473

Order 1152.

444 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 94 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
1Dic62C211yesmaximal, characteristic
2C3×#4850C211yesmaximal, characteristic
3#10590386C211yesmaximal, characteristic
4#10590310C211yesmaximal, characteristic
5#10589347C211yesmaximal, characteristic
6C3×#4484C211yesmaximal, characteristic
7#10589084C211yesmaximal, characteristic
8#71161—31nomaximal
9#68267—31nomaximal
10#64078C2211yescharacteristic
11C3×#869C2211yescharacteristic
12C3×C4×Dic6C2211yescharacteristic
13C3×C4×Dic6C2211yescharacteristic
14#63918—21no—
15#63918—21no—
16Dic3×Dic6—21no—
17Dic3×Dic6—21no—
18#63840—22no—
19C2×#3719—22no—
20C32×C4⋊C8C2211yescharacteristic
21C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
22C3×#818—21no—
23C3×#816—21no—
24C3×C4×C3⋊C8C2211yescharacteristic
25#63576—21no—
26#63565—21no—
27Q8×Dic6—31no—
28Q8×Dic6—31no—
29C3×#477—31no—
30#5092—31no—
31#5091—31no—
32#5021—31no—
33#4850D311yescharacteristic
34#4699—31no—
35C3×Q8⋊C8—31no—
36#4535—31no—
37#4484D311yescharacteristic
38#4481—31no—
39#4481—31no—
40#4481—61no—
41#4456—31no—
42C2×#634D412yes—
43C2×C3×Dic6—21no—
44C2×C3×Dic6D411yescharacteristic
45C2×C3×Dic6D411yescharacteristic
46C2×#627—22no—
47C2×C32×C8—21no—
48C32×C42C2311yescharacteristic
49C4⋊(C3⋊Dic3)—21no—
50C4⋊(C3⋊Dic3)—21no—
51C2×C3⋊(C3⋊C8)—21no—
52C3×C4⋊Dic3—21no—
53C3×C4⋊Dic3—21no—
54C3×C4⋊Dic3D411yescharacteristic
55C3×C4⋊Dic3D411yescharacteristic
56C3×Dic3⋊C4—21no—
57C3×Dic3⋊C4—21no—
58C3×C4×Dic3—21no—
59C3×C4×Dic3—21no—
60C2×C3×C3⋊C8—21no—
61Dic3⋊Dic3—22no—
62Dic3⋊Dic3—22no—
63Dic32—22no—
64#3719—44no—
65#1633—91noSylow
66C3×C4⋊Q8—31no—
67C3×C4×Q8—31no—
68C3×C4×Q8—31no—
69Q8×Dic3—61no—
70Q8×Dic3—61no—
71C2×#216—62no—
72C2×Dic12—62no—
73#888—61no—
74#888—61no—
75#888—62no—
76#888—62no—
77#869—31no—
78#869—31no—
79#869—61no—
80#869—61no—
81#869—61no—
82#869C2×D311yescharacteristic
83C4×Dic6—61no—
84C4×Dic6—61no—
85C4×Dic6C2×D311yescharacteristic
86C4×Dic6C2×D311yescharacteristic
87C3×#107—61no—
88C3×C4⋊C8—21no—
89C3×C4⋊C8C2×D311yescharacteristic
90C3×C4⋊C8C2×D311yescharacteristic
91C3×#103—61no—
92C3×C4×C8—31no—
93#835—61no—
94#818—21no—
95#816—21no—
96#810—61no—
97#807—61no—
98#807—61no—
99C4⋊(C3⋊C8)—31no—
100C4⋊(C3⋊C8)—31no—
101C4⋊(C3⋊C8)—61no—
102C4×C3⋊C8C2×D311yescharacteristic
103C2×C32×C4C2×D411yescharacteristic
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4C2×D411yescharacteristic
106C2×C3⋊Dic3—22no—
107#634—42no—
108C2×C3×Dic3—21no—
109C2×C3×Dic3—21no—
110C2×C3×Dic3—21no—
111C2×C3×Dic3—21no—
112C2×C3×Dic3—41no—
113C3×Dic6—21no—
114C3×Dic6—21no—
115C3×Dic6—42no—
116C3×Dic6Q1612yescomplemented
117C3×Dic6Q1612yescomplemented
118#627—82no—
119C32×C8—41no—
120C3⋊(C3⋊C8)—41no—
121C3×C3⋊C8—22no—
122Q82—91no—
123#494—91no—
124#477—31no—
125#477—91no—
126#333—91no—
127Q8⋊C8—31no—
128Q8⋊C8—91no—
129C2×C3×Q8—31no—
130C2×C3×Q8—31no—
131C2×C3×Q8—61no—
132C2×Dic6—21no—
133C2×Dic6—32no—
134C2×Dic6—32no—
135C2×Dic6—62no—
136C2×Dic6—62no—
137C2×Dic6—62no—
138C2×Dic6D1211yescharacteristic
139C2×Dic6#6711yescharacteristic
140C2×C3×C8—21no—
141C2×C3×C8—21no—
142C2×C3×C8—41no—
143C2×C3×C8—61no—
144C3×C4⋊C4—31no—
145C3×C4⋊C4—31no—
146C3×C4⋊C4—61no—
147C3×C4⋊C4—61no—
148C3×C4⋊C4—61no—
149C3×C4⋊C4—61no—
150C3×C42—21no—
151C3×C42—61no—
152C3×C42—61no—
153C3×C42C22×D311yescharacteristic
154C3×C42C22×D311yescharacteristic
155#216—124no—
156C4⋊Dic3—21no—
157C4⋊Dic3—21no—
158C4⋊Dic3—62no—
159C4⋊Dic3—62no—
160C4⋊Dic3—61no—
161C4⋊Dic3—61no—
162C4⋊Dic3—61no—
163C4⋊Dic3—61no—
164C4⋊Dic3—121no—
165C4⋊Dic3—121no—
166C4⋊Dic3D1211yescharacteristic
167C4⋊Dic3#6711yescharacteristic
168Dic3⋊C4—21no—
169Dic3⋊C4—21no—
170Dic3⋊C4—62no—
171Dic3⋊C4—62no—
172C4×Dic3—21no—
173C4×Dic3—21no—
174C4×Dic3—62no—
175C4×Dic3—62no—
176C2×C3⋊C8—21no—
177C2×C3⋊C8—61no—
178C2×C3⋊C8—61no—
179C2×C3⋊C8—121no—
180Dic12—124no—
181C22×C32#12011yescharacteristic
182C32×C4—21no—
183C32×C4C2×Q1611yescharacteristic
184C32×C4C2×Q1611yescharacteristic
185C32×C4#13711yescharacteristic
186C32×C4#13711yescharacteristic
187C3⋊Dic3—42no—
188C3×Dic3—22no—
189C3×Dic3—22no—
190C3×Dic3—41no—
191C3×Dic3—41no—
192C3×Dic3—81no—
193C2×Q16—182no—
194C4⋊Q8—31no—
195C4⋊Q8—91no—
196C4⋊Q8—181no—
197C4⋊Q8—181no—
198C4⋊Q8—182no—
199C4×Q8—31no—
200C4×Q8—31no—
201C4×Q8—181no—
202C4×Q8—181no—
203#107—61no—
204#107—181no—
205C4⋊C8—91no—
206C4⋊C8D3211yescharacteristic
207#103—61no—
208#103—181no—
209C4×C8—31no—
210C3×Q8—32no—
211C3×Q8—32no—
212C3×Q8—61no—
213C3×Q8—61no—
214C3×Q8—122no—
215C2×C3×C4—21no—
216C2×C3×C4—21no—
217C2×C3×C4—21no—
218C2×C3×C4—61no—
219C2×C3×C4—61no—
220C2×C3×C4—61no—
221C2×C3×C4—61no—
222C2×C3×C4—121no—
223C2×C3×C4C2×D1211yescharacteristic
224C2×C3×C4D3×D411yescharacteristic
225C2×C3×C4D3×D411yescharacteristic
226C2×C3×C4D3×D411yescharacteristic
227C2×C3×C4D3×D411yescharacteristic
228C2×C3×C4C2×#6711yescharacteristic
229C2×Dic3—21no—
230C2×Dic3—21no—
231C2×Dic3—21no—
232C2×Dic3—21no—
233C2×Dic3—41no—
234C2×Dic3—62no—
235C2×Dic3—62no—
236C2×Dic3—122no—
237Dic6—21no—
238Dic6—21no—
239Dic6—42no—
240Dic6—122no—
241Dic6—122no—
242Dic6—242no—
243Dic6—242no—
244Dic6—242no—
245Dic6Dic1212yescomplemented
246Dic6#21612yescomplemented
247C3×C8—41no—
248C3×C8—41no—
249C3×C8—62no—
250C3×C8—81no—
251C3⋊C8—22no—
252C3⋊C8—121no—
253C3⋊C8—121no—
254C3⋊C8—241no—
255C2×C32#45111yescharacteristic
256C2×C32#45111yescharacteristic
257C2×C32#45311yescharacteristic
258C2×Q8—31no—
259C2×Q8—31no—
260C2×Q8—61no—
261C2×Q8—92no—
262C2×Q8—182no—
263Q16—364no—
264C2×C8—21no—
265C2×C8—61no—
266C2×C8—181no—
267C4⋊C4—31no—
268C4⋊C4—31no—
269C4⋊C4—61no—
270C4⋊C4—61no—
271C4⋊C4—61no—
272C4⋊C4—61no—
273C4⋊C4—182no—
274C4⋊C4—182no—
275C4⋊C4—181no—
276C4⋊C4—181no—
277C42—61no—
278C42—61no—
279C42—182no—
280C42C2×D3211yescharacteristic
281C22×C3—21no—
282C22×C3#88211yescharacteristic
283C22×C3#93711yescharacteristic
284C3×C4—21no—
285C3×C4—21no—
286C3×C4—21no—
287C3×C4—21no—
288C3×C4—21no—
289C3×C4—21no—
290C3×C4—41no—
291C3×C4—62no—
292C3×C4—62no—
293C3×C4—121no—
294C3×C4—121no—
295C3×C4—241no—
296C3×C4C2×Dic1211yescharacteristic
297C3×C4#90911yescharacteristic
298C3×C4#91511yescharacteristic
299C3×C4D3×Q1611yescharacteristic
300C3×C4D3×Q1611yescharacteristic
301C3×C4#91811yescharacteristic
302C3×C4C2×#21611yescharacteristic
303C3×C4#95111yescharacteristic
304Dic3—22no—
305Dic3—22no—
306Dic3—41no—
307Dic3—41no—
308Dic3—81no—
309Dic3—122no—
310Dic3—122no—
311Dic3—242no—
312C32#163311yescharacteristic, complemented, Sylow
313Q8—32no—
314Q8—32no—
315Q8—61no—
316Q8—61no—
317Q8—122no—
318Q8—362no—
319Q8—722no—
320C2×C4—61no—
321C2×C4—61no—
322C2×C4—61no—
323C2×C4—61no—
324C2×C4—121no—
325C2×C4—182no—
326C2×C4D3×D1211yescharacteristic
327C2×C4#380211yescharacteristic
328C2×C4D3×#6711yescharacteristic
329C8—41no—
330C8—62no—
331C8—361no—
332C2×C3—21no—
333C2×C3—21no—
334C2×C3—21no—
335C2×C3#473911yescharacteristic
336C2×C3#480911yescharacteristic
337C2×C3#482211yescharacteristic
338C2×C3#505011yescharacteristic
339C2×C3#518611yescharacteristic
340C2×C3#519811yescharacteristic
341C22#6392211yescharacteristic
342C4—21no—
343C4—62no—
344C4—62no—
345C4—121no—
346C4—121no—
347C4—241no—
348C4—362no—
349C4D3×Dic1211yescharacteristic
350C4#6380111yescharacteristic
351C4#6392911yescharacteristic
352C4D3×#21611yescharacteristic
353C3—21no—
354C3#6826711yescharacteristic, complemented
355C3#7116111yescharacteristic, complemented
356C2#1059060411yescharacteristic
357C2#1059094911yescharacteristic
358C2#1059101311yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socle, prime radicalC22×C32#120
hypercenterC4⋊C8D32
hypocenterC32#1633
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
116. C3×Dic6Q16semidirect
117. C3×Dic6Q16semidirect
245. Dic6Dic12semidirect
246. Dic6#216semidirect
312. C32#1633semidirect
354. C3#68267semidirect
355. C3#71161semidirect

Maximal subgroups

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

subgroupindex
Dic622
C3×#48502
#105903862
#105903102
#105893472
C3×#44842
#105890842
#711613
#682673