Finite Group Databasebeta

← #11780006

Subgroups — #11780006

Order 1152.

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

normal subgroups only

This group has 449 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
2#10592792C211yesmaximal, characteristic
3C3×#5094C211yesmaximal, characteristic
4C3×#5090C211yesmaximal, characteristic
5#10589096C211yesmaximal, characteristic
6#10589083C211yesmaximal, characteristic
7#10589083C211yesmaximal, characteristic
8#71129—31nomaximal
9#71063—31nomaximal
10C32×C4⋊Q8C2211yescharacteristic
11#64078C2211yescharacteristic
12C2×C3×#216—21no—
13C3×C4×Dic6C2211yescharacteristic
14C3×C4×Dic6C2211yescharacteristic
15#63918—21no—
16#63918—21no—
17Dic3×Dic6—21no—
18Dic3×Dic6—21no—
19#63840—22no—
20#63637—22no—
21C4×C3⋊(C3⋊C8)C2211yescharacteristic
22C3×#835—21no—
23C3×#810—21no—
24C3×#808—21no—
25C3×C4⋊(C3⋊C8)C2211yescharacteristic
26C3×C4⋊(C3⋊C8)C2211yescharacteristic
27Q8×Dic6—31no—
28Q8×Dic6—31no—
29C3×#475—31no—
30C3×#462—31no—
31#5094D311yescharacteristic
32#5093—31no—
33#5093—31no—
34#5093—61no—
35#5090D311yescharacteristic
36#4535—31no—
37#4535—31no—
38#4484—31no—
39#4484—31no—
40#4481—31no—
41#4481—31no—
42C2×C32×Q8—21no—
43C2×#634D412yes—
44C2×C3×Dic6D411yescharacteristic
45C2×C3×Dic6D411yescharacteristic
46C2×#627—22no—
47C32×C4⋊C4—21no—
48C32×C4⋊C4—21no—
49C32×C42C2311yescharacteristic
50C4⋊(C3⋊Dic3)—21no—
51C4⋊(C3⋊Dic3)—21no—
52C2×C3⋊(C3⋊C8)—21no—
53C3×#216—42no—
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—
61C2×C3×C3⋊C8—21no—
62Dic3⋊Dic3—22no—
63Dic3⋊Dic3—22no—
64Dic32—22no—
65#1645—91noSylow
66C2×C3×Q16—61no—
67C3×C4⋊Q8—21no—
68C3×C4⋊Q8C2×D311yescharacteristic
69C3×C4⋊Q8C2×D311yescharacteristic
70C3×C4×Q8—31no—
71C3×C4×Q8—31no—
72Q8×Dic3—61no—
73Q8×Dic3—61no—
74C2×#216—21no—
75#888—61no—
76#888—61no—
77#888—62no—
78#888—62no—
79#869—31no—
80#869—31no—
81#869—61no—
82#869—61no—
83#869—61no—
84C4×Dic6—61no—
85C4×Dic6—61no—
86C4×Dic6C2×D311yescharacteristic
87C4×Dic6C2×D311yescharacteristic
88C3×#106—61no—
89C3×C4⋊C8—31no—
90C3×C4⋊C8—31no—
91C3×#103—61no—
92C3×#103—61no—
93#835—21no—
94#810—21no—
95#810—62no—
96#810—62no—
97#810—64no—
98#808—21no—
99C4⋊(C3⋊C8)C2×D311yescharacteristic
100C4⋊(C3⋊C8)C2×D311yescharacteristic
101C4×C3⋊C8—31no—
102C4×C3⋊C8—31no—
103C4×C3⋊C8—61no—
104C32×Q8—41no—
105C32×Q8—41no—
106C2×C32×C4—41no—
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C3⋊Dic3—22no—
111#634—42no—
112C2×C3×Dic3—21no—
113C2×C3×Dic3—21no—
114C2×C3×Dic3—21no—
115C2×C3×Dic3—21no—
116C3×Dic6—21no—
117C3×Dic6—21no—
118C3×Dic6SD1612yes—
119C3×Dic6Q1612yescomplemented
120#627—82no—
121C3⋊(C3⋊C8)—41no—
122C3×C3⋊C8—41no—
123C3×C3⋊C8—41no—
124Q82—91no—
125#487—91no—
126#475—31no—
127#462—31no—
128#333—91no—
129Q8⋊C8—91no—
130Q8⋊C8—91no—
131C2×C3×Q8—21no—
132C2×C3×Q8—21no—
133C2×C3×Q8—31no—
134C2×C3×Q8—31no—
135C2×C3×Q8—41no—
136C2×Dic6—32no—
137C2×Dic6—32no—
138C2×Dic6—62no—
139C2×Dic6—62no—
140C2×Dic6—62no—
141C2×Dic6#6711yescharacteristic
142C2×Dic6#6711yescharacteristic
143C3×Q16—122no—
144C2×C3×C8—61no—
145C2×C3×C8—61no—
146C3×C4⋊C4—22no—
147C3×C4⋊C4—21no—
148C3×C4⋊C4—21no—
149C3×C4⋊C4—21no—
150C3×C4⋊C4—21no—
151C3×C4⋊C4—31no—
152C3×C4⋊C4—31no—
153C3×C4⋊C4—41no—
154C3×C4⋊C4—61no—
155C3×C4⋊C4—61no—
156C3×C42—21no—
157C3×C42—61no—
158C3×C42—61no—
159C3×C42C22×D311yescharacteristic
160C3×C42C22×D311yescharacteristic
161#216—42no—
162C4⋊Dic3—62no—
163C4⋊Dic3—62no—
164C4⋊Dic3—61no—
165C4⋊Dic3—61no—
166C4⋊Dic3—61no—
167C4⋊Dic3—61no—
168C4⋊Dic3—121no—
169C4⋊Dic3—121no—
170C4⋊Dic3#6711yescharacteristic
171C4⋊Dic3#6711yescharacteristic
172Dic3⋊C4—21no—
173Dic3⋊C4—21no—
174Dic3⋊C4—62no—
175Dic3⋊C4—62no—
176C4×Dic3—21no—
177C4×Dic3—21no—
178C4×Dic3—62no—
179C4×Dic3—62no—
180C2×C3⋊C8—21no—
181C2×C3⋊C8—21no—
182C2×C3⋊C8—62no—
183C2×C3⋊C8—61no—
184C2×C3⋊C8—61no—
185C22×C32#12011yescharacteristic
186C32×C4—21no—
187C32×C4—81no—
188C32×C4C2×SD1611yescharacteristic
189C32×C4C2×Q1611yescharacteristic
190C32×C4#13711yescharacteristic
191C32×C4#13711yescharacteristic
192C3⋊Dic3—42no—
193C3×Dic3—22no—
194C3×Dic3—22no—
195C3×Dic3—41no—
196C3×Dic3—41no—
197C2×Q16—61no—
198C4⋊Q8—91no—
199C4⋊Q8—181no—
200C4⋊Q8—181no—
201C4⋊Q8—182no—
202C4⋊Q8D3211yescharacteristic
203C4×Q8—31no—
204C4×Q8—31no—
205C4×Q8—181no—
206C4×Q8—181no—
207#106—61no—
208C4⋊C8—31no—
209C4⋊C8—31no—
210#103—61no—
211#103—61no—
212#103—182no—
213C4×C8—91no—
214C3×Q8—32no—
215C3×Q8—32no—
216C3×Q8—41no—
217C3×Q8—41no—
218C3×Q8—41no—
219C3×Q8—41no—
220C3×Q8—61no—
221C3×Q8—61no—
222C3×Q8—81no—
223C3×Q8—81no—
224C2×C3×C4—21no—
225C2×C3×C4—21no—
226C2×C3×C4—21no—
227C2×C3×C4—42no—
228C2×C3×C4—41no—
229C2×C3×C4—41no—
230C2×C3×C4—61no—
231C2×C3×C4—61no—
232C2×C3×C4—61no—
233C2×C3×C4—61no—
234C2×C3×C4D3×D411yescharacteristic
235C2×C3×C4D3×D411yescharacteristic
236C2×C3×C4D3×D411yescharacteristic
237C2×C3×C4D3×D411yescharacteristic
238C2×C3×C4C2×#6711yescharacteristic
239C2×C3×C4C2×#6711yescharacteristic
240C2×Dic3—21no—
241C2×Dic3—21no—
242C2×Dic3—21no—
243C2×Dic3—21no—
244C2×Dic3—62no—
245C2×Dic3—62no—
246C2×Dic3—122no—
247Dic6—21no—
248Dic6—21no—
249Dic6—122no—
250Dic6—122no—
251Dic6—124no—
252Dic6—242no—
253Dic6—242no—
254Dic6#21412yes—
255Dic6#21612yescomplemented
256C3×C8—121no—
257C3×C8—121no—
258C3⋊C8—41no—
259C3⋊C8—41no—
260C3⋊C8—122no—
261C3⋊C8—121no—
262C3⋊C8—121no—
263C2×C32#44811yescharacteristic
264C2×C32#45111yescharacteristic
265C2×C32#45511yescharacteristic
266C2×Q8—21no—
267C2×Q8—31no—
268C2×Q8—31no—
269C2×Q8—92no—
270C2×Q8—182no—
271Q16—122no—
272C2×C8—61no—
273C2×C8—61no—
274C2×C8—181no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—31no—
278C4⋊C4—31no—
279C4⋊C4—61no—
280C4⋊C4—61no—
281C4⋊C4—182no—
282C4⋊C4—182no—
283C4⋊C4—181no—
284C4⋊C4—181no—
285C42—61no—
286C42—61no—
287C42—182no—
288C42C2×D3211yescharacteristic
289C22×C3—21no—
290C22×C3#93711yescharacteristic
291C22×C3#93711yescharacteristic
292C3×C4—22no—
293C3×C4—21no—
294C3×C4—21no—
295C3×C4—21no—
296C3×C4—21no—
297C3×C4—21no—
298C3×C4—21no—
299C3×C4—62no—
300C3×C4—62no—
301C3×C4—82no—
302C3×C4—81no—
303C3×C4—81no—
304C3×C4—121no—
305C3×C4—121no—
306C3×C4D3×SD1611yescharacteristic
307C3×C4#91511yescharacteristic
308C3×C4D3×Q1611yescharacteristic
309C3×C4#91811yescharacteristic
310C3×C4C2×#21411yescharacteristic
311C3×C4C2×#21611yescharacteristic
312C3×C4#95111yescharacteristic
313C3×C4#95111yescharacteristic
314Dic3—22no—
315Dic3—22no—
316Dic3—41no—
317Dic3—41no—
318Dic3—122no—
319Dic3—122no—
320Dic3—242no—
321C32#164511yescharacteristic, complemented, Sylow
322Q8—32no—
323Q8—32no—
324Q8—41no—
325Q8—41no—
326Q8—61no—
327Q8—61no—
328Q8—362no—
329Q8—722no—
330C2×C4—41no—
331C2×C4—61no—
332C2×C4—61no—
333C2×C4—61no—
334C2×C4—61no—
335C2×C4—182no—
336C2×C4D3×#6711yescharacteristic
337C2×C4D3×#6711yescharacteristic
338C2×C4#381111yescharacteristic
339C8—121no—
340C8—121no—
341C8—361no—
342C2×C3—21no—
343C2×C3—21no—
344C2×C3—21no—
345C2×C3#504011yescharacteristic
346C2×C3#505011yescharacteristic
347C2×C3#517011yescharacteristic
348C2×C3#518611yescharacteristic
349C2×C3#520211yescharacteristic
350C2×C3#520211yescharacteristic
351C22#6398311yescharacteristic
352C4—21no—
353C4—62no—
354C4—62no—
355C4—81no—
356C4—121no—
357C4—121no—
358C4—362no—
359C4D3×#21411yescharacteristic
360C4#6392911yescharacteristic
361C4D3×#21611yescharacteristic
362C4#6394311yescharacteristic
363C3—21no—
364C3#7106311yescharacteristic, complemented
365C3#7112911yescharacteristic, complemented
366C2#1059151711yescharacteristic
367C2#1059165311yescharacteristic
368C2#1059165811yescharacteristic
subgroupG/H
centerC22#63983
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socle, prime radicalC22×C32#120
hypercenterC4⋊Q8D32
hypocenterC32#1645
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
119. C3×Dic6Q16semidirect
255. Dic6#216semidirect
321. C32#1645semidirect
364. C3#71063semidirect
365. C3#71129semidirect

Maximal subgroups

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

subgroupindex
Dic622
#105927922
C3×#50942
C3×#50902
#105890962
#105890832
#711293
#710633