Finite Group Databasebeta

← #11780012

Subgroups — #11780012

Order 1152.

454 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 104 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
1C3×Q8×Dic6C211yesmaximal, characteristic
2#10592730C211yesmaximal, characteristic
3#10590301C211yesmaximal, characteristic
4#10590287C211yesmaximal, characteristic
5C3×#4535C211yesmaximal, characteristic
6#10589095C211yesmaximal, characteristic
7#10589084C211yesmaximal, characteristic
8#71941—31nomaximal
9#68271—31nomaximal
10C32×C4×Q8C2211yescharacteristic
11C2×#3756—21no—
12#64078C2211yescharacteristic
13C3×Q8×Dic3—21no—
14C3×#888—22no—
15C3×#888—21no—
16C3×#869—21no—
17C3×#869C2211yescharacteristic
18C3×C4×Dic6—21no—
19C3×C4×Dic6C2211yescharacteristic
20#63637—21no—
21C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4×C3⋊C8C2211yescharacteristic
24#63573—21no—
25#63566—22no—
26#63566—21no—
27C3×Q82—31no—
28Q8×Dic6D311yescharacteristic
29#5079—31no—
30#5031—31no—
31#5031—31no—
32#5031—61no—
33#5020—31no—
34#4851—31no—
35#4681—31no—
36C3×Q8⋊C8—31no—
37#4546—31no—
38#4535—31no—
39#4535D311yescharacteristic
40#4481—31no—
41#4456—31no—
42C2×C32×Q8D411yescharacteristic
43C2×#634—21no—
44C2×C3×Dic6—22no—
45C2×C3×Dic6D411yescharacteristic
46C2×C3×Dic6D412yes—
47C32×C4⋊C4—21no—
48C32×C4⋊C4D411yescharacteristic
49C32×C42—21no—
50C32×C42C2311yescharacteristic
51#3756—42no—
52C4⋊(C3⋊Dic3)—21no—
53C4⋊(C3⋊Dic3)—21no—
54C2×C3⋊(C3⋊C8)—21no—
55C3×C4⋊Dic3—22no—
56C3×C4⋊Dic3—21no—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3D411yescharacteristic
59C3×Dic3⋊C4—22no—
60C3×Dic3⋊C4—21no—
61C3×C4×Dic3—22no—
62C3×C4×Dic3—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65#1645—91noSylow
66C3×C4⋊Q8—31no—
67C3×C4⋊Q8—61no—
68C3×C4⋊Q8—62no—
69C3×C4⋊Q8—61no—
70C3×C4×Q8—21no—
71C3×C4×Q8—31no—
72C3×C4×Q8—61no—
73C3×C4×Q8—61no—
74C3×C4×Q8C2×D311yescharacteristic
75C3×C4×Q8C2×D311yescharacteristic
76Q8×Dic3—21no—
77C2×#216—62no—
78C2×#216—61no—
79C2×#216—61no—
80#888—22no—
81#888—21no—
82#869—21no—
83#869—31no—
84#869—31no—
85#869—61no—
86#869C2×D311yescharacteristic
87C4×Dic6—21no—
88C4×Dic6C2×D311yescharacteristic
89C3×C4⋊C8—31no—
90C3×C4×C8—31no—
91#835—61no—
92#835—62no—
93#817—61no—
94#816—62no—
95#816—61no—
96#810—62no—
97#810—61no—
98#810—61no—
99#808—61no—
100C4⋊(C3⋊C8)—31no—
101C4⋊(C3⋊C8)—31no—
102C4⋊(C3⋊C8)—61no—
103C4⋊(C3⋊C8)C2×D311yescharacteristic
104C4×C3⋊C8C2×D311yescharacteristic
105C32×Q8—21no—
106C32×Q8SD1612yes—
107C2×C32×C4—21no—
108C2×C32×C4—21no—
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C3⋊Dic3—41no—
113#634—41no—
114#634—41no—
115C2×C3×Dic3—21no—
116C2×C3×Dic3—22no—
117C2×C3×Dic3—21no—
118C3×Dic6—21no—
119C3×Dic6—42no—
120C3×Dic6—82no—
121C3×Dic6Q1612yescomplemented
122C3⋊(C3⋊C8)—41no—
123C3×C3⋊C8—41no—
124C3×C3⋊C8—41no—
125Q82—31no—
126#487—91no—
127#475—91no—
128#462—91no—
129#333—91no—
130Q8⋊C8—31no—
131Q8⋊C8—91no—
132C2×C3×Q8—21no—
133C2×C3×Q8—31no—
134C2×C3×Q8—32no—
135C2×C3×Q8—62no—
136C2×C3×Q8D1211yescharacteristic
137C2×C3×Q8#6711yescharacteristic
138C2×Dic6—22no—
139C2×Dic6—62no—
140C2×Dic6—61no—
141C2×Dic6—61no—
142C2×Dic6#6711yescharacteristic
143C2×Dic6#6712yes—
144C2×C3×C8—61no—
145C2×C3×C8—61no—
146C3×C4⋊C4—21no—
147C3×C4⋊C4—21no—
148C3×C4⋊C4—21no—
149C3×C4⋊C4—31no—
150C3×C4⋊C4—41no—
151C3×C4⋊C4—62no—
152C3×C4⋊C4—62no—
153C3×C4⋊C4—61no—
154C3×C4⋊C4—61no—
155C3×C4⋊C4—61no—
156C3×C4⋊C4D1211yescharacteristic
157C3×C4⋊C4#6711yescharacteristic
158C3×C42—21no—
159C3×C42—21no—
160C3×C42—21no—
161C3×C42—41no—
162C3×C42—62no—
163C3×C42—61no—
164C3×C42C22×D311yescharacteristic
165C3×C42C22×D311yescharacteristic
166#216—124no—
167#216—122no—
168#216—122no—
169C4⋊Dic3—22no—
170C4⋊Dic3—21no—
171C4⋊Dic3—21no—
172C4⋊Dic3—61no—
173C4⋊Dic3—61no—
174C4⋊Dic3—61no—
175C4⋊Dic3—61no—
176C4⋊Dic3—121no—
177C4⋊Dic3—121no—
178C4⋊Dic3#6711yescharacteristic
179Dic3⋊C4—22no—
180Dic3⋊C4—21no—
181C4×Dic3—22no—
182C4×Dic3—21no—
183C2×C3⋊C8—21no—
184C2×C3⋊C8—21no—
185C2×C3⋊C8—62no—
186C2×C3⋊C8—61no—
187C2×C3⋊C8—61no—
188C22×C32#12011yescharacteristic
189C32×C4—22no—
190C32×C4—21no—
191C32×C4—41no—
192C32×C4C2×SD1611yescharacteristic
193C32×C4C2×Q1611yescharacteristic
194C32×C4#13711yescharacteristic
195C32×C4#13711yescharacteristic
196C3⋊Dic3—81no—
197C3×Dic3—22no—
198C3×Dic3—42no—
199C3×Dic3—41no—
200C2×Q16—181no—
201C4⋊Q8—31no—
202C4⋊Q8—61no—
203C4⋊Q8—62no—
204C4⋊Q8—61no—
205C4⋊Q8—91no—
206C4×Q8—31no—
207C4×Q8—61no—
208C4×Q8—61no—
209C4×Q8D3211yescharacteristic
210#106—181no—
211C4⋊C8—31no—
212C4⋊C8—91no—
213#103—181no—
214#103—182no—
215#103—181no—
216C4×C8—31no—
217C3×Q8—21no—
218C3×Q8—21no—
219C3×Q8—22no—
220C3×Q8—32no—
221C3×Q8—41no—
222C3×Q8—61no—
223C3×Q8—122no—
224C3×Q8—242no—
225C3×Q8#20412yes—
226C3×Q8#21512yes—
227C2×C3×C4—21no—
228C2×C3×C4—21no—
229C2×C3×C4—21no—
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—41no—
235C2×C3×C4—41no—
236C2×C3×C4—61no—
237C2×C3×C4—61no—
238C2×C3×C4—62no—
239C2×C3×C4C2×D1211yescharacteristic
240C2×C3×C4D3×D411yescharacteristic
241C2×C3×C4D3×D411yescharacteristic
242C2×C3×C4C2×#6711yescharacteristic
243C2×C3×C4C2×#6711yescharacteristic
244C2×C3×C4C2×#6711yescharacteristic
245C2×Dic3—21no—
246C2×Dic3—22no—
247C2×Dic3—21no—
248C2×Dic3—122no—
249C2×Dic3—121no—
250C2×Dic3—121no—
251Dic6—21no—
252Dic6—42no—
253Dic6—82no—
254Dic6—122no—
255Dic6—122no—
256Dic6—121no—
257Dic6—121no—
258Dic6—121no—
259Dic6—121no—
260Dic6#21612yescomplemented
261C3×C8—121no—
262C3×C8—121no—
263C3⋊C8—41no—
264C3⋊C8—41no—
265C3⋊C8—122no—
266C3⋊C8—121no—
267C3⋊C8—121no—
268C2×C32#44811yescharacteristic
269C2×C32#45111yescharacteristic
270C2×C32#45511yescharacteristic
271C2×Q8—31no—
272C2×Q8—32no—
273C2×Q8—62no—
274C2×Q8—181no—
275C2×Q8#62611yescharacteristic
276Q16—362no—
277C2×C8—61no—
278C2×C8—61no—
279C2×C8—181no—
280C4⋊C4—21no—
281C4⋊C4—31no—
282C4⋊C4—62no—
283C4⋊C4—62no—
284C4⋊C4—61no—
285C4⋊C4—61no—
286C4⋊C4—61no—
287C4⋊C4—181no—
288C4⋊C4—181no—
289C4⋊C4#62611yescharacteristic
290C42—21no—
291C42—62no—
292C42—61no—
293C42C2×D3211yescharacteristic
294C22×C3—21no—
295C22×C3#88211yescharacteristic
296C22×C3#95311yescharacteristic
297C3×C4—22no—
298C3×C4—21no—
299C3×C4—22no—
300C3×C4—21no—
301C3×C4—21no—
302C3×C4—21no—
303C3×C4—21no—
304C3×C4—21no—
305C3×C4—41no—
306C3×C4—42no—
307C3×C4—41no—
308C3×C4—41no—
309C3×C4—62no—
310C3×C4—81no—
311C3×C4—122no—
312C3×C4—121no—
313C3×C4C2×#20411yescharacteristic
314C3×C4#90911yescharacteristic
315C3×C4#91511yescharacteristic
316C3×C4D3×Q1611yescharacteristic
317C3×C4C2×#21511yescharacteristic
318C3×C4#94211yescharacteristic
319C3×C4#94211yescharacteristic
320C3×C4C2×#21611yescharacteristic
321Dic3—22no—
322Dic3—42no—
323Dic3—41no—
324Dic3—242no—
325Dic3—241no—
326Dic3—241no—
327C32#164511yescharacteristic, complemented, Sylow
328Q8—21no—
329Q8—32no—
330Q8—61no—
331Q8—122no—
332Q8—242no—
333Q8—361no—
334Q8—361no—
335Q8#371712yes—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—61no—
339C2×C4—61no—
340C2×C4—62no—
341C2×C4—361no—
342C2×C4C2×#62611yescharacteristic
343C2×C4D3×#6711yescharacteristic
344C2×C4D3×#6711yescharacteristic
345C8—121no—
346C8—121no—
347C8—361no—
348C2×C3—21no—
349C2×C3—21no—
350C2×C3—21no—
351C2×C3#473811yescharacteristic
352C2×C3#480911yescharacteristic
353C2×C3#482511yescharacteristic
354C2×C3#522711yescharacteristic
355C2×C3#522811yescharacteristic
356C2×C3#524211yescharacteristic
357C22#6397711yescharacteristic
358C4—22no—
359C4—21no—
360C4—41no—
361C4—62no—
362C4—122no—
363C4—121no—
364C4—721no—
365C4C2×#371711yescharacteristic
366C4#6383311yescharacteristic
367C4D3×#21611yescharacteristic
368C4#6394611yescharacteristic
369C3—21no—
370C3#6827111yescharacteristic, complemented
371C3#7194111yescharacteristic, complemented
372C2#1059117411yescharacteristic
373C2#1059159511yescharacteristic
374C2#1059168811yescharacteristic
subgroupG/H
centerC22#63977
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
121. C3×Dic6Q16semidirect
260. Dic6#216semidirect
327. C32#1645semidirect
370. C3#68271semidirect
371. C3#71941semidirect

Maximal subgroups

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

subgroupindex
C3×Q8×Dic62
#105927302
#105903012
#105902872
C3×#45352
#105890952
#105890842
#719413
#682713