Finite Group Databasebeta

← #11780021

Subgroups — #11780021

Order 1152.

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

normal subgroups only

This group has 448 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#10592719C211yesmaximal, characteristic
3#10590385C211yesmaximal, characteristic
4#10590287C211yesmaximal, characteristic
5C3×#4535C211yesmaximal, characteristic
6#10589095C211yesmaximal, characteristic
7#10589084C211yesmaximal, characteristic
8#71941—31nomaximal
9#68255—31nomaximal
10C32×C4×Q8C2211yescharacteristic
11#64078C2211yescharacteristic
12C3×Q8×Dic3—21no—
13C3×#888—22no—
14C3×#888—21no—
15C3×#869—21no—
16C3×#869C2211yescharacteristic
17C3×C4×Dic6—21no—
18C3×C4×Dic6C2211yescharacteristic
19C2×#3719—21no—
20#63662—21no—
21#63635—21no—
22C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25#63567—21no—
26#63566—22no—
27C3×Q82—31no—
28Q8×Dic6D311yescharacteristic
29#5079—31no—
30#5031—31no—
31#5020—31no—
32#5020—31no—
33#5020—61no—
34#4849—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
51C4⋊(C3⋊Dic3)—21no—
52C4⋊(C3⋊Dic3)—21no—
53C2×C3⋊(C3⋊C8)—21no—
54C3×C4⋊Dic3—22no—
55C3×C4⋊Dic3—21no—
56C3×C4⋊Dic3—21no—
57C3×C4⋊Dic3D411yescharacteristic
58C3×Dic3⋊C4—22no—
59C3×Dic3⋊C4—21no—
60C3×C4×Dic3—22no—
61C3×C4×Dic3—21no—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64#3719—42no—
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—61no—
78C2×Dic12—61no—
79#888—22no—
80#888—21no—
81#869—21no—
82#869—31no—
83#869—31no—
84#869—61no—
85#869C2×D311yescharacteristic
86C4×Dic6—21no—
87C4×Dic6C2×D311yescharacteristic
88C3×C4⋊C8—31no—
89C3×C4×C8—31no—
90#835—62no—
91#835—62no—
92#835—61no—
93#835—61no—
94#816—62no—
95#816—61no—
96#810—61no—
97#808—62no—
98#808—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×Q8Q1612yescomplemented
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×Dic6SD1612yes—
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—61no—
140C2×Dic6—61no—
141C2×Dic6—121no—
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—122no—
167C4⋊Dic3—22no—
168C4⋊Dic3—21no—
169C4⋊Dic3—21no—
170C4⋊Dic3—62no—
171C4⋊Dic3—61no—
172C4⋊Dic3—61no—
173C4⋊Dic3—61no—
174C4⋊Dic3—61no—
175C4⋊Dic3—121no—
176C4⋊Dic3#6711yescharacteristic
177Dic3⋊C4—22no—
178Dic3⋊C4—21no—
179C4×Dic3—22no—
180C4×Dic3—21no—
181C2×C3⋊C8—21no—
182C2×C3⋊C8—21no—
183C2×C3⋊C8—62no—
184C2×C3⋊C8—61no—
185C2×C3⋊C8—61no—
186Dic12—122no—
187C22×C32#12011yescharacteristic
188C32×C4—22no—
189C32×C4—21no—
190C32×C4—41no—
191C32×C4C2×SD1611yescharacteristic
192C32×C4C2×Q1611yescharacteristic
193C32×C4#13711yescharacteristic
194C32×C4#13711yescharacteristic
195C3⋊Dic3—81no—
196C3×Dic3—22no—
197C3×Dic3—42no—
198C3×Dic3—41no—
199C2×Q16—181no—
200C4⋊Q8—31no—
201C4⋊Q8—61no—
202C4⋊Q8—62no—
203C4⋊Q8—61no—
204C4⋊Q8—91no—
205C4×Q8—31no—
206C4×Q8—61no—
207C4×Q8—61no—
208C4×Q8D3211yescharacteristic
209#106—181no—
210C4⋊C8—31no—
211C4⋊C8—91no—
212#103—181no—
213#103—182no—
214#103—181no—
215C4×C8—31no—
216C3×Q8—21no—
217C3×Q8—21no—
218C3×Q8—22no—
219C3×Q8—32no—
220C3×Q8—41no—
221C3×Q8—61no—
222C3×Q8—122no—
223C3×Q8—242no—
224C3×Q8Dic1212yescomplemented
225C3×Q8#21612yescomplemented
226C2×C3×C4—21no—
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—41no—
234C2×C3×C4—41no—
235C2×C3×C4—61no—
236C2×C3×C4—61no—
237C2×C3×C4—62no—
238C2×C3×C4C2×D1211yescharacteristic
239C2×C3×C4D3×D411yescharacteristic
240C2×C3×C4D3×D411yescharacteristic
241C2×C3×C4C2×#6711yescharacteristic
242C2×C3×C4C2×#6711yescharacteristic
243C2×C3×C4C2×#6711yescharacteristic
244C2×Dic3—21no—
245C2×Dic3—22no—
246C2×Dic3—21no—
247C2×Dic3—122no—
248C2×Dic3—121no—
249C2×Dic3—121no—
250Dic6—21no—
251Dic6—42no—
252Dic6—82no—
253Dic6—121no—
254Dic6—121no—
255Dic6—121no—
256Dic6—121no—
257Dic6—241no—
258Dic6—241no—
259Dic6#21512yes—
260C3×C8—121no—
261C3×C8—121no—
262C3⋊C8—41no—
263C3⋊C8—41no—
264C3⋊C8—122no—
265C3⋊C8—121no—
266C3⋊C8—121no—
267C2×C32#44811yescharacteristic
268C2×C32#45111yescharacteristic
269C2×C32#45511yescharacteristic
270C2×Q8—31no—
271C2×Q8—32no—
272C2×Q8—62no—
273C2×Q8—181no—
274C2×Q8#62611yescharacteristic
275Q16—362no—
276C2×C8—61no—
277C2×C8—61no—
278C2×C8—181no—
279C4⋊C4—21no—
280C4⋊C4—31no—
281C4⋊C4—62no—
282C4⋊C4—62no—
283C4⋊C4—61no—
284C4⋊C4—61no—
285C4⋊C4—61no—
286C4⋊C4—181no—
287C4⋊C4—181no—
288C4⋊C4#62611yescharacteristic
289C42—21no—
290C42—62no—
291C42—61no—
292C42C2×D3211yescharacteristic
293C22×C3—21no—
294C22×C3#88211yescharacteristic
295C22×C3#95311yescharacteristic
296C3×C4—22no—
297C3×C4—21no—
298C3×C4—22no—
299C3×C4—21no—
300C3×C4—21no—
301C3×C4—21no—
302C3×C4—21no—
303C3×C4—21no—
304C3×C4—41no—
305C3×C4—42no—
306C3×C4—41no—
307C3×C4—41no—
308C3×C4—62no—
309C3×C4—81no—
310C3×C4—122no—
311C3×C4—121no—
312C3×C4C2×Dic1211yescharacteristic
313C3×C4#90911yescharacteristic
314C3×C4D3×SD1611yescharacteristic
315C3×C4#91811yescharacteristic
316C3×C4C2×#21511yescharacteristic
317C3×C4#94211yescharacteristic
318C3×C4#94211yescharacteristic
319C3×C4C2×#21611yescharacteristic
320Dic3—22no—
321Dic3—42no—
322Dic3—41no—
323Dic3—242no—
324Dic3—241no—
325Dic3—241no—
326C32#164511yescharacteristic, complemented, Sylow
327Q8—21no—
328Q8—32no—
329Q8—61no—
330Q8—122no—
331Q8—242no—
332Q8—361no—
333Q8—361no—
334Q8#371912yescomplemented
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—61no—
338C2×C4—61no—
339C2×C4—62no—
340C2×C4—361no—
341C2×C4C2×#62611yescharacteristic
342C2×C4D3×#6711yescharacteristic
343C2×C4D3×#6711yescharacteristic
344C8—121no—
345C8—121no—
346C8—361no—
347C2×C3—21no—
348C2×C3—21no—
349C2×C3—21no—
350C2×C3#473911yescharacteristic
351C2×C3#480611yescharacteristic
352C2×C3#482511yescharacteristic
353C2×C3#522711yescharacteristic
354C2×C3#522811yescharacteristic
355C2×C3#524211yescharacteristic
356C22#6397711yescharacteristic
357C4—21no—
358C4—22no—
359C4—41no—
360C4—62no—
361C4—122no—
362C4—121no—
363C4—721no—
364C4#6383311yescharacteristic
365C4C2×#371911yescharacteristic
366C4D3×#21511yescharacteristic
367C4#6394811yescharacteristic
368C3—21no—
369C3#6825511yescharacteristic, complemented
370C3#7194111yescharacteristic, complemented
371C2#1059118611yescharacteristic
372C2#1059158411yescharacteristic
373C2#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
106. C32×Q8Q16semidirect
224. C3×Q8Dic12semidirect
225. C3×Q8#216semidirect
326. C32#1645semidirect
334. Q8#3719semidirect
369. C3#68255semidirect
370. 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
#105927192
#105903852
#105902872
C3×#45352
#105890952
#105890842
#719413
#682553