Finite Group Databasebeta

← #11781409

Subgroups — #11781409

Order 1152.

354 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 84 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
1#10592548C211yesmaximal, characteristic
2#10590307C211yesmaximal, characteristic
3#10590287C211yesmaximal, characteristic
4#10590254C211yesmaximal, characteristic
5C3×#4486C211yesmaximal, characteristic
6C3×#4480C211yesmaximal, characteristic
7#10589094C211yesmaximal, characteristic
8#68549—31nomaximal
9#68468—31nomaximal
10C2×#3746—21no—
11#64078C2211yescharacteristic
12C4×#634C2211yescharacteristic
13C3×#869C2211yescharacteristic
14C32×C4⋊C8C2211yescharacteristic
15#63643—21no—
16C3×C4⋊(C3⋊C8)C2211yescharacteristic
17C3×C4⋊(C3⋊C8)C2211yescharacteristic
18C3×C4×C3⋊C8C2211yescharacteristic
19#63573—21no—
20#63572—21no—
21#63567—21no—
22#63566—21no—
23#63566—21no—
24#63553—21no—
25#5094—31no—
26#5079—31no—
27#4851—31no—
28#4849—31no—
29#4849—31no—
30#4849—61no—
31#4830—31no—
32#4681—31no—
33C8×Dic6—31no—
34C3×#334—31no—
35C3×#332—31no—
36#4486—31no—
37#4486D311yescharacteristic
38#4482—31no—
39#4480D311yescharacteristic
40C2×#634—21no—
41C2×#634D411yescharacteristic
42C2×C3×Dic6—21no—
43C2×C32×C8—21no—
44C32×C42C2311yescharacteristic
45C4⋊(C3⋊Dic3)—21no—
46C4⋊(C3⋊Dic3)—21no—
47C4⋊(C3⋊Dic3)D411yescharacteristic
48#3750—21no—
49C4×C3⋊Dic3—21no—
50#3746—42no—
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3—21no—
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8D411yescharacteristic
56C2×C3×C3⋊C8D411yescharacteristic
57#1680—91noSylow
58C3×C4⋊Q8—31no—
59C2×Dic12—61no—
60C2×Dic12—61no—
61C2×Dic12—62no—
62#869—31no—
63#869—31no—
64#869—61no—
65#869C2×D311yescharacteristic
66C4×Dic6—31no—
67C4×Dic6—31no—
68C4×Dic6—61no—
69C3×C4⋊C8—21no—
70C3×C4⋊C8—31no—
71C3×C4⋊C8—31no—
72C3×C4⋊C8C2×D311yescharacteristic
73C3×C4⋊C8C2×D311yescharacteristic
74C3×C4×C8—31no—
75#835—61no—
76#835—61no—
77#817—61no—
78#816—61no—
79#816—61no—
80#816—61no—
81#816—62no—
82#816—61no—
83#816—61no—
84Dic3⋊C8—61no—
85Dic3⋊C8—61no—
86C8×Dic3—61no—
87C8×Dic3—61no—
88#810—61no—
89#808—61no—
90C4⋊(C3⋊C8)C2×D311yescharacteristic
91C4⋊(C3⋊C8)C2×D311yescharacteristic
92C4×C3⋊C8C2×D311yescharacteristic
93C2×C32×C4C2×D411yescharacteristic
94C2×C32×C4C2×D411yescharacteristic
95C2×C32×C4#4111yescharacteristic
96C2×C3⋊Dic3—21no—
97C2×C3⋊Dic3—21no—
98C2×C3⋊Dic3—41no—
99#634—21no—
100#634—41no—
101#634—41no—
102#634SD1612yes—
103C2×C3×Dic3—41no—
104C3×Dic6—41no—
105C3×Dic6—41no—
106C32×C8—41no—
107C3×C3⋊C8—21no—
108C3×C3⋊C8—21no—
109C3×C3⋊C8—41no—
110C3×C3⋊C8—41no—
111#487—91no—
112#475—91no—
113#462—91no—
114C8×Q8—91no—
115#334—31no—
116#332—31no—
117#332—91no—
118C2×C3×Q8—61no—
119C2×Dic6—21no—
120C2×Dic6—31no—
121C2×Dic6—31no—
122C2×Dic6—61no—
123C2×Dic6—62no—
124C2×Dic6—61no—
125C2×Dic6—61no—
126C2×C3×C8—22no—
127C2×C3×C8—21no—
128C2×C3×C8—21no—
129C2×C3×C8—31no—
130C2×C3×C8—31no—
131C2×C3×C8—61no—
132C2×C3×C8—61no—
133C3×C4⋊C4—61no—
134C3×C4⋊C4—61no—
135C3×C42—21no—
136C3×C42C22×D311yescharacteristic
137C3×C42C22×D311yescharacteristic
138C4⋊Dic3—21no—
139C4⋊Dic3—21no—
140C4⋊Dic3—31no—
141C4⋊Dic3—31no—
142C4⋊Dic3—61no—
143C4⋊Dic3—61no—
144C4⋊Dic3—61no—
145C4⋊Dic3—61no—
146C4⋊Dic3—61no—
147C4⋊Dic3—121no—
148C4⋊Dic3—121no—
149Dic3⋊C4—61no—
150Dic3⋊C4—61no—
151Dic3⋊C4—121no—
152C4×Dic3—61no—
153C4×Dic3—61no—
154C4×Dic3—121no—
155C2×C3⋊C8—21no—
156C2×C3⋊C8—21no—
157C2×C3⋊C8D1211yescharacteristic
158C2×C3⋊C8D1211yescharacteristic
159Dic12—122no—
160Dic12—122no—
161Dic12—124no—
162C22×C32#12111yescharacteristic
163C32×C4—21no—
164C32×C4C2×SD1611yescharacteristic
165C32×C4#13511yescharacteristic
166C32×C4#13511yescharacteristic
167C32×C4#13711yescharacteristic
168C3⋊Dic3—22no—
169C3⋊Dic3—41no—
170C3⋊Dic3—81no—
171C3×Dic3—81no—
172C2×Q16—181no—
173C4⋊Q8—31no—
174C4⋊Q8—91no—
175C4×Q8—91no—
176#106—181no—
177C4⋊C8—31no—
178C4⋊C8—31no—
179C4⋊C8—181no—
180C4⋊C8D3211yescharacteristic
181#103—181no—
182#103—181no—
183#103—181no—
184#103—181no—
185C4×C8—31no—
186C4×C8—181no—
187C3×Q8—121no—
188C3×Q8—121no—
189C2×C3×C4—21no—
190C2×C3×C4—21no—
191C2×C3×C4—21no—
192C2×C3×C4—121no—
193C2×C3×C4C2×D1211yescharacteristic
194C2×C3×C4#23511yescharacteristic
195C2×C3×C4D3×D411yescharacteristic
196C2×C3×C4D3×D411yescharacteristic
197C2×C3×C4D3×D411yescharacteristic
198C2×C3×C4#23911yescharacteristic
199C2×Dic3—41no—
200C2×Dic3—61no—
201C2×Dic3—61no—
202C2×Dic3—61no—
203C2×Dic3—61no—
204C2×Dic3—121no—
205C2×Dic3—121no—
206C2×Dic3—122no—
207C2×Dic3—121no—
208C2×Dic3—121no—
209Dic6—32no—
210Dic6—32no—
211Dic6—41no—
212Dic6—41no—
213Dic6—62no—
214Dic6—61no—
215Dic6—61no—
216Dic6—121no—
217Dic6—122no—
218Dic6—122no—
219Dic6—121no—
220Dic6—121no—
221Dic6—121no—
222Dic6—121no—
223C3×C8—42no—
224C3×C8—41no—
225C3×C8—41no—
226C3×C8—61no—
227C3×C8—61no—
228C3×C8—121no—
229C3×C8—121no—
230C3⋊C8—21no—
231C3⋊C8—21no—
232C3⋊C8—41no—
233C3⋊C8—41no—
234C2×C32#46411yescharacteristic
235C2×C32#46511yescharacteristic
236C2×C32#47311yescharacteristic
237C2×Q8—61no—
238C2×Q8—91no—
239C2×Q8—181no—
240Q16—362no—
241C2×C8—21no—
242C2×C8—31no—
243C2×C8—31no—
244C2×C8—61no—
245C2×C8—61no—
246C4⋊C4—61no—
247C4⋊C4—61no—
248C4⋊C4—91no—
249C4⋊C4—181no—
250C4⋊C4—181no—
251C4⋊C4—181no—
252C42—181no—
253C42C2×D3211yescharacteristic
254C22×C3—21no—
255C22×C3#88411yescharacteristic
256C22×C3#89511yescharacteristic
257C3×C4—21no—
258C3×C4—21no—
259C3×C4—21no—
260C3×C4—21no—
261C3×C4—21no—
262C3×C4—21no—
263C3×C4—41no—
264C3×C4—241no—
265C3×C4#90411yescharacteristic
266C3×C4#90911yescharacteristic
267C3×C4#91211yescharacteristic
268C3×C4D3×SD1611yescharacteristic
269C3×C4D3×SD1611yescharacteristic
270C3×C4#91511yescharacteristic
271C3×C4#91611yescharacteristic
272C3×C4#91911yescharacteristic
273Dic3—62no—
274Dic3—62no—
275Dic3—81no—
276Dic3—122no—
277Dic3—121no—
278Dic3—121no—
279Dic3—241no—
280Dic3—242no—
281Dic3—241no—
282Dic3—241no—
283C32#168011yescharacteristic, complemented, Sylow
284Q8—92no—
285Q8—121no—
286Q8—121no—
287Q8—181no—
288Q8—361no—
289Q8—361no—
290C2×C4—121no—
291C2×C4—181no—
292C2×C4—181no—
293C2×C4—361no—
294C2×C4#379911yescharacteristic
295C2×C4D3×D1211yescharacteristic
296C2×C4#381111yescharacteristic
297C8—41no—
298C8—61no—
299C8—61no—
300C8—121no—
301C8—121no—
302C2×C3—21no—
303C2×C3—21no—
304C2×C3—21no—
305C2×C3#475511yescharacteristic
306C2×C3#476711yescharacteristic
307C2×C3#480711yescharacteristic
308C2×C3#484511yescharacteristic
309C2×C3#486411yescharacteristic
310C2×C3#489611yescharacteristic
311C22#6391011yescharacteristic
312C4—21no—
313C4—182no—
314C4—241no—
315C4—361no—
316C4—721no—
317C4#6380011yescharacteristic
318C4#6380711yescharacteristic
319C4#6393011yescharacteristic
320C4#6395011yescharacteristic
321C3—21no—
322C3#6846811yescharacteristic, complemented
323C3#6854911yescharacteristic, complemented
324C2#1059052311yescharacteristic
325C2#1059086111yescharacteristic
326C2#1059099211yescharacteristic
subgroupG/H
centerC22#63910
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socle, prime radicalC22×C32#121
hypercenterC4⋊C8D32
hypocenterC32#1680
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
283. C32#1680semidirect
322. C3#68468semidirect
323. C3#68549semidirect

Maximal subgroups

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

subgroupindex
#105925482
#105903072
#105902872
#105902542
C3×#44862
C3×#44802
#105890942
#685493
#684683