Finite Group Databasebeta

← #11781406

Subgroups — #11781406

Order 1152.

351 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 351 conjugacy classes of subgroups — too many to draw. Only its 82 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#10592529C211yesmaximal, characteristic
2#10590388C211yesmaximal, characteristic
3#10590307C211yesmaximal, characteristic
4#10590290C211yesmaximal, characteristic
5C3×#4486C211yesmaximal, characteristic
6C3×#4482C211yesmaximal, characteristic
7#10589098C211yesmaximal, characteristic
8#68469—31nomaximal
9#68468—31nomaximal
10C4×#634C2211yescharacteristic
11C3×#869C2211yescharacteristic
12C3×#869C2211yescharacteristic
13C2×#3719—21no—
14C32×C4⋊C8C2211yescharacteristic
15#63641—21no—
16C8×C3⋊Dic3—21no—
17C4×C3⋊(C3⋊C8)C2211yescharacteristic
18C3×C4⋊(C3⋊C8)C2211yescharacteristic
19C3×C4⋊(C3⋊C8)C2211yescharacteristic
20#63573—21no—
21#63567—21no—
22#63566—21no—
23#63565—21no—
24#63565—21no—
25#5094—31no—
26#5093—31no—
27#5090—31no—
28#5079—31no—
29#4851—31no—
30#4849—31no—
31#4830—31no—
32#4830—31no—
33#4830—61no—
34C3×#332—31no—
35C3×#332—31no—
36#4486D311yescharacteristic
37#4482D311yescharacteristic
38#4480—31no—
39#4480—31no—
40C2×#634D411yescharacteristic
41C2×C3×Dic6—21no—
42C2×C3×Dic6—21no—
43C2×C32×C8—21no—
44C32×C42C2311yescharacteristic
45C4⋊(C3⋊Dic3)D411yescharacteristic
46#3750—21no—
47C4×C3⋊Dic3—21no—
48C2×C3⋊(C3⋊C8)D411yescharacteristic
49C2×C3⋊(C3⋊C8)D411yescharacteristic
50C3×C4⋊Dic3—21no—
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3—21no—
53C3×C4⋊Dic3—21no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8—21no—
56#3719—42no—
57#1680—91noSylow
58C3×C4⋊Q8—31no—
59C3×C4⋊Q8—31no—
60C2×#216—61no—
61C2×Dic12—61no—
62#869C2×D311yescharacteristic
63#869C2×D311yescharacteristic
64C4×Dic6—31no—
65C4×Dic6—31no—
66C4×Dic6—61no—
67C3×C4⋊C8—21no—
68C3×C4⋊C8—31no—
69C3×C4⋊C8—31no—
70C3×C4⋊C8C2×D311yescharacteristic
71C3×C4⋊C8C2×D311yescharacteristic
72#835—61no—
73#835—61no—
74#835—61no—
75#817—61no—
76#816—61no—
77#816—61no—
78Dic3⋊C8—61no—
79Dic3⋊C8—61no—
80Dic3⋊C8—62no—
81C8×Dic3—61no—
82C8×Dic3—61no—
83C8×Dic3—62no—
84#810—61no—
85#810—61no—
86#810—61no—
87#808—61no—
88C4⋊(C3⋊C8)C2×D311yescharacteristic
89C4⋊(C3⋊C8)C2×D311yescharacteristic
90C4×C3⋊C8—31no—
91C4×C3⋊C8—31no—
92C4×C3⋊C8—61no—
93C2×C32×C4C2×D411yescharacteristic
94C2×C32×C4C2×D411yescharacteristic
95C2×C32×C4#4111yescharacteristic
96C2×C3⋊Dic3—21no—
97C2×C3⋊Dic3—21no—
98#634—21no—
99#634SD1612yes—
100C2×C3×Dic3—41no—
101C2×C3×Dic3—41no—
102C3×Dic6—41no—
103C3×Dic6—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—91no—
116#332—31no—
117#332—31no—
118C2×C3×Q8—61no—
119C2×C3×Q8—61no—
120C2×Dic6—21no—
121C2×Dic6—21no—
122C2×Dic6—31no—
123C2×Dic6—31no—
124C2×Dic6—61no—
125C2×C3×C8—22no—
126C2×C3×C8—21no—
127C2×C3×C8—21no—
128C2×C3×C8—61no—
129C2×C3×C8—61no—
130C3×C4⋊C4—61no—
131C3×C4⋊C4—61no—
132C3×C4⋊C4—61no—
133C3×C4⋊C4—61no—
134C3×C42—21no—
135C3×C42C22×D311yescharacteristic
136C3×C42C22×D311yescharacteristic
137#216—122no—
138C4⋊Dic3—21no—
139C4⋊Dic3—21no—
140C4⋊Dic3—21no—
141C4⋊Dic3—21no—
142C4⋊Dic3—31no—
143C4⋊Dic3—31no—
144C4⋊Dic3—61no—
145Dic3⋊C4—62no—
146Dic3⋊C4—61no—
147Dic3⋊C4—61no—
148C4×Dic3—62no—
149C4×Dic3—61no—
150C4×Dic3—61no—
151C2×C3⋊C8—21no—
152C2×C3⋊C8—21no—
153C2×C3⋊C8—31no—
154C2×C3⋊C8—31no—
155C2×C3⋊C8—31no—
156C2×C3⋊C8—31no—
157C2×C3⋊C8—61no—
158C2×C3⋊C8—61no—
159Dic12—122no—
160C22×C32#12111yescharacteristic
161C32×C4—21no—
162C32×C4C2×SD1611yescharacteristic
163C32×C4#13511yescharacteristic
164C32×C4#13511yescharacteristic
165C32×C4#13711yescharacteristic
166C3⋊Dic3—22no—
167C3⋊Dic3—41no—
168C3×Dic3—81no—
169C3×Dic3—81no—
170C2×Q16—181no—
171C4⋊Q8—31no—
172C4⋊Q8—31no—
173C4×Q8—91no—
174#106—181no—
175C4⋊C8—31no—
176C4⋊C8—31no—
177C4⋊C8—181no—
178C4⋊C8D3211yescharacteristic
179#103—181no—
180#103—181no—
181#103—181no—
182#103—181no—
183C4×C8—91no—
184C4×C8—181no—
185C3×Q8—121no—
186C3×Q8—121no—
187C3×Q8—121no—
188C3×Q8—121no—
189C2×C3×C4—21no—
190C2×C3×C4—21no—
191C2×C3×C4—21no—
192C2×C3×C4—121no—
193C2×C3×C4—121no—
194C2×C3×C4#23511yescharacteristic
195C2×C3×C4#23511yescharacteristic
196C2×C3×C4D3×D411yescharacteristic
197C2×C3×C4D3×D411yescharacteristic
198C2×C3×C4D3×D411yescharacteristic
199C2×C3×C4D3×D411yescharacteristic
200C2×Dic3—41no—
201C2×Dic3—41no—
202C2×Dic3—62no—
203C2×Dic3—61no—
204C2×Dic3—61no—
205C2×Dic3—62no—
206C2×Dic3—61no—
207C2×Dic3—61no—
208Dic6—32no—
209Dic6—32no—
210Dic6—41no—
211Dic6—41no—
212Dic6—41no—
213Dic6—41no—
214Dic6—62no—
215Dic6—62no—
216Dic6—61no—
217Dic6—61no—
218C3×C8—42no—
219C3×C8—41no—
220C3×C8—41no—
221C3×C8—121no—
222C3×C8—121no—
223C3⋊C8—41no—
224C3⋊C8—41no—
225C3⋊C8—62no—
226C3⋊C8—61no—
227C3⋊C8—61no—
228C3⋊C8—61no—
229C3⋊C8—61no—
230C3⋊C8—121no—
231C2×C32#46411yescharacteristic
232C2×C32#46511yescharacteristic
233C2×C32#47311yescharacteristic
234C2×Q8—61no—
235C2×Q8—61no—
236C2×Q8—91no—
237Q16—362no—
238C2×C8—21no—
239C2×C8—61no—
240C2×C8—61no—
241C2×C8—91no—
242C2×C8—91no—
243C4⋊C4—61no—
244C4⋊C4—61no—
245C4⋊C4—61no—
246C4⋊C4—61no—
247C4⋊C4—91no—
248C4⋊C4—181no—
249C42—181no—
250C42C2×D3211yescharacteristic
251C22×C3—21no—
252C22×C3#88411yescharacteristic
253C22×C3#88411yescharacteristic
254C3×C4—21no—
255C3×C4—21no—
256C3×C4—21no—
257C3×C4—21no—
258C3×C4—21no—
259C3×C4—21no—
260C3×C4—41no—
261C3×C4—241no—
262C3×C4—241no—
263C3×C4#91211yescharacteristic
264C3×C4#91211yescharacteristic
265C3×C4D3×SD1611yescharacteristic
266C3×C4D3×SD1611yescharacteristic
267C3×C4#91511yescharacteristic
268C3×C4#91611yescharacteristic
269C3×C4#91811yescharacteristic
270C3×C4#91911yescharacteristic
271Dic3—64no—
272Dic3—62no—
273Dic3—62no—
274Dic3—81no—
275Dic3—81no—
276Dic3—122no—
277Dic3—121no—
278Dic3—121no—
279C32#168011yescharacteristic, complemented, Sylow
280Q8—92no—
281Q8—121no—
282Q8—121no—
283Q8—121no—
284Q8—121no—
285Q8—181no—
286C2×C4—121no—
287C2×C4—121no—
288C2×C4—181no—
289C2×C4—181no—
290C2×C4#379811yescharacteristic
291C2×C4#380211yescharacteristic
292C2×C4#381111yescharacteristic
293C8—41no—
294C8—121no—
295C8—121no—
296C8—181no—
297C8—181no—
298C2×C3—21no—
299C2×C3—21no—
300C2×C3—21no—
301C2×C3#475511yescharacteristic
302C2×C3#475511yescharacteristic
303C2×C3#476711yescharacteristic
304C2×C3#477811yescharacteristic
305C2×C3#479811yescharacteristic
306C2×C3#480711yescharacteristic
307C22#6391211yescharacteristic
308C4—21no—
309C4—182no—
310C4—241no—
311C4—241no—
312C4—361no—
313C4#6379611yescharacteristic
314C4#6381011yescharacteristic
315C4#6393611yescharacteristic
316C4#6395111yescharacteristic
317C3—21no—
318C3#6846811yescharacteristic, complemented
319C3#6846911yescharacteristic, complemented
320C2#1059053811yescharacteristic
321C2#1059084111yescharacteristic
322C2#1059099311yescharacteristic
subgroupG/H
centerC22#63912
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
279. C32#1680semidirect
318. C3#68468semidirect
319. C3#68469semidirect

Maximal subgroups

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

subgroupindex
#105925292
#105903882
#105903072
#105902902
C3×#44862
C3×#44822
#105890982
#684693
#684683