Finite Group Databasebeta

← #11781964

Subgroups — #11781964

Order 1152.

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

normal subgroups only

This group has 353 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#10592777C211yesmaximal, characteristic
2C3×#5090C211yesmaximal, characteristic
3#10590385C211yesmaximal, characteristic
4#10590259C211yesmaximal, characteristic
5C3×#4547C211yesmaximal, characteristic
6#10589098C211yesmaximal, characteristic
7#10589094C211yesmaximal, characteristic
8#71057—31nomaximal
9#68475—31nomaximal
10C32×C4⋊Q8C2211yescharacteristic
11#64078C2211yescharacteristic
12C2×C3×#216—21no—
13C3×C4×Dic6C2211yescharacteristic
14C2×#3719—21no—
15#63634—21no—
16#63634—21no—
17C4×C3⋊(C3⋊C8)C2211yescharacteristic
18C3×#835—21no—
19C3×C4⋊(C3⋊C8)C2211yescharacteristic
20C3×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22Dic3⋊(C3⋊C8)—21no—
23#63567—21no—
24#63554—21no—
25C3×#462—31no—
26#5090D311yescharacteristic
27#5078—31no—
28#5078—31no—
29#5078—61no—
30#5031—31no—
31#5024—31no—
32#4849—31no—
33#4831—31no—
34C3×#332—31no—
35#4547D311yescharacteristic
36#4486—31no—
37#4482—31no—
38#4480—31no—
39#4480—31no—
40C2×C32×Q8—21no—
41C2×#634—21no—
42C2×C3×Dic6D411yescharacteristic
43C32×C4⋊C4—21no—
44C32×C4⋊C4—21no—
45C32×C42C2311yescharacteristic
46C4⋊(C3⋊Dic3)—21no—
47C4⋊(C3⋊Dic3)—21no—
48C2×C3⋊(C3⋊C8)D411yescharacteristic
49C2×C3⋊(C3⋊C8)D411yescharacteristic
50C3×#216—42no—
51C3×C4⋊Dic3D411yescharacteristic
52C3×Dic3⋊C4—21no—
53C3×C4×Dic3—21no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8—21no—
56C2×C3×C3⋊C8—21no—
57#3719—42no—
58#1694—91noSylow
59C2×C3×Q16—61no—
60C3×C4⋊Q8—21no—
61C3×C4⋊Q8C2×D311yescharacteristic
62C3×C4⋊Q8C2×D311yescharacteristic
63C3×C4×Q8—31no—
64C2×#216—21no—
65C2×#216—61no—
66C2×Dic12—61no—
67#869—31no—
68#869—31no—
69#869—61no—
70C4×Dic6C2×D311yescharacteristic
71C3×C4⋊C8—31no—
72C3×C4⋊C8—31no—
73C3×C4⋊C8—31no—
74C3×#103—61no—
75#835—21no—
76#816—61no—
77#815—61no—
78Dic3⋊C8—61no—
79#810—61no—
80#807—61no—
81#807—61no—
82#807—61no—
83#807—61no—
84#807—62no—
85#807—62no—
86C4⋊(C3⋊C8)—61no—
87C4⋊(C3⋊C8)C2×D311yescharacteristic
88C4⋊(C3⋊C8)C2×D311yescharacteristic
89C4⋊(C3⋊C8)C2×D311yescharacteristic
90#803—61no—
91C4×C3⋊C8—31no—
92C4×C3⋊C8—31no—
93C4×C3⋊C8—61no—
94C32×Q8—41no—
95C32×Q8—41no—
96C2×C32×C4—41no—
97C2×C32×C4C2×D411yescharacteristic
98C2×C32×C4C2×D411yescharacteristic
99C2×C32×C4#4111yescharacteristic
100C2×C3⋊Dic3—41no—
101#634—41no—
102#634—41no—
103C2×C3×Dic3—21no—
104C2×C3×Dic3—21no—
105C3×Dic6—21no—
106C3×Dic6—21no—
107C3⋊(C3⋊C8)—21no—
108C3⋊(C3⋊C8)Q1612yescomplemented
109C3×C3⋊C8—41no—
110C3×C3⋊C8—41no—
111C3×C3⋊C8—41no—
112#500—91no—
113#462—31no—
114#462—91no—
115#446—91no—
116#334—91no—
117#332—31no—
118#332—91no—
119C2×C3×Q8—21no—
120C2×C3×Q8—21no—
121C2×C3×Q8—31no—
122C2×C3×Q8—41no—
123C2×Dic6—61no—
124C2×Dic6—61no—
125C2×Dic6—121no—
126C2×Dic6#6711yescharacteristic
127C3×Q16—122no—
128C2×C3×C8—61no—
129C2×C3×C8—61no—
130C2×C3×C8—61no—
131C3×C4⋊C4—22no—
132C3×C4⋊C4—21no—
133C3×C4⋊C4—21no—
134C3×C4⋊C4—21no—
135C3×C4⋊C4—21no—
136C3×C4⋊C4—31no—
137C3×C4⋊C4—41no—
138C3×C4⋊C4—61no—
139C3×C42—21no—
140C3×C42—61no—
141C3×C42C22×D311yescharacteristic
142C3×C42C22×D311yescharacteristic
143#216—42no—
144#216—122no—
145C4⋊Dic3—62no—
146C4⋊Dic3—61no—
147C4⋊Dic3—61no—
148C4⋊Dic3—61no—
149C4⋊Dic3—61no—
150C4⋊Dic3—121no—
151C4⋊Dic3#6711yescharacteristic
152Dic3⋊C4—21no—
153C4×Dic3—21no—
154C2×C3⋊C8—21no—
155C2×C3⋊C8—21no—
156C2×C3⋊C8—21no—
157C2×C3⋊C8—31no—
158C2×C3⋊C8—31no—
159C2×C3⋊C8—31no—
160C2×C3⋊C8—31no—
161C2×C3⋊C8—61no—
162C2×C3⋊C8—61no—
163Dic12—122no—
164C22×C32#12111yescharacteristic
165C32×C4—21no—
166C32×C4—81no—
167C32×C4C2×Q1611yescharacteristic
168C32×C4AGL(1,ℤ/8)11yescharacteristic
169C32×C4AGL(1,ℤ/8)11yescharacteristic
170C32×C4#13711yescharacteristic
171C3⋊Dic3—81no—
172C3×Dic3—41no—
173C3×Dic3—41no—
174C2×Q16—61no—
175C2×Q16—181no—
176C4⋊Q8—91no—
177C4⋊Q8D3211yescharacteristic
178C4×Q8—31no—
179#107—181no—
180#107—181no—
181C4⋊C8—31no—
182C4⋊C8—31no—
183C4⋊C8—31no—
184C4⋊C8—181no—
185#103—61no—
186#103—181no—
187#97—181no—
188C4×C8—91no—
189C3×Q8—41no—
190C3×Q8—41no—
191C3×Q8—41no—
192C3×Q8—41no—
193C3×Q8—61no—
194C3×Q8—61no—
195C3×Q8—81no—
196C3×Q8—81no—
197C2×C3×C4—21no—
198C2×C3×C4—21no—
199C2×C3×C4—21no—
200C2×C3×C4—42no—
201C2×C3×C4—41no—
202C2×C3×C4—41no—
203C2×C3×C4—61no—
204C2×C3×C4—61no—
205C2×C3×C4#23511yescharacteristic
206C2×C3×C4D3×D411yescharacteristic
207C2×C3×C4D3×D411yescharacteristic
208C2×C3×C4D3×D411yescharacteristic
209C2×C3×C4#23711yescharacteristic
210C2×C3×C4C2×#6711yescharacteristic
211C2×Dic3—21no—
212C2×Dic3—21no—
213C2×Dic3—122no—
214C2×Dic3—121no—
215C2×Dic3—121no—
216Dic6—21no—
217Dic6—21no—
218Dic6—121no—
219Dic6—121no—
220Dic6—121no—
221Dic6—121no—
222Dic6—241no—
223Dic6—241no—
224C3×C8—121no—
225C3×C8—121no—
226C3×C8—121no—
227C3⋊C8—32no—
228C3⋊C8—32no—
229C3⋊C8—41no—
230C3⋊C8—41no—
231C3⋊C8—41no—
232C3⋊C8—62no—
233C3⋊C8—62no—
234C3⋊C8—61no—
235C3⋊C8—61no—
236C2×C32#46211yescharacteristic
237C2×C32#46911yescharacteristic
238C2×C32#47311yescharacteristic
239C2×Q8—21no—
240C2×Q8—31no—
241C2×Q8—181no—
242Q16—122no—
243Q16—362no—
244C2×C8—61no—
245C2×C8—61no—
246C2×C8—61no—
247C2×C8—91no—
248C2×C8—91no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—31no—
252C4⋊C4—61no—
253C4⋊C4—181no—
254C4⋊C4—181no—
255C42—61no—
256C42C2×D3211yescharacteristic
257C22×C3—21no—
258C22×C3#88411yescharacteristic
259C22×C3#93911yescharacteristic
260C3×C4—22no—
261C3×C4—21no—
262C3×C4—21no—
263C3×C4—21no—
264C3×C4—21no—
265C3×C4—21no—
266C3×C4—21no—
267C3×C4—82no—
268C3×C4—81no—
269C3×C4—81no—
270C3×C4—121no—
271C3×C4—121no—
272C3×C4#91111yescharacteristic
273C3×C4#91411yescharacteristic
274C3×C4#91511yescharacteristic
275C3×C4D3×Q1611yescharacteristic
276C3×C4D3×Q1611yescharacteristic
277C3×C4#91811yescharacteristic
278C3×C4#93211yescharacteristic
279C3×C4#94911yescharacteristic
280Dic3—41no—
281Dic3—41no—
282Dic3—242no—
283Dic3—241no—
284Dic3—241no—
285C32#169411yescharacteristic, complemented, Sylow
286Q8—41no—
287Q8—41no—
288Q8—61no—
289Q8—61no—
290Q8—361no—
291Q8—361no—
292C2×C4—41no—
293C2×C4—61no—
294C2×C4—61no—
295C2×C4—361no—
296C2×C4#380411yescharacteristic
297C2×C4D3×#6711yescharacteristic
298C2×C4#381111yescharacteristic
299C8—92no—
300C8—121no—
301C8—121no—
302C8—121no—
303C8—181no—
304C2×C3—21no—
305C2×C3—21no—
306C2×C3—21no—
307C2×C3#475511yescharacteristic
308C2×C3#478211yescharacteristic
309C2×C3#479511yescharacteristic
310C2×C3#503911yescharacteristic
311C2×C3#518211yescharacteristic
312C2×C3#520411yescharacteristic
313C22#6397111yescharacteristic
314C4—21no—
315C4—81no—
316C4—121no—
317C4—121no—
318C4—721no—
319C4#6392511yescharacteristic
320C4#6393411yescharacteristic
321C4#6394411yescharacteristic
322C4#6395111yescharacteristic
323C3—21no—
324C3#6847511yescharacteristic, complemented
325C3#7105711yescharacteristic, complemented
326C2#1059145311yescharacteristic
327C2#1059158011yescharacteristic
328C2#1059164411yescharacteristic
subgroupG/H
centerC22#63971
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socle, prime radicalC22×C32#121
hypercenterC4⋊Q8D32
hypocenterC32#1694
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
108. C3⋊(C3⋊C8)Q16semidirect
285. C32#1694semidirect
324. C3#68475semidirect
325. C3#71057semidirect

Maximal subgroups

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

subgroupindex
#105927772
C3×#50902
#105903852
#105902592
C3×#45472
#105890982
#105890942
#710573
#684753