Finite Group Databasebeta

← #11781669

Subgroups — #11781669

Order 1152.

378 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 88 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×#5076C211yesmaximal, characteristic
2C3×#5075C211yesmaximal, characteristic
3#10590285C211yesmaximal, characteristic, complemented
4#10590258C211yesmaximal, characteristic, complemented
5#10589410C211yesmaximal, characteristic
6#10589099C211yesmaximal, characteristic, complemented
7#10589092C211yesmaximal, characteristic, complemented
8#71273—31nomaximal
9#71024—31nomaximal
10C32×#127C2211yescharacteristic
11C2×C3×#214—21no—
12C2×C3×#214—21no—
13C2×C3×#214—21no—
14C3×#869C2211yescharacteristic
15C3×C4×Dic6C2211yescharacteristic
16C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
17C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
18C3×#832—21no—
19C3×C4⋊(C3⋊C8)C2211yescharacteristic
20C3×C4×C3⋊C8C2211yescharacteristic
21#63574—21no—
22Dic3⋊(C3⋊C8)—21no—
23#63565—21no—
24#63554—21no—
25C3×#492—31no—
26C3×#460—31no—
27#5094—31no—
28#5076D311yescharacteristic
29#5075D311yescharacteristic
30#5024—31no—
31#5020—31no—
32#4679—31no—
33#4547—31no—
34#4544—31no—
35#4544—31no—
36#4544—61no—
37#4486—31no—
38#4479—31no—
39#4458—31no—
40C2×C32×D4—21no—
41C2×C32×D4—21no—
42C2×C32×D4—21no—
43C2×C3×Dic6—21no—
44C2×C3×Dic6D411yescharacteristic
45C32×C42C2311yescharacteristic
46C2×C3⋊(C3⋊C8)—21no—
47C2×C3⋊(C3⋊C8)—21no—
48C3×#214—42no—
49C3×#214—42no—
50C3×#214—42no—
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3—21no—
53C3×C4⋊Dic3D411yescharacteristic
54C3×Dic3⋊C4—21no—
55C3×C4×Dic3—21no—
56C2×C3×C3⋊C8—21no—
57C2×C3×C3⋊C8D411yescharacteristic
58C2×C3×C3⋊C8D411yescharacteristic
59#1686—91noSylow
60C2×C3×SD16—61no—
61C2×C3×SD16—61no—
62C2×C3×SD16—61no—
63C3×C4⋊Q8—31no—
64C3×#127—21no—
65C3×#127C2×D311yescharacteristic
66C3×#127C2×D311yescharacteristic
67C3×C4×Q8—31no—
68C2×#214—21no—
69C2×#214—21no—
70C2×#214—21no—
71#869C2×D311yescharacteristic
72C4×Dic6C2×D311yescharacteristic
73C3×C4⋊C8—31no—
74C3×#102—61no—
75C3×C4×C8—31no—
76#835—61no—
77#832—21no—
78#815—61no—
79Dic3⋊C8—61no—
80#810—61no—
81#808—61no—
82#808—61no—
83C4⋊(C3⋊C8)—31no—
84C4⋊(C3⋊C8)—31no—
85C4⋊(C3⋊C8)—31no—
86C4⋊(C3⋊C8)—31no—
87C4⋊(C3⋊C8)—61no—
88C4⋊(C3⋊C8)—61no—
89C4⋊(C3⋊C8)—61no—
90C4⋊(C3⋊C8)C2×D311yescharacteristic
91#803—61no—
92C4×C3⋊C8C2×D311yescharacteristic
93C23×C32—41no—
94C32×D4—41no—
95C32×D4—41no—
96C32×D4—41no—
97C32×D4—41no—
98C32×D4—81no—
99C2×C32×C4C2×D411yescharacteristic
100C2×C32×C4C2×D411yescharacteristic
101C2×C32×C4#4111yescharacteristic
102C2×C3×Dic3—21no—
103C2×C3×Dic3—21no—
104C2×C3×Dic3—41no—
105C3×Dic6—21no—
106C3×Dic6—21no—
107C3×Dic6—41no—
108C3×Dic6—41no—
109C3⋊(C3⋊C8)—41no—
110C3⋊(C3⋊C8)—41no—
111C3×C3⋊C8—21no—
112C3×C3⋊C8—41no—
113C3×C3⋊C8SD1612yescomplemented
114#492—31no—
115#475—91no—
116#460—31no—
117#446—91no—
118#335—91no—
119#332—91no—
120#331—91no—
121C2×C3×Q8—31no—
122C2×C3×Q8—61no—
123C2×C3×D4—22no—
124C2×C3×D4—21no—
125C2×C3×D4—21no—
126C2×C3×D4—21no—
127C2×C3×D4—21no—
128C2×C3×D4—21no—
129C2×C3×D4—21no—
130C2×C3×D4—41no—
131C2×C3×D4—41no—
132C2×Dic6—21no—
133C2×Dic6#6711yescharacteristic
134C3×SD16—122no—
135C3×SD16—122no—
136C3×SD16—122no—
137C2×C3×C8—31no—
138C2×C3×C8—31no—
139C2×C3×C8—61no—
140C3×C4⋊C4—31no—
141C3×C4⋊C4—61no—
142C3×C4⋊C4—61no—
143C3×C4⋊C4—61no—
144C3×C42—21no—
145C3×C42—61no—
146C3×C42C22×D311yescharacteristic
147C3×C42C22×D311yescharacteristic
148#214—42no—
149#214—42no—
150#214—42no—
151C4⋊Dic3—21no—
152C4⋊Dic3—21no—
153C4⋊Dic3#6711yescharacteristic
154Dic3⋊C4—21no—
155C4×Dic3—21no—
156C2×C3⋊C8—21no—
157C2×C3⋊C8—61no—
158C2×C3⋊C8—61no—
159C2×C3⋊C8—61no—
160C2×C3⋊C8—61no—
161C2×C3⋊C8—121no—
162C2×C3⋊C8—121no—
163C2×C3⋊C8#6711yescharacteristic
164C2×C3⋊C8#6711yescharacteristic
165C22×C32—81no—
166C22×C32—81no—
167C22×C32—81no—
168C22×C32#12111yescharacteristic
169C32×C4—21no—
170C32×C4C2×SD1611yescharacteristic
171C32×C4AGL(1,ℤ/8)11yescharacteristic
172C32×C4AGL(1,ℤ/8)11yescharacteristic
173C32×C4#13711yescharacteristic
174C3×Dic3—41no—
175C3×Dic3—41no—
176C3×Dic3—81no—
177C2×SD16—61no—
178C2×SD16—61no—
179C2×SD16—61no—
180C4⋊Q8—31no—
181#127D3211yescharacteristic
182C4×Q8—31no—
183#106—181no—
184C4⋊C8—31no—
185C4⋊C8—91no—
186C4⋊C8—91no—
187C4⋊C8—181no—
188#103—181no—
189#102—61no—
190#97—181no—
191C4×C8—31no—
192C23×C3—42no—
193C23×C3—41no—
194C23×C3—41no—
195C3×Q8—61no—
196C3×Q8—61no—
197C3×Q8—121no—
198C3×Q8—121no—
199C3×D4—41no—
200C3×D4—41no—
201C3×D4—41no—
202C3×D4—41no—
203C3×D4—41no—
204C3×D4—41no—
205C3×D4—41no—
206C3×D4—41no—
207C3×D4—81no—
208C3×D4—81no—
209C3×D4—81no—
210C3×D4—81no—
211C3×D4—81no—
212C3×D4—81no—
213C3×D4—82no—
214C2×C3×C4—21no—
215C2×C3×C4—21no—
216C2×C3×C4—21no—
217C2×C3×C4—61no—
218C2×C3×C4—61no—
219C2×C3×C4—121no—
220C2×C3×C4D3×D411yescharacteristic
221C2×C3×C4D3×D411yescharacteristic
222C2×C3×C4#23711yescharacteristic
223C2×C3×C4#23711yescharacteristic
224C2×C3×C4C2×#6711yescharacteristic
225C2×C3×C4C2×#6711yescharacteristic
226C2×Dic3—21no—
227C2×Dic3—21no—
228C2×Dic3—41no—
229Dic6—21no—
230Dic6—21no—
231Dic6—41no—
232Dic6—41no—
233C3×C8—32no—
234C3×C8—61no—
235C3×C8—121no—
236C3⋊C8—21no—
237C3⋊C8—41no—
238C3⋊C8—121no—
239C3⋊C8—121no—
240C3⋊C8—121no—
241C3⋊C8—121no—
242C3⋊C8—241no—
243C3⋊C8—241no—
244C3⋊C8#21412yescomplemented
245C2×C32—161no—
246C2×C32#46011yescharacteristic
247C2×C32#46811yescharacteristic
248C2×C32#47111yescharacteristic
249C2×Q8—31no—
250C2×Q8—61no—
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—21no—
254SD16—122no—
255SD16—122no—
256SD16—122no—
257C2×C8—31no—
258C2×C8—31no—
259C2×C8—61no—
260C2×C8—181no—
261C2×C8—181no—
262C4⋊C4—31no—
263C4⋊C4—61no—
264C4⋊C4—61no—
265C4⋊C4—61no—
266C42—61no—
267C42C2×D3211yescharacteristic
268C22×C3—21no—
269C22×C3—82no—
270C22×C3—82no—
271C22×C3—82no—
272C22×C3—81no—
273C22×C3—81no—
274C22×C3—81no—
275C22×C3—81no—
276C22×C3—81no—
277C22×C3—81no—
278C22×C3#93811yescharacteristic
279C22×C3#93911yescharacteristic
280C3×C4—21no—
281C3×C4—21no—
282C3×C4—21no—
283C3×C4—21no—
284C3×C4—21no—
285C3×C4—21no—
286C3×C4—41no—
287C3×C4—121no—
288C3×C4—121no—
289C3×C4—241no—
290C3×C4D3×SD1611yescharacteristic
291C3×C4#91411yescharacteristic
292C3×C4#91411yescharacteristic
293C3×C4#91511yescharacteristic
294C3×C4#93211yescharacteristic
295C3×C4#93211yescharacteristic
296C3×C4C2×#21411yescharacteristic
297C3×C4#95111yescharacteristic
298Dic3—41no—
299Dic3—41no—
300Dic3—81no—
301C32#168611yescharacteristic, complemented, Sylow
302C23—41no—
303Q8—61no—
304Q8—61no—
305Q8—121no—
306Q8—121no—
307D4—41no—
308D4—41no—
309D4—41no—
310D4—41no—
311D4—81no—
312C2×C4—61no—
313C2×C4—61no—
314C2×C4—121no—
315C2×C4#380511yescharacteristic
316C2×C4D3×#6711yescharacteristic
317C2×C4D3×#6711yescharacteristic
318C8—32no—
319C8—61no—
320C8—121no—
321C8—361no—
322C8—361no—
323C2×C3—21no—
324C2×C3—21no—
325C2×C3—21no—
326C2×C3—162no—
327C2×C3—161no—
328C2×C3—161no—
329C2×C3#504211yescharacteristic
330C2×C3#507511yescharacteristic
331C2×C3#516311yescharacteristic
332C2×C3#517411yescharacteristic
333C2×C3#517711yescharacteristic
334C2×C3#520011yescharacteristic
335C22—81no—
336C22—81no—
337C22—81no—
338C22#6397011yescharacteristic
339C4—21no—
340C4—121no—
341C4—121no—
342C4—241no—
343C4D3×#21411yescharacteristic
344C4#6392911yescharacteristic
345C4#6393411yescharacteristic
346C4#6393411yescharacteristic
347C3—21no—
348C3#7102411yescharacteristic, complemented
349C3#7127311yescharacteristic, complemented
350C2—161no—
351C2#1059143811yescharacteristic
352C2#1059150211yescharacteristic
353C2#1059150611yescharacteristic
subgroupG/H
centerC22#63970
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
Fitting, prime radicalC32×#127C22
socleC22×C32#121
hypercenter#127D32
hypocenterC32#1686
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #10590285C2semidirect
4. #10590258C2semidirect
6. #10589099C2semidirect
7. #10589092C2semidirect
113. C3×C3⋊C8SD16semidirect
244. C3⋊C8#214semidirect
301. C32#1686semidirect
348. C3#71024semidirect
349. C3#71273semidirect

Maximal subgroups

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

subgroupindex
C3×#50762
C3×#50752
#105902852
#105902582
#105894102
#105890992
#105890922
#712733
#710243