Finite Group Databasebeta

← #11781850

Subgroups — #11781850

Order 1152.

380 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 92 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#10592718C211yesmaximal, characteristic
2C3×#5012C211yesmaximal, characteristic
3C3×#5008C211yesmaximal, characteristic
4#10590303C211yesmaximal, characteristic, complemented
5#10589099C211yesmaximal, characteristic, complemented
6#10589095C211yesmaximal, characteristic, complemented
7#10589094C211yesmaximal, characteristic, complemented
8#71136—31nomaximal
9#70872—31nomaximal
10C32×C4×D4C2211yescharacteristic
11C2×#3754—21no—
12#64078C2211yescharacteristic
13C2×C3×#208—21no—
14C3×#869C2211yescharacteristic
15#63637—21no—
16C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
17C3×#832—21no—
18C3×#830—21no—
19C3×#808—21no—
20C3×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×C4×C3⋊C8C2211yescharacteristic
23#63573—21no—
24#63573—21no—
25C3×#476—31no—
26C3×#436—31no—
27#5080—31no—
28#5019—31no—
29#5019—31no—
30#5019—61no—
31#5012D311yescharacteristic
32#5008D311yescharacteristic
33#4680—31no—
34#4546—31no—
35#4486—31no—
36#4482—31no—
37#4481—31no—
38#4479—31no—
39#4458—31no—
40C2×C32×D4D411yescharacteristic
41C22×C32×C4—21no—
42C2×#634—21no—
43C2×C3×Dic6—21no—
44C32×C4⋊C4D411yescharacteristic
45C32×C22⋊C4—21no—
46C32×C42C2311yescharacteristic
47#3754—42no—
48C4⋊(C3⋊Dic3)—21no—
49C4⋊(C3⋊Dic3)—21no—
50C2×C3⋊(C3⋊C8)—21no—
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3—21no—
53C3×#208—42no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8—21no—
56C2×C3×C3⋊C8D411yescharacteristic
57C2×C3×C3⋊C8D411yescharacteristic
58#1691—91noSylow
59C2×C3×M16—61no—
60C3×C4⋊Q8—31no—
61C3×C4×D4—21no—
62C3×C4×D4C2×D311yescharacteristic
63C3×C4×D4C2×D311yescharacteristic
64C2×#214—62no—
65C2×#214—61no—
66C2×#214—61no—
67C2×#208—21no—
68#869—31no—
69#869—31no—
70#869—61no—
71#869C2×D311yescharacteristic
72C3×#106—61no—
73C3×C4⋊C8—31no—
74C3×C4⋊C8—31no—
75C3×#102—61no—
76C3×C22⋊C8—61no—
77C3×C4×C8—31no—
78#832—21no—
79#830—21no—
80#817—61no—
81#817—61no—
82#810—62no—
83#810—61no—
84#810—61no—
85#808—21no—
86#808—61no—
87#808—61no—
88C4⋊(C3⋊C8)—31no—
89C4⋊(C3⋊C8)—31no—
90C4⋊(C3⋊C8)—61no—
91C4⋊(C3⋊C8)C2×D311yescharacteristic
92C4⋊(C3⋊C8)C2×D311yescharacteristic
93C4×C3⋊C8C2×D311yescharacteristic
94C23×C32—21no—
95C32×D4—21no—
96C32×D4—21no—
97C2×C32×C4—21no—
98C2×C32×C4—41no—
99C2×C32×C4—41no—
100C2×C32×C4C2×D411yescharacteristic
101C2×C32×C4C2×D411yescharacteristic
102C2×C32×C4#4111yescharacteristic
103C2×C3⋊Dic3—41no—
104#634—41no—
105#634—41no—
106C2×C3×Dic3—41no—
107C3×Dic6—81no—
108C3⋊(C3⋊C8)—41no—
109C3×C3⋊C8—21no—
110C3×C3⋊C8—41no—
111C3×C3⋊C8—41no—
112C3×C3⋊C8SD1612yescomplemented
113#498—91no—
114#476—31no—
115#461—91no—
116#436—31no—
117#335—91no—
118#333—91no—
119#332—91no—
120C2×C3×Q8—61no—
121C2×C3×D4—21no—
122C2×C3×D4D1211yescharacteristic
123C2×C3×D4#6711yescharacteristic
124C22×C3×C4—21no—
125C22×C3×C4—21no—
126C22×C3×C4—41no—
127C2×Dic6—21no—
128C2×Dic6—62no—
129C2×Dic6—61no—
130C2×Dic6—61no—
131C3×M16—122no—
132C2×C3×C8—31no—
133C2×C3×C8—31no—
134C2×C3×C8—61no—
135C2×C3×C8—61no—
136C3×C4⋊C4—21no—
137C3×C4⋊C4—61no—
138C3×C4⋊C4—61no—
139C3×C4⋊C4D1211yescharacteristic
140C3×C4⋊C4#6711yescharacteristic
141C3×C22⋊C4—21no—
142C3×C22⋊C4—21no—
143C3×C22⋊C4—41no—
144C3×C42—21no—
145C3×C42C22×D311yescharacteristic
146C3×C42C22×D311yescharacteristic
147#214—124no—
148#214—122no—
149#214—122no—
150C4⋊Dic3—21no—
151C4⋊Dic3—21no—
152C4⋊Dic3—61no—
153C4⋊Dic3—61no—
154C4⋊Dic3—61no—
155C4⋊Dic3—61no—
156C4⋊Dic3—121no—
157C4⋊Dic3—121no—
158#208—42no—
159C2×C3⋊C8—21no—
160C2×C3⋊C8—21no—
161C2×C3⋊C8—62no—
162C2×C3⋊C8—61no—
163C2×C3⋊C8—61no—
164C2×C3⋊C8#6711yescharacteristic
165C2×C3⋊C8#6711yescharacteristic
166C22×C32—41no—
167C22×C32—41no—
168C22×C32—41no—
169C22×C32#12111yescharacteristic
170C32×C4—21no—
171C32×C4—41no—
172C32×C4C2×SD1611yescharacteristic
173C32×C4AGL(1,ℤ/8)11yescharacteristic
174C32×C4#13711yescharacteristic
175C32×C4#13711yescharacteristic
176C3⋊Dic3—81no—
177C3×Dic3—81no—
178C2×SD16—181no—
179C2×M16—61no—
180C4⋊Q8—31no—
181C4⋊Q8—91no—
182C4×D4D3211yescharacteristic
183#106—61no—
184#106—181no—
185#106—181no—
186C4⋊C8—31no—
187C4⋊C8—31no—
188C4⋊C8—91no—
189#103—181no—
190#102—61no—
191C22⋊C8—61no—
192C4×C8—31no—
193C23×C3—21no—
194C23×C3—21no—
195C23×C3—41no—
196C3×Q8—241no—
197C3×D4—22no—
198C3×D4—21no—
199C3×D4—21no—
200C3×D4—21no—
201C3×D4—21no—
202C3×D4—41no—
203C2×C3×C4—21no—
204C2×C3×C4—21no—
205C2×C3×C4—21no—
206C2×C3×C4—21no—
207C2×C3×C4—21no—
208C2×C3×C4—41no—
209C2×C3×C4—41no—
210C2×C3×C4—41no—
211C2×C3×C4—41no—
212C2×C3×C4—41no—
213C2×C3×C4—81no—
214C2×C3×C4—81no—
215C2×C3×C4—121no—
216C2×C3×C4C2×D1211yescharacteristic
217C2×C3×C4#23511yescharacteristic
218C2×C3×C4D3×D411yescharacteristic
219C2×C3×C4#23711yescharacteristic
220C2×C3×C4C2×#6711yescharacteristic
221C2×C3×C4C2×#6711yescharacteristic
222C2×Dic3—41no—
223C2×Dic3—122no—
224C2×Dic3—121no—
225C2×Dic3—121no—
226Dic6—81no—
227Dic6—122no—
228Dic6—122no—
229Dic6—121no—
230Dic6—121no—
231Dic6—121no—
232Dic6—121no—
233C3×C8—32no—
234C3×C8—61no—
235C3×C8—121no—
236C3×C8—121no—
237C3⋊C8—21no—
238C3⋊C8—41no—
239C3⋊C8—41no—
240C3⋊C8—122no—
241C3⋊C8—121no—
242C3⋊C8—121no—
243C3⋊C8#21412yescomplemented
244C2×C32—81no—
245C2×C32#46111yescharacteristic
246C2×C32#46811yescharacteristic
247C2×C32#47111yescharacteristic
248C2×Q8—61no—
249C2×Q8—181no—
250C2×D4#62611yescharacteristic
251C22×C4—21no—
252SD16—362no—
253M16—122no—
254C2×C8—31no—
255C2×C8—31no—
256C2×C8—61no—
257C2×C8—61no—
258C2×C8—181no—
259C4⋊C4—61no—
260C4⋊C4—61no—
261C4⋊C4—181no—
262C4⋊C4—181no—
263C4⋊C4#62611yescharacteristic
264C22⋊C4—21no—
265C42C2×D3211yescharacteristic
266C22×C3—21no—
267C22×C3—42no—
268C22×C3—41no—
269C22×C3—41no—
270C22×C3—41no—
271C22×C3—41no—
272C22×C3—41no—
273C22×C3—41no—
274C22×C3—81no—
275C22×C3—81no—
276C22×C3#93011yescharacteristic
277C22×C3#93911yescharacteristic
278C3×C4—21no—
279C3×C4—21no—
280C3×C4—21no—
281C3×C4—21no—
282C3×C4—21no—
283C3×C4—21no—
284C3×C4—41no—
285C3×C4—41no—
286C3×C4—41no—
287C3×C4—81no—
288C3×C4—241no—
289C3×C4#90811yescharacteristic
290C3×C4#90911yescharacteristic
291C3×C4D3×SD1611yescharacteristic
292C3×C4#91511yescharacteristic
293C3×C4C2×#21411yescharacteristic
294C3×C4#94211yescharacteristic
295C3×C4#94911yescharacteristic
296C3×C4#95111yescharacteristic
297Dic3—81no—
298Dic3—242no—
299Dic3—241no—
300Dic3—241no—
301C32#169111yescharacteristic, complemented, Sylow
302C23—21no—
303Q8—241no—
304Q8—361no—
305Q8—361no—
306D4—21no—
307D4—21no—
308C2×C4—21no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—121no—
312C2×C4—361no—
313C2×C4#380411yescharacteristic
314C2×C4C2×#62611yescharacteristic
315C2×C4D3×#6711yescharacteristic
316C8—32no—
317C8—61no—
318C8—121no—
319C8—121no—
320C8—361no—
321C2×C3—21no—
322C2×C3—21no—
323C2×C3—21no—
324C2×C3—82no—
325C2×C3—81no—
326C2×C3—81no—
327C2×C3#501911yescharacteristic
328C2×C3#504911yescharacteristic
329C2×C3#513411yescharacteristic
330C2×C3#514111yescharacteristic
331C2×C3#516211yescharacteristic
332C2×C3#520011yescharacteristic
333C22—41no—
334C22—41no—
335C22—41no—
336C22#6397811yescharacteristic
337C4—21no—
338C4—41no—
339C4—241no—
340C4—721no—
341C4#6382511yescharacteristic
342C4#6383311yescharacteristic
343C4D3×#21411yescharacteristic
344C4#6392911yescharacteristic
345C3—21no—
346C3#7087211yescharacteristic, complemented
347C3#7113611yescharacteristic, complemented
348C2—81no—
349C2#1059117811yescharacteristic
350C2#1059148911yescharacteristic
351C2#1059167911yescharacteristic
subgroupG/H
centerC22#63978
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×D4C22
socleC22×C32#121
prime radicalC2×C32×D4D4
hypercenterC4×D4D32
hypocenterC32#1691
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
4. #10590303C2semidirect
5. #10589099C2semidirect
6. #10589095C2semidirect
7. #10589094C2semidirect
112. C3×C3⋊C8SD16semidirect
243. C3⋊C8#214semidirect
301. C32#1691semidirect
346. C3#70872semidirect
347. C3#71136semidirect

Maximal subgroups

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

subgroupindex
#105927182
C3×#50122
C3×#50082
#105903032
#105890992
#105890952
#105890942
#711363
#708723