Finite Group Databasebeta

← #11782920

Subgroups — #11782920

Order 1152.

517 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 517 conjugacy classes of subgroups — too many to draw. Only its 100 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×#4695C211yesmaximal, characteristic, complemented
2C3×#4694C211yesmaximal, characteristic, complemented
3#10590375C211yesmaximal, characteristic, complemented
4#10590352C211yesmaximal, characteristic, complemented
5#10590352C211yesmaximal, characteristic, complemented
6#10590277C211yesmaximal, characteristic, complemented
7#10589320C211yesmaximal, characteristic, complemented
8#71279—31nomaximal
9#71194—31nomaximal
10C2×C3×D24—22no—
11C3×#874C2211yescharacteristic
12C3×#874C2211yescharacteristic
13C3×#874C2211yescharacteristic
14C3×#869C2211yescharacteristic
15C2×#3715—22no—
16C2×#3713—22no—
17C2×#3713—22no—
18C32×C4×C8C2211yescharacteristic
19C4×C3⋊(C3⋊C8)C2211yescharacteristic
20C4×C3⋊(C3⋊C8)C2211yescharacteristic
21C3×#821—22no—
22#63562—22no—
23C3×#493—31no—
24C3×#486—31no—
25#5088—31no—
26#5085—31no—
27#5076—31no—
28#5073—31no—
29#5073—31no—
30#5073—31no—
31#5073—31no—
32#5070—31no—
33#4695D311yescharacteristic, complemented
34#4694D311yescharacteristic, complemented
35#4454—31no—
36#4454—31no—
37#4454—61no—
38C2×C3×D12—21no—
39C2×C3×D12—21no—
40C2×C3×D12—21no—
41C2×C3×D12—21no—
42C2×C3×D12—21no—
43C2×C3×D12—21no—
44C2×C3×D12—21no—
45C2×C3×D12—21no—
46C2×C3×D12—21no—
47C2×C3×Dic6—21no—
48C2×C32×C8D412yes—
49C32×C42C2311yescharacteristic
50C2×C3⋊(C3⋊C8)D412yes—
51C2×C3⋊(C3⋊C8)D412yes—
52C3×C4⋊Dic3—21no—
53C3×C4⋊Dic3—21no—
54C3×D24—44no—
55#3715—44no—
56#3713—44no—
57#3713—44no—
58#1721—91noSylow
59C2×C3×D8—62no—
60C3×C4⋊Q8—31no—
61C3×#127—31no—
62C3×#127—31no—
63C3×#127—31no—
64C2×#215—62no—
65C2×#214—62no—
66C2×#213—62no—
67C2×#213—62no—
68C2×#213—62no—
69C2×#213—62no—
70C2×D24—22no—
71#874C2×D311yescharacteristic
72#874C2×D311yescharacteristic
73#874C2×D311yescharacteristic
74#869C2×D311yescharacteristic
75C3×#102—62no—
76C3×C4×C8—21no—
77C3×C4×C8C2×D311yescharacteristic
78C3×C4×C8C2×D311yescharacteristic
79#832—62no—
80#821—22no—
81#809—62no—
82C4×C3⋊C8—31no—
83C4×C3⋊C8—31no—
84C4×C3⋊C8—31no—
85C4×C3⋊C8—31no—
86C4×C3⋊C8—61no—
87C4×C3⋊C8—61no—
88C22×C3×D3—41no—
89C22×C3×D3—41no—
90C22×C3×D3—41no—
91C2×C32×C4C2×D411yescharacteristic
92C2×C32×C4C2×D411yescharacteristic
93C2×C32×C4C2×D411yescharacteristic
94C2×C3×Dic3—41no—
95C3×D12—42no—
96C3×D12—42no—
97C3×D12—42no—
98C3×D12—42no—
99C3×D12—42no—
100C3×D12—42no—
101C3×D12—42no—
102C3×D12—42no—
103C3×D12—42no—
104C3×Dic6—42no—
105C32×C8—22no—
106C3⋊(C3⋊C8)—22no—
107C3⋊(C3⋊C8)D814yescomplemented
108#493—31no—
109#493—91no—
110#493—91no—
111#492—91no—
112#486—31no—
113#486—91no—
114#322—91no—
115C2×C3×Q8—61no—
116C2×C3×D4—61no—
117C2×C3×D4—61no—
118C2×C3×D4—61no—
119C2×C3×D4—61no—
120C2×C3×D4—61no—
121C2×C3×D4—61no—
122C2×C3×D4—61no—
123C2×C3×D4—61no—
124C2×C3×D4—61no—
125C2×D12—21no—
126C2×D12—21no—
127C2×D12—21no—
128C2×D12—21no—
129C2×D12—21no—
130C2×D12—21no—
131C2×D12—21no—
132C2×D12—21no—
133C2×D12—21no—
134C2×Dic6—21no—
135C3×D8—124no—
136C2×C3×C8—22no—
137C2×C3×C8#6712yes—
138C2×C3×C8#6712yes—
139C3×C4⋊C4—61no—
140C3×C4⋊C4—61no—
141C3×C42—21no—
142C3×C42C22×D311yescharacteristic
143C3×C42C22×D311yescharacteristic
144#215—124no—
145#214—124no—
146#213—124no—
147#213—124no—
148#213—124no—
149#213—124no—
150C4⋊Dic3—21no—
151C4⋊Dic3—21no—
152C2×C3⋊C8—32no—
153C2×C3⋊C8—32no—
154C2×C3⋊C8—32no—
155C2×C3⋊C8—32no—
156C2×C3⋊C8—62no—
157C2×C3⋊C8—62no—
158D24—44no—
159C22×C32#12711yescharacteristic
160C2×C3×D3—81no—
161C2×C3×D3—81no—
162C2×C3×D3—81no—
163C2×C3×D3—81no—
164C2×C3×D3—81no—
165C2×C3×D3—81no—
166C2×C3×D3—81no—
167C2×C3×D3—81no—
168C2×C3×D3—81no—
169C32×C4C2×D812yes—
170C32×C4AGL(1,ℤ/8)12yes—
171C32×C4AGL(1,ℤ/8)12yes—
172C3×Dic3—81no—
173C2×SD16—182no—
174C2×D8—62no—
175C2×D8—182no—
176C2×D8—182no—
177C4⋊Q8—31no—
178#127—31no—
179#127—31no—
180#127—31no—
181#102—62no—
182#102—182no—
183C4×C8—91no—
184C4×C8—91no—
185C4×C8D3211yescharacteristic
186C23×C3—121no—
187C23×C3—121no—
188C23×C3—121no—
189C22×D3—41no—
190C22×D3—41no—
191C22×D3—41no—
192C3×Q8—122no—
193C3×D4—122no—
194C3×D4—122no—
195C3×D4—122no—
196C3×D4—122no—
197C3×D4—122no—
198C3×D4—122no—
199C3×D4—122no—
200C3×D4—122no—
201C3×D4—122no—
202C2×C3×C4—21no—
203C2×C3×C4—21no—
204C2×C3×C4—21no—
205C2×C3×C4—121no—
206C2×C3×C4D3×D411yescharacteristic
207C2×C3×C4D3×D411yescharacteristic
208C2×C3×C4D3×D411yescharacteristic
209C2×C3×C4D3×D411yescharacteristic
210C2×C3×C4C2×#6711yescharacteristic
211C2×C3×C4C2×#6711yescharacteristic
212C2×Dic3—41no—
213D12—42no—
214D12—42no—
215D12—42no—
216D12—42no—
217D12—42no—
218D12—42no—
219D12—42no—
220D12—42no—
221D12—42no—
222Dic6—42no—
223C3×C8—22no—
224C3×C8—22no—
225C3×C8—42no—
226C3⋊C8—34no—
227C3⋊C8—34no—
228C3⋊C8—64no—
229C3⋊C8—62no—
230C3⋊C8—62no—
231C3⋊C8—122no—
232C2×C32#49311yescharacteristic
233C2×C32#49611yescharacteristic
234C2×C32#49611yescharacteristic
235C3×D3—161no—
236C3×D3—161no—
237C3×D3—161no—
238C2×Q8—61no—
239C2×D4—61no—
240C2×D4—61no—
241C2×D4—61no—
242C2×D4—61no—
243C2×D4—61no—
244C2×D4—61no—
245C2×D4—61no—
246C2×D4—61no—
247C2×D4—61no—
248SD16—364no—
249D8—124no—
250D8—364no—
251D8—364no—
252C2×C8—92no—
253C2×C8—92no—
254C2×C8#62512yes—
255C4⋊C4—61no—
256C4⋊C4—61no—
257C42C2×D3211yescharacteristic
258C22×C3—21no—
259C22×C3—241no—
260C22×C3—241no—
261C22×C3—241no—
262C22×C3—241no—
263C22×C3—241no—
264C22×C3—241no—
265C22×C3—241no—
266C22×C3—241no—
267C22×C3—241no—
268C22×C3#94011yescharacteristic
269C22×C3#94011yescharacteristic
270C2×D3—81no—
271C2×D3—81no—
272C2×D3—81no—
273C2×D3—81no—
274C2×D3—81no—
275C2×D3—81no—
276C2×D3—81no—
277C2×D3—81no—
278C2×D3—81no—
279C3×C4—22no—
280C3×C4—22no—
281C3×C4—22no—
282C3×C4—241no—
283C3×C4D3×D812yes—
284C3×C4D3×D812yes—
285C3×C4#91112yes—
286C3×C4#91412yes—
287C3×C4#93212yes—
288C3×C4#94912yes—
289Dic3—81no—
290C32#172111yescharacteristic, complemented, Sylow
291C23—121no—
292C23—121no—
293C23—121no—
294Q8—122no—
295D4—122no—
296D4—122no—
297D4—122no—
298D4—122no—
299D4—122no—
300D4—122no—
301D4—122no—
302D4—122no—
303D4—122no—
304C2×C4—121no—
305C2×C4#380211yescharacteristic
306C2×C4#380211yescharacteristic
307C2×C4C2×#62511yescharacteristic
308C8—22no—
309C8—94no—
310C8—182no—
311C2×C3—21no—
312C2×C3—21no—
313C2×C3—21no—
314C2×C3—481no—
315C2×C3—481no—
316C2×C3—481no—
317C2×C3#505811yescharacteristic
318C2×C3#507411yescharacteristic
319C2×C3#515111yescharacteristic
320C2×C3#515111yescharacteristic
321C2×C3#515411yescharacteristic
322C2×C3#517611yescharacteristic
323D3—161no—
324D3—161no—
325D3—161no—
326C22—241no—
327C22—241no—
328C22—241no—
329C22—241no—
330C22—241no—
331C22—241no—
332C22—241no—
333C22—241no—
334C22—241no—
335C22#6391411yescharacteristic
336C4—241no—
337C4#6379712yes—
338C4#6379812yes—
339C4#6382312yes—
340C3—21no—
341C3#7119411yescharacteristic, complemented
342C3#7127911yescharacteristic, complemented
343C2—481no—
344C2—481no—
345C2—481no—
346C2#1059035411yescharacteristic
347C2#1059088611yescharacteristic
348C2#1059088711yescharacteristic
subgroupG/H
centerC22#63914
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×C8C22
socleC22×C32#127
hypercenterC4×C8D32
hypocenterC32#1721
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
1. C3×#4695C2semidirect
2. C3×#4694C2semidirect
3. #10590375C2semidirect
4. #10590352C2semidirect
5. #10590352C2semidirect
6. #10590277C2semidirect
7. #10589320C2semidirect
33. #4695D3semidirect
34. #4694D3semidirect
107. C3⋊(C3⋊C8)D8semidirect
290. C32#1721semidirect
341. C3#71194semidirect
342. C3#71279semidirect

Maximal subgroups

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

subgroupindex
C3×#46952
C3×#46942
#105903752
#105903522
#105902772
#105893202
#712793
#711943