Finite Group Databasebeta

← #11793978

Subgroups — #11793978

Order 1152.

792 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 792 conjugacy classes of subgroups — too many to draw. Only its 165 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#10596293C211yesmaximal, characteristic
2C32×#410C211yesmaximal, characteristic, complemented
3#10592932C211yesmaximal, characteristic, complemented
4#10592705C211yesmaximal, characteristic, complemented
5#10592701C211yesmaximal, characteristic, complemented
6#10592698C211yesmaximal, characteristic, complemented
7#10589397C211yesmaximal, characteristic, complemented
8#70043—34nomaximal
9C2×C32×#41C2211yescharacteristic
10C2×#3828C2211yescharacteristic
11C32×#117C2211yescharacteristic
12C32×#117C2211yescharacteristic
13#64160—21no—
14#64159—22no—
15#64158—21no—
16#64151—21no—
17#64141—21no—
18#64135C2211yescharacteristic
19C2×#3748C2211yescharacteristic
20C22×C3⋊(C3⋊C8)C2211yescharacteristic
21C32×#99—22no—
22#63662—21no—
23#63659—21no—
24#63637—21no—
25#63636—21no—
26#63633—22no—
27C4⋊(C3⋊(C3⋊C8))—22no—
28#5822—34no—
29C3×#410D314yescomplemented
30#5233—34no—
31#5006—34no—
32#5002—34no—
33#4999—34no—
34#4531—34no—
35C32×#41—21no—
36C32×#41—21no—
37C32×#41—21no—
38C32×#41—21no—
39C2×C32×Q8D411yescharacteristic
40C2×C32×D4—21no—
41C2×C32×D4D411yescharacteristic
42C22×C32×C4—21no—
43C22×C32×C4C2311yescharacteristic
44C2×#638—21no—
45#3828—21no—
46#3828—21no—
47#3828—21no—
48#3828—21no—
49C2×C4⋊(C3⋊D3)D411yescharacteristic
50C2×C4×C3⋊D3—21no—
51C2×#634D411yescharacteristic
52C32×C4⋊C4—21no—
53C32×C4⋊C4—21no—
54C32×C22⋊C4—21no—
55C32×C22⋊C4D412yes—
56C32×C42—21no—
57C32×C42—21no—
58#3757—21no—
59#3756—22no—
60#3755—22no—
61#3754—22no—
62#3753—22no—
63C4⋊(C3⋊Dic3)—21no—
64C4×C3⋊Dic3—21no—
65#3748—21no—
66#3748—21no—
67C2×C3⋊(C3⋊C8)—21no—
68C2×C3⋊(C3⋊C8)—21no—
69C2×C3⋊(C3⋊C8)—21no—
70C2×C3⋊(C3⋊C8)D412yes—
71#2053—91noSylow
72C2×C3×#41C2×D314yes—
73C2×#235—34no—
74C3×#117C2×D314yes—
75C3×#117C2×D314yes—
76#951—64no—
77#950—68no—
78#949—64no—
79#942—64no—
80#932—64no—
81#926—34no—
82C2×#208—34no—
83C22×C3⋊C8—34no—
84C3×#99—28no—
85#835—64no—
86#832—64no—
87#810—64no—
88#809—64no—
89#806—68no—
90C4⋊(C3⋊C8)—68no—
91C23×C32—21no—
92C23×C32C2×D411yescharacteristic
93C22×C3⋊D3—21no—
94C32×Q8—21no—
95C32×Q8—21no—
96C32×D4—21no—
97C32×D4—21no—
98C32×D4—41no—
99C32×D4—41no—
100C2×C32×C4—22no—
101C2×C32×C4—21no—
102C2×C32×C4—41no—
103C2×C32×C4—41no—
104C2×C32×C4—41no—
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4C2×D411yescharacteristic
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4#4111yescharacteristic
109C2×C32×C4#4111yescharacteristic
110C2×C32×C4#4111yescharacteristic
111#638—41no—
112#638—41no—
113C2×C3⋊Dic3—21no—
114C2×C3⋊Dic3—41no—
115C4⋊(C3⋊D3)—21no—
116C4⋊(C3⋊D3)—21no—
117C4×C3⋊D3—41no—
118C4×C3⋊D3—41no—
119#634—21no—
120#634—21no—
121C3⋊(C3⋊C8)—22no—
122C3⋊(C3⋊C8)—41no—
123#575—91no—
124#424—91no—
125#416—91no—
126#416—91no—
127#410—91no—
128#410C3⋊D311yescharacteristic, complemented
129H(3,ℤ/4)—91no—
130C3×#41—24no—
131C3×#41—24no—
132C3×#41—24no—
133C3×#41—24no—
134C2×C3×Q8D1214yes—
135C2×C3×D4—24no—
136C2×C3×D4D1214yes—
137C22×C3×C4—24no—
138C22×C3×C4C22×D314yes—
139C2×#67—64no—
140#235—64no—
141#235—64no—
142#235—64no—
143#235—64no—
144C2×D12—34no—
145C2×C4×D3—64no—
146C2×Dic6—34no—
147C3×C4⋊C4—24no—
148C3×C4⋊C4—24no—
149C3×C22⋊C4—24no—
150C3×C22⋊C4#6718yes—
151C3×C42—24no—
152C3×C42—24no—
153#217—64no—
154#216—68no—
155#215—68no—
156#214—68no—
157#213—68no—
158C4⋊Dic3—64no—
159C4×Dic3—64no—
160#208—64no—
161#208—64no—
162C2×C3⋊C8—38no—
163C2×C3⋊C8—64no—
164C2×C3⋊C8—64no—
165C2×C3⋊C8—64no—
166C22×C32—41no—
167C22×C32—41no—
168C22×C32—81no—
169C22×C32#12111yescharacteristic
170C22×C32#12111yescharacteristic
171C22×C32#12111yescharacteristic
172C2×C3⋊D3—41no—
173C2×C3⋊D3—81no—
174C32×C4—42no—
175C32×C4—41no—
176C32×C4—81no—
177C32×C4#12011yescharacteristic
178C32×C4#12311yescharacteristic
179C32×C4#12311yescharacteristic
180C32×C4#12411yescharacteristic
181C3⋊Dic3—41no—
182C3⋊Dic3—81no—
183C2×#41—91no—
184C2×#41C2×C3⋊D311yescharacteristic
185#137—181no—
186#137—181no—
187AGL(1,ℤ/8)—181no—
188AGL(1,ℤ/8)—181no—
189#135—182no—
190C2×M16—91no—
191C22×C8—91no—
192#117—91no—
193#117C2×C3⋊D311yescharacteristic
194#117C2×C3⋊D311yescharacteristic
195C4⋊C8—182no—
196#103—181no—
197#103—181no—
198#102—181no—
199#102—181no—
200#99—22no—
201#99—182no—
202C23×C3—24no—
203C23×C3C2×#6714yes—
204C22×D3—64no—
205C3×Q8—24no—
206C3×Q8—24no—
207C3×D4—24no—
208C3×D4—24no—
209C3×D4—44no—
210C3×D4—44no—
211C2×C3×C4—24no—
212C2×C3×C4—28no—
213C2×C3×C4—44no—
214C2×C3×C4—44no—
215C2×C3×C4—44no—
216C2×C3×C4C2×D1214yes—
217C2×C3×C4#23514yes—
218C2×C3×C4D3×D414yes—
219C2×C3×C4D3×D414yes—
220C2×C3×C4#23714yes—
221C2×C3×C4#23714yes—
222#67—124no—
223#67—124no—
224C2×Dic3—64no—
225C2×Dic3—124no—
226D12—64no—
227D12—64no—
228C4×D3—124no—
229C4×D3—124no—
230Dic6—64no—
231Dic6—64no—
232C3⋊C8—68no—
233C3⋊C8—124no—
234C2×C32—21no—
235C2×C32—21no—
236C2×C32—21no—
237C2×C32—81no—
238C2×C32#39411yescharacteristic
239C3⋊D3—81no—
240#41—21no—
241#41—21no—
242#41—21no—
243#41—21no—
244#41—181no—
245#41—181no—
246#41—181no—
247#41—181no—
248C2×Q8—91no—
249C2×Q8C4⋊(C3⋊D3)11yescharacteristic
250C2×D4—21no—
251C2×D4—91no—
252C2×D4—181no—
253C2×D4C4⋊(C3⋊D3)11yescharacteristic
254C22×C4—21no—
255C22×C4—181no—
256C22×C4C22×C3⋊D311yescharacteristic
257Q16—182no—
258SD16—182no—
259SD16—182no—
260D8—182no—
261M16—181no—
262M16—181no—
263C2×C8—92no—
264C2×C8—181no—
265C2×C8—181no—
266C2×C8—181no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—181no—
270C22⋊C4—21no—
271C22⋊C4—181no—
272C22⋊C4#63812yes—
273C42—21no—
274C42—21no—
275C42—181no—
276C22×C3—44no—
277C22×C3—44no—
278C22×C3—84no—
279C22×C3#93014yes—
280C22×C3#93814yes—
281C22×C3#93914yes—
282C2×D3—124no—
283C2×D3—244no—
284C3×C4—48no—
285C3×C4—44no—
286C3×C4—84no—
287C3×C4#88214yes—
288C3×C4#88314yes—
289C3×C4#88514yes—
290C3×C4#88614yes—
291Dic3—124no—
292Dic3—244no—
293C32#205311yescharacteristic, complemented, Sylow
294C23—21no—
295C23—181no—
296C23C2×#63811yescharacteristic
297Q8—21no—
298Q8—21no—
299Q8—181no—
300Q8—181no—
301D4—21no—
302D4—21no—
303D4—41no—
304D4—41no—
305D4—181no—
306D4—181no—
307D4—361no—
308D4—361no—
309C2×C4—21no—
310C2×C4—22no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—181no—
315C2×C4—361no—
316C2×C4—361no—
317C2×C4—361no—
318C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
319C2×C4#382811yescharacteristic
320C2×C4D4×C3⋊D311yescharacteristic
321C2×C4D4×C3⋊D311yescharacteristic
322C2×C4#383011yescharacteristic
323C2×C4#383011yescharacteristic
324C8—182no—
325C8—361no—
326C2×C3—24no—
327C2×C3—24no—
328C2×C3—24no—
329C2×C3—84no—
330C2×C3#496114yes—
331D3—244no—
332C22—41no—
333C22—41no—
334C22—81no—
335C22—361no—
336C22—721no—
337C22#6413911yescharacteristic
338C22#6414711yescharacteristic
339C22#6414811yescharacteristic
340C4—42no—
341C4—41no—
342C4—81no—
343C4—361no—
344C4—721no—
345C4#6409111yescharacteristic
346C4#6409211yescharacteristic
347C4#6409411yescharacteristic
348C4#6409511yescharacteristic
349C3#7004314yescomplemented
350C2—21no—
351C2—21no—
352C2—21no—
353C2—81no—
354C2—721no—
355C2#1059266011yescharacteristic
subgroupG/H
centerC4#64094
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC32×#410C2
socleC2×C32#394
prime radical#10596293C2
hypercenter#410C3⋊D3
hypocenterC32#2053
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
2. C32×#410C2semidirect
3. #10592932C2semidirect
4. #10592705C2semidirect
5. #10592701C2semidirect
6. #10592698C2semidirect
7. #10589397C2semidirect
29. C3×#410D3semidirect
128. #410C3⋊D3semidirect
293. C32#2053semidirect
349. C3#70043semidirect

Maximal subgroups

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

subgroupindex
#105962932
C32×#4102
#105929322
#105927052
#105927012
#105926982
#105893972
#700433