Finite Group Databasebeta

← #11888020

Subgroups — #11888020

Order 1152.

1158 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596022C211yesmaximal, characteristic
2#10596013C211yesmaximal, characteristic, complemented
3C32×C8×D4C211yesmaximal, characteristic, complemented
4#10592815C212yesmaximal, complemented
5#10592812C212yesmaximal, complemented
6#10592548C211yesmaximal, characteristic, complemented
7#10592545C211yesmaximal, characteristic, complemented
8#10592432C212yesmaximal, complemented
9#10592422C212yesmaximal, complemented
10C4×#3744C211yesmaximal, characteristic, complemented
11#10592380C211yesmaximal, characteristic, complemented
12#79442—34nomaximal
13C2×#3828C2212yes—
14C22×C32×C8C2212yes—
15C32×C4×D4C2211yescharacteristic
16#64147—21no—
17#64145—21no—
18#64135C2212yes—
19#64133C2212yes—
20#64133C2212yes—
21C2×#3746C2212yes—
22C2×#3744C2211yescharacteristic
23C4⋊C4×C3⋊D3—21no—
24#64096—21no—
25#64092—22no—
26#64088—22no—
27C4×C4⋊(C3⋊D3)C2211yescharacteristic
28#64078C2211yescharacteristic
29#64078C2211yescharacteristic
30C4×#634C2211yescharacteristic
31C32×C4⋊C8C2211yescharacteristic
32C32×C22⋊C8C2212yes—
33C32×C4×C8C2211yescharacteristic
34#63648C2212yes—
35#63648C2211yescharacteristic
36#63645C2212yes—
37#63644C2211yescharacteristic
38#63643C2212yes—
39#63643C2212yes—
40#63643C2211yescharacteristic
41#63643C2212yes—
42#5551—34no—
43#5542—34no—
44C3×C8×D4D314yescomplemented
45#5116—38no—
46#5113—38no—
47#4849—34no—
48#4846—34no—
49#4733—38no—
50#4723—38no—
51C4×#204—34no—
52#4681—34no—
53C2×C32×D4D411yescharacteristic
54C22×C32×C4C2312yes—
55C2×#638—22no—
56#3828—24no—
57#3828—42no—
58C2×C4⋊(C3⋊D3)C2311yescharacteristic
59C2×C4×C3⋊D3—21no—
60C2×C4×C3⋊D3—22no—
61C2×#634—21no—
62C2×#634C2311yescharacteristic
63C2×#634C2312yes—
64C2×C32×C8—42no—
65C2×C32×C8C2311yescharacteristic
66C2×C32×C8C2312yes—
67C2×C32×C8C2311yescharacteristic
68C32×C4⋊C4D411yescharacteristic
69C32×C22⋊C4D412yes—
70C32×C42C2311yescharacteristic
71#3757—22no—
72#3757—22no—
73#3757—22no—
74#3752—21no—
75C4⋊(C3⋊Dic3)—21no—
76C4⋊(C3⋊Dic3)—21no—
77C4⋊(C3⋊Dic3)—21no—
78C4⋊(C3⋊Dic3)C2311yescharacteristic
79C4⋊(C3⋊Dic3)C2312yes—
80C4⋊(C3⋊Dic3)C2311yescharacteristic
81#3750—21no—
82#3750—22no—
83#3750—22no—
84C4×C3⋊Dic3—21no—
85C4×C3⋊Dic3—22no—
86#3746—42no—
87#3744—22no—
88#3302—91noSylow
89C2×#235—38no—
90C22×C3×C8C2×D318yes—
91C3×C4×D4C2×D314yes—
92#938—64no—
93#936—64no—
94#926—38no—
95#924—38no—
96#924—38no—
97C2×Dic12—38no—
98C2×#204—34no—
99D3×C4⋊C4—64no—
100#887—64no—
101#883—68no—
102#879—68no—
103C4×D12—34no—
104#869—34no—
105#869—34no—
106C4×Dic6—34no—
107C3×C4⋊C8C2×D314yes—
108C3×C22⋊C8C2×D318yes—
109C3×C4×C8C2×D314yes—
110#821—34no—
111#821—38no—
112#818—38no—
113#817—34no—
114#816—38no—
115#816—38no—
116#816—34no—
117#816—38no—
118C23×C32C2×D412yes—
119C22×C3⋊D3—21no—
120C32×D4—22no—
121C2×C32×C4—22no—
122C2×C32×C4—22no—
123C2×C32×C4C2×D412yes—
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2411yescharacteristic
127#638—44no—
128C2×C3⋊Dic3—21no—
129C2×C3⋊Dic3—21no—
130C2×C3⋊Dic3—22no—
131C2×C3⋊Dic3—21no—
132C2×C3⋊Dic3—22no—
133C4⋊(C3⋊D3)—21no—
134C4⋊(C3⋊D3)#4112yes—
135C4×C3⋊D3—44no—
136C4×C3⋊D3—42no—
137#634—21no—
138#634—22no—
139#634—21no—
140#634—22no—
141#634—42no—
142C32×C8—21no—
143C32×C8—22no—
144C32×C8—21no—
145#556—91no—
146#547—91no—
147#487—91no—
148#485—92no—
149#474—91no—
150#467—92no—
151#462—91no—
152#452—92no—
153C4×SD16—91no—
154C8×D4C3⋊D311yescharacteristic, complemented
155#416—92no—
156C2×C3×D4D1214yes—
157C22×C3×C4C22×D318yes—
158C2×#67—68no—
159#235—616no—
160#235—128no—
161C2×D12—34no—
162C2×C4×D3—64no—
163C2×C4×D3—68no—
164C2×Dic6—38no—
165C2×Dic6—34no—
166C2×Dic6—64no—
167C2×C3×C8—48no—
168C2×C3×C8C22×D314yes—
169C2×C3×C8C22×D314yes—
170C2×C3×C8C22×D318yes—
171C3×C4⋊C4D1214yes—
172C3×C22⋊C4D1218yes—
173C3×C42C22×D314yes—
174#217—68no—
175#217—68no—
176#217—68no—
177(C2×D3)⋊C4—64no—
178C4⋊Dic3—34no—
179C4⋊Dic3—38no—
180C4⋊Dic3—34no—
181C4⋊Dic3—64no—
182C4⋊Dic3—64no—
183C4⋊Dic3—64no—
184Dic3⋊C4—64no—
185Dic3⋊C4—68no—
186Dic3⋊C4—68no—
187C4×Dic3—64no—
188C4×Dic3—68no—
189Dic12—128no—
190#204—68no—
191C22×C32—22no—
192C22×C32—22no—
193C22×C32—22no—
194C22×C32C22×D411yescharacteristic
195C2×C3⋊D3—22no—
196C2×C3⋊D3—41no—
197C2×C3⋊D3—41no—
198C32×C4—22no—
199C32×C4—21no—
200C32×C4#13512yes—
201C32×C4C2×#4111yescharacteristic
202C32×C4H(5,𝔽2)11yescharacteristic
203C3⋊Dic3—42no—
204C3⋊Dic3—41no—
205C3⋊Dic3—42no—
206C3⋊Dic3—41no—
207C3⋊Dic3—41no—
208C2×#41—92no—
209C2×Q16—92no—
210C2×SD16—91no—
211C22×C8C2×C3⋊D312yes—
212C4⋊Q8—91no—
213C4⋊Q8—91no—
214#126—182no—
215#124—181no—
216#123—182no—
217C22⋊Q8—92no—
218C22⋊Q8—92no—
219#121—181no—
220C4×Q8—91no—
221C4×Q8—181no—
222C4×D4—91no—
223C4×D4C2×C3⋊D311yescharacteristic
224#117—92no—
225C2×C4⋊C4—181no—
226#107—92no—
227#106—91no—
228C4⋊C8C2×C3⋊D311yescharacteristic
229#103—92no—
230#103—92no—
231#103—91no—
232#103—92no—
233#102—91no—
234#102—92no—
235C22⋊C8C2×C3⋊D312yes—
236C4×C8C2×C3⋊D311yescharacteristic
237C23×C3C2×D1218yes—
238C22×D3—64no—
239C3×D4—28no—
240C2×C3×C4—28no—
241C2×C3×C4—28no—
242C2×C3×C4C2×D1218yes—
243C2×C3×C4C2×D1214yes—
244C2×C3×C4C2×D1214yes—
245C2×C3×C4C23×D314yes—
246#67—1216no—
247C2×Dic3—64no—
248C2×Dic3—64no—
249C2×Dic3—68no—
250C2×Dic3—64no—
251C2×Dic3—68no—
252D12—38no—
253D12—64no—
254C4×D3—1216no—
255C4×D3—128no—
256Dic6—64no—
257Dic6—68no—
258Dic6—64no—
259Dic6—68no—
260Dic6—128no—
261C3×C8—28no—
262C3×C8—24no—
263C3×C8—24no—
264C2×C32—42no—
265C2×C32#54611yescharacteristic
266C2×C32C2×#13511yescharacteristic
267C2×C32#57811yescharacteristic
268C3⋊D3—42no—
269#41—184no—
270#41—362no—
271C2×Q8—92no—
272C2×Q8—91no—
273C2×Q8—181no—
274C2×D4—91no—
275C2×D4—182no—
276C2×D4C4⋊(C3⋊D3)11yescharacteristic
277C22×C4—181no—
278C22×C4—182no—
279C22×C4C22×C3⋊D312yes—
280Q16—362no—
281SD16—182no—
282C2×C8—42no—
283C2×C8C22×C3⋊D311yescharacteristic
284C2×C8C22×C3⋊D311yescharacteristic
285C2×C8C22×C3⋊D312yes—
286C4⋊C4—91no—
287C4⋊C4—92no—
288C4⋊C4—91no—
289C4⋊C4—181no—
290C4⋊C4—182no—
291C4⋊C4—181no—
292C4⋊C4—182no—
293C4⋊C4—181no—
294C4⋊C4—181no—
295C4⋊C4C4⋊(C3⋊D3)11yescharacteristic
296C22⋊C4—182no—
297C22⋊C4—182no—
298C22⋊C4—182no—
299C22⋊C4—181no—
300C22⋊C4C4⋊(C3⋊D3)12yes—
301C42—182no—
302C42—181no—
303C42C22×C3⋊D311yescharacteristic
304C22×C3—28no—
305C22×C3—28no—
306C22×C3—28no—
307C22×C3C22×D1214yes—
308C2×D3—68no—
309C2×D3—124no—
310C2×D3—124no—
311C3×C4—24no—
312C3×C4—28no—
313C3×C4#90418yes—
314C3×C4#100414yes—
315C3×C4D3×#4114yes—
316Dic3—128no—
317Dic3—124no—
318Dic3—124no—
319Dic3—128no—
320Dic3—124no—
321C32#330211yescharacteristic, complemented, Sylow
322C23—181no—
323C23C2×C4⋊(C3⋊D3)12yes—
324Q8—181no—
325Q8—182no—
326Q8—181no—
327Q8—182no—
328Q8—362no—
329D4—22no—
330D4—92no—
331D4—181no—
332D4—364no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—181no—
336C2×C4—182no—
337C2×C4—181no—
338C2×C4—181no—
339C2×C4—182no—
340C2×C4—364no—
341C2×C4—362no—
342C2×C4C2×C4⋊(C3⋊D3)12yes—
343C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
344C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
345C2×C4C23×C3⋊D311yescharacteristic
346C8—21no—
347C8—22no—
348C8—21no—
349C2×C3—48no—
350C2×C3#555414yes—
351C2×C3C2×#90414yes—
352C2×C3#575314yes—
353D3—128no—
354C22—22no—
355C22—22no—
356C22—22no—
357C22—182no—
358C22—361no—
359C22—361no—
360C22C22×C4⋊(C3⋊D3)11yescharacteristic
361C4—21no—
362C4—22no—
363C4—361no—
364C4—362no—
365C4—361no—
366C4—362no—
367C4—361no—
368C4#6411312yes—
369C4#6436111yescharacteristic
370C4#41×C3⋊D311yescharacteristic
371C3#7944214yescomplemented
372C2—42no—
373C2—362no—
374C2#1059602511yescharacteristic
375C2C2×#6411311yescharacteristic
376C2#1059622411yescharacteristic
subgroupG/H
centerC22C22×C4⋊(C3⋊D3)
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×C8×D4C2
socleC22×C32C22×D4
prime radical#10596022C2
hypercenterC8×D4C3⋊D3
hypocenterC32#3302
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
2. #10596013C2semidirect
3. C32×C8×D4C2semidirect
4. #10592815C2semidirect
5. #10592812C2semidirect
6. #10592548C2semidirect
7. #10592545C2semidirect
8. #10592432C2semidirect
9. #10592422C2semidirect
10. C4×#3744C2semidirect
11. #10592380C2semidirect
44. C3×C8×D4D3semidirect
154. C8×D4C3⋊D3semidirect
321. C32#3302semidirect
371. C3#79442semidirect

Maximal subgroups

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

subgroupindex
#105960222
#105960132
C32×C8×D42
#105928152
#105928122
#105925482
#105925452
#105924322
#105924222
C4×#37442
#105923802
#794423