Finite Group Databasebeta

← #11860364

Subgroups — #11860364

Order 1152.

1452 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64118C211yesmaximal, characteristic
2#10595993C211yesmaximal, characteristic
3C2×#64096C211yesmaximal, characteristic, complemented
4C32×#428C211yesmaximal, characteristic, complemented
5M16×C3⋊Dic3C211yesmaximal, characteristic, complemented
6#10592703C211yesmaximal, characteristic, complemented
7#10592665C211yesmaximal, characteristic
8#10592588C212yesmaximal, complemented
9#10592572C212yesmaximal, complemented
10#10592552C212yesmaximal, complemented
11#10592551C212yesmaximal, complemented
12#79200—34nomaximal
13C2×#3828C2211yescharacteristic
14C22×#634C2211yescharacteristic
15C2×C32×M16C2211yescharacteristic
16C32×#117C2211yescharacteristic
17C2×C32×C4⋊C4C2211yescharacteristic
18C2×#3750—21no—
19C2×C4×C3⋊Dic3—21no—
20C2×C4×C3⋊Dic3C2211yescharacteristic
21C2×#3748C2211yescharacteristic
22#64118C418yescomplemented
23C2×#3746C2212yes—
24C2×#3744C2212yes—
25#64102C2211yescharacteristic
26#64102C2211yescharacteristic
27#64096—21no—
28#64096—21no—
29#64096C2212yes—
30#64096C2211yescharacteristic
31#64096C2212yes—
32#64096C2211yescharacteristic
33#64090—21no—
34#64090—21no—
35#64081—21no—
36C42×C3⋊D3—21no—
37C32×#107C2212yes—
38C32×#106C2212yes—
39#63642C2212yes—
40C8×C3⋊Dic3C2212yes—
41#63637C2212yes—
42#63637C2212yes—
43#63637C2212yes—
44#63636C2212yes—
45C2×#909—34no—
46#5522—34no—
47C2×#887—34no—
48C3×#428D314yescomplemented
49Dic3×M16—34no—
50#5004—34no—
51#4966—34no—
52#4889—38no—
53#4873—38no—
54#4853—38no—
55#4852—38no—
56C22×C32×C4—21no—
57C22×C32×C4C2311yescharacteristic
58C2×#638—21no—
59C22×C3⋊Dic3—21no—
60C22×C3⋊Dic3D411yescharacteristic
61C22×C3⋊Dic3D411yescharacteristic
62#3828—22no—
63#3828C2×C414yes—
64C2×C4⋊(C3⋊D3)C2311yescharacteristic
65C2×C4×C3⋊D3—21no—
66C2×C4×C3⋊D3—21no—
67C2×C4×C3⋊D3—21no—
68C2×#634—21no—
69C2×#634—22no—
70C2×#634C2×C414yescomplemented
71C2×#634C2312yes—
72C2×#634C2311yescharacteristic
73C32×M16C2×C414yescomplemented
74C2×C32×C8C2312yes—
75C32×C4⋊C4—21no—
76C32×C4⋊C4C2312yes—
77C32×C4⋊C4C2311yescharacteristic
78C32×C4⋊C4C2311yescharacteristic
79C32×C22⋊C4—21no—
80C32×C42—21no—
81#3752—21no—
82#3752—21no—
83#3750—21no—
84#3750—21no—
85#3750—22no—
86#3750—22no—
87C4×C3⋊Dic3—21no—
88C4×C3⋊Dic3—21no—
89C4×C3⋊Dic3—22no—
90C4×C3⋊Dic3—22no—
91C4×C3⋊Dic3D411yescharacteristic
92C4×C3⋊Dic3D411yescharacteristic
93C4×C3⋊Dic3C2311yescharacteristic
94C4×C3⋊Dic3C2311yescharacteristic
95#3748—22no—
96C2×C3⋊(C3⋊C8)C2312yes—
97#3746C2×C418yescomplemented
98#3744C2×C418yescomplemented
99C4×#137—91noSylow
100C2×#235—34no—
101C22×Dic6—34no—
102C2×C3×M16C2×D314yes—
103C3×#117C2×D314yes—
104C2×C3×C4⋊C4C2×D314yes—
105C2×Dic3⋊C4—64no—
106C2×C4×Dic3—34no—
107C2×C4×Dic3—64no—
108C2×#208—34no—
109#909—332no—
110C2×Dic12—38no—
111C2×#204—38no—
112#893—34no—
113#893—34no—
114#887—34no—
115#887—38no—
116#887—38no—
117#887—34no—
118#887—64no—
119#887—64no—
120#67⋊C4—64no—
121#67⋊C4—64no—
122#872—64no—
123C42×D3—64no—
124C3×#107C2×D318yes—
125C3×#106C2×D318yes—
126#815—38no—
127C8×Dic3—38no—
128#810—38no—
129#810—38no—
130#810—38no—
131#809—38no—
132C23×C32C2×D411yescharacteristic
133C22×C3⋊D3—21no—
134C2×C32×C4—22no—
135C2×C32×C4—21no—
136C2×C32×C4—21no—
137C2×C32×C4—42no—
138C2×C32×C4C22×C412yes—
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4#4112yes—
141C2×C32×C4C2411yescharacteristic
142#638—24no—
143C2×C3⋊Dic3—24no—
144C2×C3⋊Dic3—22no—
145C2×C3⋊Dic3—21no—
146C2×C3⋊Dic3—22no—
147C2×C3⋊Dic3—41no—
148C2×C3⋊Dic3C2×D411yescharacteristic
149C2×C3⋊Dic3C2×D411yescharacteristic
150C2×C3⋊Dic3C2×D411yescharacteristic
151C2×C3⋊Dic3C2×D411yescharacteristic
152C4⋊(C3⋊D3)—21no—
153C4⋊(C3⋊D3)C22×C412yes—
154C4×C3⋊D3—24no—
155C4×C3⋊D3—42no—
156C4×C3⋊D3—42no—
157#634—24no—
158#634—22no—
159#634—21no—
160#634C22×C414yes—
161#634C22×C412yes—
162C32×C8C22×C414yes—
163C3⋊(C3⋊C8)—22no—
164C2×#137—91no—
165C4×#41—91no—
166C2×C4×Q8—91no—
167#441—92no—
168#440—92no—
169C4×Q16—92no—
170C4×SD16—92no—
171#428C3⋊D311yescharacteristic, complemented
172#419—91no—
173#417—91no—
174C4×M16—91no—
175C22×C3×C4—24no—
176C22×C3×C4C22×D314yes—
177C2×#67—64no—
178C22×Dic3—34no—
179C22×Dic3—34no—
180C22×Dic3—64no—
181#235—316no—
182#235—68no—
183C2×D12—34no—
184C2×C4×D3—64no—
185C2×C4×D3—64no—
186C2×C4×D3—64no—
187C2×Dic6—316no—
188C2×Dic6—38no—
189C2×Dic6—34no—
190C2×Dic6—64no—
191C2×Dic6—68no—
192C3×M16C4×D3116yescomplemented
193C2×C3×C8C22×D318yes—
194C3×C4⋊C4—24no—
195C3×C4⋊C4C22×D318yes—
196C3×C4⋊C4C22×D314yes—
197C3×C4⋊C4C22×D314yes—
198C3×C22⋊C4—24no—
199C3×C42—24no—
200(C2×D3)⋊C4—64no—
201(C2×D3)⋊C4—64no—
202Dic3⋊C4—64no—
203Dic3⋊C4—64no—
204Dic3⋊C4—68no—
205Dic3⋊C4—68no—
206C4×Dic3—34no—
207C4×Dic3—34no—
208C4×Dic3—34no—
209C4×Dic3—34no—
210C4×Dic3—64no—
211C4×Dic3—64no—
212C4×Dic3—68no—
213C4×Dic3—68no—
214#208—68no—
215C2×C3⋊C8—38no—
216Dic12—332no—
217#204—332no—
218C22×C32—21no—
219C22×C32—21no—
220C22×C32C4×D412yes—
221C22×C32C22×D411yescharacteristic
222C2×C3⋊D3—22no—
223C2×C3⋊D3—41no—
224C2×C3⋊D3—41no—
225C32×C4—41no—
226C32×C4—41no—
227C32×C4—42no—
228C32×C4C4×D412yes—
229C32×C4C23×C411yescharacteristic
230C32×C4C2×#4111yescharacteristic
231C3⋊Dic3—24no—
232C3⋊Dic3—22no—
233C3⋊Dic3—21no—
234C3⋊Dic3—21no—
235C3⋊Dic3—21no—
236C3⋊Dic3#13712yescomplemented
237C2×#41—91no—
238C22×Q8—91no—
239#137—98no—
240C2×Q16—92no—
241C2×SD16—92no—
242C2×M16—91no—
243C2×M16C2×C3⋊D311yescharacteristic
244C4×Q8—92no—
245C4×Q8—92no—
246C4×Q8—91no—
247C4×Q8—91no—
248C4×Q8—181no—
249C4×Q8—181no—
250C4×D4—91no—
251C4×D4—91no—
252C4×D4—181no—
253C4×D4—181no—
254#117—181no—
255#117C2×C3⋊D311yescharacteristic
256C2×C4⋊C4—181no—
257C2×C4⋊C4C2×C3⋊D311yescharacteristic
258C2×C42—91no—
259C2×C42—181no—
260C2×C42—181no—
261#107C2×C3⋊D312yes—
262#106C2×C3⋊D312yes—
263#103—92no—
264#103—92no—
265#103—92no—
266#102—92no—
267#97—92no—
268C4×C8—92no—
269C23×C3D3×D414yes—
270C22×D3—64no—
271C2×C3×C4—28no—
272C2×C3×C4—24no—
273C2×C3×C4—24no—
274C2×C3×C4—48no—
275C2×C3×C4C2×C4×D318yes—
276C2×C3×C4D3×D414yes—
277C2×C3×C4#23918yes—
278C2×C3×C4C23×D314yes—
279#67—616no—
280C2×Dic3—34no—
281C2×Dic3—34no—
282C2×Dic3—34no—
283C2×Dic3—34no—
284C2×Dic3—68no—
285C2×Dic3—616no—
286C2×Dic3—68no—
287C2×Dic3—64no—
288C2×Dic3—124no—
289D12—38no—
290D12—64no—
291C4×D3—616no—
292C4×D3—128no—
293C4×D3—128no—
294Dic6—316no—
295Dic6—38no—
296Dic6—616no—
297Dic6—68no—
298Dic6—64no—
299C3×C8C2×C4×D3116yes—
300C3⋊C8—68no—
301C2×C32—22no—
302C2×C32C2×C4×D411yescharacteristic
303C2×C32C2×#13711yescharacteristic
304C2×C32#57511yescharacteristic
305C3⋊D3—42no—
306#41—94no—
307#41—182no—
308C2×Q8—92no—
309C2×Q8—91no—
310C2×Q8—94no—
311C2×Q8—181no—
312C2×Q8—182no—
313C2×D4—91no—
314C2×D4—181no—
315C22×C4—21no—
316C22×C4—91no—
317C22×C4—91no—
318C22×C4—181no—
319C22×C4—181no—
320C22×C4—181no—
321C22×C4—181no—
322C22×C4C22×C3⋊D311yescharacteristic
323Q16—98no—
324SD16—98no—
325M16—182no—
326M16C4×C3⋊D314yescomplemented
327C2×C8—92no—
328C2×C8C22×C3⋊D312yes—
329C4⋊C4—21no—
330C4⋊C4—182no—
331C4⋊C4—182no—
332C4⋊C4—181no—
333C4⋊C4—181no—
334C4⋊C4C22×C3⋊D312yes—
335C4⋊C4C22×C3⋊D311yescharacteristic
336C4⋊C4C22×C3⋊D311yescharacteristic
337C22⋊C4—21no—
338C22⋊C4—181no—
339C22⋊C4—181no—
340C42—21no—
341C42—91no—
342C42—91no—
343C42—91no—
344C42—91no—
345C42—181no—
346C42—181no—
347C42—182no—
348C42—182no—
349C22×C3—24no—
350C22×C3—24no—
351C22×C3#89318yes—
352C22×C3C2×D3×D414yes—
353C2×D3—68no—
354C2×D3—124no—
355C2×D3—124no—
356C3×C4—44no—
357C3×C4—48no—
358C3×C4—44no—
359C3×C4#89318yes—
360C3×C4C22×C4×D314yes—
361C3×C4C2×#23914yes—
362Dic3—38no—
363Dic3—616no—
364Dic3—68no—
365Dic3—64no—
366Dic3—64no—
367Dic3—64no—
368C32C4×#13711yescharacteristic, complemented, Sylow
369C23—181no—
370C23D4×C3⋊D311yescharacteristic
371Q8—94no—
372Q8—92no—
373Q8—184no—
374Q8—182no—
375Q8—181no—
376D4—92no—
377D4—184no—
378D4—181no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—22no—
382C2×C4—42no—
383C2×C4—91no—
384C2×C4—91no—
385C2×C4—91no—
386C2×C4—91no—
387C2×C4—182no—
388C2×C4—184no—
389C2×C4—181no—
390C2×C4—182no—
391C2×C4—184no—
392C2×C4—362no—
393C2×C4—362no—
394C2×C4—361no—
395C2×C4C2×C4×C3⋊D312yes—
396C2×C4D4×C3⋊D311yescharacteristic
397C2×C4#383212yes—
398C2×C4C23×C3⋊D311yescharacteristic
399C8—182no—
400C8C2×C4×C3⋊D314yes—
401C2×C3—28no—
402C2×C3C2×#89314yes—
403C2×C3#577314yes—
404C2×C3D3×#13714yes—
405D3—128no—
406C22—21no—
407C22—21no—
408C22—182no—
409C22—361no—
410C22—361no—
411C22#6410212yes—
412C22C2×D4×C3⋊D311yescharacteristic
413C4—42no—
414C4—41no—
415C4—41no—
416C4—92no—
417C4—182no—
418C4—184no—
419C4—181no—
420C4—181no—
421C4—181no—
422C4#6410212yes—
423C4C22×C4×C3⋊D311yescharacteristic
424C4C2×#383211yescharacteristic
425C3#7920014yescomplemented
426C2—22no—
427C2—362no—
428C2C2×#6410211yescharacteristic
429C2#1059624411yescharacteristic
430C2C3⋊D3×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutatorC32×C4C23×C4
FrattiniC2×C4C23×C3⋊D3
FittingC32×#428C2
socleC22×C32C22×D4
prime radicalC2×#3828C22
cosocleC2×C32×C4C24
hypercenter#428C3⋊D3
hypocenterC32C4×#137
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
3. C2×#64096C2semidirect
4. C32×#428C2semidirect
5. M16×C3⋊Dic3C2semidirect
6. #10592703C2semidirect
8. #10592588C2semidirect
9. #10592572C2semidirect
10. #10592552C2semidirect
11. #10592551C2semidirect
22. #64118C4semidirect
48. C3×#428D3semidirect
70. C2×#634C2×C4semidirect
73. C32×M16C2×C4semidirect
97. #3746C2×C4semidirect
98. #3744C2×C4semidirect
171. #428C3⋊D3semidirect
192. C3×M16C4×D3semidirect
236. C3⋊Dic3#137semidirect
326. M16C4×C3⋊D3semidirect
368. C32C4×#137semidirect
425. C3#79200semidirect

Maximal subgroups

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

subgroupindex
C2×#641182
#105959932
C2×#640962
C32×#4282
M16×C3⋊Dic32
#105927032
#105926652
#105925882
#105925722
#105925522
#105925512
#792003