Finite Group Databasebeta

← #11860589

Subgroups — #11860589

Order 1152.

728 conjugacy classes of subgroups.

The subgroup lattice has 453 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596650C211yesmaximal, characteristic
2#10596646C211yesmaximal, characteristic, complemented
3C3⋊D3×#137C211yesmaximal, characteristic
4#10593841C211yesmaximal, characteristic
5C2×#63784C211yesmaximal, characteristic, complemented
6#10593786C212yesmaximal, complemented
7Q16×#157C212yesmaximal, complemented
8#10593782C212yesmaximal, complemented
9SD16×#157C212yesmaximal, complemented
10#10593775C211yesmaximal, characteristic, complemented
11#10593774C211yesmaximal, characteristic, complemented
12#41×C3⋊D3C2211yescharacteristic
13C2×Q8×C3⋊D3C2211yescharacteristic
14Q8×#157—21no—
15Q8×#157—21no—
16Q8×#157C2212yes—
17Q8×#157C2212yes—
18Q8×#157C2212yes—
19D4×#157—22no—
20D4×#157C2212yes—
21#64286—22no—
22#64286—21no—
23#64286C2211yescharacteristic
24#64286C2211yescharacteristic
25C2×C4⋊#157—21no—
26C2×C4⋊#157C2211yescharacteristic
27C2×#3787C2211yescharacteristic
28C32×#137C411yescharacteristic, complemented
29#64160C411yescharacteristic, complemented
30#64151C411yescharacteristic, complemented
31#64127C412yescomplemented
32Q16×C3⋊D3C2212yes—
33#64124C412yescomplemented
34SD16×C3⋊D3C2212yes—
35#64118C411yescharacteristic, complemented
36M16×C3⋊D3C2211yescharacteristic
37#63784C2212yes—
38#63784C2212yes—
39#63784C2211yescharacteristic
40#63784C2211yescharacteristic
41#63782C2211yescharacteristic
42#63782C2211yescharacteristic
43#63769C2212yes—
44#63768C2212yes—
45#63767C2212yes—
46C8×#157C2212yes—
47D3×#137—62no—
48C22×#157—21no—
49C22×#157—22no—
50C32×#41C2×C411yescharacteristic
51C2×C32×Q8C2×C411yescharacteristic, complemented
52#3832C2×C411yescharacteristic
53Q8×C3⋊D3—21no—
54Q8×C3⋊D3—21no—
55Q8×C3⋊D3C2×C412yescomplemented
56Q8×C3⋊D3C2312yes—
57Q8×C3⋊D3C2311yescharacteristic
58#3830—21no—
59#3830C2×C411yescharacteristic
60D4×C3⋊D3—21no—
61D4×C3⋊D3C2311yescharacteristic
62#3828—21no—
63#3828C2×C411yescharacteristic
64C2×C4×C3⋊D3—21no—
65C2×C4×C3⋊D3—21no—
66C2×C4×C3⋊D3C2311yescharacteristic
67C2×#634—21no—
68C2×#634C2×C411yescharacteristic, complemented
69C22⋊#157—21no—
70C22⋊#157—22no—
71C22⋊#157D412yes—
72C2×#622—21no—
73C4⋊#157—22no—
74C4⋊#157—22no—
75C4⋊#157—22no—
76C4⋊#157—21no—
77C4⋊#157D411yescharacteristic
78C4⋊#157D411yescharacteristic
79C4⋊#157C2311yescharacteristic
80C4⋊#157C2312yes—
81C4⋊#157C2311yescharacteristic
82C4×#157—22no—
83C4×#157—22no—
84C4×#157—22no—
85C4×#157—21no—
86C4×#157C2312yes—
87#3787—21no—
88#3787C2311yescharacteristic
89#3787C2311yescharacteristic
90C32×Q16C2×C412yescomplemented
91C32×SD16C2×C412yescomplemented
92C32×M16C2×C411yescharacteristic, complemented
93#3756C2×C412yescomplemented
94#3756C2×C412yescomplemented
95#3755C2×C412yescomplemented
96#3754C2×C412yescomplemented
97#3748C2×C411yescharacteristic, complemented
98#3746C2×C412yescomplemented
99#3744C2×C412yescomplemented
100#3743C2×C412yescomplemented
101C8×C3⋊D3C2312yes—
102#2947—91nomaximal, Sylow
103D3×#41—62no—
104C2×D3×Q8—62no—
105C3×#137—22no—
106#951—62no—
107#942—62no—
108#918—64no—
109D3×Q16—64no—
110#915—64no—
111D3×SD16—64no—
112#909—62no—
113D3×M16—62no—
114C22×C3⋊D3—21no—
115C22×C3⋊D3C2×D411yescharacteristic
116C2×#157—22no—
117C2×#157—21no—
118C2×#157—21no—
119C2×#157—82no—
120C2×#157—81no—
121C2×#157C2×D412yes—
122C2×#157C2×D412yes—
123C32×Q8—21no—
124C32×Q8C22×C412yes—
125C32×Q8C22×C411yescharacteristic
126C32×D4—21no—
127C32×D4C22×C411yescharacteristic
128C2×C32×C4—21no—
129C2×C32×C4—21no—
130C2×C32×C4C22×C411yescharacteristic
131#638—21no—
132#638—21no—
133#638—21no—
134C2×C3⋊Dic3—21no—
135C2×C3⋊Dic3—21no—
136C2×C3⋊Dic3#4111yescharacteristic
137C4⋊(C3⋊D3)—21no—
138C4⋊(C3⋊D3)C22×C411yescharacteristic
139C4×C3⋊D3—22no—
140C4×C3⋊D3—21no—
141C4×C3⋊D3—22no—
142C4×C3⋊D3—21no—
143C4×C3⋊D3—21no—
144C4×C3⋊D3C22×C411yescharacteristic
145C4×C3⋊D3C2×D411yescharacteristic
146C4×C3⋊D3#4111yescharacteristic
147C4×C3⋊D3C2411yescharacteristic
148#634—21no—
149#634—22no—
150#634—22no—
151#634—21no—
152#634C22×C412yes—
153#634C22×C411yescharacteristic
154#622—21no—
155#622—21no—
156C32×C8C22×C412yes—
157C3⋊(C3⋊C8)C22×C412yes—
158C2×#137—91no—
159#520—91no—
160#519—91no—
161#441—92no—
162#440—92no—
163C4×Q16—92no—
164C4×SD16—92no—
165#428—91no—
166#416—91no—
167C2×#103—91no—
168#405—91no—
169C3×#41—22no—
170C2×C3×Q8—22no—
171#239—62no—
172D3×Q8—64no—
173D3×Q8—64no—
174D3×Q8—62no—
175D3×Q8—122no—
176D3×Q8—122no—
177#237—62no—
178#237—122no—
179D3×D4—62no—
180D3×D4—122no—
181#235—62no—
182#235—122no—
183C2×C4×D3—62no—
184C2×C4×D3—122no—
185C2×C4×D3—122no—
186C2×Dic6—62no—
187C2×Dic6—122no—
188C3×Q16—24no—
189C3×SD16—24no—
190C3×M16—22no—
191#216—64no—
192#216—64no—
193#215—64no—
194#214—64no—
195#208—62no—
196Dic12—64no—
197#204—64no—
198ΓL(1,𝔽25)—64no—
199D3×C8—64no—
200C22×C32—21no—
201C22×C32C4×D411yescharacteristic
202C2×C3⋊D3—21no—
203C2×C3⋊D3—21no—
204C2×C3⋊D3—21no—
205C2×C3⋊D3—41no—
206C2×C3⋊D3—41no—
207C2×C3⋊D3C4×D411yescharacteristic
208C2×C3⋊D3C22×D411yescharacteristic
209#157—22no—
210#157—22no—
211#157—41no—
212#157—42no—
213#157—41no—
214C32×C4—22no—
215C32×C4—21no—
216C32×C4C4×D411yescharacteristic
217C32×C4C23×C411yescharacteristic
218C3⋊Dic3—22no—
219C3⋊Dic3—21no—
220C3⋊Dic3C4×D411yescharacteristic
221C3⋊Dic3C2×#4111yescharacteristic
222C2×#41—91no—
223C22×Q8—91no—
224#137—91no—
225#137—91no—
226#137—92no—
227#137—92no—
228#137—91no—
229#137#15711yescharacteristic, complemented
230C2×Q16—92no—
231C2×SD16—92no—
232C2×M16—91no—
233C22×C8—91no—
234C4×Q8—92no—
235C4×Q8—92no—
236C4×Q8—92no—
237C4×Q8—181no—
238C4×Q8—181no—
239C4×D4—92no—
240C4×D4—182no—
241#117—91no—
242#117—91no—
243#117—182no—
244#117—181no—
245C2×C4⋊C4—91no—
246C2×C4⋊C4—181no—
247#107—92no—
248#106—92no—
249#103—92no—
250#103—92no—
251#103—91no—
252#103—91no—
253#102—91no—
254#102—91no—
255#97—92no—
256C4×C8—92no—
257C22×D3—62no—
258C22×D3—122no—
259C3×Q8—24no—
260C3×Q8—22no—
261C3×Q8—42no—
262C3×D4—22no—
263C3×D4—42no—
264C2×C3×C4—22no—
265C2×C3×C4—42no—
266C2×C3×C4—42no—
267#67—122no—
268#67—122no—
269#67—122no—
270C2×Dic3—62no—
271C2×Dic3—122no—
272C2×Dic3—122no—
273D12—62no—
274D12—122no—
275C4×D3—62no—
276C4×D3—62no—
277C4×D3—62no—
278C4×D3—62no—
279C4×D3—122no—
280C4×D3—122no—
281C4×D3—122no—
282C4×D3—124no—
283C4×D3—124no—
284Dic6—64no—
285Dic6—62no—
286Dic6—124no—
287Dic6—124no—
288Dic6—122no—
289Dic6—122no—
290C3×C8—24no—
291C3⋊C8—64no—
292C2×C32—21no—
293C2×C32—41no—
294C2×C32C2×C4×D411yescharacteristic
295C3⋊D3—21no—
296C3⋊D3—41no—
297C3⋊D3#57711yescharacteristic
298C3⋊D3#57811yescharacteristic
299#41—91no—
300#41—91no—
301#41—91no—
302#41—181no—
303#41—181no—
304#41C2×#15711yescharacteristic
305C2×Q8—92no—
306C2×Q8—91no—
307C2×Q8—92no—
308C2×Q8—91no—
309C2×Q8—181no—
310C2×Q8—181no—
311C2×Q8—181no—
312C2×Q8C2×#15711yescharacteristic, complemented
313C2×D4—91no—
314C2×D4—181no—
315C22×C4—91no—
316C22×C4—181no—
317C22×C4—181no—
318C22×C4—182no—
319C22×C4—181no—
320Q16—92no—
321Q16—92no—
322Q16—92no—
323Q16C2×#15712yescomplemented
324SD16—92no—
325SD16—92no—
326SD16—92no—
327SD16C2×#15712yescomplemented
328M16—91no—
329M16—92no—
330M16C2×#15711yescharacteristic, complemented
331C2×C8—92no—
332C2×C8—91no—
333C2×C8—91no—
334C2×C8—181no—
335C2×C8—181no—
336C4⋊C4—91no—
337C4⋊C4—91no—
338C4⋊C4—91no—
339C4⋊C4—91no—
340C4⋊C4—92no—
341C4⋊C4—181no—
342C4⋊C4—182no—
343C4⋊C4—182no—
344C4⋊C4—182no—
345C22⋊C4—92no—
346C22⋊C4—182no—
347C22⋊C4—181no—
348C42—92no—
349C42—181no—
350C42—182no—
351C42—182no—
352C42—182no—
353C22×C3—22no—
354C22×C3—42no—
355C2×D3—62no—
356C2×D3—62no—
357C2×D3—122no—
358C2×D3—122no—
359C2×D3—122no—
360C2×D3—242no—
361C2×D3—242no—
362C3×C4—22no—
363C3×C4—22no—
364C3×C4—44no—
365C3×C4—42no—
366Dic3—62no—
367Dic3—62no—
368Dic3—124no—
369Dic3—122no—
370C32#294711yescharacteristic, complemented, Sylow
371C23—91no—
372C23—181no—
373Q8—21no—
374Q8—92no—
375Q8—91no—
376Q8—182no—
377Q8—182no—
378Q8—181no—
379Q8—181no—
380Q8C22×#15712yes—
381Q8C22×#15711yescharacteristic
382D4—21no—
383D4—91no—
384D4—181no—
385D4—181no—
386D4—181no—
387D4—181no—
388D4C22×#15711yescharacteristic
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—91no—
392C2×C4—91no—
393C2×C4—91no—
394C2×C4—91no—
395C2×C4—91no—
396C2×C4—92no—
397C2×C4—92no—
398C2×C4—181no—
399C2×C4—181no—
400C2×C4—182no—
401C2×C4—182no—
402C2×C4—181no—
403C2×C4—181no—
404C2×C4—181no—
405C2×C4—181no—
406C2×C4—181no—
407C2×C4—182no—
408C2×C4—722no—
409C2×C4—721no—
410C2×C4C22×#15711yescharacteristic
411C8—92no—
412C8—181no—
413C8—181no—
414C8C22×#15712yes—
415C2×C3—22no—
416C2×C3—42no—
417C2×C3—82no—
418D3—62no—
419D3—62no—
420D3—122no—
421D3—242no—
422C22—21no—
423C22—91no—
424C22—91no—
425C22—181no—
426C22—181no—
427C22—181no—
428C22—361no—
429C22—361no—
430C22D4×#15711yescharacteristic
431C4—21no—
432C4—22no—
433C4—91no—
434C4—91no—
435C4—182no—
436C4—182no—
437C4—181no—
438C4—182no—
439C4—362no—
440C4—361no—
441C4—361no—
442C4D4×#15711yescharacteristic
443C4C23×#15711yescharacteristic
444C3—22no—
445C2—21no—
446C2—41no—
447C2—91no—
448C2—91no—
449C2—181no—
450C2—361no—
451C2C2×D4×#15711yescharacteristic
subgroupG/H
centerC2C2×D4×#157
commutatorC32×C4C23×C4
FrattiniC4C23×#157
FittingC32×#137C4
socleC2×C32C2×C4×D4
prime radical#41×C3⋊D3C22
cosocleC4×C3⋊D3C24
hypercenter#137#157
hypocenterC32#2947
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ #137

Complements

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

NH ≅ G/Ntype
2. #10596646C2semidirect
5. C2×#63784C2semidirect
6. #10593786C2semidirect
7. Q16×#157C2semidirect
8. #10593782C2semidirect
9. SD16×#157C2semidirect
10. #10593775C2semidirect
11. #10593774C2semidirect
28. C32×#137C4semidirect
29. #64160C4semidirect
30. #64151C4semidirect
31. #64127C4semidirect
33. #64124C4semidirect
35. #64118C4semidirect
51. C2×C32×Q8C2×C4semidirect
55. Q8×C3⋊D3C2×C4semidirect
68. C2×#634C2×C4semidirect
90. C32×Q16C2×C4semidirect
91. C32×SD16C2×C4semidirect
92. C32×M16C2×C4semidirect
93. #3756C2×C4semidirect
94. #3756C2×C4semidirect
95. #3755C2×C4semidirect
96. #3754C2×C4semidirect
97. #3748C2×C4semidirect
98. #3746C2×C4semidirect
99. #3744C2×C4semidirect
100. #3743C2×C4semidirect
229. #137#157semidirect
312. C2×Q8C2×#157semidirect
323. Q16C2×#157semidirect
327. SD16C2×#157semidirect
330. M16C2×#157semidirect
370. C32#2947semidirect

Maximal subgroups

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

subgroupindex
#105966502
#105966462
C3⋊D3×#1372
#105938412
C2×#637842
#105937862
Q16×#1572
#105937822
SD16×#1572
#105937752
#105937742
#29479