Finite Group Databasebeta

← #11860768

Subgroups — #11860768

Order 1152.

1049 conjugacy classes of subgroups.

The subgroup lattice has 451 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594982C211yesmaximal, characteristic
2#10594818C211yesmaximal, characteristic, complemented
3C22×#3715C211yesmaximal, characteristic
4#10592821C211yesmaximal, characteristic, complemented
5C3×#5131C211yesmaximal, characteristic
6C3×#5120C211yesmaximal, characteristic, complemented
7#10591138C211yesmaximal, characteristic, complemented
8#10590743C214yesmaximal, complemented
9#10590742C214yesmaximal, complemented
10#78947—31nomaximal
11#78916—31nomaximal
12C22×C3×D12C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C2×C32×M16C2211yescharacteristic
15#64135C2211yescharacteristic
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C3×#926C2211yescharacteristic
18C3×#926C2211yescharacteristic
19D3×#217—22no—
20#63955—22no—
21#63898C2214yes—
22Dic3×D12—22no—
23#63843C2214yescomplemented
24Dic3×Dic6—22no—
25C2×#3715C418yescomplemented
26C2×#3715C2212yes—
27C2×#3715C2212yes—
28#63642C2212yescomplemented
29C8×C3⋊Dic3C2212yescomplemented
30C3×#821C2214yes—
31C3×#816C2214yescomplemented
32#63576C2212yescomplemented
33#63574C2212yescomplemented
34#5812—31no—
35C22×#215—31no—
36#5798—31no—
37C22×#214—31no—
38#5521—31no—
39#5516—31no—
40C3×#419—31no—
41C3×#418—31no—
42#5131D311yescharacteristic
43#5122—31no—
44#5122—31no—
45#5122—61no—
46#5120D311yescharacteristic, complemented
47#4998—31no—
48#4998—31no—
49#4817—34no—
50#4788—34no—
51#4758—34no—
52#4757—34no—
53C23×C3×D3—21no—
54C22×C32×C4C2311yescharacteristic
55C22×C3×Dic3—21no—
56C2×C3×D12—21no—
57C2×C3×D12—22no—
58C2×C3×D12C2×C414yes—
59C2×C3×D12C2312yes—
60C2×C3×Dic6—21no—
61C2×C3×Dic6—22no—
62C2×C3×Dic6C2×C414yescomplemented
63C2×C3×Dic6C2312yes—
64C2×D3×Dic3—24no—
65C32×M16—22no—
66C2×C32×C8C2312yes—
67#3757D412yes—
68C4⋊(C3⋊Dic3)D412yes—
69C4×C3⋊Dic3C2312yes—
70C2×C3⋊(C3⋊C8)C2×C414yescomplemented
71C2×C3⋊(C3⋊C8)C2311yescharacteristic
72C2×C3⋊(C3⋊C8)C2311yescharacteristic
73C3×#217—21no—
74C3×#217—21no—
75C3×C4⋊Dic3C2312yes—
76C3×C4⋊Dic3C2312yes—
77C3×C4×Dic3—21no—
78C3×C4×Dic3—21no—
79Dic3⋊Dic3—24no—
80(C2×D3)⋊Dic3—24no—
81Dic32—24no—
82#3715C2×C418yescomplemented
83#3715C2×C418yescomplemented
84#2949—91noSylow
85C22×C3×Q8—31no—
86C22×C3×D4—31no—
87C22×D12C2×D311yescharacteristic
88C22×Dic6C2×D311yescharacteristic
89C2×C3×M16—21no—
90C2×C3×M16C2×D311yescharacteristic
91C2×C3×M16C2×D311yescharacteristic
92C3×#117—31no—
93C3×#117—31no—
94C2×#217—62no—
95Q8×Dic3—34no—
96Q8×Dic3—62no—
97C2×#215—38no—
98C2×#215—32no—
99C2×#215—32no—
100D4×Dic3—34no—
101D4×Dic3—62no—
102C2×#214—38no—
103C2×#214—32no—
104C2×#214—32no—
105#926—31no—
106#926—31no—
107#926—61no—
108#926—62no—
109#926C2×D311yescharacteristic
110#926C2×D311yescharacteristic
111C22×C3⋊C8—31no—
112C22×C3⋊C8—31no—
113C22×C3⋊C8—61no—
114#893—34no—
115#887—34no—
116D3×C22⋊C4—62no—
117#877—62no—
118C4×D12—62no—
119C4×Dic6—62no—
120C3×#103—34no—
121C3×#102—34no—
122#821C2×D314yes—
123#816C2×D314yescomplemented
124#815—32no—
125#815—32no—
126#815—62no—
127C8×Dic3—32no—
128C8×Dic3—32no—
129C8×Dic3—62no—
130#808—32no—
131#808—32no—
132#807—32no—
133#807—32no—
134C23×C32C2×D411yescharacteristic
135C22×C3×D3—22no—
136C22×C3×D3—24no—
137C22×C3×D3—82no—
138C2×C32×C4C22×C412yes—
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4#4112yes—
141C2×C32×C4C2411yescharacteristic
142C2×C3⋊Dic3C2×D414yes—
143C2×C3×Dic3—24no—
144C2×C3×Dic3—22no—
145C2×C3×Dic3—22no—
146C2×C3×Dic3—22no—
147C3×D12—24no—
148C3×D12—22no—
149C3×D12C22×C414yes—
150C3×Dic6—24no—
151C3×Dic6—22no—
152C3×Dic6C22×C414yes—
153D3×Dic3—84no—
154C32×C8—22no—
155C3⋊(C3⋊C8)C22×C412yes—
156C3⋊(C3⋊C8)C22×C412yes—
157C22×SD16—91no—
158#519—91no—
159#518—91no—
160#440—94no—
161C4×SD16—94no—
162#427—91no—
163#419—31no—
164#418—31no—
165#405—91no—
166C24×C3—61no—
167C23×D3—21no—
168C2×C3×Q8—34no—
169C2×C3×Q8—32no—
170C2×C3×Q8—61no—
171C2×C3×Q8—62no—
172C2×C3×D4—34no—
173C2×C3×D4—32no—
174C2×C3×D4—61no—
175C2×C3×D4—62no—
176C22×C3×C4—21no—
177C22×C3×C4—61no—
178C22×C3×C4C22×D311yescharacteristic
179C22×C3×C4C22×D311yescharacteristic
180C22×Dic3—21no—
181C22×Dic3—64no—
182C2×D12—21no—
183C2×D12—22no—
184C2×D12C4×D314yes—
185C2×D12C22×D312yes—
186C2×C4×D3—64no—
187C2×Dic6—21no—
188C2×Dic6—22no—
189C2×Dic6C4×D314yescomplemented
190C2×Dic6C22×D312yes—
191C3×M16—24no—
192C3×M16—22no—
193C3×M16—22no—
194C2×C3×C8—22no—
195C2×C3×C8C22×D312yes—
196C2×C3×C8C22×D312yes—
197C3×C4⋊C4—32no—
198C3×C4⋊C4—32no—
199C3×C22⋊C4—61no—
200C3×C22⋊C4—61no—
201C3×C42—61no—
202C3×C42—61no—
203#217—21no—
204#217—21no—
205#217—32no—
206#217—32no—
207#217—62no—
208#217—64no—
209#215—38no—
210#215—38no—
211#214—38no—
212#214—38no—
213(C2×D3)⋊C4—64no—
214C4⋊Dic3—32no—
215C4⋊Dic3—32no—
216C4⋊Dic3—62no—
217C4⋊Dic3—64no—
218C4⋊Dic3C22×D312yes—
219C4⋊Dic3C22×D312yes—
220Dic3⋊C4—64no—
221C4×Dic3—21no—
222C4×Dic3—21no—
223C4×Dic3—32no—
224C4×Dic3—32no—
225C4×Dic3—62no—
226C4×Dic3—64no—
227C4×Dic3—64no—
228C2×C3⋊C8—34no—
229C2×C3⋊C8—34no—
230C2×C3⋊C8—31no—
231C2×C3⋊C8—31no—
232C2×C3⋊C8—31no—
233C2×C3⋊C8—31no—
234C2×C3⋊C8—61no—
235C2×C3⋊C8—61no—
236C2×C3⋊C8—64no—
237C22×C32—22no—
238C22×C32C4×D412yes—
239C22×C32C22×D411yescharacteristic
240C2×C3×D3—24no—
241C2×C3×D3—44no—
242C2×C3×D3—84no—
243C32×C4C4×D412yes—
244C32×C4C23×C411yescharacteristic
245C32×C4C2×#4111yescharacteristic
246C3⋊Dic3—24no—
247C3×Dic3—24no—
248C3×Dic3—42no—
249C3×Dic3—42no—
250C22×Q8—31no—
251C22×D4—31no—
252C2×SD16—98no—
253C2×SD16—92no—
254C2×SD16—92no—
255C2×M16D3211yescharacteristic
256C22×C8—91no—
257C4×Q8—94no—
258C4×Q8—182no—
259C4×D4—94no—
260C4×D4—182no—
261#117—31no—
262#117—31no—
263#117—91no—
264#117—182no—
265C2×C22⋊C4—182no—
266#107—92no—
267#106—92no—
268#103—34no—
269#102—34no—
270#97—92no—
271C4×C8—92no—
272C23×C3—21no—
273C23×C3—62no—
274C23×C3—64no—
275C23×C3—242no—
276C23×C3D3×D411yescharacteristic
277C23×C3D3×D411yescharacteristic
278C22×D3—22no—
279C22×D3—24no—
280C22×D3—82no—
281C3×Q8—34no—
282C3×Q8—64no—
283C3×Q8—62no—
284C3×D4—34no—
285C3×D4—64no—
286C3×D4—62no—
287C2×C3×C4—21no—
288C2×C3×C4—22no—
289C2×C3×C4—21no—
290C2×C3×C4—22no—
291C2×C3×C4—64no—
292C2×C3×C4—62no—
293C2×C3×C4—62no—
294C2×C3×C4—62no—
295C2×C3×C4C2×C4×D312yes—
296C2×C3×C4C2×C4×D312yes—
297C2×C3×C4D3×D411yescharacteristic
298C2×C3×C4D3×D411yescharacteristic
299C2×C3×C4#23712yes—
300C2×C3×C4#23712yes—
301C2×C3×C4C23×D311yescharacteristic
302C2×C3×C4C23×D311yescharacteristic
303C2×Dic3—24no—
304C2×Dic3—22no—
305C2×Dic3—22no—
306C2×Dic3—22no—
307C2×Dic3—34no—
308C2×Dic3—34no—
309C2×Dic3—64no—
310C2×Dic3—244no—
311D12—24no—
312D12—22no—
313D12C2×C4×D314yes—
314C4×D3—244no—
315Dic6—24no—
316Dic6—22no—
317Dic6C2×C4×D314yes—
318C3×C8—24no—
319C3×C8—22no—
320C3×C8—22no—
321C3⋊C8—32no—
322C3⋊C8—32no—
323C3⋊C8—32no—
324C3⋊C8—32no—
325C3⋊C8—62no—
326C3⋊C8—62no—
327C2×C32—22no—
328C2×C32C2×C4×D411yescharacteristic
329C2×C32#57712yes—
330C3×D3—44no—
331C24—61no—
332C2×Q8—32no—
333C2×Q8—34no—
334C2×Q8—61no—
335C2×Q8—62no—
336C2×D4—32no—
337C2×D4—34no—
338C2×D4—61no—
339C2×D4—62no—
340C22×C4—61no—
341C22×C4—184no—
342C22×C4C2×D3211yescharacteristic
343SD16—98no—
344SD16—98no—
345M16—22no—
346C2×C8—91no—
347C2×C8—91no—
348C2×C8—94no—
349C2×C8C2×D3212yes—
350C4⋊C4—32no—
351C4⋊C4—32no—
352C4⋊C4—92no—
353C4⋊C4—184no—
354C22⋊C4—61no—
355C22⋊C4—61no—
356C22⋊C4—92no—
357C22⋊C4—184no—
358C42—61no—
359C42—61no—
360C42—92no—
361C42—184no—
362C22×C3—22no—
363C22×C3—22no—
364C22×C3—21no—
365C22×C3—22no—
366C22×C3—42no—
367C22×C3—64no—
368C22×C3—124no—
369C22×C3—244no—
370C22×C3#67⋊C412yes—
371C22×C3#67⋊C412yes—
372C22×C3C2×D3×D411yescharacteristic
373C22×C3C2×D3×D411yescharacteristic
374C2×D3—24no—
375C2×D3—44no—
376C2×D3—84no—
377C3×C4—21no—
378C3×C4—21no—
379C3×C4—22no—
380C3×C4—64no—
381C3×C4—122no—
382C3×C4—122no—
383C3×C4#67⋊C412yes—
384C3×C4#67⋊C412yes—
385C3×C4C22×C4×D311yescharacteristic
386C3×C4C22×C4×D311yescharacteristic
387C3×C4C2×#23711yescharacteristic
388C3×C4C2×#23711yescharacteristic
389Dic3—24no—
390Dic3—42no—
391Dic3—42no—
392Dic3—64no—
393Dic3—64no—
394Dic3—124no—
395C32#294911yescharacteristic, complemented, Sylow
396C23—62no—
397C23—64no—
398C23—242no—
399C23#380211yescharacteristic
400Q8—34no—
401Q8—62no—
402Q8—64no—
403D4—34no—
404D4—62no—
405D4—64no—
406C2×C4—62no—
407C2×C4—64no—
408C2×C4—62no—
409C2×C4—62no—
410C2×C4—94no—
411C2×C4—724no—
412C2×C4C4×D3212yes—
413C2×C4#380211yescharacteristic
414C2×C4#380512yes—
415C2×C4C22×D3211yescharacteristic
416C8—22no—
417C8—92no—
418C8—92no—
419C2×C3—22no—
420C2×C3—22no—
421C2×C3—22no—
422C2×C3—21no—
423C2×C3—42no—
424C2×C3—124no—
425C2×C3C2×#67⋊C411yescharacteristic
426C2×C3C2×#67⋊C411yescharacteristic
427C2×C3#577512yes—
428C2×C3#577812yes—
429D3—44no—
430C22—22no—
431C22—64no—
432C22—124no—
433C22—244no—
434C22#6390212yes—
435C22C2×#380211yescharacteristic
436C4—64no—
437C4—122no—
438C4—122no—
439C4—184no—
440C4#6390212yes—
441C4C2×C4×D3211yescharacteristic
442C4C2×#380511yescharacteristic
443C3—21no—
444C3#7891611yescharacteristic, complemented
445C3#7894711yescharacteristic, complemented
446C2—22no—
447C2—124no—
448C2#1059471912yes—
449C2C2×#6390211yescharacteristic
subgroupG/H
centerC22C2×#3802
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
prime radicalC22×C3×D12C22
cosocleC2×C32×C4C24
hypercenterC2×M16D32
hypocenterC32#2949
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. #10594818C2semidirect
4. #10592821C2semidirect
6. C3×#5120C2semidirect
7. #10591138C2semidirect
8. #10590743C2semidirect
9. #10590742C2semidirect
23. #63843C22semidirect
25. C2×#3715C4semidirect
28. #63642C22semidirect
29. C8×C3⋊Dic3C22semidirect
31. C3×#816C22semidirect
32. #63576C22semidirect
33. #63574C22semidirect
46. #5120D3semidirect
62. C2×C3×Dic6C2×C4semidirect
70. C2×C3⋊(C3⋊C8)C2×C4semidirect
82. #3715C2×C4semidirect
83. #3715C2×C4semidirect
123. #816C2×D3semidirect
189. C2×Dic6C4×D3semidirect
395. C32#2949semidirect
444. C3#78916semidirect
445. C3#78947semidirect

Maximal subgroups

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

subgroupindex
#105949822
#105948182
C22×#37152
#105928212
C3×#51312
C3×#51202
#105911382
#105907432
#105907422
#789473
#789163