Finite Group Databasebeta

← #11859343

Subgroups — #11859343

Order 1152.

1173 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64116C211yesmaximal, characteristic, complemented
2#10595023C211yesmaximal, characteristic
3C22×D3×C3⋊C8C211yesmaximal, characteristic, complemented
4C3×#5126C211yesmaximal, characteristic, complemented
5C3×#5119C211yesmaximal, characteristic, complemented
6#10591073C211yesmaximal, characteristic, complemented
7#10591057C211yesmaximal, characteristic, complemented
8#10590907C214yesmaximal, complemented
9#10590906C214yesmaximal, complemented
10#79073—31nomaximal
11#78626—31nomaximal
12C2×#3828C2211yescharacteristic
13C22×C3×C4×D3C2211yescharacteristic
14C2×C32×M16C2211yescharacteristic
15C22×C3⋊(C3⋊C8)C2211yescharacteristic
16#64116—24no—
17C2×#3743C2212yescomplemented
18C2×C8×C3⋊D3C2212yescomplemented
19C3×#926C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22#63977C412yes—
23#63966C412yes—
24#63909C412yes—
25C4×#626C2214yes—
26#63857C412yes—
27C2×D3×C3⋊C8—24no—
28C2×D3×C3⋊C8C2212yes—
29C2×D3×C3⋊C8C2212yes—
30C3×(C2×D3)⋊C8C2214yes—
31C3×Dic3⋊C8C2214yescomplemented
32#63557C2214yescomplemented
33#63554C2212yescomplemented
34Dic3×C3⋊C8C2212yescomplemented
35#5791—31no—
36C23×C3⋊C8—31no—
37C2×#907—31no—
38C2×#907—31no—
39C2×#907—61no—
40C22×D3×C8—31no—
41#5524—31no—
42C3×#424—31no—
43C3×#407—31no—
44#5129—31no—
45#5126D311yescharacteristic, complemented
46#5122—31no—
47#5119D311yescharacteristic, complemented
48#5110—31no—
49#4997—31no—
50#4836—34no—
51#4834—34no—
52#4730—34no—
53#67⋊C8—34no—
54C23×C3×D3C2×C411yescharacteristic
55C22×C32×C4C2311yescharacteristic
56C2×#638C2×C412yes—
57#3828—22no—
58#3828—22no—
59C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
60C2×C4×C3⋊D3C2312yes—
61C2×#634C2×C411yescharacteristic
62C22×C3×Dic3C2×C411yescharacteristic
63C2×C3×C4×D3—22no—
64C2×C3×C4×D3—22no—
65C2×C3×C4×D3C2×C412yes—
66C2×C3×C4×D3C2312yes—
67C2×#626C2×C414yes—
68C32×M16—22no—
69C2×C32×C8C2312yes—
70C2×C3⋊(C3⋊C8)D414yescomplemented
71C2×C3⋊(C3⋊C8)C2311yescharacteristic
72C2×C3⋊(C3⋊C8)C2311yescharacteristic
73#3743—24no—
74C8×C3⋊D3—24no—
75C3×#217C2×C412yes—
76C3×C4⋊Dic3C2×C412yes—
77C3×C4×Dic3C2312yes—
78C3×#208—22no—
79C2×C3×C3⋊C8—22no—
80C2×C3×C3⋊C8C2312yes—
81C2×C3×C3⋊C8C2312yes—
82Dic3⋊Dic3C2×C414yes—
83#3722C2×C414yes—
84(C2×D3)⋊Dic3C2×C414yes—
85D3×C3⋊C8—24no—
86D3×C3⋊C8—24no—
87#2929—91noSylow
88C23×C3×C4—31no—
89C2×#235—31no—
90C2×#235—31no—
91C2×#235—61no—
92C22×C4×D3C2×D311yescharacteristic
93C2×C3×M16—21no—
94C2×C3×M16—31no—
95C2×C3×M16C2×D311yescharacteristic
96C2×C3×M16C2×D311yescharacteristic
97C22×C3×C8—31no—
98C3×#117—31no—
99#953—32no—
100#930—32no—
101#929—32no—
102C4×#67—34no—
103#926C2×D311yescharacteristic
104#924—32no—
105C2×#208C2×D311yescharacteristic
106C22×C3⋊C8—31no—
107C22×C3⋊C8—31no—
108C22×C3⋊C8—32no—
109C22×C3⋊C8—32no—
110C22×C3⋊C8—61no—
111C22×C3⋊C8—64no—
112C22×C3⋊C8C2×D311yescharacteristic
113#907—64no—
114#907—64no—
115#907—68no—
116C2×ΓL(1,𝔽25)—32no—
117C2×ΓL(1,𝔽25)—32no—
118C2×ΓL(1,𝔽25)—62no—
119C2×D3×C8—32no—
120C2×D3×C8—32no—
121C2×D3×C8—32no—
122C2×D3×C8—32no—
123C2×D3×C8—62no—
124C2×D3×C8—64no—
125#897—32no—
126#895—32no—
127#886—32no—
128#882—32no—
129C4×D12—34no—
130C3×C4⋊C8—34no—
131C3×C22⋊C8—34no—
132(C2×D3)⋊C8—34no—
133(C2×D3)⋊C8—34no—
134(C2×D3)⋊C8C2×D314yes—
135#815—32no—
136Dic3⋊C8C2×D314yescomplemented
137C8×Dic3—32no—
138#803—32no—
139C4×C3⋊C8—32no—
140C23×C32C22×C411yescharacteristic
141C22×C3⋊D3C22×C412yes—
142C22×C3×D3—22no—
143C22×C3×D3—24no—
144C22×C3×D3C22×C412yes—
145C2×C32×C4C22×C411yescharacteristic
146C2×C32×C4C2×D412yes—
147C2×C32×C4#4112yes—
148C2×C32×C4C2411yescharacteristic
149#638—24no—
150C2×C3⋊Dic3C22×C412yes—
151C4⋊(C3⋊D3)—22no—
152C4×C3⋊D3—22no—
153C4×C3⋊D3—22no—
154#634—22no—
155C2×C3×Dic3—22no—
156C2×C3×Dic3C22×C414yes—
157C2×C3×Dic3C22×C412yes—
158C3×C4×D3—24no—
159C3×C4×D3—22no—
160C3×C4×D3—22no—
161#626—28no—
162C32×C8—22no—
163C3⋊(C3⋊C8)C2×D412yes—
164C3⋊(C3⋊C8)C2×D412yes—
165C3×C3⋊C8—22no—
166C3×C3⋊C8—22no—
167C2×#131—91no—
168C23×C8—91no—
169#525—91no—
170#435—94no—
171C8×D4—94no—
172#424—31no—
173#408—91no—
174#407—31no—
175#405—91no—
176C24×C3—31no—
177C23×D3C4×D311yescharacteristic
178C22×C3×C4—21no—
179C22×C3×C4—31no—
180C22×C3×C4—32no—
181C22×C3×C4—32no—
182C22×C3×C4—62no—
183C22×C3×C4—62no—
184C22×C3×C4C22×D311yescharacteristic
185C22×C3×C4C22×D311yescharacteristic
186C2×#67—32no—
187C2×#67—32no—
188C2×#67—34no—
189C2×#67—62no—
190C22×Dic3C4×D311yescharacteristic
191#235—64no—
192#235—64no—
193#235—62no—
194#235—62no—
195#235—62no—
196#235—62no—
197C2×D12—34no—
198C2×D12—31no—
199C2×D12—31no—
200C2×D12—61no—
201C2×C4×D3—22no—
202C2×C4×D3—22no—
203C2×C4×D3—32no—
204C2×C4×D3—32no—
205C2×C4×D3—62no—
206C2×C4×D3C4×D312yes—
207C2×C4×D3C22×D312yes—
208C2×Dic6—31no—
209C2×Dic6—31no—
210C2×Dic6—61no—
211C3×M16—24no—
212C3×M16—22no—
213C3×M16—22no—
214C3×M16—62no—
215C2×C3×C8—22no—
216C2×C3×C8—32no—
217C2×C3×C8—32no—
218C2×C3×C8—62no—
219C2×C3×C8C22×D312yes—
220C2×C3×C8C22×D312yes—
221C3×C4⋊C4—32no—
222C3×C22⋊C4—32no—
223C3×C42—32no—
224#217—34no—
225#217C4×D312yes—
226(C2×D3)⋊C4—34no—
227(C2×D3)⋊C4—34no—
228(C2×D3)⋊C4—34no—
229C4⋊Dic3—34no—
230C4⋊Dic3C4×D312yes—
231Dic3⋊C4—34no—
232C4×Dic3C22×D312yes—
233#208—22no—
234C2×C3⋊C8—22no—
235C2×C3⋊C8—34no—
236C2×C3⋊C8—34no—
237C2×C3⋊C8—31no—
238C2×C3⋊C8—31no—
239C2×C3⋊C8—31no—
240C2×C3⋊C8—31no—
241C2×C3⋊C8—61no—
242C2×C3⋊C8—61no—
243C2×C3⋊C8—64no—
244C2×C3⋊C8—64no—
245C2×C3⋊C8—64no—
246C2×C3⋊C8C22×D312yes—
247C2×C3⋊C8C22×D312yes—
248ΓL(1,𝔽25)—64no—
249ΓL(1,𝔽25)—64no—
250ΓL(1,𝔽25)—68no—
251D3×C8—64no—
252D3×C8—64no—
253D3×C8—64no—
254D3×C8—64no—
255D3×C8—68no—
256C22×C32—22no—
257C22×C32C4×D412yes—
258C22×C32C23×C411yescharacteristic
259C2×C3⋊D3—22no—
260C2×C3⋊D3—24no—
261C2×C3×D3—28no—
262C2×C3×D3—22no—
263C2×C3×D3—22no—
264C2×C3×D3#13114yescomplemented
265C32×C4C4×D412yes—
266C32×C4C22×D411yescharacteristic
267C32×C4C2×#4111yescharacteristic
268C3⋊Dic3—22no—
269C3×Dic3—22no—
270C3×Dic3—24no—
271C2×#41—91no—
272C23×C4—31no—
273#131—184no—
274C2×M16—31no—
275C2×M16—92no—
276C2×M16D3211yescharacteristic
277C22×C8—31no—
278C22×C8—92no—
279C22×C8—92no—
280C22×C8—91no—
281C22×C8—92no—
282C22×C8—184no—
283#123—92no—
284C22⋊Q8—92no—
285#121—92no—
286#120—92no—
287C4×D4—94no—
288#117—31no—
289C4⋊C8—34no—
290C22⋊C8—34no—
291C22⋊C8—94no—
292#97—92no—
293C4×C8—92no—
294C23×C3—21no—
295C23×C3—32no—
296C23×C3—64no—
297C23×C3—62no—
298C23×C3C2×C4×D311yescharacteristic
299C23×C3C2×C4×D311yescharacteristic
300C22×D3—22no—
301C22×D3—24no—
302C22×D3—32no—
303C22×D3—32no—
304C22×D3—62no—
305C22×D3C2×C4×D312yes—
306C2×C3×C4—21no—
307C2×C3×C4—22no—
308C2×C3×C4—21no—
309C2×C3×C4—22no—
310C2×C3×C4—32no—
311C2×C3×C4—34no—
312C2×C3×C4—62no—
313C2×C3×C4—64no—
314C2×C3×C4—62no—
315C2×C3×C4—62no—
316C2×C3×C4C2×C4×D311yescharacteristic
317C2×C3×C4C2×C4×D311yescharacteristic
318C2×C3×C4D3×D412yes—
319C2×C3×C4D3×D412yes—
320C2×C3×C4#23712yes—
321C2×C3×C4#23912yes—
322C2×C3×C4C23×D311yescharacteristic
323C2×C3×C4C23×D311yescharacteristic
324#67—68no—
325#67—68no—
326#67—64no—
327#67—64no—
328C2×Dic3—22no—
329C2×Dic3—32no—
330C2×Dic3—32no—
331C2×Dic3—62no—
332C2×Dic3C2×C4×D314yes—
333C2×Dic3C2×C4×D312yes—
334D12—64no—
335D12—68no—
336D12—62no—
337D12—62no—
338C4×D3—24no—
339C4×D3—22no—
340C4×D3—22no—
341C4×D3—64no—
342C4×D3—64no—
343C4×D3—62no—
344C4×D3—62no—
345C4×D3—62no—
346C4×D3—62no—
347Dic6—64no—
348Dic6—62no—
349Dic6—62no—
350C3×C8—24no—
351C3×C8—22no—
352C3×C8—22no—
353C3×C8—62no—
354C3×C8—62no—
355C3⋊C8—22no—
356C3⋊C8—22no—
357C3⋊C8—32no—
358C3⋊C8—32no—
359C3⋊C8—32no—
360C3⋊C8—32no—
361C3⋊C8—62no—
362C3⋊C8—62no—
363C2×C32—22no—
364C2×C32C2×C4×D411yescharacteristic
365C2×C32C2×#13112yes—
366C3⋊D3—42no—
367C3×D3—24no—
368C24—31no—
369#41—182no—
370#41—182no—
371C2×Q8—91no—
372C2×D4—94no—
373C2×D4—92no—
374C2×D4—91no—
375C22×C4—31no—
376C22×C4—32no—
377C22×C4—32no—
378C22×C4—62no—
379C22×C4—62no—
380C22×C4—92no—
381C22×C4C2×D3211yescharacteristic
382M16—22no—
383M16—62no—
384M16—184no—
385C2×C8—32no—
386C2×C8—32no—
387C2×C8—62no—
388C2×C8—91no—
389C2×C8—91no—
390C2×C8—94no—
391C2×C8—184no—
392C2×C8—184no—
393C2×C8—184no—
394C2×C8C2×D3212yes—
395C4⋊C4—32no—
396C4⋊C4—94no—
397C22⋊C4—32no—
398C22⋊C4—94no—
399C22⋊C4—94no—
400C42—32no—
401C22×C3—22no—
402C22×C3—22no—
403C22×C3—21no—
404C22×C3—22no—
405C22×C3—34no—
406C22×C3—42no—
407C22×C3—68no—
408C22×C3—62no—
409C22×C3—62no—
410C22×C3#67⋊C412yes—
411C22×C3#89312yes—
412C22×C3C22×C4×D311yescharacteristic
413C22×C3C22×C4×D311yescharacteristic
414C2×D3—28no—
415C2×D3—22no—
416C2×D3—22no—
417C2×D3—64no—
418C2×D3—62no—
419C2×D3—64no—
420C2×D3—64no—
421C2×D3—62no—
422C2×D3—124no—
423C2×D3#90714yescomplemented
424C3×C4—21no—
425C3×C4—21no—
426C3×C4—22no—
427C3×C4—64no—
428C3×C4—62no—
429C3×C4#67⋊C412yes—
430C3×C4#89312yes—
431C3×C4C2×D3×D411yescharacteristic
432C3×C4C2×D3×D411yescharacteristic
433C3×C4C2×#23711yescharacteristic
434C3×C4C2×#23911yescharacteristic
435Dic3—22no—
436Dic3—24no—
437Dic3—64no—
438Dic3—62no—
439Dic3—62no—
440C32#292911yescharacteristic, complemented, Sylow
441C23—32no—
442C23—64no—
443C23—62no—
444C23—92no—
445C23C4×D3211yescharacteristic
446Q8—182no—
447D4—188no—
448D4—184no—
449D4—182no—
450C2×C4—34no—
451C2×C4—32no—
452C2×C4—62no—
453C2×C4—62no—
454C2×C4—62no—
455C2×C4—64no—
456C2×C4—92no—
457C2×C4—182no—
458C2×C4—182no—
459C2×C4#379612yes—
460C2×C4C4×D3211yescharacteristic
461C2×C4#381112yes—
462C2×C4C22×D3211yescharacteristic
463C8—22no—
464C8—62no—
465C8—62no—
466C8—92no—
467C8—92no—
468C2×C3—22no—
469C2×C3—22no—
470C2×C3—21no—
471C2×C3—22no—
472C2×C3—42no—
473C2×C3—64no—
474C2×C3C2×#67⋊C411yescharacteristic
475C2×C3C2×#89311yescharacteristic
476C2×C3C2×#90712yes—
477C2×C3D3×#13112yes—
478D3—24no—
479D3—124no—
480D3—122no—
481D3—122no—
482C22—22no—
483C22—34no—
484C22—68no—
485C22—62no—
486C22—62no—
487C22—182no—
488C22—184no—
489C22#6388112yes—
490C22C2×C4×D3211yescharacteristic
491C4—62no—
492C4—64no—
493C4—182no—
494C4#6388112yes—
495C4C2×#379611yescharacteristic
496C4C2×#381111yescharacteristic
497C3—21no—
498C3#7862611yescharacteristic, complemented
499C3#7907311yescharacteristic, complemented
500C2—22no—
501C2—64no—
502C2—362no—
503C2D3×#90712yes—
504C2C2×#6388111yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC2×C32×M16C22
prime radical#10595023C2
cosocleC2×C32×C4C24
hypercenterC2×M16D32
hypocenterC32#2929
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C2×#64116C2semidirect
3. C22×D3×C3⋊C8C2semidirect
4. C3×#5126C2semidirect
5. C3×#5119C2semidirect
6. #10591073C2semidirect
7. #10591057C2semidirect
8. #10590907C2semidirect
9. #10590906C2semidirect
17. C2×#3743C22semidirect
18. C2×C8×C3⋊D3C22semidirect
31. C3×Dic3⋊C8C22semidirect
32. #63557C22semidirect
33. #63554C22semidirect
34. Dic3×C3⋊C8C22semidirect
45. #5126D3semidirect
47. #5119D3semidirect
70. C2×C3⋊(C3⋊C8)D4semidirect
136. Dic3⋊C8C2×D3semidirect
264. C2×C3×D3#131semidirect
423. C2×D3#907semidirect
440. C32#2929semidirect
498. C3#78626semidirect
499. C3#79073semidirect

Maximal subgroups

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

subgroupindex
C2×#641162
#105950232
C22×D3×C3⋊C82
C3×#51262
C3×#51192
#105910732
#105910572
#105909072
#105909062
#790733
#786263