Finite Group Databasebeta

← #11859357

Subgroups — #11859357

Order 1152.

1097 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D3×C8C211yesmaximal, characteristic, complemented
2#10595022C211yesmaximal, characteristic
3C2×#63814C211yesmaximal, characteristic, complemented
4#10592801C211yesmaximal, characteristic, complemented
5C3×#5110C211yesmaximal, characteristic, complemented
6#10591069C211yesmaximal, characteristic, complemented
7#10591059C211yesmaximal, characteristic, complemented
8#10590723C214yesmaximal, complemented
9#10590717C214yesmaximal, complemented
10#83734—31nomaximal
11#78655—31nomaximal
12C2×C3×#235C2211yescharacteristic
13C22×C3×C4×D3C2211yescharacteristic
14C22×C32×C8C2211yescharacteristic
15#64135C2211yescharacteristic
16C2×#3748C2211yescharacteristic
17C2×C3×#208C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C2×C3×D3×C8—24no—
20C2×C3×D3×C8C2212yes—
21C2×C3×D3×C8C2212yes—
22#63976C412yes—
23#63961C412yes—
24#63908C412yes—
25C4×#625C2214yes—
26#63856C412yes—
27C2×#3711C2212yescomplemented
28#63814—24no—
29C2×D3×C3⋊C8C2212yescomplemented
30#63641C2214yescomplemented
31C3×(C2×D3)⋊C8C2214yescomplemented
32(C2×D3)⋊(C3⋊C8)C2214yes—
33#63555C2212yescomplemented
34#63553C2212yescomplemented
35C23×C3×C8—31no—
36#5828—31no—
37C2×#948—31no—
38#5791—31no—
39C2×#901—31no—
40C22×D3×C8D311yescharacteristic, complemented
41C3×#408—31no—
42#5207—31no—
43#5126—31no—
44#5122—31no—
45#5111—34no—
46#5110D311yescharacteristic, complemented
47C8×#67—34no—
48#5102—31no—
49#5102—31no—
50#5102—61no—
51#5101—31no—
52#4728—34no—
53#67⋊C8—34no—
54C23×C3×D3C2×C411yescharacteristic
55C22×C32×C4C2311yescharacteristic
56C2×C3×#67C2×C412yes—
57C22×C3×Dic3C2×C411yescharacteristic
58C3×#235—22no—
59C3×#235—22no—
60C2×C3×D12C2×C411yescharacteristic
61C2×C3×C4×D3—22no—
62C2×C3×C4×D3—22no—
63C2×C3×C4×D3C2×C412yes—
64C2×C3×C4×D3C2312yes—
65C2×C3×C4×D3C2312yes—
66C2×C3×Dic6C2×C411yescharacteristic
67C2×#625C2×C414yes—
68C2×C32×C8—22no—
69C2×C32×C8C2312yes—
70#3757C2×C412yes—
71C4⋊(C3⋊Dic3)C2×C412yes—
72C4×C3⋊Dic3C2312yes—
73#3748—22no—
74C2×C3⋊(C3⋊C8)C2312yes—
75C3×#208—22no—
76C2×C3×C3⋊C8D414yescomplemented
77C2×C3×C3⋊C8C2312yes—
78C2×C3×C3⋊C8C2311yescharacteristic
79C2×C3×C3⋊C8C2311yescharacteristic
80C3×D3×C8—24no—
81C3×D3×C8—24no—
82#3724C2×C414yes—
83(C2×D3)⋊Dic3C2×C414yes—
84(C2×D3)⋊Dic3C2×C414yes—
85#3711—24no—
86D3×C3⋊C8—24no—
87#2929—91noSylow
88C2×C3×#41—31no—
89C23×C3×C4—31no—
90C2×#235C2×D311yescharacteristic
91C22×C4×D3C2×D311yescharacteristic
92C2×C3×M16—31no—
93C22×C3×C8—21no—
94C22×C3×C8—31no—
95C22×C3×C8—32no—
96C22×C3×C8—32no—
97C22×C3×C8—64no—
98C22×C3×C8C2×D311yescharacteristic
99C22×C3×C8C2×D311yescharacteristic
100#953—32no—
101#948—64no—
102#946—32no—
103#938—32no—
104#937—32no—
105#935—32no—
106#930—32no—
107#929—32no—
108C4×#67—34no—
109C4×#67—34no—
110#926—31no—
111#926—31no—
112#926—61no—
113#924—32no—
114C2×#208—31no—
115C2×#208—31no—
116C2×#208—32no—
117C2×#208—61no—
118C2×#208C2×D311yescharacteristic
119C22×C3⋊C8—32no—
120C22×C3⋊C8C2×D311yescharacteristic
121#901—64no—
122C2×ΓL(1,𝔽25)—32no—
123C2×D3×C8—24no—
124C2×D3×C8—32no—
125C2×D3×C8C2×D312yes—
126C2×D3×C8C2×D312yes—
127C3×C22⋊C8—34no—
128#830—34no—
129(C2×D3)⋊C8—34no—
130(C2×D3)⋊C8C2×D314yescomplemented
131#815—32no—
132#815—32no—
133Dic3⋊C8—34no—
134Dic3⋊C8—34no—
135Dic3⋊C8—64no—
136C8×Dic3—32no—
137C8×Dic3—32no—
138C23×C32C22×C411yescharacteristic
139C22×C3×D3—22no—
140C22×C3×D3—24no—
141C22×C3×D3C22×C412yes—
142C22×C3×D3C22×C412yes—
143C2×C32×C4C22×C411yescharacteristic
144C2×C32×C4C2×D412yes—
145C2×C32×C4#4112yes—
146C2×C32×C4C2411yescharacteristic
147C2×C3⋊Dic3C22×C414yes—
148C3×#67—24no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3C22×C412yes—
151C2×C3×Dic3C22×C412yes—
152C3×D12—22no—
153C3×C4×D3—24no—
154C3×C4×D3—22no—
155C3×C4×D3—22no—
156C3×C4×D3—22no—
157C3×C4×D3—22no—
158C3×Dic6—22no—
159#625—28no—
160C32×C8—22no—
161C3⋊(C3⋊C8)—22no—
162C3×C3⋊C8—22no—
163C3×C3⋊C8C2×D412yes—
164C3×C3⋊C8C2×D412yes—
165C2×#131—91no—
166C23×C8—31no—
167#525—91no—
168#435—94no—
169C8×D4—94no—
170#424—91no—
171#408—31no—
172#407—91no—
173#405—91no—
174C24×C3—31no—
175C23×D3C4×D311yescharacteristic
176C3×#41—62no—
177C3×#41—62no—
178C2×C3×Q8—31no—
179C2×C3×D4—32no—
180C2×C3×D4—31no—
181C22×C3×C4—21no—
182C22×C3×C4—31no—
183C22×C3×C4—32no—
184C22×C3×C4—32no—
185C22×C3×C4—32no—
186C22×C3×C4—62no—
187C22×C3×C4—62no—
188C22×C3×C4C22×D311yescharacteristic
189C22×C3×C4C22×D311yescharacteristic
190C2×#67—34no—
191C2×#67—34no—
192C2×#67C4×D312yes—
193C22×Dic3C4×D311yescharacteristic
194#235—22no—
195#235—22no—
196C2×D12C4×D311yescharacteristic
197C2×C4×D3—22no—
198C2×C4×D3—22no—
199C2×C4×D3C4×D312yes—
200C2×C4×D3C22×D312yes—
201C2×C4×D3C22×D312yes—
202C2×Dic6C4×D311yescharacteristic
203C3×M16—62no—
204C2×C3×C8—22no—
205C2×C3×C8—22no—
206C2×C3×C8—22no—
207C2×C3×C8—34no—
208C2×C3×C8—31no—
209C2×C3×C8—31no—
210C2×C3×C8—32no—
211C2×C3×C8—42no—
212C2×C3×C8—64no—
213C2×C3×C8—64no—
214C2×C3×C8C22×D312yes—
215C2×C3×C8C22×D312yes—
216#217—32no—
217#217—32no—
218#217—34no—
219#217—34no—
220#217—62no—
221(C2×D3)⋊C4—34no—
222(C2×D3)⋊C4—34no—
223C4⋊Dic3—32no—
224C4⋊Dic3—32no—
225C4⋊Dic3—62no—
226Dic3⋊C4—34no—
227Dic3⋊C4—34no—
228C4×Dic3—32no—
229C4×Dic3—32no—
230C4×Dic3—62no—
231#208—22no—
232#208—62no—
233#208—62no—
234#208—64no—
235#208—122no—
236C2×C3⋊C8—32no—
237C2×C3⋊C8—32no—
238C2×C3⋊C8—62no—
239C2×C3⋊C8—64no—
240C2×C3⋊C8#6714yescomplemented
241C2×C3⋊C8C22×D312yes—
242C2×C3⋊C8C22×D311yescharacteristic
243C2×C3⋊C8C22×D311yescharacteristic
244ΓL(1,𝔽25)—64no—
245D3×C8—24no—
246D3×C8—24no—
247D3×C8—64no—
248C22×C32—22no—
249C22×C32C4×D412yes—
250C22×C32C23×C411yescharacteristic
251C2×C3×D3—28no—
252C2×C3×D3—22no—
253C2×C3×D3—22no—
254C2×C3×D3—22no—
255C2×C3×D3—24no—
256C2×C3×D3#13114yescomplemented
257C32×C4C4×D412yes—
258C32×C4C22×D411yescharacteristic
259C32×C4C2×#4111yescharacteristic
260C3⋊Dic3—24no—
261C3×Dic3—22no—
262C3×Dic3—22no—
263C2×#41—31no—
264C23×C4—31no—
265#131—184no—
266C2×M16—31no—
267C2×M16—92no—
268C2×M16—91no—
269C22×C8—31no—
270C22×C8—32no—
271C22×C8—32no—
272C22×C8—64no—
273C22×C8—92no—
274C22×C8D3211yescharacteristic
275#123—92no—
276C22⋊Q8—92no—
277#121—92no—
278#120—92no—
279C4×D4—94no—
280#117—91no—
281C4⋊C8—94no—
282C22⋊C8—34no—
283C22⋊C8—94no—
284#97—92no—
285C4×C8—92no—
286C23×C3—21no—
287C23×C3—32no—
288C23×C3—32no—
289C23×C3—64no—
290C23×C3—62no—
291C23×C3C2×C4×D311yescharacteristic
292C23×C3C2×C4×D311yescharacteristic
293C22×D3—22no—
294C22×D3—24no—
295C22×D3C2×C4×D312yes—
296C22×D3C2×C4×D312yes—
297C3×Q8—62no—
298C3×D4—64no—
299C3×D4—62no—
300C2×C3×C4—21no—
301C2×C3×C4—22no—
302C2×C3×C4—21no—
303C2×C3×C4—22no—
304C2×C3×C4—32no—
305C2×C3×C4—32no—
306C2×C3×C4—62no—
307C2×C3×C4—64no—
308C2×C3×C4—62no—
309C2×C3×C4—62no—
310C2×C3×C4—62no—
311C2×C3×C4—62no—
312C2×C3×C4C2×C4×D311yescharacteristic
313C2×C3×C4C2×C4×D311yescharacteristic
314C2×C3×C4#23512yes—
315C2×C3×C4D3×D412yes—
316C2×C3×C4#23712yes—
317C2×C3×C4C2×#6712yes—
318C2×C3×C4C23×D311yescharacteristic
319C2×C3×C4C23×D311yescharacteristic
320#67—24no—
321#67—68no—
322#67—68no—
323C2×Dic3—22no—
324C2×Dic3—34no—
325C2×Dic3—34no—
326C2×Dic3—64no—
327C2×Dic3C2×C4×D312yes—
328C2×Dic3C2×C4×D312yes—
329D12—22no—
330C4×D3—24no—
331C4×D3—22no—
332C4×D3—22no—
333C4×D3—22no—
334C4×D3—22no—
335Dic6—22no—
336C3×C8—22no—
337C3×C8—22no—
338C3×C8—32no—
339C3×C8—32no—
340C3×C8—42no—
341C3×C8—62no—
342C3⋊C8—22no—
343C3⋊C8—62no—
344C3⋊C8—62no—
345C3⋊C8—122no—
346C3⋊C8C2×#6712yes—
347C3⋊C8C2×#6712yes—
348C2×C32—22no—
349C2×C32C2×C4×D411yescharacteristic
350C2×C32C2×#13112yes—
351C3×D3—24no—
352C3×D3—42no—
353C24—31no—
354#41—62no—
355#41—62no—
356C2×Q8—31no—
357C2×D4—32no—
358C2×D4—31no—
359C2×D4—94no—
360C22×C4—31no—
361C22×C4—32no—
362C22×C4—32no—
363C22×C4—32no—
364C22×C4—62no—
365C22×C4—62no—
366C22×C4C2×D3211yescharacteristic
367M16—62no—
368M16—184no—
369M16—182no—
370C2×C8—22no—
371C2×C8—31no—
372C2×C8—31no—
373C2×C8—34no—
374C2×C8—32no—
375C2×C8—64no—
376C2×C8—64no—
377C2×C8—92no—
378C2×C8—184no—
379C2×C8C2×D3212yes—
380C4⋊C4—94no—
381C4⋊C4—92no—
382C22⋊C4—94no—
383C22⋊C4—94no—
384C22⋊C4—92no—
385C42—92no—
386C22×C3—22no—
387C22×C3—22no—
388C22×C3—21no—
389C22×C3—22no—
390C22×C3—34no—
391C22×C3—42no—
392C22×C3—68no—
393C22×C3—62no—
394C22×C3—62no—
395C22×C3—64no—
396C22×C3—62no—
397C22×C3#67⋊C412yes—
398C22×C3C4×#6712yes—
399C22×C3C22×C4×D311yescharacteristic
400C22×C3C22×C4×D311yescharacteristic
401C2×D3—28no—
402C2×D3—22no—
403C2×D3—22no—
404C2×D3—22no—
405C2×D3—24no—
406C2×D3#90114yescomplemented
407C3×C4—21no—
408C3×C4—21no—
409C3×C4—22no—
410C3×C4—62no—
411C3×C4—62no—
412C3×C4#67⋊C412yes—
413C3×C4C4×#6712yes—
414C3×C4C2×#23511yescharacteristic
415C3×C4C2×D3×D411yescharacteristic
416C3×C4C2×#23711yescharacteristic
417C3×C4C22×#6711yescharacteristic
418Dic3—22no—
419Dic3—22no—
420Dic3—64no—
421Dic3—64no—
422Dic3—124no—
423C32#292911yescharacteristic, complemented, Sylow
424C23—32no—
425C23—32no—
426C23—64no—
427C23—62no—
428C23C4×D3211yescharacteristic
429Q8—62no—
430D4—64no—
431D4—62no—
432D4—188no—
433C2×C4—32no—
434C2×C4—32no—
435C2×C4—62no—
436C2×C4—62no—
437C2×C4—62no—
438C2×C4—62no—
439C2×C4—62no—
440C2×C4—64no—
441C2×C4—94no—
442C2×C4#379512yes—
443C2×C4C4×D3211yescharacteristic
444C2×C4D3×#6712yes—
445C2×C4C22×D3211yescharacteristic
446C8—22no—
447C8—32no—
448C8—32no—
449C8—62no—
450C8—182no—
451C2×C3—22no—
452C2×C3—22no—
453C2×C3—21no—
454C2×C3—22no—
455C2×C3—42no—
456C2×C3—64no—
457C2×C3—122no—
458C2×C3C2×#67⋊C411yescharacteristic
459C2×C3C2×#90112yes—
460C2×C3D3×#13112yes—
461C2×C3C2×C4×#6711yescharacteristic
462D3—24no—
463D3—42no—
464C22—22no—
465C22—34no—
466C22—68no—
467C22—62no—
468C22—62no—
469C22—62no—
470C22—64no—
471C22#6387912yes—
472C22C2×C4×D3211yescharacteristic
473C4—62no—
474C4—62no—
475C4—184no—
476C4#6387912yes—
477C4C2×#379511yescharacteristic
478C4C2×D3×#6711yescharacteristic
479C3—21no—
480C3#7865511yescharacteristic, complemented
481C3#8373411yescharacteristic, complemented
482C2—22no—
483C2—64no—
484C2—122no—
485C2D3×#90112yes—
486C2C2×#6387911yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC22×C32×C8C22
prime radical#10595022C2
cosocleC2×C32×C4C24
hypercenterC22×C8D32
hypocenterC32#2929
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C22×C3×D3×C8C2semidirect
3. C2×#63814C2semidirect
4. #10592801C2semidirect
5. C3×#5110C2semidirect
6. #10591069C2semidirect
7. #10591059C2semidirect
8. #10590723C2semidirect
9. #10590717C2semidirect
27. C2×#3711C22semidirect
29. C2×D3×C3⋊C8C22semidirect
30. #63641C22semidirect
31. C3×(C2×D3)⋊C8C22semidirect
33. #63555C22semidirect
34. #63553C22semidirect
40. C22×D3×C8D3semidirect
46. #5110D3semidirect
76. C2×C3×C3⋊C8D4semidirect
130. (C2×D3)⋊C8C2×D3semidirect
240. C2×C3⋊C8#67semidirect
256. C2×C3×D3#131semidirect
406. C2×D3#901semidirect
423. C32#2929semidirect
480. C3#78655semidirect
481. C3#83734semidirect

Maximal subgroups

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

subgroupindex
C22×C3×D3×C82
#105950222
C2×#638142
#105928012
C3×#51102
#105910692
#105910592
#105907232
#105907172
#837343
#786553