Finite Group Databasebeta

← #11788691

Subgroups — #11788691

Order 1152.

673 conjugacy classes of subgroups.

The subgroup lattice has 509 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#909C211yesmaximal, characteristic
2C2×#63814C211yesmaximal, characteristic
3C2×#63566C211yesmaximal, characteristic, complemented
4#10591088C211yesmaximal, characteristic
5C2×#63560C211yesmaximal, characteristic, complemented
6#10589420C211yesmaximal, characteristic, complemented
7C3×#4558C211yesmaximal, characteristic, complemented
8#72103—31nomaximal
9#68949—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C3×#909—22no—
18C3×#909C414yescomplemented
19C2×C3×Dic12—21no—
20C2×C3×#204—21no—
21C2×#3711—21no—
22#63814—22no—
23#63814—22no—
24C2×D3×C3⋊C8—21no—
25#63566—21no—
26#63566—21no—
27#63566—21no—
28#63563—21no—
29#63560—22no—
30C2×C3×#137—31no—
31C2×#948—31no—
32C2×#909D311yescharacteristic
33C2×#901—31no—
34#5232—31no—
35C2×#836—31no—
36C2×#835—31no—
37C2×#824—31no—
38#5133—31no—
39C2×#816—31no—
40C3×#341—31no—
41#4558D311yescharacteristic, complemented
42#4554—31no—
43#4554—31no—
44#4554—61no—
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3—21no—
47C2×C3×#67—21no—
48C22×C3×Dic3—21no—
49C3×#235—21no—
50C3×#235—21no—
51C3×#235C2×C412yes—
52C3×#235D412yes—
53C2×C3×D12D411yescharacteristic
54C2×C3×C4×D3—21no—
55C2×C3×Dic6—21no—
56C2×C3×Dic6—21no—
57C2×C3×Dic6—21no—
58C2×C3×Dic6—21no—
59C2×C3×Dic6—21no—
60C2×C3×Dic6C2×C412yes—
61C2×C3×Dic6D411yescharacteristic
62C32×M16—21no—
63C32×M16C2×C412yes—
64C2×C32×C8—21no—
65C4⋊(C3⋊Dic3)—21no—
66C4⋊(C3⋊Dic3)—21no—
67#3748—21no—
68#3748D412yes—
69C2×C3⋊(C3⋊C8)—21no—
70C3×#208—21no—
71C3×#208—21no—
72C2×C3×C3⋊C8—21no—
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8D411yescharacteristic
76C2×C3×C3⋊C8D411yescharacteristic
77C3×Dic12—24no—
78C3×#204—24no—
79#3711—24no—
80D3×C3⋊C8—24no—
81#1908—91noSylow
82C2×C3×#41—31no—
83C22×C3×Q8—31no—
84C2×#235C2×D311yescharacteristic
85C22×Dic6C2×D311yescharacteristic
86C3×#137—34no—
87C3×#137—62no—
88C2×C3×Q16—61no—
89C2×C3×SD16—61no—
90C2×C3×M16—21no—
91C2×C3×M16—31no—
92C2×C3×M16C2×D311yescharacteristic
93C2×C3×M16C2×D311yescharacteristic
94C22×C3×C8—31no—
95#948—62no—
96#948—62no—
97C2×C4⋊Dic3—31no—
98C2×C4⋊Dic3—31no—
99C2×C4⋊Dic3—61no—
100C2×#208—31no—
101C2×#208—31no—
102C2×#208—61no—
103C2×#208—61no—
104C2×#208C2×D311yescharacteristic
105C22×C3⋊C8—61no—
106C22×C3⋊C8C2×D311yescharacteristic
107#909—22no—
108#909Dic314yescomplemented
109C2×Dic12—21no—
110C2×#204—21no—
111#901—62no—
112#901—62no—
113C2×ΓL(1,𝔽25)—61no—
114C2×D3×C8—61no—
115#836—62no—
116#835—61no—
117#835—61no—
118#835—61no—
119#832—61no—
120#824—62no—
121#821—61no—
122#816—61no—
123#816—61no—
124#816—61no—
125C23×C32#4111yescharacteristic
126C22×C3×D3—21no—
127C2×C32×C4C22×C411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4#4111yescharacteristic
133C2×C3⋊Dic3—41no—
134C2×C3⋊Dic3—81no—
135C3×#67—22no—
136C3×#67—22no—
137C2×C3×Dic3—21no—
138C2×C3×Dic3—22no—
139C2×C3×Dic3—41no—
140C2×C3×Dic3—41no—
141C3×D12—21no—
142C3×D12C22⋊C412yes—
143C3×C4×D3—22no—
144C3×C4×D3—22no—
145C3×Dic6—21no—
146C3×Dic6—22no—
147C3×Dic6—22no—
148C3×Dic6—41no—
149C3×Dic6—41no—
150C3×Dic6C22⋊C412yes—
151C32×C8—22no—
152C3⋊(C3⋊C8)—22no—
153C3×C3⋊C8—21no—
154C3×C3⋊C8—21no—
155C3×C3⋊C8—41no—
156C2×#137—31no—
157C2×#131—91no—
158#417—91no—
159C2×#103—91no—
160C2×#101—91no—
161#343—91no—
162#341—31no—
163C3×#41—32no—
164C3×#41—32no—
165C3×#41—61no—
166C3×#41—61no—
167C2×C3×Q8—32no—
168C2×C3×Q8—31no—
169C2×C3×Q8—61no—
170C2×C3×Q8—61no—
171C2×C3×Q8—61no—
172C2×C3×Q8—61no—
173C2×C3×Q8—61no—
174C2×C3×D4—31no—
175C2×C3×D4—61no—
176C22×C3×C4—21no—
177C22×C3×C4—61no—
178C22×C3×C4—61no—
179C22×C3×C4C22×D311yescharacteristic
180C22×C3×C4C22×D311yescharacteristic
181C2×#67—21no—
182C22×Dic3—21no—
183C22×Dic3—62no—
184C22×Dic3—61no—
185C22×Dic3—61no—
186#235—21no—
187#235—21no—
188#235C2×Dic312yes—
189#235#6712yes—
190C2×D12#6711yescharacteristic
191C2×C4×D3—21no—
192C2×Dic6—21no—
193C2×Dic6—21no—
194C2×Dic6—21no—
195C2×Dic6—21no—
196C2×Dic6—21no—
197C2×Dic6C2×Dic312yes—
198C2×Dic6#6711yescharacteristic
199C3×Q16—64no—
200C3×SD16—64no—
201C3×M16—21no—
202C3×M16—21no—
203C3×M16—22no—
204C3×M16—41no—
205C3×M16—61no—
206C3×M16—61no—
207C3×M16C4×D312yes—
208C3×M16C2×Dic312yes—
209C2×C3×C8—21no—
210C2×C3×C8—21no—
211C2×C3×C8—31no—
212C2×C3×C8—31no—
213C2×C3×C8—41no—
214C2×C3×C8—61no—
215C2×C3×C8—61no—
216C2×C3×C8—61no—
217C4⋊Dic3—61no—
218C4⋊Dic3—61no—
219C4⋊Dic3—61no—
220C4⋊Dic3—61no—
221C4⋊Dic3—121no—
222C4⋊Dic3—121no—
223#208—21no—
224#208—21no—
225#208—32no—
226#208—32no—
227#208—62no—
228#208—64no—
229#208—61no—
230#208—61no—
231#208—121no—
232C2×C3⋊C8—21no—
233C2×C3⋊C8—21no—
234C2×C3⋊C8—21no—
235C2×C3⋊C8—64no—
236C2×C3⋊C8—61no—
237C2×C3⋊C8—61no—
238C2×C3⋊C8—121no—
239C2×C3⋊C8D1211yescharacteristic
240C2×C3⋊C8D1211yescharacteristic
241Dic12—24no—
242#204—24no—
243ΓL(1,𝔽25)—64no—
244D3×C8—64no—
245C22×C32—21no—
246C22×C32—21no—
247C22×C32C4×D411yescharacteristic
248C22×C32#12111yescharacteristic
249C22×C32#12311yescharacteristic
250C2×C3×D3—22no—
251C2×C3×D3—41no—
252C2×C3×D3—41no—
253C32×C4C2×C22⋊C411yescharacteristic
254C32×C4C4×D411yescharacteristic
255C32×C4#12011yescharacteristic
256C32×C4#12111yescharacteristic
257C3⋊Dic3—81no—
258C3×Dic3—22no—
259C3×Dic3—42no—
260C2×#41—31no—
261C22×Q8—31no—
262#137—34no—
263#137—62no—
264C2×Q16—61no—
265C2×SD16—61no—
266#131—182no—
267#131—182no—
268C2×M16—31no—
269C2×M16—91no—
270C2×M16—181no—
271C2×M16D3211yescharacteristic
272C22×C8—31no—
273C22×C8—181no—
274C2×C4⋊C4—91no—
275#103—181no—
276#103—181no—
277#103—181no—
278#102—181no—
279#101—182no—
280C23×C3—21no—
281C23×C3—61no—
282C23×C3#23711yescharacteristic
283C23×C3#23911yescharacteristic
284C22×D3—21no—
285C3×Q8—32no—
286C3×Q8—61no—
287C3×Q8—62no—
288C3×Q8—62no—
289C3×Q8—121no—
290C3×Q8—121no—
291C3×D4—32no—
292C3×D4—62no—
293C3×D4—62no—
294C3×D4—61no—
295C2×C3×C4—21no—
296C2×C3×C4—21no—
297C2×C3×C4—21no—
298C2×C3×C4—21no—
299C2×C3×C4—21no—
300C2×C3×C4—21no—
301C2×C3×C4—61no—
302C2×C3×C4—62no—
303C2×C3×C4—62no—
304C2×C3×C4—62no—
305C2×C3×C4—121no—
306C2×C3×C4—121no—
307C2×C3×C4C2×C4×D311yescharacteristic
308C2×C3×C4C2×D1211yescharacteristic
309C2×C3×C4#23511yescharacteristic
310C2×C3×C4D3×D411yescharacteristic
311C2×C3×C4D3×D411yescharacteristic
312C2×C3×C4D3×D411yescharacteristic
313C2×C3×C4D3×D411yescharacteristic
314C2×C3×C4D3×D411yescharacteristic
315C2×C3×C4#23711yescharacteristic
316C2×C3×C4C22×Dic311yescharacteristic
317C2×C3×C4C2×#6711yescharacteristic
318C2×C3×C4C2×#6711yescharacteristic
319#67—22no—
320#67—22no—
321C2×Dic3—21no—
322C2×Dic3—22no—
323C2×Dic3—41no—
324C2×Dic3—41no—
325C2×Dic3—122no—
326C2×Dic3—121no—
327C2×Dic3—121no—
328C2×Dic3—241no—
329C2×Dic3—241no—
330C2×Dic3—242no—
331D12—21no—
332D12#21712yes—
333C4×D3—22no—
334C4×D3—22no—
335Dic6—21no—
336Dic6—22no—
337Dic6—22no—
338Dic6—41no—
339Dic6—41no—
340Dic6#21712yes—
341C3×C8—22no—
342C3×C8—22no—
343C3×C8—42no—
344C3×C8—61no—
345C3×C8—61no—
346C3×C8—121no—
347C3⋊C8—21no—
348C3⋊C8—21no—
349C3⋊C8—41no—
350C3⋊C8—62no—
351C3⋊C8—62no—
352C3⋊C8—122no—
353C2×C32—21no—
354C2×C32—21no—
355C2×C32#38611yescharacteristic
356C2×C32#47111yescharacteristic
357C2×C32#47311yescharacteristic
358C3×D3—42no—
359#41—32no—
360#41—32no—
361#41—61no—
362#41—61no—
363C2×Q8—32no—
364C2×Q8—31no—
365C2×Q8—61no—
366C2×Q8—61no—
367C2×Q8—61no—
368C2×Q8—61no—
369C2×Q8—61no—
370C2×D4—31no—
371C2×D4—61no—
372C22×C4—61no—
373C22×C4—61no—
374C22×C4—181no—
375C22×C4C2×D3211yescharacteristic
376Q16—64no—
377SD16—64no—
378M16—21no—
379M16—61no—
380M16—61no—
381M16—92no—
382M16—184no—
383M16—181no—
384M16D3×Dic312yes—
385C2×C8—21no—
386C2×C8—31no—
387C2×C8—31no—
388C2×C8—61no—
389C2×C8—61no—
390C2×C8—61no—
391C2×C8—184no—
392C2×C8—181no—
393C4⋊C4—181no—
394C4⋊C4—181no—
395C22×C3—21no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—21no—
399C22×C3—21no—
400C22×C3—21no—
401C22×C3—21no—
402C22×C3—41no—
403C22×C3—41no—
404C22×C3—62no—
405C22×C3—121no—
406C22×C3—121no—
407C22×C3#89311yescharacteristic
408C22×C3#89411yescharacteristic
409C22×C3#89511yescharacteristic
410C22×C3D4×Dic311yescharacteristic
411C22×C3#93511yescharacteristic
412C22×C3#93911yescharacteristic
413C2×D3—22no—
414C2×D3—41no—
415C2×D3—41no—
416C3×C4—21no—
417C3×C4—21no—
418C3×C4—21no—
419C3×C4—21no—
420C3×C4—62no—
421C3×C4—122no—
422C3×C4C4×D1211yescharacteristic
423C3×C4D3×C22⋊C411yescharacteristic
424C3×C4#88211yescharacteristic
425C3×C4#88411yescharacteristic
426C3×C4D4×Dic311yescharacteristic
427C3×C4#93711yescharacteristic
428C3×C4#93911yescharacteristic
429C3×C4C2×#21711yescharacteristic
430Dic3—22no—
431Dic3—42no—
432Dic3—242no—
433Dic3—241no—
434Dic3—241no—
435C32#190811yescharacteristic, complemented, Sylow
436C23—61no—
437C23#379611yescharacteristic
438Q8—32no—
439Q8—61no—
440Q8—62no—
441Q8—62no—
442Q8—121no—
443Q8—121no—
444D4—32no—
445D4—62no—
446D4—62no—
447D4—61no—
448C2×C4—61no—
449C2×C4—62no—
450C2×C4—62no—
451C2×C4—62no—
452C2×C4—121no—
453C2×C4—121no—
454C2×C4—361no—
455C2×C4—721no—
456C2×C4#379511yescharacteristic
457C2×C4D3×D1211yescharacteristic
458C2×C4#380211yescharacteristic
459C2×C4C2×D3×Dic311yescharacteristic
460C2×C4D3×#6711yescharacteristic
461C2×C4D3×#6711yescharacteristic
462C8—22no—
463C8—61no—
464C8—61no—
465C8—121no—
466C8—182no—
467C2×C3—21no—
468C2×C3—21no—
469C2×C3—21no—
470C2×C3—21no—
471C2×C3—21no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—41no—
475C2×C3—41no—
476C2×C3—122no—
477C2×C3#466511yescharacteristic
478C2×C3#489611yescharacteristic
479C2×C3#489811yescharacteristic
480C2×C3#520311yescharacteristic
481C2×C3#520411yescharacteristic
482C2×C3#522011yescharacteristic
483D3—42no—
484C22—21no—
485C22—21no—
486C22—62no—
487C22—121no—
488C22—121no—
489C22#6388411yescharacteristic
490C22#6388611yescharacteristic
491C22#6389811yescharacteristic
492C4—62no—
493C4—122no—
494C4—721no—
495C4#6388511yescharacteristic
496C4Dic3×D1211yescharacteristic
497C4#6392211yescharacteristic
498C4D3×#21711yescharacteristic
499C3—21no—
500C3#6894911yescharacteristic, complemented
501C3#7210311yescharacteristic, complemented
502C2—21no—
503C2—21no—
504C2—122no—
505C2#1059098311yescharacteristic
506C2#1059098511yescharacteristic
507C2#1059137611yescharacteristic
subgroupG/H
centerC22#63886
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32#121
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1908
LCSG ▷ C2×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
3. C2×#63566C2semidirect
5. C2×#63560C2semidirect
6. #10589420C2semidirect
7. C3×#4558C2semidirect
18. C3×#909C4semidirect
41. #4558D3semidirect
108. #909Dic3semidirect
435. C32#1908semidirect
500. C3#68949semidirect
501. C3#72103semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9092
C2×#638142
C2×#635662
#105910882
C2×#635602
#105894202
C3×#45582
#721033
#689493