Finite Group Databasebeta

← #11788688

Subgroups — #11788688

Order 1152.

669 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×#901C211yesmaximal, characteristic
2C2×#63827C211yesmaximal, characteristic
3C2×C3×#816C211yesmaximal, characteristic, complemented
4#10591087C211yesmaximal, characteristic
5C2×#63560C211yesmaximal, characteristic, complemented
6#10589418C211yesmaximal, characteristic, complemented
7#10589167C211yesmaximal, characteristic, complemented
8#72019—31nomaximal
9#70286—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C3×#901—22no—
18C3×#901—22no—
19C2×C3×ΓL(1,𝔽25)—21no—
20C2×C3×D3×C8—21no—
21C2×#3718—21no—
22#63827—22no—
23#63827C414yescomplemented
24C2×#3715—21no—
25C3×#816—21no—
26C3×#816—21no—
27#63565—21no—
28#63562—21no—
29#63560—22no—
30C2×C3×#131—31no—
31C2×#951—31no—
32C2×#942—31no—
33C2×#901D311yescharacteristic
34C2×C3×#103—31no—
35#5232—31no—
36C2×#836—31no—
37C2×#824—31no—
38C2×#816D311yescharacteristic, complemented
39#4966—31no—
40#4554—31no—
41#4552—31no—
42#4552—31no—
43#4552—61no—
44#4530—31no—
45C22×C32×C4C2311yescharacteristic
46C2×C3×#67—21no—
47C22×C3×Dic3—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
62C2×C32×C8—21no—
63C2×C32×C8—21no—
64C2×C32×C8D411yescharacteristic
65C2×C32×C8D411yescharacteristic
66#3748—21no—
67#3748—21no—
68#3748—21no—
69#3748C2×C412yes—
70C2×C3⋊(C3⋊C8)—21no—
71C2×C3⋊(C3⋊C8)—21no—
72C3×C4⋊Dic3—21no—
73C3×C4⋊Dic3—21no—
74C3×#208—21no—
75C3×#208D412yes—
76C2×C3×C3⋊C8—21no—
77C3×ΓL(1,𝔽25)—24no—
78C3×D3×C8—24no—
79#3718—24no—
80#3715—24no—
81#1908—91noSylow
82C2×C3×#41—31no—
83C22×C3×Q8—31no—
84C2×#235C2×D311yescharacteristic
85C22×Dic6C2×D311yescharacteristic
86C3×#131—62no—
87C3×#131—62no—
88C2×C3×M16—31no—
89C2×C3×M16—61no—
90C22×C3×C8—21no—
91C22×C3×C8—61no—
92C22×C3×C8C2×D311yescharacteristic
93C22×C3×C8C2×D311yescharacteristic
94C2×C3×C4⋊C4—31no—
95#951—34no—
96#951—62no—
97C2×#216—61no—
98C2×#216—61no—
99#942—34no—
100#942—62no—
101C2×#215—61no—
102C2×#214—61no—
103C2×C4⋊Dic3C2×D311yescharacteristic
104C2×#208—31no—
105C2×#208—31no—
106C2×#208—31no—
107C2×#208—31no—
108C2×#208—61no—
109C2×#208—61no—
110C2×#208C2×D311yescharacteristic
111#901—22no—
112#901—22no—
113C2×ΓL(1,𝔽25)—21no—
114C2×D3×C8—21no—
115C3×#103—61no—
116C3×#103—61no—
117#836—62no—
118#835—61no—
119#832—61no—
120#824—62no—
121#816—21no—
122#816—21no—
123#810—61no—
124#809—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
133C3×#67—22no—
134C3×#67—22no—
135C2×C3×Dic3—21no—
136C2×C3×Dic3—22no—
137C2×C3×Dic3—41no—
138C2×C3×Dic3—41no—
139C2×C3×Dic3—41no—
140C2×C3×Dic3—81no—
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—21no—
152C32×C8—21no—
153C3⋊(C3⋊C8)—22no—
154C3⋊(C3⋊C8)—41no—
155C3×C3⋊C8—22no—
156C2×#137—91no—
157C2×#131—31no—
158#417—91no—
159C2×#103—31no—
160C2×#101—91no—
161#343—91no—
162#341—91no—
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×C4—61no—
180C22×C3×C4C22×D311yescharacteristic
181C22×C3×C4C22×D311yescharacteristic
182C2×#67—21no—
183C22×Dic3—21no—
184C22×Dic3—21no—
185#235—21no—
186#235—21no—
187#235C4×D312yes—
188#235#6712yes—
189C2×D12D1211yescharacteristic
190C2×C4×D3—21no—
191C2×Dic6—21no—
192C2×Dic6—21no—
193C2×Dic6—21no—
194C2×Dic6—21no—
195C2×Dic6—21no—
196C2×Dic6C4×D312yes—
197C2×Dic6D1211yescharacteristic
198C3×M16—32no—
199C3×M16—64no—
200C3×M16—61no—
201C2×C3×C8—21no—
202C2×C3×C8—21no—
203C2×C3×C8—21no—
204C2×C3×C8—21no—
205C2×C3×C8—21no—
206C2×C3×C8—21no—
207C2×C3×C8—41no—
208C2×C3×C8—41no—
209C2×C3×C8—64no—
210C2×C3×C8—61no—
211C2×C3×C8#6711yescharacteristic
212C2×C3×C8#6711yescharacteristic
213C2×C3×C8#6711yescharacteristic
214C2×C3×C8#6711yescharacteristic
215C3×C4⋊C4—61no—
216C3×C4⋊C4—61no—
217#216—64no—
218#216—64no—
219#215—64no—
220#214—64no—
221C4⋊Dic3—21no—
222C4⋊Dic3—21no—
223#208—21no—
224#208—32no—
225#208—32no—
226#208—62no—
227#208—61no—
228#208—61no—
229#208—62no—
230#208—61no—
231#208—61no—
232#208—61no—
233#208—61no—
234#208—121no—
235#208—121no—
236#208#6712yes—
237C2×C3⋊C8—21no—
238C2×C3⋊C8—61no—
239C2×C3⋊C8—61no—
240C2×C3⋊C8—61no—
241C2×C3⋊C8—61no—
242C2×C3⋊C8—121no—
243C2×C3⋊C8—121no—
244ΓL(1,𝔽25)—24no—
245D3×C8—24no—
246C22×C32—21no—
247C22×C32—21no—
248C22×C32C4×D411yescharacteristic
249C22×C32#12111yescharacteristic
250C22×C32#12311yescharacteristic
251C2×C3×D3—22no—
252C2×C3×D3—41no—
253C2×C3×D3—41no—
254C32×C4C2×C22⋊C411yescharacteristic
255C32×C4C4×D411yescharacteristic
256C32×C4#12011yescharacteristic
257C32×C4#12111yescharacteristic
258C3×Dic3—22no—
259C3×Dic3—42no—
260C3×Dic3—81no—
261C2×#41—31no—
262C22×Q8—31no—
263#137—94no—
264#137—182no—
265C2×Q16—181no—
266C2×SD16—181no—
267#131—62no—
268#131—62no—
269C2×M16—31no—
270C2×M16—61no—
271C2×M16—91no—
272C2×M16—91no—
273C22×C8—61no—
274C22×C8D3211yescharacteristic
275C2×C4⋊C4—31no—
276#103—61no—
277#103—61no—
278#103—181no—
279#102—181no—
280#101—182no—
281C23×C3—21no—
282C23×C3—61no—
283C23×C3#23511yescharacteristic
284C23×C3#23711yescharacteristic
285C22×D3—21no—
286C3×Q8—32no—
287C3×Q8—61no—
288C3×Q8—62no—
289C3×Q8—62no—
290C3×Q8—121no—
291C3×Q8—121no—
292C3×D4—32no—
293C3×D4—62no—
294C3×D4—62no—
295C3×D4—61no—
296C2×C3×C4—21no—
297C2×C3×C4—21no—
298C2×C3×C4—21no—
299C2×C3×C4—21no—
300C2×C3×C4—21no—
301C2×C3×C4—21no—
302C2×C3×C4—61no—
303C2×C3×C4—62no—
304C2×C3×C4—62no—
305C2×C3×C4—62no—
306C2×C3×C4—121no—
307C2×C3×C4—121no—
308C2×C3×C4—121no—
309C2×C3×C4—241no—
310C2×C3×C4C2×C4×D311yescharacteristic
311C2×C3×C4C2×C4×D311yescharacteristic
312C2×C3×C4C2×D1211yescharacteristic
313C2×C3×C4#23511yescharacteristic
314C2×C3×C4#23511yescharacteristic
315C2×C3×C4D3×D411yescharacteristic
316C2×C3×C4D3×D411yescharacteristic
317C2×C3×C4D3×D411yescharacteristic
318C2×C3×C4C2×#6711yescharacteristic
319C2×C3×C4C2×#6711yescharacteristic
320C2×C3×C4C2×#6711yescharacteristic
321C2×C3×C4C2×#6711yescharacteristic
322#67—22no—
323#67—22no—
324C2×Dic3—21no—
325C2×Dic3—22no—
326C2×Dic3—41no—
327C2×Dic3—41no—
328C2×Dic3—41no—
329C2×Dic3—81no—
330D12—21no—
331D12(C2×D3)⋊C412yes—
332C4×D3—22no—
333C4×D3—22no—
334Dic6—21no—
335Dic6—22no—
336Dic6—22no—
337Dic6—41no—
338Dic6—41no—
339Dic6(C2×D3)⋊C412yes—
340C3×C8—21no—
341C3×C8—21no—
342C3×C8—21no—
343C3×C8—21no—
344C3×C8—41no—
345C3×C8—41no—
346C3×C8—62no—
347C3⋊C8—22no—
348C3⋊C8—62no—
349C3⋊C8—62no—
350C3⋊C8—122no—
351C3⋊C8—122no—
352C3⋊C8—121no—
353C3⋊C8—121no—
354C2×C32—21no—
355C2×C32—21no—
356C2×C32#38611yescharacteristic
357C2×C32#47111yescharacteristic
358C2×C32#47311yescharacteristic
359C3×D3—42no—
360#41—32no—
361#41—32no—
362#41—61no—
363#41—61no—
364C2×Q8—32no—
365C2×Q8—31no—
366C2×Q8—61no—
367C2×Q8—61no—
368C2×Q8—61no—
369C2×Q8—61no—
370C2×Q8—61no—
371C2×D4—31no—
372C2×D4—61no—
373C22×C4—61no—
374C22×C4—61no—
375C22×C4—61no—
376C22×C4C2×D3211yescharacteristic
377Q16—184no—
378SD16—184no—
379M16—32no—
380M16—64no—
381M16—61no—
382M16—92no—
383M16—181no—
384M16—181no—
385M16—181no—
386C2×C8—21no—
387C2×C8—21no—
388C2×C8—64no—
389C2×C8—61no—
390C2×C8—181no—
391C2×C8—181no—
392C2×C8#62511yescharacteristic
393C2×C8#62511yescharacteristic
394C4⋊C4—61no—
395C4⋊C4—61no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—21no—
399C22×C3—21no—
400C22×C3—21no—
401C22×C3—21no—
402C22×C3—21no—
403C22×C3—41no—
404C22×C3—41no—
405C22×C3—62no—
406C22×C3—121no—
407C22×C3—121no—
408C22×C3#67⋊C411yescharacteristic
409C22×C3#88311yescharacteristic
410C22×C3C4×#6711yescharacteristic
411C22×C3#92911yescharacteristic
412C22×C3#93011yescharacteristic
413C22×C3#93811yescharacteristic
414C2×D3—22no—
415C2×D3—41no—
416C2×D3—41no—
417C3×C4—21no—
418C3×C4—21no—
419C3×C4—21no—
420C3×C4—21no—
421C3×C4—62no—
422C3×C4—122no—
423C3×C4—241no—
424C3×C4D3×C22⋊C411yescharacteristic
425C3×C4#88411yescharacteristic
426C3×C4C2×(C2×D3)⋊C411yescharacteristic
427C3×C4C4×#6711yescharacteristic
428C3×C4C4×#6711yescharacteristic
429C3×C4#93011yescharacteristic
430C3×C4#93711yescharacteristic
431C3×C4#95311yescharacteristic
432Dic3—22no—
433Dic3—42no—
434Dic3—81no—
435C32#190811yescharacteristic, complemented, Sylow
436C23—61no—
437C23#379511yescharacteristic
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—121no—
455C2×C4—241no—
456C2×C4#379811yescharacteristic
457C2×C4C4×D3211yescharacteristic
458C2×C4D3×D1211yescharacteristic
459C2×C4C2×#62511yescharacteristic
460C2×C4D3×#6711yescharacteristic
461C2×C4D3×#6711yescharacteristic
462C8—21no—
463C8—21no—
464C8—62no—
465C8—182no—
466C8—361no—
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#495611yescharacteristic
478C2×C3#514111yescharacteristic
479C2×C3#514311yescharacteristic
480C2×C3#517711yescharacteristic
481C2×C3#519211yescharacteristic
482C2×C3#521311yescharacteristic
483D3—42no—
484C22—21no—
485C22—21no—
486C22—62no—
487C22—121no—
488C22—121no—
489C22#6387911yescharacteristic
490C22#6390511yescharacteristic
491C22#6390811yescharacteristic
492C4—62no—
493C4—122no—
494C4—241no—
495C4C4×#62511yescharacteristic
496C4#6390611yescharacteristic
497C4D3×(C2×D3)⋊C411yescharacteristic
498C4#6397611yescharacteristic
499C3—21no—
500C3#7028611yescharacteristic, complemented
501C3#7201911yescharacteristic, complemented
502C2—21no—
503C2—21no—
504C2—122no—
505C2#1059092511yescharacteristic
506C2#1059093011yescharacteristic
507C2#1059138111yescharacteristic
subgroupG/H
centerC22#63908
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC22×C32#121
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1908
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
3. C2×C3×#816C2semidirect
5. C2×#63560C2semidirect
6. #10589418C2semidirect
7. #10589167C2semidirect
23. #63827C4semidirect
38. C2×#816D3semidirect
435. C32#1908semidirect
500. C3#70286semidirect
501. C3#72019semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9012
C2×#638272
C2×C3×#8162
#105910872
C2×#635602
#105894182
#105891672
#720193
#702863