Finite Group Databasebeta

← #11788690

Subgroups — #11788690

Order 1152.

705 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#901C211yesmaximal, characteristic
2C2×#63831C211yesmaximal, characteristic
3C2×#63643C211yesmaximal, characteristic, complemented
4#10591088C211yesmaximal, characteristic
5C2×#63561C211yesmaximal, characteristic, complemented
6C3×#4552C211yesmaximal, characteristic, complemented
7#10589168C211yesmaximal, characteristic, complemented
8#72019—31nomaximal
9#68949—31nomaximal
10C22×#634C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C3×#901—22no—
18C3×#901—22no—
19C2×C3×ΓL(1,𝔽25)—21no—
20C2×C3×D3×C8—21no—
21C2×#3719—21no—
22#63831—22no—
23#63831C414yescomplemented
24C2×#3716—21no—
25#63643—21no—
26#63643—21no—
27#63566—21no—
28#63563—21no—
29#63561—22no—
30C2×C3×#131—31no—
31C2×#951—31no—
32C2×#909—31no—
33C2×#901D311yescharacteristic
34#5232—31no—
35C2×#824—31no—
36C2×#824—31no—
37#5133—31no—
38C2×#816—31no—
39C2×#816—31no—
40C2×#816—61no—
41C3×#341—31no—
42#4554—31no—
43#4554—31no—
44#4552D311yescharacteristic, complemented
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3—21no—
47C22×C3⋊Dic3—21no—
48C2×#634—21no—
49C2×#634—21no—
50C2×#634—21no—
51C2×#634—21no—
52C2×#634—21no—
53C2×#634C2×C412yes—
54C2×C3×#67—21no—
55C3×#235—21no—
56C3×#235—21no—
57C3×#235C2×C412yes—
58C3×#235D412yes—
59C2×C3×D12D411yescharacteristic
60C2×C3×C4×D3—21no—
61C2×C3×Dic6D411yescharacteristic
62C2×C32×C8—21no—
63C2×C32×C8—21no—
64C2×C32×C8D411yescharacteristic
65C2×C32×C8D411yescharacteristic
66C4⋊(C3⋊Dic3)—21no—
67C4⋊(C3⋊Dic3)—21no—
68C3×#208—21no—
69C3×#208—21no—
70C3×#208—21no—
71C3×#208—21no—
72C3×#208C2×C412yes—
73C3×#208D412yes—
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8—21no—
76C2×C3×C3⋊C8—21no—
77C3×ΓL(1,𝔽25)—24no—
78C3×D3×C8—24no—
79#3719—24no—
80#3716—24no—
81#1908—91noSylow
82C2×C3×#41—31no—
83C2×#235C2×D311yescharacteristic
84C22×Dic6—31no—
85C22×Dic6—31no—
86C22×Dic6—61no—
87C3×#131—62no—
88C3×#131—62no—
89C2×C3×M16—31no—
90C2×C3×M16—31no—
91C2×C3×M16—31no—
92C2×C3×M16—61no—
93C22×C3×C8—21no—
94C22×C3×C8—61no—
95C22×C3×C8C2×D311yescharacteristic
96C22×C3×C8C2×D311yescharacteristic
97#951—34no—
98#951—62no—
99C2×#216—61no—
100C2×#214—61no—
101C2×C4⋊Dic3—31no—
102C2×C4⋊Dic3—31no—
103C2×C4⋊Dic3—61no—
104C2×#208C2×D311yescharacteristic
105C2×#208C2×D311yescharacteristic
106C2×#208C2×D311yescharacteristic
107#909—34no—
108#909—62no—
109C2×Dic12—61no—
110C2×#204—61no—
111#901—22no—
112#901—22no—
113C2×ΓL(1,𝔽25)—21no—
114C2×D3×C8—21no—
115#835—61no—
116#832—61no—
117#824—62no—
118#824—62no—
119#821—61no—
120#816—62no—
121#816—62no—
122#816—61no—
123#816—61no—
124#816—61no—
125#816—61no—
126#816—61no—
127C23×C32#4111yescharacteristic
128C22×C3×D3—21no—
129C2×C32×C4C22×C411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4#4111yescharacteristic
135C2×C3⋊Dic3—22no—
136C2×C3⋊Dic3—41no—
137C2×C3⋊Dic3—41no—
138C2×C3⋊Dic3—41no—
139C2×C3⋊Dic3—81no—
140#634—22no—
141#634—22no—
142#634—41no—
143#634—41no—
144C3×#67—22no—
145C3×#67—22no—
146C2×C3×Dic3—21no—
147C3×D12—21no—
148C3×D12C22⋊C412yes—
149C3×C4×D3—22no—
150C3×C4×D3—22no—
151C3×Dic6—21no—
152C3×Dic6C22⋊C412yes—
153C32×C8—21no—
154C32×C8—21no—
155C3×C3⋊C8—22no—
156C3×C3⋊C8—22no—
157C3×C3⋊C8—41no—
158C2×#137—91no—
159C2×#131—31no—
160#417—91no—
161C2×#103—91no—
162C2×#101—91no—
163#343—91no—
164#341—31no—
165C3×#41—32no—
166C3×#41—32no—
167C3×#41—61no—
168C3×#41—61no—
169C2×C3×Q8—31no—
170C2×C3×D4—31no—
171C2×C3×D4—61no—
172C22×C3×C4—21no—
173C22×C3×C4—61no—
174C22×C3×C4C22×D311yescharacteristic
175C22×C3×C4C22×D311yescharacteristic
176C2×#67—21no—
177C22×Dic3—61no—
178C22×Dic3—61no—
179C22×Dic3—61no—
180C22×Dic3—61no—
181C22×Dic3—121no—
182C22×Dic3—121no—
183#235—21no—
184#235—21no—
185#235C4×D312yes—
186#235#6712yes—
187C2×D12D1211yescharacteristic
188C2×C4×D3—21no—
189C2×Dic6—32no—
190C2×Dic6—32no—
191C2×Dic6—62no—
192C2×Dic6—62no—
193C2×Dic6—62no—
194C2×Dic6—61no—
195C2×Dic6—61no—
196C2×Dic6—61no—
197C2×Dic6—61no—
198C2×Dic6—61no—
199C2×Dic6—61no—
200C2×Dic6—61no—
201C2×Dic6—61no—
202C2×Dic6—61no—
203C2×Dic6—61no—
204C2×Dic6—121no—
205C2×Dic6—121no—
206C2×Dic6—121no—
207C2×Dic6D1211yescharacteristic
208C3×M16—32no—
209C3×M16—32no—
210C3×M16—64no—
211C3×M16—61no—
212C3×M16—61no—
213C3×M16—61no—
214C3×M16—61no—
215C2×C3×C8—21no—
216C2×C3×C8—21no—
217C2×C3×C8—21no—
218C2×C3×C8—21no—
219C2×C3×C8—21no—
220C2×C3×C8—21no—
221C2×C3×C8—41no—
222C2×C3×C8—41no—
223C2×C3×C8—64no—
224C2×C3×C8—61no—
225C2×C3×C8—61no—
226C2×C3×C8—61no—
227C2×C3×C8D1211yescharacteristic
228C2×C3×C8D1211yescharacteristic
229C2×C3×C8#6711yescharacteristic
230C2×C3×C8#6711yescharacteristic
231#216—64no—
232#214—64no—
233C4⋊Dic3—62no—
234C4⋊Dic3—61no—
235C4⋊Dic3—61no—
236C4⋊Dic3—61no—
237C4⋊Dic3—61no—
238C4⋊Dic3—121no—
239#208—21no—
240#208—21no—
241#208—21no—
242#208—21no—
243#208C4×D312yes—
244#208#6712yes—
245C2×C3⋊C8—21no—
246C2×C3⋊C8—21no—
247C2×C3⋊C8—21no—
248Dic12—64no—
249#204—64no—
250ΓL(1,𝔽25)—24no—
251D3×C8—24no—
252C22×C32—21no—
253C22×C32—21no—
254C22×C32C4×D411yescharacteristic
255C22×C32#12111yescharacteristic
256C22×C32#12311yescharacteristic
257C2×C3×D3—22no—
258C2×C3×D3—41no—
259C2×C3×D3—41no—
260C32×C4C2×C22⋊C411yescharacteristic
261C32×C4C4×D411yescharacteristic
262C32×C4#12011yescharacteristic
263C32×C4#12111yescharacteristic
264C3⋊Dic3—42no—
265C3⋊Dic3—81no—
266C3×Dic3—22no—
267C2×#41—31no—
268C22×Q8—91no—
269#137—94no—
270#137—182no—
271C2×Q16—181no—
272C2×SD16—181no—
273#131—62no—
274#131—62no—
275C2×M16—31no—
276C2×M16—31no—
277C2×M16—31no—
278C2×M16—61no—
279C22×C8—61no—
280C22×C8D3211yescharacteristic
281C2×C4⋊C4—91no—
282#103—181no—
283#103—181no—
284#103—181no—
285#102—181no—
286#101—182no—
287C23×C3—21no—
288C23×C3—61no—
289C23×C3#23511yescharacteristic
290C23×C3#23911yescharacteristic
291C22×D3—21no—
292C3×Q8—32no—
293C3×Q8—61no—
294C3×D4—32no—
295C3×D4—62no—
296C3×D4—62no—
297C3×D4—61no—
298C2×C3×C4—21no—
299C2×C3×C4—21no—
300C2×C3×C4—21no—
301C2×C3×C4—21no—
302C2×C3×C4—21no—
303C2×C3×C4—21no—
304C2×C3×C4—61no—
305C2×C3×C4—62no—
306C2×C3×C4—62no—
307C2×C3×C4C2×C4×D311yescharacteristic
308C2×C3×C4C2×C4×D311yescharacteristic
309C2×C3×C4C2×D1211yescharacteristic
310C2×C3×C4C2×D1211yescharacteristic
311C2×C3×C4#23511yescharacteristic
312C2×C3×C4#23511yescharacteristic
313C2×C3×C4D3×D411yescharacteristic
314C2×C3×C4D3×D411yescharacteristic
315C2×C3×C4D3×D411yescharacteristic
316C2×C3×C4C2×#6711yescharacteristic
317C2×C3×C4C2×#6711yescharacteristic
318C2×C3×C4C2×#6711yescharacteristic
319#67—22no—
320#67—22no—
321C2×Dic3—21no—
322C2×Dic3—62no—
323C2×Dic3—62no—
324C2×Dic3—122no—
325C2×Dic3—122no—
326C2×Dic3—122no—
327C2×Dic3—121no—
328C2×Dic3—121no—
329C2×Dic3—121no—
330C2×Dic3—121no—
331C2×Dic3—122no—
332C2×Dic3—121no—
333C2×Dic3—121no—
334C2×Dic3—242no—
335C2×Dic3—241no—
336C2×Dic3—241no—
337D12—21no—
338D12(C2×D3)⋊C412yes—
339C4×D3—22no—
340C4×D3—22no—
341Dic6—21no—
342Dic6—64no—
343Dic6—62no—
344Dic6—62no—
345Dic6—62no—
346Dic6—62no—
347Dic6—122no—
348Dic6—122no—
349Dic6—122no—
350Dic6—121no—
351Dic6—121no—
352Dic6—121no—
353Dic6—121no—
354Dic6(C2×D3)⋊C412yes—
355C3×C8—21no—
356C3×C8—21no—
357C3×C8—21no—
358C3×C8—21no—
359C3×C8—41no—
360C3×C8—41no—
361C3×C8—62no—
362C3×C8—62no—
363C3×C8—121no—
364C3⋊C8—22no—
365C3⋊C8—22no—
366C3⋊C8—41no—
367C2×C32—21no—
368C2×C32—21no—
369C2×C32#38611yescharacteristic
370C2×C32#47111yescharacteristic
371C2×C32#47311yescharacteristic
372C3×D3—42no—
373#41—32no—
374#41—32no—
375#41—61no—
376#41—61no—
377C2×Q8—31no—
378C2×Q8—92no—
379C2×Q8—181no—
380C2×Q8—181no—
381C2×Q8—181no—
382C2×Q8—181no—
383C2×Q8—181no—
384C2×D4—31no—
385C2×D4—61no—
386C22×C4—61no—
387C22×C4—181no—
388C22×C4—181no—
389C22×C4C2×D3211yescharacteristic
390Q16—184no—
391SD16—184no—
392M16—32no—
393M16—32no—
394M16—64no—
395M16—61no—
396M16—61no—
397M16—61no—
398M16—61no—
399C2×C8—21no—
400C2×C8—21no—
401C2×C8—64no—
402C2×C8—61no—
403C2×C8—61no—
404C2×C8—61no—
405C2×C8#62611yescharacteristic
406C2×C8#62611yescharacteristic
407C4⋊C4—181no—
408C4⋊C4—181no—
409C22×C3—22no—
410C22×C3—22no—
411C22×C3—21no—
412C22×C3—21no—
413C22×C3—21no—
414C22×C3—21no—
415C22×C3—21no—
416C22×C3—21no—
417C22×C3—21no—
418C22×C3—62no—
419C22×C3—121no—
420C22×C3—121no—
421C22×C3#89311yescharacteristic
422C22×C3#89411yescharacteristic
423C22×C3#89511yescharacteristic
424C22×C3C4×#6711yescharacteristic
425C22×C3#92911yescharacteristic
426C22×C3#93011yescharacteristic
427C2×D3—22no—
428C2×D3—41no—
429C2×D3—41no—
430C3×C4—21no—
431C3×C4—21no—
432C3×C4—21no—
433C3×C4—21no—
434C3×C4—62no—
435C3×C4C4×D1211yescharacteristic
436C3×C4D3×C22⋊C411yescharacteristic
437C3×C4#88211yescharacteristic
438C3×C4#88411yescharacteristic
439C3×C4C2×(C2×D3)⋊C411yescharacteristic
440C3×C4C4×#6711yescharacteristic
441C3×C4#93011yescharacteristic
442C3×C4#95311yescharacteristic
443Dic3—22no—
444Dic3—124no—
445Dic3—122no—
446Dic3—122no—
447Dic3—242no—
448Dic3—241no—
449Dic3—241no—
450C32#190811yescharacteristic, complemented, Sylow
451C23—61no—
452C23#379911yescharacteristic
453Q8—32no—
454Q8—61no—
455Q8—182no—
456Q8—182no—
457Q8—361no—
458Q8—361no—
459D4—32no—
460D4—62no—
461D4—62no—
462D4—61no—
463C2×C4—61no—
464C2×C4—62no—
465C2×C4—62no—
466C2×C4—182no—
467C2×C4—361no—
468C2×C4—361no—
469C2×C4—361no—
470C2×C4—721no—
471C2×C4#379811yescharacteristic
472C2×C4C4×D3211yescharacteristic
473C2×C4D3×D1211yescharacteristic
474C2×C4C2×#62611yescharacteristic
475C2×C4D3×#6711yescharacteristic
476C2×C4D3×#6711yescharacteristic
477C8—21no—
478C8—21no—
479C8—62no—
480C8—62no—
481C8—121no—
482C2×C3—22no—
483C2×C3—22no—
484C2×C3—21no—
485C2×C3—21no—
486C2×C3—21no—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—122no—
492C2×C3#466511yescharacteristic
493C2×C3#489611yescharacteristic
494C2×C3#489811yescharacteristic
495C2×C3#514111yescharacteristic
496C2×C3#514311yescharacteristic
497C2×C3#521311yescharacteristic
498D3—42no—
499C22—21no—
500C22—21no—
501C22—62no—
502C22—121no—
503C22—121no—
504C22#6385011yescharacteristic
505C22#6390411yescharacteristic
506C22#6390911yescharacteristic
507C4—62no—
508C4—362no—
509C4—721no—
510C4C4×#62611yescharacteristic
511C4#6390611yescharacteristic
512C4D3×(C2×D3)⋊C411yescharacteristic
513C4#6397711yescharacteristic
514C3—21no—
515C3#6894911yescharacteristic, complemented
516C3#7201911yescharacteristic, complemented
517C2—21no—
518C2—21no—
519C2—122no—
520C2#1059093111yescharacteristic
521C2#1059093211yescharacteristic
522C2#1059138211yescharacteristic
subgroupG/H
centerC22#63909
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×#63643C2semidirect
5. C2×#63561C2semidirect
6. C3×#4552C2semidirect
7. #10589168C2semidirect
23. #63831C4semidirect
44. #4552D3semidirect
450. C32#1908semidirect
515. C3#68949semidirect
516. 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×#638312
C2×#636432
#105910882
C2×#635612
C3×#45522
#105891682
#720193
#689493