Finite Group Databasebeta

← #11788631

Subgroups — #11788631

Order 1152.

797 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64157C211yesmaximal, characteristic, complemented
2C2×C3×#949C211yesmaximal, characteristic
3C3×#5232C211yesmaximal, characteristic, complemented
4C2×#63562C211yesmaximal, characteristic, complemented
5C2×#63558C211yesmaximal, characteristic, complemented
6#10589167C211yesmaximal, characteristic, complemented
7#10589165C211yesmaximal, characteristic, complemented
8#72091—31nomaximal
9#70303—31nomaximal
10C2×C32×#41C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12#64157—22no—
13#64157—22no—
14C2×#3748—21no—
15C2×#3748C2211yescharacteristic
16C22×C3⋊(C3⋊C8)—21no—
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C3×#949—22no—
19C3×#949C414yescomplemented
20C2×C3×#215—21no—
21C2×C3×#213—21no—
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×#208C2211yescharacteristic
24C2×C3×#208C2211yescharacteristic
25C3×#835—21no—
26C3×#832—21no—
27#63562—21no—
28#63562—21no—
29#63558—22no—
30C2×C3×AGL(1,ℤ/8)—31no—
31C2×#949D311yescharacteristic
32C2×#948—31no—
33C2×#948—31no—
34C2×#948—61no—
35C3×#417—31no—
36#5232D311yescharacteristic, complemented
37C2×#833—31no—
38C2×#832—31no—
39C2×#823—31no—
40C2×#809—31no—
41#4558—31no—
42#4558—31no—
43#4554—31no—
44#4530—31no—
45C23×C3×D3—21no—
46C32×#41—21no—
47C32×#41—21no—
48C32×#41C2×C412yes—
49C32×#41D412yes—
50C2×C32×Q8D411yescharacteristic
51C2×C32×D4—21no—
52C2×C32×D4D411yescharacteristic
53C22×C32×C4—21no—
54C22×C32×C4C2311yescharacteristic
55C22×C3×Dic3—21no—
56C2×C3×D12—21no—
57C2×C3×D12—21no—
58C2×C3×D12—21no—
59C2×C3×D12—21no—
60C2×C3×D12—21no—
61C2×C3×D12C2×C412yes—
62#3748—24no—
63#3748—21no—
64#3748D412yes—
65C2×C3⋊(C3⋊C8)—24no—
66C2×C3⋊(C3⋊C8)—21no—
67C2×C3⋊(C3⋊C8)—21no—
68C2×C3⋊(C3⋊C8)—21no—
69C2×C3⋊(C3⋊C8)D411yescharacteristic
70C2×C3⋊(C3⋊C8)D411yescharacteristic
71C3×#215—24no—
72C3×#213—24no—
73C3×C4⋊Dic3—21no—
74C3×C4⋊Dic3—21no—
75C3×#208—21no—
76C3×#208—21no—
77C3×#208—21no—
78C3×#208C2×C412yes—
79C2×C3×C3⋊C8—21no—
80C2×C3×C3⋊C8—21no—
81#1907—91noSylow
82C2×C3×#41—21no—
83C2×C3×#41C2×D311yescharacteristic
84C2×C3×#41C2×D311yescharacteristic
85C22×C3×D4—31no—
86C22×D12C2×D311yescharacteristic
87C3×AGL(1,ℤ/8)—34no—
88C3×AGL(1,ℤ/8)—62no—
89C2×C3×SD16—61no—
90C2×C3×D8—61no—
91C2×C3×M16—31no—
92C2×C3×M16—31no—
93C2×C3×C4⋊C4—31no—
94#949—22no—
95#949Dic314yescomplemented
96#948—62no—
97#948—62no—
98#948—64no—
99#948—64no—
100#948—62no—
101#948—62no—
102C2×#215—21no—
103C2×#213—21no—
104C2×C4⋊Dic3C2×D311yescharacteristic
105C2×#208—31no—
106C2×#208—31no—
107C2×#208—61no—
108C2×#208—61no—
109C2×#208—61no—
110C2×#208—62no—
111C2×#208C2×D311yescharacteristic
112C2×#208C2×D311yescharacteristic
113C22×C3⋊C8—31no—
114C22×C3⋊C8—31no—
115C22×C3⋊C8—61no—
116C22×C3⋊C8—61no—
117C22×C3⋊C8—61no—
118C22×C3⋊C8—62no—
119C3×#103—61no—
120C3×#102—61no—
121#835—21no—
122#833—62no—
123#832—21no—
124#832—61no—
125#832—61no—
126#823—62no—
127#809—61no—
128#809—61no—
129C23×C32—21no—
130C23×C32#4111yescharacteristic
131C22×C3×D3—22no—
132C22×C3×D3—41no—
133C22×C3×D3—41no—
134C22×C3×D3—81no—
135C22×C3×D3—81no—
136C32×Q8—21no—
137C32×Q8C22⋊C412yes—
138C32×D4—22no—
139C32×D4—22no—
140C32×D4—21no—
141C32×D4C22⋊C412yes—
142C2×C32×C4—21no—
143C2×C32×C4—22no—
144C2×C32×C4—22no—
145C2×C32×C4C22×C411yescharacteristic
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4C2×D411yescharacteristic
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4#4111yescharacteristic
151C2×C3×Dic3—41no—
152C2×C3×Dic3—81no—
153C3×D12—22no—
154C3×D12—22no—
155C3×D12—41no—
156C3×D12—41no—
157C3⋊(C3⋊C8)—21no—
158C3⋊(C3⋊C8)—22no—
159C3⋊(C3⋊C8)—21no—
160C3×C3⋊C8—22no—
161C3×C3⋊C8—41no—
162C2×AGL(1,ℤ/8)—31no—
163C2×#131—91no—
164#417—31no—
165C2×#102—91no—
166C2×#100—91no—
167#343—91no—
168#341—91no—
169C24×C3—61no—
170C23×D3—21no—
171C3×#41—22no—
172C3×#41—22no—
173C3×#41—21no—
174C3×#41—21no—
175C3×#41—21no—
176C3×#41—21no—
177C3×#41—22no—
178C3×#41—22no—
179C3×#41C4×D312yes—
180C3×#41D1212yes—
181C3×#41C2×Dic312yes—
182C3×#41#6712yes—
183C2×C3×Q8—21no—
184C2×C3×Q8#6711yescharacteristic
185C2×C3×Q8#6711yescharacteristic
186C2×C3×D4—22no—
187C2×C3×D4—21no—
188C2×C3×D4—21no—
189C2×C3×D4—21no—
190C2×C3×D4—32no—
191C2×C3×D4—61no—
192C2×C3×D4—61no—
193C2×C3×D4—61no—
194C2×C3×D4—61no—
195C2×C3×D4—61no—
196C2×C3×D4#6711yescharacteristic
197C2×C3×D4#6711yescharacteristic
198C22×C3×C4—22no—
199C22×C3×C4—21no—
200C22×C3×C4—21no—
201C22×C3×C4—21no—
202C22×C3×C4—61no—
203C22×C3×C4C22×D311yescharacteristic
204C22×C3×C4C22×D311yescharacteristic
205C22×Dic3—21no—
206C2×D12—21no—
207C2×D12—21no—
208C2×D12—21no—
209C2×D12—21no—
210C2×D12—21no—
211C2×D12C2×Dic312yes—
212C3×SD16—64no—
213C3×D8—64no—
214C3×M16—32no—
215C3×M16—61no—
216C3×M16—61no—
217C3×M16—61no—
218C2×C3×C8—61no—
219C2×C3×C8—61no—
220C3×C4⋊C4—61no—
221C3×C4⋊C4—61no—
222#215—24no—
223#213—24no—
224C4⋊Dic3—21no—
225C4⋊Dic3—21no—
226#208—21no—
227#208—21no—
228#208—21no—
229#208—32no—
230#208—32no—
231#208—62no—
232#208—68no—
233#208—64no—
234#208—64no—
235#208—62no—
236#208—61no—
237#208—61no—
238#208C2×Dic312yes—
239C2×C3⋊C8—21no—
240C2×C3⋊C8—21no—
241C2×C3⋊C8—31no—
242C2×C3⋊C8—31no—
243C2×C3⋊C8—31no—
244C2×C3⋊C8—31no—
245C2×C3⋊C8—61no—
246C2×C3⋊C8—61no—
247C2×C3⋊C8—62no—
248C2×C3⋊C8—68no—
249C2×C3⋊C8—64no—
250C2×C3⋊C8—64no—
251C2×C3⋊C8—62no—
252C2×C3⋊C8—62no—
253C2×C3⋊C8—61no—
254C2×C3⋊C8—61no—
255C2×C3⋊C8—61no—
256C2×C3⋊C8—61no—
257C2×C3⋊C8—61no—
258C2×C3⋊C8—61no—
259C22×C32—22no—
260C22×C32—21no—
261C22×C32—21no—
262C22×C32—41no—
263C22×C32—41no—
264C22×C32C4×D411yescharacteristic
265C22×C32#12111yescharacteristic
266C22×C32#12311yescharacteristic
267C2×C3×D3—42no—
268C2×C3×D3—82no—
269C2×C3×D3—81no—
270C2×C3×D3—81no—
271C2×C3×D3—82no—
272C32×C4—22no—
273C32×C4C2×C22⋊C411yescharacteristic
274C32×C4C4×D411yescharacteristic
275C32×C4#12011yescharacteristic
276C32×C4#12111yescharacteristic
277C3×Dic3—81no—
278C2×#41D3211yescharacteristic
279C22×D4—31no—
280AGL(1,ℤ/8)—34no—
281AGL(1,ℤ/8)—62no—
282C2×SD16—61no—
283C2×D8—61no—
284#131—182no—
285#131—182no—
286C2×M16—31no—
287C2×M16—31no—
288C2×M16—91no—
289C2×M16—181no—
290C22×C8—91no—
291C22×C8—181no—
292C2×C4⋊C4—31no—
293#103—61no—
294#102—61no—
295#102—181no—
296#102—181no—
297#100—182no—
298C23×C3—22no—
299C23×C3—21no—
300C23×C3—21no—
301C23×C3—21no—
302C23×C3—62no—
303C23×C3—121no—
304C23×C3—121no—
305C23×C3—241no—
306C23×C3—241no—
307C23×C3#23711yescharacteristic
308C23×C3#23711yescharacteristic
309C22×D3—22no—
310C22×D3—41no—
311C22×D3—41no—
312C22×D3—81no—
313C22×D3—81no—
314C3×Q8—22no—
315C3×Q8—21no—
316C3×Q8—21no—
317C3×Q8—22no—
318C3×Q8(C2×D3)⋊C412yes—
319C3×Q8#21712yes—
320C3×D4—24no—
321C3×D4—24no—
322C3×D4—22no—
323C3×D4—22no—
324C3×D4—22no—
325C3×D4—22no—
326C3×D4—22no—
327C3×D4—21no—
328C3×D4—21no—
329C3×D4—22no—
330C3×D4—62no—
331C3×D4—62no—
332C3×D4—121no—
333C3×D4—121no—
334C3×D4(C2×D3)⋊C412yes—
335C3×D4#21712yes—
336C2×C3×C4—24no—
337C2×C3×C4—22no—
338C2×C3×C4—24no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—22no—
342C2×C3×C4—22no—
343C2×C3×C4—22no—
344C2×C3×C4—22no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—121no—
352C2×C3×C4—241no—
353C2×C3×C4C2×C4×D311yescharacteristic
354C2×C3×C4C2×D1211yescharacteristic
355C2×C3×C4D3×D411yescharacteristic
356C2×C3×C4D3×D411yescharacteristic
357C2×C3×C4D3×D411yescharacteristic
358C2×C3×C4D3×D411yescharacteristic
359C2×C3×C4#23711yescharacteristic
360C2×C3×C4#23711yescharacteristic
361C2×C3×C4C22×Dic311yescharacteristic
362C2×C3×C4C2×#6711yescharacteristic
363C2×C3×C4C2×#6711yescharacteristic
364C2×C3×C4C2×#6711yescharacteristic
365C2×Dic3—41no—
366C2×Dic3—81no—
367D12—22no—
368D12—22no—
369D12—41no—
370D12—41no—
371C3×C8—62no—
372C3×C8—121no—
373C3⋊C8—22no—
374C3⋊C8—41no—
375C3⋊C8—62no—
376C3⋊C8—62no—
377C3⋊C8—64no—
378C3⋊C8—61no—
379C3⋊C8—61no—
380C3⋊C8—62no—
381C3⋊C8—61no—
382C3⋊C8—61no—
383C3⋊C8—62no—
384C2×C32—21no—
385C2×C32—21no—
386C2×C32—42no—
387C2×C32#38611yescharacteristic
388C2×C32#47111yescharacteristic
389C2×C32#47211yescharacteristic
390C3×D3—82no—
391C24—61no—
392#41—21no—
393#41—21no—
394#41D3×Dic312yes—
395#41#62612yes—
396C2×Q8#62511yescharacteristic
397C2×D4—21no—
398C2×D4—32no—
399C2×D4—61no—
400C2×D4—61no—
401C2×D4—61no—
402C2×D4—61no—
403C2×D4—61no—
404C2×D4#62511yescharacteristic
405C22×C4—21no—
406C22×C4—61no—
407C22×C4C2×D3211yescharacteristic
408SD16—64no—
409D8—64no—
410M16—32no—
411M16—61no—
412M16—61no—
413M16—61no—
414M16—92no—
415M16—184no—
416M16—181no—
417C2×C8—61no—
418C2×C8—61no—
419C2×C8—91no—
420C2×C8—91no—
421C2×C8—184no—
422C2×C8—181no—
423C2×C8—181no—
424C2×C8—181no—
425C4⋊C4—61no—
426C4⋊C4—61no—
427C22×C3—21no—
428C22×C3—21no—
429C22×C3—21no—
430C22×C3—21no—
431C22×C3—24no—
432C22×C3—22no—
433C22×C3—22no—
434C22×C3—21no—
435C22×C3—21no—
436C22×C3—21no—
437C22×C3—41no—
438C22×C3—41no—
439C22×C3—42no—
440C22×C3—42no—
441C22×C3—41no—
442C22×C3—41no—
443C22×C3—41no—
444C22×C3—41no—
445C22×C3—122no—
446C22×C3—242no—
447C22×C3—242no—
448C22×C3—241no—
449C22×C3—241no—
450C22×C3#67⋊C411yescharacteristic
451C22×C3#88611yescharacteristic
452C22×C3D4×Dic311yescharacteristic
453C22×C3#93511yescharacteristic
454C22×C3#93911yescharacteristic
455C22×C3#93911yescharacteristic
456C2×D3—42no—
457C2×D3—82no—
458C2×D3—81no—
459C2×D3—81no—
460C2×D3—82no—
461C3×C4—24no—
462C3×C4—22no—
463C3×C4—22no—
464C3×C4—21no—
465C3×C4—21no—
466C3×C4—21no—
467C3×C4—21no—
468C3×C4—241no—
469C3×C4#67⋊C411yescharacteristic
470C3×C4#88211yescharacteristic
471C3×C4C2×(C2×D3)⋊C411yescharacteristic
472C3×C4D4×Dic311yescharacteristic
473C3×C4#93711yescharacteristic
474C3×C4#93911yescharacteristic
475C3×C4#93911yescharacteristic
476C3×C4C2×#21711yescharacteristic
477Dic3—81no—
478C32#190711yescharacteristic, complemented, Sylow
479C23—21no—
480C23—62no—
481C23—121no—
482C23—121no—
483C23—241no—
484C23—241no—
485C23#380511yescharacteristic
486Q8—21no—
487Q8(C2×D3)⋊Dic312yes—
488D4—22no—
489D4—22no—
490D4—21no—
491D4—62no—
492D4—62no—
493D4—121no—
494D4—121no—
495D4(C2×D3)⋊Dic312yes—
496C2×C4—21no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—121no—
500C2×C4—241no—
501C2×C4C2×D3×Dic311yescharacteristic
502C2×C4#380511yescharacteristic
503C2×C4C2×#62511yescharacteristic
504C2×C4C2×#62611yescharacteristic
505C2×C4#381111yescharacteristic
506C2×C4#381111yescharacteristic
507C8—62no—
508C8—121no—
509C8—181no—
510C8—181no—
511C8—182no—
512C2×C3—21no—
513C2×C3—21no—
514C2×C3—21no—
515C2×C3—21no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—41no—
520C2×C3—41no—
521C2×C3—44no—
522C2×C3—42no—
523C2×C3—42no—
524C2×C3—242no—
525C2×C3#495811yescharacteristic
526C2×C3#519911yescharacteristic
527C2×C3#519911yescharacteristic
528C2×C3#520011yescharacteristic
529C2×C3#520311yescharacteristic
530C2×C3#522011yescharacteristic
531D3—82no—
532C22—21no—
533C22—21no—
534C22—22no—
535C22—41no—
536C22—41no—
537C22—122no—
538C22—242no—
539C22—242no—
540C22—241no—
541C22—241no—
542C22#6396211yescharacteristic
543C22#67⋊Dic311yescharacteristic
544C22#6398011yescharacteristic
545C4—22no—
546C4—241no—
547C4C2×(C2×D3)⋊Dic311yescharacteristic
548C4#67⋊Dic311yescharacteristic
549C4#6398011yescharacteristic
550C4#6398111yescharacteristic
551C3—21no—
552C3#7030311yescharacteristic, complemented
553C3#7209111yescharacteristic, complemented
554C2—21no—
555C2—21no—
556C2—42no—
557C2—242no—
558C2#1059167811yescharacteristic
559C2#1059168111yescharacteristic
560C2#1059171311yescharacteristic
subgroupG/H
centerC22#63980
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×#41C22
socleC22×C32#121
prime radicalC2×C3×#949C2
cosocleC22×C32×C4C23
hypercenterC2×#41D32
hypocenterC32#1907
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#64157C2semidirect
3. C3×#5232C2semidirect
4. C2×#63562C2semidirect
5. C2×#63558C2semidirect
6. #10589167C2semidirect
7. #10589165C2semidirect
19. C3×#949C4semidirect
36. #5232D3semidirect
95. #949Dic3semidirect
478. C32#1907semidirect
552. C3#70303semidirect
553. C3#72091semidirect

Maximal subgroups

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

subgroupindex
C2×#641572
C2×C3×#9492
C3×#52322
C2×#635622
C2×#635582
#105891672
#105891652
#720913
#703033