Finite Group Databasebeta

← #11791492

Subgroups — #11791492

Order 1152.

789 conjugacy classes of subgroups.

The subgroup lattice has 593 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63864C211yesmaximal, characteristic
2C2×#63636C211yesmaximal, characteristic
3C3×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
4C2×C3×#810C211yesmaximal, characteristic, complemented
5C2×Dic3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6C2×#63565C211yesmaximal, characteristic, complemented
7C2×#63564C211yesmaximal, characteristic
8#70230—31nomaximal
9#69488—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×C4×Dic3—21no—
16C2×C3×C4×Dic3C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C2×#3722—21no—
19C2×#3722—21no—
20#63864—22no—
21#63864C414yescomplemented
22#63636—22no—
23C3×C3⋊#95—21no—
24C3×#810—22no—
25Dic3⋊(C3⋊C8)—22no—
26#63565—22no—
27#63564—22no—
28C2×#947—31no—
29C2×#875—31no—
30C2×C3×#103—31no—
31C3×C4×C4⋊C4—31no—
32C2×#835—31no—
33C2×#821—31no—
34C2×Dic3⋊C8—31no—
35Dic3×C4⋊C4D311yescharacteristic, complemented
36C2×#810—31no—
37C2×#810D311yescharacteristic, complemented
38C2×#809—31no—
39C2×#809—31no—
40C2×#809—31no—
41C2×#809—61no—
42C2×C4⋊(C3⋊C8)—31no—
43C23×C3⋊D3—21no—
44C22×C32×C4—21no—
45C22×C32×C4C2311yescharacteristic
46C2×C4⋊(C3⋊D3)—21no—
47C2×C4⋊(C3⋊D3)—21no—
48C2×C4⋊(C3⋊D3)—21no—
49C2×C4⋊(C3⋊D3)—21no—
50C2×C4⋊(C3⋊D3)—21no—
51C2×C4⋊(C3⋊D3)C2×C412yes—
52C22×C3×Dic3—21no—
53C22×C3×Dic3—21no—
54C22×C3×Dic3D411yescharacteristic
55C22×C3×Dic3D411yescharacteristic
56C2×C3×Dic6—21no—
57C2×C3×Dic6—21no—
58C2×C3×Dic6—21no—
59C2×C3×Dic6—21no—
60C2×C3×Dic6—21no—
61C2×C3×Dic6C2×C412yes—
62C32×C4⋊C4—21no—
63C32×C4⋊C4D412yes—
64C2×C3⋊(C3⋊C8)—21no—
65C2×C3⋊(C3⋊C8)—21no—
66C2×C3⋊(C3⋊C8)—21no—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3D412yes—
69C3×C4×Dic3—42no—
70C3×C4×Dic3C2×C412yes—
71C3×C4×Dic3D412yes—
72C2×C3×C3⋊C8—21no—
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8—21no—
75#3722—24no—
76#3722—24no—
77#1983—91noSylow
78C22×C3×Q8—31no—
79C22×D12—31no—
80C22×D12—31no—
81C22×D12—61no—
82C22×Dic6C2×D311yescharacteristic
83C22×C3×C8—31no—
84C2×C3×C4⋊C4—21no—
85C2×C3×C4⋊C4—31no—
86C2×C3×C4⋊C4C2×D311yescharacteristic
87C2×C3×C4⋊C4C2×D311yescharacteristic
88C2×C3×C42—31no—
89C2×C3×C42—61no—
90#947—34no—
91#947—62no—
92C2×(C2×D3)⋊C4—61no—
93C2×(C2×D3)⋊C4—61no—
94C2×(C2×D3)⋊C4—61no—
95C2×(C2×D3)⋊C4—61no—
96C2×C4⋊Dic3C2×D311yescharacteristic
97C2×C4×Dic3—21no—
98C2×C4×Dic3C2×D311yescharacteristic
99C22×C3⋊C8—31no—
100C22×C3⋊C8—31no—
101C22×C3⋊C8—61no—
102C22×C3⋊C8C2×D311yescharacteristic
103#875—34no—
104#875—62no—
105C3×#103—62no—
106C3×#95—61no—
107#835—62no—
108C3⋊#95—21no—
109#821—62no—
110Dic3⋊C8—62no—
111#810—22no—
112#810—62no—
113#809—62no—
114#809—64no—
115#809—62no—
116#809—62no—
117C4⋊(C3⋊C8)—62no—
118C23×C32C2×D411yescharacteristic
119C22×C3⋊D3—22no—
120C22×C3⋊D3—41no—
121C22×C3⋊D3—41no—
122C22×C3⋊D3—41no—
123C22×C3⋊D3—41no—
124C22×C3⋊D3—41no—
125C22×C3⋊D3—41no—
126C2×C32×C4—22no—
127C2×C32×C4—41no—
128C2×C32×C4—41no—
129C2×C32×C4C22×C411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4#4111yescharacteristic
134C2×C32×C4#4111yescharacteristic
135C4⋊(C3⋊D3)—22no—
136C4⋊(C3⋊D3)—22no—
137C4⋊(C3⋊D3)—41no—
138C4⋊(C3⋊D3)—41no—
139C2×C3×Dic3—21no—
140C2×C3×Dic3—21no—
141C2×C3×Dic3—21no—
142C2×C3×Dic3—21no—
143C2×C3×Dic3—22no—
144C2×C3×Dic3—22no—
145C2×C3×Dic3—41no—
146C2×C3×Dic3—41no—
147C2×C3×Dic3—41no—
148C2×C3×Dic3—41no—
149C2×C3×Dic3C22⋊C412yes—
150C2×C3×Dic3C22⋊C412yes—
151C3×Dic6—22no—
152C3×Dic6—22no—
153C3×Dic6—41no—
154C3×Dic6—41no—
155C3⋊(C3⋊C8)—41no—
156C3×C3⋊C8—41no—
157C2×#124—91no—
158C2×C4⋊C8—91no—
159C2×#103—31no—
160C2×#103—91no—
161C2×#102—91no—
162C2×#102—91no—
163C4×C4⋊C4—31no—
164C23×D3—61no—
165C23×D3—61no—
166C23×D3—121no—
167C2×C3×Q8—32no—
168C2×C3×Q8—61no—
169C2×C3×Q8—61no—
170C2×C3×Q8—61no—
171C2×C3×Q8—61no—
172C2×C3×Q8—61no—
173C22×C3×C4—21no—
174C22×C3×C4—21no—
175C22×C3×C4—21no—
176C22×C3×C4—31no—
177C22×C3×C4—31no—
178C22×C3×C4—41no—
179C22×C3×C4—61no—
180C22×C3×C4—61no—
181C22×C3×C4C22×D311yescharacteristic
182C22×C3×C4C22×D311yescharacteristic
183C22×Dic3—21no—
184C22×Dic3—21no—
185C22×Dic3#6711yescharacteristic
186C22×Dic3#6711yescharacteristic
187C2×D12—32no—
188C2×D12—32no—
189C2×D12—62no—
190C2×D12—62no—
191C2×D12—62no—
192C2×D12—61no—
193C2×D12—61no—
194C2×D12—61no—
195C2×D12—61no—
196C2×D12—61no—
197C2×D12—61no—
198C2×D12—61no—
199C2×D12—61no—
200C2×D12—61no—
201C2×D12—61no—
202C2×D12—121no—
203C2×D12—121no—
204C2×D12—121no—
205C2×Dic6—21no—
206C2×Dic6—21no—
207C2×Dic6—21no—
208C2×Dic6—21no—
209C2×Dic6—21no—
210C2×Dic6C4×D312yes—
211C2×C3×C8—61no—
212C2×C3×C8—61no—
213C2×C3×C8—61no—
214C3×C4⋊C4—21no—
215C3×C4⋊C4—21no—
216C3×C4⋊C4—22no—
217C3×C4⋊C4—32no—
218C3×C4⋊C4—41no—
219C3×C4⋊C4—61no—
220C3×C4⋊C4D1212yes—
221C3×C4⋊C4#6712yes—
222C3×C42—32no—
223C3×C42—32no—
224C3×C42—122no—
225(C2×D3)⋊C4—64no—
226(C2×D3)⋊C4—64no—
227(C2×D3)⋊C4—64no—
228(C2×D3)⋊C4—64no—
229C4⋊Dic3—21no—
230C4⋊Dic3D1212yes—
231C4×Dic3—42no—
232C4×Dic3C4×D312yes—
233C4×Dic3D1212yes—
234C2×C3⋊C8—21no—
235C2×C3⋊C8—21no—
236C2×C3⋊C8—21no—
237C2×C3⋊C8—62no—
238C2×C3⋊C8—61no—
239C2×C3⋊C8—61no—
240C2×C3⋊C8—61no—
241C2×C3⋊C8—61no—
242C2×C3⋊C8—61no—
243C2×C3⋊C8—61no—
244C2×C3⋊C8—121no—
245C2×C3⋊C8—121no—
246C22×C32C2×C22⋊C411yescharacteristic
247C22×C32#12111yescharacteristic
248C22×C32#12111yescharacteristic
249C22×C32#13511yescharacteristic
250C22×C32#13511yescharacteristic
251C22×C32AGL(1,ℤ/8)11yescharacteristic
252C22×C32#13711yescharacteristic
253C2×C3⋊D3—42no—
254C2×C3⋊D3—42no—
255C2×C3⋊D3—42no—
256C2×C3⋊D3—81no—
257C2×C3⋊D3—81no—
258C2×C3⋊D3—81no—
259C2×C3⋊D3—81no—
260C32×C4—42no—
261C32×C4C4×D411yescharacteristic
262C32×C4C4×D411yescharacteristic
263C32×C4#12411yescharacteristic
264C32×C4#12711yescharacteristic
265C3×Dic3—22no—
266C3×Dic3—22no—
267C3×Dic3—42no—
268C3×Dic3—42no—
269C22×Q8—31no—
270C22×D4—91no—
271C22×C8—31no—
272C22×C8—91no—
273#124—94no—
274#124—182no—
275C2×C4⋊C4—31no—
276C2×C4⋊C4D3211yescharacteristic
277C2×C22⋊C4—181no—
278C2×C22⋊C4—181no—
279C2×C42—31no—
280C2×C42—61no—
281C4⋊C8—182no—
282#103—62no—
283#103—182no—
284#102—182no—
285#102—182no—
286#95—61no—
287C23×C3—21no—
288C23×C3D3×D411yescharacteristic
289C23×C3C2×#6711yescharacteristic
290C22×D3—62no—
291C22×D3—62no—
292C22×D3—122no—
293C22×D3—122no—
294C22×D3—122no—
295C22×D3—121no—
296C22×D3—121no—
297C22×D3—121no—
298C22×D3—121no—
299C22×D3—121no—
300C22×D3—121no—
301C22×D3—121no—
302C22×D3—121no—
303C22×D3—121no—
304C22×D3—121no—
305C22×D3—121no—
306C22×D3—121no—
307C22×D3—241no—
308C22×D3—241no—
309C22×D3—241no—
310C22×D3—241no—
311C3×Q8—62no—
312C3×Q8—62no—
313C3×Q8—121no—
314C3×Q8—121no—
315C2×C3×C4—22no—
316C2×C3×C4—22no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—21no—
322C2×C3×C4—21no—
323C2×C3×C4—32no—
324C2×C3×C4—32no—
325C2×C3×C4—42no—
326C2×C3×C4—41no—
327C2×C3×C4—41no—
328C2×C3×C4—41no—
329C2×C3×C4—41no—
330C2×C3×C4—61no—
331C2×C3×C4—61no—
332C2×C3×C4—61no—
333C2×C3×C4—61no—
334C2×C3×C4—62no—
335C2×C3×C4—62no—
336C2×C3×C4—81no—
337C2×C3×C4—81no—
338C2×C3×C4—121no—
339C2×C3×C4—121no—
340C2×C3×C4—121no—
341C2×C3×C4—121no—
342C2×C3×C4C2×C4×D311yescharacteristic
343C2×C3×C4C2×C4×D311yescharacteristic
344C2×C3×C4C2×D1211yescharacteristic
345C2×C3×C4C2×D1211yescharacteristic
346C2×C3×C4C2×D1211yescharacteristic
347C2×C3×C4#23511yescharacteristic
348C2×C3×C4#23511yescharacteristic
349C2×C3×C4#23511yescharacteristic
350C2×C3×C4D3×D411yescharacteristic
351C2×C3×C4D3×D411yescharacteristic
352C2×C3×C4#23711yescharacteristic
353C2×C3×C4C2×#6711yescharacteristic
354C2×Dic3—21no—
355C2×Dic3—21no—
356C2×Dic3—21no—
357C2×Dic3—21no—
358C2×Dic3—22no—
359C2×Dic3—22no—
360C2×Dic3—41no—
361C2×Dic3—41no—
362C2×Dic3—41no—
363C2×Dic3—41no—
364C2×Dic3(C2×D3)⋊C412yes—
365C2×Dic3(C2×D3)⋊C412yes—
366D12—64no—
367D12—62no—
368D12—62no—
369D12—62no—
370D12—62no—
371D12—122no—
372D12—122no—
373D12—122no—
374D12—121no—
375D12—121no—
376D12—121no—
377D12—121no—
378Dic6—22no—
379Dic6—22no—
380Dic6—41no—
381Dic6—41no—
382C3×C8—121no—
383C3⋊C8—41no—
384C3⋊C8—122no—
385C3⋊C8—121no—
386C3⋊C8—121no—
387C2×C32#39011yescharacteristic
388C2×C32#41611yescharacteristic
389C2×C32#41711yescharacteristic
390C2×C32#46311yescharacteristic
391C2×C32#46311yescharacteristic
392C2×C32#46411yescharacteristic
393C2×C32#46411yescharacteristic
394C3⋊D3—82no—
395C24—181no—
396C2×Q8—32no—
397C2×Q8—61no—
398C2×Q8—61no—
399C2×Q8—61no—
400C2×Q8—61no—
401C2×Q8—61no—
402C2×D4—92no—
403C2×D4—181no—
404C2×D4—181no—
405C2×D4—181no—
406C2×D4—181no—
407C2×D4—181no—
408C22×C4—21no—
409C22×C4—31no—
410C22×C4—31no—
411C22×C4—61no—
412C22×C4—61no—
413C22×C4C2×D3211yescharacteristic
414C2×C8—61no—
415C2×C8—61no—
416C2×C8—61no—
417C2×C8—181no—
418C2×C8—181no—
419C2×C8—181no—
420C4⋊C4—21no—
421C4⋊C4—32no—
422C4⋊C4—61no—
423C4⋊C4#62612yes—
424C22⋊C4—184no—
425C22⋊C4—184no—
426C42—32no—
427C42—32no—
428C42—122no—
429C22×C3—21no—
430C22×C3—21no—
431C22×C3—21no—
432C22×C3—21no—
433C22×C3—21no—
434C22×C3—21no—
435C22×C3—21no—
436C22×C3D3×C22⋊C411yescharacteristic
437C22×C3#88411yescharacteristic
438C22×C3#91411yescharacteristic
439C22×C3#91611yescharacteristic
440C22×C3#91811yescharacteristic
441C22×C3#91911yescharacteristic
442C22×C3C2×(C2×D3)⋊C411yescharacteristic
443C22×C3#93011yescharacteristic
444C22×C3#93011yescharacteristic
445C22×C3#93211yescharacteristic
446C22×C3#93911yescharacteristic
447C22×C3#94211yescharacteristic
448C22×C3#95011yescharacteristic
449C22×C3#95011yescharacteristic
450C2×D3—124no—
451C2×D3—122no—
452C2×D3—122no—
453C2×D3—122no—
454C2×D3—122no—
455C2×D3—122no—
456C2×D3—122no—
457C2×D3—242no—
458C2×D3—242no—
459C2×D3—242no—
460C2×D3—242no—
461C2×D3—242no—
462C2×D3—242no—
463C2×D3—241no—
464C2×D3—241no—
465C2×D3—241no—
466C2×D3—241no—
467C2×D3—241no—
468C2×D3—241no—
469C2×D3—241no—
470C2×D3—241no—
471C3×C4—21no—
472C3×C4—21no—
473C3×C4—21no—
474C3×C4—21no—
475C3×C4—42no—
476C3×C4—42no—
477C3×C4—62no—
478C3×C4—62no—
479C3×C4—82no—
480C3×C4—122no—
481C3×C4—122no—
482C3×C4C4×D1211yescharacteristic
483C3×C4C4×D1211yescharacteristic
484C3×C4#87411yescharacteristic
485C3×C4#87511yescharacteristic
486C3×C4#67⋊C411yescharacteristic
487C3×C4#88511yescharacteristic
488C3×C4C4×#6711yescharacteristic
489C3×C4#94011yescharacteristic
490Dic3—22no—
491Dic3—22no—
492Dic3—42no—
493Dic3—42no—
494C32#198311yescharacteristic, complemented, Sylow
495C23—182no—
496C23—361no—
497C23—361no—
498C23—361no—
499C23—361no—
500C23—361no—
501C23—361no—
502C23D3×#6711yescharacteristic
503Q8—62no—
504Q8—62no—
505Q8—121no—
506Q8—121no—
507D4—182no—
508D4—182no—
509D4—361no—
510D4—361no—
511C2×C4—22no—
512C2×C4—32no—
513C2×C4—32no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—61no—
517C2×C4—61no—
518C2×C4—61no—
519C2×C4—61no—
520C2×C4—62no—
521C2×C4—62no—
522C2×C4—121no—
523C2×C4—121no—
524C2×C4—121no—
525C2×C4—121no—
526C2×C4#379811yescharacteristic
527C2×C4C4×D3211yescharacteristic
528C2×C4D3×D1211yescharacteristic
529C2×C4D3×D1211yescharacteristic
530C2×C4#380411yescharacteristic
531C2×C4C2×#62611yescharacteristic
532C8—121no—
533C8—361no—
534C2×C3—21no—
535C2×C3—21no—
536C2×C3—21no—
537C2×C3—21no—
538C2×C3—21no—
539C2×C3—21no—
540C2×C3—21no—
541C2×C3#479811yescharacteristic
542C2×C3#480311yescharacteristic
543C2×C3#480411yescharacteristic
544C2×C3#481911yescharacteristic
545C2×C3#493911yescharacteristic
546C2×C3#495711yescharacteristic
547C2×C3#496611yescharacteristic
548C2×C3#500211yescharacteristic
549C2×C3#501611yescharacteristic
550C2×C3#501611yescharacteristic
551C2×C3#502811yescharacteristic
552C2×C3#502811yescharacteristic
553C2×C3#516511yescharacteristic
554C2×C3#518511yescharacteristic
555D3—244no—
556D3—242no—
557D3—242no—
558C22—362no—
559C22—362no—
560C22—362no—
561C22—721no—
562C22—721no—
563C22—721no—
564C22—721no—
565C22#6390611yescharacteristic
566C22D3×(C2×D3)⋊C411yescharacteristic
567C22#6393411yescharacteristic
568C22#6393511yescharacteristic
569C22#6394811yescharacteristic
570C22#6394911yescharacteristic
571C22#6397811yescharacteristic
572C4—42no—
573C4—62no—
574C4—62no—
575C4—122no—
576C4—122no—
577C4#6385211yescharacteristic
578C4#6388011yescharacteristic
579C4C4×#62611yescharacteristic
580C4#6391111yescharacteristic
581C3—21no—
582C3#6948811yescharacteristic, complemented
583C3#7023011yescharacteristic, complemented
584C2—722no—
585C2#1059053411yescharacteristic
586C2#1059053611yescharacteristic
587C2#1059060911yescharacteristic
588C2#1059061011yescharacteristic
589C2#1059138311yescharacteristic
590C2#1059147111yescharacteristic
591C2#1059160711yescharacteristic
subgroupG/H
centerC23D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1983
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C3×Dic3×C4⋊C4C2semidirect
4. C2×C3×#810C2semidirect
5. C2×Dic3⋊(C3⋊C8)C2semidirect
6. C2×#63565C2semidirect
21. #63864C4semidirect
35. Dic3×C4⋊C4D3semidirect
37. C2×#810D3semidirect
494. C32#1983semidirect
582. C3#69488semidirect
583. C3#70230semidirect

Maximal subgroups

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

subgroupindex
C2×#638642
C2×#636362
C3×Dic3×C4⋊C42
C2×C3×#8102
C2×Dic3⋊(C3⋊C8)2
C2×#635652
C2×#635642
#702303
#694883