Finite Group Databasebeta

← #11791490

Subgroups — #11791490

Order 1152.

769 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63860C211yesmaximal, characteristic
2C2×#63637C211yesmaximal, characteristic, complemented
3C3×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
4C2×C3×#809C211yesmaximal, characteristic
5C2×Dic3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6C2×#63567C211yesmaximal, characteristic, complemented
7C2×#63562C211yesmaximal, characteristic
8#70162—31nomaximal
9#69488—31nomaximal
10C22×#634C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
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×(C2×D3)⋊Dic3—21no—
19C2×(C2×D3)⋊Dic3—21no—
20#63860—22no—
21#63860C414yescomplemented
22#63637—22no—
23C3×C3⋊#95—21no—
24C3×#809—22no—
25Dic3⋊(C3⋊C8)—22no—
26#63567—22no—
27#63562—22no—
28C2×#936—31no—
29C2×#875—31no—
30C2×C3×#102—31no—
31C3×C4×C4⋊C4—31no—
32C2×#832—31no—
33C2×#816—31no—
34C2×Dic3⋊C8—31no—
35Dic3×C4⋊C4D311yescharacteristic, complemented
36C2×#810—31no—
37C2×#810—31no—
38C2×#810—31no—
39C2×#810—61no—
40C2×#809—31no—
41C2×#809D311yescharacteristic
42C2×C4⋊(C3⋊C8)—31no—
43C23×C3×D3—21no—
44C22×C32×C4—21no—
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3—21no—
47C2×#634—21no—
48C2×#634—21no—
49C2×#634—21no—
50C2×#634—21no—
51C2×#634—21no—
52C2×#634C2×C412yes—
53C22×C3×Dic3—21no—
54C22×C3×Dic3D411yescharacteristic
55C22×C3×Dic3D411yescharacteristic
56C2×C3×D12—21no—
57C2×C3×D12—21no—
58C2×C3×D12—21no—
59C2×C3×D12—21no—
60C2×C3×D12—21no—
61C2×C3×D12C2×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(C2×D3)⋊Dic3—24no—
76(C2×D3)⋊Dic3—24no—
77#1983—91noSylow
78C22×C3×D4—31no—
79C22×D12C2×D311yescharacteristic
80C22×Dic6—31no—
81C22×Dic6—31no—
82C22×Dic6—61no—
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—
90C2×#217—61no—
91C2×#217—61no—
92#936—34no—
93#936—62no—
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×#102—62no—
106C3×#95—61no—
107#832—62no—
108C3⋊#95—21no—
109#816—62no—
110Dic3⋊C8—62no—
111#810—62no—
112#810—64no—
113#810—62no—
114#810—62no—
115#809—22no—
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
135C2×C3⋊Dic3—22no—
136C2×C3⋊Dic3—41no—
137C2×C3⋊Dic3—41no—
138#634—22no—
139#634—22no—
140#634—41no—
141#634—41no—
142C2×C3×Dic3—21no—
143C2×C3×Dic3—21no—
144C2×C3×Dic3—21no—
145C2×C3×Dic3—21no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—41no—
148C2×C3×Dic3—41no—
149C2×C3×Dic3C22⋊C412yes—
150C2×C3×Dic3C22⋊C412yes—
151C3×D12—22no—
152C3×D12—22no—
153C3×D12—41no—
154C3×D12—41no—
155C3⋊(C3⋊C8)—41no—
156C3×C3⋊C8—41no—
157C2×#124—91no—
158C2×C4⋊C8—91no—
159C2×#103—91no—
160C2×#103—91no—
161C2×#102—31no—
162C2×#102—91no—
163C4×C4⋊C4—31no—
164C24×C3—61no—
165C23×D3—21no—
166C2×C3×D4—32no—
167C2×C3×D4—61no—
168C2×C3×D4—61no—
169C2×C3×D4—61no—
170C2×C3×D4—61no—
171C2×C3×D4—61no—
172C22×C3×C4—21no—
173C22×C3×C4—21no—
174C22×C3×C4—21no—
175C22×C3×C4—31no—
176C22×C3×C4—31no—
177C22×C3×C4—41no—
178C22×C3×C4—61no—
179C22×C3×C4C22×D311yescharacteristic
180C22×C3×C4C22×D311yescharacteristic
181C22×Dic3—21no—
182C22×Dic3—61no—
183C22×Dic3—61no—
184C22×Dic3—121no—
185C22×Dic3#6711yescharacteristic
186C22×Dic3#6711yescharacteristic
187C2×D12—21no—
188C2×D12—21no—
189C2×D12—21no—
190C2×D12—21no—
191C2×D12—21no—
192C2×D12C4×D312yes—
193C2×Dic6—32no—
194C2×Dic6—32no—
195C2×Dic6—62no—
196C2×Dic6—62no—
197C2×Dic6—62no—
198C2×Dic6—61no—
199C2×Dic6—61no—
200C2×Dic6—61no—
201C2×Dic6—61no—
202C2×Dic6—61no—
203C2×Dic6—61no—
204C2×Dic6—61no—
205C2×Dic6—61no—
206C2×Dic6—61no—
207C2×Dic6—61no—
208C2×Dic6—121no—
209C2×Dic6—121no—
210C2×Dic6—121no—
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#217—64no—
226#217—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—42no—
266C3×Dic3—22no—
267C3×Dic3—22no—
268C3×Dic3—42no—
269C22×Q8—91no—
270C22×D4—31no—
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—182no—
283#103—182no—
284#102—62no—
285#102—182no—
286#95—61no—
287C23×C3—21no—
288C23×C3—62no—
289C23×C3—121no—
290C23×C3—121no—
291C23×C3—121no—
292C23×C3—121no—
293C23×C3—121no—
294C23×C3—121no—
295C23×C3D3×D411yescharacteristic
296C23×C3C2×#6711yescharacteristic
297C22×D3—22no—
298C22×D3—41no—
299C22×D3—41no—
300C22×D3—41no—
301C22×D3—41no—
302C22×D3—41no—
303C22×D3—41no—
304C3×D4—62no—
305C3×D4—62no—
306C3×D4—121no—
307C3×D4—121no—
308C2×C3×C4—22no—
309C2×C3×C4—22no—
310C2×C3×C4—21no—
311C2×C3×C4—21no—
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—32no—
317C2×C3×C4—32no—
318C2×C3×C4—42no—
319C2×C3×C4—41no—
320C2×C3×C4—41no—
321C2×C3×C4—41no—
322C2×C3×C4—41no—
323C2×C3×C4—61no—
324C2×C3×C4—61no—
325C2×C3×C4—61no—
326C2×C3×C4—61no—
327C2×C3×C4—62no—
328C2×C3×C4—81no—
329C2×C3×C4—81no—
330C2×C3×C4—121no—
331C2×C3×C4—121no—
332C2×C3×C4C2×C4×D311yescharacteristic
333C2×C3×C4C2×C4×D311yescharacteristic
334C2×C3×C4C2×D1211yescharacteristic
335C2×C3×C4C2×D1211yescharacteristic
336C2×C3×C4C2×D1211yescharacteristic
337C2×C3×C4#23511yescharacteristic
338C2×C3×C4#23511yescharacteristic
339C2×C3×C4#23511yescharacteristic
340C2×C3×C4D3×D411yescharacteristic
341C2×C3×C4D3×D411yescharacteristic
342C2×C3×C4#23711yescharacteristic
343C2×C3×C4C2×#6711yescharacteristic
344C2×Dic3—21no—
345C2×Dic3—21no—
346C2×Dic3—21no—
347C2×Dic3—21no—
348C2×Dic3—22no—
349C2×Dic3—41no—
350C2×Dic3—41no—
351C2×Dic3—62no—
352C2×Dic3—62no—
353C2×Dic3—122no—
354C2×Dic3—122no—
355C2×Dic3—122no—
356C2×Dic3—121no—
357C2×Dic3—121no—
358C2×Dic3—121no—
359C2×Dic3—121no—
360C2×Dic3(C2×D3)⋊C412yes—
361C2×Dic3(C2×D3)⋊C412yes—
362D12—22no—
363D12—22no—
364D12—41no—
365D12—41no—
366Dic6—64no—
367Dic6—62no—
368Dic6—62no—
369Dic6—62no—
370Dic6—62no—
371Dic6—122no—
372Dic6—122no—
373Dic6—122no—
374Dic6—121no—
375Dic6—121no—
376Dic6—121no—
377Dic6—121no—
378C3×C8—121no—
379C3⋊C8—41no—
380C3⋊C8—122no—
381C3⋊C8—121no—
382C3⋊C8—121no—
383C2×C32#39011yescharacteristic
384C2×C32#41611yescharacteristic
385C2×C32#41711yescharacteristic
386C2×C32#46311yescharacteristic
387C2×C32#46311yescharacteristic
388C2×C32#46411yescharacteristic
389C2×C32#46411yescharacteristic
390C3×D3—82no—
391C24—61no—
392C2×Q8—92no—
393C2×Q8—181no—
394C2×Q8—181no—
395C2×Q8—181no—
396C2×Q8—181no—
397C2×Q8—181no—
398C2×D4—32no—
399C2×D4—61no—
400C2×D4—61no—
401C2×D4—61no—
402C2×D4—61no—
403C2×D4—61no—
404C22×C4—21no—
405C22×C4—31no—
406C22×C4—31no—
407C22×C4—61no—
408C22×C4—181no—
409C22×C4C2×D3211yescharacteristic
410C2×C8—61no—
411C2×C8—61no—
412C2×C8—61no—
413C2×C8—181no—
414C2×C8—181no—
415C2×C8—181no—
416C4⋊C4—21no—
417C4⋊C4—32no—
418C4⋊C4—61no—
419C4⋊C4#62612yes—
420C22⋊C4—184no—
421C22⋊C4—184no—
422C42—32no—
423C42—32no—
424C42—122no—
425C22×C3—21no—
426C22×C3—21no—
427C22×C3—21no—
428C22×C3—21no—
429C22×C3—21no—
430C22×C3—21no—
431C22×C3—21no—
432C22×C3—122no—
433C22×C3—122no—
434C22×C3—122no—
435C22×C3—241no—
436C22×C3—241no—
437C22×C3—241no—
438C22×C3—241no—
439C22×C3D3×C22⋊C411yescharacteristic
440C22×C3#88411yescharacteristic
441C22×C3#91111yescharacteristic
442C22×C3#91211yescharacteristic
443C22×C3#91511yescharacteristic
444C22×C3#91611yescharacteristic
445C22×C3C2×(C2×D3)⋊C411yescharacteristic
446C22×C3#93011yescharacteristic
447C22×C3#93011yescharacteristic
448C22×C3#93211yescharacteristic
449C22×C3#93911yescharacteristic
450C22×C3#94211yescharacteristic
451C22×C3#95011yescharacteristic
452C22×C3#95011yescharacteristic
453C2×D3—42no—
454C2×D3—42no—
455C2×D3—42no—
456C2×D3—81no—
457C2×D3—81no—
458C2×D3—81no—
459C2×D3—81no—
460C3×C4—21no—
461C3×C4—21no—
462C3×C4—21no—
463C3×C4—21no—
464C3×C4—42no—
465C3×C4—42no—
466C3×C4—62no—
467C3×C4—62no—
468C3×C4—82no—
469C3×C4—122no—
470C3×C4C4×D1211yescharacteristic
471C3×C4C4×D1211yescharacteristic
472C3×C4#87411yescharacteristic
473C3×C4#87511yescharacteristic
474C3×C4#67⋊C411yescharacteristic
475C3×C4#88511yescharacteristic
476C3×C4C4×#6711yescharacteristic
477C3×C4#94011yescharacteristic
478Dic3—22no—
479Dic3—22no—
480Dic3—42no—
481Dic3—124no—
482Dic3—122no—
483Dic3—122no—
484C32#198311yescharacteristic, complemented, Sylow
485C23—62no—
486C23—121no—
487C23—121no—
488C23—121no—
489C23—121no—
490C23—121no—
491C23—121no—
492C23D3×#6711yescharacteristic
493Q8—182no—
494Q8—182no—
495Q8—361no—
496Q8—361no—
497D4—62no—
498D4—62no—
499D4—121no—
500D4—121no—
501C2×C4—22no—
502C2×C4—32no—
503C2×C4—32no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—61no—
507C2×C4—61no—
508C2×C4—61no—
509C2×C4—61no—
510C2×C4—62no—
511C2×C4—121no—
512C2×C4—121no—
513C2×C4—182no—
514C2×C4—361no—
515C2×C4—361no—
516C2×C4#379811yescharacteristic
517C2×C4C4×D3211yescharacteristic
518C2×C4D3×D1211yescharacteristic
519C2×C4D3×D1211yescharacteristic
520C2×C4#380411yescharacteristic
521C2×C4C2×#62611yescharacteristic
522C8—121no—
523C8—361no—
524C2×C3—21no—
525C2×C3—21no—
526C2×C3—21no—
527C2×C3—21no—
528C2×C3—21no—
529C2×C3—21no—
530C2×C3—21no—
531C2×C3—242no—
532C2×C3#476711yescharacteristic
533C2×C3#477111yescharacteristic
534C2×C3#477211yescharacteristic
535C2×C3#478711yescharacteristic
536C2×C3#493911yescharacteristic
537C2×C3#495711yescharacteristic
538C2×C3#496611yescharacteristic
539C2×C3#500211yescharacteristic
540C2×C3#501611yescharacteristic
541C2×C3#501611yescharacteristic
542C2×C3#502811yescharacteristic
543C2×C3#502811yescharacteristic
544C2×C3#515311yescharacteristic
545C2×C3#516611yescharacteristic
546D3—82no—
547C22—122no—
548C22—122no—
549C22—122no—
550C22—241no—
551C22—241no—
552C22—241no—
553C22—241no—
554C22#6390611yescharacteristic
555C22D3×(C2×D3)⋊C411yescharacteristic
556C22#6393211yescharacteristic
557C22#6393311yescharacteristic
558C22#6394611yescharacteristic
559C22#6394711yescharacteristic
560C22#6397811yescharacteristic
561C4—42no—
562C4—62no—
563C4—62no—
564C4—122no—
565C4—362no—
566C4#6385211yescharacteristic
567C4#6388011yescharacteristic
568C4C4×#62611yescharacteristic
569C4#6391111yescharacteristic
570C3—21no—
571C3#6948811yescharacteristic, complemented
572C3#7016211yescharacteristic, complemented
573C2—242no—
574C2#1059053011yescharacteristic
575C2#1059053211yescharacteristic
576C2#1059060711yescharacteristic
577C2#1059060811yescharacteristic
578C2#1059138311yescharacteristic
579C2#1059146811yescharacteristic
580C2#1059160411yescharacteristic
subgroupG/H
centerC23D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
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
2. C2×#63637C2semidirect
3. C3×Dic3×C4⋊C4C2semidirect
5. C2×Dic3⋊(C3⋊C8)C2semidirect
6. C2×#63567C2semidirect
21. #63860C4semidirect
35. Dic3×C4⋊C4D3semidirect
484. C32#1983semidirect
571. C3#69488semidirect
572. C3#70162semidirect

Maximal subgroups

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

subgroupindex
C2×#638602
C2×#636372
C3×Dic3×C4⋊C42
C2×C3×#8092
C2×Dic3⋊(C3⋊C8)2
C2×#635672
C2×#635622
#701623
#694883