Finite Group Databasebeta

← #11810331

Subgroups — #11810331

Order 1152.

1719 conjugacy classes of subgroups.

The subgroup lattice has 1094 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#937C211yesmaximal, characteristic
2C2×C3×#935C211yesmaximal, characteristic, complemented
3C2×Dic3×#67C211yesmaximal, characteristic, complemented
4C2×D3×#217C211yesmaximal, characteristic, complemented
5#10592921C211yesmaximal, characteristic, complemented
6#10591721C211yesmaximal, characteristic, complemented
7#10591717C211yesmaximal, characteristic, complemented
8#10591710C211yesmaximal, characteristic, complemented
9#10591709C211yesmaximal, characteristic, complemented
10#10591706C211yesmaximal, characteristic, complemented
11#10591701C211yesmaximal, characteristic, complemented
12#10591372C211yesmaximal, characteristic, complemented
13#10591366C211yesmaximal, characteristic, complemented
14#10591303C211yesmaximal, characteristic, complemented
15#10591285C211yesmaximal, characteristic, complemented
16#82896—31nomaximal
17#82585—31nomaximal
18C24×C3×D3C2211yescharacteristic
19C22×C32×D4C2211yescharacteristic
20C22×C3×#67C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C23×C3×Dic3C2211yescharacteristic, complemented
23C22×D3×Dic3C2211yescharacteristic
24C22×D3×Dic3C2211yescharacteristic
25C2×#3757C2211yescharacteristic
26C2×#3757C2211yescharacteristic
27C2×#3757C2211yescharacteristic, complemented
28C2×#3757C2211yescharacteristic, complemented
29C2×#3750C2211yescharacteristic, complemented
30C2×C3×#217C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C2×C3×#217C2211yescharacteristic
33C2×C3×#217C2211yescharacteristic, complemented
34C3×#937—24no—
35C3×#935—24no—
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic
38C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
39C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
40Dic3×#67—24no—
41D3×#217—24no—
42C2×Dic3⋊Dic3C2211yescharacteristic, complemented
43C2×Dic3⋊Dic3C2211yescharacteristic, complemented
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic
46C2×(C2×D3)⋊Dic3C2211yescharacteristic
47C2×(C2×D3)⋊Dic3C2211yescharacteristic
48C2×(C2×D3)⋊Dic3C2211yescharacteristic
49C2×(C2×D3)⋊Dic3C2211yescharacteristic
50C2×Dic32C2211yescharacteristic, complemented
51#63658C2211yescharacteristic, complemented
52#63579C2211yescharacteristic, complemented
53#63579C2211yescharacteristic, complemented
54#63579C2211yescharacteristic, complemented
55#63579C2211yescharacteristic, complemented
56#63579C2211yescharacteristic, complemented
57C2×C3×#123—31no—
58C2×C3×#120—31no—
59C22×#217—31no—
60C2×#937D311yescharacteristic
61C2×#935D311yescharacteristic, complemented
62C2×D4×Dic3—31no—
63C2×C4×#67—31no—
64C2×D3×C22⋊C4—31no—
65#5247—31no—
66#5222—31no—
67#5222—31no—
68#5222—31no—
69#5222—61no—
70#5220—31no—
71#5220—31no—
72#5213—31no—
73#4993—31no—
74#4990—31no—
75#4989—31no—
76#4987—31no—
77#4961—31no—
78#4956—31no—
79#4955—31no—
80#4953—31no—
81#4952—31no—
82#4951—31no—
83#4949—31no—
84#4946—31no—
85#4944—31no—
86#4944—31no—
87#4942—31no—
88C24×C32C2311yescharacteristic
89C24×C32C2311yescharacteristic
90C23×C3×D3—22no—
91C23×C3×D3—22no—
92C23×C3×D3—22no—
93C23×C3×D3—22no—
94C23×C3×D3—22no—
95C23×C3×D3—41no—
96C23×C3×D3—41no—
97C23×C3×D3C2311yescharacteristic
98C23×C3×D3C2311yescharacteristic
99C2×C32×D4—22no—
100C2×C32×D4—22no—
101C2×C32×D4—41no—
102C22×C32×C4C2311yescharacteristic
103C22×C3⋊Dic3C2311yescharacteristic
104C22×C3⋊Dic3C2311yescharacteristic
105C22×C3⋊Dic3C2311yescharacteristic
106C22×C3⋊Dic3C2311yescharacteristic
107C2×C3×#67—22no—
108C2×C3×#67—22no—
109C2×C3×#67—22no—
110C2×C3×#67—22no—
111C2×C3×#67—41no—
112C2×C3×#67D414yes—
113C22×C3×Dic3—22no—
114C22×C3×Dic3—22no—
115C22×C3×Dic3—41no—
116C22×C3×Dic3C2311yescharacteristic
117C22×C3×Dic3C2311yescharacteristic
118C22×C3×Dic3C2311yescharacteristic
119C22×C3×Dic3C2311yescharacteristic
120C22×C3×Dic3C2311yescharacteristic
121C22×C3×Dic3C2311yescharacteristic
122C2×D3×Dic3—22no—
123C2×D3×Dic3—22no—
124C2×D3×Dic3—22no—
125C2×D3×Dic3—22no—
126C2×D3×Dic3—41no—
127C2×D3×Dic3—41no—
128#3757—22no—
129#3757—22no—
130#3757—41no—
131#3757—41no—
132#3750—41no—
133C3×#217—22no—
134C3×#217—22no—
135C3×#217—22no—
136C3×#217D414yescomplemented
137C3×(C2×D3)⋊C4—22no—
138C3×(C2×D3)⋊C4—22no—
139C3×Dic3⋊C4—22no—
140C3×Dic3⋊C4—22no—
141Dic3⋊Dic3—22no—
142Dic3⋊Dic3—41no—
143(C2×D3)⋊Dic3—22no—
144(C2×D3)⋊Dic3—22no—
145(C2×D3)⋊Dic3—22no—
146(C2×D3)⋊Dic3—22no—
147(C2×D3)⋊Dic3—22no—
148(C2×D3)⋊Dic3—41no—
149Dic32—22no—
150#2418—91noSylow
151C25×C3—31no—
152C24×D3C2×D311yescharacteristic
153C22×C3×D4—21no—
154C22×C3×D4—31no—
155C22×C3×D4—31no—
156C22×C3×D4C2×D311yescharacteristic
157C22×C3×D4C2×D311yescharacteristic
158C23×C3×C4—31no—
159C22×#67C2×D311yescharacteristic
160C22×#67C2×D311yescharacteristic
161C23×Dic3—31no—
162C23×Dic3—31no—
163C23×Dic3C2×D311yescharacteristic, complemented
164C22×C4×D3—31no—
165C22×C4×D3—31no—
166C3×#123—64no—
167C3×#120—64no—
168C2×C3×C4⋊C4—31no—
169C2×C3×C4⋊C4—31no—
170C2×C3×C22⋊C4—31no—
171C2×C3×C22⋊C4—31no—
172C2×C3×C22⋊C4—31no—
173C2×C3×C22⋊C4—31no—
174C2×C3×C22⋊C4—31no—
175C2×C3×C22⋊C4—31no—
176C2×#217—31no—
177C2×#217—31no—
178C2×#217—31no—
179C2×#217—31no—
180C2×#217—31no—
181C2×#217—31no—
182C2×#217—31no—
183C2×#217—31no—
184C2×#217—31no—
185C2×#217—31no—
186C2×#217—31no—
187C2×#217—31no—
188C2×#217—31no—
189C2×#217—31no—
190C2×#217—61no—
191C2×#217—61no—
192C2×#217—61no—
193C2×#217—61no—
194C2×#217—64no—
195C2×#217C2×D311yescharacteristic
196C2×#217C2×D311yescharacteristic
197C2×#217C2×D311yescharacteristic
198C2×#217C2×D311yescharacteristic, complemented
199#937—24no—
200#935—24no—
201D4×Dic3—64no—
202C4×#67—64no—
203C2×(C2×D3)⋊C4—31no—
204C2×(C2×D3)⋊C4—31no—
205C2×(C2×D3)⋊C4—31no—
206C2×(C2×D3)⋊C4—31no—
207C2×(C2×D3)⋊C4—31no—
208C2×(C2×D3)⋊C4—31no—
209C2×(C2×D3)⋊C4C2×D311yescharacteristic
210C2×(C2×D3)⋊C4C2×D311yescharacteristic
211C2×C4⋊Dic3—31no—
212C2×C4⋊Dic3—31no—
213C2×Dic3⋊C4—31no—
214C2×Dic3⋊C4—31no—
215C2×Dic3⋊C4—31no—
216C2×Dic3⋊C4—31no—
217C2×Dic3⋊C4—61no—
218C2×Dic3⋊C4C2×D311yescharacteristic, complemented
219C2×Dic3⋊C4C2×D311yescharacteristic, complemented
220C2×C4×Dic3—31no—
221C2×C4×Dic3—31no—
222D3×C22⋊C4—64no—
223C3⋊#95—31no—
224C3⋊#95—31no—
225C3⋊#95—31no—
226C3⋊#95—31no—
227C3⋊#95—31no—
228C3⋊#95—31no—
229C3⋊#95—31no—
230C3⋊#95—31no—
231C3⋊#95—31no—
232C3⋊#95—31no—
233C3⋊#95—31no—
234C3⋊#95—31no—
235C3⋊#95—61no—
236C23×C32—21no—
237C23×C32—21no—
238C23×C32—21no—
239C23×C32—21no—
240C23×C32—21no—
241C23×C32—21no—
242C23×C32—21no—
243C23×C32—21no—
244C23×C32—21no—
245C23×C32—21no—
246C23×C32—21no—
247C23×C32—21no—
248C23×C32C2×D412yes—
249C23×C32C2×D412yes—
250C23×C32C2411yescharacteristic
251C22×C3×D3—21no—
252C22×C3×D3—21no—
253C22×C3×D3—21no—
254C22×C3×D3—21no—
255C22×C3×D3—28no—
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—21no—
260C22×C3×D3—21no—
261C22×C3×D3—21no—
262C22×C3×D3—44no—
263C22×C3×D3—44no—
264C22×C3×D3—44no—
265C22×C3×D3—44no—
266C22×C3×D3—44no—
267C22×C3×D3—44no—
268C22×C3×D3C2×D412yes—
269C22×C3×D3#4112yes—
270C22×C3×D3#4112yes—
271C22×C3×D3#4112yes—
272C32×D4—44no—
273C2×C32×C4—21no—
274C2×C32×C4—21no—
275C2×C32×C4—21no—
276C2×C3⋊Dic3—21no—
277C2×C3⋊Dic3—21no—
278C2×C3⋊Dic3—21no—
279C2×C3⋊Dic3—21no—
280C2×C3⋊Dic3—21no—
281C2×C3⋊Dic3—21no—
282C2×C3⋊Dic3—21no—
283C2×C3⋊Dic3—21no—
284C2×C3⋊Dic3—21no—
285C2×C3⋊Dic3—21no—
286C2×C3⋊Dic3—21no—
287C2×C3⋊Dic3—21no—
288C3×#67—28no—
289C3×#67—44no—
290C2×C3×Dic3—21no—
291C2×C3×Dic3—21no—
292C2×C3×Dic3—21no—
293C2×C3×Dic3—21no—
294C2×C3×Dic3—21no—
295C2×C3×Dic3—21no—
296C2×C3×Dic3—21no—
297C2×C3×Dic3—21no—
298C2×C3×Dic3—21no—
299C2×C3×Dic3—21no—
300C2×C3×Dic3—21no—
301C2×C3×Dic3—21no—
302C2×C3×Dic3—21no—
303C2×C3×Dic3—21no—
304C2×C3×Dic3—21no—
305C2×C3×Dic3—44no—
306C2×C3×Dic3C2×D412yes—
307C2×C3×Dic3C2×D412yes—
308C2×C3×Dic3C2×D412yes—
309D3×Dic3—44no—
310D3×Dic3—44no—
311C2×#123—31no—
312C2×#120—31no—
313C2×C4×D4—91no—
314C22×C22⋊C4—91no—
315#399—91no—
316#397—91no—
317#394—91no—
318#394—91no—
319#388—91no—
320#388—91no—
321#386—91no—
322#386—91no—
323#385—91no—
324#380—91no—
325#379—91no—
326C24×C3—21no—
327C24×C3—21no—
328C24×C3—31no—
329C24×C3—31no—
330C24×C3—62no—
331C24×C3—62no—
332C24×C3—62no—
333C24×C3—62no—
334C24×C3—62no—
335C24×C3—121no—
336C24×C3—121no—
337C24×C3C22×D311yescharacteristic
338C24×C3C22×D311yescharacteristic
339C24×C3C22×D311yescharacteristic
340C24×C3C22×D311yescharacteristic
341C23×D3—22no—
342C23×D3—22no—
343C23×D3—22no—
344C23×D3—22no—
345C23×D3—22no—
346C23×D3—41no—
347C23×D3—41no—
348C23×D3C22×D311yescharacteristic
349C23×D3C22×D311yescharacteristic
350C2×C3×D4—22no—
351C2×C3×D4—22no—
352C2×C3×D4—22no—
353C2×C3×D4—22no—
354C2×C3×D4—34no—
355C2×C3×D4—42no—
356C2×C3×D4—42no—
357C2×C3×D4—41no—
358C2×C3×D4—41no—
359C2×C3×D4—42no—
360C2×C3×D4—62no—
361C2×C3×D4—62no—
362C2×C3×D4—62no—
363C2×C3×D4—62no—
364C2×C3×D4—121no—
365C22×C3×C4—21no—
366C22×C3×C4—31no—
367C22×C3×C4—31no—
368C22×C3×C4—31no—
369C22×C3×C4—31no—
370C22×C3×C4—31no—
371C22×C3×C4—31no—
372C22×C3×C4—62no—
373C22×C3×C4—62no—
374C22×C3×C4—121no—
375C22×C3×C4C22×D311yescharacteristic
376C22×C3×C4C22×D311yescharacteristic
377C2×#67—22no—
378C2×#67—22no—
379C2×#67—22no—
380C2×#67—22no—
381C2×#67—41no—
382C2×#67#6714yes—
383C22×Dic3—22no—
384C22×Dic3—22no—
385C22×Dic3—31no—
386C22×Dic3—31no—
387C22×Dic3—31no—
388C22×Dic3—31no—
389C22×Dic3—31no—
390C22×Dic3—31no—
391C22×Dic3—31no—
392C22×Dic3—31no—
393C22×Dic3—41no—
394C22×Dic3—61no—
395C22×Dic3—61no—
396C22×Dic3—61no—
397C22×Dic3—61no—
398C22×Dic3—62no—
399C22×Dic3—62no—
400C22×Dic3—62no—
401C22×Dic3—62no—
402C22×Dic3—121no—
403C22×Dic3—121no—
404C22×Dic3C22×D311yescharacteristic
405C22×Dic3C22×D311yescharacteristic
406C22×Dic3C22×D311yescharacteristic
407C22×Dic3C22×D311yescharacteristic
408C22×Dic3C22×D311yescharacteristic
409C22×Dic3C22×D311yescharacteristic
410C2×C4×D3—62no—
411C2×C4×D3—62no—
412C2×C4×D3—62no—
413C2×C4×D3—62no—
414C2×C4×D3—121no—
415C2×C4×D3—121no—
416C3×C4⋊C4—62no—
417C3×C4⋊C4—62no—
418C3×C22⋊C4—34no—
419C3×C22⋊C4—62no—
420C3×C22⋊C4—62no—
421C3×C22⋊C4—62no—
422C3×C22⋊C4—62no—
423C3×C22⋊C4—62no—
424#217—22no—
425#217—22no—
426#217—22no—
427#217—62no—
428#217—62no—
429#217—62no—
430#217—62no—
431#217—62no—
432#217—62no—
433#217—62no—
434#217—62no—
435#217—62no—
436#217—122no—
437#217—122no—
438#217—121no—
439#217—121no—
440#217—121no—
441#217—121no—
442#217—121no—
443#217—122no—
444#217—122no—
445#217#6714yescomplemented
446(C2×D3)⋊C4—22no—
447(C2×D3)⋊C4—22no—
448(C2×D3)⋊C4—62no—
449(C2×D3)⋊C4—62no—
450(C2×D3)⋊C4—62no—
451(C2×D3)⋊C4—62no—
452(C2×D3)⋊C4—62no—
453(C2×D3)⋊C4—121no—
454C4⋊Dic3—62no—
455C4⋊Dic3—121no—
456Dic3⋊C4—22no—
457Dic3⋊C4—22no—
458Dic3⋊C4—62no—
459Dic3⋊C4—121no—
460Dic3⋊C4—121no—
461Dic3⋊C4—121no—
462Dic3⋊C4—122no—
463C4×Dic3—62no—
464C4×Dic3—62no—
465C22×C32—22no—
466C22×C32—22no—
467C22×C32—22no—
468C22×C32—22no—
469C22×C32—22no—
470C22×C32—22no—
471C22×C32—41no—
472C22×C32—41no—
473C22×C32—41no—
474C22×C32—41no—
475C22×C32—41no—
476C22×C32—41no—
477C22×C32—41no—
478C22×C32—41no—
479C22×C32C22×D411yescharacteristic
480C22×C32C22×D411yescharacteristic
481C22×C32C2×#4111yescharacteristic
482C22×C32C2×#4111yescharacteristic
483C22×C32C2×#4111yescharacteristic
484C22×C32H(5,𝔽2)11yescharacteristic
485C22×C32H(5,𝔽2)11yescharacteristic
486C2×C3×D3—22no—
487C2×C3×D3—22no—
488C2×C3×D3—22no—
489C2×C3×D3—22no—
490C2×C3×D3—22no—
491C2×C3×D3—22no—
492C2×C3×D3—22no—
493C2×C3×D3—22no—
494C2×C3×D3—22no—
495C2×C3×D3—416no—
496C2×C3×D3—41no—
497C2×C3×D3—41no—
498C2×C3×D3—41no—
499C2×C3×D3—41no—
500C2×C3×D3#12314yescomplemented
501C32×C4—41no—
502C3⋊Dic3—41no—
503C3⋊Dic3—41no—
504C3⋊Dic3—41no—
505C3⋊Dic3—41no—
506C3×Dic3—22no—
507C3×Dic3—22no—
508C3×Dic3—22no—
509C3×Dic3—41no—
510C3×Dic3—41no—
511C3×Dic3—41no—
512C25—31no—
513C22×D4—31no—
514C22×D4—31no—
515C22×D4D3211yescharacteristic
516C23×C4—31no—
517C23×C4—91no—
518C23×C4—91no—
519#123—64no—
520#120—64no—
521C4×D4—184no—
522C2×C4⋊C4—31no—
523C2×C4⋊C4—31no—
524C2×C4⋊C4—91no—
525C2×C4⋊C4—91no—
526C2×C4⋊C4—91no—
527C2×C22⋊C4—31no—
528C2×C22⋊C4—31no—
529C2×C22⋊C4—31no—
530C2×C22⋊C4—31no—
531C2×C22⋊C4—31no—
532C2×C22⋊C4—31no—
533C2×C22⋊C4—91no—
534C2×C22⋊C4—91no—
535C2×C22⋊C4—91no—
536C2×C22⋊C4—91no—
537C2×C22⋊C4—91no—
538C2×C22⋊C4—91no—
539C2×C22⋊C4—91no—
540C2×C22⋊C4—91no—
541C2×C22⋊C4—91no—
542C2×C22⋊C4—91no—
543C2×C22⋊C4—184no—
544C2×C42—91no—
545#95—91no—
546#95—91no—
547#95—91no—
548#95—91no—
549#95—91no—
550#95—91no—
551C23×C3—21no—
552C23×C3—21no—
553C23×C3—21no—
554C23×C3—21no—
555C23×C3—21no—
556C23×C3—21no—
557C23×C3—21no—
558C23×C3—21no—
559C23×C3—21no—
560C23×C3—21no—
561C23×C3—21no—
562C23×C3—21no—
563C23×C3—21no—
564C23×C3—21no—
565C23×C3—21no—
566C23×C3—21no—
567C23×C3—21no—
568C23×C3—21no—
569C23×C3—21no—
570C23×C3—21no—
571C23×C3—21no—
572C23×C3—21no—
573C23×C3—21no—
574C23×C3—21no—
575C23×C3—21no—
576C23×C3—22no—
577C23×C3—22no—
578C23×C3—32no—
579C23×C3—32no—
580C23×C3—32no—
581C23×C3—32no—
582C23×C3—41no—
583C23×C3—41no—
584C23×C3—41no—
585C23×C3—41no—
586C23×C3—41no—
587C23×C3—41no—
588C23×C3—41no—
589C23×C3—41no—
590C23×C3—41no—
591C23×C3—41no—
592C23×C3—41no—
593C23×C3—41no—
594C23×C3—68no—
595C23×C3—61no—
596C23×C3—61no—
597C23×C3—61no—
598C23×C3—61no—
599C23×C3—61no—
600C23×C3—61no—
601C23×C3—61no—
602C23×C3—61no—
603C23×C3—61no—
604C23×C3—61no—
605C23×C3—124no—
606C23×C3—124no—
607C23×C3—124no—
608C23×C3—124no—
609C23×C3—124no—
610C23×C3—124no—
611C23×C3D3×D412yes—
612C23×C3D3×D412yes—
613C23×C3C2×#6712yes—
614C23×C3C2×#6712yes—
615C23×C3C23×D311yescharacteristic
616C23×C3C23×D311yescharacteristic
617C22×D3—21no—
618C22×D3—21no—
619C22×D3—21no—
620C22×D3—21no—
621C22×D3—28no—
622C22×D3—21no—
623C22×D3—21no—
624C22×D3—21no—
625C22×D3—21no—
626C22×D3—21no—
627C22×D3—21no—
628C22×D3—44no—
629C22×D3—44no—
630C22×D3—44no—
631C22×D3—44no—
632C22×D3—44no—
633C22×D3—44no—
634C22×D3#23712yes—
635C22×D3#23712yes—
636C22×D3#23712yes—
637C22×D3C2×#6712yes—
638C3×D4—44no—
639C3×D4—44no—
640C3×D4—48no—
641C3×D4—68no—
642C3×D4—124no—
643C2×C3×C4—22no—
644C2×C3×C4—21no—
645C2×C3×C4—21no—
646C2×C3×C4—21no—
647C2×C3×C4—21no—
648C2×C3×C4—21no—
649C2×C3×C4—21no—
650C2×C3×C4—32no—
651C2×C3×C4—32no—
652C2×C3×C4—32no—
653C2×C3×C4—41no—
654C2×C3×C4—41no—
655C2×C3×C4—61no—
656C2×C3×C4—61no—
657C2×C3×C4—61no—
658C2×C3×C4—61no—
659C2×C3×C4—61no—
660C2×C3×C4—61no—
661C2×C3×C4—61no—
662C2×C3×C4—61no—
663C2×C3×C4—61no—
664C2×C3×C4—61no—
665C2×C3×C4—61no—
666C2×C3×C4—61no—
667C2×C3×C4—61no—
668C2×C3×C4—61no—
669C2×C3×C4—61no—
670C2×C3×C4—124no—
671#67—28no—
672#67—44no—
673C2×Dic3—21no—
674C2×Dic3—21no—
675C2×Dic3—21no—
676C2×Dic3—21no—
677C2×Dic3—21no—
678C2×Dic3—21no—
679C2×Dic3—21no—
680C2×Dic3—21no—
681C2×Dic3—21no—
682C2×Dic3—21no—
683C2×Dic3—21no—
684C2×Dic3—21no—
685C2×Dic3—21no—
686C2×Dic3—21no—
687C2×Dic3—21no—
688C2×Dic3—44no—
689C2×Dic3—62no—
690C2×Dic3—61no—
691C2×Dic3—61no—
692C2×Dic3—61no—
693C2×Dic3—61no—
694C2×Dic3—61no—
695C2×Dic3—61no—
696C2×Dic3—61no—
697C2×Dic3—61no—
698C2×Dic3—61no—
699C2×Dic3—61no—
700C2×Dic3—61no—
701C2×Dic3—61no—
702C2×Dic3—61no—
703C2×Dic3—61no—
704C2×Dic3—61no—
705C2×Dic3—61no—
706C2×Dic3—61no—
707C2×Dic3—61no—
708C2×Dic3—61no—
709C2×Dic3—61no—
710C2×Dic3—61no—
711C2×Dic3—61no—
712C2×Dic3—61no—
713C2×Dic3—61no—
714C2×Dic3—121no—
715C2×Dic3—121no—
716C2×Dic3—121no—
717C2×Dic3—121no—
718C2×Dic3—121no—
719C2×Dic3—121no—
720C2×Dic3—121no—
721C2×Dic3—121no—
722C2×Dic3—121no—
723C2×Dic3—121no—
724C2×Dic3—121no—
725C2×Dic3—124no—
726C2×Dic3—124no—
727C2×Dic3C2×#6712yes—
728C2×Dic3C2×#6712yes—
729C2×Dic3C2×#6712yes—
730C4×D3—124no—
731C4×D3—124no—
732C2×C32—42no—
733C2×C32—42no—
734C2×C32C2×#12311yescharacteristic
735C2×C32#52511yescharacteristic
736C2×C32#53811yescharacteristic
737C2×C32D4211yescharacteristic
738C2×C32#54611yescharacteristic
739C2×C32#54611yescharacteristic
740C2×C32#55111yescharacteristic
741C3×D3—24no—
742C3×D3—42no—
743C24—31no—
744C24—31no—
745C24—62no—
746C24—62no—
747C24—62no—
748C24—62no—
749C24—62no—
750C24—121no—
751C24—121no—
752C24C2×D3211yescharacteristic
753C24C2×D3211yescharacteristic
754C2×D4—22no—
755C2×D4—22no—
756C2×D4—34no—
757C2×D4—41no—
758C2×D4—62no—
759C2×D4—62no—
760C2×D4—62no—
761C2×D4—62no—
762C2×D4—121no—
763C22×C4—31no—
764C22×C4—31no—
765C22×C4—31no—
766C22×C4—31no—
767C22×C4—31no—
768C22×C4—31no—
769C22×C4—62no—
770C22×C4—62no—
771C22×C4—91no—
772C22×C4—91no—
773C22×C4—91no—
774C22×C4—91no—
775C22×C4—121no—
776C22×C4—182no—
777C22×C4—182no—
778C22×C4—182no—
779C22×C4—182no—
780C22×C4—361no—
781C22×C4—361no—
782C22×C4C2×D3211yescharacteristic
783C4⋊C4—62no—
784C4⋊C4—62no—
785C4⋊C4—182no—
786C4⋊C4—361no—
787C4⋊C4—361no—
788C22⋊C4—34no—
789C22⋊C4—62no—
790C22⋊C4—62no—
791C22⋊C4—62no—
792C22⋊C4—62no—
793C22⋊C4—62no—
794C22⋊C4—182no—
795C22⋊C4—182no—
796C22⋊C4—182no—
797C22⋊C4—182no—
798C22⋊C4—182no—
799C22⋊C4—182no—
800C22⋊C4—182no—
801C22⋊C4—361no—
802C22⋊C4—361no—
803C22⋊C4—361no—
804C42—182no—
805C22×C3—22no—
806C22×C3—22no—
807C22×C3—22no—
808C22×C3—22no—
809C22×C3—22no—
810C22×C3—22no—
811C22×C3—22no—
812C22×C3—22no—
813C22×C3—22no—
814C22×C3—22no—
815C22×C3—22no—
816C22×C3—22no—
817C22×C3—21no—
818C22×C3—21no—
819C22×C3—21no—
820C22×C3—21no—
821C22×C3—21no—
822C22×C3—21no—
823C22×C3—21no—
824C22×C3—34no—
825C22×C3—42no—
826C22×C3—42no—
827C22×C3—42no—
828C22×C3—42no—
829C22×C3—42no—
830C22×C3—42no—
831C22×C3—41no—
832C22×C3—41no—
833C22×C3—41no—
834C22×C3—41no—
835C22×C3—41no—
836C22×C3—41no—
837C22×C3—41no—
838C22×C3—41no—
839C22×C3—41no—
840C22×C3—41no—
841C22×C3—41no—
842C22×C3—41no—
843C22×C3—41no—
844C22×C3—41no—
845C22×C3—41no—
846C22×C3—41no—
847C22×C3—62no—
848C22×C3—62no—
849C22×C3—62no—
850C22×C3—62no—
851C22×C3—62no—
852C22×C3—62no—
853C22×C3—62no—
854C22×C3—62no—
855C22×C3—62no—
856C22×C3—81no—
857C22×C3—81no—
858C22×C3—81no—
859C22×C3—81no—
860C22×C3—81no—
861C22×C3—81no—
862C22×C3—81no—
863C22×C3—81no—
864C22×C3—1216no—
865C22×C3—121no—
866C22×C3—121no—
867C22×C3—121no—
868C22×C3—121no—
869C22×C3C2×D3×D411yescharacteristic
870C22×C3C2×D3×D411yescharacteristic
871C22×C3C2×#23711yescharacteristic
872C22×C3C2×#23711yescharacteristic
873C22×C3C2×#23711yescharacteristic
874C22×C3#100411yescharacteristic
875C22×C3#100411yescharacteristic
876C22×C3#100411yescharacteristic
877C22×C3D3×#4111yescharacteristic
878C22×C3D3×#4111yescharacteristic
879C22×C3D3×#4111yescharacteristic
880C22×C3#100911yescharacteristic
881C22×C3C22×#6711yescharacteristic
882C22×C3C22×#6711yescharacteristic
883C2×D3—22no—
884C2×D3—22no—
885C2×D3—22no—
886C2×D3—22no—
887C2×D3—22no—
888C2×D3—22no—
889C2×D3—22no—
890C2×D3—22no—
891C2×D3—22no—
892C2×D3—416no—
893C2×D3—41no—
894C2×D3—41no—
895C2×D3—41no—
896C2×D3—41no—
897C2×D3#93514yescomplemented
898C3×C4—42no—
899C3×C4—41no—
900C3×C4—41no—
901C3×C4—62no—
902C3×C4—62no—
903C3×C4—62no—
904C3×C4—121no—
905C3×C4—121no—
906C3×C4—121no—
907Dic3—22no—
908Dic3—22no—
909Dic3—22no—
910Dic3—41no—
911Dic3—41no—
912Dic3—41no—
913Dic3—122no—
914Dic3—121no—
915Dic3—121no—
916Dic3—121no—
917Dic3—121no—
918Dic3—121no—
919Dic3—121no—
920Dic3—121no—
921Dic3—121no—
922Dic3—241no—
923Dic3—241no—
924Dic3—241no—
925C32#241811yescharacteristic, complemented, Sylow
926C23—21no—
927C23—21no—
928C23—21no—
929C23—21no—
930C23—21no—
931C23—21no—
932C23—21no—
933C23—21no—
934C23—21no—
935C23—21no—
936C23—21no—
937C23—21no—
938C23—32no—
939C23—32no—
940C23—32no—
941C23—32no—
942C23—68no—
943C23—61no—
944C23—61no—
945C23—61no—
946C23—61no—
947C23—61no—
948C23—61no—
949C23—61no—
950C23—61no—
951C23—61no—
952C23—61no—
953C23—124no—
954C23—124no—
955C23—124no—
956C23—124no—
957C23—124no—
958C23—124no—
959C23D3×#6712yes—
960C23D3×#6712yes—
961C23C22×D3211yescharacteristic
962D4—44no—
963D4—68no—
964D4—124no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—32no—
969C2×C4—32no—
970C2×C4—32no—
971C2×C4—61no—
972C2×C4—61no—
973C2×C4—61no—
974C2×C4—61no—
975C2×C4—61no—
976C2×C4—61no—
977C2×C4—61no—
978C2×C4—61no—
979C2×C4—61no—
980C2×C4—61no—
981C2×C4—61no—
982C2×C4—61no—
983C2×C4—61no—
984C2×C4—61no—
985C2×C4—61no—
986C2×C4—124no—
987C2×C4—181no—
988C2×C4—181no—
989C2×C4—181no—
990C2×C4—181no—
991C2×C4—181no—
992C2×C4—181no—
993C2×C4—181no—
994C2×C4—181no—
995C2×C4—181no—
996C2×C4—181no—
997C2×C4—181no—
998C2×C4—181no—
999C2×C4—364no—
1000C2×C4—364no—
1001C2×C3—21no—
1002C2×C3—21no—
1003C2×C3—21no—
1004C2×C3—21no—
1005C2×C3—21no—
1006C2×C3—21no—
1007C2×C3—21no—
1008C2×C3—42no—
1009C2×C3—42no—
1010C2×C3—42no—
1011C2×C3—42no—
1012C2×C3—64no—
1013C2×C3—82no—
1014C2×C3—82no—
1015C2×C3—122no—
1016C2×C3#558611yescharacteristic
1017C2×C3#558711yescharacteristic
1018C2×C3#559111yescharacteristic
1019C2×C3#559311yescharacteristic
1020C2×C3D3×#12311yescharacteristic
1021C2×C3#565411yescharacteristic
1022C2×C3#565711yescharacteristic
1023C2×C3#565911yescharacteristic
1024C2×C3C2×#93511yescharacteristic
1025C2×C3D4×#6711yescharacteristic
1026C2×C3D4×#6711yescharacteristic
1027C2×C3#580611yescharacteristic
1028C2×C3#582811yescharacteristic
1029C2×C3#582911yescharacteristic
1030D3—24no—
1031D3—42no—
1032C22—22no—
1033C22—22no—
1034C22—22no—
1035C22—22no—
1036C22—22no—
1037C22—22no—
1038C22—34no—
1039C22—41no—
1040C22—41no—
1041C22—41no—
1042C22—41no—
1043C22—41no—
1044C22—41no—
1045C22—41no—
1046C22—41no—
1047C22—62no—
1048C22—62no—
1049C22—62no—
1050C22—62no—
1051C22—62no—
1052C22—62no—
1053C22—62no—
1054C22—62no—
1055C22—62no—
1056C22—1216no—
1057C22—121no—
1058C22—121no—
1059C22—121no—
1060C22—121no—
1061C22D3×#23711yescharacteristic
1062C22D3×#23711yescharacteristic
1063C22D3×#23711yescharacteristic
1064C22#6431411yescharacteristic
1065C22C2×D3×#6711yescharacteristic
1066C22C2×D3×#6711yescharacteristic
1067C22#6433011yescharacteristic
1068C4—41no—
1069C4—62no—
1070C4—62no—
1071C4—62no—
1072C4—121no—
1073C4—121no—
1074C4—121no—
1075C4—361no—
1076C4—361no—
1077C4—361no—
1078C4—361no—
1079C3—21no—
1080C3#8258511yescharacteristic, complemented
1081C3#8289611yescharacteristic, complemented
1082C2—42no—
1083C2—42no—
1084C2—64no—
1085C2—122no—
1086C2D3×#93511yescharacteristic
1087C2#1059514811yescharacteristic
1088C2#1059515411yescharacteristic
1089C2#1059517811yescharacteristic
1090C2#1059518511yescharacteristic
1091C2#1059530411yescharacteristic
1092C2#67211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC22×C32×D4C22
prime radicalC2×C3×#937C2
hypercenterC22×D4D32
hypocenterC32#2418
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#935C2semidirect
3. C2×Dic3×#67C2semidirect
4. C2×D3×#217C2semidirect
5. #10592921C2semidirect
6. #10591721C2semidirect
7. #10591717C2semidirect
8. #10591710C2semidirect
9. #10591709C2semidirect
10. #10591706C2semidirect
11. #10591701C2semidirect
12. #10591372C2semidirect
13. #10591366C2semidirect
14. #10591303C2semidirect
15. #10591285C2semidirect
22. C23×C3×Dic3C22semidirect
27. C2×#3757C22semidirect
28. C2×#3757C22semidirect
29. C2×#3750C22semidirect
33. C2×C3×#217C22semidirect
38. C2×C3×Dic3⋊C4C22semidirect
39. C2×C3×Dic3⋊C4C22semidirect
42. C2×Dic3⋊Dic3C22semidirect
43. C2×Dic3⋊Dic3C22semidirect
50. C2×Dic32C22semidirect
51. #63658C22semidirect
52. #63579C22semidirect
53. #63579C22semidirect
54. #63579C22semidirect
55. #63579C22semidirect
56. #63579C22semidirect
61. C2×#935D3semidirect
136. C3×#217D4semidirect
163. C23×Dic3C2×D3semidirect
198. C2×#217C2×D3semidirect
218. C2×Dic3⋊C4C2×D3semidirect
219. C2×Dic3⋊C4C2×D3semidirect
445. #217#67semidirect
500. C2×C3×D3#123semidirect
897. C2×D3#935semidirect
925. C32#2418semidirect
1080. C3#82585semidirect
1081. C3#82896semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9372
C2×C3×#9352
C2×Dic3×#672
C2×D3×#2172
#105929212
#105917212
#105917172
#105917102
#105917092
#105917062
#105917012
#105913722
#105913662
#105913032
#105912852
#828963
#825853