Finite Group Databasebeta

← #11803288

Subgroups — #11803288

Order 1152.

1745 conjugacy classes of subgroups.

The subgroup lattice has 1091 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#937C211yesmaximal, characteristic
2C2×Dic3×#67C211yesmaximal, characteristic, complemented
3C2×D3×#217C211yesmaximal, characteristic, complemented
4#10592920C211yesmaximal, characteristic, complemented
5C3×#5220C211yesmaximal, characteristic, complemented
6#10591721C211yesmaximal, characteristic, complemented
7#10591710C211yesmaximal, characteristic, complemented
8#10591707C211yesmaximal, characteristic, complemented
9#10591706C211yesmaximal, characteristic, complemented
10#10591701C211yesmaximal, characteristic, complemented
11#10591701C211yesmaximal, characteristic, complemented
12#10591379C211yesmaximal, characteristic, complemented
13#10591368C211yesmaximal, characteristic, complemented
14#10591316C211yesmaximal, characteristic, complemented
15#10591286C211yesmaximal, characteristic, complemented
16#82578—31nomaximal
17#74876—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×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
30C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
31C2×C3×#217C2211yescharacteristic
32C2×C3×#217C2211yescharacteristic
33C2×C3×#217C2211yescharacteristic
34C2×C3×#217C2211yescharacteristic, complemented
35C3×#937C418yescomplemented
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic
38Dic3×#67—24no—
39D3×#217—24no—
40C2×Dic3⋊Dic3C2211yescharacteristic, complemented
41C2×Dic3⋊Dic3C2211yescharacteristic, complemented
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic
46C2×(C2×D3)⋊Dic3C2211yescharacteristic
47C2×(C2×D3)⋊Dic3C2211yescharacteristic
48C2×Dic32C2211yescharacteristic, complemented
49C2×Dic32C2211yescharacteristic, complemented
50C3×C3⋊#95C2211yescharacteristic, complemented
51C3×C3⋊#95C2211yescharacteristic, complemented
52#63579C2211yescharacteristic, complemented
53#63579C2211yescharacteristic, complemented
54#63579C2211yescharacteristic, complemented
55#63579C2211yescharacteristic, complemented
56C2×C3×#120—31no—
57C22×#217—31no—
58C2×#937D311yescharacteristic
59C2×D4×Dic3—31no—
60C2×C4×#67—31no—
61C2×D3×C22⋊C4—31no—
62C3×#386—31no—
63#5247—31no—
64#5221—31no—
65#5221—31no—
66#5221—31no—
67#5221—61no—
68#5220—31no—
69#5220—31no—
70#5220D311yescharacteristic, complemented
71#5213—31no—
72#4957—31no—
73#4956—31no—
74#4955—31no—
75#4951—31no—
76#4951—31no—
77#4951—31no—
78#4951—31no—
79#4950—31no—
80#4944—31no—
81#4944—31no—
82Dic3×C22⋊C4—31no—
83#4670—31no—
84#4669—31no—
85#4668—31no—
86#4666—31no—
87C24×C32C2311yescharacteristic
88C24×C32C2311yescharacteristic
89C23×C3×D3—22no—
90C23×C3×D3—22no—
91C23×C3×D3—41no—
92C23×C3×D3—41no—
93C23×C3×D3—41no—
94C23×C3×D3—41no—
95C23×C3×D3C2×C414yescomplemented
96C23×C3×D3C2311yescharacteristic
97C23×C3×D3C2311yescharacteristic
98C2×C32×D4—41no—
99C2×C32×D4—41no—
100C2×C32×D4C2×C414yescomplemented
101C22×C32×C4C2311yescharacteristic
102C22×C3⋊Dic3C2311yescharacteristic
103C22×C3⋊Dic3C2311yescharacteristic
104C22×C3⋊Dic3C2311yescharacteristic
105C22×C3⋊Dic3C2311yescharacteristic
106C2×C3×#67—22no—
107C2×C3×#67—22no—
108C2×C3×#67—41no—
109C2×C3×#67—41no—
110C2×C3×#67C2×C414yes—
111C2×C3×#67C2×C414yescomplemented
112C22×C3×Dic3—22no—
113C22×C3×Dic3—41no—
114C22×C3×Dic3—41no—
115C22×C3×Dic3C2311yescharacteristic
116C22×C3×Dic3C2311yescharacteristic
117C22×C3×Dic3C2311yescharacteristic
118C22×C3×Dic3C2311yescharacteristic
119C22×C3×Dic3C2311yescharacteristic
120C22×C3×Dic3C2311yescharacteristic
121C2×D3×Dic3—22no—
122C2×D3×Dic3—41no—
123C2×D3×Dic3—41no—
124C2×D3×Dic3—41no—
125C2×D3×Dic3—41no—
126C2×D3×Dic3D414yescomplemented
127#3757—22no—
128#3757—22no—
129#3757—41no—
130#3757—41no—
131C4⋊(C3⋊Dic3)—41no—
132C4×C3⋊Dic3—41no—
133C3×#217—22no—
134C3×#217—41no—
135C3×#217—41no—
136C3×#217C2×C414yescomplemented
137C3×(C2×D3)⋊C4C2×C414yescomplemented
138C3×(C2×D3)⋊C4C2×C414yescomplemented
139Dic3⋊Dic3—22no—
140Dic3⋊Dic3—41no—
141(C2×D3)⋊Dic3—22no—
142(C2×D3)⋊Dic3—22no—
143(C2×D3)⋊Dic3—22no—
144(C2×D3)⋊Dic3—22no—
145(C2×D3)⋊Dic3—41no—
146(C2×D3)⋊Dic3—41no—
147Dic32—22no—
148Dic32—41no—
149#2321—91noSylow
150C25×C3—31no—
151C24×D3C2×D311yescharacteristic
152C22×C3×D4—21no—
153C22×C3×D4—31no—
154C22×C3×D4—31no—
155C22×C3×D4C2×D311yescharacteristic
156C22×C3×D4C2×D311yescharacteristic
157C23×C3×C4—31no—
158C22×#67C2×D311yescharacteristic
159C22×#67C2×D311yescharacteristic
160C23×Dic3—31no—
161C23×Dic3—31no—
162C23×Dic3C2×D311yescharacteristic, complemented
163C22×C4×D3—31no—
164C22×C4×D3—31no—
165C3×#120—38no—
166C2×C3×C22⋊C4—31no—
167C2×C3×C22⋊C4—31no—
168C2×C3×C22⋊C4—31no—
169C2×C3×C22⋊C4—31no—
170C2×C3×C22⋊C4—31no—
171C2×C3×C22⋊C4—31no—
172C2×#217—31no—
173C2×#217—31no—
174C2×#217—31no—
175C2×#217—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—61no—
187C2×#217—61no—
188C2×#217—61no—
189C2×#217—61no—
190C2×#217—64no—
191C2×#217C2×D311yescharacteristic
192C2×#217C2×D311yescharacteristic
193C2×#217C2×D311yescharacteristic
194C2×#217C2×D311yescharacteristic, complemented
195#937Dic318yescomplemented
196D4×Dic3—64no—
197C4×#67—64no—
198C2×(C2×D3)⋊C4—31no—
199C2×(C2×D3)⋊C4—31no—
200C2×(C2×D3)⋊C4—31no—
201C2×(C2×D3)⋊C4—31no—
202C2×(C2×D3)⋊C4—31no—
203C2×(C2×D3)⋊C4—31no—
204C2×(C2×D3)⋊C4C2×D311yescharacteristic
205C2×(C2×D3)⋊C4C2×D311yescharacteristic
206C2×C4⋊Dic3—31no—
207C2×C4⋊Dic3—31no—
208C2×C4⋊Dic3—31no—
209C2×C4⋊Dic3—31no—
210C2×C4⋊Dic3—61no—
211C2×Dic3⋊C4—31no—
212C2×Dic3⋊C4—31no—
213C2×C4×Dic3—31no—
214C2×C4×Dic3—31no—
215C2×C4×Dic3—31no—
216C2×C4×Dic3—31no—
217C2×C4×Dic3—31no—
218C2×C4×Dic3—31no—
219C2×C4×Dic3—61no—
220D3×C22⋊C4—64no—
221C3×#95—31no—
222C3×#95—31no—
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⋊#95C2×D311yescharacteristic, complemented
232C3⋊#95C2×D311yescharacteristic, complemented
233C23×C32—21no—
234C23×C32—21no—
235C23×C32—21no—
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×C32C22×C412yes—
246C23×C32C22×C412yes—
247C23×C32C2411yescharacteristic
248C22×C3×D3—21no—
249C22×C3×D3—21no—
250C22×C3×D3—21no—
251C22×C3×D3—21no—
252C22×C3×D3—21no—
253C22×C3×D3—21no—
254C22×C3×D3—21no—
255C22×C3×D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—28no—
259C22×C3×D3—44no—
260C22×C3×D3—44no—
261C22×C3×D3—44no—
262C22×C3×D3—44no—
263C22×C3×D3—44no—
264C22×C3×D3—44no—
265C22×C3×D3C22×C412yes—
266C22×C3×D3C22×C412yes—
267C22×C3×D3C2×D412yes—
268C22×C3×D3#4112yes—
269C32×D4—44no—
270C2×C32×C4—21no—
271C2×C32×C4—21no—
272C2×C32×C4C22×C412yes—
273C2×C3⋊Dic3—21no—
274C2×C3⋊Dic3—21no—
275C2×C3⋊Dic3—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⋊Dic3C2×D412yes—
285C3×#67—28no—
286C3×#67—44no—
287C2×C3×Dic3—21no—
288C2×C3×Dic3—21no—
289C2×C3×Dic3—21no—
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—44no—
303C2×C3×Dic3C22×C412yes—
304C2×C3×Dic3C22×C412yes—
305C2×C3×Dic3C2×D412yes—
306D3×Dic3—44no—
307D3×Dic3—44no—
308C2×#120—31no—
309C2×C4×D4—91no—
310C22×C22⋊C4—91no—
311#390—91no—
312#390—91no—
313#388—91no—
314#388—91no—
315#388—91no—
316#388—91no—
317#386—31no—
318#386—91no—
319#386—91no—
320#385—91no—
321#379—91no—
322C4×C22⋊C4—91no—
323C24×C3—21no—
324C24×C3—21no—
325C24×C3—31no—
326C24×C3—31no—
327C24×C3—34no—
328C24×C3—62no—
329C24×C3—62no—
330C24×C3—121no—
331C24×C3—121no—
332C24×C3—121no—
333C24×C3—121no—
334C24×C3C22×D311yescharacteristic
335C24×C3C22×D311yescharacteristic
336C24×C3C22×D311yescharacteristic
337C24×C3C22×D311yescharacteristic
338C23×D3—22no—
339C23×D3—22no—
340C23×D3—41no—
341C23×D3—41no—
342C23×D3—41no—
343C23×D3—41no—
344C23×D3C2×Dic314yescomplemented
345C23×D3C22×D311yescharacteristic
346C23×D3C22×D311yescharacteristic
347C2×C3×D4—24no—
348C2×C3×D4—34no—
349C2×C3×D4—34no—
350C2×C3×D4—41no—
351C2×C3×D4—41no—
352C2×C3×D4—41no—
353C2×C3×D4—41no—
354C2×C3×D4—42no—
355C2×C3×D4—42no—
356C2×C3×D4—62no—
357C2×C3×D4—62no—
358C2×C3×D4—121no—
359C2×C3×D4—121no—
360C2×C3×D4C4×D314yescomplemented
361C2×C3×D4C2×Dic314yescomplemented
362C22×C3×C4—21no—
363C22×C3×C4—31no—
364C22×C3×C4—31no—
365C22×C3×C4—31no—
366C22×C3×C4—31no—
367C22×C3×C4—31no—
368C22×C3×C4—31no—
369C22×C3×C4—62no—
370C22×C3×C4—121no—
371C22×C3×C4—121no—
372C22×C3×C4C22×D311yescharacteristic
373C22×C3×C4C22×D311yescharacteristic
374C2×#67—22no—
375C2×#67—22no—
376C2×#67—41no—
377C2×#67—41no—
378C2×#67C2×Dic314yes—
379C2×#67C2×Dic314yescomplemented
380C22×Dic3—22no—
381C22×Dic3—31no—
382C22×Dic3—31no—
383C22×Dic3—34no—
384C22×Dic3—31no—
385C22×Dic3—31no—
386C22×Dic3—31no—
387C22×Dic3—31no—
388C22×Dic3—31no—
389C22×Dic3—31no—
390C22×Dic3—41no—
391C22×Dic3—41no—
392C22×Dic3—61no—
393C22×Dic3—61no—
394C22×Dic3—61no—
395C22×Dic3—61no—
396C22×Dic3—62no—
397C22×Dic3—121no—
398C22×Dic3—121no—
399C22×Dic3—121no—
400C22×Dic3—121no—
401C22×Dic3C22×D311yescharacteristic
402C22×Dic3C22×D311yescharacteristic
403C22×Dic3C22×D311yescharacteristic
404C22×Dic3C22×D311yescharacteristic
405C22×Dic3C22×D311yescharacteristic
406C22×Dic3C22×D311yescharacteristic
407C2×C4×D3—34no—
408C2×C4×D3—62no—
409C2×C4×D3—121no—
410C2×C4×D3—121no—
411C2×C4×D3—121no—
412C2×C4×D3—121no—
413C3×C22⋊C4—34no—
414C3×C22⋊C4—34no—
415C3×C22⋊C4—34no—
416C3×C22⋊C4—62no—
417C3×C22⋊C4—121no—
418C3×C22⋊C4—121no—
419#217—22no—
420#217—41no—
421#217—41no—
422#217—62no—
423#217—62no—
424#217—62no—
425#217—62no—
426#217—62no—
427#217—62no—
428#217—62no—
429#217—62no—
430#217—122no—
431#217—122no—
432#217—121no—
433#217—121no—
434#217—121no—
435#217—121no—
436#217—121no—
437#217—121no—
438#217—122no—
439#217—122no—
440#217C2×Dic314yescomplemented
441(C2×D3)⋊C4—62no—
442(C2×D3)⋊C4—62no—
443(C2×D3)⋊C4—62no—
444(C2×D3)⋊C4—62no—
445(C2×D3)⋊C4—121no—
446(C2×D3)⋊C4—121no—
447(C2×D3)⋊C4C2×Dic314yescomplemented
448(C2×D3)⋊C4C2×Dic314yescomplemented
449C4⋊Dic3—62no—
450C4⋊Dic3—121no—
451C4⋊Dic3—121no—
452C4⋊Dic3—121no—
453C4⋊Dic3—122no—
454Dic3⋊C4—62no—
455Dic3⋊C4—121no—
456C4×Dic3—62no—
457C4×Dic3—62no—
458C4×Dic3—121no—
459C4×Dic3—121no—
460C4×Dic3—121no—
461C4×Dic3—121no—
462C4×Dic3—122no—
463C22×C32—22no—
464C22×C32—22no—
465C22×C32—22no—
466C22×C32—22no—
467C22×C32—22no—
468C22×C32—22no—
469C22×C32—41no—
470C22×C32—41no—
471C22×C32—41no—
472C22×C32—41no—
473C22×C32—41no—
474C22×C32—41no—
475C22×C32—41no—
476C22×C32—41no—
477C22×C32C23×C411yescharacteristic
478C22×C32C22×D411yescharacteristic
479C22×C32C2×#4111yescharacteristic
480C22×C32H(5,𝔽2)11yescharacteristic
481C22×C32H(5,𝔽2)11yescharacteristic
482C22×C32H(5,𝔽2)11yescharacteristic
483C22×C32H(5,𝔽2)11yescharacteristic
484C2×C3×D3—22no—
485C2×C3×D3—22no—
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—416no—
494C2×C3×D3—41no—
495C2×C3×D3—41no—
496C2×C3×D3—41no—
497C2×C3×D3—41no—
498C2×C3×D3C4×D414yes—
499C32×C4—22no—
500C3⋊Dic3—22no—
501C3⋊Dic3—41no—
502C3⋊Dic3—41no—
503C3⋊Dic3—41no—
504C3×Dic3—22no—
505C3×Dic3—22no—
506C3×Dic3—22no—
507C3×Dic3—41no—
508C3×Dic3—41no—
509C3×Dic3—41no—
510C25—31no—
511C22×D4—31no—
512C22×D4—31no—
513C22×D4D3211yescharacteristic
514C23×C4—31no—
515C23×C4—91no—
516C23×C4—91no—
517#120—38no—
518C4×D4—184no—
519C2×C4⋊C4—91no—
520C2×C4⋊C4—91no—
521C2×C4⋊C4—91no—
522C2×C22⋊C4—31no—
523C2×C22⋊C4—31no—
524C2×C22⋊C4—31no—
525C2×C22⋊C4—31no—
526C2×C22⋊C4—31no—
527C2×C22⋊C4—31no—
528C2×C22⋊C4—91no—
529C2×C22⋊C4—91no—
530C2×C22⋊C4—91no—
531C2×C22⋊C4—91no—
532C2×C22⋊C4—91no—
533C2×C22⋊C4—91no—
534C2×C22⋊C4—91no—
535C2×C22⋊C4—91no—
536C2×C22⋊C4—91no—
537C2×C22⋊C4—91no—
538C2×C22⋊C4—184no—
539C2×C42—91no—
540C2×C42—91no—
541C2×C42—91no—
542#95—31no—
543#95—31no—
544#95—91no—
545#95—91no—
546#95—91no—
547#95—91no—
548C23×C3—21no—
549C23×C3—21no—
550C23×C3—21no—
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—22no—
574C23×C3—22no—
575C23×C3—32no—
576C23×C3—32no—
577C23×C3—32no—
578C23×C3—32no—
579C23×C3—41no—
580C23×C3—41no—
581C23×C3—41no—
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—68no—
592C23×C3—61no—
593C23×C3—61no—
594C23×C3—61no—
595C23×C3—61no—
596C23×C3—61no—
597C23×C3—61no—
598C23×C3—61no—
599C23×C3—61no—
600C23×C3—61no—
601C23×C3—61no—
602C23×C3—124no—
603C23×C3—124no—
604C23×C3—124no—
605C23×C3—124no—
606C23×C3—124no—
607C23×C3—124no—
608C23×C3C2×C4×D312yes—
609C23×C3C2×C4×D312yes—
610C23×C3C22×Dic312yes—
611C23×C3C22×Dic312yes—
612C23×C3C23×D311yescharacteristic
613C23×C3C23×D311yescharacteristic
614C22×D3—21no—
615C22×D3—21no—
616C22×D3—21no—
617C22×D3—21no—
618C22×D3—21no—
619C22×D3—21no—
620C22×D3—21no—
621C22×D3—21no—
622C22×D3—21no—
623C22×D3—21no—
624C22×D3—28no—
625C22×D3—44no—
626C22×D3—44no—
627C22×D3—44no—
628C22×D3—44no—
629C22×D3—44no—
630C22×D3—44no—
631C22×D3D3×D412yes—
632C22×D3#23712yes—
633C22×D3C22×Dic312yes—
634C22×D3C22×Dic312yes—
635C3×D4—44no—
636C3×D4—44no—
637C3×D4—48no—
638C3×D4—68no—
639C3×D4—124no—
640C2×C3×C4—22no—
641C2×C3×C4—22no—
642C2×C3×C4—21no—
643C2×C3×C4—21no—
644C2×C3×C4—21no—
645C2×C3×C4—21no—
646C2×C3×C4—22no—
647C2×C3×C4—32no—
648C2×C3×C4—32no—
649C2×C3×C4—32no—
650C2×C3×C4—61no—
651C2×C3×C4—61no—
652C2×C3×C4—61no—
653C2×C3×C4—61no—
654C2×C3×C4—61no—
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—124no—
666C2×C3×C4C2×C4×D312yes—
667C2×C3×C4C22×Dic312yes—
668#67—28no—
669#67—44no—
670C2×Dic3—21no—
671C2×Dic3—21no—
672C2×Dic3—21no—
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—32no—
686C2×Dic3—32no—
687C2×Dic3—44no—
688C2×Dic3—62no—
689C2×Dic3—61no—
690C2×Dic3—61no—
691C2×Dic3—61no—
692C2×Dic3—61no—
693C2×Dic3—62no—
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—121no—
713C2×Dic3—121no—
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—124no—
723C2×Dic3—124no—
724C2×Dic3D3×D412yes—
725C2×Dic3C22×Dic312yes—
726C2×Dic3C22×Dic312yes—
727C4×D3—124no—
728C4×D3—124no—
729C2×C32—42no—
730C2×C32—42no—
731C2×C32C2×C4×D411yescharacteristic
732C2×C32#51811yescharacteristic
733C2×C32#51811yescharacteristic
734C2×C32#53411yescharacteristic
735C2×C32#53511yescharacteristic
736C2×C32#53811yescharacteristic
737C2×C32#53811yescharacteristic
738C3×D3—24no—
739C3×D3—42no—
740C24—31no—
741C24—31no—
742C24—34no—
743C24—62no—
744C24—62no—
745C24—121no—
746C24—121no—
747C24—121no—
748C24—121no—
749C24C2×D3211yescharacteristic
750C24C2×D3211yescharacteristic
751C2×D4—34no—
752C2×D4—34no—
753C2×D4—41no—
754C2×D4—41no—
755C2×D4—62no—
756C2×D4—62no—
757C2×D4—121no—
758C2×D4—121no—
759C2×D4D3×Dic314yescomplemented
760C22×C4—31no—
761C22×C4—31no—
762C22×C4—31no—
763C22×C4—31no—
764C22×C4—31no—
765C22×C4—31no—
766C22×C4—62no—
767C22×C4—94no—
768C22×C4—91no—
769C22×C4—91no—
770C22×C4—91no—
771C22×C4—91no—
772C22×C4—121no—
773C22×C4—121no—
774C22×C4—182no—
775C22×C4—361no—
776C22×C4—361no—
777C22×C4—361no—
778C22×C4—361no—
779C22×C4C2×D3211yescharacteristic
780C4⋊C4—182no—
781C4⋊C4—361no—
782C4⋊C4—361no—
783C22⋊C4—34no—
784C22⋊C4—34no—
785C22⋊C4—34no—
786C22⋊C4—62no—
787C22⋊C4—121no—
788C22⋊C4—121no—
789C22⋊C4—182no—
790C22⋊C4—182no—
791C22⋊C4—182no—
792C22⋊C4—182no—
793C22⋊C4—182no—
794C22⋊C4—182no—
795C22⋊C4—361no—
796C22⋊C4—361no—
797C22⋊C4—361no—
798C22⋊C4—361no—
799C42—182no—
800C42—361no—
801C42—361no—
802C22×C3—22no—
803C22×C3—22no—
804C22×C3—22no—
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—21no—
815C22×C3—21no—
816C22×C3—21no—
817C22×C3—21no—
818C22×C3—21no—
819C22×C3—21no—
820C22×C3—21no—
821C22×C3—34no—
822C22×C3—42no—
823C22×C3—42no—
824C22×C3—42no—
825C22×C3—42no—
826C22×C3—42no—
827C22×C3—42no—
828C22×C3—41no—
829C22×C3—41no—
830C22×C3—41no—
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—62no—
845C22×C3—62no—
846C22×C3—62no—
847C22×C3—62no—
848C22×C3—62no—
849C22×C3—62no—
850C22×C3—62no—
851C22×C3—62no—
852C22×C3—62no—
853C22×C3—81no—
854C22×C3—81no—
855C22×C3—81no—
856C22×C3—81no—
857C22×C3—81no—
858C22×C3—81no—
859C22×C3—81no—
860C22×C3—81no—
861C22×C3—1216no—
862C22×C3—121no—
863C22×C3—121no—
864C22×C3—121no—
865C22×C3—121no—
866C22×C3C22×C4×D311yescharacteristic
867C22×C3C2×D3×D411yescharacteristic
868C22×C3C2×D3×D411yescharacteristic
869C22×C3C2×#23711yescharacteristic
870C22×C3#100411yescharacteristic
871C22×C3#100411yescharacteristic
872C22×C3#100411yescharacteristic
873C22×C3#100411yescharacteristic
874C22×C3#100411yescharacteristic
875C22×C3#100411yescharacteristic
876C22×C3#100411yescharacteristic
877C22×C3D3×#4111yescharacteristic
878C22×C3#100911yescharacteristic
879C22×C3C23×Dic311yescharacteristic
880C2×D3—22no—
881C2×D3—22no—
882C2×D3—22no—
883C2×D3—22no—
884C2×D3—22no—
885C2×D3—22no—
886C2×D3—22no—
887C2×D3—22no—
888C2×D3—22no—
889C2×D3—416no—
890C2×D3—41no—
891C2×D3—41no—
892C2×D3—41no—
893C2×D3—41no—
894C2×D3D4×Dic314yes—
895C3×C4—24no—
896C3×C4—22no—
897C3×C4—22no—
898C3×C4—62no—
899C3×C4—62no—
900C3×C4—62no—
901C3×C4—121no—
902C3×C4—121no—
903C3×C4—121no—
904Dic3—22no—
905Dic3—22no—
906Dic3—22no—
907Dic3—41no—
908Dic3—41no—
909Dic3—41no—
910Dic3—62no—
911Dic3—62no—
912Dic3—122no—
913Dic3—122no—
914Dic3—121no—
915Dic3—121no—
916Dic3—121no—
917Dic3—121no—
918Dic3—121no—
919Dic3—121no—
920Dic3—241no—
921Dic3—241no—
922C32#232111yescharacteristic, complemented, Sylow
923C23—21no—
924C23—21no—
925C23—21no—
926C23—21no—
927C23—21no—
928C23—21no—
929C23—21no—
930C23—21no—
931C23—21no—
932C23—21no—
933C23—21no—
934C23—21no—
935C23—32no—
936C23—32no—
937C23—32no—
938C23—32no—
939C23—68no—
940C23—61no—
941C23—61no—
942C23—61no—
943C23—61no—
944C23—61no—
945C23—61no—
946C23—61no—
947C23—61no—
948C23—61no—
949C23—61no—
950C23—124no—
951C23—124no—
952C23—124no—
953C23—124no—
954C23—124no—
955C23—124no—
956C23C2×D3×Dic312yes—
957C23C2×D3×Dic312yes—
958C23C22×D3211yescharacteristic
959D4—44no—
960D4—68no—
961D4—124no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—32no—
965C2×C4—32no—
966C2×C4—32no—
967C2×C4—61no—
968C2×C4—61no—
969C2×C4—61no—
970C2×C4—61no—
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—92no—
983C2×C4—124no—
984C2×C4—181no—
985C2×C4—181no—
986C2×C4—181no—
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—364no—
996C2×C4—364no—
997C2×C4C2×D3×Dic312yes—
998C2×C3—21no—
999C2×C3—21no—
1000C2×C3—21no—
1001C2×C3—21no—
1002C2×C3—21no—
1003C2×C3—21no—
1004C2×C3—21no—
1005C2×C3—42no—
1006C2×C3—42no—
1007C2×C3—42no—
1008C2×C3—42no—
1009C2×C3—64no—
1010C2×C3—82no—
1011C2×C3—82no—
1012C2×C3—122no—
1013C2×C3#548611yescharacteristic
1014C2×C3C4×D3×D411yescharacteristic
1015C2×C3#554511yescharacteristic
1016C2×C3#558911yescharacteristic
1017C2×C3#558911yescharacteristic
1018C2×C3#559211yescharacteristic
1019C2×C3#559311yescharacteristic
1020C2×C3#559311yescharacteristic
1021C2×C3#560711yescharacteristic
1022C2×C3#561311yescharacteristic
1023C2×C3#565711yescharacteristic
1024C2×C3C2×D4×Dic311yescharacteristic
1025C2×C3#579811yescharacteristic
1026C2×C3#579811yescharacteristic
1027D3—24no—
1028D3—42no—
1029C22—22no—
1030C22—22no—
1031C22—22no—
1032C22—22no—
1033C22—22no—
1034C22—22no—
1035C22—34no—
1036C22—41no—
1037C22—41no—
1038C22—41no—
1039C22—41no—
1040C22—41no—
1041C22—41no—
1042C22—41no—
1043C22—41no—
1044C22—62no—
1045C22—62no—
1046C22—62no—
1047C22—62no—
1048C22—62no—
1049C22—62no—
1050C22—62no—
1051C22—62no—
1052C22—62no—
1053C22—1216no—
1054C22—121no—
1055C22—121no—
1056C22—121no—
1057C22—121no—
1058C22D32×D411yescharacteristic
1059C22D3×#23711yescharacteristic
1060C22#6431311yescharacteristic
1061C22#6431411yescharacteristic
1062C22C22×D3×Dic311yescharacteristic
1063C22#6433011yescharacteristic
1064C22#6433011yescharacteristic
1065C4—22no—
1066C4—62no—
1067C4—62no—
1068C4—62no—
1069C4—121no—
1070C4—121no—
1071C4—121no—
1072C4—182no—
1073C4—361no—
1074C4—361no—
1075C4—361no—
1076C3—21no—
1077C3#7487611yescharacteristic, complemented
1078C3#8257811yescharacteristic, complemented
1079C2—42no—
1080C2—42no—
1081C2—64no—
1082C2—122no—
1083C2D3×D4×Dic311yescharacteristic
1084C2#1059518111yescharacteristic
1085C2#1059518511yescharacteristic
1086C2#1059521511yescharacteristic
1087C2#1059528011yescharacteristic
1088C2#1059528511yescharacteristic
1089C2#1059550611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC22×C32×D4C22
socle, cosocleC23×C32C24
prime radicalC2×C3×#937C2
hypercenterC22×D4D32
hypocenterC32#2321
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×Dic3×#67C2semidirect
3. C2×D3×#217C2semidirect
4. #10592920C2semidirect
5. C3×#5220C2semidirect
6. #10591721C2semidirect
7. #10591710C2semidirect
8. #10591707C2semidirect
9. #10591706C2semidirect
10. #10591701C2semidirect
11. #10591701C2semidirect
12. #10591379C2semidirect
13. #10591368C2semidirect
14. #10591316C2semidirect
15. #10591286C2semidirect
22. C23×C3×Dic3C22semidirect
27. C2×#3757C22semidirect
28. C2×#3757C22semidirect
29. C2×C4⋊(C3⋊Dic3)C22semidirect
30. C2×C4×C3⋊Dic3C22semidirect
34. C2×C3×#217C22semidirect
35. C3×#937C4semidirect
40. C2×Dic3⋊Dic3C22semidirect
41. C2×Dic3⋊Dic3C22semidirect
48. C2×Dic32C22semidirect
49. C2×Dic32C22semidirect
50. C3×C3⋊#95C22semidirect
51. C3×C3⋊#95C22semidirect
52. #63579C22semidirect
53. #63579C22semidirect
54. #63579C22semidirect
55. #63579C22semidirect
70. #5220D3semidirect
95. C23×C3×D3C2×C4semidirect
100. C2×C32×D4C2×C4semidirect
111. C2×C3×#67C2×C4semidirect
126. C2×D3×Dic3D4semidirect
136. C3×#217C2×C4semidirect
137. C3×(C2×D3)⋊C4C2×C4semidirect
138. C3×(C2×D3)⋊C4C2×C4semidirect
162. C23×Dic3C2×D3semidirect
194. C2×#217C2×D3semidirect
195. #937Dic3semidirect
231. C3⋊#95C2×D3semidirect
232. C3⋊#95C2×D3semidirect
344. C23×D3C2×Dic3semidirect
360. C2×C3×D4C4×D3semidirect
361. C2×C3×D4C2×Dic3semidirect
379. C2×#67C2×Dic3semidirect
440. #217C2×Dic3semidirect
447. (C2×D3)⋊C4C2×Dic3semidirect
448. (C2×D3)⋊C4C2×Dic3semidirect
759. C2×D4D3×Dic3semidirect
922. C32#2321semidirect
1077. C3#74876semidirect
1078. C3#82578semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9372
C2×Dic3×#672
C2×D3×#2172
#105929202
C3×#52202
#105917212
#105917102
#105917072
#105917062
#105917012
#105913792
#105913682
#105913162
#105912862
#825783
#748763