Finite Group Databasebeta

← #11803290

Subgroups — #11803290

Order 1152.

1759 conjugacy classes of subgroups.

The subgroup lattice has 1092 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#937C211yesmaximal, characteristic
2C2×#67⋊Dic3C211yesmaximal, characteristic, complemented
3C2×D3×#217C211yesmaximal, characteristic, complemented
4#10592919C211yesmaximal, characteristic, complemented
5C3×#5221C211yesmaximal, characteristic, complemented
6#10591721C211yesmaximal, characteristic, complemented
7#10591713C211yesmaximal, characteristic, complemented
8#10591707C211yesmaximal, characteristic, complemented
9#10591706C211yesmaximal, characteristic, complemented
10#10591702C211yesmaximal, characteristic, complemented
11#10591702C211yesmaximal, characteristic, complemented
12#10591377C211yesmaximal, characteristic, complemented
13Dic3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
14#10591307C211yesmaximal, characteristic, complemented
15#10591305C211yesmaximal, characteristic, complemented
16#82578—31nomaximal
17#76429—31nomaximal
18C24×C3×D3C2211yescharacteristic
19C22×C32×D4C2211yescharacteristic
20C23×C3⋊Dic3C2211yescharacteristic, complemented
21C22×C3×#67C2211yescharacteristic
22C22×C3×#67C2211yescharacteristic
23C22×D3×Dic3C2211yescharacteristic
24C22×D3×Dic3C2211yescharacteristic
25C2×#3757C2211yescharacteristic
26C2×#3757C2211yescharacteristic
27C2×#3757C2211yescharacteristic, complemented
28C2×C3×#217C2211yescharacteristic
29C2×C3×#217C2211yescharacteristic
30C2×C3×#217C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic, complemented
32C2×C3×#217C2211yescharacteristic, complemented
33C3×#937C418yescomplemented
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
37C2×C3×C4×Dic3C2211yescharacteristic, complemented
38#67⋊Dic3—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
50#63658C2211yescharacteristic, complemented
51#63658C2211yescharacteristic, 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×#67⋊C4—31no—
61C2×D3×C22⋊C4—31no—
62C3×#390—31no—
63#5247—31no—
64#5221—31no—
65#5221D311yescharacteristic, complemented
66#5220—31no—
67#5220—31no—
68#5220—31no—
69#5220—31no—
70#5220—61no—
71#4990—31no—
72#4989—31no—
73#4958—31no—
74#4957—31no—
75#4956—31no—
76#4955—31no—
77#4951—31no—
78#4951—31no—
79#4951—31no—
80#4951—31no—
81#4950—31no—
82#4945—31no—
83#4945—31no—
84Dic3×C22⋊C4—31no—
85#4940—31no—
86C4×(C2×D3)⋊C4—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⋊Dic3—22no—
103C22×C3⋊Dic3—41no—
104C22×C3⋊Dic3—41no—
105C22×C3⋊Dic3C2311yescharacteristic
106C22×C3⋊Dic3C2311yescharacteristic
107C22×C3⋊Dic3C2311yescharacteristic
108C22×C3⋊Dic3C2311yescharacteristic
109C2×C3×#67—22no—
110C2×C3×#67—22no—
111C2×C3×#67—41no—
112C2×C3×#67—41no—
113C2×C3×#67C2×C414yes—
114C2×C3×#67C2×C414yescomplemented
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—41no—
129#3757—41no—
130C3×#217—22no—
131C3×#217—22no—
132C3×#217—41no—
133C3×#217—41no—
134C3×#217C2×C414yescomplemented
135C3×(C2×D3)⋊C4C2×C414yescomplemented
136C3×(C2×D3)⋊C4C2×C414yescomplemented
137C3×C4⋊Dic3—41no—
138C3×C4×Dic3—41no—
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
157C22×#67C2×D311yescharacteristic
158C22×#67C2×D311yescharacteristic
159C23×Dic3—31no—
160C23×Dic3—31no—
161C23×Dic3—31no—
162C23×Dic3—31no—
163C23×Dic3—61no—
164C22×C4×D3—31no—
165C22×C4×D3—31no—
166C3×#120—38no—
167C2×C3×C4⋊C4—31no—
168C2×C3×C22⋊C4—31no—
169C2×C3×C22⋊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×C42—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—61no—
189C2×#217—61no—
190C2×#217—61no—
191C2×#217—64no—
192C2×#217C2×D311yescharacteristic
193C2×#217C2×D311yescharacteristic
194C2×#217C2×D311yescharacteristic
195C2×#217C2×D311yescharacteristic, complemented
196C2×#217C2×D311yescharacteristic, complemented
197#937Dic318yescomplemented
198D4×Dic3—64no—
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)⋊C4—31no—
205C2×(C2×D3)⋊C4C2×D311yescharacteristic
206C2×(C2×D3)⋊C4C2×D311yescharacteristic
207C2×C4⋊Dic3—31no—
208C2×C4⋊Dic3—31no—
209C2×C4⋊Dic3C2×D311yescharacteristic, complemented
210C2×Dic3⋊C4—31no—
211C2×Dic3⋊C4—31no—
212C2×C4×Dic3—31no—
213C2×C4×Dic3—31no—
214C2×C4×Dic3—31no—
215C2×C4×Dic3—31no—
216C2×C4×Dic3C2×D311yescharacteristic, complemented
217#67⋊C4—64no—
218D3×C22⋊C4—64no—
219C3⋊#95—31no—
220C3⋊#95—31no—
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⋊#95—61no—
232C3⋊#95—61no—
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⋊Dic3—44no—
285C2×C3⋊Dic3C2×D412yes—
286C3×#67—28no—
287C3×#67—44no—
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—21no—
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—31no—
312#390—91no—
313#388—91no—
314#388—91no—
315#388—91no—
316#388—91no—
317#386—91no—
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×C4C22×D311yescharacteristic
370C22×C3×C4C22×D311yescharacteristic
371C2×#67—22no—
372C2×#67—22no—
373C2×#67—41no—
374C2×#67—41no—
375C2×#67C2×Dic314yes—
376C2×#67C2×Dic314yescomplemented
377C22×Dic3—31no—
378C22×Dic3—31no—
379C22×Dic3—34no—
380C22×Dic3—31no—
381C22×Dic3—31no—
382C22×Dic3—31no—
383C22×Dic3—31no—
384C22×Dic3—31no—
385C22×Dic3—31no—
386C22×Dic3—61no—
387C22×Dic3—61no—
388C22×Dic3—61no—
389C22×Dic3—61no—
390C22×Dic3—62no—
391C22×Dic3—62no—
392C22×Dic3—62no—
393C22×Dic3—122no—
394C22×Dic3—121no—
395C22×Dic3—121no—
396C22×Dic3—121no—
397C22×Dic3—121no—
398C22×Dic3—121no—
399C22×Dic3—121no—
400C22×Dic3—121no—
401C22×Dic3—121no—
402C22×Dic3—122no—
403C22×Dic3—122no—
404C22×Dic3C22×D311yescharacteristic
405C22×Dic3C22×D311yescharacteristic
406C22×Dic3C22×D311yescharacteristic
407C22×Dic3C22×D311yescharacteristic
408C22×Dic3C22×D311yescharacteristic
409C22×Dic3C22×D311yescharacteristic
410C2×C4×D3—34no—
411C2×C4×D3—62no—
412C2×C4×D3—121no—
413C2×C4×D3—121no—
414C2×C4×D3—121no—
415C2×C4×D3—121no—
416C3×C4⋊C4—121no—
417C3×C22⋊C4—34no—
418C3×C22⋊C4—34no—
419C3×C22⋊C4—34no—
420C3×C22⋊C4—62no—
421C3×C22⋊C4—62no—
422C3×C22⋊C4—121no—
423C3×C22⋊C4—121no—
424C3×C42—121no—
425#217—22no—
426#217—22no—
427#217—41no—
428#217—41no—
429#217—62no—
430#217—62no—
431#217—62no—
432#217—62no—
433#217—62no—
434#217—62no—
435#217—122no—
436#217—121no—
437#217—121no—
438#217—121no—
439#217—121no—
440#217—121no—
441#217—121no—
442#217—122no—
443#217—122no—
444#217C2×Dic314yescomplemented
445(C2×D3)⋊C4—62no—
446(C2×D3)⋊C4—62no—
447(C2×D3)⋊C4—62no—
448(C2×D3)⋊C4—62no—
449(C2×D3)⋊C4—121no—
450(C2×D3)⋊C4—121no—
451(C2×D3)⋊C4C2×Dic314yescomplemented
452(C2×D3)⋊C4C2×Dic314yescomplemented
453C4⋊Dic3—41no—
454C4⋊Dic3—62no—
455C4⋊Dic3—121no—
456Dic3⋊C4—62no—
457Dic3⋊C4—121no—
458C4×Dic3—41no—
459C4×Dic3—62no—
460C4×Dic3—62no—
461C4×Dic3—121no—
462C4×Dic3—121no—
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—91no—
515C23×C4—91no—
516C23×C4—91no—
517#120—38no—
518C4×D4—184no—
519C2×C4⋊C4—31no—
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—31no—
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—31no—
540C2×C42—91no—
541C2×C42—91no—
542#95—91no—
543#95—91no—
544#95—91no—
545#95—91no—
546#95—91no—
547#95—91no—
548C23×C3—22no—
549C23×C3—22no—
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—21no—
574C23×C3—21no—
575C23×C3—22no—
576C23×C3—22no—
577C23×C3—32no—
578C23×C3—32no—
579C23×C3—32no—
580C23×C3—32no—
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—21no—
641C2×C3×C4—21no—
642C2×C3×C4—21no—
643C2×C3×C4—21no—
644C2×C3×C4—22no—
645C2×C3×C4—32no—
646C2×C3×C4—32no—
647C2×C3×C4—32no—
648C2×C3×C4—41no—
649C2×C3×C4—41no—
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×C4C2×C4×D312yes—
666C2×C3×C4C22×Dic312yes—
667#67—28no—
668#67—44no—
669C2×Dic3—21no—
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—32no—
685C2×Dic3—32no—
686C2×Dic3—62no—
687C2×Dic3—61no—
688C2×Dic3—61no—
689C2×Dic3—61no—
690C2×Dic3—61no—
691C2×Dic3—62no—
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—121no—
711C2×Dic3—121no—
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—124no—
721C2×Dic3—124no—
722C2×Dic3—124no—
723C2×Dic3—124no—
724C2×Dic3—128no—
725C2×Dic3D3×D412yes—
726C2×Dic3C22×Dic312yes—
727C2×Dic3C22×Dic312yes—
728C4×D3—124no—
729C4×D3—124no—
730C2×C32—42no—
731C2×C32—42no—
732C2×C32C2×C4×D411yescharacteristic
733C2×C32#51811yescharacteristic
734C2×C32#51811yescharacteristic
735C2×C32#53411yescharacteristic
736C2×C32#53511yescharacteristic
737C2×C32#53811yescharacteristic
738C2×C32#53811yescharacteristic
739C3×D3—24no—
740C3×D3—42no—
741C24—31no—
742C24—31no—
743C24—34no—
744C24—62no—
745C24—62no—
746C24—121no—
747C24—121no—
748C24—121no—
749C24—121no—
750C24C2×D3211yescharacteristic
751C24C2×D3211yescharacteristic
752C2×D4—34no—
753C2×D4—34no—
754C2×D4—41no—
755C2×D4—41no—
756C2×D4—62no—
757C2×D4—62no—
758C2×D4—121no—
759C2×D4—121no—
760C2×D4D3×Dic314yescomplemented
761C22×C4—31no—
762C22×C4—31no—
763C22×C4—31no—
764C22×C4—31no—
765C22×C4—31no—
766C22×C4—31no—
767C22×C4—94no—
768C22×C4—91no—
769C22×C4—91no—
770C22×C4—91no—
771C22×C4—91no—
772C22×C4—182no—
773C22×C4—182no—
774C22×C4—361no—
775C22×C4—361no—
776C22×C4—361no—
777C22×C4—361no—
778C22×C4—361no—
779C22×C4—361no—
780C22×C4C2×D3211yescharacteristic
781C4⋊C4—121no—
782C4⋊C4—182no—
783C4⋊C4—361no—
784C22⋊C4—34no—
785C22⋊C4—34no—
786C22⋊C4—34no—
787C22⋊C4—62no—
788C22⋊C4—62no—
789C22⋊C4—121no—
790C22⋊C4—121no—
791C22⋊C4—182no—
792C22⋊C4—182no—
793C22⋊C4—182no—
794C22⋊C4—182no—
795C22⋊C4—182no—
796C22⋊C4—361no—
797C22⋊C4—361no—
798C22⋊C4—361no—
799C22⋊C4—361no—
800C42—121no—
801C42—182no—
802C42—361no—
803C22×C3—24no—
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—22no—
815C22×C3—22no—
816C22×C3—21no—
817C22×C3—21no—
818C22×C3—21no—
819C22×C3—21no—
820C22×C3—21no—
821C22×C3—21no—
822C22×C3—21no—
823C22×C3—34no—
824C22×C3—42no—
825C22×C3—42no—
826C22×C3—42no—
827C22×C3—42no—
828C22×C3—42no—
829C22×C3—42no—
830C22×C3—42no—
831C22×C3—42no—
832C22×C3—42no—
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—41no—
848C22×C3—41no—
849C22×C3—62no—
850C22×C3—62no—
851C22×C3—62no—
852C22×C3—62no—
853C22×C3—62no—
854C22×C3—62no—
855C22×C3—62no—
856C22×C3—62no—
857C22×C3—62no—
858C22×C3—81no—
859C22×C3—81no—
860C22×C3—81no—
861C22×C3—81no—
862C22×C3—1216no—
863C22×C3—121no—
864C22×C3—121no—
865C22×C3—121no—
866C22×C3—121no—
867C22×C3C22×C4×D311yescharacteristic
868C22×C3C2×D3×D411yescharacteristic
869C22×C3C2×D3×D411yescharacteristic
870C22×C3C2×#23711yescharacteristic
871C22×C3#100411yescharacteristic
872C22×C3#100411yescharacteristic
873C22×C3#100411yescharacteristic
874C22×C3#100411yescharacteristic
875C22×C3#100411yescharacteristic
876C22×C3#100411yescharacteristic
877C22×C3#100411yescharacteristic
878C22×C3D3×#4111yescharacteristic
879C22×C3#100911yescharacteristic
880C22×C3C23×Dic311yescharacteristic
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—22no—
890C2×D3—416no—
891C2×D3—41no—
892C2×D3—41no—
893C2×D3—41no—
894C2×D3—41no—
895C2×D3D4×Dic314yes—
896C3×C4—22no—
897C3×C4—22no—
898C3×C4—42no—
899C3×C4—62no—
900C3×C4—62no—
901C3×C4—62no—
902C3×C4—121no—
903C3×C4—121no—
904C3×C4—121no—
905Dic3—22no—
906Dic3—22no—
907Dic3—22no—
908Dic3—41no—
909Dic3—41no—
910Dic3—41no—
911Dic3—62no—
912Dic3—62no—
913Dic3—122no—
914Dic3—122no—
915Dic3—121no—
916Dic3—121no—
917Dic3—121no—
918Dic3—121no—
919Dic3—121no—
920Dic3—121no—
921Dic3—241no—
922Dic3—241no—
923C32#232111yescharacteristic, complemented, Sylow
924C23—21no—
925C23—21no—
926C23—21no—
927C23—21no—
928C23—21no—
929C23—21no—
930C23—21no—
931C23—21no—
932C23—21no—
933C23—21no—
934C23—21no—
935C23—21no—
936C23—32no—
937C23—32no—
938C23—32no—
939C23—32no—
940C23—68no—
941C23—61no—
942C23—61no—
943C23—61no—
944C23—61no—
945C23—61no—
946C23—61no—
947C23—61no—
948C23—61no—
949C23—61no—
950C23—61no—
951C23—124no—
952C23—124no—
953C23—124no—
954C23—124no—
955C23—124no—
956C23—124no—
957C23C2×D3×Dic312yes—
958C23C2×D3×Dic312yes—
959C23C22×D3211yescharacteristic
960D4—44no—
961D4—68no—
962D4—124no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—32no—
966C2×C4—32no—
967C2×C4—32no—
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—61no—
983C2×C4—92no—
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×C4—364no—
998C2×C4C2×D3×Dic312yes—
999C2×C3—21no—
1000C2×C3—21no—
1001C2×C3—21no—
1002C2×C3—21no—
1003C2×C3—21no—
1004C2×C3—21no—
1005C2×C3—21no—
1006C2×C3—44no—
1007C2×C3—42no—
1008C2×C3—42no—
1009C2×C3—42no—
1010C2×C3—42no—
1011C2×C3—64no—
1012C2×C3—82no—
1013C2×C3—122no—
1014C2×C3#548611yescharacteristic
1015C2×C3C4×D3×D411yescharacteristic
1016C2×C3#554511yescharacteristic
1017C2×C3#558911yescharacteristic
1018C2×C3#559211yescharacteristic
1019C2×C3#559311yescharacteristic
1020C2×C3#559311yescharacteristic
1021C2×C3#560511yescharacteristic
1022C2×C3#561311yescharacteristic
1023C2×C3#567811yescharacteristic
1024C2×C3#571511yescharacteristic
1025C2×C3C2×D4×Dic311yescharacteristic
1026C2×C3#579811yescharacteristic
1027C2×C3#579811yescharacteristic
1028D3—24no—
1029D3—42no—
1030C22—22no—
1031C22—22no—
1032C22—22no—
1033C22—22no—
1034C22—22no—
1035C22—22no—
1036C22—34no—
1037C22—41no—
1038C22—41no—
1039C22—41no—
1040C22—41no—
1041C22—41no—
1042C22—41no—
1043C22—41no—
1044C22—41no—
1045C22—62no—
1046C22—62no—
1047C22—62no—
1048C22—62no—
1049C22—62no—
1050C22—62no—
1051C22—62no—
1052C22—62no—
1053C22—62no—
1054C22—1216no—
1055C22—121no—
1056C22—121no—
1057C22—121no—
1058C22—121no—
1059C22D32×D411yescharacteristic
1060C22D3×#23711yescharacteristic
1061C22#6431311yescharacteristic
1062C22#6431411yescharacteristic
1063C22C22×D3×Dic311yescharacteristic
1064C22#6433011yescharacteristic
1065C22#6433011yescharacteristic
1066C4—22no—
1067C4—62no—
1068C4—62no—
1069C4—62no—
1070C4—121no—
1071C4—121no—
1072C4—121no—
1073C4—182no—
1074C4—361no—
1075C4—361no—
1076C4—361no—
1077C3—21no—
1078C3#7642911yescharacteristic, complemented
1079C3#8257811yescharacteristic, complemented
1080C2—42no—
1081C2—42no—
1082C2—64no—
1083C2—122no—
1084C2D3×D4×Dic311yescharacteristic
1085C2#1059518011yescharacteristic
1086C2#1059518411yescharacteristic
1087C2#1059521511yescharacteristic
1088C2#1059528111yescharacteristic
1089C2#1059528611yescharacteristic
1090C2#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×#67⋊Dic3C2semidirect
3. C2×D3×#217C2semidirect
4. #10592919C2semidirect
5. C3×#5221C2semidirect
6. #10591721C2semidirect
7. #10591713C2semidirect
8. #10591707C2semidirect
9. #10591706C2semidirect
10. #10591702C2semidirect
11. #10591702C2semidirect
12. #10591377C2semidirect
13. Dic3×(C2×D3)⋊C4C2semidirect
14. #10591307C2semidirect
15. #10591305C2semidirect
20. C23×C3⋊Dic3C22semidirect
27. C2×#3757C22semidirect
31. C2×C3×#217C22semidirect
32. C2×C3×#217C22semidirect
33. C3×#937C4semidirect
36. C2×C3×C4⋊Dic3C22semidirect
37. C2×C3×C4×Dic3C22semidirect
40. C2×Dic3⋊Dic3C22semidirect
41. C2×Dic3⋊Dic3C22semidirect
48. C2×Dic32C22semidirect
49. C2×Dic32C22semidirect
50. #63658C22semidirect
51. #63658C22semidirect
52. #63579C22semidirect
53. #63579C22semidirect
54. #63579C22semidirect
55. #63579C22semidirect
65. #5221D3semidirect
95. C23×C3×D3C2×C4semidirect
100. C2×C32×D4C2×C4semidirect
114. C2×C3×#67C2×C4semidirect
126. C2×D3×Dic3D4semidirect
134. C3×#217C2×C4semidirect
135. C3×(C2×D3)⋊C4C2×C4semidirect
136. C3×(C2×D3)⋊C4C2×C4semidirect
195. C2×#217C2×D3semidirect
196. C2×#217C2×D3semidirect
197. #937Dic3semidirect
209. C2×C4⋊Dic3C2×D3semidirect
216. C2×C4×Dic3C2×D3semidirect
344. C23×D3C2×Dic3semidirect
360. C2×C3×D4C4×D3semidirect
361. C2×C3×D4C2×Dic3semidirect
376. C2×#67C2×Dic3semidirect
444. #217C2×Dic3semidirect
451. (C2×D3)⋊C4C2×Dic3semidirect
452. (C2×D3)⋊C4C2×Dic3semidirect
760. C2×D4D3×Dic3semidirect
923. C32#2321semidirect
1078. C3#76429semidirect
1079. 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×#67⋊Dic32
C2×D3×#2172
#105929192
C3×#52212
#105917212
#105917132
#105917072
#105917062
#105917022
#105913772
Dic3×(C2×D3)⋊C42
#105913072
#105913052
#825783
#764293