Finite Group Databasebeta

← #11803579

Subgroups — #11803579

Order 1152.

1479 conjugacy classes of subgroups.

The subgroup lattice has 992 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#939C211yesmaximal, characteristic
2C2×#67⋊Dic3C211yesmaximal, characteristic, complemented
3C2×#63955C211yesmaximal, characteristic, complemented
4#10592919C211yesmaximal, characteristic, complemented
5C3×#5221C211yesmaximal, characteristic, complemented
6#10591721C211yesmaximal, characteristic, complemented
7#10591719C211yesmaximal, characteristic, complemented
8#10591716C211yesmaximal, characteristic, complemented
9#10591707C211yesmaximal, characteristic, complemented
10#10591707C211yesmaximal, characteristic, complemented
11#10591702C211yesmaximal, characteristic, complemented
12#10591377C211yesmaximal, characteristic, complemented
13#10591305C211yesmaximal, characteristic, complemented
14#10591265C211yesmaximal, characteristic, complemented
15Dic3×Dic3⋊C4C211yesmaximal, characteristic, complemented
16#82633—31nomaximal
17#76296—31nomaximal
18C22×C32×D4C2211yescharacteristic
19C23×C3⋊Dic3C2211yescharacteristic
20C22×C3×#67C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C23×C3×Dic3C2211yescharacteristic
23C22×D3×Dic3C2211yescharacteristic
24C2×#3757C2211yescharacteristic
25C2×#3757C2211yescharacteristic
26C2×#3757C2211yescharacteristic
27C2×C3×#217C2211yescharacteristic
28C2×C3×#217C2211yescharacteristic
29C2×C3×#217C2211yescharacteristic
30C2×C3×#217C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C3×#939C418yescomplemented
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×C4⋊Dic3C2211yescharacteristic
35C2×C3×Dic3⋊C4C2211yescharacteristic
36C2×C3×C4×Dic3C2211yescharacteristic
37#67⋊Dic3—24no—
38C2×Dic3⋊Dic3C2211yescharacteristic
39C2×Dic3⋊Dic3C2211yescharacteristic
40C2×Dic3⋊Dic3C2211yescharacteristic
41C2×Dic3⋊Dic3C2211yescharacteristic
42C2×Dic3⋊Dic3C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic
46#63955—24no—
47C2×Dic32C2211yescharacteristic
48C2×Dic32C2211yescharacteristic
49C2×Dic32C2211yescharacteristic
50#63658C2211yescharacteristic
51#63658C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56C2×C3×#121—31no—
57C2×#939D311yescharacteristic
58C2×D4×Dic3—31no—
59C2×#926—31no—
60C2×#67⋊C4—31no—
61C2×#877—31no—
62C3×#390—31no—
63#5221—31no—
64#5221—31no—
65#5221D311yescharacteristic, complemented
66#5220—31no—
67#5220—31no—
68#5220—31no—
69#5220—61no—
70#5212—31no—
71#4989—31no—
72#4984—31no—
73#4976—31no—
74Dic3×C4⋊C4—31no—
75#4957—31no—
76#4957—31no—
77#4956—31no—
78#4951—31no—
79#4951—31no—
80#4950—31no—
81#4950—31no—
82#4946—31no—
83#4945—31no—
84#4942—31no—
85#4940—31no—
86C4×Dic3⋊C4—31no—
87C24×C32C2311yescharacteristic
88C24×C32C2311yescharacteristic
89C23×C3×D3C2311yescharacteristic
90C2×C32×D4—41no—
91C2×C32×D4—41no—
92C2×C32×D4C2×C414yescomplemented
93C22×C32×C4C2311yescharacteristic
94C22×C3⋊Dic3—22no—
95C22×C3⋊Dic3—41no—
96C22×C3⋊Dic3—41no—
97C22×C3⋊Dic3C2311yescharacteristic
98C22×C3⋊Dic3C2311yescharacteristic
99C22×C3⋊Dic3C2311yescharacteristic
100C22×C3⋊Dic3C2311yescharacteristic
101C2×C3×#67—22no—
102C2×C3×#67—22no—
103C2×C3×#67—41no—
104C2×C3×#67—41no—
105C2×C3×#67C2×C414yes—
106C2×C3×#67C2×C414yescomplemented
107C22×C3×Dic3—22no—
108C22×C3×Dic3—22no—
109C22×C3×Dic3C2×C414yescomplemented
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C22×C3×Dic3C2311yescharacteristic
116C22×C3×Dic3C2311yescharacteristic
117C2×D3×Dic3—22no—
118C2×D3×Dic3—41no—
119C2×D3×Dic3—41no—
120#3757—22no—
121#3757—41no—
122#3757—41no—
123C3×#217—22no—
124C3×#217—22no—
125C3×#217—41no—
126C3×#217—41no—
127C3×#217C2×C414yescomplemented
128C3×(C2×D3)⋊C4C2×C414yescomplemented
129C3×C4⋊Dic3—41no—
130C3×Dic3⋊C4C2×C414yescomplemented
131C3×C4×Dic3—41no—
132Dic3⋊Dic3—22no—
133Dic3⋊Dic3—22no—
134Dic3⋊Dic3—22no—
135Dic3⋊Dic3—22no—
136Dic3⋊Dic3—41no—
137(C2×D3)⋊Dic3—22no—
138(C2×D3)⋊Dic3—41no—
139(C2×D3)⋊Dic3—41no—
140Dic32—22no—
141Dic32—41no—
142Dic32D414yescomplemented
143#2324—91noSylow
144C22×C3×D4—21no—
145C22×C3×D4—31no—
146C22×C3×D4—31no—
147C22×C3×D4C2×D311yescharacteristic
148C22×C3×D4C2×D311yescharacteristic
149C23×C3×C4—31no—
150C22×#67C2×D311yescharacteristic
151C22×#67C2×D311yescharacteristic
152C23×Dic3—31no—
153C23×Dic3—31no—
154C23×Dic3—31no—
155C23×Dic3—61no—
156C23×Dic3C2×D311yescharacteristic
157C22×C4×D3—31no—
158C3×#121—38no—
159C2×C3×C4⋊C4—31no—
160C2×C3×C4⋊C4—31no—
161C2×C3×C22⋊C4—31no—
162C2×C3×C22⋊C4—31no—
163C2×C3×C22⋊C4—31no—
164C2×C3×C22⋊C4—31no—
165C2×C3×C22⋊C4—31no—
166C2×C3×C22⋊C4—31no—
167C2×C3×C42—31no—
168C2×#217—31no—
169C2×#217—31no—
170C2×#217—31no—
171C2×#217—31no—
172C2×#217—31no—
173C2×#217—31no—
174C2×#217—31no—
175C2×#217—31no—
176C2×#217—31no—
177C2×#217—61no—
178C2×#217—61no—
179C2×#217—61no—
180C2×#217C2×D311yescharacteristic
181C2×#217C2×D311yescharacteristic
182C2×#217C2×D311yescharacteristic
183C2×#217C2×D311yescharacteristic
184C2×#217C2×D311yescharacteristic
185#939Dic318yescomplemented
186D4×Dic3—64no—
187C2×(C2×D3)⋊C4—31no—
188C2×(C2×D3)⋊C4—31no—
189C2×(C2×D3)⋊C4—31no—
190C2×(C2×D3)⋊C4C2×D311yescharacteristic
191#926—64no—
192C2×C4⋊Dic3—31no—
193C2×C4⋊Dic3—31no—
194C2×C4⋊Dic3—31no—
195C2×C4⋊Dic3—31no—
196C2×C4⋊Dic3—31no—
197C2×C4⋊Dic3C2×D311yescharacteristic
198C2×Dic3⋊C4—31no—
199C2×Dic3⋊C4—31no—
200C2×Dic3⋊C4—31no—
201C2×Dic3⋊C4—31no—
202C2×Dic3⋊C4—31no—
203C2×Dic3⋊C4C2×D311yescharacteristic
204C2×C4×Dic3—31no—
205C2×C4×Dic3—31no—
206C2×C4×Dic3—31no—
207C2×C4×Dic3—31no—
208C2×C4×Dic3—31no—
209C2×C4×Dic3—31no—
210C2×C4×Dic3C2×D311yescharacteristic
211#67⋊C4—64no—
212#877—64no—
213C3⋊#95—31no—
214C3⋊#95—31no—
215C3⋊#95—31no—
216C3⋊#95—31no—
217C3⋊#95—31no—
218C3⋊#95—31no—
219C3⋊#95—31no—
220C3⋊#95—31no—
221C3⋊#95—31no—
222C3⋊#95—31no—
223C3⋊#95—31no—
224C3⋊#95—31no—
225C3⋊#95—61no—
226C3⋊#95—61no—
227C23×C32—21no—
228C23×C32—21no—
229C23×C32—21no—
230C23×C32—21no—
231C23×C32—21no—
232C23×C32—21no—
233C23×C32—21no—
234C23×C32—21no—
235C23×C32—21no—
236C23×C32—21no—
237C23×C32—21no—
238C23×C32—21no—
239C23×C32C22×C412yes—
240C23×C32C22×C412yes—
241C23×C32C2411yescharacteristic
242C22×C3×D3—21no—
243C22×C3×D3—21no—
244C22×C3×D3—21no—
245C22×C3×D3—21no—
246C22×C3×D3—21no—
247C22×C3×D3—21no—
248C22×C3×D3C22×C412yes—
249C32×D4—44no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4C22×C412yes—
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3—21no—
255C2×C3⋊Dic3—21no—
256C2×C3⋊Dic3—21no—
257C2×C3⋊Dic3—21no—
258C2×C3⋊Dic3—21no—
259C2×C3⋊Dic3—21no—
260C2×C3⋊Dic3—21no—
261C2×C3⋊Dic3—21no—
262C2×C3⋊Dic3—21no—
263C2×C3⋊Dic3—21no—
264C2×C3⋊Dic3—44no—
265C2×C3⋊Dic3C2×D412yes—
266C3×#67—28no—
267C3×#67—44no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3—21no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—28no—
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×Dic3C22×C412yes—
285C2×C3×Dic3C22×C412yes—
286C2×C3×Dic3C22×C412yes—
287C2×C3×Dic3C2×D412yes—
288C2×C3×Dic3C2×D412yes—
289C2×C3×Dic3#4112yes—
290D3×Dic3—44no—
291C2×#121—31no—
292C2×C4×D4—91no—
293C2×#117—91no—
294#390—31no—
295#390—91no—
296#390—91no—
297#389—91no—
298#388—91no—
299#388—91no—
300#386—91no—
301#386—91no—
302#385—91no—
303#385—91no—
304#380—91no—
305C4×C4⋊C4—91no—
306C24×C3—21no—
307C24×C3—21no—
308C24×C3—31no—
309C24×C3C22×D311yescharacteristic
310C24×C3C22×D311yescharacteristic
311C24×C3C22×D311yescharacteristic
312C24×C3C22×D311yescharacteristic
313C23×D3C22×D311yescharacteristic
314C2×C3×D4—24no—
315C2×C3×D4—34no—
316C2×C3×D4—34no—
317C2×C3×D4—41no—
318C2×C3×D4—41no—
319C2×C3×D4—41no—
320C2×C3×D4—41no—
321C2×C3×D4—42no—
322C2×C3×D4—42no—
323C2×C3×D4—62no—
324C2×C3×D4—62no—
325C2×C3×D4—121no—
326C2×C3×D4—121no—
327C2×C3×D4C4×D314yescomplemented
328C2×C3×D4C2×Dic314yescomplemented
329C22×C3×C4—21no—
330C22×C3×C4—31no—
331C22×C3×C4—34no—
332C22×C3×C4—31no—
333C22×C3×C4—31no—
334C22×C3×C4—31no—
335C22×C3×C4—31no—
336C22×C3×C4—31no—
337C22×C3×C4—31no—
338C22×C3×C4—62no—
339C22×C3×C4—62no—
340C22×C3×C4C22×D311yescharacteristic
341C22×C3×C4C22×D311yescharacteristic
342C2×#67—22no—
343C2×#67—22no—
344C2×#67—41no—
345C2×#67—41no—
346C2×#67C2×Dic314yes—
347C2×#67C2×Dic314yescomplemented
348C22×Dic3—22no—
349C22×Dic3—22no—
350C22×Dic3—31no—
351C22×Dic3—31no—
352C22×Dic3—31no—
353C22×Dic3—31no—
354C22×Dic3—31no—
355C22×Dic3—31no—
356C22×Dic3—31no—
357C22×Dic3—31no—
358C22×Dic3—61no—
359C22×Dic3—61no—
360C22×Dic3—61no—
361C22×Dic3—61no—
362C22×Dic3—62no—
363C22×Dic3—62no—
364C22×Dic3—62no—
365C22×Dic3—122no—
366C22×Dic3—121no—
367C22×Dic3—121no—
368C22×Dic3—121no—
369C22×Dic3—121no—
370C22×Dic3—121no—
371C22×Dic3—121no—
372C22×Dic3—122no—
373C22×Dic3—122no—
374C22×Dic3C2×Dic314yescomplemented
375C22×Dic3C22×D311yescharacteristic
376C22×Dic3C22×D311yescharacteristic
377C22×Dic3C22×D311yescharacteristic
378C22×Dic3C22×D311yescharacteristic
379C22×Dic3C22×D311yescharacteristic
380C22×Dic3C22×D311yescharacteristic
381C22×Dic3C22×D311yescharacteristic
382C2×C4×D3—62no—
383C2×C4×D3—121no—
384C2×C4×D3—121no—
385C3×C4⋊C4—34no—
386C3×C4⋊C4—121no—
387C3×C22⋊C4—34no—
388C3×C22⋊C4—34no—
389C3×C22⋊C4—62no—
390C3×C22⋊C4—62no—
391C3×C22⋊C4—121no—
392C3×C22⋊C4—121no—
393C3×C42—121no—
394#217—22no—
395#217—22no—
396#217—41no—
397#217—41no—
398#217—62no—
399#217—62no—
400#217—62no—
401#217—122no—
402#217—121no—
403#217—121no—
404#217—121no—
405#217—121no—
406#217—121no—
407#217—121no—
408#217—122no—
409#217—122no—
410#217C2×Dic314yescomplemented
411(C2×D3)⋊C4—62no—
412(C2×D3)⋊C4—121no—
413(C2×D3)⋊C4—121no—
414(C2×D3)⋊C4C2×Dic314yescomplemented
415C4⋊Dic3—41no—
416C4⋊Dic3—62no—
417C4⋊Dic3—62no—
418C4⋊Dic3—62no—
419C4⋊Dic3—62no—
420C4⋊Dic3—121no—
421Dic3⋊C4—62no—
422Dic3⋊C4—62no—
423Dic3⋊C4—62no—
424Dic3⋊C4—62no—
425Dic3⋊C4—121no—
426Dic3⋊C4C2×Dic314yescomplemented
427C4×Dic3—34no—
428C4×Dic3—34no—
429C4×Dic3—41no—
430C4×Dic3—62no—
431C4×Dic3—62no—
432C4×Dic3—121no—
433C4×Dic3—121no—
434C22×C32—22no—
435C22×C32—22no—
436C22×C32—22no—
437C22×C32—22no—
438C22×C32—22no—
439C22×C32—22no—
440C22×C32—41no—
441C22×C32—41no—
442C22×C32—41no—
443C22×C32—41no—
444C22×C32—41no—
445C22×C32—41no—
446C22×C32—41no—
447C22×C32—41no—
448C22×C32C23×C411yescharacteristic
449C22×C32C22×D411yescharacteristic
450C22×C32C2×#4111yescharacteristic
451C22×C32H(5,𝔽2)11yescharacteristic
452C22×C32H(5,𝔽2)11yescharacteristic
453C22×C32H(5,𝔽2)11yescharacteristic
454C22×C322−1+411yescharacteristic
455C2×C3×D3—22no—
456C2×C3×D3—22no—
457C2×C3×D3—22no—
458C2×C3×D3—41no—
459C2×C3×D3—41no—
460C2×C3×D3—41no—
461C2×C3×D3—41no—
462C32×C4—22no—
463C3⋊Dic3—22no—
464C3⋊Dic3—41no—
465C3⋊Dic3—41no—
466C3⋊Dic3—41no—
467C3×Dic3—22no—
468C3×Dic3—22no—
469C3×Dic3—22no—
470C3×Dic3—41no—
471C3×Dic3—41no—
472C3×Dic3—41no—
473C3×Dic3C4×D414yes—
474C22×D4—31no—
475C22×D4—31no—
476C22×D4D3211yescharacteristic
477C23×C4—31no—
478C23×C4—91no—
479C23×C4—91no—
480#121—38no—
481C4×D4—184no—
482#117—184no—
483C2×C4⋊C4—31no—
484C2×C4⋊C4—31no—
485C2×C4⋊C4—91no—
486C2×C4⋊C4—91no—
487C2×C4⋊C4—91no—
488C2×C4⋊C4—91no—
489C2×C4⋊C4—91no—
490C2×C22⋊C4—31no—
491C2×C22⋊C4—31no—
492C2×C22⋊C4—31no—
493C2×C22⋊C4—31no—
494C2×C22⋊C4—31no—
495C2×C22⋊C4—31no—
496C2×C22⋊C4—91no—
497C2×C22⋊C4—91no—
498C2×C22⋊C4—91no—
499C2×C22⋊C4—91no—
500C2×C22⋊C4—91no—
501C2×C22⋊C4—91no—
502C2×C42—31no—
503C2×C42—91no—
504C2×C42—91no—
505C2×C42—91no—
506#95—91no—
507#95—91no—
508#95—91no—
509#95—91no—
510#95—91no—
511#95—91no—
512C23×C3—22no—
513C23×C3—22no—
514C23×C3—21no—
515C23×C3—21no—
516C23×C3—21no—
517C23×C3—21no—
518C23×C3—21no—
519C23×C3—21no—
520C23×C3—21no—
521C23×C3—21no—
522C23×C3—21no—
523C23×C3—21no—
524C23×C3—21no—
525C23×C3—21no—
526C23×C3—21no—
527C23×C3—21no—
528C23×C3—21no—
529C23×C3—21no—
530C23×C3—21no—
531C23×C3—21no—
532C23×C3—21no—
533C23×C3—21no—
534C23×C3—21no—
535C23×C3—21no—
536C23×C3—21no—
537C23×C3—21no—
538C23×C3—21no—
539C23×C3—22no—
540C23×C3—22no—
541C23×C3—32no—
542C23×C3—41no—
543C23×C3—41no—
544C23×C3—41no—
545C23×C3—41no—
546C23×C3—41no—
547C23×C3—41no—
548C23×C3—41no—
549C23×C3—41no—
550C23×C3—41no—
551C23×C3—41no—
552C23×C3—61no—
553C23×C3—61no—
554C23×C3—61no—
555C23×C3—61no—
556C23×C3—61no—
557C23×C3—61no—
558C23×C3C2×C4×D312yes—
559C23×C3C2×C4×D312yes—
560C23×C3C22×Dic312yes—
561C23×C3C22×Dic312yes—
562C23×C3C23×D311yescharacteristic
563C23×C3C23×D311yescharacteristic
564C22×D3—21no—
565C22×D3—21no—
566C22×D3—21no—
567C22×D3—21no—
568C22×D3—21no—
569C22×D3—21no—
570C22×D3C22×Dic312yes—
571C3×D4—44no—
572C3×D4—44no—
573C3×D4—48no—
574C3×D4—68no—
575C3×D4—124no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—22no—
581C2×C3×C4—32no—
582C2×C3×C4—32no—
583C2×C3×C4—32no—
584C2×C3×C4—32no—
585C2×C3×C4—32no—
586C2×C3×C4—32no—
587C2×C3×C4—41no—
588C2×C3×C4—41no—
589C2×C3×C4—68no—
590C2×C3×C4—61no—
591C2×C3×C4—61no—
592C2×C3×C4—61no—
593C2×C3×C4—61no—
594C2×C3×C4—61no—
595C2×C3×C4—61no—
596C2×C3×C4—61no—
597C2×C3×C4—61no—
598C2×C3×C4—61no—
599C2×C3×C4—61no—
600C2×C3×C4—61no—
601C2×C3×C4—61no—
602C2×C3×C4—61no—
603C2×C3×C4—61no—
604C2×C3×C4—61no—
605C2×C3×C4C2×C4×D312yes—
606C2×C3×C4C22×Dic312yes—
607#67—28no—
608#67—44no—
609C2×Dic3—21no—
610C2×Dic3—21no—
611C2×Dic3—21no—
612C2×Dic3—21no—
613C2×Dic3—21no—
614C2×Dic3—21no—
615C2×Dic3—28no—
616C2×Dic3—21no—
617C2×Dic3—21no—
618C2×Dic3—21no—
619C2×Dic3—21no—
620C2×Dic3—21no—
621C2×Dic3—21no—
622C2×Dic3—21no—
623C2×Dic3—21no—
624C2×Dic3—21no—
625C2×Dic3—32no—
626C2×Dic3—32no—
627C2×Dic3—62no—
628C2×Dic3—61no—
629C2×Dic3—61no—
630C2×Dic3—61no—
631C2×Dic3—61no—
632C2×Dic3—62no—
633C2×Dic3—61no—
634C2×Dic3—61no—
635C2×Dic3—61no—
636C2×Dic3—61no—
637C2×Dic3—61no—
638C2×Dic3—61no—
639C2×Dic3—61no—
640C2×Dic3—61no—
641C2×Dic3—61no—
642C2×Dic3—61no—
643C2×Dic3—61no—
644C2×Dic3—61no—
645C2×Dic3—61no—
646C2×Dic3—61no—
647C2×Dic3—61no—
648C2×Dic3—61no—
649C2×Dic3—61no—
650C2×Dic3—61no—
651C2×Dic3—121no—
652C2×Dic3—121no—
653C2×Dic3—121no—
654C2×Dic3—121no—
655C2×Dic3—121no—
656C2×Dic3—121no—
657C2×Dic3—121no—
658C2×Dic3—121no—
659C2×Dic3—121no—
660C2×Dic3—121no—
661C2×Dic3—124no—
662C2×Dic3—124no—
663C2×Dic3—124no—
664C2×Dic3—128no—
665C2×Dic3D3×D412yes—
666C2×Dic3D3×D412yes—
667C2×Dic3#23712yes—
668C2×Dic3C22×Dic312yes—
669C2×Dic3C22×Dic312yes—
670C2×Dic3C22×Dic312yes—
671C4×D3—124no—
672C2×C32—42no—
673C2×C32—42no—
674C2×C32C2×C4×D411yescharacteristic
675C2×C32#51811yescharacteristic
676C2×C32#52011yescharacteristic
677C2×C32#53511yescharacteristic
678C2×C32#53711yescharacteristic
679C2×C32#54011yescharacteristic
680C2×C32#54211yescharacteristic
681C3×D3—42no—
682C24—31no—
683C24C2×D3211yescharacteristic
684C24C2×D3211yescharacteristic
685C2×D4—34no—
686C2×D4—34no—
687C2×D4—41no—
688C2×D4—41no—
689C2×D4—62no—
690C2×D4—62no—
691C2×D4—121no—
692C2×D4—121no—
693C2×D4D3×Dic314yescomplemented
694C22×C4—31no—
695C22×C4—31no—
696C22×C4—31no—
697C22×C4—31no—
698C22×C4—34no—
699C22×C4—31no—
700C22×C4—31no—
701C22×C4—31no—
702C22×C4—62no—
703C22×C4—62no—
704C22×C4—91no—
705C22×C4—91no—
706C22×C4—91no—
707C22×C4—91no—
708C22×C4—182no—
709C22×C4—182no—
710C22×C4—361no—
711C22×C4—361no—
712C22×C4—361no—
713C22×C4—361no—
714C22×C4C2×D3211yescharacteristic
715C4⋊C4—34no—
716C4⋊C4—121no—
717C4⋊C4—182no—
718C4⋊C4—182no—
719C4⋊C4—182no—
720C4⋊C4—182no—
721C4⋊C4—361no—
722C22⋊C4—34no—
723C22⋊C4—34no—
724C22⋊C4—62no—
725C22⋊C4—62no—
726C22⋊C4—121no—
727C22⋊C4—121no—
728C22⋊C4—182no—
729C22⋊C4—182no—
730C22⋊C4—361no—
731C22⋊C4—361no—
732C22⋊C4—361no—
733C22⋊C4—361no—
734C42—94no—
735C42—121no—
736C42—182no—
737C42—361no—
738C22×C3—24no—
739C22×C3—22no—
740C22×C3—22no—
741C22×C3—22no—
742C22×C3—22no—
743C22×C3—22no—
744C22×C3—22no—
745C22×C3—22no—
746C22×C3—22no—
747C22×C3—22no—
748C22×C3—22no—
749C22×C3—22no—
750C22×C3—22no—
751C22×C3—21no—
752C22×C3—21no—
753C22×C3—21no—
754C22×C3—21no—
755C22×C3—21no—
756C22×C3—21no—
757C22×C3—21no—
758C22×C3—42no—
759C22×C3—42no—
760C22×C3—42no—
761C22×C3—42no—
762C22×C3—42no—
763C22×C3—42no—
764C22×C3—42no—
765C22×C3—42no—
766C22×C3—42no—
767C22×C3—41no—
768C22×C3—41no—
769C22×C3—41no—
770C22×C3—41no—
771C22×C3—41no—
772C22×C3—41no—
773C22×C3—41no—
774C22×C3—41no—
775C22×C3—41no—
776C22×C3—41no—
777C22×C3—41no—
778C22×C3—41no—
779C22×C3—41no—
780C22×C3—41no—
781C22×C3—41no—
782C22×C3—41no—
783C22×C3—62no—
784C22×C3—62no—
785C22×C3—62no—
786C22×C3—81no—
787C22×C3—81no—
788C22×C3—81no—
789C22×C3—81no—
790C22×C3—121no—
791C22×C3—121no—
792C22×C3—121no—
793C22×C3—121no—
794C22×C3C22×C4×D311yescharacteristic
795C22×C3C2×D3×D411yescharacteristic
796C22×C3C2×D3×D411yescharacteristic
797C22×C3C2×#23711yescharacteristic
798C22×C3#100411yescharacteristic
799C22×C3#100411yescharacteristic
800C22×C3#100411yescharacteristic
801C22×C3#100411yescharacteristic
802C22×C3#100411yescharacteristic
803C22×C3D3×#4111yescharacteristic
804C22×C3#100911yescharacteristic
805C22×C3#101011yescharacteristic
806C22×C3#101011yescharacteristic
807C22×C3C23×Dic311yescharacteristic
808C2×D3—22no—
809C2×D3—22no—
810C2×D3—22no—
811C2×D3—41no—
812C2×D3—41no—
813C2×D3—41no—
814C2×D3—41no—
815C3×C4—22no—
816C3×C4—22no—
817C3×C4—34no—
818C3×C4—42no—
819C3×C4—62no—
820C3×C4—62no—
821C3×C4—62no—
822C3×C4—121no—
823C3×C4—121no—
824C3×C4—121no—
825Dic3—22no—
826Dic3—22no—
827Dic3—22no—
828Dic3—41no—
829Dic3—41no—
830Dic3—41no—
831Dic3—62no—
832Dic3—62no—
833Dic3—122no—
834Dic3—122no—
835Dic3—121no—
836Dic3—121no—
837Dic3—121no—
838Dic3—121no—
839Dic3—121no—
840Dic3—121no—
841Dic3—241no—
842Dic3—241no—
843Dic3D4×Dic314yes—
844C32#232411yescharacteristic, complemented, Sylow
845C23—21no—
846C23—21no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—21no—
851C23—21no—
852C23—21no—
853C23—21no—
854C23—21no—
855C23—21no—
856C23—21no—
857C23—32no—
858C23—61no—
859C23—61no—
860C23—61no—
861C23—61no—
862C23—61no—
863C23—61no—
864C23C2×D3×Dic312yes—
865C23C2×D3×Dic312yes—
866C23C22×D3211yescharacteristic
867D4—44no—
868D4—68no—
869D4—124no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—32no—
873C2×C4—32no—
874C2×C4—32no—
875C2×C4—32no—
876C2×C4—32no—
877C2×C4—32no—
878C2×C4—68no—
879C2×C4—61no—
880C2×C4—61no—
881C2×C4—61no—
882C2×C4—61no—
883C2×C4—61no—
884C2×C4—61no—
885C2×C4—61no—
886C2×C4—61no—
887C2×C4—61no—
888C2×C4—61no—
889C2×C4—61no—
890C2×C4—61no—
891C2×C4—61no—
892C2×C4—61no—
893C2×C4—61no—
894C2×C4—92no—
895C2×C4—181no—
896C2×C4—181no—
897C2×C4—181no—
898C2×C4—181no—
899C2×C4—181no—
900C2×C4—181no—
901C2×C4—181no—
902C2×C4—181no—
903C2×C4—181no—
904C2×C4—181no—
905C2×C4—181no—
906C2×C4—364no—
907C2×C4—364no—
908C2×C4C2×D3×Dic312yes—
909C2×C3—21no—
910C2×C3—21no—
911C2×C3—21no—
912C2×C3—21no—
913C2×C3—21no—
914C2×C3—21no—
915C2×C3—21no—
916C2×C3—44no—
917C2×C3—42no—
918C2×C3—42no—
919C2×C3—42no—
920C2×C3—42no—
921C2×C3—82no—
922C2×C3—122no—
923C2×C3#548611yescharacteristic
924C2×C3C4×D3×D411yescharacteristic
925C2×C3#554611yescharacteristic
926C2×C3#559711yescharacteristic
927C2×C3#560311yescharacteristic
928C2×C3#560711yescharacteristic
929C2×C3#560811yescharacteristic
930C2×C3#561511yescharacteristic
931C2×C3#561911yescharacteristic
932C2×C3#566911yescharacteristic
933C2×C3#571511yescharacteristic
934C2×C3C2×D4×Dic311yescharacteristic
935C2×C3#579811yescharacteristic
936C2×C3#582711yescharacteristic
937D3—42no—
938C22—22no—
939C22—22no—
940C22—22no—
941C22—22no—
942C22—22no—
943C22—22no—
944C22—41no—
945C22—41no—
946C22—41no—
947C22—41no—
948C22—41no—
949C22—41no—
950C22—41no—
951C22—41no—
952C22—62no—
953C22—62no—
954C22—62no—
955C22—121no—
956C22—121no—
957C22—121no—
958C22—121no—
959C22#6430911yescharacteristic
960C22D32×D411yescharacteristic
961C22D3×#23711yescharacteristic
962C22#6431411yescharacteristic
963C22C22×D3×Dic311yescharacteristic
964C22#6433011yescharacteristic
965C22#6433011yescharacteristic
966C4—22no—
967C4—34no—
968C4—62no—
969C4—62no—
970C4—62no—
971C4—121no—
972C4—121no—
973C4—121no—
974C4—182no—
975C4—361no—
976C4—361no—
977C4—361no—
978C3—21no—
979C3#7629611yescharacteristic, complemented
980C3#8263311yescharacteristic, complemented
981C2—42no—
982C2—42no—
983C2—122no—
984C2D3×D4×Dic311yescharacteristic
985C2#1059513211yescharacteristic
986C2#1059520111yescharacteristic
987C2#1059522211yescharacteristic
988C2#1059525011yescharacteristic
989C2#1059529911yescharacteristic
990C2#1059550611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC22×C32×D4C22
socle, cosocleC23×C32C24
prime radicalC2×C3×#939C2
hypercenterC22×D4D32
hypocenterC32#2324
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×#63955C2semidirect
4. #10592919C2semidirect
5. C3×#5221C2semidirect
6. #10591721C2semidirect
7. #10591719C2semidirect
8. #10591716C2semidirect
9. #10591707C2semidirect
10. #10591707C2semidirect
11. #10591702C2semidirect
12. #10591377C2semidirect
13. #10591305C2semidirect
14. #10591265C2semidirect
15. Dic3×Dic3⋊C4C2semidirect
32. C3×#939C4semidirect
65. #5221D3semidirect
92. C2×C32×D4C2×C4semidirect
106. C2×C3×#67C2×C4semidirect
109. C22×C3×Dic3C2×C4semidirect
127. C3×#217C2×C4semidirect
128. C3×(C2×D3)⋊C4C2×C4semidirect
130. C3×Dic3⋊C4C2×C4semidirect
142. Dic32D4semidirect
185. #939Dic3semidirect
327. C2×C3×D4C4×D3semidirect
328. C2×C3×D4C2×Dic3semidirect
347. C2×#67C2×Dic3semidirect
374. C22×Dic3C2×Dic3semidirect
410. #217C2×Dic3semidirect
414. (C2×D3)⋊C4C2×Dic3semidirect
426. Dic3⋊C4C2×Dic3semidirect
693. C2×D4D3×Dic3semidirect
844. C32#2324semidirect
979. C3#76296semidirect
980. C3#82633semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9392
C2×#67⋊Dic32
C2×#639552
#105929192
C3×#52212
#105917212
#105917192
#105917162
#105917072
#105917022
#105913772
#105913052
#105912652
Dic3×Dic3⋊C42
#826333
#762963