Finite Group Databasebeta

← #11805788

Subgroups — #11805788

Order 1152.

1319 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D4×Dic3C211yesmaximal, characteristic
2#10592919C211yesmaximal, characteristic
3C3×#5220C211yesmaximal, characteristic
4#10591716C211yesmaximal, characteristic, complemented
5#10591705C211yesmaximal, characteristic, complemented
6#10591702C211yesmaximal, characteristic, complemented
7#10591701C211yesmaximal, characteristic, complemented
8Dic3×#217C211yesmaximal, characteristic, complemented
9Dic3×#217C211yesmaximal, characteristic, complemented
10#10591696C211yesmaximal, characteristic, complemented
11C2×#63579C211yesmaximal, characteristic, complemented
12#10591270C211yesmaximal, characteristic, complemented
13#10591269C211yesmaximal, characteristic, complemented
14#10591239C211yesmaximal, characteristic, complemented
15#10591223C211yesmaximal, characteristic, complemented
16#82336—31nomaximal
17#74674—31nomaximal
18C22×C32×D4C2211yescharacteristic
19C23×C3⋊Dic3C2211yescharacteristic
20C23×C3×Dic3C2211yescharacteristic
21C23×C3×Dic3C2211yescharacteristic
22C23×C3×Dic3C2211yescharacteristic
23C2×#3757C2211yescharacteristic
24C2×#3757C2211yescharacteristic
25C2×#3757C2211yescharacteristic
26C2×C3×#217C2211yescharacteristic
27C2×C3×#217C2211yescharacteristic
28C2×C3×#217C2211yescharacteristic
29C2×C3×#217C2211yescharacteristic
30C2×C3×#217C2211yescharacteristic
31C3×D4×Dic3C418yescomplemented
32C2×C3×C4⋊Dic3C2211yescharacteristic
33C2×C3×C4×Dic3C2211yescharacteristic
34C2×Dic3⋊Dic3C2211yescharacteristic
35C2×Dic3⋊Dic3C2211yescharacteristic
36C2×Dic32C2211yescharacteristic
37C2×Dic32C2211yescharacteristic
38C2×Dic32C2211yescharacteristic
39C2×Dic32C2211yescharacteristic
40#63658C2211yescharacteristic
41#63658C2211yescharacteristic
42C3×C3⋊#95C2211yescharacteristic
43C3×C3⋊#95C2211yescharacteristic
44#63579C2211yescharacteristic
45#63579C2211yescharacteristic
46#63579C2211yescharacteristic
47#63579C2211yescharacteristic
48#63579C2211yescharacteristic
49#63579C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54C2×C3×C4×D4—31no—
55C2×D4×Dic3D311yescharacteristic
56C3×#386—31no—
57#5220—31no—
58#5220—31no—
59#5220—61no—
60#5220D311yescharacteristic
61#5212—31no—
62#5211—31no—
63C4×#217—31no—
64C4×#217—31no—
65C2×C3⋊#95—31no—
66C2×C3⋊#95—31no—
67#4980—31no—
68#4980—31no—
69#4951—31no—
70#4951—31no—
71#4945—31no—
72#4944—31no—
73#4943—31no—
74#4942—31no—
75Dic3×C22⋊C4—31no—
76Dic3×C22⋊C4—31no—
77Dic3×C22⋊C4—31no—
78Dic3×C22⋊C4—31no—
79#4937—31no—
80#4932—31no—
81#4654—31no—
82#4653—31no—
83#4651—31no—
84#4648—31no—
85C24×C32C2311yescharacteristic
86C24×C32C2311yescharacteristic
87C2×C32×D4—22no—
88C2×C32×D4—22no—
89C2×C32×D4C2×C414yes—
90C22×C32×C4C2311yescharacteristic
91C22×C3⋊Dic3—22no—
92C22×C3⋊Dic3—22no—
93C22×C3⋊Dic3—41no—
94C22×C3⋊Dic3C2311yescharacteristic
95C22×C3⋊Dic3C2311yescharacteristic
96C22×C3⋊Dic3C2311yescharacteristic
97C22×C3⋊Dic3C2311yescharacteristic
98C22×C3×Dic3—22no—
99C22×C3×Dic3—22no—
100C22×C3×Dic3—41no—
101C22×C3×Dic3—41no—
102C22×C3×Dic3—41no—
103C22×C3×Dic3—41no—
104C22×C3×Dic3—41no—
105C22×C3×Dic3C2×C414yes—
106C22×C3×Dic3C2×C414yescomplemented
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115#3757—22no—
116#3757—22no—
117#3757—41no—
118C3×#217—22no—
119C3×#217—22no—
120C3×#217—41no—
121C3×#217C2×C414yes—
122C3×#217C2×C414yescomplemented
123C3×C4⋊Dic3C2×C414yescomplemented
124C3×C4×Dic3C2×C414yescomplemented
125Dic3⋊Dic3—41no—
126Dic3⋊Dic3—41no—
127Dic32—22no—
128Dic32—22no—
129Dic32—41no—
130Dic32—41no—
131#2353—91noSylow
132C22×C3×D4—21no—
133C22×C3×D4C2×D311yescharacteristic
134C22×C3×D4C2×D311yescharacteristic
135C23×C3×C4—31no—
136C23×C3×C4—31no—
137C23×C3×C4—31no—
138C23×Dic3—31no—
139C23×Dic3—31no—
140C23×Dic3—61no—
141C23×Dic3C2×D311yescharacteristic
142C23×Dic3C2×D311yescharacteristic
143C23×Dic3C2×D311yescharacteristic
144C3×C4×D4—38no—
145C2×C3×C4⋊C4—31no—
146C2×C3×C22⋊C4—31no—
147C2×C3×C22⋊C4—31no—
148C2×C3×C22⋊C4—31no—
149C2×C3×C22⋊C4—31no—
150C2×C3×C22⋊C4—31no—
151C2×C3×C42—31no—
152C2×#217—31no—
153C2×#217—31no—
154C2×#217—31no—
155C2×#217—31no—
156C2×#217—31no—
157C2×#217—31no—
158C2×#217—61no—
159C2×#217—61no—
160C2×#217—61no—
161C2×#217C2×D311yescharacteristic
162C2×#217C2×D311yescharacteristic
163C2×#217C2×D311yescharacteristic
164C2×#217C2×D311yescharacteristic
165C2×#217C2×D311yescharacteristic
166D4×Dic3Dic318yescomplemented
167C2×C4⋊Dic3—31no—
168C2×C4⋊Dic3—31no—
169C2×C4⋊Dic3C2×D311yescharacteristic
170C2×Dic3⋊C4—31no—
171C2×Dic3⋊C4—31no—
172C2×C4×Dic3—31no—
173C2×C4×Dic3—31no—
174C2×C4×Dic3—31no—
175C2×C4×Dic3—31no—
176C2×C4×Dic3—31no—
177C2×C4×Dic3—31no—
178C2×C4×Dic3—31no—
179C2×C4×Dic3—31no—
180C2×C4×Dic3C2×D311yescharacteristic
181C3×#95—31no—
182C3×#95—31no—
183C3⋊#95—31no—
184C3⋊#95—31no—
185C3⋊#95—31no—
186C3⋊#95—31no—
187C3⋊#95—31no—
188C3⋊#95—31no—
189C3⋊#95—31no—
190C3⋊#95—31no—
191C3⋊#95—31no—
192C3⋊#95—31no—
193C3⋊#95—31no—
194C3⋊#95—31no—
195C3⋊#95—31no—
196C3⋊#95—31no—
197C3⋊#95—31no—
198C3⋊#95—31no—
199C3⋊#95—31no—
200C3⋊#95—31no—
201C3⋊#95—31no—
202C3⋊#95—31no—
203C3⋊#95—31no—
204C3⋊#95—31no—
205C3⋊#95—31no—
206C3⋊#95—31no—
207C3⋊#95—61no—
208C3⋊#95—61no—
209C3⋊#95C2×D311yescharacteristic
210C3⋊#95C2×D311yescharacteristic
211C23×C32—21no—
212C23×C32—21no—
213C23×C32—21no—
214C23×C32—21no—
215C23×C32—21no—
216C23×C32—21no—
217C23×C32—21no—
218C23×C32—21no—
219C23×C32—21no—
220C23×C32—21no—
221C23×C32C22×C412yes—
222C23×C32C22×C412yes—
223C23×C32#4112yes—
224C23×C32#4112yes—
225C23×C32C2411yescharacteristic
226C32×D4—28no—
227C2×C32×C4—21no—
228C2×C32×C4—21no—
229C2×C32×C4C22×C412yes—
230C2×C3⋊Dic3—21no—
231C2×C3⋊Dic3—21no—
232C2×C3⋊Dic3—21no—
233C2×C3⋊Dic3—21no—
234C2×C3⋊Dic3—21no—
235C2×C3⋊Dic3—21no—
236C2×C3⋊Dic3—21no—
237C2×C3⋊Dic3—21no—
238C2×C3⋊Dic3—21no—
239C2×C3⋊Dic3—21no—
240C2×C3⋊Dic3—21no—
241C2×C3⋊Dic3—44no—
242C2×C3⋊Dic3#4112yes—
243C2×C3×Dic3—21no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
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—44no—
263C2×C3×Dic3—44no—
264C2×C3×Dic3—44no—
265C2×C3×Dic3C22×C412yes—
266C2×C3×Dic3C22×C412yes—
267C2×C3×Dic3C22×C412yes—
268C2×C3×Dic3C22×C412yes—
269C2×C3×Dic3#4112yes—
270C2×C4×D4—31no—
271#388—91no—
272#388—91no—
273#387—91no—
274#387—91no—
275#386—31no—
276#386—91no—
277#383—91no—
278#381—91no—
279#380—91no—
280C4×C22⋊C4—91no—
281C4×C22⋊C4—91no—
282C4×C22⋊C4—91no—
283#376—91no—
284C2×#95—91no—
285C24×C3—21no—
286C24×C3—21no—
287C24×C3C22×D311yescharacteristic
288C24×C3C22×D311yescharacteristic
289C24×C3C22×D311yescharacteristic
290C24×C3C22×D311yescharacteristic
291C2×C3×D4—22no—
292C2×C3×D4—22no—
293C2×C3×D4—22no—
294C2×C3×D4—22no—
295C2×C3×D4—24no—
296C2×C3×D4—42no—
297C2×C3×D4—42no—
298C2×C3×D4C4×D314yes—
299C2×C3×D4C2×Dic314yes—
300C22×C3×C4—21no—
301C22×C3×C4—31no—
302C22×C3×C4—31no—
303C22×C3×C4—31no—
304C22×C3×C4—31no—
305C22×C3×C4—31no—
306C22×C3×C4—34no—
307C22×C3×C4—34no—
308C22×C3×C4—31no—
309C22×C3×C4—31no—
310C22×C3×C4—31no—
311C22×C3×C4—62no—
312C22×C3×C4—62no—
313C22×C3×C4—121no—
314C22×C3×C4—121no—
315C22×C3×C4—121no—
316C22×C3×C4—121no—
317C22×C3×C4—121no—
318C22×C3×C4C22×D311yescharacteristic
319C22×C3×C4C22×D311yescharacteristic
320C22×Dic3—22no—
321C22×Dic3—22no—
322C22×Dic3—31no—
323C22×Dic3—31no—
324C22×Dic3—31no—
325C22×Dic3—31no—
326C22×Dic3—31no—
327C22×Dic3—31no—
328C22×Dic3—31no—
329C22×Dic3—31no—
330C22×Dic3—41no—
331C22×Dic3—41no—
332C22×Dic3—41no—
333C22×Dic3—41no—
334C22×Dic3—41no—
335C22×Dic3—61no—
336C22×Dic3—61no—
337C22×Dic3—61no—
338C22×Dic3—61no—
339C22×Dic3—62no—
340C22×Dic3—62no—
341C22×Dic3—62no—
342C22×Dic3—62no—
343C22×Dic3—122no—
344C22×Dic3—122no—
345C22×Dic3—121no—
346C22×Dic3—121no—
347C22×Dic3—122no—
348C22×Dic3C2×Dic314yes—
349C22×Dic3C2×Dic314yescomplemented
350C22×Dic3C22×D311yescharacteristic
351C22×Dic3C22×D311yescharacteristic
352C22×Dic3C22×D311yescharacteristic
353C22×Dic3C22×D311yescharacteristic
354C22×Dic3C22×D311yescharacteristic
355C22×Dic3C22×D311yescharacteristic
356C22×Dic3C22×D311yescharacteristic
357C22×Dic3C22×D311yescharacteristic
358C3×C4⋊C4—34no—
359C3×C22⋊C4—34no—
360C3×C22⋊C4—34no—
361C3×C22⋊C4—62no—
362C3×C22⋊C4—62no—
363C3×C22⋊C4—121no—
364C3×C42—34no—
365#217—22no—
366#217—22no—
367#217—41no—
368#217—62no—
369#217—62no—
370#217—62no—
371#217—62no—
372#217—122no—
373#217—122no—
374#217—121no—
375#217—121no—
376#217—122no—
377#217C2×Dic314yes—
378#217C2×Dic314yescomplemented
379C4⋊Dic3—121no—
380C4⋊Dic3—121no—
381C4⋊Dic3C2×Dic314yescomplemented
382Dic3⋊C4—121no—
383Dic3⋊C4—121no—
384C4×Dic3—62no—
385C4×Dic3—62no—
386C4×Dic3—62no—
387C4×Dic3—62no—
388C4×Dic3—121no—
389C4×Dic3—121no—
390C4×Dic3—121no—
391C4×Dic3—121no—
392C4×Dic3C2×Dic314yescomplemented
393C22×C32—22no—
394C22×C32—22no—
395C22×C32—22no—
396C22×C32—22no—
397C22×C32—22no—
398C22×C32—22no—
399C22×C32—22no—
400C22×C32—22no—
401C22×C32—22no—
402C22×C32—41no—
403C22×C32—41no—
404C22×C32—41no—
405C22×C32—41no—
406C22×C32#11714yes—
407C22×C32C23×C411yescharacteristic
408C22×C32C2×#4111yescharacteristic
409C22×C32C2×#4111yescharacteristic
410C22×C32C2×#4111yescharacteristic
411C22×C32C2×#4111yescharacteristic
412C22×C32H(5,𝔽2)11yescharacteristic
413C22×C32H(5,𝔽2)11yescharacteristic
414C32×C4—22no—
415C3⋊Dic3—22no—
416C3⋊Dic3—41no—
417C3⋊Dic3—41no—
418C3⋊Dic3—41no—
419C3×Dic3—22no—
420C3×Dic3—22no—
421C3×Dic3—22no—
422C3×Dic3—22no—
423C3×Dic3—22no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C22×D4D3211yescharacteristic
428C23×C4—31no—
429C23×C4—31no—
430C23×C4—31no—
431C23×C4—91no—
432C4×D4—38no—
433C2×C4⋊C4—31no—
434C2×C4⋊C4—91no—
435C2×C4⋊C4—91no—
436C2×C22⋊C4—31no—
437C2×C22⋊C4—31no—
438C2×C22⋊C4—31no—
439C2×C22⋊C4—31no—
440C2×C22⋊C4—31no—
441C2×C22⋊C4—91no—
442C2×C22⋊C4—91no—
443C2×C22⋊C4—91no—
444C2×C42—31no—
445C2×C42—91no—
446C2×C42—91no—
447C2×C42—91no—
448C2×C42—91no—
449#95—31no—
450#95—31no—
451#95—91no—
452#95—91no—
453#95—91no—
454#95—91no—
455#95—91no—
456#95—91no—
457#95—91no—
458#95—91no—
459#95—91no—
460#95—91no—
461#95—91no—
462#95—91no—
463C23×C3—21no—
464C23×C3—21no—
465C23×C3—21no—
466C23×C3—21no—
467C23×C3—21no—
468C23×C3—21no—
469C23×C3—21no—
470C23×C3—21no—
471C23×C3—21no—
472C23×C3—21no—
473C23×C3—21no—
474C23×C3—21no—
475C23×C3—21no—
476C23×C3—21no—
477C23×C3—21no—
478C23×C3—21no—
479C23×C3—21no—
480C23×C3—21no—
481C23×C3—21no—
482C23×C3—21no—
483C23×C3—21no—
484C23×C3—22no—
485C23×C3—22no—
486C23×C3—22no—
487C23×C3—22no—
488C23×C3—41no—
489C23×C3—41no—
490C23×C3—41no—
491C23×C3—41no—
492C23×C3—41no—
493C23×C3—41no—
494C23×C3—41no—
495C23×C3—41no—
496C23×C3—41no—
497C23×C3—41no—
498C23×C3C2×C4×D312yes—
499C23×C3C2×C4×D312yes—
500C23×C3#23512yes—
501C23×C3#23512yes—
502C23×C3#23712yes—
503C23×C3#23712yes—
504C23×C3C22×Dic312yes—
505C23×C3C22×Dic312yes—
506C23×C3C23×D311yescharacteristic
507C23×C3C23×D311yescharacteristic
508C3×D4—28no—
509C3×D4—28no—
510C3×D4—48no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—22no—
516C2×C3×C4—32no—
517C2×C3×C4—32no—
518C2×C3×C4—32no—
519C2×C3×C4—32no—
520C2×C3×C4—32no—
521C2×C3×C4—41no—
522C2×C3×C4—41no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—61no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4—61no—
539C2×C3×C4—61no—
540C2×C3×C4—61no—
541C2×C3×C4—61no—
542C2×C3×C4—124no—
543C2×C3×C4—124no—
544C2×C3×C4—124no—
545C2×C3×C4C2×C4×D312yes—
546C2×C3×C4C22×Dic312yes—
547C2×Dic3—21no—
548C2×Dic3—21no—
549C2×Dic3—21no—
550C2×Dic3—21no—
551C2×Dic3—21no—
552C2×Dic3—21no—
553C2×Dic3—21no—
554C2×Dic3—21no—
555C2×Dic3—21no—
556C2×Dic3—21no—
557C2×Dic3—21no—
558C2×Dic3—21no—
559C2×Dic3—21no—
560C2×Dic3—21no—
561C2×Dic3—21no—
562C2×Dic3—21no—
563C2×Dic3—21no—
564C2×Dic3—21no—
565C2×Dic3—21no—
566C2×Dic3—32no—
567C2×Dic3—32no—
568C2×Dic3—44no—
569C2×Dic3—44no—
570C2×Dic3—44no—
571C2×Dic3—62no—
572C2×Dic3—61no—
573C2×Dic3—61no—
574C2×Dic3—61no—
575C2×Dic3—61no—
576C2×Dic3—62no—
577C2×Dic3—61no—
578C2×Dic3—61no—
579C2×Dic3—61no—
580C2×Dic3—61no—
581C2×Dic3—61no—
582C2×Dic3—61no—
583C2×Dic3—61no—
584C2×Dic3—61no—
585C2×Dic3—61no—
586C2×Dic3—61no—
587C2×Dic3—61no—
588C2×Dic3—61no—
589C2×Dic3—61no—
590C2×Dic3—61no—
591C2×Dic3—61no—
592C2×Dic3—61no—
593C2×Dic3—61no—
594C2×Dic3—61no—
595C2×Dic3—121no—
596C2×Dic3—121no—
597C2×Dic3—121no—
598C2×Dic3—121no—
599C2×Dic3—121no—
600C2×Dic3—121no—
601C2×Dic3—121no—
602C2×Dic3—121no—
603C2×Dic3—121no—
604C2×Dic3—121no—
605C2×Dic3—124no—
606C2×Dic3—124no—
607C2×Dic3—128no—
608C2×Dic3#23712yes—
609C2×Dic3C22×Dic312yes—
610C2×Dic3C22×Dic312yes—
611C2×Dic3C22×Dic312yes—
612C2×Dic3C22×Dic312yes—
613C2×C32—24no—
614C2×C32—42no—
615C2×C32C2×#11711yescharacteristic
616C2×C32C4×#4111yescharacteristic
617C2×C32#51811yescharacteristic
618C2×C32#55111yescharacteristic
619C2×C32#55111yescharacteristic
620C2×C32#55311yescharacteristic
621C2×C32#55311yescharacteristic
622C24C2×D3211yescharacteristic
623C24C2×D3211yescharacteristic
624C2×D4—22no—
625C2×D4—22no—
626C2×D4D3×Dic314yes—
627C22×C4—31no—
628C22×C4—31no—
629C22×C4—31no—
630C22×C4—31no—
631C22×C4—31no—
632C22×C4—34no—
633C22×C4—34no—
634C22×C4—31no—
635C22×C4—31no—
636C22×C4—31no—
637C22×C4—62no—
638C22×C4—62no—
639C22×C4—91no—
640C22×C4—91no—
641C22×C4—91no—
642C22×C4—91no—
643C22×C4—121no—
644C22×C4—121no—
645C22×C4—121no—
646C22×C4—121no—
647C22×C4—121no—
648C22×C4—182no—
649C22×C4—182no—
650C22×C4—361no—
651C22×C4C2×D3211yescharacteristic
652C4⋊C4—34no—
653C4⋊C4—361no—
654C4⋊C4—361no—
655C22⋊C4—34no—
656C22⋊C4—34no—
657C22⋊C4—62no—
658C22⋊C4—62no—
659C22⋊C4—121no—
660C22⋊C4—182no—
661C22⋊C4—182no—
662C22⋊C4—361no—
663C42—34no—
664C42—182no—
665C42—182no—
666C42—361no—
667C42—361no—
668C22×C3—22no—
669C22×C3—22no—
670C22×C3—22no—
671C22×C3—22no—
672C22×C3—22no—
673C22×C3—22no—
674C22×C3—22no—
675C22×C3—22no—
676C22×C3—22no—
677C22×C3—22no—
678C22×C3—22no—
679C22×C3—22no—
680C22×C3—22no—
681C22×C3—22no—
682C22×C3—22no—
683C22×C3—22no—
684C22×C3—22no—
685C22×C3—22no—
686C22×C3—21no—
687C22×C3—21no—
688C22×C3—21no—
689C22×C3—21no—
690C22×C3—21no—
691C22×C3—21no—
692C22×C3—21no—
693C22×C3—24no—
694C22×C3—42no—
695C22×C3—42no—
696C22×C3—42no—
697C22×C3—42no—
698C22×C3—42no—
699C22×C3—42no—
700C22×C3—42no—
701C22×C3—42no—
702C22×C3—42no—
703C22×C3—41no—
704C22×C3—41no—
705C22×C3—41no—
706C22×C3—41no—
707C22×C3—41no—
708C22×C3—41no—
709C22×C3—41no—
710C22×C3—41no—
711C22×C3—81no—
712C22×C3—81no—
713C22×C3—81no—
714C22×C3—81no—
715C22×C3#87714yes—
716C22×C3#92614yes—
717C22×C3C22×C4×D311yescharacteristic
718C22×C3C2×#23511yescharacteristic
719C22×C3C2×#23511yescharacteristic
720C22×C3C2×#23711yescharacteristic
721C22×C3C2×#23711yescharacteristic
722C22×C3C2×#23711yescharacteristic
723C22×C3#100411yescharacteristic
724C22×C3#100411yescharacteristic
725C22×C3#100411yescharacteristic
726C22×C3D3×#4111yescharacteristic
727C22×C3D3×#4111yescharacteristic
728C22×C3D3×#4111yescharacteristic
729C22×C3#100911yescharacteristic
730C22×C3C23×Dic311yescharacteristic
731C3×C4—22no—
732C3×C4—22no—
733C3×C4—42no—
734C3×C4—62no—
735C3×C4—62no—
736C3×C4—62no—
737C3×C4—62no—
738C3×C4—62no—
739C3×C4—121no—
740C3×C4—121no—
741C3×C4—121no—
742Dic3—22no—
743Dic3—22no—
744Dic3—22no—
745Dic3—22no—
746Dic3—22no—
747Dic3—41no—
748Dic3—41no—
749Dic3—41no—
750Dic3—62no—
751Dic3—62no—
752Dic3—122no—
753Dic3—122no—
754Dic3—121no—
755Dic3—121no—
756Dic3—121no—
757Dic3—121no—
758Dic3—121no—
759Dic3—121no—
760Dic3—241no—
761Dic3—241no—
762C32#235311yescharacteristic, complemented, Sylow
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—21no—
772C23—21no—
773C23C2×D3×Dic312yes—
774C23C2×D3×Dic312yes—
775C23#380412yes—
776C23#380412yes—
777C23C22×D3211yescharacteristic
778D4—28no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—32no—
782C2×C4—32no—
783C2×C4—32no—
784C2×C4—32no—
785C2×C4—32no—
786C2×C4—61no—
787C2×C4—61no—
788C2×C4—61no—
789C2×C4—61no—
790C2×C4—61no—
791C2×C4—61no—
792C2×C4—61no—
793C2×C4—61no—
794C2×C4—61no—
795C2×C4—61no—
796C2×C4—61no—
797C2×C4—61no—
798C2×C4—61no—
799C2×C4—61no—
800C2×C4—61no—
801C2×C4—61no—
802C2×C4—61no—
803C2×C4—61no—
804C2×C4—61no—
805C2×C4—92no—
806C2×C4—124no—
807C2×C4—124no—
808C2×C4—124no—
809C2×C4—181no—
810C2×C4—181no—
811C2×C4—181no—
812C2×C4—181no—
813C2×C4—181no—
814C2×C4—181no—
815C2×C4—181no—
816C2×C4—181no—
817C2×C4—181no—
818C2×C4—181no—
819C2×C4—181no—
820C2×C4—364no—
821C2×C4C2×D3×Dic312yes—
822C2×C3—24no—
823C2×C3—24no—
824C2×C3—21no—
825C2×C3—21no—
826C2×C3—21no—
827C2×C3—21no—
828C2×C3—21no—
829C2×C3—21no—
830C2×C3—21no—
831C2×C3—44no—
832C2×C3—42no—
833C2×C3—42no—
834C2×C3—82no—
835C2×C3C2×#87711yescharacteristic
836C2×C3C4×#23711yescharacteristic
837C2×C3#554011yescharacteristic
838C2×C3#554011yescharacteristic
839C2×C3#554511yescharacteristic
840C2×C3#555611yescharacteristic
841C2×C3#555611yescharacteristic
842C2×C3#558711yescharacteristic
843C2×C3#560111yescharacteristic
844C2×C3#561811yescharacteristic
845C2×C3#565811yescharacteristic
846C2×C3C2×#92611yescharacteristic
847C2×C3#579811yescharacteristic
848C2×C3Dic3×#4111yescharacteristic
849C22—22no—
850C22—22no—
851C22—22no—
852C22—22no—
853C22—22no—
854C22—22no—
855C22—22no—
856C22—22no—
857C22—22no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22#6395514yes—
863C22D3×#23711yescharacteristic
864C22#6431211yescharacteristic
865C22#6431311yescharacteristic
866C22#6431411yescharacteristic
867C22C22×D3×Dic311yescharacteristic
868C22C2×#380411yescharacteristic
869C22C2×#380411yescharacteristic
870C4—22no—
871C4—62no—
872C4—62no—
873C4—62no—
874C4—62no—
875C4—62no—
876C4—121no—
877C4—121no—
878C4—121no—
879C4—182no—
880C4—361no—
881C4—361no—
882C4—361no—
883C3—21no—
884C3#7467411yescharacteristic, complemented
885C3#8233611yescharacteristic, complemented
886C2—24no—
887C2—42no—
888C2#1059511811yescharacteristic
889C2#1059517511yescharacteristic
890C2Dic3×#23711yescharacteristic
891C2#1059519311yescharacteristic
892C2#1059520411yescharacteristic
893C2#1059521511yescharacteristic
894C2C2×#6395511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
Fitting, prime radicalC22×C32×D4C22
socle, cosocleC23×C32C24
hypercenterC22×D4D32
hypocenterC32#2353
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
4. #10591716C2semidirect
5. #10591705C2semidirect
6. #10591702C2semidirect
7. #10591701C2semidirect
8. Dic3×#217C2semidirect
9. Dic3×#217C2semidirect
10. #10591696C2semidirect
11. C2×#63579C2semidirect
12. #10591270C2semidirect
13. #10591269C2semidirect
14. #10591239C2semidirect
15. #10591223C2semidirect
31. C3×D4×Dic3C4semidirect
106. C22×C3×Dic3C2×C4semidirect
122. C3×#217C2×C4semidirect
123. C3×C4⋊Dic3C2×C4semidirect
124. C3×C4×Dic3C2×C4semidirect
166. D4×Dic3Dic3semidirect
349. C22×Dic3C2×Dic3semidirect
378. #217C2×Dic3semidirect
381. C4⋊Dic3C2×Dic3semidirect
392. C4×Dic3C2×Dic3semidirect
762. C32#2353semidirect
884. C3#74674semidirect
885. C3#82336semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D4×Dic32
#105929192
C3×#52202
#105917162
#105917052
#105917022
#105917012
Dic3×#2172
#105916962
C2×#635792
#105912702
#105912692
#105912392
#105912232
#823363
#746743