Finite Group Databasebeta

← C3×#69916 #11790551

Subgroups — C3×#69916 #11790551

Order 1152.

893 conjugacy classes of subgroups.

The subgroup lattice has 675 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×#67C211yesmaximal, characteristic
2C2×C32×C22⋊C8C211yesmaximal, characteristic, complemented
3C2×C3×#830C211yesmaximal, characteristic, complemented
4C2×C3×(C2×D3)⋊C8C211yesmaximal, characteristic, complemented
5C2×C3×(C2×D3)⋊C8C211yesmaximal, characteristic, complemented
6C2×C3×Dic3⋊C8C211yesmaximal, characteristic, complemented
7C2×C3×C8×Dic3C211yesmaximal, characteristic, complemented
8C3×#1954—31nomaximal
9#69916C311yesmaximal, characteristic, direct product factor
10C23×C32×C4C2211yescharacteristic
11C22×C3×#67C411yescharacteristic
12C22×C3×C4×D3C2211yescharacteristic
13C22×C32×C8C2211yescharacteristic
14C22×C32×C8C2211yescharacteristic
15C2×C3×#217C411yescharacteristic
16C3×C4×#67—22no—
17C3×C4×#67—22no—
18C2×C3×(C2×D3)⋊C4C411yescharacteristic
19C2×C3×Dic3⋊C4C411yescharacteristic
20C2×C3×C4×Dic3C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C22×C3×C3⋊C8C2211yescharacteristic
23C32×C22⋊C8—22no—
24C3×#830—22no—
25C3×(C2×D3)⋊C8—22no—
26C3×(C2×D3)⋊C8—22no—
27C3×Dic3⋊C8—22no—
28C3×C8×Dic3—22no—
29C2×C3×C4×D4—31no—
30C2×C4×#67C2×C311yescharacteristic
31C2×C3×C4⋊C8—31no—
32C2×C3×C22⋊C8—21no—
33C2×C3×C22⋊C8—31no—
34C2×C3×C22⋊C8—31no—
35C2×C3×C22⋊C8—31no—
36C2×C3×C22⋊C8D311yescharacteristic, complemented
37C2×C3×C22⋊C8C2×C311yescharacteristic, complemented
38C2×C3×C4×C8—31no—
39C2×#830C2×C311yescharacteristic, complemented
40C2×(C2×D3)⋊C8C2×C311yescharacteristic, complemented
41C2×(C2×D3)⋊C8C2×C311yescharacteristic, complemented
42C2×Dic3⋊C8C2×C311yescharacteristic, complemented
43C2×C8×Dic3C2×C311yescharacteristic, complemented
44C24×C32C2×C411yescharacteristic
45C23×C3×D3C2×C411yescharacteristic
46C22×C32×C4—21no—
47C22×C32×C4—21no—
48C22×C32×C4—21no—
49C22×C32×C4—21no—
50C22×C32×C4—21no—
51C22×C32×C4—21no—
52C22×C32×C4C2×C411yescharacteristic
53C22×C32×C4C2311yescharacteristic
54C2×C3×#67—22no—
55C2×C3×#67—22no—
56C2×C3×#67C814yescomplemented
57C22×C3×Dic3C2×C411yescharacteristic
58C22×C3×Dic3C2×C411yescharacteristic
59C22×C3×Dic3C2×C411yescharacteristic
60C2×C3×C4×D3—21no—
61C2×C3×C4×D3—21no—
62C2×C3×C4×D3—21no—
63C2×C3×C4×D3—21no—
64C2×C3×C4×D3—21no—
65C2×C3×C4×D3—21no—
66C2×C32×C8—21no—
67C2×C32×C8—21no—
68C2×C32×C8—21no—
69C2×C32×C8—21no—
70C2×C32×C8—21no—
71C2×C32×C8D412yescomplemented
72C3×#217—22no—
73C3×(C2×D3)⋊C4—22no—
74C3×Dic3⋊C4—22no—
75C3×C4×Dic3D412yes—
76C3×C4×Dic3D412yes—
77C2×C3×C3⋊C8—21no—
78C2×C3×C3⋊C8—21no—
79C2×C3×C3⋊C8—21no—
80C2×C3×C3⋊C8—21no—
81C2×C3×C3⋊C8—21no—
82C2×C3×C3⋊C8D412yescomplemented
83#1954—31noSylow
84C22×C3×D4—31no—
85C23×C3×C4—21no—
86C23×C3×C4—31no—
87C23×C3×C4C2×D311yescharacteristic
88C23×C3×C4C22×C311yescharacteristic
89C22×#67C3×C411yescharacteristic
90C22×C4×D3C22×C311yescharacteristic
91C22×C3×C8—21no—
92C22×C3×C8—21no—
93C22×C3×C8—31no—
94C22×C3×C8—31no—
95C22×C3×C8C2×D311yescharacteristic
96C22×C3×C8C2×D311yescharacteristic
97C22×C3×C8C22×C311yescharacteristic
98C22×C3×C8C22×C311yescharacteristic
99C3×C4×D4—62no—
100C3×C4×D4—62no—
101C2×C3×C4⋊C4—31no—
102C2×C3×C22⋊C4—31no—
103C2×C3×C22⋊C4—31no—
104C2×C3×C42—31no—
105C2×#217C3×C411yescharacteristic
106C4×#67—22no—
107C4×#67—22no—
108C2×(C2×D3)⋊C4C3×C411yescharacteristic
109C2×Dic3⋊C4C3×C411yescharacteristic
110C2×C4×Dic3C22×C311yescharacteristic
111C22×C3⋊C8C22×C311yescharacteristic
112C22×C3⋊C8C22×C311yescharacteristic
113C3×C4⋊C8—62no—
114C3×C22⋊C8—24no—
115C3×C22⋊C8—22no—
116C3×C22⋊C8—22no—
117C3×C22⋊C8—62no—
118C3×C22⋊C8—62no—
119C3×C22⋊C8—62no—
120C3×C4×C8—62no—
121#830—22no—
122(C2×D3)⋊C8—22no—
123(C2×D3)⋊C8—22no—
124Dic3⋊C8—22no—
125C8×Dic3—22no—
126C23×C32—21no—
127C23×C32—21no—
128C23×C32—21no—
129C23×C32—21no—
130C23×C32—21no—
131C23×C32—21no—
132C23×C32C2×C812yes—
133C23×C32C22×C411yescharacteristic
134C22×C3×D3—21no—
135C22×C3×D3—21no—
136C22×C3×D3—21no—
137C22×C3×D3—21no—
138C22×C3×D3—21no—
139C22×C3×D3—21no—
140C22×C3×D3C2×C812yes—
141C2×C32×C4—21no—
142C2×C32×C4—21no—
143C2×C32×C4—21no—
144C2×C32×C4—41no—
145C2×C32×C4—41no—
146C2×C32×C4—41no—
147C2×C32×C4—41no—
148C2×C32×C4C2×D411yescharacteristic
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4C2×D411yescharacteristic
151C2×C32×C4C2×D411yescharacteristic
152C2×C32×C4#4111yescharacteristic
153C2×C32×C4#4111yescharacteristic
154C3×#67—28no—
155C2×C3×Dic3—21no—
156C2×C3×Dic3—21no—
157C2×C3×Dic3—21no—
158C2×C3×Dic3—21no—
159C2×C3×Dic3—21no—
160C2×C3×Dic3C22⋊C412yes—
161C2×C3×Dic3C22⋊C412yes—
162C2×C3×Dic3C2×C812yes—
163C2×C3×Dic3M1612yes—
164C3×C4×D3—41no—
165C3×C4×D3—41no—
166C3×C4×D3—41no—
167C3×C4×D3—41no—
168C32×C8—22no—
169C32×C8—41no—
170C3×C3⋊C8—22no—
171C3×C3⋊C8—41no—
172C2×C4×D4—31no—
173C2×C4⋊C8—31no—
174C2×C22⋊C8—31no—
175C2×C22⋊C8—31no—
176C2×C22⋊C8—31no—
177C2×C22⋊C8C3×D311yescharacteristic, complemented
178C2×C4×C8—31no—
179C24×C3—21no—
180C24×C3—31no—
181C24×C3C4×D311yescharacteristic
182C24×C3C2×C3×C411yescharacteristic
183C23×D3C2×C3×C411yescharacteristic
184C2×C3×D4—34no—
185C2×C3×D4—62no—
186C2×C3×D4—62no—
187C22×C3×C4—22no—
188C22×C3×C4—22no—
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4—21no—
192C22×C3×C4—21no—
193C22×C3×C4—21no—
194C22×C3×C4—21no—
195C22×C3×C4—21no—
196C22×C3×C4—21no—
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—21no—
200C22×C3×C4—21no—
201C22×C3×C4—21no—
202C22×C3×C4—21no—
203C22×C3×C4—31no—
204C22×C3×C4—31no—
205C22×C3×C4—31no—
206C22×C3×C4—41no—
207C22×C3×C4—41no—
208C22×C3×C4—41no—
209C22×C3×C4—41no—
210C22×C3×C4—61no—
211C22×C3×C4—61no—
212C22×C3×C4—61no—
213C22×C3×C4—61no—
214C22×C3×C4—61no—
215C22×C3×C4—61no—
216C22×C3×C4C4×D311yescharacteristic
217C22×C3×C4C2×C3×C411yescharacteristic
218C22×C3×C4C22×D311yescharacteristic
219C22×C3×C4C23×C311yescharacteristic
220C2×#67—22no—
221C2×#67—22no—
222C2×#67C3×C814yescomplemented
223C22×Dic3C2×C3×C411yescharacteristic
224C22×Dic3C2×C3×C411yescharacteristic
225C22×Dic3C2×C3×C411yescharacteristic
226C2×C4×D3—21no—
227C2×C4×D3—21no—
228C2×C4×D3—21no—
229C2×C4×D3—21no—
230C2×C4×D3—21no—
231C2×C4×D3—21no—
232C2×C3×C8—21no—
233C2×C3×C8—21no—
234C2×C3×C8—21no—
235C2×C3×C8—21no—
236C2×C3×C8—22no—
237C2×C3×C8—21no—
238C2×C3×C8—21no—
239C2×C3×C8—21no—
240C2×C3×C8—21no—
241C2×C3×C8—21no—
242C2×C3×C8—21no—
243C2×C3×C8—22no—
244C2×C3×C8—32no—
245C2×C3×C8—41no—
246C2×C3×C8—41no—
247C2×C3×C8—41no—
248C2×C3×C8—41no—
249C2×C3×C8—61no—
250C2×C3×C8—61no—
251C2×C3×C8—61no—
252C2×C3×C8—61no—
253C2×C3×C8—61no—
254C2×C3×C8#6712yescomplemented
255C2×C3×C8C3×D412yescomplemented
256C3×C4⋊C4—62no—
257C3×C22⋊C4—62no—
258C3×C22⋊C4—62no—
259C3×C42—32no—
260C3×C42—32no—
261#217—22no—
262(C2×D3)⋊C4—22no—
263Dic3⋊C4—22no—
264C4×Dic3C3×D412yes—
265C4×Dic3C3×D412yes—
266C2×C3⋊C8—21no—
267C2×C3⋊C8—21no—
268C2×C3⋊C8—21no—
269C2×C3⋊C8—21no—
270C2×C3⋊C8—21no—
271C2×C3⋊C8C3×D412yescomplemented
272C22×C32—22no—
273C22×C32—22no—
274C22×C32—22no—
275C22×C32—41no—
276C22×C32—41no—
277C22×C32—41no—
278C22×C32—41no—
279C22×C32C2×C22⋊C411yescharacteristic
280C22×C32C4×D411yescharacteristic
281C22×C32C4×D411yescharacteristic
282C22×C32C22×C811yescharacteristic
283C22×C32C2×M1611yescharacteristic
284C22×C32#13111yescharacteristic
285C22×C32#13111yescharacteristic
286C2×C3×D3—22no—
287C2×C3×D3—22no—
288C2×C3×D3—22no—
289C2×C3×D3—41no—
290C2×C3×D3—41no—
291C2×C3×D3—41no—
292C2×C3×D3—41no—
293C32×C4—41no—
294C32×C4#12111yescharacteristic
295C32×C4#12111yescharacteristic
296C32×C4#12411yescharacteristic
297C32×C4#12711yescharacteristic
298C3×Dic3—22no—
299C3×Dic3—41no—
300C3×Dic3C22⋊C814yescomplemented
301C22×D4—31no—
302C23×C4—31no—
303C23×C4C2×C3×D311yescharacteristic
304C22×C8—31no—
305C22×C8—31no—
306C22×C8C2×C3×D311yescharacteristic
307C22×C8C2×C3×D311yescharacteristic
308C4×D4—62no—
309C4×D4—62no—
310C2×C4⋊C4—31no—
311C2×C22⋊C4—31no—
312C2×C22⋊C4—31no—
313C2×C42—31no—
314C4⋊C8—62no—
315C22⋊C8—22no—
316C22⋊C8—62no—
317C22⋊C8—62no—
318C22⋊C8—62no—
319C4×C8—62no—
320C23×C3—22no—
321C23×C3—22no—
322C23×C3—21no—
323C23×C3—21no—
324C23×C3—21no—
325C23×C3—21no—
326C23×C3—21no—
327C23×C3—21no—
328C23×C3—21no—
329C23×C3—21no—
330C23×C3—21no—
331C23×C3—21no—
332C23×C3—21no—
333C23×C3—21no—
334C23×C3—22no—
335C23×C3—21no—
336C23×C3—32no—
337C23×C3—41no—
338C23×C3—41no—
339C23×C3—41no—
340C23×C3—41no—
341C23×C3—61no—
342C23×C3—61no—
343C23×C3—61no—
344C23×C3—61no—
345C23×C3—61no—
346C23×C3—61no—
347C23×C3D3×C812yes—
348C23×C3C2×C3×C812yes—
349C23×C3C2×C4×D311yescharacteristic
350C23×C3C22×C3×C411yescharacteristic
351C22×D3—21no—
352C22×D3—21no—
353C22×D3—21no—
354C22×D3—21no—
355C22×D3—21no—
356C22×D3—21no—
357C22×D3C2×C3×C812yes—
358C3×D4—68no—
359C2×C3×C4—22no—
360C2×C3×C4—21no—
361C2×C3×C4—21no—
362C2×C3×C4—21no—
363C2×C3×C4—21no—
364C2×C3×C4—21no—
365C2×C3×C4—21no—
366C2×C3×C4—21no—
367C2×C3×C4—21no—
368C2×C3×C4—21no—
369C2×C3×C4—21no—
370C2×C3×C4—21no—
371C2×C3×C4—21no—
372C2×C3×C4—32no—
373C2×C3×C4—32no—
374C2×C3×C4—32no—
375C2×C3×C4—32no—
376C2×C3×C4—41no—
377C2×C3×C4—41no—
378C2×C3×C4—42no—
379C2×C3×C4—42no—
380C2×C3×C4—42no—
381C2×C3×C4—42no—
382C2×C3×C4—41no—
383C2×C3×C4—41no—
384C2×C3×C4—41no—
385C2×C3×C4—41no—
386C2×C3×C4—41no—
387C2×C3×C4—41no—
388C2×C3×C4—41no—
389C2×C3×C4—41no—
390C2×C3×C4—61no—
391C2×C3×C4—61no—
392C2×C3×C4—61no—
393C2×C3×C4—61no—
394C2×C3×C4—61no—
395C2×C3×C4—121no—
396C2×C3×C4—121no—
397C2×C3×C4—121no—
398C2×C3×C4—121no—
399C2×C3×C4#23511yescharacteristic
400C2×C3×C4D3×D411yescharacteristic
401C2×C3×C4D3×D411yescharacteristic
402C2×C3×C4D3×D411yescharacteristic
403C2×C3×C4#23711yescharacteristic
404C2×C3×C4C2×#6711yescharacteristic
405C2×C3×C4C2×C3×D411yescharacteristic
406C2×C3×C4C2×C3×D411yescharacteristic
407C2×C3×C4C2×C3×D411yescharacteristic
408C2×C3×C4C2×C3×D411yescharacteristic
409C2×C3×C4C3×#4111yescharacteristic
410C2×C3×C4C3×#4111yescharacteristic
411#67—28no—
412C2×Dic3—21no—
413C2×Dic3—21no—
414C2×Dic3—21no—
415C2×Dic3—21no—
416C2×Dic3—21no—
417C2×Dic3C3×C22⋊C412yes—
418C2×Dic3C3×C22⋊C412yes—
419C2×Dic3C2×C3×C812yes—
420C2×Dic3C3×M1612yes—
421C4×D3—41no—
422C4×D3—41no—
423C4×D3—41no—
424C4×D3—41no—
425C3×C8—22no—
426C3×C8—22no—
427C3×C8—42no—
428C3×C8—42no—
429C3×C8—41no—
430C3×C8—41no—
431C3×C8—62no—
432C3×C8—121no—
433C3⋊C8—22no—
434C3⋊C8—41no—
435C2×C32—42no—
436C2×C32#39011yescharacteristic
437C2×C32C2×C22⋊C811yescharacteristic
438C2×C32#40811yescharacteristic
439C2×C32C8×D411yescharacteristic
440C2×C32C8×D411yescharacteristic
441C2×C32#43611yescharacteristic
442C2×C32#43611yescharacteristic
443C3×D3—42no—
444C24—31no—
445C24C3×C4×D311yescharacteristic
446C2×D4—34no—
447C2×D4—62no—
448C2×D4—62no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—31no—
456C22×C4—31no—
457C22×C4—31no—
458C22×C4—61no—
459C22×C4—61no—
460C22×C4—61no—
461C22×C4—61no—
462C22×C4—61no—
463C22×C4—61no—
464C22×C4C3×C4×D311yescharacteristic
465C22×C4C22×C3×D311yescharacteristic
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—32no—
472C2×C8—61no—
473C2×C8—61no—
474C2×C8—61no—
475C2×C8—61no—
476C2×C8—61no—
477C2×C8C3×#6712yescomplemented
478C4⋊C4—62no—
479C22⋊C4—62no—
480C22⋊C4—62no—
481C42—32no—
482C42—32no—
483C22×C3—24no—
484C22×C3—22no—
485C22×C3—22no—
486C22×C3—22no—
487C22×C3—22no—
488C22×C3—22no—
489C22×C3—22no—
490C22×C3—21no—
491C22×C3—21no—
492C22×C3—21no—
493C22×C3—21no—
494C22×C3—21no—
495C22×C3—21no—
496C22×C3—21no—
497C22×C3—42no—
498C22×C3—42no—
499C22×C3—42no—
500C22×C3—42no—
501C22×C3—42no—
502C22×C3—42no—
503C22×C3—41no—
504C22×C3—41no—
505C22×C3—41no—
506C22×C3—41no—
507C22×C3—41no—
508C22×C3—41no—
509C22×C3—41no—
510C22×C3—41no—
511C22×C3—62no—
512C22×C3—62no—
513C22×C3—62no—
514C22×C3—121no—
515C22×C3—121no—
516C22×C3—121no—
517C22×C3—121no—
518C22×C3D3×C22⋊C411yescharacteristic
519C22×C3#67⋊C411yescharacteristic
520C22×C3C2×D3×C811yescharacteristic
521C22×C3#90111yescharacteristic
522C22×C3D3×M1611yescharacteristic
523C22×C3#90711yescharacteristic
524C22×C3C4×#6711yescharacteristic
525C22×C3C2×C3×C22⋊C411yescharacteristic
526C22×C3C3×C4×D411yescharacteristic
527C22×C3C3×C4×D411yescharacteristic
528C22×C3C22×C3×C811yescharacteristic
529C22×C3C2×C3×M1611yescharacteristic
530C22×C3C3×#13111yescharacteristic
531C22×C3C3×#13111yescharacteristic
532C2×D3—22no—
533C2×D3—22no—
534C2×D3—22no—
535C2×D3—41no—
536C2×D3—41no—
537C2×D3—41no—
538C2×D3—41no—
539C3×C4—21no—
540C3×C4—21no—
541C3×C4—21no—
542C3×C4—21no—
543C3×C4—34no—
544C3×C4—42no—
545C3×C4—41no—
546C3×C4—41no—
547C3×C4—62no—
548C3×C4—121no—
549C3×C4#88411yescharacteristic
550C3×C4#88511yescharacteristic
551C3×C4#93911yescharacteristic
552C3×C4#94011yescharacteristic
553C3×C4C3×#12111yescharacteristic
554C3×C4C3×#12111yescharacteristic
555C3×C4C3×#12411yescharacteristic
556C3×C4C3×#12711yescharacteristic
557Dic3—22no—
558Dic3—41no—
559Dic3C3×C22⋊C814yescomplemented
560C32#195411yescharacteristic, complemented, Sylow
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—32no—
568C23—61no—
569C23—61no—
570C23—61no—
571C23—61no—
572C23—61no—
573C23—61no—
574C23C3×D3×C812yes—
575C23C2×C3×C4×D311yescharacteristic
576D4—68no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—32no—
581C2×C4—32no—
582C2×C4—32no—
583C2×C4—32no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—61no—
589C2×C4—61no—
590C2×C4—61no—
591C2×C4—61no—
592C2×C4—61no—
593C2×C4—121no—
594C2×C4—121no—
595C2×C4—121no—
596C2×C4—121no—
597C2×C4C3×#23511yescharacteristic
598C2×C4C3×D3×D411yescharacteristic
599C2×C4C3×D3×D411yescharacteristic
600C2×C4C3×D3×D411yescharacteristic
601C2×C4C3×#23711yescharacteristic
602C2×C4C2×C3×#6711yescharacteristic
603C8—22no—
604C8—41no—
605C8—62no—
606C8—121no—
607C2×C3—21no—
608C2×C3—21no—
609C2×C3—21no—
610C2×C3—21no—
611C2×C3—21no—
612C2×C3—21no—
613C2×C3—21no—
614C2×C3—44no—
615C2×C3—42no—
616C2×C3—42no—
617C2×C3—122no—
618C2×C3D3×C22⋊C811yescharacteristic
619C2×C3#67⋊C811yescharacteristic
620C2×C3#472711yescharacteristic
621C2×C3#472911yescharacteristic
622C2×C3#495711yescharacteristic
623C2×C3C8×#6711yescharacteristic
624C2×C3#512811yescharacteristic
625C2×C3C3×#39011yescharacteristic
626C2×C3C2×C3×C22⋊C811yescharacteristic
627C2×C3C3×#40811yescharacteristic
628C2×C3C3×C8×D411yescharacteristic
629C2×C3C3×C8×D411yescharacteristic
630C2×C3C3×#43611yescharacteristic
631C2×C3C3×#43611yescharacteristic
632D3—42no—
633C22—22no—
634C22—22no—
635C22—22no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—62no—
641C22—62no—
642C22—62no—
643C22—121no—
644C22—121no—
645C22—121no—
646C22—121no—
647C22C3×D3×C22⋊C411yescharacteristic
648C22C3×#67⋊C411yescharacteristic
649C22C2×C3×D3×C811yescharacteristic
650C22C3×#90111yescharacteristic
651C22C3×D3×M1611yescharacteristic
652C22C3×#90711yescharacteristic
653C22C3×C4×#6711yescharacteristic
654C4—34no—
655C4—41no—
656C4—62no—
657C4—121no—
658C4C3×#88411yescharacteristic
659C4C3×#88511yescharacteristic
660C4C3×#93911yescharacteristic
661C4C3×#94011yescharacteristic
662C3—21no—
663C3#6991611yescharacteristic, direct product factor
664C3C3×#195411yescharacteristic, complemented
665C2—42no—
666C2—122no—
667C2C3×D3×C22⋊C811yescharacteristic
668C2C3×#67⋊C811yescharacteristic
669C2C3×#472711yescharacteristic
670C2C3×#472911yescharacteristic
671C2C3×#495711yescharacteristic
672C2C3×C8×#6711yescharacteristic
673C2C3×#512811yescharacteristic
subgroupG/H
centerC22×C3×C4C22×D3
commutatorC22×C3C22×C3×C8
FrattiniC22×C4C22×C3×D3
FittingC2×C32×C22⋊C8C2
socleC23×C32C22×C4
prime radicalC22×C3×#67C4
cosocleC22×C3×C4C23×C3
hypercenterC2×C3×C22⋊C8D3
hypocenterC3C3×#1954
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3×C4 ◁ C2×C3×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×C32×C22⋊C8C2semidirect
3. C2×C3×#830C2semidirect
4. C2×C3×(C2×D3)⋊C8C2semidirect
5. C2×C3×(C2×D3)⋊C8C2semidirect
6. C2×C3×Dic3⋊C8C2semidirect
7. C2×C3×C8×Dic3C2semidirect
9. #69916C3direct (N × H)
36. C2×C3×C22⋊C8D3semidirect
37. C2×C3×C22⋊C8C2×C3semidirect
39. C2×#830C2×C3semidirect
40. C2×(C2×D3)⋊C8C2×C3semidirect
41. C2×(C2×D3)⋊C8C2×C3semidirect
42. C2×Dic3⋊C8C2×C3semidirect
43. C2×C8×Dic3C2×C3semidirect
56. C2×C3×#67C8semidirect
71. C2×C32×C8D4semidirect
82. C2×C3×C3⋊C8D4semidirect
177. C2×C22⋊C8C3×D3semidirect
222. C2×#67C3×C8semidirect
254. C2×C3×C8#67semidirect
255. C2×C3×C8C3×D4semidirect
271. C2×C3⋊C8C3×D4semidirect
300. C3×Dic3C22⋊C8semidirect
477. C2×C8C3×#67semidirect
559. Dic3C3×C22⋊C8semidirect
560. C32#1954semidirect
663. C3#69916direct (N × H)
664. C3C3×#1954semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×#672
C2×C32×C22⋊C82
C2×C3×#8302
C2×C3×(C2×D3)⋊C82
C2×C3×Dic3⋊C82
C2×C3×C8×Dic32
C3×#19543
#699163