Finite Group Databasebeta

← C3×#82621 #11867114

Subgroups — C3×#82621 #11867114

Order 1152.

1309 conjugacy classes of subgroups.

The subgroup lattice has 783 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#121C211yesmaximal, characteristic, complemented
2C2×C3×#932C211yesmaximal, characteristic, complemented
3C3×#5791C211yesmaximal, characteristic, complemented
4C22×C3×#208C211yesmaximal, characteristic, complemented
5C3×#5215C211yesmaximal, characteristic, complemented
6C3×#5042C212yesmaximal, complemented
7C3×#5041C212yesmaximal, complemented
8C3×#5039C212yesmaximal, complemented
9C3×#5038C212yesmaximal, complemented
10C3×#4966C211yesmaximal, characteristic, complemented
11C3×#4964C211yesmaximal, characteristic, complemented
12C3×#3055—31nomaximal
13#82621C311yesmaximal, characteristic, direct product factor
14C22×C32×D4—21no—
15C22×C32×D4C2211yescharacteristic
16C23×C32×C4C2211yescharacteristic
17C2×C3×#235C2211yescharacteristic
18C32×#121—21no—
19C32×#121—21no—
20C32×#121C2212yes—
21C32×#121C2212yes—
22C2×C32×C4⋊C4C2211yescharacteristic
23C2×C32×C22⋊C4—21no—
24C3×#953—21no—
25C2×C3×#214C2212yescomplemented
26C3×#932—24no—
27C2×C3×#213C2212yescomplemented
28C3×#930C2211yescharacteristic, complemented
29C3×#930C2211yescharacteristic, complemented
30C3×#929—21no—
31C3×C4×#67—21no—
32C3×C4×#67—21no—
33C3×#926C2211yescharacteristic
34C3×#924C2211yescharacteristic, complemented
35C3×#924C2211yescharacteristic, complemented
36C2×C3×#208—24no—
37C2×C3×#208C2211yescharacteristic
38C2×C3×#208C2211yescharacteristic
39C2×C3×#208C2212yescomplemented
40C22×C3×C3⋊C8C2212yescomplemented
41C3×#832C2212yescomplemented
42C3×#832C2212yescomplemented
43C3×#810C2212yescomplemented
44C3×#809C2212yescomplemented
45C3×#808C2212yescomplemented
46C3×#807C2212yescomplemented
47C2×C3×AGL(1,ℤ/8)—31no—
48C22×C3×M16—31no—
49C3×#525—31no—
50C2×C3×#121—21no—
51C2×C3×#121D311yescharacteristic, complemented
52C2×C3×#121C2×C311yescharacteristic, complemented
53C2×#932C2×C311yescharacteristic, complemented
54#5791C2×C311yescharacteristic, complemented
55C22×#208C2×C311yescharacteristic, complemented
56C3×#469—32no—
57C3×#468—32no—
58C3×#466—32no—
59C3×#465—32no—
60C3×#428—31no—
61C3×#418—31no—
62C3×#417—31no—
63#5215C2×C311yescharacteristic, complemented
64#5042C2×C312yescomplemented
65#5041C2×C312yescomplemented
66#5039C2×C312yescomplemented
67#5038C2×C312yescomplemented
68#4966C2×C311yescharacteristic, complemented
69#4964C2×C311yescharacteristic, complemented
70C24×C32—21no—
71C24×C32D411yescharacteristic
72C2×C32×D4—22no—
73C2×C32×D4—22no—
74C2×C32×D4—22no—
75C2×C32×D4—21no—
76C2×C32×D4—22no—
77C2×C32×D4—44no—
78C2×C32×D4C2312yes—
79C22×C32×C4—22no—
80C22×C32×C4—22no—
81C22×C32×C4—21no—
82C22×C32×C4D411yescharacteristic
83C22×C32×C4D411yescharacteristic
84C22×C32×C4D411yescharacteristic
85C22×C32×C4C2311yescharacteristic
86C22×C32×C4C2311yescharacteristic
87C22×C32×C4C2311yescharacteristic
88C2×C3×#67—21no—
89C2×C3×#67—21no—
90C2×C3×#67—21no—
91C3×#235—22no—
92C3×#235—22no—
93C2×C3×D12C2311yescharacteristic
94C2×C3×C4×D3—21no—
95C2×C3×Dic6C2311yescharacteristic
96C32×C4⋊C4—21no—
97C32×C4⋊C4C2312yes—
98C32×C22⋊C4—22no—
99C32×C22⋊C4—22no—
100C3×#217—21no—
101C3×#217—21no—
102C3×#217—21no—
103C3×#214—24no—
104C3×#213—24no—
105C3×(C2×D3)⋊C4—21no—
106C3×(C2×D3)⋊C4—21no—
107C3×C4⋊Dic3C2311yescharacteristic
108C3×C4⋊Dic3C2311yescharacteristic
109C3×Dic3⋊C4—21no—
110C3×Dic3⋊C4—21no—
111C3×C4×Dic3—21no—
112C3×#208—22no—
113C3×#208—24no—
114C3×#208D414yescomplemented
115C2×C3×C3⋊C8—24no—
116C2×C3×C3⋊C8C2312yes—
117C2×C3×C3⋊C8C2312yes—
118#3055—31noSylow
119C2×C3×#41—31no—
120C22×C3×D4—22no—
121C22×C3×D4—21no—
122C22×C3×D4—21no—
123C22×C3×D4—21no—
124C22×C3×D4C2×D311yescharacteristic
125C22×C3×D4C22×C311yescharacteristic
126C23×C3×C4—21no—
127C23×C3×C4C2×D311yescharacteristic
128C23×C3×C4C22×C311yescharacteristic
129C2×#235C22×C311yescharacteristic
130C3×AGL(1,ℤ/8)—64no—
131C2×C3×SD16—32no—
132C2×C3×D8—32no—
133C2×C3×M16—31no—
134C2×C3×M16—31no—
135C2×C3×M16—32no—
136C2×C3×M16—64no—
137C22×C3×C8—32no—
138C3×#123—61no—
139C3×C22⋊Q8—31no—
140C3×C22⋊Q8—31no—
141C3×#121—22no—
142C3×#121—22no—
143C3×#121—21no—
144C3×#121—21no—
145C3×#121—21no—
146C3×#121—21no—
147C3×#121—22no—
148C3×#121—22no—
149C3×#121—31no—
150C3×#121—31no—
151C3×#121C2×D312yes—
152C3×#121C2×D312yes—
153C3×#121C22×C312yes—
154C3×#121C22×C312yes—
155C3×#120—61no—
156C3×C4×D4—61no—
157C3×C4×D4—61no—
158C3×#117—31no—
159C2×C3×C4⋊C4—21no—
160C2×C3×C4⋊C4C2×D311yescharacteristic
161C2×C3×C4⋊C4C22×C311yescharacteristic
162C2×C3×C22⋊C4—22no—
163C2×C3×C22⋊C4—21no—
164C2×C3×C22⋊C4—21no—
165#953—21no—
166C2×#214C22×C312yescomplemented
167#932—24no—
168C2×#213C22×C312yescomplemented
169#930C22×C311yescharacteristic, complemented
170#930C22×C311yescharacteristic, complemented
171#929—21no—
172C4×#67—21no—
173C4×#67—21no—
174#926C22×C311yescharacteristic
175#924C22×C311yescharacteristic, complemented
176#924C22×C311yescharacteristic, complemented
177C2×#208—24no—
178C2×#208C22×C311yescharacteristic
179C2×#208C22×C311yescharacteristic
180C2×#208C22×C312yescomplemented
181C22×C3⋊C8C22×C312yescomplemented
182C3×#107—32no—
183C3×#106—32no—
184C3×#103—32no—
185C3×#102—32no—
186C3×#102—32no—
187C3×#102—32no—
188#832C22×C312yescomplemented
189#832C22×C312yescomplemented
190#810C22×C312yescomplemented
191#809C22×C312yescomplemented
192#808C22×C312yescomplemented
193#807C22×C312yescomplemented
194C23×C32—22no—
195C23×C32—22no—
196C23×C32—22no—
197C23×C32—41no—
198C23×C32—42no—
199C23×C32—42no—
200C23×C32—42no—
201C23×C32C2×D411yescharacteristic
202C23×C32C2×D411yescharacteristic
203C23×C32C2×D411yescharacteristic
204C22×C3×D3—21no—
205C32×D4—22no—
206C32×D4—22no—
207C32×D4—44no—
208C32×D4—44no—
209C32×D4—42no—
210C2×C32×C4—22no—
211C2×C32×C4—22no—
212C2×C32×C4—22no—
213C2×C32×C4—22no—
214C2×C32×C4—21no—
215C2×C32×C4—21no—
216C2×C32×C4—21no—
217C2×C32×C4—21no—
218C2×C32×C4—42no—
219C2×C32×C4C2×D412yes—
220C2×C32×C4C2×D411yescharacteristic
221C2×C32×C4C2×D411yescharacteristic
222C2×C32×C4C2×D411yescharacteristic
223C2×C32×C4#4112yes—
224C2×C32×C4C2411yescharacteristic
225C3×#67—42no—
226C3×#67—42no—
227C3×#67—42no—
228C2×C3×Dic3—21no—
229C2×C3×Dic3—21no—
230C2×C3×Dic3—21no—
231C3×D12—21no—
232C3×D12—21no—
233C3×C4×D3—42no—
234C3×Dic6—21no—
235C3×Dic6—21no—
236C3×C3⋊C8—22no—
237C3×C3⋊C8C2×D414yescomplemented
238C2×AGL(1,ℤ/8)—31no—
239C22×M16—31no—
240#525—31no—
241C2×#121C3×D311yescharacteristic, complemented
242#469—32no—
243#468—32no—
244#466—32no—
245#465—32no—
246#428—31no—
247#418—31no—
248#417—31no—
249C24×C3—22no—
250C24×C3—21no—
251C24×C3—21no—
252C24×C3—21no—
253C24×C3#6711yescharacteristic
254C24×C3C3×D411yescharacteristic
255C3×#41—62no—
256C3×#41—62no—
257C2×C3×Q8—31no—
258C2×C3×D4—24no—
259C2×C3×D4—24no—
260C2×C3×D4—22no—
261C2×C3×D4—22no—
262C2×C3×D4—22no—
263C2×C3×D4—22no—
264C2×C3×D4—22no—
265C2×C3×D4—22no—
266C2×C3×D4—22no—
267C2×C3×D4—21no—
268C2×C3×D4—22no—
269C2×C3×D4—21no—
270C2×C3×D4—22no—
271C2×C3×D4—22no—
272C2×C3×D4—31no—
273C2×C3×D4—42no—
274C2×C3×D4—42no—
275C2×C3×D4—48no—
276C2×C3×D4—44no—
277C2×C3×D4—44no—
278C2×C3×D4—61no—
279C2×C3×D4—61no—
280C2×C3×D4—61no—
281C2×C3×D4C22×D312yes—
282C2×C3×D4C23×C312yes—
283C22×C3×C4—22no—
284C22×C3×C4—22no—
285C22×C3×C4—22no—
286C22×C3×C4—22no—
287C22×C3×C4—22no—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4—42no—
297C22×C3×C4—42no—
298C22×C3×C4—61no—
299C22×C3×C4#6711yescharacteristic
300C22×C3×C4#6711yescharacteristic
301C22×C3×C4#6711yescharacteristic
302C22×C3×C4C3×D411yescharacteristic
303C22×C3×C4C3×D411yescharacteristic
304C22×C3×C4C3×D411yescharacteristic
305C22×C3×C4C22×D311yescharacteristic
306C22×C3×C4C22×D311yescharacteristic
307C22×C3×C4C22×D311yescharacteristic
308C22×C3×C4C23×C311yescharacteristic
309C22×C3×C4C23×C311yescharacteristic
310C22×C3×C4C23×C311yescharacteristic
311C2×#67—21no—
312C2×#67—21no—
313C2×#67—21no—
314#235—22no—
315#235—22no—
316C2×D12C23×C311yescharacteristic
317C2×C4×D3—21no—
318C2×Dic6C23×C311yescharacteristic
319C3×SD16—64no—
320C3×D8—64no—
321C3×M16—34no—
322C3×M16—64no—
323C3×M16—62no—
324C2×C3×C8—32no—
325C2×C3×C8—32no—
326C2×C3×C8—64no—
327C3×C4⋊C4—22no—
328C3×C4⋊C4—21no—
329C3×C4⋊C4—21no—
330C3×C4⋊C4—22no—
331C3×C4⋊C4—31no—
332C3×C4⋊C4—31no—
333C3×C4⋊C4—61no—
334C3×C4⋊C4—61no—
335C3×C4⋊C4C22×D312yes—
336C3×C4⋊C4C23×C312yes—
337C3×C22⋊C4—24no—
338C3×C22⋊C4—24no—
339C3×C22⋊C4—22no—
340C3×C22⋊C4—22no—
341C3×C22⋊C4—22no—
342C3×C22⋊C4—22no—
343C3×C22⋊C4—61no—
344C3×C22⋊C4—61no—
345C3×C22⋊C4—61no—
346C3×C22⋊C4—61no—
347C3×C22⋊C4—61no—
348C3×C42—61no—
349#217—21no—
350#217—21no—
351#217—21no—
352#214—24no—
353#213—24no—
354(C2×D3)⋊C4—21no—
355(C2×D3)⋊C4—21no—
356C4⋊Dic3C23×C311yescharacteristic
357C4⋊Dic3C23×C311yescharacteristic
358Dic3⋊C4—21no—
359Dic3⋊C4—21no—
360C4×Dic3—21no—
361#208—22no—
362#208—24no—
363#208C3×D414yescomplemented
364C2×C3⋊C8—24no—
365C2×C3⋊C8C23×C312yes—
366C2×C3⋊C8C23×C312yes—
367C22×C32—21no—
368C22×C32—21no—
369C22×C32—21no—
370C22×C32—21no—
371C22×C32—21no—
372C22×C32—21no—
373C22×C32—21no—
374C22×C32—44no—
375C22×C32—42no—
376C22×C32—42no—
377C22×C32—42no—
378C22×C32—84no—
379C22×C32#12112yes—
380C22×C32AGL(1,ℤ/8)12yescomplemented
381C22×C32C22×D411yescharacteristic
382C2×C3×D3—41no—
383C2×C3×D3—41no—
384C2×C3×D3—41no—
385C32×C4—21no—
386C32×C4—21no—
387C32×C4—42no—
388C32×C4#12112yes—
389C32×C4C22×D411yescharacteristic
390C32×C4C2×#4111yescharacteristic
391C3×Dic3—41no—
392C3×Dic3—41no—
393C3×Dic3—41no—
394C2×#41—31no—
395C22×D4—21no—
396C22×D4C2×C3×D311yescharacteristic
397C23×C4C2×C3×D311yescharacteristic
398AGL(1,ℤ/8)—64no—
399C2×SD16—32no—
400C2×D8—32no—
401C2×M16—31no—
402C2×M16—31no—
403C2×M16—32no—
404C2×M16—64no—
405C22×C8—32no—
406#123—61no—
407C22⋊Q8—31no—
408C22⋊Q8—31no—
409#121—21no—
410#121—21no—
411#121—31no—
412#121—31no—
413#121C2×C3×D312yes—
414#121C2×C3×D312yes—
415#120—61no—
416C4×D4—61no—
417C4×D4—61no—
418#117—31no—
419C2×C4⋊C4C2×C3×D311yescharacteristic
420C2×C22⋊C4—21no—
421#107—32no—
422#106—32no—
423#103—32no—
424#102—32no—
425#102—32no—
426#102—32no—
427C23×C3—24no—
428C23×C3—22no—
429C23×C3—22no—
430C23×C3—22no—
431C23×C3—22no—
432C23×C3—24no—
433C23×C3—22no—
434C23×C3—22no—
435C23×C3—21no—
436C23×C3—21no—
437C23×C3—21no—
438C23×C3—42no—
439C23×C3—41no—
440C23×C3—41no—
441C23×C3—42no—
442C23×C3—44no—
443C23×C3—42no—
444C23×C3—42no—
445C23×C3—44no—
446C23×C3—44no—
447C23×C3—42no—
448C23×C3—42no—
449C23×C3—42no—
450C23×C3—42no—
451C23×C3—61no—
452C23×C3C2×#6711yescharacteristic
453C23×C3C2×#6711yescharacteristic
454C23×C3C2×#6711yescharacteristic
455C23×C3C2×C3×D411yescharacteristic
456C23×C3C2×C3×D411yescharacteristic
457C23×C3C2×C3×D411yescharacteristic
458C22×D3—21no—
459C3×Q8—61no—
460C3×Q8—61no—
461C3×D4—22no—
462C3×D4—22no—
463C3×D4—22no—
464C3×D4—22no—
465C3×D4—42no—
466C3×D4—42no—
467C3×D4—44no—
468C3×D4—48no—
469C3×D4—44no—
470C3×D4—44no—
471C3×D4—48no—
472C3×D4—44no—
473C3×D4—44no—
474C3×D4—42no—
475C3×D4—42no—
476C3×D4—61no—
477C3×D4—61no—
478C3×D4—122no—
479C3×D4—122no—
480C3×D4—122no—
481C2×C3×C4—22no—
482C2×C3×C4—22no—
483C2×C3×C4—22no—
484C2×C3×C4—22no—
485C2×C3×C4—22no—
486C2×C3×C4—22no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—24no—
496C2×C3×C4—22no—
497C2×C3×C4—22no—
498C2×C3×C4—21no—
499C2×C3×C4—22no—
500C2×C3×C4—22no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—42no—
505C2×C3×C4—42no—
506C2×C3×C4—41no—
507C2×C3×C4—41no—
508C2×C3×C4—41no—
509C2×C3×C4—41no—
510C2×C3×C4—42no—
511C2×C3×C4—44no—
512C2×C3×C4—42no—
513C2×C3×C4—42no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—122no—
518C2×C3×C4D3×D412yes—
519C2×C3×C4#23712yes—
520C2×C3×C4C2×#6711yescharacteristic
521C2×C3×C4C2×#6711yescharacteristic
522C2×C3×C4C2×#6711yescharacteristic
523C2×C3×C4C2×C3×D412yes—
524C2×C3×C4C2×C3×D411yescharacteristic
525C2×C3×C4C2×C3×D411yescharacteristic
526C2×C3×C4C2×C3×D411yescharacteristic
527C2×C3×C4C3×#4112yes—
528C2×C3×C4C23×D311yescharacteristic
529C2×C3×C4C24×C311yescharacteristic
530#67—42no—
531#67—42no—
532#67—42no—
533C2×Dic3—21no—
534C2×Dic3—21no—
535C2×Dic3—21no—
536D12—21no—
537D12—21no—
538C4×D3—42no—
539Dic6—21no—
540Dic6—21no—
541C3×C8—34no—
542C3×C8—62no—
543C3⋊C8—22no—
544C3⋊C8C2×C3×D414yescomplemented
545C2×C32—22no—
546C2×C32—22no—
547C2×C32—41no—
548C2×C32—82no—
549C2×C32C2×#12111yescharacteristic
550C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
551C2×C32#57511yescharacteristic
552C3×D3—81no—
553C24—21no—
554C24C3×#6711yescharacteristic
555#41—62no—
556#41—62no—
557C2×Q8—31no—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—21no—
563C2×D4—31no—
564C2×D4—44no—
565C2×D4—61no—
566C2×D4—61no—
567C2×D4—61no—
568C2×D4C22×C3×D312yes—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—21no—
572C22×C4—61no—
573C22×C4C3×#6711yescharacteristic
574C22×C4C3×#6711yescharacteristic
575C22×C4C3×#6711yescharacteristic
576C22×C4C22×C3×D311yescharacteristic
577C22×C4C22×C3×D311yescharacteristic
578C22×C4C22×C3×D311yescharacteristic
579SD16—64no—
580D8—64no—
581M16—34no—
582M16—64no—
583M16—62no—
584C2×C8—32no—
585C2×C8—32no—
586C2×C8—64no—
587C4⋊C4—21no—
588C4⋊C4—31no—
589C4⋊C4—31no—
590C4⋊C4—61no—
591C4⋊C4—61no—
592C4⋊C4C22×C3×D312yes—
593C22⋊C4—22no—
594C22⋊C4—22no—
595C22⋊C4—61no—
596C22⋊C4—61no—
597C22⋊C4—61no—
598C22⋊C4—61no—
599C22⋊C4—61no—
600C42—61no—
601C22×C3—22no—
602C22×C3—22no—
603C22×C3—21no—
604C22×C3—21no—
605C22×C3—21no—
606C22×C3—21no—
607C22×C3—21no—
608C22×C3—21no—
609C22×C3—21no—
610C22×C3—21no—
611C22×C3—22no—
612C22×C3—21no—
613C22×C3—21no—
614C22×C3—21no—
615C22×C3—21no—
616C22×C3—21no—
617C22×C3—21no—
618C22×C3—22no—
619C22×C3—22no—
620C22×C3—21no—
621C22×C3—41no—
622C22×C3—41no—
623C22×C3—41no—
624C22×C3—41no—
625C22×C3—44no—
626C22×C3—44no—
627C22×C3—48no—
628C22×C3—44no—
629C22×C3—44no—
630C22×C3—44no—
631C22×C3—42no—
632C22×C3—42no—
633C22×C3—42no—
634C22×C3—42no—
635C22×C3—42no—
636C22×C3—42no—
637C22×C3—88no—
638C22×C3—84no—
639C22×C3—84no—
640C22×C3—121no—
641C22×C3—121no—
642C22×C3—121no—
643C22×C3#93212yescomplemented
644C22×C3#93912yes—
645C22×C3C3×#12112yes—
646C22×C3C3×AGL(1,ℤ/8)12yescomplemented
647C22×C3C22×#6711yescharacteristic
648C22×C3C22×C3×D411yescharacteristic
649C2×D3—41no—
650C2×D3—41no—
651C2×D3—41no—
652C3×C4—21no—
653C3×C4—21no—
654C3×C4—21no—
655C3×C4—21no—
656C3×C4—22no—
657C3×C4—21no—
658C3×C4—21no—
659C3×C4—41no—
660C3×C4—41no—
661C3×C4—44no—
662C3×C4—42no—
663C3×C4—42no—
664C3×C4—121no—
665C3×C4—121no—
666C3×C4—121no—
667C3×C4#93912yes—
668C3×C4C3×#12112yes—
669C3×C4C2×D3×D411yescharacteristic
670C3×C4C2×#23711yescharacteristic
671C3×C4C22×C3×D411yescharacteristic
672C3×C4C2×C3×#4111yescharacteristic
673Dic3—41no—
674Dic3—41no—
675Dic3—41no—
676C32#305511yescharacteristic, complemented, Sylow
677C23—22no—
678C23—22no—
679C23—22no—
680C23—41no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—61no—
685C23C2×C3×#6711yescharacteristic
686C23C2×C3×#6711yescharacteristic
687C23C2×C3×#6711yescharacteristic
688Q8—61no—
689Q8—61no—
690D4—22no—
691D4—22no—
692D4—44no—
693D4—44no—
694D4—42no—
695D4—61no—
696D4—61no—
697D4—122no—
698D4—122no—
699D4—122no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—42no—
709C2×C4—61no—
710C2×C4—61no—
711C2×C4—61no—
712C2×C4—122no—
713C2×C4C3×D3×D412yes—
714C2×C4C3×#23712yes—
715C2×C4C2×C3×#6711yescharacteristic
716C2×C4C2×C3×#6711yescharacteristic
717C2×C4C2×C3×#6711yescharacteristic
718C2×C4C23×C3×D311yescharacteristic
719C8—34no—
720C8—62no—
721C2×C3—24no—
722C2×C3—22no—
723C2×C3—22no—
724C2×C3—22no—
725C2×C3—22no—
726C2×C3—21no—
727C2×C3—21no—
728C2×C3—21no—
729C2×C3—42no—
730C2×C3—42no—
731C2×C3—41no—
732C2×C3—41no—
733C2×C3—84no—
734C2×C3—82no—
735C2×C3—82no—
736C2×C3—241no—
737C2×C3C2×#93211yescharacteristic
738C2×C3C2×#93911yescharacteristic
739C2×C3#582211yescharacteristic
740C2×C3C2×C3×#12111yescharacteristic
741C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
742C2×C3C3×#57511yescharacteristic
743D3—81no—
744C22—21no—
745C22—21no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—44no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—84no—
756C22—121no—
757C22—121no—
758C22—121no—
759C22C3×#93212yescomplemented
760C22C3×#93912yes—
761C22C22×C3×#6711yescharacteristic
762C4—21no—
763C4—21no—
764C4—42no—
765C4—121no—
766C4—121no—
767C4—121no—
768C4C3×#93912yes—
769C4C2×C3×D3×D411yescharacteristic
770C4C2×C3×#23711yescharacteristic
771C3—21no—
772C3#8262111yescharacteristic, direct product factor
773C3C3×#305511yescharacteristic, complemented
774C2—22no—
775C2—22no—
776C2—41no—
777C2—82no—
778C2—241no—
779C2C2×C3×#93211yescharacteristic
780C2C2×C3×#93911yescharacteristic
781C2C3×#582211yescharacteristic
subgroupG/H
centerC22×C3C22×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC2×C32×#121C2
socleC22×C32C22×D4
hypercenterC2×C3×#121D3
hypocenterC3C3×#3055
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ C2×C3×#121

Complements

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

NH ≅ G/Ntype
1. C2×C32×#121C2semidirect
2. C2×C3×#932C2semidirect
3. C3×#5791C2semidirect
4. C22×C3×#208C2semidirect
5. C3×#5215C2semidirect
6. C3×#5042C2semidirect
7. C3×#5041C2semidirect
8. C3×#5039C2semidirect
9. C3×#5038C2semidirect
10. C3×#4966C2semidirect
11. C3×#4964C2semidirect
13. #82621C3direct (N × H)
25. C2×C3×#214C22semidirect
27. C2×C3×#213C22semidirect
28. C3×#930C22semidirect
29. C3×#930C22semidirect
34. C3×#924C22semidirect
35. C3×#924C22semidirect
39. C2×C3×#208C22semidirect
40. C22×C3×C3⋊C8C22semidirect
41. C3×#832C22semidirect
42. C3×#832C22semidirect
43. C3×#810C22semidirect
44. C3×#809C22semidirect
45. C3×#808C22semidirect
46. C3×#807C22semidirect
51. C2×C3×#121D3semidirect
52. C2×C3×#121C2×C3semidirect
53. C2×#932C2×C3semidirect
54. #5791C2×C3semidirect
55. C22×#208C2×C3semidirect
63. #5215C2×C3semidirect
64. #5042C2×C3semidirect
65. #5041C2×C3semidirect
66. #5039C2×C3semidirect
67. #5038C2×C3semidirect
68. #4966C2×C3semidirect
69. #4964C2×C3semidirect
114. C3×#208D4semidirect
166. C2×#214C22×C3semidirect
168. C2×#213C22×C3semidirect
169. #930C22×C3semidirect
170. #930C22×C3semidirect
175. #924C22×C3semidirect
176. #924C22×C3semidirect
180. C2×#208C22×C3semidirect
181. C22×C3⋊C8C22×C3semidirect
188. #832C22×C3semidirect
189. #832C22×C3semidirect
190. #810C22×C3semidirect
191. #809C22×C3semidirect
192. #808C22×C3semidirect
193. #807C22×C3semidirect
237. C3×C3⋊C8C2×D4semidirect
241. C2×#121C3×D3semidirect
363. #208C3×D4semidirect
380. C22×C32AGL(1,ℤ/8)semidirect
544. C3⋊C8C2×C3×D4semidirect
643. C22×C3#932semidirect
646. C22×C3C3×AGL(1,ℤ/8)semidirect
676. C32#3055semidirect
759. C22C3×#932semidirect
772. C3#82621direct (N × H)
773. C3C3×#3055semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1212
C2×C3×#9322
C3×#57912
C22×C3×#2082
C3×#52152
C3×#50422
C3×#50412
C3×#50392
C3×#50382
C3×#49662
C3×#49642
C3×#30553
#826213