Finite Group Databasebeta

← C3×#83984 #11864665

Subgroups — C3×#83984 #11864665

Order 1152.

1553 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1007C211yesmaximal, characteristic, complemented
2C2×C32×#137C211yesmaximal, characteristic, complemented
3C3×#5833C211yesmaximal, characteristic, complemented
4C2×C3×#950C211yesmaximal, characteristic, complemented
5C2×C3×#835C211yesmaximal, characteristic, complemented
6C3×#5187C212yesmaximal, complemented
7C3×#5186C212yesmaximal, complemented
8C3×#5172C212yesmaximal, complemented
9C3×#5170C212yesmaximal, complemented
10C3×#5133C211yesmaximal, characteristic, complemented
11C3×#5129C211yesmaximal, characteristic, complemented
12C3×#3013—31nomaximal
13#83984C311yesmaximal, characteristic, direct product factor
14C2×C32×#41C2211yescharacteristic
15C22×C32×Q8C2211yescharacteristic
16C3×#1007—24no—
17C3×#1007—24no—
18C2×C3×#239—21no—
19C2×C3×#239C2212yes—
20C2×C3×D3×Q8—21no—
21C2×C3×D3×Q8C2212yes—
22C2×C3×#235—22no—
23C2×C3×#235C2211yescharacteristic
24C2×C3×#235C2211yescharacteristic
25C32×#137—24no—
26C2×C32×Q16C2212yes—
27C2×C32×SD16C2212yes—
28C2×C32×M16C2211yescharacteristic
29C3×#950—24no—
30C3×#946C2212yes—
31C2×C3×#216C2211yescharacteristic
32C2×C3×#215C2211yescharacteristic
33C3×#939—22no—
34C3×#938C2212yes—
35C2×C3×#214C2211yescharacteristic
36C2×C3×#213C2211yescharacteristic
37C3×#930—21no—
38C2×C3×C4⋊Dic3C2211yescharacteristic
39C3×#924—21no—
40C22×C3×C3⋊C8C2211yescharacteristic
41C3×#835C2212yes—
42C3×#835C2212yes—
43C3×#821C2212yes—
44C3×(C2×D3)⋊C8C2212yes—
45C3×(C2×D3)⋊C8C2212yes—
46C3×#816C2212yes—
47C2×C3×2−1+4—31no—
48C2×#1007C2×C311yescharacteristic, complemented
49C2×C3×#137—21no—
50C2×C3×#137D311yescharacteristic, complemented
51C2×C3×#137C2×C311yescharacteristic, complemented
52C2×C3×#135—31no—
53C3×#537—31no—
54#5833C2×C311yescharacteristic, complemented
55C2×#950C2×C311yescharacteristic, complemented
56C3×#452—32no—
57C3×#451—32no—
58C3×#449—32no—
59C3×#448—32no—
60C3×#417—31no—
61C2×C3×#103—31no—
62C3×#408—31no—
63C2×#835C2×C311yescharacteristic, complemented
64#5187C2×C312yescomplemented
65#5186C2×C312yescomplemented
66#5172C2×C312yescomplemented
67#5170C2×C312yescomplemented
68#5133C2×C311yescharacteristic, complemented
69#5129C2×C311yescharacteristic, complemented
70C32×#41—22no—
71C32×#41—22no—
72C2×C32×Q8—21no—
73C2×C32×Q8—22no—
74C2×C32×Q8D414yescomplemented
75C2×C32×Q8C2311yescharacteristic
76C2×C32×Q8C2312yes—
77C2×C32×D4—21no—
78C2×C32×D4C2311yescharacteristic
79C22×C32×C4—21no—
80C22×C32×C4—21no—
81C22×C32×C4C2311yescharacteristic
82C2×C3×#67—21no—
83C2×C3×#67—22no—
84C2×C3×#67D412yes—
85C22×C3×Dic3—21no—
86C3×#239—28no—
87C3×#239—24no—
88C3×#239—24no—
89C3×D3×Q8—28no—
90C3×D3×Q8—24no—
91C3×D3×Q8—24no—
92C3×#235—216no—
93C3×#235—22no—
94C3×#235—22no—
95C3×#235—22no—
96C3×#235D414yescomplemented
97C2×C3×D12—22no—
98C2×C3×D12D411yescharacteristic
99C2×C3×D12C2311yescharacteristic
100C2×C3×C4×D3—22no—
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3—22no—
103C2×C3×C4×D3C2312yes—
104C2×C3×Dic6—22no—
105C2×C3×Dic6D411yescharacteristic
106C2×C3×Dic6C2311yescharacteristic
107C32×Q16—24no—
108C32×SD16—24no—
109C32×M16—22no—
110C2×C32×C8C2312yes—
111C3×#217—22no—
112C3×#216—22no—
113C3×#215—22no—
114C3×#214—22no—
115C3×#213—22no—
116C3×(C2×D3)⋊C4—22no—
117C3×C4⋊Dic3—21no—
118C3×C4⋊Dic3C2312yes—
119C3×Dic3⋊C4—22no—
120C2×C3×C3⋊C8—22no—
121C2×C3×C3⋊C8C2311yescharacteristic
122C2×C3×C3⋊C8C2311yescharacteristic
123#3013—31noSylow
124C3×2−1+4—64no—
125C3×2−1+4—64no—
126C2×C3×#41—21no—
127C2×C3×#41—31no—
128C2×C3×#41—32no—
129C2×C3×#41—31no—
130C2×C3×#41—62no—
131C2×C3×#41—61no—
132C2×C3×#41C2×D311yescharacteristic
133C2×C3×#41C22×C311yescharacteristic
134C22×C3×Q8—21no—
135C22×C3×Q8—32no—
136C22×C3×Q8—61no—
137C22×C3×Q8C2×D311yescharacteristic
138C22×C3×Q8C22×C311yescharacteristic
139#1007—24no—
140#1007—24no—
141C2×#239—21no—
142C2×#239C22×C312yes—
143C2×D3×Q8—21no—
144C2×D3×Q8C22×C312yes—
145C2×#235—22no—
146C2×#235C22×C311yescharacteristic
147C2×#235C22×C311yescharacteristic
148C3×#137—28no—
149C3×#137—24no—
150C3×#137—24no—
151C3×#135—64no—
152C2×C3×Q16—22no—
153C2×C3×Q16—31no—
154C2×C3×Q16C2×D312yes—
155C2×C3×Q16C22×C312yes—
156C2×C3×SD16—22no—
157C2×C3×SD16—31no—
158C2×C3×SD16—31no—
159C2×C3×SD16C2×D312yes—
160C2×C3×SD16C22×C312yes—
161C2×C3×D8—31no—
162C2×C3×M16—21no—
163C2×C3×M16C2×D311yescharacteristic
164C2×C3×M16C22×C311yescharacteristic
165C22×C3×C8—31no—
166C3×C22⋊Q8—32no—
167C3×C22⋊Q8—61no—
168C3×#121—32no—
169C3×#121—61no—
170C3×#121—62no—
171C2×C3×C4⋊C4—31no—
172#950—24no—
173#946C22×C312yes—
174C2×#216C22×C311yescharacteristic
175C2×#215C22×C311yescharacteristic
176#939—22no—
177#938C22×C312yes—
178C2×#214C22×C311yescharacteristic
179C2×#213C22×C311yescharacteristic
180#930—21no—
181C2×C4⋊Dic3C22×C311yescharacteristic
182#924—21no—
183C22×C3⋊C8C22×C311yescharacteristic
184C3×#103—32no—
185C3×#103—32no—
186C3×#103—32no—
187C3×#102—32no—
188C3×C22⋊C8—32no—
189C3×C22⋊C8—32no—
190#835C22×C312yes—
191#835C22×C312yes—
192#821C22×C312yes—
193(C2×D3)⋊C8C22×C312yes—
194(C2×D3)⋊C8C22×C312yes—
195#816C22×C312yes—
196C23×C32—21no—
197C23×C32C2×D411yescharacteristic
198C22×C3×D3—21no—
199C22×C3×D3C2×D412yes—
200C32×Q8—21no—
201C32×Q8—24no—
202C32×Q8—22no—
203C32×Q8—21no—
204C32×Q8C2×D414yes—
205C32×D4—21no—
206C32×D4—21no—
207C32×D4—42no—
208C2×C32×C4—24no—
209C2×C32×C4—22no—
210C2×C32×C4—21no—
211C2×C32×C4—42no—
212C2×C32×C4C2×D411yescharacteristic
213C2×C32×C4C2×D412yes—
214C2×C32×C4C2×D412yes—
215C2×C32×C4C2411yescharacteristic
216C3×#67—24no—
217C3×#67—24no—
218C3×#67—82no—
219C2×C3×Dic3—21no—
220C2×C3×Dic3—22no—
221C2×C3×Dic3—81no—
222C2×C3×Dic3C2×D412yes—
223C3×D12—28no—
224C3×D12—22no—
225C3×D12—21no—
226C3×D12C2×D412yes—
227C3×C4×D3—28no—
228C3×C4×D3—28no—
229C3×C4×D3—24no—
230C3×C4×D3—22no—
231C3×C4×D3—22no—
232C3×Dic6—28no—
233C3×Dic6—22no—
234C3×Dic6—21no—
235C3×Dic6C2×D412yes—
236C32×C8—22no—
237C3×C3⋊C8—21no—
238C3×C3⋊C8—21no—
239C2×2−1+4—31no—
240C2×#137C3×D311yescharacteristic, complemented
241C2×#135—31no—
242#537—31no—
243#452—32no—
244#451—32no—
245#449—32no—
246#448—32no—
247#417—31no—
248C2×#103—31no—
249#408—31no—
250C3×#41—24no—
251C3×#41—22no—
252C3×#41—22no—
253C3×#41—22no—
254C3×#41—22no—
255C3×#41—34no—
256C3×#41—42no—
257C3×#41—616no—
258C3×#41—64no—
259C3×#41—68no—
260C3×#41—64no—
261C3×#41—62no—
262C3×#41—62no—
263C3×#41—62no—
264C2×C3×Q8—21no—
265C2×C3×Q8—22no—
266C2×C3×Q8—21no—
267C2×C3×Q8—22no—
268C2×C3×Q8—24no—
269C2×C3×Q8—22no—
270C2×C3×Q8—21no—
271C2×C3×Q8—31no—
272C2×C3×Q8—31no—
273C2×C3×Q8—41no—
274C2×C3×Q8—42no—
275C2×C3×Q8—62no—
276C2×C3×Q8—64no—
277C2×C3×Q8—68no—
278C2×C3×Q8—64no—
279C2×C3×Q8#6714yescomplemented
280C2×C3×Q8C3×D414yescomplemented
281C2×C3×Q8C22×D311yescharacteristic
282C2×C3×Q8C22×D312yes—
283C2×C3×Q8C23×C311yescharacteristic
284C2×C3×Q8C23×C312yes—
285C2×C3×D4—21no—
286C2×C3×D4—21no—
287C2×C3×D4—21no—
288C2×C3×D4—32no—
289C2×C3×D4—31no—
290C2×C3×D4—31no—
291C2×C3×D4—41no—
292C2×C3×D4—62no—
293C2×C3×D4—61no—
294C2×C3×D4—62no—
295C2×C3×D4C22×D311yescharacteristic
296C2×C3×D4C23×C311yescharacteristic
297C22×C3×C4—21no—
298C22×C3×C4—21no—
299C22×C3×C4—21no—
300C22×C3×C4—21no—
301C22×C3×C4—21no—
302C22×C3×C4—32no—
303C22×C3×C4—41no—
304C22×C3×C4—41no—
305C22×C3×C4—62no—
306C22×C3×C4—62no—
307C22×C3×C4—61no—
308C22×C3×C4—61no—
309C22×C3×C4C22×D311yescharacteristic
310C22×C3×C4C23×C311yescharacteristic
311C2×#67—21no—
312C2×#67—22no—
313C2×#67C3×D412yes—
314C22×Dic3—21no—
315#239—28no—
316#239—24no—
317#239—24no—
318D3×Q8—28no—
319D3×Q8—24no—
320D3×Q8—24no—
321#235—216no—
322#235—22no—
323#235—22no—
324#235—22no—
325#235C3×D414yescomplemented
326C2×D12—22no—
327C2×D12C3×D411yescharacteristic
328C2×D12C23×C311yescharacteristic
329C2×C4×D3—22no—
330C2×C4×D3—21no—
331C2×C4×D3—22no—
332C2×C4×D3C23×C312yes—
333C2×Dic6—22no—
334C2×Dic6C3×D411yescharacteristic
335C2×Dic6C23×C311yescharacteristic
336C3×Q16—28no—
337C3×Q16—24no—
338C3×Q16—24no—
339C3×Q16—62no—
340C3×SD16—28no—
341C3×SD16—24no—
342C3×SD16—24no—
343C3×SD16—62no—
344C3×SD16—62no—
345C3×D8—62no—
346C3×M16—24no—
347C3×M16—22no—
348C3×M16—22no—
349C2×C3×C8—22no—
350C2×C3×C8—31no—
351C2×C3×C8—31no—
352C2×C3×C8—62no—
353C2×C3×C8C22×D312yes—
354C2×C3×C8C23×C312yes—
355C3×C4⋊C4—32no—
356C3×C4⋊C4—62no—
357C3×C4⋊C4—61no—
358C3×C22⋊C4—62no—
359C3×C22⋊C4—62no—
360#217—22no—
361#216—22no—
362#215—22no—
363#214—22no—
364#213—22no—
365(C2×D3)⋊C4—22no—
366C4⋊Dic3—21no—
367C4⋊Dic3C23×C312yes—
368Dic3⋊C4—22no—
369C2×C3⋊C8—22no—
370C2×C3⋊C8C23×C311yescharacteristic
371C2×C3⋊C8C23×C311yescharacteristic
372C22×C32—21no—
373C22×C32—21no—
374C22×C32—41no—
375C22×C32—41no—
376C22×C32—41no—
377C22×C32#12012yes—
378C22×C32C22×D411yescharacteristic
379C2×C3×D3—22no—
380C2×C3×D3—22no—
381C2×C3×D3—22no—
382C2×C3×D3—22no—
383C2×C3×D3—41no—
384C2×C3×D3—41no—
385C32×C4—24no—
386C32×C4—41no—
387C32×C4#12012yes—
388C32×C4C22×D411yescharacteristic
389C32×C4C22×D411yescharacteristic
390C3×Dic3—22no—
391C3×Dic3—22no—
392C3×Dic3—42no—
3932−1+4—64no—
3942−1+4—64no—
395C2×#41—31no—
396C2×#41—32no—
397C2×#41—31no—
398C2×#41—62no—
399C2×#41—61no—
400C2×#41C2×C3×D311yescharacteristic
401C22×Q8—32no—
402C22×Q8—61no—
403C22×Q8C2×C3×D311yescharacteristic
404#137—24no—
405#135—64no—
406C2×Q16—31no—
407C2×Q16C2×C3×D312yes—
408C2×SD16—31no—
409C2×SD16—31no—
410C2×SD16C2×C3×D312yes—
411C2×D8—31no—
412C2×M16C2×C3×D311yescharacteristic
413C22×C8—31no—
414C22⋊Q8—32no—
415C22⋊Q8—61no—
416#121—32no—
417#121—61no—
418#121—62no—
419C2×C4⋊C4—31no—
420#103—32no—
421#103—32no—
422#103—32no—
423#102—32no—
424C22⋊C8—32no—
425C22⋊C8—32no—
426C23×C3—21no—
427C23×C3—21no—
428C23×C3—21no—
429C23×C3—32no—
430C23×C3—41no—
431C23×C3—61no—
432C23×C3D3×D411yescharacteristic
433C23×C3C2×C3×D411yescharacteristic
434C22×D3—21no—
435C22×D3C2×C3×D412yes—
436C3×Q8—24no—
437C3×Q8—24no—
438C3×Q8—22no—
439C3×Q8—22no—
440C3×Q8—22no—
441C3×Q8—21no—
442C3×Q8—21no—
443C3×Q8—21no—
444C3×Q8—21no—
445C3×Q8—24no—
446C3×Q8—32no—
447C3×Q8—44no—
448C3×Q8—42no—
449C3×Q8—41no—
450C3×Q8—68no—
451C3×Q8—62no—
452C3×Q8—61no—
453C3×Q8C2×#6714yes—
454C3×Q8C2×C3×D414yes—
455C3×D4—22no—
456C3×D4—21no—
457C3×D4—21no—
458C3×D4—21no—
459C3×D4—21no—
460C3×D4—32no—
461C3×D4—41no—
462C3×D4—44no—
463C3×D4—42no—
464C3×D4—42no—
465C3×D4—68no—
466C3×D4—64no—
467C3×D4—64no—
468C3×D4—62no—
469C3×D4—61no—
470C3×D4—242no—
471C2×C3×C4—24no—
472C2×C3×C4—24no—
473C2×C3×C4—22no—
474C2×C3×C4—22no—
475C2×C3×C4—21no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—22no—
480C2×C3×C4—22no—
481C2×C3×C4—32no—
482C2×C3×C4—41no—
483C2×C3×C4—44no—
484C2×C3×C4—42no—
485C2×C3×C4—44no—
486C2×C3×C4—42no—
487C2×C3×C4—42no—
488C2×C3×C4—68no—
489C2×C3×C4—68no—
490C2×C3×C4—61no—
491C2×C3×C4—64no—
492C2×C3×C4—62no—
493C2×C3×C4—62no—
494C2×C3×C4—62no—
495C2×C3×C4—241no—
496C2×C3×C4D3×D411yescharacteristic
497C2×C3×C4D3×D412yes—
498C2×C3×C4C2×#6712yes—
499C2×C3×C4C2×C3×D411yescharacteristic
500C2×C3×C4C2×C3×D412yes—
501C2×C3×C4C2×C3×D412yes—
502C2×C3×C4C23×D311yescharacteristic
503C2×C3×C4C24×C311yescharacteristic
504#67—24no—
505#67—24no—
506#67—82no—
507C2×Dic3—21no—
508C2×Dic3—22no—
509C2×Dic3—81no—
510C2×Dic3C2×C3×D412yes—
511D12—28no—
512D12—22no—
513D12—21no—
514D12C2×C3×D412yes—
515C4×D3—28no—
516C4×D3—28no—
517C4×D3—24no—
518C4×D3—22no—
519C4×D3—22no—
520Dic6—28no—
521Dic6—22no—
522Dic6—21no—
523Dic6C2×C3×D412yes—
524C3×C8—24no—
525C3×C8—22no—
526C3×C8—22no—
527C3×C8—61no—
528C3×C8—61no—
529C3⋊C8—21no—
530C3⋊C8—21no—
531C2×C32—22no—
532C2×C32—81no—
533C2×C32C2×#12011yescharacteristic
534C2×C32#57711yescharacteristic
535C2×C32#57811yescharacteristic
536C3×D3—42no—
537C3×D3—42no—
538#41—22no—
539#41—22no—
540#41—34no—
541#41—616no—
542#41—64no—
543#41—68no—
544#41—64no—
545#41—62no—
546#41—62no—
547#41—62no—
548C2×Q8—21no—
549C2×Q8—22no—
550C2×Q8—31no—
551C2×Q8—31no—
552C2×Q8—62no—
553C2×Q8—64no—
554C2×Q8—68no—
555C2×Q8—64no—
556C2×Q8C3×#6714yescomplemented
557C2×Q8C22×C3×D311yescharacteristic
558C2×Q8C22×C3×D312yes—
559C2×D4—21no—
560C2×D4—32no—
561C2×D4—31no—
562C2×D4—31no—
563C2×D4—62no—
564C2×D4—61no—
565C2×D4—62no—
566C2×D4C22×C3×D311yescharacteristic
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—32no—
570C22×C4—62no—
571C22×C4—62no—
572C22×C4—61no—
573C22×C4—61no—
574C22×C4C22×C3×D311yescharacteristic
575Q16—24no—
576Q16—62no—
577SD16—24no—
578SD16—62no—
579SD16—62no—
580D8—62no—
581M16—22no—
582C2×C8—31no—
583C2×C8—31no—
584C2×C8—62no—
585C2×C8C22×C3×D312yes—
586C4⋊C4—32no—
587C4⋊C4—62no—
588C4⋊C4—61no—
589C22⋊C4—62no—
590C22⋊C4—62no—
591C22×C3—21no—
592C22×C3—21no—
593C22×C3—21no—
594C22×C3—21no—
595C22×C3—22no—
596C22×C3—21no—
597C22×C3—41no—
598C22×C3—41no—
599C22×C3—42no—
600C22×C3—41no—
601C22×C3—41no—
602C22×C3—41no—
603C22×C3—41no—
604C22×C3—41no—
605C22×C3—41no—
606C22×C3—62no—
607C22×C3—62no—
608C22×C3—62no—
609C22×C3—62no—
610C22×C3—81no—
611C22×C3—81no—
612C22×C3—121no—
613C22×C3—121no—
614C22×C3#93712yes—
615C22×C3C3×#12012yes—
616C22×C3C2×D3×D411yescharacteristic
617C22×C3C22×C3×D411yescharacteristic
618C2×D3—22no—
619C2×D3—22no—
620C2×D3—22no—
621C2×D3—22no—
622C2×D3—41no—
623C2×D3—41no—
624C3×C4—24no—
625C3×C4—24no—
626C3×C4—22no—
627C3×C4—21no—
628C3×C4—21no—
629C3×C4—44no—
630C3×C4—42no—
631C3×C4—41no—
632C3×C4—41no—
633C3×C4—62no—
634C3×C4—62no—
635C3×C4—122no—
636C3×C4#93712yes—
637C3×C4C3×#12012yes—
638C3×C4C2×D3×D411yescharacteristic
639C3×C4C22×#6711yescharacteristic
640C3×C4C22×C3×D411yescharacteristic
641C3×C4C22×C3×D411yescharacteristic
642Dic3—22no—
643Dic3—22no—
644Dic3—42no—
645C32#301311yescharacteristic, complemented, Sylow
646C23—21no—
647C23—32no—
648C23—61no—
649C23C3×D3×D411yescharacteristic
650Q8—24no—
651Q8—22no—
652Q8—21no—
653Q8—21no—
654Q8—32no—
655Q8—68no—
656Q8—62no—
657Q8—61no—
658Q8C2×C3×#6714yes—
659D4—21no—
660D4—21no—
661D4—32no—
662D4—42no—
663D4—68no—
664D4—64no—
665D4—64no—
666D4—62no—
667D4—61no—
668D4—242no—
669C2×C4—24no—
670C2×C4—22no—
671C2×C4—21no—
672C2×C4—32no—
673C2×C4—42no—
674C2×C4—68no—
675C2×C4—68no—
676C2×C4—61no—
677C2×C4—64no—
678C2×C4—62no—
679C2×C4—62no—
680C2×C4—62no—
681C2×C4—241no—
682C2×C4C3×D3×D411yescharacteristic
683C2×C4C3×D3×D412yes—
684C2×C4C2×C3×#6712yes—
685C2×C4C23×C3×D311yescharacteristic
686C8—22no—
687C8—61no—
688C8—61no—
689C2×C3—22no—
690C2×C3—22no—
691C2×C3—21no—
692C2×C3—21no—
693C2×C3—21no—
694C2×C3—42no—
695C2×C3—82no—
696C2×C3—81no—
697C2×C3—81no—
698C2×C3—122no—
699C2×C3—122no—
700C2×C3#577811yescharacteristic
701C2×C3#577911yescharacteristic
702C2×C3C2×#93711yescharacteristic
703C2×C3C2×C3×#12011yescharacteristic
704C2×C3C3×#57711yescharacteristic
705C2×C3C3×#57811yescharacteristic
706D3—42no—
707D3—42no—
708C22—21no—
709C22—21no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—62no—
714C22—62no—
715C22—62no—
716C22—62no—
717C22—121no—
718C22—121no—
719C22C3×#93712yes—
720C22C2×C3×D3×D411yescharacteristic
721C4—24no—
722C4—41no—
723C4—62no—
724C4—62no—
725C4—122no—
726C4C3×#93712yes—
727C4C2×C3×D3×D411yescharacteristic
728C4C22×C3×#6711yescharacteristic
729C3—21no—
730C3#8398411yescharacteristic, direct product factor
731C3C3×#301311yescharacteristic, complemented
732C2—22no—
733C2—81no—
734C2—122no—
735C2—122no—
736C2C3×#577811yescharacteristic
737C2C3×#577911yescharacteristic
738C2C2×C3×#93711yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC2×C32×#137C2
socleC22×C32C22×D4
hypercenterC2×C3×#137D3
hypocenterC3C3×#3013
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×#137

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1007C2semidirect
2. C2×C32×#137C2semidirect
3. C3×#5833C2semidirect
4. C2×C3×#950C2semidirect
5. C2×C3×#835C2semidirect
6. C3×#5187C2semidirect
7. C3×#5186C2semidirect
8. C3×#5172C2semidirect
9. C3×#5170C2semidirect
10. C3×#5133C2semidirect
11. C3×#5129C2semidirect
13. #83984C3direct (N × H)
48. C2×#1007C2×C3semidirect
50. C2×C3×#137D3semidirect
51. C2×C3×#137C2×C3semidirect
54. #5833C2×C3semidirect
55. C2×#950C2×C3semidirect
63. C2×#835C2×C3semidirect
64. #5187C2×C3semidirect
65. #5186C2×C3semidirect
66. #5172C2×C3semidirect
67. #5170C2×C3semidirect
68. #5133C2×C3semidirect
69. #5129C2×C3semidirect
74. C2×C32×Q8D4semidirect
96. C3×#235D4semidirect
240. C2×#137C3×D3semidirect
279. C2×C3×Q8#67semidirect
280. C2×C3×Q8C3×D4semidirect
325. #235C3×D4semidirect
556. C2×Q8C3×#67semidirect
645. C32#3013semidirect
730. C3#83984direct (N × H)
731. C3C3×#3013semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10072
C2×C32×#1372
C3×#58332
C2×C3×#9502
C2×C3×#8352
C3×#51872
C3×#51862
C3×#51722
C3×#51702
C3×#51332
C3×#51292
C3×#30133
#839843