Finite Group Databasebeta

← C3×#81223 #11897630

Subgroups — C3×#81223 #11897630

Order 1152.

725 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
1C3×#5690C211yesmaximal, characteristic
2C3×Q8×Dic6C211yesmaximal, characteristic, complemented
3C32×#479C211yesmaximal, characteristic, complemented
4C3×#5064C211yesmaximal, characteristic, complemented
5C3×#5026C211yesmaximal, characteristic
6C3×#4890C211yesmaximal, characteristic
7C3×#4874C211yesmaximal, characteristic, complemented
8C3×#4870C211yesmaximal, characteristic
9C3×#4856C211yesmaximal, characteristic, complemented
10C3×#4846C211yesmaximal, characteristic
11C3×#4828C211yesmaximal, characteristic, complemented
12C3×#4817C211yesmaximal, characteristic
13C3×#4796C211yesmaximal, characteristic, complemented
14C3×#4793C211yesmaximal, characteristic, complemented
15C3×#4788C211yesmaximal, characteristic
16C3×#3385—31nomaximal
17#81223C311yesmaximal, characteristic, direct product factor
18C32×#125C2211yescharacteristic
19C32×C4×Q8C2211yescharacteristic
20C3×Q8×Dic3C2211yescharacteristic
21C3×Q8×Dic3C2211yescharacteristic
22C2×C3×#215C2211yescharacteristic
23C3×#897—21no—
24C3×#896—21no—
25C3×#896—21no—
26C3×#893C2211yescharacteristic
27C3×#893C2211yescharacteristic
28C3×D3×C4⋊C4—21no—
29C3×#890C2211yescharacteristic
30C3×#888—21no—
31C3×#888—21no—
32C3×#888C2211yescharacteristic
33C3×#888C2211yescharacteristic
34C3×#888C2211yescharacteristic
35C3×C4×D12C2211yescharacteristic
36C3×#869—21no—
37C3×#869C2211yescharacteristic
38C3×C4×Dic6—21no—
39C3×C4×Dic6C2211yescharacteristic
40C32×#107C2211yescharacteristic
41C32×#106C2211yescharacteristic
42C32×C4⋊C8C2211yescharacteristic
43C32×#103C2211yescharacteristic
44C32×#103C2211yescharacteristic
45C3×#835C2211yescharacteristic
46C3×#821C2211yescharacteristic
47C3×#821C2211yescharacteristic
48C3×#818C2211yescharacteristic
49C3×#818C2211yescharacteristic
50C3×#815C2211yescharacteristic
51C3×Dic3⋊C8C2211yescharacteristic
52C3×Dic3⋊C8C2211yescharacteristic
53C3×C8×Dic3C2211yescharacteristic
54C3×#809C2211yescharacteristic
55C3×#808C2211yescharacteristic
56C3×#808C2211yescharacteristic
57C3×#807C2211yescharacteristic
58C3×#807C2211yescharacteristic
59C3×#807C2211yescharacteristic
60C3×#803C2211yescharacteristic
61C3×Q82—31no—
62C3×#554—31no—
63#5690C2×C311yescharacteristic
64Q8×Dic6C2×C311yescharacteristic, complemented
65C3×#501—31no—
66C3×#501—31no—
67C3×#500—31no—
68C3×#479—21no—
69C3×#479—31no—
70C3×#479D311yescharacteristic, complemented
71C3×#479C2×C311yescharacteristic, complemented
72C3×#477—31no—
73C3×#476—31no—
74C3×#474—31no—
75C3×#474—31no—
76C3×#446—31no—
77C3×#440—31no—
78C3×#440—31no—
79C3×C4×SD16—31no—
80#5064C2×C311yescharacteristic, complemented
81#5026C2×C311yescharacteristic
82#4890C2×C311yescharacteristic
83#4874C2×C311yescharacteristic, complemented
84#4870C2×C311yescharacteristic
85#4856C2×C311yescharacteristic, complemented
86#4846C2×C311yescharacteristic
87#4828C2×C311yescharacteristic, complemented
88#4817C2×C311yescharacteristic
89#4796C2×C311yescharacteristic, complemented
90#4793C2×C311yescharacteristic, complemented
91#4788C2×C311yescharacteristic
92C2×C32×Q8C2311yescharacteristic
93C2×C3×D12C2311yescharacteristic
94C2×C3×C4×D3—21no—
95C2×C3×C4×D3—21no—
96C2×C3×C4×D3—21no—
97C2×C3×Dic6—21no—
98C2×C3×Dic6—21no—
99C2×C3×Dic6—21no—
100C2×C3×Dic6—21no—
101C2×C3×Dic6D411yescharacteristic
102C2×C32×C8C2311yescharacteristic
103C2×C32×C8C2311yescharacteristic
104C32×C4⋊C4—21no—
105C32×C4⋊C4—21no—
106C32×C4⋊C4—21no—
107C32×C4⋊C4C2311yescharacteristic
108C32×C4⋊C4C2311yescharacteristic
109C32×C4⋊C4C2311yescharacteristic
110C32×C42—21no—
111C32×C42C2311yescharacteristic
112C3×#215Q814yescomplemented
113C3×(C2×D3)⋊C4—21no—
114C3×(C2×D3)⋊C4—21no—
115C3×(C2×D3)⋊C4—21no—
116C3×C4⋊Dic3—21no—
117C3×C4⋊Dic3—21no—
118C3×C4⋊Dic3—21no—
119C3×C4⋊Dic3—21no—
120C3×C4⋊Dic3D411yescharacteristic
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4D411yescharacteristic
129C3×Dic3⋊C4D411yescharacteristic
130C3×C4×Dic3—21no—
131C3×C4×Dic3—21no—
132C3×C4×Dic3C2311yescharacteristic
133C3×C4×Dic3C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136#3385—31noSylow
137C2×C3×SD16—31no—
138C3×C4⋊Q8—31no—
139C3×C4⋊Q8—31no—
140C3×C4⋊Q8—31no—
141C3×C4⋊Q8—31no—
142C3×C4⋊Q8—61no—
143C3×C4⋊Q8—61no—
144C3×C4⋊Q8—61no—
145C3×#125—21no—
146C3×#125—31no—
147C3×#125C2×D311yescharacteristic
148C3×#125C22×C311yescharacteristic
149C3×C22⋊Q8—61no—
150C3×C22⋊Q8—61no—
151C3×C22⋊Q8—61no—
152C3×C4×Q8—21no—
153C3×C4×Q8—31no—
154C3×C4×Q8—31no—
155C3×C4×Q8—31no—
156C3×C4×Q8—61no—
157C3×C4×Q8C2×D311yescharacteristic
158C3×C4×Q8C22×C311yescharacteristic
159C3×C4×D4—31no—
160C3×C4×D4—31no—
161C3×C4×D4—31no—
162C2×C3×C4⋊C4—61no—
163Q8×Dic3C22×C311yescharacteristic
164Q8×Dic3C22×C311yescharacteristic
165C2×#215C22×C311yescharacteristic
166#897—21no—
167#896—21no—
168#896—21no—
169#893C22×C311yescharacteristic
170#893C22×C311yescharacteristic
171D3×C4⋊C4—21no—
172#890C22×C311yescharacteristic
173#888—21no—
174#888—21no—
175#888C22×C311yescharacteristic
176#888C22×C311yescharacteristic
177#888C22×C311yescharacteristic
178C4×D12C22×C311yescharacteristic
179#869—21no—
180#869C22×C311yescharacteristic
181C4×Dic6—21no—
182C4×Dic6C22×C311yescharacteristic
183C3×#107—21no—
184C3×#107—31no—
185C3×#107—31no—
186C3×#107—31no—
187C3×#107—31no—
188C3×#107—31no—
189C3×#107C2×D311yescharacteristic
190C3×#107C22×C311yescharacteristic
191C3×#106—21no—
192C3×#106—31no—
193C3×#106—31no—
194C3×#106C2×D311yescharacteristic
195C3×#106C22×C311yescharacteristic
196C3×C4⋊C8—21no—
197C3×C4⋊C8—31no—
198C3×C4⋊C8—31no—
199C3×C4⋊C8C2×D311yescharacteristic
200C3×C4⋊C8C22×C311yescharacteristic
201C3×#103—21no—
202C3×#103—21no—
203C3×#103—31no—
204C3×#103C2×D311yescharacteristic
205C3×#103C2×D311yescharacteristic
206C3×#103C22×C311yescharacteristic
207C3×#103C22×C311yescharacteristic
208C3×#102—31no—
209C3×#102—31no—
210C3×#102—31no—
211C3×#97—31no—
212C3×#97—31no—
213C3×C4×C8—31no—
214#835C22×C311yescharacteristic
215#821C22×C311yescharacteristic
216#821C22×C311yescharacteristic
217#818C22×C311yescharacteristic
218#818C22×C311yescharacteristic
219#815C22×C311yescharacteristic
220Dic3⋊C8C22×C311yescharacteristic
221Dic3⋊C8C22×C311yescharacteristic
222C8×Dic3C22×C311yescharacteristic
223#809C22×C311yescharacteristic
224#808C22×C311yescharacteristic
225#808C22×C311yescharacteristic
226#807C22×C311yescharacteristic
227#807C22×C311yescharacteristic
228#807C22×C311yescharacteristic
229#803C22×C311yescharacteristic
230C22×C3×D3—21no—
231C32×Q8—21no—
232C32×Q8C2×Q812yes—
233C2×C32×C4—21no—
234C2×C32×C4—21no—
235C2×C32×C4—21no—
236C2×C32×C4—21no—
237C2×C32×C4C2×D411yescharacteristic
238C2×C32×C4C2×D411yescharacteristic
239C2×C32×C4C2411yescharacteristic
240C2×C3×Dic3—21no—
241C2×C3×Dic3—21no—
242C2×C3×Dic3—21no—
243C2×C3×Dic3C2×D411yescharacteristic
244C2×C3×Dic3C2×D411yescharacteristic
245C2×C3×Dic3C2×D411yescharacteristic
246C2×C3×Dic3C2×D411yescharacteristic
247C3×D12—21no—
248C3×D12C2×Q812yes—
249C3×C4×D3—42no—
250C3×C4×D3—81no—
251C3×C4×D3—81no—
252C3×Dic6—22no—
253C3×Dic6—81no—
254C3×Dic6—81no—
255C3×Dic6—81no—
256C3×Dic6—81no—
257C32×C8—21no—
258C32×C8—21no—
259C3×C3⋊C8—21no—
260C3×C3⋊C8C2×Q812yes—
261Q82—31no—
262#554—31no—
263#501—31no—
264#501—31no—
265#500—31no—
266#479—31no—
267#479C3×D311yescharacteristic, complemented
268#477—31no—
269#476—31no—
270#474—31no—
271#474—31no—
272#446—31no—
273#440—31no—
274#440—31no—
275C4×SD16—31no—
276C2×C3×Q8—21no—
277C2×C3×Q8—31no—
278C2×C3×Q8—61no—
279C2×C3×Q8—61no—
280C2×C3×Q8—61no—
281C2×C3×Q8—61no—
282C2×C3×Q8C22×D311yescharacteristic
283C2×C3×Q8C23×C311yescharacteristic
284C2×C3×D4—31no—
285C22×C3×C4—61no—
286C22×C3×C4—61no—
287C22×C3×C4—61no—
288C2×D12C23×C311yescharacteristic
289C2×C4×D3—21no—
290C2×C4×D3—21no—
291C2×C4×D3—21no—
292C2×Dic6—21no—
293C2×Dic6—21no—
294C2×Dic6—21no—
295C2×Dic6—21no—
296C2×Dic6C3×D411yescharacteristic
297C3×SD16—34no—
298C2×C3×C8—21no—
299C2×C3×C8—21no—
300C2×C3×C8—31no—
301C2×C3×C8—31no—
302C2×C3×C8C22×D311yescharacteristic
303C2×C3×C8C22×D311yescharacteristic
304C2×C3×C8C23×C311yescharacteristic
305C2×C3×C8C23×C311yescharacteristic
306C3×C4⋊C4—21no—
307C3×C4⋊C4—21no—
308C3×C4⋊C4—21no—
309C3×C4⋊C4—21no—
310C3×C4⋊C4—21no—
311C3×C4⋊C4—21no—
312C3×C4⋊C4—21no—
313C3×C4⋊C4—21no—
314C3×C4⋊C4—21no—
315C3×C4⋊C4—31no—
316C3×C4⋊C4—31no—
317C3×C4⋊C4—31no—
318C3×C4⋊C4—31no—
319C3×C4⋊C4—31no—
320C3×C4⋊C4—31no—
321C3×C4⋊C4—41no—
322C3×C4⋊C4—41no—
323C3×C4⋊C4—41no—
324C3×C4⋊C4—61no—
325C3×C4⋊C4—61no—
326C3×C4⋊C4—61no—
327C3×C4⋊C4—61no—
328C3×C4⋊C4—61no—
329C3×C4⋊C4—61no—
330C3×C4⋊C4—61no—
331C3×C4⋊C4—61no—
332C3×C4⋊C4C22×D311yescharacteristic
333C3×C4⋊C4C22×D311yescharacteristic
334C3×C4⋊C4C22×D311yescharacteristic
335C3×C4⋊C4C23×C311yescharacteristic
336C3×C4⋊C4C23×C311yescharacteristic
337C3×C4⋊C4C23×C311yescharacteristic
338C3×C22⋊C4—61no—
339C3×C22⋊C4—61no—
340C3×C22⋊C4—61no—
341C3×C42—21no—
342C3×C42—21no—
343C3×C42—21no—
344C3×C42—31no—
345C3×C42—31no—
346C3×C42—41no—
347C3×C42—61no—
348C3×C42—61no—
349C3×C42C22×D311yescharacteristic
350C3×C42C23×C311yescharacteristic
351#215C3×Q814yescomplemented
352(C2×D3)⋊C4—21no—
353(C2×D3)⋊C4—21no—
354(C2×D3)⋊C4—21no—
355C4⋊Dic3—21no—
356C4⋊Dic3—21no—
357C4⋊Dic3—21no—
358C4⋊Dic3—21no—
359C4⋊Dic3C3×D411yescharacteristic
360C4⋊Dic3C23×C311yescharacteristic
361C4⋊Dic3C23×C311yescharacteristic
362C4⋊Dic3C23×C311yescharacteristic
363Dic3⋊C4—21no—
364Dic3⋊C4—21no—
365Dic3⋊C4—21no—
366Dic3⋊C4—21no—
367Dic3⋊C4C3×D411yescharacteristic
368Dic3⋊C4C3×D411yescharacteristic
369C4×Dic3—21no—
370C4×Dic3—21no—
371C4×Dic3C23×C311yescharacteristic
372C4×Dic3C23×C311yescharacteristic
373C2×C3⋊C8C23×C311yescharacteristic
374C2×C3⋊C8C23×C311yescharacteristic
375C22×C32C22×D411yescharacteristic
376C2×C3×D3—22no—
377C2×C3×D3—41no—
378C2×C3×D3—41no—
379C32×C4—22no—
380C32×C4—21no—
381C32×C4—21no—
382C32×C4—41no—
383C32×C4—41no—
384C32×C4—41no—
385C32×C4C22×Q811yescharacteristic
386C32×C42−1+411yescharacteristic
387C3×Dic3—21no—
388C3×Dic3—21no—
389C3×Dic3—21no—
390C3×Dic3—41no—
391C3×Dic3—41no—
392C3×Dic3—41no—
393C3×Dic3#13712yes—
394C2×SD16—31no—
395C4⋊Q8—31no—
396C4⋊Q8—31no—
397C4⋊Q8—31no—
398C4⋊Q8—31no—
399C4⋊Q8—61no—
400C4⋊Q8—61no—
401C4⋊Q8—61no—
402#125—31no—
403#125C2×C3×D311yescharacteristic
404C22⋊Q8—61no—
405C22⋊Q8—61no—
406C22⋊Q8—61no—
407C4×Q8—31no—
408C4×Q8—31no—
409C4×Q8—31no—
410C4×Q8—61no—
411C4×Q8C2×C3×D311yescharacteristic
412C4×D4—31no—
413C4×D4—31no—
414C4×D4—31no—
415C2×C4⋊C4—61no—
416#107—31no—
417#107—31no—
418#107—31no—
419#107—31no—
420#107—31no—
421#107C2×C3×D311yescharacteristic
422#106—31no—
423#106—31no—
424#106C2×C3×D311yescharacteristic
425C4⋊C8—31no—
426C4⋊C8—31no—
427C4⋊C8C2×C3×D311yescharacteristic
428#103—31no—
429#103C2×C3×D311yescharacteristic
430#103C2×C3×D311yescharacteristic
431#102—31no—
432#102—31no—
433#102—31no—
434#97—31no—
435#97—31no—
436C4×C8—31no—
437C23×C3—61no—
438C22×D3—21no—
439C3×Q8—21no—
440C3×Q8—21no—
441C3×Q8—22no—
442C3×Q8—41no—
443C3×Q8—62no—
444C3×Q8—241no—
445C3×Q8—241no—
446C3×Q8—241no—
447C3×Q8—241no—
448C3×Q8D3×Q812yes—
449C3×Q8C2×C3×Q812yes—
450C3×D4—32no—
451C3×D4—61no—
452C2×C3×C4—21no—
453C2×C3×C4—21no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—21no—
463C2×C3×C4—31no—
464C2×C3×C4—31no—
465C2×C3×C4—31no—
466C2×C3×C4—31no—
467C2×C3×C4—41no—
468C2×C3×C4—41no—
469C2×C3×C4—41no—
470C2×C3×C4—41no—
471C2×C3×C4—61no—
472C2×C3×C4—61no—
473C2×C3×C4—61no—
474C2×C3×C4—122no—
475C2×C3×C4—241no—
476C2×C3×C4—241no—
477C2×C3×C4D3×D411yescharacteristic
478C2×C3×C4D3×D411yescharacteristic
479C2×C3×C4C2×C3×D411yescharacteristic
480C2×C3×C4C2×C3×D411yescharacteristic
481C2×C3×C4C23×D311yescharacteristic
482C2×C3×C4C24×C311yescharacteristic
483C2×Dic3—21no—
484C2×Dic3—21no—
485C2×Dic3—21no—
486C2×Dic3C2×C3×D411yescharacteristic
487C2×Dic3C2×C3×D411yescharacteristic
488C2×Dic3C2×C3×D411yescharacteristic
489C2×Dic3C2×C3×D411yescharacteristic
490D12—21no—
491D12C2×C3×Q812yes—
492C4×D3—42no—
493C4×D3—81no—
494C4×D3—81no—
495Dic6—22no—
496Dic6—81no—
497Dic6—81no—
498Dic6—81no—
499Dic6—81no—
500C3×C8—21no—
501C3×C8—21no—
502C3×C8—21no—
503C3×C8—21no—
504C3×C8—32no—
505C3×C8—41no—
506C3×C8—41no—
507C3×C8—61no—
508C3⋊C8—21no—
509C3⋊C8C2×C3×Q812yes—
510C2×C32D4×Q811yescharacteristic
511C2×C32C2×#13711yescharacteristic
512C2×C32#57611yescharacteristic
513C3×D3—42no—
514C2×Q8—31no—
515C2×Q8—61no—
516C2×Q8—61no—
517C2×Q8—61no—
518C2×Q8—61no—
519C2×Q8C22×C3×D311yescharacteristic
520C2×D4—31no—
521C22×C4—61no—
522C22×C4—61no—
523C22×C4—61no—
524SD16—34no—
525C2×C8—31no—
526C2×C8—31no—
527C2×C8C22×C3×D311yescharacteristic
528C2×C8C22×C3×D311yescharacteristic
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—31no—
533C4⋊C4—31no—
534C4⋊C4—31no—
535C4⋊C4—31no—
536C4⋊C4—31no—
537C4⋊C4—31no—
538C4⋊C4—61no—
539C4⋊C4—61no—
540C4⋊C4—61no—
541C4⋊C4—61no—
542C4⋊C4—61no—
543C4⋊C4—61no—
544C4⋊C4—61no—
545C4⋊C4—61no—
546C4⋊C4C22×C3×D311yescharacteristic
547C4⋊C4C22×C3×D311yescharacteristic
548C4⋊C4C22×C3×D311yescharacteristic
549C22⋊C4—61no—
550C22⋊C4—61no—
551C22⋊C4—61no—
552C42—21no—
553C42—31no—
554C42—31no—
555C42—61no—
556C42—61no—
557C42C22×C3×D311yescharacteristic
558C22×C3—21no—
559C22×C3—62no—
560C22×C3—121no—
561C22×C3—121no—
562C22×C3C2×D3×D411yescharacteristic
563C22×C3C22×C3×D411yescharacteristic
564C2×D3—22no—
565C2×D3—41no—
566C2×D3—41no—
567C3×C4—22no—
568C3×C4—21no—
569C3×C4—21no—
570C3×C4—21no—
571C3×C4—21no—
572C3×C4—22no—
573C3×C4—21no—
574C3×C4—21no—
575C3×C4—32no—
576C3×C4—41no—
577C3×C4—41no—
578C3×C4—42no—
579C3×C4—41no—
580C3×C4—41no—
581C3×C4—41no—
582C3×C4—41no—
583C3×C4—41no—
584C3×C4—41no—
585C3×C4—61no—
586C3×C4—61no—
587C3×C4—61no—
588C3×C4—81no—
589C3×C4—81no—
590C3×C4—81no—
591C3×C4—121no—
592C3×C4—121no—
593C3×C4—121no—
594C3×C4C2×D3×Q811yescharacteristic
595C3×C4#101011yescharacteristic
596C3×C4C22×C3×Q811yescharacteristic
597C3×C4C3×2−1+411yescharacteristic
598Dic3—21no—
599Dic3—21no—
600Dic3—21no—
601Dic3—41no—
602Dic3—41no—
603Dic3—41no—
604Dic3C3×#13712yes—
605C32#338511yescharacteristic, complemented, Sylow
606C23—61no—
607Q8—21no—
608Q8—62no—
609Q8—241no—
610Q8—241no—
611Q8—241no—
612Q8—241no—
613Q8C3×D3×Q812yes—
614D4—32no—
615D4—61no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—31no—
621C2×C4—31no—
622C2×C4—31no—
623C2×C4—31no—
624C2×C4—61no—
625C2×C4—61no—
626C2×C4—61no—
627C2×C4—122no—
628C2×C4—241no—
629C2×C4—241no—
630C2×C4C3×D3×D411yescharacteristic
631C2×C4C3×D3×D411yescharacteristic
632C2×C4C23×C3×D311yescharacteristic
633C8—21no—
634C8—21no—
635C8—32no—
636C8—61no—
637C2×C3—21no—
638C2×C3—21no—
639C2×C3—21no—
640C2×C3—122no—
641C2×C3#563211yescharacteristic
642C2×C3#576911yescharacteristic
643C2×C3D3×#13711yescharacteristic
644C2×C3C3×D4×Q811yescharacteristic
645C2×C3C2×C3×#13711yescharacteristic
646C2×C3C3×#57611yescharacteristic
647D3—42no—
648C22—62no—
649C22—121no—
650C22—121no—
651C22C2×C3×D3×D411yescharacteristic
652C4—21no—
653C4—21no—
654C4—22no—
655C4—32no—
656C4—41no—
657C4—41no—
658C4—41no—
659C4—61no—
660C4—61no—
661C4—61no—
662C4—121no—
663C4—121no—
664C4—121no—
665C4C2×C3×D3×Q811yescharacteristic
666C4C3×#101011yescharacteristic
667C3—21no—
668C3#8122311yescharacteristic, direct product factor
669C3C3×#338511yescharacteristic, complemented
670C2—122no—
671C2C3×#563211yescharacteristic
672C2C3×#576911yescharacteristic
673C2C3×D3×#13711yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#479C2
socleC22×C32C22×D4
prime radicalC2×C3×D12C23
hypercenterC3×#479D3
hypocenterC3C3×#3385
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#479

Complements

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

NH ≅ G/Ntype
2. C3×Q8×Dic6C2semidirect
3. C32×#479C2semidirect
4. C3×#5064C2semidirect
7. C3×#4874C2semidirect
9. C3×#4856C2semidirect
11. C3×#4828C2semidirect
13. C3×#4796C2semidirect
14. C3×#4793C2semidirect
17. #81223C3direct (N × H)
64. Q8×Dic6C2×C3semidirect
70. C3×#479D3semidirect
71. C3×#479C2×C3semidirect
80. #5064C2×C3semidirect
83. #4874C2×C3semidirect
85. #4856C2×C3semidirect
87. #4828C2×C3semidirect
89. #4796C2×C3semidirect
90. #4793C2×C3semidirect
112. C3×#215Q8semidirect
267. #479C3×D3semidirect
351. #215C3×Q8semidirect
605. C32#3385semidirect
668. C3#81223direct (N × H)
669. C3C3×#3385semidirect

Maximal subgroups

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

subgroupindex
C3×#56902
C3×Q8×Dic62
C32×#4792
C3×#50642
C3×#50262
C3×#48902
C3×#48742
C3×#48702
C3×#48562
C3×#48462
C3×#48282
C3×#48172
C3×#47962
C3×#47932
C3×#47882
C3×#33853
#812233