Finite Group Databasebeta

← C3×#81965 #11897612

Subgroups — C3×#81965 #11897612

Order 1152.

725 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5722C211yesmaximal, characteristic, complemented
2C3×#5690C211yesmaximal, characteristic
3C32×#501C211yesmaximal, characteristic, complemented
4C3×#5087C211yesmaximal, characteristic
5C3×#5063C211yesmaximal, characteristic, complemented
6C3×#4890C211yesmaximal, characteristic
7C3×#4889C211yesmaximal, characteristic
8C3×#4875C211yesmaximal, characteristic, complemented
9C3×#4874C211yesmaximal, characteristic, complemented
10C3×#4870C211yesmaximal, characteristic
11C3×#4857C211yesmaximal, characteristic, complemented
12C3×#4856C211yesmaximal, characteristic, complemented
13C3×#4852C211yesmaximal, characteristic
14C3×#4710C211yesmaximal, characteristic
15C3×#4701C211yesmaximal, characteristic, complemented
16C3×#3385—31nomaximal
17#81965C311yesmaximal, characteristic, direct product factor
18C32×C4⋊Q8C2211yescharacteristic
19C32×#125C2211yescharacteristic
20C3×#944—21no—
21C3×#944—21no—
22C2×C3×#204C2211yescharacteristic
23C3×#897—21no—
24C3×#896—21no—
25C3×#896—21no—
26C3×#893C2211yescharacteristic
27C3×#893C2211yescharacteristic
28C3×D3×C4⋊C4—21no—
29C3×#890C2211yescharacteristic
30C3×#888—21no—
31C3×#888C2211yescharacteristic
32C3×#888C2211yescharacteristic
33C3×#888C2211yescharacteristic
34C3×#887—21no—
35C3×#887C2211yescharacteristic
36C3×#887C2211yescharacteristic
37C3×C4×D12C2211yescharacteristic
38C3×C4×Dic6C2211yescharacteristic
39C3×C4×Dic6C2211yescharacteristic
40C32×#107C2211yescharacteristic
41C32×#107C2211yescharacteristic
42C32×#106C2211yescharacteristic
43C32×#106C2211yescharacteristic
44C32×#97C2211yescharacteristic
45C3×#821C2211yescharacteristic
46C3×#818C2211yescharacteristic
47C3×#816C2211yescharacteristic
48C3×#815C2211yescharacteristic
49C3×Dic3⋊C8C2211yescharacteristic
50C3×Dic3⋊C8C2211yescharacteristic
51C3×C8×Dic3C2211yescharacteristic
52C3×#810C2211yescharacteristic
53C3×#810C2211yescharacteristic
54C3×#809C2211yescharacteristic
55C3×#809C2211yescharacteristic
56C3×#808C2211yescharacteristic
57C3×#807C2211yescharacteristic
58C3×#807C2211yescharacteristic
59C3×#807C2211yescharacteristic
60C3×C4⋊(C3⋊C8)C2211yescharacteristic
61C3×Q82—31no—
62C3×#554—31no—
63#5722C2×C311yescharacteristic, complemented
64#5690C2×C311yescharacteristic
65C3×#501—21no—
66C3×#501—31no—
67C3×#501D311yescharacteristic, complemented
68C3×#501C2×C311yescharacteristic, complemented
69C3×#500—31no—
70C3×#479—31no—
71C3×#479—31no—
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#5087C2×C311yescharacteristic
81#5063C2×C311yescharacteristic, complemented
82#4890C2×C311yescharacteristic
83#4889C2×C311yescharacteristic
84#4875C2×C311yescharacteristic, complemented
85#4874C2×C311yescharacteristic, complemented
86#4870C2×C311yescharacteristic
87#4857C2×C311yescharacteristic, complemented
88#4856C2×C311yescharacteristic, complemented
89#4852C2×C311yescharacteristic
90#4710C2×C311yescharacteristic
91#4701C2×C311yescharacteristic, complemented
92C2×C32×Q8—21no—
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×Dic6D411yescharacteristic
101C2×C3×Dic6C2311yescharacteristic
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×C4⋊C4C2311yescharacteristic
111C32×C42C2311yescharacteristic
112C3×(C2×D3)⋊C4—21no—
113C3×(C2×D3)⋊C4—21no—
114C3×(C2×D3)⋊C4—21no—
115C3×C4⋊Dic3—21no—
116C3×C4⋊Dic3D411yescharacteristic
117C3×C4⋊Dic3C2311yescharacteristic
118C3×C4⋊Dic3C2311yescharacteristic
119C3×Dic3⋊C4—21no—
120C3×Dic3⋊C4—21no—
121C3×Dic3⋊C4—21no—
122C3×Dic3⋊C4—21no—
123C3×Dic3⋊C4—21no—
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4D411yescharacteristic
127C3×Dic3⋊C4D411yescharacteristic
128C3×C4×Dic3—21no—
129C3×C4×Dic3—21no—
130C3×C4×Dic3—21no—
131C3×C4×Dic3C2311yescharacteristic
132C3×C4×Dic3C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C3×#204Q814yescomplemented
136#3385—31noSylow
137C2×C3×SD16—31no—
138C3×C4⋊Q8—21no—
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×C4⋊Q8C2×D311yescharacteristic
146C3×C4⋊Q8C22×C311yescharacteristic
147C3×#125—21no—
148C3×#125—31no—
149C3×#125C2×D311yescharacteristic
150C3×#125C22×C311yescharacteristic
151C3×C22⋊Q8—61no—
152C3×C22⋊Q8—61no—
153C3×C22⋊Q8—61no—
154C3×C4×Q8—31no—
155C3×C4×Q8—31no—
156C3×C4×Q8—31no—
157C3×C4×Q8—31no—
158C3×C4×Q8—61no—
159C3×C4×D4—31no—
160C3×C4×D4—31no—
161C3×C4×D4—31no—
162C2×C3×C4⋊C4—61no—
163#944—21no—
164#944—21no—
165C2×#204C22×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#888C22×C311yescharacteristic
175#888C22×C311yescharacteristic
176#888C22×C311yescharacteristic
177#887—21no—
178#887C22×C311yescharacteristic
179#887C22×C311yescharacteristic
180C4×D12C22×C311yescharacteristic
181C4×Dic6C22×C311yescharacteristic
182C4×Dic6C22×C311yescharacteristic
183C3×#107—21no—
184C3×#107—21no—
185C3×#107—31no—
186C3×#107—31no—
187C3×#107—31no—
188C3×#107—31no—
189C3×#107C2×D311yescharacteristic
190C3×#107C2×D311yescharacteristic
191C3×#107C22×C311yescharacteristic
192C3×#107C22×C311yescharacteristic
193C3×#106—21no—
194C3×#106—21no—
195C3×#106—31no—
196C3×#106C2×D311yescharacteristic
197C3×#106C2×D311yescharacteristic
198C3×#106C22×C311yescharacteristic
199C3×#106C22×C311yescharacteristic
200C3×C4⋊C8—31no—
201C3×C4⋊C8—31no—
202C3×C4⋊C8—31no—
203C3×#103—31no—
204C3×#103—31no—
205C3×#103—31no—
206C3×#102—31no—
207C3×#102—31no—
208C3×#102—31no—
209C3×#97—21no—
210C3×#97—31no—
211C3×#97C2×D311yescharacteristic
212C3×#97C22×C311yescharacteristic
213C3×C4×C8—31no—
214#821C22×C311yescharacteristic
215#818C22×C311yescharacteristic
216#816C22×C311yescharacteristic
217#815C22×C311yescharacteristic
218Dic3⋊C8C22×C311yescharacteristic
219Dic3⋊C8C22×C311yescharacteristic
220C8×Dic3C22×C311yescharacteristic
221#810C22×C311yescharacteristic
222#810C22×C311yescharacteristic
223#809C22×C311yescharacteristic
224#809C22×C311yescharacteristic
225#808C22×C311yescharacteristic
226#807C22×C311yescharacteristic
227#807C22×C311yescharacteristic
228#807C22×C311yescharacteristic
229C4⋊(C3⋊C8)C22×C311yescharacteristic
230C22×C3×D3—21no—
231C32×Q8—81no—
232C2×C32×C4—21no—
233C2×C32×C4—21no—
234C2×C32×C4—21no—
235C2×C32×C4—21no—
236C2×C32×C4C2×D411yescharacteristic
237C2×C32×C4C2×D411yescharacteristic
238C2×C32×C4C2411yescharacteristic
239C2×C3×Dic3—21no—
240C2×C3×Dic3—21no—
241C2×C3×Dic3—21no—
242C2×C3×Dic3C2×D411yescharacteristic
243C2×C3×Dic3C2×D411yescharacteristic
244C2×C3×Dic3C2×D411yescharacteristic
245C2×C3×Dic3C2×D411yescharacteristic
246C3×D12—21no—
247C3×D12C2×Q812yes—
248C3×C4×D3—42no—
249C3×C4×D3—81no—
250C3×C4×D3—81no—
251C3×Dic6—21no—
252C3×Dic6—22no—
253C3×Dic6—81no—
254C3×Dic6—81no—
255C3×Dic6—81no—
256C3×Dic6C2×Q812yes—
257C32×C8—21no—
258C32×C8C2×Q812yes—
259C3×C3⋊C8—21no—
260C3×C3⋊C8—21no—
261Q82—31no—
262#554—31no—
263#501—31no—
264#501C3×D311yescharacteristic, complemented
265#500—31no—
266#479—31no—
267#479—31no—
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—21no—
278C2×C3×Q8—31no—
279C2×C3×Q8—31no—
280C2×C3×Q8—41no—
281C2×C3×Q8—61no—
282C2×C3×Q8—61no—
283C2×C3×Q8—61no—
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×Dic6C3×D411yescharacteristic
296C2×Dic6C23×C311yescharacteristic
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—21no—
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⋊C4C22×D311yescharacteristic
336C3×C4⋊C4C23×C311yescharacteristic
337C3×C4⋊C4C23×C311yescharacteristic
338C3×C4⋊C4C23×C311yescharacteristic
339C3×C4⋊C4C23×C311yescharacteristic
340C3×C22⋊C4—61no—
341C3×C22⋊C4—61no—
342C3×C22⋊C4—61no—
343C3×C42—21no—
344C3×C42—31no—
345C3×C42—31no—
346C3×C42—61no—
347C3×C42—61no—
348C3×C42—61no—
349C3×C42C22×D311yescharacteristic
350C3×C42C23×C311yescharacteristic
351(C2×D3)⋊C4—21no—
352(C2×D3)⋊C4—21no—
353(C2×D3)⋊C4—21no—
354C4⋊Dic3—21no—
355C4⋊Dic3C3×D411yescharacteristic
356C4⋊Dic3C23×C311yescharacteristic
357C4⋊Dic3C23×C311yescharacteristic
358Dic3⋊C4—21no—
359Dic3⋊C4—21no—
360Dic3⋊C4—21no—
361Dic3⋊C4—21no—
362Dic3⋊C4—21no—
363Dic3⋊C4—21no—
364Dic3⋊C4—21no—
365Dic3⋊C4C3×D411yescharacteristic
366Dic3⋊C4C3×D411yescharacteristic
367C4×Dic3—21no—
368C4×Dic3—21no—
369C4×Dic3—21no—
370C4×Dic3C23×C311yescharacteristic
371C4×Dic3C23×C311yescharacteristic
372C2×C3⋊C8C23×C311yescharacteristic
373C2×C3⋊C8C23×C311yescharacteristic
374#204C3×Q814yescomplemented
375C22×C32C22×D411yescharacteristic
376C2×C3×D3—22no—
377C2×C3×D3—41no—
378C2×C3×D3—41no—
379C32×C4—21no—
380C32×C4—21no—
381C32×C4—41no—
382C32×C4—41no—
383C32×C4—41no—
384C32×C4—41no—
385C32×C4C22×Q811yescharacteristic
386C32×C42−1+411yescharacteristic
387C3×Dic3—22no—
388C3×Dic3—21no—
389C3×Dic3—21no—
390C3×Dic3—21no—
391C3×Dic3—41no—
392C3×Dic3—41no—
393C3×Dic3#13712yes—
394C2×SD16—31no—
395C4⋊Q8—31no—
396C4⋊Q8—31no—
397C4⋊Q8—31no—
398C4⋊Q8—61no—
399C4⋊Q8—61no—
400C4⋊Q8—61no—
401C4⋊Q8C2×C3×D311yescharacteristic
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—31no—
411C4×Q8—61no—
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#107C2×C3×D311yescharacteristic
421#107C2×C3×D311yescharacteristic
422#106—31no—
423#106C2×C3×D311yescharacteristic
424#106C2×C3×D311yescharacteristic
425C4⋊C8—31no—
426C4⋊C8—31no—
427C4⋊C8—31no—
428#103—31no—
429#103—31no—
430#103—31no—
431#102—31no—
432#102—31no—
433#102—31no—
434#97—31no—
435#97C2×C3×D311yescharacteristic
436C4×C8—31no—
437C23×C3—61no—
438C22×D3—21no—
439C3×Q8—32no—
440C3×Q8—62no—
441C3×Q8—61no—
442C3×Q8—81no—
443C3×Q8—81no—
444C3×Q8—82no—
445C3×Q8—241no—
446C3×Q8—241no—
447C3×Q8—241no—
448C3×D4—32no—
449C3×D4—61no—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
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—31no—
462C2×C3×C4—31no—
463C2×C3×C4—31no—
464C2×C3×C4—31no—
465C2×C3×C4—41no—
466C2×C3×C4—41no—
467C2×C3×C4—41no—
468C2×C3×C4—41no—
469C2×C3×C4—61no—
470C2×C3×C4—61no—
471C2×C3×C4—61no—
472C2×C3×C4—122no—
473C2×C3×C4—241no—
474C2×C3×C4—241no—
475C2×C3×C4D3×D411yescharacteristic
476C2×C3×C4D3×D411yescharacteristic
477C2×C3×C4C2×C3×D411yescharacteristic
478C2×C3×C4C2×C3×D411yescharacteristic
479C2×C3×C4C23×D311yescharacteristic
480C2×C3×C4C24×C311yescharacteristic
481C2×Dic3—21no—
482C2×Dic3—21no—
483C2×Dic3—21no—
484C2×Dic3C2×C3×D411yescharacteristic
485C2×Dic3C2×C3×D411yescharacteristic
486C2×Dic3C2×C3×D411yescharacteristic
487C2×Dic3C2×C3×D411yescharacteristic
488D12—21no—
489D12C2×C3×Q812yes—
490C4×D3—42no—
491C4×D3—81no—
492C4×D3—81no—
493Dic6—21no—
494Dic6—22no—
495Dic6—81no—
496Dic6—81no—
497Dic6—81no—
498Dic6C2×C3×Q812yes—
499C3×C8—22no—
500C3×C8—21no—
501C3×C8—21no—
502C3×C8—22no—
503C3×C8—61no—
504C3×C8—61no—
505C3×C8D3×Q812yes—
506C3×C8C2×C3×Q812yes—
507C3⋊C8—21no—
508C3⋊C8—21no—
509C2×C32D4×Q811yescharacteristic
510C2×C32C2×#13711yescharacteristic
511C2×C32#57611yescharacteristic
512C3×D3—42no—
513C2×Q8—21no—
514C2×Q8—31no—
515C2×Q8—31no—
516C2×Q8—61no—
517C2×Q8—61no—
518C2×Q8—61no—
519C2×D4—31no—
520C22×C4—61no—
521C22×C4—61no—
522C22×C4—61no—
523SD16—34no—
524C2×C8—31no—
525C2×C8—31no—
526C2×C8C22×C3×D311yescharacteristic
527C2×C8C22×C3×D311yescharacteristic
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—31no—
532C4⋊C4—31no—
533C4⋊C4—31no—
534C4⋊C4—31no—
535C4⋊C4—31no—
536C4⋊C4—61no—
537C4⋊C4—61no—
538C4⋊C4—61no—
539C4⋊C4—61no—
540C4⋊C4—61no—
541C4⋊C4—61no—
542C4⋊C4—61no—
543C4⋊C4—61no—
544C4⋊C4C22×C3×D311yescharacteristic
545C4⋊C4C22×C3×D311yescharacteristic
546C4⋊C4C22×C3×D311yescharacteristic
547C4⋊C4C22×C3×D311yescharacteristic
548C22⋊C4—61no—
549C22⋊C4—61no—
550C22⋊C4—61no—
551C42—31no—
552C42—31no—
553C42—61no—
554C42—61no—
555C42—61no—
556C42C22×C3×D311yescharacteristic
557C22×C3—21no—
558C22×C3—62no—
559C22×C3—121no—
560C22×C3—121no—
561C22×C3C2×D3×D411yescharacteristic
562C22×C3C22×C3×D411yescharacteristic
563C2×D3—22no—
564C2×D3—41no—
565C2×D3—41no—
566C3×C4—21no—
567C3×C4—21no—
568C3×C4—21no—
569C3×C4—21no—
570C3×C4—21no—
571C3×C4—21no—
572C3×C4—32no—
573C3×C4—41no—
574C3×C4—41no—
575C3×C4—41no—
576C3×C4—41no—
577C3×C4—41no—
578C3×C4—41no—
579C3×C4—41no—
580C3×C4—41no—
581C3×C4—41no—
582C3×C4—41no—
583C3×C4—62no—
584C3×C4—61no—
585C3×C4—61no—
586C3×C4—61no—
587C3×C4—81no—
588C3×C4—81no—
589C3×C4—81no—
590C3×C4—81no—
591C3×C4—121no—
592C3×C4—121no—
593C3×C4C2×D3×Q811yescharacteristic
594C3×C4#100711yescharacteristic
595C3×C4C22×C3×Q811yescharacteristic
596C3×C4C3×2−1+411yescharacteristic
597Dic3—21no—
598Dic3—21no—
599Dic3—21no—
600Dic3—22no—
601Dic3—41no—
602Dic3—41no—
603Dic3C3×#13712yes—
604C32#338511yescharacteristic, complemented, Sylow
605C23—61no—
606Q8—32no—
607Q8—62no—
608Q8—61no—
609Q8—81no—
610Q8—241no—
611Q8—241no—
612Q8—241no—
613D4—32no—
614D4—61no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—31no—
620C2×C4—31no—
621C2×C4—31no—
622C2×C4—31no—
623C2×C4—61no—
624C2×C4—61no—
625C2×C4—61no—
626C2×C4—122no—
627C2×C4—241no—
628C2×C4—241no—
629C2×C4C3×D3×D411yescharacteristic
630C2×C4C3×D3×D411yescharacteristic
631C2×C4C23×C3×D311yescharacteristic
632C8—21no—
633C8—61no—
634C8—61no—
635C8C3×D3×Q812yes—
636C2×C3—21no—
637C2×C3—21no—
638C2×C3—21no—
639C2×C3—122no—
640C2×C3#572711yescharacteristic
641C2×C3#577411yescharacteristic
642C2×C3D3×#13711yescharacteristic
643C2×C3C3×D4×Q811yescharacteristic
644C2×C3C2×C3×#13711yescharacteristic
645C2×C3C3×#57611yescharacteristic
646D3—42no—
647C22—62no—
648C22—121no—
649C22—121no—
650C22C2×C3×D3×D411yescharacteristic
651C4—21no—
652C4—21no—
653C4—32no—
654C4—41no—
655C4—41no—
656C4—41no—
657C4—41no—
658C4—61no—
659C4—61no—
660C4—61no—
661C4—62no—
662C4—121no—
663C4—121no—
664C4C2×C3×D3×Q811yescharacteristic
665C4C3×#100711yescharacteristic
666C3—21no—
667C3#8196511yescharacteristic, direct product factor
668C3C3×#338511yescharacteristic, complemented
669C2—122no—
670C2C3×#572711yescharacteristic
671C2C3×#577411yescharacteristic
672C2C3×D3×#13711yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#501C2
socleC22×C32C22×D4
prime radicalC2×C3×D12C23
hypercenterC3×#501D3
hypocenterC3C3×#3385
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#501

Complements

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

NH ≅ G/Ntype
1. C3×#5722C2semidirect
3. C32×#501C2semidirect
5. C3×#5063C2semidirect
8. C3×#4875C2semidirect
9. C3×#4874C2semidirect
11. C3×#4857C2semidirect
12. C3×#4856C2semidirect
15. C3×#4701C2semidirect
17. #81965C3direct (N × H)
63. #5722C2×C3semidirect
67. C3×#501D3semidirect
68. C3×#501C2×C3semidirect
81. #5063C2×C3semidirect
84. #4875C2×C3semidirect
85. #4874C2×C3semidirect
87. #4857C2×C3semidirect
88. #4856C2×C3semidirect
91. #4701C2×C3semidirect
135. C3×#204Q8semidirect
264. #501C3×D3semidirect
374. #204C3×Q8semidirect
604. C32#3385semidirect
667. C3#81965direct (N × H)
668. C3C3×#3385semidirect

Maximal subgroups

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

subgroupindex
C3×#57222
C3×#56902
C32×#5012
C3×#50872
C3×#50632
C3×#48902
C3×#48892
C3×#48752
C3×#48742
C3×#48702
C3×#48572
C3×#48562
C3×#48522
C3×#47102
C3×#47012
C3×#33853
#819653