Finite Group Databasebeta

← C3×#81004 #11896035

Subgroups — C3×#81004 #11896035

Order 1152.

724 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5722C211yesmaximal, characteristic, complemented
2C3×#5568C211yesmaximal, characteristic
3C32×#475C211yesmaximal, characteristic, complemented
4C3×#5089C211yesmaximal, characteristic
5C3×#5030C211yesmaximal, characteristic, complemented
6C3×#4870C211yesmaximal, characteristic
7C3×#4854C211yesmaximal, characteristic, complemented
8C3×#4853C211yesmaximal, characteristic, complemented
9C3×#4852C211yesmaximal, characteristic
10C3×#4845C211yesmaximal, characteristic
11C3×#4828C211yesmaximal, characteristic, complemented
12C3×#4798C211yesmaximal, characteristic
13C3×#4795C211yesmaximal, characteristic, complemented
14C3×#4794C211yesmaximal, characteristic
15C3×#4792C211yesmaximal, characteristic, complemented
16C3×#3369—31nomaximal
17#81004C311yesmaximal, characteristic, direct product factor
18C32×C4⋊Q8C2211yescharacteristic
19C32×C4×Q8C2211yescharacteristic
20C3×#947C2211yescharacteristic
21C3×#944—21no—
22C3×#944—21no—
23C3×#944C2211yescharacteristic
24C2×C3×#216C2211yescharacteristic
25C2×C3×Dic12C2211yescharacteristic
26C2×C3×#204C2211yescharacteristic
27C3×#898—21no—
28C3×#896—21no—
29C3×#893C2211yescharacteristic
30C3×#888—21no—
31C3×#888C2211yescharacteristic
32C3×#888C2211yescharacteristic
33C3×#887—21no—
34C3×#887C2211yescharacteristic
35C3×#887C2211yescharacteristic
36C3×#887C2211yescharacteristic
37C3×#876—21no—
38C3×#875C2211yescharacteristic
39C3×#872—21no—
40C3×C4×Dic6C2211yescharacteristic
41C3×C4×Dic6C2211yescharacteristic
42C32×#106C2211yescharacteristic
43C32×#106C2211yescharacteristic
44C32×C4⋊C8C2211yescharacteristic
45C32×#103C2211yescharacteristic
46C32×#103C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#821C2211yescharacteristic
49C3×#816C2211yescharacteristic
50C3×#815C2211yescharacteristic
51C3×Dic3⋊C8C2211yescharacteristic
52C3×Dic3⋊C8C2211yescharacteristic
53C3×C8×Dic3C2211yescharacteristic
54C3×#810C2211yescharacteristic
55C3×#810C2211yescharacteristic
56C3×#810C2211yescharacteristic
57C3×#809C2211yescharacteristic
58C3×#809C2211yescharacteristic
59C3×#808C2211yescharacteristic
60C3×#803C2211yescharacteristic
61C3×Q82—31no—
62C3×#556—31no—
63#5722C2×C311yescharacteristic, complemented
64#5568C2×C311yescharacteristic
65C3×#489—31no—
66C3×#489—31no—
67C3×#487—31no—
68C3×#476—31no—
69C3×#475—21no—
70C3×#475—31no—
71C3×#475D311yescharacteristic, complemented
72C3×#475C2×C311yescharacteristic, complemented
73C3×#464—31no—
74C3×#464—31no—
75C3×#462—31no—
76C3×#446—31no—
77C3×#441—31no—
78C3×#441—31no—
79C3×C4×SD16—31no—
80#5089C2×C311yescharacteristic
81#5030C2×C311yescharacteristic, complemented
82#4870C2×C311yescharacteristic
83#4854C2×C311yescharacteristic, complemented
84#4853C2×C311yescharacteristic, complemented
85#4852C2×C311yescharacteristic
86#4845C2×C311yescharacteristic
87#4828C2×C311yescharacteristic, complemented
88#4798C2×C311yescharacteristic
89#4795C2×C311yescharacteristic, complemented
90#4794C2×C311yescharacteristic
91#4792C2×C311yescharacteristic, complemented
92C2×C32×Q8—21no—
93C2×C32×Q8C2311yescharacteristic
94C2×C3×D12C2311yescharacteristic
95C2×C3×C4×D3—21no—
96C2×C3×Dic6—21no—
97C2×C3×Dic6—21no—
98C2×C3×Dic6D411yescharacteristic
99C2×C3×Dic6C2311yescharacteristic
100C2×C3×Dic6C2311yescharacteristic
101C2×C32×C8C2311yescharacteristic
102C2×C32×C8C2311yescharacteristic
103C32×C4⋊C4—21no—
104C32×C4⋊C4—21no—
105C32×C4⋊C4C2311yescharacteristic
106C32×C4⋊C4C2311yescharacteristic
107C32×C4⋊C4C2311yescharacteristic
108C32×C42—21no—
109C32×C42C2311yescharacteristic
110C3×#216—22no—
111C3×(C2×D3)⋊C4—21no—
112C3×(C2×D3)⋊C4—21no—
113C3×(C2×D3)⋊C4—21no—
114C3×(C2×D3)⋊C4—21no—
115C3×(C2×D3)⋊C4—21no—
116C3×C4⋊Dic3D411yescharacteristic
117C3×C4⋊Dic3C2311yescharacteristic
118C3×Dic3⋊C4—21no—
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×Dic3—21no—
132C3×C4×Dic3C2311yescharacteristic
133C3×C4×Dic3C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C3×Dic12—22no—
137C3×#204—22no—
138#3369—31noSylow
139C2×C3×Q16—31no—
140C2×C3×Q16—31no—
141C2×C3×SD16—31no—
142C3×C4⋊Q8—21no—
143C3×C4⋊Q8—31no—
144C3×C4⋊Q8—31no—
145C3×C4⋊Q8—31no—
146C3×C4⋊Q8—61no—
147C3×C4⋊Q8—61no—
148C3×C4⋊Q8—61no—
149C3×C4⋊Q8C2×D311yescharacteristic
150C3×C4⋊Q8C22×C311yescharacteristic
151C3×#126—61no—
152C3×#126—61no—
153C3×#124—31no—
154C3×#124—31no—
155C3×C22⋊Q8—61no—
156C3×C4×Q8—21no—
157C3×C4×Q8—31no—
158C3×C4×Q8—31no—
159C3×C4×Q8—31no—
160C3×C4×Q8—31no—
161C3×C4×Q8—31no—
162C3×C4×Q8—61no—
163C3×C4×Q8C2×D311yescharacteristic
164C3×C4×Q8C22×C311yescharacteristic
165C3×C4×D4—31no—
166C3×#117—61no—
167#947C22×C311yescharacteristic
168#944—21no—
169#944—21no—
170#944C22×C311yescharacteristic
171C2×#216C22×C311yescharacteristic
172C2×Dic12C22×C311yescharacteristic
173C2×#204C22×C311yescharacteristic
174#898—21no—
175#896—21no—
176#893C22×C311yescharacteristic
177#888—21no—
178#888C22×C311yescharacteristic
179#888C22×C311yescharacteristic
180#887—21no—
181#887C22×C311yescharacteristic
182#887C22×C311yescharacteristic
183#887C22×C311yescharacteristic
184#876—21no—
185#875C22×C311yescharacteristic
186#872—21no—
187C4×Dic6C22×C311yescharacteristic
188C4×Dic6C22×C311yescharacteristic
189C3×#106—21no—
190C3×#106—21no—
191C3×#106—31no—
192C3×#106C2×D311yescharacteristic
193C3×#106C2×D311yescharacteristic
194C3×#106C22×C311yescharacteristic
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×#103—31no—
205C3×#103—31no—
206C3×#103—31no—
207C3×#103—31no—
208C3×#103C2×D311yescharacteristic
209C3×#103C2×D311yescharacteristic
210C3×#103C22×C311yescharacteristic
211C3×#103C22×C311yescharacteristic
212C3×#102—31no—
213C3×#102—31no—
214C3×#102—31no—
215C3×#97—31no—
216C3×#97—31no—
217C3×C4×C8—31no—
218#835C22×C311yescharacteristic
219#821C22×C311yescharacteristic
220#816C22×C311yescharacteristic
221#815C22×C311yescharacteristic
222Dic3⋊C8C22×C311yescharacteristic
223Dic3⋊C8C22×C311yescharacteristic
224C8×Dic3C22×C311yescharacteristic
225#810C22×C311yescharacteristic
226#810C22×C311yescharacteristic
227#810C22×C311yescharacteristic
228#809C22×C311yescharacteristic
229#809C22×C311yescharacteristic
230#808C22×C311yescharacteristic
231#803C22×C311yescharacteristic
232C22×C3×D3—21no—
233C32×Q8—21no—
234C32×Q8—21no—
235C32×Q8—81no—
236C2×C32×C4—21no—
237C2×C32×C4—21no—
238C2×C32×C4—21no—
239C2×C32×C4—21no—
240C2×C32×C4C2×D411yescharacteristic
241C2×C32×C4C2×D411yescharacteristic
242C2×C32×C4C2411yescharacteristic
243C2×C3×Dic3—21no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3C2×D411yescharacteristic
247C2×C3×Dic3C2×D411yescharacteristic
248C2×C3×Dic3C2×D411yescharacteristic
249C2×C3×Dic3C2×D411yescharacteristic
250C3×D12—21no—
251C3×D12—21no—
252C3×C4×D3—42no—
253C3×Dic6—21no—
254C3×Dic6—22no—
255C3×Dic6—21no—
256C3×Dic6—21no—
257C3×Dic6—81no—
258C3×Dic6—81no—
259C3×Dic6#4112yes—
260C32×C8—21no—
261C32×C8—21no—
262C3×C3⋊C8—21no—
263C3×C3⋊C8—21no—
264Q82—31no—
265#556—31no—
266#489—31no—
267#489—31no—
268#487—31no—
269#476—31no—
270#475—31no—
271#475C3×D311yescharacteristic, complemented
272#464—31no—
273#464—31no—
274#462—31no—
275#446—31no—
276#441—31no—
277#441—31no—
278C4×SD16—31no—
279C2×C3×Q8—21no—
280C2×C3×Q8—21no—
281C2×C3×Q8—21no—
282C2×C3×Q8—31no—
283C2×C3×Q8—31no—
284C2×C3×Q8—31no—
285C2×C3×Q8—41no—
286C2×C3×Q8—61no—
287C2×C3×Q8—61no—
288C2×C3×Q8C22×D311yescharacteristic
289C2×C3×Q8C23×C311yescharacteristic
290C2×C3×D4—31no—
291C22×C3×C4—61no—
292C2×D12C23×C311yescharacteristic
293C2×C4×D3—21no—
294C2×Dic6—21no—
295C2×Dic6—21no—
296C2×Dic6C3×D411yescharacteristic
297C2×Dic6C23×C311yescharacteristic
298C2×Dic6C23×C311yescharacteristic
299C3×Q16—62no—
300C3×Q16—62no—
301C3×SD16—62no—
302C2×C3×C8—21no—
303C2×C3×C8—21no—
304C2×C3×C8—31no—
305C2×C3×C8—31no—
306C2×C3×C8C22×D311yescharacteristic
307C2×C3×C8C22×D311yescharacteristic
308C2×C3×C8C23×C311yescharacteristic
309C2×C3×C8C23×C311yescharacteristic
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—21no—
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—61no—
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⋊C4C22×D311yescharacteristic
332C3×C4⋊C4C22×D311yescharacteristic
333C3×C4⋊C4C22×D311yescharacteristic
334C3×C4⋊C4C23×C311yescharacteristic
335C3×C4⋊C4C23×C311yescharacteristic
336C3×C4⋊C4C23×C311yescharacteristic
337C3×C22⋊C4—61no—
338C3×C22⋊C4—61no—
339C3×C22⋊C4—61no—
340C3×C22⋊C4—61no—
341C3×C22⋊C4—61no—
342C3×C42—21no—
343C3×C42—21no—
344C3×C42—21no—
345C3×C42—31no—
346C3×C42—31no—
347C3×C42—41no—
348C3×C42—61no—
349C3×C42—61no—
350C3×C42—61no—
351C3×C42—61no—
352C3×C42C22×D311yescharacteristic
353C3×C42C23×C311yescharacteristic
354#216—22no—
355(C2×D3)⋊C4—21no—
356(C2×D3)⋊C4—21no—
357(C2×D3)⋊C4—21no—
358(C2×D3)⋊C4—21no—
359(C2×D3)⋊C4—21no—
360C4⋊Dic3C3×D411yescharacteristic
361C4⋊Dic3C23×C311yescharacteristic
362Dic3⋊C4—21no—
363Dic3⋊C4—21no—
364Dic3⋊C4—21no—
365Dic3⋊C4—21no—
366Dic3⋊C4—21no—
367Dic3⋊C4—21no—
368Dic3⋊C4—21no—
369Dic3⋊C4—21no—
370Dic3⋊C4C3×D411yescharacteristic
371Dic3⋊C4C3×D411yescharacteristic
372C4×Dic3—21no—
373C4×Dic3—21no—
374C4×Dic3—21no—
375C4×Dic3—21no—
376C4×Dic3C23×C311yescharacteristic
377C4×Dic3C23×C311yescharacteristic
378C2×C3⋊C8C23×C311yescharacteristic
379C2×C3⋊C8C23×C311yescharacteristic
380Dic12—22no—
381#204—22no—
382C22×C32C22×D411yescharacteristic
383C2×C3×D3—41no—
384C2×C3×D3—41no—
385C2×C3×D3—41no—
386C32×C4—21no—
387C32×C4—21no—
388C32×C4—41no—
389C32×C4—41no—
390C32×C4—41no—
391C32×C4—41no—
392C32×C4C2×#4111yescharacteristic
393C32×C42−1+411yescharacteristic
394C3×Dic3—22no—
395C3×Dic3—21no—
396C3×Dic3—21no—
397C3×Dic3—21no—
398C3×Dic3—41no—
399C3×Dic3—41no—
400C3×Dic3#13712yes—
401C2×Q16—31no—
402C2×Q16—31no—
403C2×SD16—31no—
404C4⋊Q8—31no—
405C4⋊Q8—31no—
406C4⋊Q8—31no—
407C4⋊Q8—61no—
408C4⋊Q8—61no—
409C4⋊Q8—61no—
410C4⋊Q8C2×C3×D311yescharacteristic
411#126—61no—
412#126—61no—
413#124—31no—
414#124—31no—
415C22⋊Q8—61no—
416C4×Q8—31no—
417C4×Q8—31no—
418C4×Q8—31no—
419C4×Q8—31no—
420C4×Q8—31no—
421C4×Q8—61no—
422C4×Q8C2×C3×D311yescharacteristic
423C4×D4—31no—
424#117—61no—
425#106—31no—
426#106C2×C3×D311yescharacteristic
427#106C2×C3×D311yescharacteristic
428C4⋊C8—31no—
429C4⋊C8—31no—
430C4⋊C8C2×C3×D311yescharacteristic
431#103—31no—
432#103—31no—
433#103—31no—
434#103—31no—
435#103—31no—
436#103C2×C3×D311yescharacteristic
437#103C2×C3×D311yescharacteristic
438#102—31no—
439#102—31no—
440#102—31no—
441#97—31no—
442#97—31no—
443C4×C8—31no—
444C23×C3—61no—
445C22×D3—21no—
446C3×Q8—22no—
447C3×Q8—21no—
448C3×Q8—21no—
449C3×Q8—21no—
450C3×Q8—21no—
451C3×Q8—32no—
452C3×Q8—41no—
453C3×Q8—62no—
454C3×Q8—61no—
455C3×Q8—61no—
456C3×Q8—61no—
457C3×Q8—81no—
458C3×Q8—81no—
459C3×Q8—82no—
460C3×Q8—241no—
461C3×Q8—241no—
462C3×D4—61no—
463C3×D4—61no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—31no—
476C2×C3×C4—31no—
477C2×C3×C4—31no—
478C2×C3×C4—31no—
479C2×C3×C4—41no—
480C2×C3×C4—41no—
481C2×C3×C4—41no—
482C2×C3×C4—41no—
483C2×C3×C4—61no—
484C2×C3×C4—61no—
485C2×C3×C4—61no—
486C2×C3×C4—122no—
487C2×C3×C4D3×D411yescharacteristic
488C2×C3×C4D3×D411yescharacteristic
489C2×C3×C4C2×C3×D411yescharacteristic
490C2×C3×C4C2×C3×D411yescharacteristic
491C2×C3×C4C23×D311yescharacteristic
492C2×C3×C4C24×C311yescharacteristic
493C2×Dic3—21no—
494C2×Dic3—21no—
495C2×Dic3—21no—
496C2×Dic3C2×C3×D411yescharacteristic
497C2×Dic3C2×C3×D411yescharacteristic
498C2×Dic3C2×C3×D411yescharacteristic
499C2×Dic3C2×C3×D411yescharacteristic
500D12—21no—
501D12—21no—
502C4×D3—42no—
503Dic6—21no—
504Dic6—22no—
505Dic6—21no—
506Dic6—21no—
507Dic6—81no—
508Dic6—81no—
509Dic6C3×#4112yes—
510C3×C8—21no—
511C3×C8—21no—
512C3×C8—21no—
513C3×C8—21no—
514C3×C8—41no—
515C3×C8—41no—
516C3×C8—61no—
517C3×C8—61no—
518C3⋊C8—21no—
519C3⋊C8—21no—
520C2×C32#54811yescharacteristic
521C2×C32C2×#13711yescharacteristic
522C2×C32#57711yescharacteristic
523C3×D3—81no—
524C2×Q8—21no—
525C2×Q8—31no—
526C2×Q8—31no—
527C2×Q8—31no—
528C2×Q8—61no—
529C2×Q8—61no—
530C2×Q8C22×C3×D311yescharacteristic
531C2×D4—31no—
532C22×C4—61no—
533Q16—62no—
534Q16—62no—
535SD16—62no—
536C2×C8—31no—
537C2×C8—31no—
538C2×C8C22×C3×D311yescharacteristic
539C2×C8C22×C3×D311yescharacteristic
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—31no—
543C4⋊C4—31no—
544C4⋊C4—31no—
545C4⋊C4—31no—
546C4⋊C4—61no—
547C4⋊C4—61no—
548C4⋊C4—61no—
549C4⋊C4—61no—
550C4⋊C4—61no—
551C4⋊C4—61no—
552C4⋊C4—61no—
553C4⋊C4—61no—
554C4⋊C4C22×C3×D311yescharacteristic
555C4⋊C4C22×C3×D311yescharacteristic
556C4⋊C4C22×C3×D311yescharacteristic
557C22⋊C4—61no—
558C22⋊C4—61no—
559C22⋊C4—61no—
560C22⋊C4—61no—
561C22⋊C4—61no—
562C42—21no—
563C42—31no—
564C42—31no—
565C42—61no—
566C42—61no—
567C42—61no—
568C42—61no—
569C42C22×C3×D311yescharacteristic
570C22×C3—21no—
571C22×C3—121no—
572C22×C3—121no—
573C22×C3—121no—
574C22×C3C2×D3×D411yescharacteristic
575C22×C3C22×C3×D411yescharacteristic
576C2×D3—41no—
577C2×D3—41no—
578C2×D3—41no—
579C3×C4—22no—
580C3×C4—21no—
581C3×C4—21no—
582C3×C4—21no—
583C3×C4—21no—
584C3×C4—21no—
585C3×C4—21no—
586C3×C4—32no—
587C3×C4—41no—
588C3×C4—42no—
589C3×C4—41no—
590C3×C4—41no—
591C3×C4—41no—
592C3×C4—41no—
593C3×C4—41no—
594C3×C4—41no—
595C3×C4—41no—
596C3×C4—41no—
597C3×C4—62no—
598C3×C4—61no—
599C3×C4—61no—
600C3×C4—61no—
601C3×C4—81no—
602C3×C4—81no—
603C3×C4—81no—
604C3×C4—121no—
605C3×C4—121no—
606C3×C4#100711yescharacteristic
607C3×C4D3×#4111yescharacteristic
608C3×C4C2×C3×#4111yescharacteristic
609C3×C4C3×2−1+411yescharacteristic
610Dic3—21no—
611Dic3—21no—
612Dic3—21no—
613Dic3—22no—
614Dic3—41no—
615Dic3—41no—
616Dic3C3×#13712yes—
617C32#336911yescharacteristic, complemented, Sylow
618C23—61no—
619Q8—21no—
620Q8—21no—
621Q8—32no—
622Q8—62no—
623Q8—61no—
624Q8—61no—
625Q8—61no—
626Q8—81no—
627Q8—241no—
628Q8—241no—
629D4—61no—
630D4—61no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—31no—
636C2×C4—31no—
637C2×C4—31no—
638C2×C4—31no—
639C2×C4—61no—
640C2×C4—61no—
641C2×C4—61no—
642C2×C4—122no—
643C2×C4C3×D3×D411yescharacteristic
644C2×C4C3×D3×D411yescharacteristic
645C2×C4C23×C3×D311yescharacteristic
646C8—21no—
647C8—21no—
648C8—61no—
649C8—61no—
650C2×C3—21no—
651C2×C3—21no—
652C2×C3—21no—
653C2×C3—241no—
654C2×C3#563311yescharacteristic
655C2×C3#576211yescharacteristic
656C2×C3D3×#13711yescharacteristic
657C2×C3C3×#54811yescharacteristic
658C2×C3C2×C3×#13711yescharacteristic
659C2×C3C3×#57711yescharacteristic
660D3—81no—
661C22—121no—
662C22—121no—
663C22—121no—
664C22C2×C3×D3×D411yescharacteristic
665C4—21no—
666C4—21no—
667C4—32no—
668C4—41no—
669C4—41no—
670C4—41no—
671C4—41no—
672C4—61no—
673C4—61no—
674C4—61no—
675C4—62no—
676C4—121no—
677C4—121no—
678C4C3×#100711yescharacteristic
679C4C3×D3×#4111yescharacteristic
680C3—21no—
681C3#8100411yescharacteristic, direct product factor
682C3C3×#336911yescharacteristic, complemented
683C2—241no—
684C2C3×#563311yescharacteristic
685C2C3×#576211yescharacteristic
686C2C3×D3×#13711yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#475C2
socleC22×C32C22×D4
prime radicalC2×C3×D12C23
hypercenterC3×#475D3
hypocenterC3C3×#3369
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#475

Complements

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

NH ≅ G/Ntype
1. C3×#5722C2semidirect
3. C32×#475C2semidirect
5. C3×#5030C2semidirect
7. C3×#4854C2semidirect
8. C3×#4853C2semidirect
11. C3×#4828C2semidirect
13. C3×#4795C2semidirect
15. C3×#4792C2semidirect
17. #81004C3direct (N × H)
63. #5722C2×C3semidirect
71. C3×#475D3semidirect
72. C3×#475C2×C3semidirect
81. #5030C2×C3semidirect
83. #4854C2×C3semidirect
84. #4853C2×C3semidirect
87. #4828C2×C3semidirect
89. #4795C2×C3semidirect
91. #4792C2×C3semidirect
271. #475C3×D3semidirect
617. C32#3369semidirect
681. C3#81004direct (N × H)
682. C3C3×#3369semidirect

Maximal subgroups

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

subgroupindex
C3×#57222
C3×#55682
C32×#4752
C3×#50892
C3×#50302
C3×#48702
C3×#48542
C3×#48532
C3×#48522
C3×#48452
C3×#48282
C3×#47982
C3×#47952
C3×#47942
C3×#47922
C3×#33693
#810043