Finite Group Databasebeta

← C3×#81671 #11896017

Subgroups — C3×#81671 #11896017

Order 1152.

726 conjugacy classes of subgroups.

The subgroup lattice has 693 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5722C211yesmaximal, characteristic, complemented
2C3×#5671C211yesmaximal, characteristic
3C32×#489C211yesmaximal, characteristic
4C3×#5094C211yesmaximal, characteristic, complemented
5C3×#5054C211yesmaximal, characteristic
6C3×#4795C211yesmaximal, characteristic, complemented
7C3×#4792C211yesmaximal, characteristic, complemented
8C3×#4791C211yesmaximal, characteristic, complemented
9C3×#4789C211yesmaximal, characteristic, complemented
10C3×#4767C211yesmaximal, characteristic
11C3×#4765C211yesmaximal, characteristic
12C3×#4761C211yesmaximal, characteristic
13C3×#4758C211yesmaximal, characteristic
14C3×#4716C211yesmaximal, characteristic, complemented
15C3×#4701C211yesmaximal, characteristic, complemented
16C3×#3369—31nomaximal
17#81671C311yesmaximal, characteristic, direct product factor
18C32×C4⋊Q8C2211yescharacteristic
19C32×#124C2211yescharacteristic
20C3×Q8×Dic3C2211yescharacteristic
21C3×#944—21no—
22C3×#944—21no—
23C3×#944C2211yescharacteristic
24C2×C3×#216C2211yescharacteristic
25C3×#936C2211yescharacteristic
26C3×D4×Dic3C2211yescharacteristic
27C2×C3×#214C2211yescharacteristic
28C2×C3×Dic12C2211yescharacteristic
29C3×#888—21no—
30C3×#888C2211yescharacteristic
31C3×#888C2211yescharacteristic
32C3×#887—21no—
33C3×#887C2211yescharacteristic
34C3×#887C2211yescharacteristic
35C3×#879—21no—
36C3×#879—21no—
37C3×#878—21no—
38C3×#877—21no—
39C3×C4×Dic6C2211yescharacteristic
40C3×C4×Dic6C2211yescharacteristic
41C3×C4×Dic6C2211yescharacteristic
42C32×#103C2211yescharacteristic
43C32×#103C2211yescharacteristic
44C32×#102C2211yescharacteristic
45C32×#102C2211yescharacteristic
46C32×#97C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#817C2211yescharacteristic
50C3×#816C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×#815C2211yescharacteristic
53C3×Dic3⋊C8C2211yescharacteristic
54C3×Dic3⋊C8C2211yescharacteristic
55C3×C8×Dic3C2211yescharacteristic
56C3×#810C2211yescharacteristic
57C3×#810C2211yescharacteristic
58C3×#808C2211yescharacteristic
59C3×#808C2211yescharacteristic
60C3×C4⋊(C3⋊C8)C2211yescharacteristic
61C3×Q82—31no—
62C3×#556—31no—
63#5722C2×C311yescharacteristic, complemented
64#5671C2×C311yescharacteristic
65C3×#489—21no—
66C3×#489—31no—
67C3×#489D311yescharacteristic
68C3×#489C2×C311yescharacteristic
69C3×#487—31no—
70C3×#476—31no—
71C3×#475—31no—
72C3×#475—31no—
73C3×#464—31no—
74C3×#464—31no—
75C3×#462—31no—
76C3×#446—31no—
77C3×#441—31no—
78C3×#441—31no—
79C3×C4×SD16—31no—
80#5094C2×C311yescharacteristic, complemented
81#5054C2×C311yescharacteristic
82#4795C2×C311yescharacteristic, complemented
83#4792C2×C311yescharacteristic, complemented
84#4791C2×C311yescharacteristic, complemented
85#4789C2×C311yescharacteristic, complemented
86#4767C2×C311yescharacteristic
87#4765C2×C311yescharacteristic
88#4761C2×C311yescharacteristic
89#4758C2×C311yescharacteristic
90#4716C2×C311yescharacteristic, complemented
91#4701C2×C311yescharacteristic, complemented
92C2×C32×Q8—21no—
93C2×C32×Q8C2311yescharacteristic
94C2×C32×D4C2311yescharacteristic
95C22×C3×Dic3—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⋊C4C2311yescharacteristic
105C32×C4⋊C4C2311yescharacteristic
106C32×C22⋊C4—21no—
107C32×C22⋊C4—21no—
108C32×C42C2311yescharacteristic
109C3×#217—21no—
110C3×#217—21no—
111C3×#217—21no—
112C3×#216—22no—
113C3×#214—22no—
114C3×C4⋊Dic3—21no—
115C3×C4⋊Dic3D411yescharacteristic
116C3×C4⋊Dic3C2311yescharacteristic
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×Dic3—21no—
133C3×C4×Dic3C2311yescharacteristic
134C3×C4×Dic3C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C3×Dic12—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—21no—
154C3×#124—31no—
155C3×#124C2×D311yescharacteristic
156C3×#124C22×C311yescharacteristic
157C3×C22⋊Q8—61no—
158C3×C4×Q8—31no—
159C3×C4×Q8—31no—
160C3×C4×Q8—31no—
161C3×C4×Q8—31no—
162C3×C4×Q8—31no—
163C3×C4×Q8—31no—
164C3×C4×Q8—61no—
165C3×C4×D4—31no—
166C3×#117—61no—
167Q8×Dic3C22×C311yescharacteristic
168#944—21no—
169#944—21no—
170#944C22×C311yescharacteristic
171C2×#216C22×C311yescharacteristic
172#936C22×C311yescharacteristic
173D4×Dic3C22×C311yescharacteristic
174C2×#214C22×C311yescharacteristic
175C2×Dic12C22×C311yescharacteristic
176#888—21no—
177#888C22×C311yescharacteristic
178#888C22×C311yescharacteristic
179#887—21no—
180#887C22×C311yescharacteristic
181#887C22×C311yescharacteristic
182#879—21no—
183#879—21no—
184#878—21no—
185#877—21no—
186C4×Dic6C22×C311yescharacteristic
187C4×Dic6C22×C311yescharacteristic
188C4×Dic6C22×C311yescharacteristic
189C3×#106—31no—
190C3×#106—31no—
191C3×#106—31no—
192C3×C4⋊C8—31no—
193C3×C4⋊C8—31no—
194C3×C4⋊C8—31no—
195C3×#103—21no—
196C3×#103—21no—
197C3×#103—31no—
198C3×#103—31no—
199C3×#103—31no—
200C3×#103—31no—
201C3×#103—31no—
202C3×#103C2×D311yescharacteristic
203C3×#103C2×D311yescharacteristic
204C3×#103C22×C311yescharacteristic
205C3×#103C22×C311yescharacteristic
206C3×#102—21no—
207C3×#102—21no—
208C3×#102—31no—
209C3×#102C2×D311yescharacteristic
210C3×#102C2×D311yescharacteristic
211C3×#102C22×C311yescharacteristic
212C3×#102C22×C311yescharacteristic
213C3×#97—21no—
214C3×#97—31no—
215C3×#97C2×D311yescharacteristic
216C3×#97C22×C311yescharacteristic
217C3×C4×C8—31no—
218#835C22×C311yescharacteristic
219#832C22×C311yescharacteristic
220#817C22×C311yescharacteristic
221#816C22×C311yescharacteristic
222#816C22×C311yescharacteristic
223#815C22×C311yescharacteristic
224Dic3⋊C8C22×C311yescharacteristic
225Dic3⋊C8C22×C311yescharacteristic
226C8×Dic3C22×C311yescharacteristic
227#810C22×C311yescharacteristic
228#810C22×C311yescharacteristic
229#808C22×C311yescharacteristic
230#808C22×C311yescharacteristic
231C4⋊(C3⋊C8)C22×C311yescharacteristic
232C23×C32—21no—
233C32×Q8—21no—
234C32×Q8—21no—
235C32×Q8—81no—
236C32×D4—21no—
237C32×D4—21no—
238C2×C32×C4—21no—
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4C2×D411yescharacteristic
242C2×C32×C4C2×D411yescharacteristic
243C2×C32×C4C2411yescharacteristic
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—42no—
249C2×C3×Dic3C2×D411yescharacteristic
250C2×C3×Dic3C2×D411yescharacteristic
251C2×C3×Dic3C2×D411yescharacteristic
252C2×C3×Dic3C2×D411yescharacteristic
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#489C3×D311yescharacteristic
268#487—31no—
269#476—31no—
270#475—31no—
271#475—31no—
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—21no—
291C2×C3×D4C22×D311yescharacteristic
292C2×C3×D4C23×C311yescharacteristic
293C22×C3×C4—61no—
294C22×Dic3—21no—
295C2×Dic6—21no—
296C2×Dic6—21no—
297C2×Dic6C3×D411yescharacteristic
298C2×Dic6C23×C311yescharacteristic
299C2×Dic6C23×C311yescharacteristic
300C3×Q16—62no—
301C3×Q16—62no—
302C3×SD16—62no—
303C2×C3×C8—21no—
304C2×C3×C8—21no—
305C2×C3×C8—31no—
306C2×C3×C8—31no—
307C2×C3×C8C22×D311yescharacteristic
308C2×C3×C8C22×D311yescharacteristic
309C2×C3×C8C23×C311yescharacteristic
310C2×C3×C8C23×C311yescharacteristic
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—41no—
321C3×C4⋊C4—61no—
322C3×C4⋊C4—61no—
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⋊C4C22×D311yescharacteristic
331C3×C4⋊C4C22×D311yescharacteristic
332C3×C4⋊C4C23×C311yescharacteristic
333C3×C4⋊C4C23×C311yescharacteristic
334C3×C22⋊C4—21no—
335C3×C22⋊C4—21no—
336C3×C22⋊C4—21no—
337C3×C22⋊C4—21no—
338C3×C22⋊C4—41no—
339C3×C22⋊C4—41no—
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×C42—61no—
350C3×C42—61no—
351C3×C42C22×D311yescharacteristic
352C3×C42C23×C311yescharacteristic
353#217—21no—
354#217—21no—
355#217—21no—
356#216—22no—
357#214—22no—
358C4⋊Dic3—21no—
359C4⋊Dic3C3×D411yescharacteristic
360C4⋊Dic3C23×C311yescharacteristic
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×Dic3—21no—
377C4×Dic3C23×C311yescharacteristic
378C4×Dic3C23×C311yescharacteristic
379C2×C3⋊C8C23×C311yescharacteristic
380C2×C3⋊C8C23×C311yescharacteristic
381Dic12—22no—
382C22×C32—41no—
383C22×C32—41no—
384C22×C32—41no—
385C22×C32C22×D411yescharacteristic
386C32×C4—21no—
387C32×C4—21no—
388C32×C4—41no—
389C32×C4—41no—
390C32×C4—41no—
391C32×C4C2×#4111yescharacteristic
392C32×C42−1+411yescharacteristic
393C3×Dic3—22no—
394C3×Dic3—21no—
395C3×Dic3—21no—
396C3×Dic3—21no—
397C3×Dic3—41no—
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#124C2×C3×D311yescharacteristic
415C22⋊Q8—61no—
416C4×Q8—31no—
417C4×Q8—31no—
418C4×Q8—31no—
419C4×Q8—31no—
420C4×Q8—31no—
421C4×Q8—31no—
422C4×Q8—61no—
423C4×D4—31no—
424#117—61no—
425#106—31no—
426#106—31no—
427#106—31no—
428C4⋊C8—31no—
429C4⋊C8—31no—
430C4⋊C8—31no—
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#102C2×C3×D311yescharacteristic
440#102C2×C3×D311yescharacteristic
441#97—31no—
442#97C2×C3×D311yescharacteristic
443C4×C8—31no—
444C23×C3—21no—
445C23×C3—21no—
446C23×C3—41no—
447C3×Q8—21no—
448C3×Q8—21no—
449C3×Q8—21no—
450C3×Q8—21no—
451C3×Q8—32no—
452C3×Q8—41no—
453C3×Q8—41no—
454C3×Q8—62no—
455C3×Q8—61no—
456C3×Q8—61no—
457C3×Q8—61no—
458C3×Q8—81no—
459C3×Q8—81no—
460C3×Q8—82no—
461C3×Q8—241no—
462C3×Q8—241no—
463C3×D4—21no—
464C3×D4—21no—
465C3×D4—21no—
466C3×D4—21no—
467C3×D4—41no—
468C3×D4—41no—
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—21no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—31no—
479C2×C3×C4—31no—
480C2×C3×C4—31no—
481C2×C3×C4—31no—
482C2×C3×C4—41no—
483C2×C3×C4—41no—
484C2×C3×C4—41no—
485C2×C3×C4—61no—
486C2×C3×C4—61no—
487C2×C3×C4—61no—
488C2×C3×C4—61no—
489C2×C3×C4—122no—
490C2×C3×C4D3×D411yescharacteristic
491C2×C3×C4D3×D411yescharacteristic
492C2×C3×C4C2×C3×D411yescharacteristic
493C2×C3×C4C2×C3×D411yescharacteristic
494C2×C3×C4C23×D311yescharacteristic
495C2×C3×C4C24×C311yescharacteristic
496C2×Dic3—21no—
497C2×Dic3—21no—
498C2×Dic3—21no—
499C2×Dic3—21no—
500C2×Dic3—42no—
501C2×Dic3C2×C3×D411yescharacteristic
502C2×Dic3C2×C3×D411yescharacteristic
503C2×Dic3C2×C3×D411yescharacteristic
504C2×Dic3C2×C3×D411yescharacteristic
505Dic6—21no—
506Dic6—22no—
507Dic6—21no—
508Dic6—21no—
509Dic6—81no—
510Dic6—81no—
511Dic6C3×#4112yes—
512C3×C8—21no—
513C3×C8—21no—
514C3×C8—21no—
515C3×C8—21no—
516C3×C8—41no—
517C3×C8—41no—
518C3×C8—61no—
519C3×C8—61no—
520C3⋊C8—21no—
521C3⋊C8—21no—
522C2×C32—81no—
523C2×C32#54811yescharacteristic
524C2×C32C2×#13711yescharacteristic
525C2×C32#57711yescharacteristic
526C2×Q8—21no—
527C2×Q8—31no—
528C2×Q8—31no—
529C2×Q8—31no—
530C2×Q8—61no—
531C2×Q8—61no—
532C2×Q8C22×C3×D311yescharacteristic
533C2×D4C22×C3×D311yescharacteristic
534C22×C4—61no—
535Q16—62no—
536Q16—62no—
537SD16—62no—
538C2×C8—31no—
539C2×C8—31no—
540C2×C8C22×C3×D311yescharacteristic
541C2×C8C22×C3×D311yescharacteristic
542C4⋊C4—21no—
543C4⋊C4—31no—
544C4⋊C4—31no—
545C4⋊C4—31no—
546C4⋊C4—31no—
547C4⋊C4—31no—
548C4⋊C4—61no—
549C4⋊C4—61no—
550C4⋊C4—61no—
551C4⋊C4—61no—
552C4⋊C4—61no—
553C4⋊C4—61no—
554C4⋊C4—61no—
555C4⋊C4—61no—
556C4⋊C4—61no—
557C4⋊C4C22×C3×D311yescharacteristic
558C4⋊C4C22×C3×D311yescharacteristic
559C22⋊C4—21no—
560C22⋊C4—21no—
561C22⋊C4—61no—
562C22⋊C4—61no—
563C22⋊C4—61no—
564C42—31no—
565C42—31no—
566C42—61no—
567C42—61no—
568C42—61no—
569C42—61no—
570C42—61no—
571C42C22×C3×D311yescharacteristic
572C22×C3—21no—
573C22×C3—41no—
574C22×C3—41no—
575C22×C3—41no—
576C22×C3—41no—
577C22×C3—41no—
578C22×C3—41no—
579C22×C3—81no—
580C22×C3—81no—
581C22×C3—81no—
582C22×C3C2×D3×D411yescharacteristic
583C22×C3C22×C3×D411yescharacteristic
584C3×C4—21no—
585C3×C4—21no—
586C3×C4—21no—
587C3×C4—21no—
588C3×C4—21no—
589C3×C4—21no—
590C3×C4—32no—
591C3×C4—41no—
592C3×C4—41no—
593C3×C4—41no—
594C3×C4—41no—
595C3×C4—41no—
596C3×C4—41no—
597C3×C4—41no—
598C3×C4—41no—
599C3×C4—62no—
600C3×C4—61no—
601C3×C4—61no—
602C3×C4—61no—
603C3×C4—81no—
604C3×C4—81no—
605C3×C4—81no—
606C3×C4—121no—
607C3×C4—121no—
608C3×C4—121no—
609C3×C4D3×#4111yescharacteristic
610C3×C4#101011yescharacteristic
611C3×C4C2×C3×#4111yescharacteristic
612C3×C4C3×2−1+411yescharacteristic
613Dic3—21no—
614Dic3—21no—
615Dic3—21no—
616Dic3—22no—
617Dic3—41no—
618Dic3—41no—
619Dic3—41no—
620Dic3C3×#13712yes—
621C32#336911yescharacteristic, complemented, Sylow
622C23—21no—
623Q8—21no—
624Q8—21no—
625Q8—32no—
626Q8—62no—
627Q8—61no—
628Q8—61no—
629Q8—61no—
630Q8—81no—
631Q8—241no—
632Q8—241no—
633D4—21no—
634D4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—31no—
639C2×C4—31no—
640C2×C4—31no—
641C2×C4—31no—
642C2×C4—61no—
643C2×C4—61no—
644C2×C4—61no—
645C2×C4—61no—
646C2×C4—122no—
647C2×C4C3×D3×D411yescharacteristic
648C2×C4C3×D3×D411yescharacteristic
649C2×C4C23×C3×D311yescharacteristic
650C8—21no—
651C8—21no—
652C8—61no—
653C8—61no—
654C2×C3—21no—
655C2×C3—21no—
656C2×C3—21no—
657C2×C3—81no—
658C2×C3—81no—
659C2×C3—161no—
660C2×C3#567711yescharacteristic
661C2×C3#577511yescharacteristic
662C2×C3D3×#13711yescharacteristic
663C2×C3C3×#54811yescharacteristic
664C2×C3C2×C3×#13711yescharacteristic
665C2×C3C3×#57711yescharacteristic
666C22—41no—
667C22—41no—
668C22—41no—
669C22C2×C3×D3×D411yescharacteristic
670C4—21no—
671C4—21no—
672C4—32no—
673C4—41no—
674C4—41no—
675C4—41no—
676C4—61no—
677C4—61no—
678C4—61no—
679C4—62no—
680C4—121no—
681C4—121no—
682C4—121no—
683C4C3×D3×#4111yescharacteristic
684C4C3×#101011yescharacteristic
685C3—21no—
686C3#8167111yescharacteristic, direct product factor
687C3C3×#336911yescharacteristic, complemented
688C2—81no—
689C2C3×#567711yescharacteristic
690C2C3×#577511yescharacteristic
691C2C3×D3×#13711yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#489C2
socleC22×C32C22×D4
prime radicalC2×C32×D4C23
hypercenterC3×#489D3
hypocenterC3C3×#3369
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#489

Complements

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

NH ≅ G/Ntype
1. C3×#5722C2semidirect
4. C3×#5094C2semidirect
6. C3×#4795C2semidirect
7. C3×#4792C2semidirect
8. C3×#4791C2semidirect
9. C3×#4789C2semidirect
14. C3×#4716C2semidirect
15. C3×#4701C2semidirect
17. #81671C3direct (N × H)
63. #5722C2×C3semidirect
80. #5094C2×C3semidirect
82. #4795C2×C3semidirect
83. #4792C2×C3semidirect
84. #4791C2×C3semidirect
85. #4789C2×C3semidirect
90. #4716C2×C3semidirect
91. #4701C2×C3semidirect
621. C32#3369semidirect
686. C3#81671direct (N × H)
687. 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×#56712
C32×#4892
C3×#50942
C3×#50542
C3×#47952
C3×#47922
C3×#47912
C3×#47892
C3×#47672
C3×#47652
C3×#47612
C3×#47582
C3×#47162
C3×#47012
C3×#33693
#816713