Finite Group Databasebeta

← C3×#80582 #11896011

Subgroups — C3×#80582 #11896011

Order 1152.

732 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5671C211yesmaximal, characteristic
2C3×Q8×Dic6C211yesmaximal, characteristic, complemented
3C32×#464C211yesmaximal, characteristic
4C3×#5184C211yesmaximal, characteristic, complemented
5C3×#5182C211yesmaximal, characteristic, complemented
6C3×#5166C211yesmaximal, characteristic
7C3×Dic3×SD16C211yesmaximal, characteristic
8C3×#5055C211yesmaximal, characteristic
9C3×#5030C211yesmaximal, characteristic, complemented
10C3×#4851C211yesmaximal, characteristic, complemented
11C3×#4828C211yesmaximal, characteristic, complemented
12C3×#4792C211yesmaximal, characteristic, complemented
13C3×#4791C211yesmaximal, characteristic, complemented
14C3×#4765C211yesmaximal, characteristic
15C3×#4761C211yesmaximal, characteristic
16C3×#3369—31nomaximal
17#80582C311yesmaximal, characteristic, direct product factor
18C2×C32×Q16C2211yescharacteristic
19C2×C32×SD16C2211yescharacteristic
20C32×#124C2211yescharacteristic
21C32×C4×Q8C2211yescharacteristic
22C3×Q8×Dic3C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic
24C3×Q8×Dic3C2211yescharacteristic
25C3×#944C2211yescharacteristic
26C2×C3×#216C2211yescharacteristic
27C3×#936C2211yescharacteristic
28C3×D4×Dic3C2211yescharacteristic
29C3×#888—21no—
30C3×#888—21no—
31C3×#888C2211yescharacteristic
32C3×#888C2211yescharacteristic
33C3×#879—21no—
34C3×#879—21no—
35C3×#878—21no—
36C3×#877—21no—
37C3×#869—21no—
38C3×#869C2211yescharacteristic
39C3×C4×Dic6—21no—
40C3×C4×Dic6C2211yescharacteristic
41C3×C4×Dic6C2211yescharacteristic
42C32×C4⋊C8C2211yescharacteristic
43C32×#103C2211yescharacteristic
44C32×#102C2211yescharacteristic
45C3×#835C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×#817C2211yescharacteristic
51C3×#817C2211yescharacteristic
52C3×#816C2211yescharacteristic
53C3×#816C2211yescharacteristic
54C3×#815C2211yescharacteristic
55C3×Dic3⋊C8C2211yescharacteristic
56C3×Dic3⋊C8C2211yescharacteristic
57C3×C8×Dic3C2211yescharacteristic
58C3×#810C2211yescharacteristic
59C3×#808C2211yescharacteristic
60C3×#803C2211yescharacteristic
61C3×Q82—31no—
62C3×#556—31no—
63#5671C2×C311yescharacteristic
64Q8×Dic6C2×C311yescharacteristic, complemented
65C3×#489—31no—
66C3×#489—31no—
67C3×#487—31no—
68C3×#476—31no—
69C3×#475—31no—
70C3×#475—31no—
71C3×#464—21no—
72C3×#464—31no—
73C3×#464D311yescharacteristic
74C3×#464C2×C311yescharacteristic
75C3×#462—31no—
76C3×#446—31no—
77C3×#441—31no—
78C3×#441—31no—
79C3×C4×SD16—31no—
80#5184C2×C311yescharacteristic, complemented
81#5182C2×C311yescharacteristic, complemented
82#5166C2×C311yescharacteristic
83Dic3×SD16C2×C311yescharacteristic
84#5055C2×C311yescharacteristic
85#5030C2×C311yescharacteristic, complemented
86#4851C2×C311yescharacteristic, complemented
87#4828C2×C311yescharacteristic, complemented
88#4792C2×C311yescharacteristic, complemented
89#4791C2×C311yescharacteristic, complemented
90#4765C2×C311yescharacteristic
91#4761C2×C311yescharacteristic
92C2×C32×Q8C2311yescharacteristic
93C2×C32×Q8C2311yescharacteristic
94C2×C32×D4C2311yescharacteristic
95C22×C3×Dic3—21no—
96C2×C3×Dic6—21no—
97C2×C3×Dic6—21no—
98C2×C3×Dic6—21no—
99C2×C3×Dic6D411yescharacteristic
100C2×C3×Dic6C2311yescharacteristic
101C32×Q16—22no—
102C32×SD16—22no—
103C2×C32×C8C2311yescharacteristic
104C2×C32×C8C2311yescharacteristic
105C32×C4⋊C4—21no—
106C32×C4⋊C4C2311yescharacteristic
107C32×C22⋊C4—21no—
108C32×C22⋊C4—21no—
109C32×C42—21no—
110C32×C42C2311yescharacteristic
111C3×#217—21no—
112C3×#217—21no—
113C3×#217—21no—
114C3×#216—22no—
115C3×C4⋊Dic3—21no—
116C3×C4⋊Dic3—21no—
117C3×C4⋊Dic3—21no—
118C3×C4⋊Dic3—21no—
119C3×C4⋊Dic3D411yescharacteristic
120C3×C4⋊Dic3C2311yescharacteristic
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×Dic3⋊C4—21no—
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×Dic3—21no—
133C3×C4×Dic3—21no—
134C3×C4×Dic3C2311yescharacteristic
135C3×C4×Dic3C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138#3369—31noSylow
139C2×C3×Q16—21no—
140C2×C3×Q16—31no—
141C2×C3×Q16C2×D311yescharacteristic
142C2×C3×Q16C22×C311yescharacteristic
143C2×C3×SD16—21no—
144C2×C3×SD16C2×D311yescharacteristic
145C2×C3×SD16C22×C311yescharacteristic
146C3×C4⋊Q8—31no—
147C3×C4⋊Q8—31no—
148C3×C4⋊Q8—31no—
149C3×C4⋊Q8—31no—
150C3×C4⋊Q8—61no—
151C3×C4⋊Q8—61no—
152C3×C4⋊Q8—61no—
153C3×#126—61no—
154C3×#126—61no—
155C3×#124—21no—
156C3×#124—31no—
157C3×#124C2×D311yescharacteristic
158C3×#124C22×C311yescharacteristic
159C3×C22⋊Q8—61no—
160C3×C4×Q8—21no—
161C3×C4×Q8—31no—
162C3×C4×Q8—31no—
163C3×C4×Q8—31no—
164C3×C4×Q8—31no—
165C3×C4×Q8—31no—
166C3×C4×Q8—61no—
167C3×C4×Q8C2×D311yescharacteristic
168C3×C4×Q8C22×C311yescharacteristic
169C3×C4×D4—31no—
170C3×#117—61no—
171Q8×Dic3C22×C311yescharacteristic
172Q8×Dic3C22×C311yescharacteristic
173Q8×Dic3C22×C311yescharacteristic
174#944C22×C311yescharacteristic
175C2×#216C22×C311yescharacteristic
176#936C22×C311yescharacteristic
177D4×Dic3C22×C311yescharacteristic
178#888—21no—
179#888—21no—
180#888C22×C311yescharacteristic
181#888C22×C311yescharacteristic
182#879—21no—
183#879—21no—
184#878—21no—
185#877—21no—
186#869—21no—
187#869C22×C311yescharacteristic
188C4×Dic6—21no—
189C4×Dic6C22×C311yescharacteristic
190C4×Dic6C22×C311yescharacteristic
191C3×#106—31no—
192C3×#106—31no—
193C3×#106—31no—
194C3×C4⋊C8—21no—
195C3×C4⋊C8—31no—
196C3×C4⋊C8—31no—
197C3×C4⋊C8C2×D311yescharacteristic
198C3×C4⋊C8C22×C311yescharacteristic
199C3×#103—21no—
200C3×#103—31no—
201C3×#103—31no—
202C3×#103—31no—
203C3×#103—31no—
204C3×#103—31no—
205C3×#103—31no—
206C3×#103C2×D311yescharacteristic
207C3×#103C22×C311yescharacteristic
208C3×#102—21no—
209C3×#102—31no—
210C3×#102—31no—
211C3×#102C2×D311yescharacteristic
212C3×#102C22×C311yescharacteristic
213C3×#97—31no—
214C3×#97—31no—
215C3×C4×C8—31no—
216#835C22×C311yescharacteristic
217#835C22×C311yescharacteristic
218#835C22×C311yescharacteristic
219#832C22×C311yescharacteristic
220#832C22×C311yescharacteristic
221#817C22×C311yescharacteristic
222#817C22×C311yescharacteristic
223#816C22×C311yescharacteristic
224#816C22×C311yescharacteristic
225#815C22×C311yescharacteristic
226Dic3⋊C8C22×C311yescharacteristic
227Dic3⋊C8C22×C311yescharacteristic
228C8×Dic3C22×C311yescharacteristic
229#810C22×C311yescharacteristic
230#808C22×C311yescharacteristic
231#803C22×C311yescharacteristic
232C23×C32—21no—
233C32×Q8—21no—
234C32×Q8—21no—
235C32×Q8—21no—
236C32×Q8#4112yes—
237C32×D4—21no—
238C32×D4—21no—
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4C2×D411yescharacteristic
243C2×C32×C4C2×D411yescharacteristic
244C2×C32×C4C2411yescharacteristic
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—42no—
250C2×C3×Dic3C2×D411yescharacteristic
251C2×C3×Dic3C2×D411yescharacteristic
252C2×C3×Dic3C2×D411yescharacteristic
253C2×C3×Dic3C2×D411yescharacteristic
254C3×Dic6—22no—
255C3×Dic6—21no—
256C3×Dic6—21no—
257C3×Dic6—81no—
258C3×Dic6—81no—
259C3×Dic6—81no—
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#475—31no—
272#464—31no—
273#464C3×D311yescharacteristic
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—31no—
282C2×C3×Q8—31no—
283C2×C3×Q8—61no—
284C2×C3×Q8—61no—
285C2×C3×Q8—61no—
286C2×C3×Q8C22×D311yescharacteristic
287C2×C3×Q8C22×D311yescharacteristic
288C2×C3×Q8C23×C311yescharacteristic
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×Dic6—21no—
298C2×Dic6C3×D411yescharacteristic
299C2×Dic6C23×C311yescharacteristic
300C3×Q16—22no—
301C3×Q16—22no—
302C3×Q16—42no—
303C3×Q16—62no—
304C3×SD16—22no—
305C3×SD16—22no—
306C3×SD16—42no—
307C2×C3×C8—21no—
308C2×C3×C8—21no—
309C2×C3×C8—31no—
310C2×C3×C8—31no—
311C2×C3×C8C22×D311yescharacteristic
312C2×C3×C8C22×D311yescharacteristic
313C2×C3×C8C23×C311yescharacteristic
314C2×C3×C8C23×C311yescharacteristic
315C3×C4⋊C4—21no—
316C3×C4⋊C4—21no—
317C3×C4⋊C4—21no—
318C3×C4⋊C4—31no—
319C3×C4⋊C4—31no—
320C3×C4⋊C4—31no—
321C3×C4⋊C4—31no—
322C3×C4⋊C4—31no—
323C3×C4⋊C4—31no—
324C3×C4⋊C4—41no—
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⋊C4—61no—
333C3×C4⋊C4—61no—
334C3×C4⋊C4C22×D311yescharacteristic
335C3×C4⋊C4C23×C311yescharacteristic
336C3×C22⋊C4—21no—
337C3×C22⋊C4—21no—
338C3×C22⋊C4—21no—
339C3×C22⋊C4—21no—
340C3×C22⋊C4—41no—
341C3×C22⋊C4—41no—
342C3×C22⋊C4—61no—
343C3×C22⋊C4—61no—
344C3×C22⋊C4—61no—
345C3×C42—21no—
346C3×C42—21no—
347C3×C42—21no—
348C3×C42—31no—
349C3×C42—31no—
350C3×C42—41no—
351C3×C42—61no—
352C3×C42—61no—
353C3×C42—61no—
354C3×C42—61no—
355C3×C42C22×D311yescharacteristic
356C3×C42C23×C311yescharacteristic
357#217—21no—
358#217—21no—
359#217—21no—
360#216—22no—
361C4⋊Dic3—21no—
362C4⋊Dic3—21no—
363C4⋊Dic3—21no—
364C4⋊Dic3—21no—
365C4⋊Dic3C3×D411yescharacteristic
366C4⋊Dic3C23×C311yescharacteristic
367C4⋊Dic3C23×C311yescharacteristic
368C4⋊Dic3C23×C311yescharacteristic
369Dic3⋊C4—21no—
370Dic3⋊C4—21no—
371Dic3⋊C4—21no—
372Dic3⋊C4—21no—
373Dic3⋊C4—21no—
374Dic3⋊C4C3×D411yescharacteristic
375Dic3⋊C4C3×D411yescharacteristic
376C4×Dic3—21no—
377C4×Dic3—21no—
378C4×Dic3—21no—
379C4×Dic3—21no—
380C4×Dic3C23×C311yescharacteristic
381C4×Dic3C23×C311yescharacteristic
382C2×C3⋊C8C23×C311yescharacteristic
383C2×C3⋊C8C23×C311yescharacteristic
384C22×C32—41no—
385C22×C32—41no—
386C22×C32—41no—
387C22×C32C22×D411yescharacteristic
388C32×C4—22no—
389C32×C4—21no—
390C32×C4—21no—
391C32×C4—41no—
392C32×C4—41no—
393C32×C4C2×#4111yescharacteristic
394C32×C42−1+411yescharacteristic
395C3×Dic3—21no—
396C3×Dic3—21no—
397C3×Dic3—21no—
398C3×Dic3—41no—
399C3×Dic3—41no—
400C3×Dic3—41no—
401C3×Dic3—41no—
402C3×Dic3#13712yes—
403C2×Q16—31no—
404C2×Q16C2×C3×D311yescharacteristic
405C2×SD16C2×C3×D311yescharacteristic
406C4⋊Q8—31no—
407C4⋊Q8—31no—
408C4⋊Q8—31no—
409C4⋊Q8—31no—
410C4⋊Q8—61no—
411C4⋊Q8—61no—
412C4⋊Q8—61no—
413#126—61no—
414#126—61no—
415#124—31no—
416#124C2×C3×D311yescharacteristic
417C22⋊Q8—61no—
418C4×Q8—31no—
419C4×Q8—31no—
420C4×Q8—31no—
421C4×Q8—31no—
422C4×Q8—31no—
423C4×Q8—61no—
424C4×Q8C2×C3×D311yescharacteristic
425C4×D4—31no—
426#117—61no—
427#106—31no—
428#106—31no—
429#106—31no—
430C4⋊C8—31no—
431C4⋊C8—31no—
432C4⋊C8C2×C3×D311yescharacteristic
433#103—31no—
434#103—31no—
435#103—31no—
436#103—31no—
437#103—31no—
438#103—31no—
439#103C2×C3×D311yescharacteristic
440#102—31no—
441#102—31no—
442#102C2×C3×D311yescharacteristic
443#97—31no—
444#97—31no—
445C4×C8—31no—
446C23×C3—21no—
447C23×C3—21no—
448C23×C3—41no—
449C3×Q8—21no—
450C3×Q8—21no—
451C3×Q8—21no—
452C3×Q8—21no—
453C3×Q8—21no—
454C3×Q8—21no—
455C3×Q8—22no—
456C3×Q8—41no—
457C3×Q8—41no—
458C3×Q8—41no—
459C3×Q8—62no—
460C3×Q8—61no—
461C3×Q8—61no—
462C3×Q8—241no—
463C3×Q8—241no—
464C3×Q8—241no—
465C3×Q8#23712yes—
466C3×Q8C3×#4112yes—
467C3×D4—21no—
468C3×D4—21no—
469C3×D4—21no—
470C3×D4—21no—
471C3×D4—41no—
472C3×D4—41no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—31no—
483C2×C3×C4—31no—
484C2×C3×C4—31no—
485C2×C3×C4—31no—
486C2×C3×C4—41no—
487C2×C3×C4—41no—
488C2×C3×C4—41no—
489C2×C3×C4—61no—
490C2×C3×C4—61no—
491C2×C3×C4—61no—
492C2×C3×C4—61no—
493C2×C3×C4—122no—
494C2×C3×C4D3×D411yescharacteristic
495C2×C3×C4D3×D411yescharacteristic
496C2×C3×C4C2×C3×D411yescharacteristic
497C2×C3×C4C2×C3×D411yescharacteristic
498C2×C3×C4C23×D311yescharacteristic
499C2×C3×C4C24×C311yescharacteristic
500C2×Dic3—21no—
501C2×Dic3—21no—
502C2×Dic3—21no—
503C2×Dic3—21no—
504C2×Dic3—42no—
505C2×Dic3C2×C3×D411yescharacteristic
506C2×Dic3C2×C3×D411yescharacteristic
507C2×Dic3C2×C3×D411yescharacteristic
508C2×Dic3C2×C3×D411yescharacteristic
509Dic6—22no—
510Dic6—21no—
511Dic6—21no—
512Dic6—81no—
513Dic6—81no—
514Dic6—81no—
515C3×C8—21no—
516C3×C8—21no—
517C3×C8—21no—
518C3×C8—21no—
519C3×C8—41no—
520C3×C8—41no—
521C3×C8—61no—
522C3×C8—61no—
523C3⋊C8—21no—
524C3⋊C8—21no—
525C2×C32—81no—
526C2×C32#54811yescharacteristic
527C2×C32C2×#13711yescharacteristic
528C2×C32#57711yescharacteristic
529C2×Q8—31no—
530C2×Q8—31no—
531C2×Q8—61no—
532C2×Q8—61no—
533C2×Q8—61no—
534C2×Q8C22×C3×D311yescharacteristic
535C2×Q8C22×C3×D311yescharacteristic
536C2×D4C22×C3×D311yescharacteristic
537C22×C4—61no—
538Q16—22no—
539Q16—62no—
540SD16—22no—
541C2×C8—31no—
542C2×C8—31no—
543C2×C8C22×C3×D311yescharacteristic
544C2×C8C22×C3×D311yescharacteristic
545C4⋊C4—21no—
546C4⋊C4—31no—
547C4⋊C4—31no—
548C4⋊C4—31no—
549C4⋊C4—31no—
550C4⋊C4—31no—
551C4⋊C4—31no—
552C4⋊C4—61no—
553C4⋊C4—61no—
554C4⋊C4—61no—
555C4⋊C4—61no—
556C4⋊C4—61no—
557C4⋊C4—61no—
558C4⋊C4—61no—
559C4⋊C4—61no—
560C4⋊C4—61no—
561C4⋊C4C22×C3×D311yescharacteristic
562C22⋊C4—21no—
563C22⋊C4—21no—
564C22⋊C4—61no—
565C22⋊C4—61no—
566C22⋊C4—61no—
567C42—21no—
568C42—31no—
569C42—31no—
570C42—61no—
571C42—61no—
572C42—61no—
573C42—61no—
574C42C22×C3×D311yescharacteristic
575C22×C3—21no—
576C22×C3—41no—
577C22×C3—41no—
578C22×C3—41no—
579C22×C3—41no—
580C22×C3—41no—
581C22×C3—41no—
582C22×C3—81no—
583C22×C3—81no—
584C22×C3—81no—
585C22×C3C2×D3×D411yescharacteristic
586C22×C3C22×C3×D411yescharacteristic
587C3×C4—21no—
588C3×C4—21no—
589C3×C4—21no—
590C3×C4—21no—
591C3×C4—22no—
592C3×C4—22no—
593C3×C4—21no—
594C3×C4—21no—
595C3×C4—32no—
596C3×C4—41no—
597C3×C4—41no—
598C3×C4—42no—
599C3×C4—41no—
600C3×C4—41no—
601C3×C4—41no—
602C3×C4—41no—
603C3×C4—61no—
604C3×C4—61no—
605C3×C4—61no—
606C3×C4—81no—
607C3×C4—81no—
608C3×C4—121no—
609C3×C4—121no—
610C3×C4—121no—
611C3×C4—121no—
612C3×C4C2×#23711yescharacteristic
613C3×C4#101011yescharacteristic
614C3×C4C2×C3×#4111yescharacteristic
615C3×C4C3×2−1+411yescharacteristic
616Dic3—21no—
617Dic3—21no—
618Dic3—21no—
619Dic3—41no—
620Dic3—41no—
621Dic3—41no—
622Dic3—41no—
623Dic3C3×#13712yes—
624C32#336911yescharacteristic, complemented, Sylow
625C23—21no—
626Q8—21no—
627Q8—21no—
628Q8—21no—
629Q8—62no—
630Q8—61no—
631Q8—61no—
632Q8—241no—
633Q8—241no—
634Q8—241no—
635Q8C3×#23712yes—
636D4—21no—
637D4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—31no—
642C2×C4—31no—
643C2×C4—31no—
644C2×C4—31no—
645C2×C4—61no—
646C2×C4—61no—
647C2×C4—61no—
648C2×C4—61no—
649C2×C4—122no—
650C2×C4C3×D3×D411yescharacteristic
651C2×C4C3×D3×D411yescharacteristic
652C2×C4C23×C3×D311yescharacteristic
653C8—21no—
654C8—21no—
655C8—61no—
656C8—61no—
657C2×C3—21no—
658C2×C3—21no—
659C2×C3—21no—
660C2×C3—81no—
661C2×C3—81no—
662C2×C3—161no—
663C2×C3#559811yescharacteristic
664C2×C3#577011yescharacteristic
665C2×C3D3×#13711yescharacteristic
666C2×C3C3×#54811yescharacteristic
667C2×C3C2×C3×#13711yescharacteristic
668C2×C3C3×#57711yescharacteristic
669C22—41no—
670C22—41no—
671C22—41no—
672C22C2×C3×D3×D411yescharacteristic
673C4—21no—
674C4—21no—
675C4—22no—
676C4—32no—
677C4—41no—
678C4—41no—
679C4—61no—
680C4—61no—
681C4—61no—
682C4—121no—
683C4—121no—
684C4—121no—
685C4—121no—
686C4C2×C3×#23711yescharacteristic
687C4C3×#101011yescharacteristic
688C3—21no—
689C3#8058211yescharacteristic, direct product factor
690C3C3×#336911yescharacteristic, complemented
691C2—81no—
692C2C3×#559811yescharacteristic
693C2C3×#577011yescharacteristic
694C2C3×D3×#13711yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#464C2
socleC22×C32C22×D4
prime radicalC2×C32×D4C23
hypercenterC3×#464D3
hypocenterC3C3×#3369
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#464

Complements

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

NH ≅ G/Ntype
2. C3×Q8×Dic6C2semidirect
4. C3×#5184C2semidirect
5. C3×#5182C2semidirect
9. C3×#5030C2semidirect
10. C3×#4851C2semidirect
11. C3×#4828C2semidirect
12. C3×#4792C2semidirect
13. C3×#4791C2semidirect
17. #80582C3direct (N × H)
64. Q8×Dic6C2×C3semidirect
80. #5184C2×C3semidirect
81. #5182C2×C3semidirect
85. #5030C2×C3semidirect
86. #4851C2×C3semidirect
87. #4828C2×C3semidirect
88. #4792C2×C3semidirect
89. #4791C2×C3semidirect
624. C32#3369semidirect
689. C3#80582direct (N × H)
690. C3C3×#3369semidirect

Maximal subgroups

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

subgroupindex
C3×#56712
C3×Q8×Dic62
C32×#4642
C3×#51842
C3×#51822
C3×#51662
C3×Dic3×SD162
C3×#50552
C3×#50302
C3×#48512
C3×#48282
C3×#47922
C3×#47912
C3×#47652
C3×#47612
C3×#33693
#805823