Finite Group Databasebeta

← C3×#80960 #11897606

Subgroups — C3×#80960 #11897606

Order 1152.

734 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5722C211yesmaximal, characteristic, complemented
2C3×#5539C211yesmaximal, characteristic
3C32×#474C211yesmaximal, characteristic
4C3×#5081C211yesmaximal, characteristic, complemented
5C3×#5018C211yesmaximal, characteristic
6C3×#4877C211yesmaximal, characteristic, complemented
7C3×#4876C211yesmaximal, characteristic, complemented
8C3×#4875C211yesmaximal, characteristic, complemented
9C3×#4874C211yesmaximal, characteristic, complemented
10C3×#4829C211yesmaximal, characteristic, complemented
11C3×#4828C211yesmaximal, characteristic, complemented
12C3×#4761C211yesmaximal, characteristic
13C3×#4759C211yesmaximal, characteristic
14C3×#4758C211yesmaximal, characteristic
15C3×#4757C211yesmaximal, characteristic
16C3×#3385—31nomaximal
17#80960C311yesmaximal, characteristic, direct product factor
18C32×C4⋊Q8C2211yescharacteristic
19C32×C4×D4C2211yescharacteristic
20C3×#944—21no—
21C3×#944—21no—
22C3×D4×Dic3C2211yescharacteristic
23C3×D4×Dic3C2211yescharacteristic
24C2×C3×#214C2211yescharacteristic
25C3×#924—21no—
26C2×C3×Dic3⋊C4—21no—
27C3×#890C2211yescharacteristic
28C3×#888—21no—
29C3×#888C2211yescharacteristic
30C3×#888C2211yescharacteristic
31C3×#888C2211yescharacteristic
32C3×#887—21no—
33C3×#887C2211yescharacteristic
34C3×#887C2211yescharacteristic
35C3×#878—21no—
36C3×#878—21no—
37C3×#870C2211yescharacteristic
38C3×C4×Dic6C2211yescharacteristic
39C3×C4×Dic6C2211yescharacteristic
40C32×#107C2211yescharacteristic
41C32×#107C2211yescharacteristic
42C32×C4⋊C8C2211yescharacteristic
43C32×#102C2211yescharacteristic
44C32×#102C2211yescharacteristic
45C3×#832C2211yescharacteristic
46C3×#818C2211yescharacteristic
47C3×#817C2211yescharacteristic
48C3×#816C2211yescharacteristic
49C3×#816C2211yescharacteristic
50C3×#815C2211yescharacteristic
51C3×Dic3⋊C8C2211yescharacteristic
52C3×Dic3⋊C8C2211yescharacteristic
53C3×C8×Dic3C2211yescharacteristic
54C3×#810C2211yescharacteristic
55C3×#808C2211yescharacteristic
56C3×#808C2211yescharacteristic
57C3×#807C2211yescharacteristic
58C3×#807C2211yescharacteristic
59C3×#807C2211yescharacteristic
60C3×#803C2211yescharacteristic
61C3×Q82—31no—
62C3×#554—31no—
63#5722C2×C311yescharacteristic, complemented
64#5539C2×C311yescharacteristic
65C3×#501—31no—
66C3×#501—31no—
67C3×#500—31no—
68C3×#479—31no—
69C3×#479—31no—
70C3×#477—31no—
71C3×#476—31no—
72C3×#474—21no—
73C3×#474—31no—
74C3×#474D311yescharacteristic
75C3×#474C2×C311yescharacteristic
76C3×#446—31no—
77C3×#440—31no—
78C3×#440—31no—
79C3×C4×SD16—31no—
80#5081C2×C311yescharacteristic, complemented
81#5018C2×C311yescharacteristic
82#4877C2×C311yescharacteristic, complemented
83#4876C2×C311yescharacteristic, complemented
84#4875C2×C311yescharacteristic, complemented
85#4874C2×C311yescharacteristic, complemented
86#4829C2×C311yescharacteristic, complemented
87#4828C2×C311yescharacteristic, complemented
88#4761C2×C311yescharacteristic
89#4759C2×C311yescharacteristic
90#4758C2×C311yescharacteristic
91#4757C2×C311yescharacteristic
92C2×C32×Q8—21no—
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4—21no—
95C22×C3×Dic3—21no—
96C22×C3×Dic3—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⋊C4C2311yescharacteristic
106C32×C4⋊C4C2311yescharacteristic
107C32×C4⋊C4C2311yescharacteristic
108C32×C22⋊C4—21no—
109C32×C42C2311yescharacteristic
110C3×#217—21no—
111C3×#217—21no—
112C3×#214Q814yescomplemented
113C3×C4⋊Dic3—21no—
114C3×C4⋊Dic3D411yescharacteristic
115C3×C4⋊Dic3C2311yescharacteristic
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⋊C4—21no—
127C3×Dic3⋊C4D411yescharacteristic
128C3×Dic3⋊C4D411yescharacteristic
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
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—31no—
148C3×#125—31no—
149C3×C22⋊Q8—61no—
150C3×C22⋊Q8—61no—
151C3×C22⋊Q8—61no—
152C3×C4×Q8—31no—
153C3×C4×Q8—31no—
154C3×C4×Q8—31no—
155C3×C4×Q8—31no—
156C3×C4×Q8—61no—
157C3×C4×D4—21no—
158C3×C4×D4—31no—
159C3×C4×D4—31no—
160C3×C4×D4C2×D311yescharacteristic
161C3×C4×D4C22×C311yescharacteristic
162C2×C3×C4⋊C4—61no—
163#944—21no—
164#944—21no—
165D4×Dic3C22×C311yescharacteristic
166D4×Dic3C22×C311yescharacteristic
167C2×#214C22×C311yescharacteristic
168#924—21no—
169C2×Dic3⋊C4—21no—
170#890C22×C311yescharacteristic
171#888—21no—
172#888C22×C311yescharacteristic
173#888C22×C311yescharacteristic
174#888C22×C311yescharacteristic
175#887—21no—
176#887C22×C311yescharacteristic
177#887C22×C311yescharacteristic
178#878—21no—
179#878—21no—
180#870C22×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—31no—
194C3×#106—31no—
195C3×#106—31no—
196C3×C4⋊C8—21no—
197C3×C4⋊C8—31no—
198C3×C4⋊C8—31no—
199C3×C4⋊C8C2×D311yescharacteristic
200C3×C4⋊C8C22×C311yescharacteristic
201C3×#103—31no—
202C3×#103—31no—
203C3×#103—31no—
204C3×#102—21no—
205C3×#102—21no—
206C3×#102—31no—
207C3×#102C2×D311yescharacteristic
208C3×#102C2×D311yescharacteristic
209C3×#102C22×C311yescharacteristic
210C3×#102C22×C311yescharacteristic
211C3×#97—31no—
212C3×#97—31no—
213C3×C4×C8—31no—
214#832C22×C311yescharacteristic
215#818C22×C311yescharacteristic
216#817C22×C311yescharacteristic
217#816C22×C311yescharacteristic
218#816C22×C311yescharacteristic
219#815C22×C311yescharacteristic
220Dic3⋊C8C22×C311yescharacteristic
221Dic3⋊C8C22×C311yescharacteristic
222C8×Dic3C22×C311yescharacteristic
223#810C22×C311yescharacteristic
224#808C22×C311yescharacteristic
225#808C22×C311yescharacteristic
226#807C22×C311yescharacteristic
227#807C22×C311yescharacteristic
228#807C22×C311yescharacteristic
229#803C22×C311yescharacteristic
230C23×C32—21no—
231C32×Q8—81no—
232C32×D4—21no—
233C32×D4C2×Q812yes—
234C2×C32×C4—21no—
235C2×C32×C4—21no—
236C2×C32×C4—21no—
237C2×C32×C4—81no—
238C2×C32×C4C2×D411yescharacteristic
239C2×C32×C4C2×D411yescharacteristic
240C2×C32×C4C2411yescharacteristic
241C2×C3×Dic3—21no—
242C2×C3×Dic3—21no—
243C2×C3×Dic3—21no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—42no—
246C2×C3×Dic3—81no—
247C2×C3×Dic3C2×D411yescharacteristic
248C2×C3×Dic3C2×D411yescharacteristic
249C2×C3×Dic3C2×D411yescharacteristic
250C2×C3×Dic3C2×D411yescharacteristic
251C3×Dic6—21no—
252C3×Dic6—22no—
253C3×Dic6—81no—
254C3×Dic6—81no—
255C3×Dic6—81no—
256C3×Dic6C2×Q812yes—
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#479—31no—
268#477—31no—
269#476—31no—
270#474—31no—
271#474C3×D311yescharacteristic
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—21no—
285C2×C3×D4C22×D311yescharacteristic
286C2×C3×D4C23×C311yescharacteristic
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—41no—
290C22×C3×C4—61no—
291C22×C3×C4—61no—
292C22×Dic3—21no—
293C22×Dic3—21no—
294C2×Dic6—21no—
295C2×Dic6—21no—
296C2×Dic6—21no—
297C2×Dic6C3×D411yescharacteristic
298C2×Dic6C23×C311yescharacteristic
299C3×SD16—34no—
300C2×C3×C8—21no—
301C2×C3×C8—21no—
302C2×C3×C8—31no—
303C2×C3×C8—31no—
304C2×C3×C8C22×D311yescharacteristic
305C2×C3×C8C22×D311yescharacteristic
306C2×C3×C8C23×C311yescharacteristic
307C2×C3×C8C23×C311yescharacteristic
308C3×C4⋊C4—21no—
309C3×C4⋊C4—21no—
310C3×C4⋊C4—21no—
311C3×C4⋊C4—21no—
312C3×C4⋊C4—21no—
313C3×C4⋊C4—31no—
314C3×C4⋊C4—31no—
315C3×C4⋊C4—31no—
316C3×C4⋊C4—31no—
317C3×C4⋊C4—31no—
318C3×C4⋊C4—31no—
319C3×C4⋊C4—41no—
320C3×C4⋊C4—61no—
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⋊C4C22×D311yescharacteristic
333C3×C4⋊C4C23×C311yescharacteristic
334C3×C4⋊C4C23×C311yescharacteristic
335C3×C4⋊C4C23×C311yescharacteristic
336C3×C22⋊C4—21no—
337C3×C22⋊C4—21no—
338C3×C22⋊C4—41no—
339C3×C22⋊C4—61no—
340C3×C22⋊C4—61no—
341C3×C42—21no—
342C3×C42—31no—
343C3×C42—31no—
344C3×C42—61no—
345C3×C42—61no—
346C3×C42—61no—
347C3×C42C22×D311yescharacteristic
348C3×C42C23×C311yescharacteristic
349#217—21no—
350#217—21no—
351#214C3×Q814yescomplemented
352C4⋊Dic3—21no—
353C4⋊Dic3C3×D411yescharacteristic
354C4⋊Dic3C23×C311yescharacteristic
355C4⋊Dic3C23×C311yescharacteristic
356C4⋊Dic3C23×C311yescharacteristic
357Dic3⋊C4—21no—
358Dic3⋊C4—21no—
359Dic3⋊C4—21no—
360Dic3⋊C4—21no—
361Dic3⋊C4—21no—
362Dic3⋊C4—21no—
363Dic3⋊C4—21no—
364Dic3⋊C4—21no—
365Dic3⋊C4—21no—
366Dic3⋊C4C3×D411yescharacteristic
367Dic3⋊C4C3×D411yescharacteristic
368C4×Dic3—21no—
369C4×Dic3—21no—
370C4×Dic3—21no—
371C4×Dic3C23×C311yescharacteristic
372C4×Dic3C23×C311yescharacteristic
373C2×C3⋊C8C23×C311yescharacteristic
374C2×C3⋊C8C23×C311yescharacteristic
375C22×C32—22no—
376C22×C32—41no—
377C22×C32—41no—
378C22×C32C22×D411yescharacteristic
379C32×C4—21no—
380C32×C4—21no—
381C32×C4—41no—
382C32×C4—41no—
383C32×C4—41no—
384C32×C4C22×Q811yescharacteristic
385C32×C42−1+411yescharacteristic
386C3×Dic3—22no—
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—61no—
399C4⋊Q8—61no—
400C4⋊Q8—61no—
401C4⋊Q8C2×C3×D311yescharacteristic
402#125—31no—
403#125—31no—
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×D4C2×C3×D311yescharacteristic
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#106—31no—
424#106—31no—
425C4⋊C8—31no—
426C4⋊C8—31no—
427C4⋊C8C2×C3×D311yescharacteristic
428#103—31no—
429#103—31no—
430#103—31no—
431#102—31no—
432#102C2×C3×D311yescharacteristic
433#102C2×C3×D311yescharacteristic
434#97—31no—
435#97—31no—
436C4×C8—31no—
437C23×C3—21no—
438C23×C3—21no—
439C23×C3—41no—
440C3×Q8—32no—
441C3×Q8—62no—
442C3×Q8—61no—
443C3×Q8—81no—
444C3×Q8—81no—
445C3×Q8—82no—
446C3×Q8—241no—
447C3×Q8—241no—
448C3×Q8—241no—
449C3×D4—21no—
450C3×D4—21no—
451C3×D4—22no—
452C3×D4—41no—
453C3×D4D3×Q812yes—
454C3×D4C2×C3×Q812yes—
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—21no—
464C2×C3×C4—31no—
465C2×C3×C4—31no—
466C2×C3×C4—31no—
467C2×C3×C4—31no—
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—61no—
475C2×C3×C4—81no—
476C2×C3×C4—81no—
477C2×C3×C4—82no—
478C2×C3×C4—122no—
479C2×C3×C4—241no—
480C2×C3×C4D3×D411yescharacteristic
481C2×C3×C4D3×D411yescharacteristic
482C2×C3×C4C2×C3×D411yescharacteristic
483C2×C3×C4C2×C3×D411yescharacteristic
484C2×C3×C4C23×D311yescharacteristic
485C2×C3×C4C24×C311yescharacteristic
486C2×Dic3—21no—
487C2×Dic3—21no—
488C2×Dic3—21no—
489C2×Dic3—21no—
490C2×Dic3—42no—
491C2×Dic3—81no—
492C2×Dic3C2×C3×D411yescharacteristic
493C2×Dic3C2×C3×D411yescharacteristic
494C2×Dic3C2×C3×D411yescharacteristic
495C2×Dic3C2×C3×D411yescharacteristic
496Dic6—21no—
497Dic6—22no—
498Dic6—81no—
499Dic6—81no—
500Dic6—81no—
501Dic6C2×C3×Q812yes—
502C3×C8—21no—
503C3×C8—21no—
504C3×C8—21no—
505C3×C8—21no—
506C3×C8—32no—
507C3×C8—41no—
508C3×C8—41no—
509C3×C8—61no—
510C3⋊C8—21no—
511C3⋊C8C2×C3×Q812yes—
512C2×C32—42no—
513C2×C32D4×Q811yescharacteristic
514C2×C32C2×#13711yescharacteristic
515C2×C32#57611yescharacteristic
516C2×Q8—21no—
517C2×Q8—31no—
518C2×Q8—31no—
519C2×Q8—61no—
520C2×Q8—61no—
521C2×Q8—61no—
522C2×D4C22×C3×D311yescharacteristic
523C22×C4—21no—
524C22×C4—61no—
525C22×C4—61no—
526SD16—34no—
527C2×C8—31no—
528C2×C8—31no—
529C2×C8C22×C3×D311yescharacteristic
530C2×C8C22×C3×D311yescharacteristic
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⋊C4—61no—
547C4⋊C4—61no—
548C4⋊C4C22×C3×D311yescharacteristic
549C4⋊C4C22×C3×D311yescharacteristic
550C4⋊C4C22×C3×D311yescharacteristic
551C22⋊C4—21no—
552C22⋊C4—61no—
553C22⋊C4—61no—
554C42—31no—
555C42—31no—
556C42—61no—
557C42—61no—
558C42—61no—
559C42C22×C3×D311yescharacteristic
560C22×C3—22no—
561C22×C3—22no—
562C22×C3—21no—
563C22×C3—42no—
564C22×C3—41no—
565C22×C3—41no—
566C22×C3—41no—
567C22×C3—41no—
568C22×C3—81no—
569C22×C3—81no—
570C22×C3C2×D3×D411yescharacteristic
571C22×C3C22×C3×D411yescharacteristic
572C3×C4—22no—
573C3×C4—21no—
574C3×C4—21no—
575C3×C4—21no—
576C3×C4—21no—
577C3×C4—21no—
578C3×C4—21no—
579C3×C4—32no—
580C3×C4—41no—
581C3×C4—41no—
582C3×C4—41no—
583C3×C4—41no—
584C3×C4—41no—
585C3×C4—41no—
586C3×C4—41no—
587C3×C4—62no—
588C3×C4—61no—
589C3×C4—61no—
590C3×C4—61no—
591C3×C4—81no—
592C3×C4—81no—
593C3×C4—81no—
594C3×C4—121no—
595C3×C4—121no—
596C3×C4—121no—
597C3×C4C2×D3×Q811yescharacteristic
598C3×C4#101011yescharacteristic
599C3×C4C22×C3×Q811yescharacteristic
600C3×C4C3×2−1+411yescharacteristic
601Dic3—21no—
602Dic3—21no—
603Dic3—21no—
604Dic3—22no—
605Dic3—41no—
606Dic3—41no—
607Dic3—41no—
608Dic3C3×#13712yes—
609C32#338511yescharacteristic, complemented, Sylow
610C23—21no—
611Q8—32no—
612Q8—62no—
613Q8—61no—
614Q8—81no—
615Q8—241no—
616Q8—241no—
617Q8—241no—
618D4—21no—
619D4C3×D3×Q812yes—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—31no—
624C2×C4—31no—
625C2×C4—31no—
626C2×C4—31no—
627C2×C4—61no—
628C2×C4—61no—
629C2×C4—61no—
630C2×C4—61no—
631C2×C4—81no—
632C2×C4—122no—
633C2×C4—241no—
634C2×C4C3×D3×D411yescharacteristic
635C2×C4C3×D3×D411yescharacteristic
636C2×C4C23×C3×D311yescharacteristic
637C8—21no—
638C8—21no—
639C8—32no—
640C8—61no—
641C2×C3—21no—
642C2×C3—21no—
643C2×C3—21no—
644C2×C3—42no—
645C2×C3—42no—
646C2×C3—82no—
647C2×C3#563211yescharacteristic
648C2×C3#575711yescharacteristic
649C2×C3D3×#13711yescharacteristic
650C2×C3C3×D4×Q811yescharacteristic
651C2×C3C2×C3×#13711yescharacteristic
652C2×C3C3×#57611yescharacteristic
653C22—22no—
654C22—41no—
655C22—41no—
656C22C2×C3×D3×D411yescharacteristic
657C4—21no—
658C4—21no—
659C4—32no—
660C4—41no—
661C4—41no—
662C4—41no—
663C4—61no—
664C4—61no—
665C4—61no—
666C4—62no—
667C4—121no—
668C4—121no—
669C4—121no—
670C4C2×C3×D3×Q811yescharacteristic
671C4C3×#101011yescharacteristic
672C3—21no—
673C3#8096011yescharacteristic, direct product factor
674C3C3×#338511yescharacteristic, complemented
675C2—42no—
676C2C3×#563211yescharacteristic
677C2C3×#575711yescharacteristic
678C2C3×D3×#13711yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#474C2
socleC22×C32C22×D4
prime radicalC2×C32×D4C23
hypercenterC3×#474D3
hypocenterC3C3×#3385
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#474

Complements

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

NH ≅ G/Ntype
1. C3×#5722C2semidirect
4. C3×#5081C2semidirect
6. C3×#4877C2semidirect
7. C3×#4876C2semidirect
8. C3×#4875C2semidirect
9. C3×#4874C2semidirect
10. C3×#4829C2semidirect
11. C3×#4828C2semidirect
17. #80960C3direct (N × H)
63. #5722C2×C3semidirect
80. #5081C2×C3semidirect
82. #4877C2×C3semidirect
83. #4876C2×C3semidirect
84. #4875C2×C3semidirect
85. #4874C2×C3semidirect
86. #4829C2×C3semidirect
87. #4828C2×C3semidirect
112. C3×#214Q8semidirect
351. #214C3×Q8semidirect
609. C32#3385semidirect
673. C3#80960direct (N × H)
674. 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×#55392
C32×#4742
C3×#50812
C3×#50182
C3×#48772
C3×#48762
C3×#48752
C3×#48742
C3×#48292
C3×#48282
C3×#47612
C3×#47592
C3×#47582
C3×#47572
C3×#33853
#809603