Finite Group Databasebeta

← C3×#81096 #11872579

Subgroups — C3×#81096 #11872579

Order 1152.

788 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5733C211yesmaximal, characteristic
2C3×#5572C211yesmaximal, characteristic, complemented
3C32×#477C211yesmaximal, characteristic, complemented
4C3×#5094C211yesmaximal, characteristic, complemented
5C3×#5028C211yesmaximal, characteristic, complemented
6C3×#4889C211yesmaximal, characteristic, complemented
7C3×#4888C211yesmaximal, characteristic, complemented
8C3×#4885C211yesmaximal, characteristic
9C3×#4873C211yesmaximal, characteristic, complemented
10C3×#4845C211yesmaximal, characteristic, complemented
11C3×#4840C211yesmaximal, characteristic, complemented
12C3×#4809C211yesmaximal, characteristic, complemented
13C3×#4806C211yesmaximal, characteristic
14C3×#4789C211yesmaximal, characteristic, complemented
15C3×#4788C211yesmaximal, characteristic, complemented
16C3×#3121—31nomaximal
17#81096C311yesmaximal, characteristic, direct product factor
18C2×C3×D3×Q8C2211yescharacteristic
19C32×C4⋊Q8C2211yescharacteristic
20C32×C4×Q8C2211yescharacteristic
21C3×#947—21no—
22C3×#946—21no—
23C3×Q8×Dic3C2211yescharacteristic
24C2×C3×#216C2211yescharacteristic
25C2×C3×#215C2211yescharacteristic
26C2×C3×Dic12C2211yescharacteristic
27C2×C3×#204C2211yescharacteristic
28C3×#898—21no—
29C3×#897C2211yescharacteristic
30C3×#895C2211yescharacteristic
31C3×#894—21no—
32C3×#893C2211yescharacteristic
33C3×#892—21no—
34C3×#892C2211yescharacteristic
35C3×#887—21no—
36C3×#887C2211yescharacteristic
37C3×#887C2211yescharacteristic
38C3×#875C2211yescharacteristic
39C3×#872—21no—
40C3×#872C2211yescharacteristic
41C3×C4×Dic6—21no—
42C3×C4×Dic6C2211yescharacteristic
43C32×#107C2211yescharacteristic
44C32×#107C2211yescharacteristic
45C32×C4⋊C8C2211yescharacteristic
46C32×#103C2211yescharacteristic
47C32×#103C2211yescharacteristic
48C3×#821C2211yescharacteristic
49C3×(C2×D3)⋊C8C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×#815C2211yescharacteristic
53C3×C8×Dic3C2211yescharacteristic
54C3×#810C2211yescharacteristic
55C3×#810C2211yescharacteristic
56C3×#810C2211yescharacteristic
57C3×#809C2211yescharacteristic
58C3×#808C2211yescharacteristic
59C3×#808C2211yescharacteristic
60C3×C4⋊(C3⋊C8)C2211yescharacteristic
61C3×#542—31no—
62C3×#519—31no—
63#5733C2×C311yescharacteristic
64#5572C2×C311yescharacteristic, complemented
65C3×#485—31no—
66C3×#482—31no—
67C3×#477—21no—
68C3×#477D311yescharacteristic, complemented
69C3×#477C2×C311yescharacteristic, complemented
70C3×#475—31no—
71C3×#464—31no—
72C3×#464—31no—
73C3×#451—31no—
74C3×#448—31no—
75C3×#441—31no—
76C3×#440—31no—
77C3×C4×Q16—31no—
78C3×C4×SD16—31no—
79C3×#433—31no—
80#5094C2×C311yescharacteristic, complemented
81#5028C2×C311yescharacteristic, complemented
82#4889C2×C311yescharacteristic, complemented
83#4888C2×C311yescharacteristic, complemented
84#4885C2×C311yescharacteristic
85#4873C2×C311yescharacteristic, complemented
86#4845C2×C311yescharacteristic, complemented
87#4840C2×C311yescharacteristic, complemented
88#4809C2×C311yescharacteristic, complemented
89#4806C2×C311yescharacteristic
90#4789C2×C311yescharacteristic, complemented
91#4788C2×C311yescharacteristic, complemented
92C2×C32×Q8—21no—
93C2×C32×Q8C2311yescharacteristic
94C3×D3×Q8—22no—
95C3×D3×Q8—22no—
96C2×C3×D12—21no—
97C2×C3×D12C2311yescharacteristic
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3C2311yescharacteristic
101C2×C3×Dic6—21no—
102C2×C3×Dic6C2311yescharacteristic
103C2×C3×Dic6C2311yescharacteristic
104C2×C32×C8C2311yescharacteristic
105C2×C32×C8C2311yescharacteristic
106C32×C4⋊C4—21no—
107C32×C4⋊C4—21no—
108C32×C4⋊C4C2311yescharacteristic
109C32×C4⋊C4C2311yescharacteristic
110C32×C4⋊C4C2311yescharacteristic
111C32×C42—21no—
112C32×C42C2311yescharacteristic
113C3×#216—22no—
114C3×#215—22no—
115C3×(C2×D3)⋊C4—21no—
116C3×(C2×D3)⋊C4—21no—
117C3×(C2×D3)⋊C4—21no—
118C3×(C2×D3)⋊C4—21no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4D411yescharacteristic
122C3×(C2×D3)⋊C4D411yescharacteristic
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3—21no—
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4D411yescharacteristic
130C3×Dic3⋊C4D411yescharacteristic
131C3×C4×Dic3—21no—
132C3×C4×Dic3—21no—
133C3×C4×Dic3—21no—
134C3×C4×Dic3—21no—
135C3×C4×Dic3—21no—
136C3×C4×Dic3C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C3×Dic12—22no—
140C3×#204—22no—
141#3121—31noSylow
142C22×C3×Q8—31no—
143C2×D3×Q8C22×C311yescharacteristic
144C2×C3×Q16—31no—
145C2×C3×Q16—31no—
146C2×C3×SD16—31no—
147C2×C3×SD16—31no—
148C3×C4⋊Q8—21no—
149C3×C4⋊Q8C2×D311yescharacteristic
150C3×C4⋊Q8C22×C311yescharacteristic
151C3×#126—61no—
152C3×#124—31no—
153C3×#124—61no—
154C3×#123—61no—
155C3×C22⋊Q8—31no—
156C3×C22⋊Q8—61no—
157C3×#121—31no—
158C3×C4×Q8—21no—
159C3×C4×Q8—31no—
160C3×C4×Q8—31no—
161C3×C4×Q8—31no—
162C3×C4×Q8—31no—
163C3×C4×Q8—61no—
164C3×C4×Q8—61no—
165C3×C4×Q8C2×D311yescharacteristic
166C3×C4×Q8C22×C311yescharacteristic
167C3×C4×D4—31no—
168C3×#117—31no—
169C3×#117—31no—
170C3×#117—61no—
171C3×#117—61no—
172#947—21no—
173#946—21no—
174Q8×Dic3C22×C311yescharacteristic
175C2×#216C22×C311yescharacteristic
176C2×#215C22×C311yescharacteristic
177C2×Dic12C22×C311yescharacteristic
178C2×#204C22×C311yescharacteristic
179#898—21no—
180#897C22×C311yescharacteristic
181#895C22×C311yescharacteristic
182#894—21no—
183#893C22×C311yescharacteristic
184#892—21no—
185#892C22×C311yescharacteristic
186#887—21no—
187#887C22×C311yescharacteristic
188#887C22×C311yescharacteristic
189#875C22×C311yescharacteristic
190#872—21no—
191#872C22×C311yescharacteristic
192C4×Dic6—21no—
193C4×Dic6C22×C311yescharacteristic
194C3×#107—21no—
195C3×#107—21no—
196C3×#107C2×D311yescharacteristic
197C3×#107C2×D311yescharacteristic
198C3×#107C22×C311yescharacteristic
199C3×#107C22×C311yescharacteristic
200C3×#106—31no—
201C3×#106—31no—
202C3×C4⋊C8—21no—
203C3×C4⋊C8—31no—
204C3×C4⋊C8C2×D311yescharacteristic
205C3×C4⋊C8C22×C311yescharacteristic
206C3×#103—21no—
207C3×#103—21no—
208C3×#103—31no—
209C3×#103—31no—
210C3×#103—31no—
211C3×#103—31no—
212C3×#103C2×D311yescharacteristic
213C3×#103C2×D311yescharacteristic
214C3×#103C22×C311yescharacteristic
215C3×#103C22×C311yescharacteristic
216C3×#102—31no—
217C3×#102—31no—
218C3×C22⋊C8—31no—
219C3×C22⋊C8—31no—
220C3×#97—31no—
221C3×C4×C8—31no—
222#821C22×C311yescharacteristic
223(C2×D3)⋊C8C22×C311yescharacteristic
224(C2×D3)⋊C8C22×C311yescharacteristic
225#816C22×C311yescharacteristic
226#815C22×C311yescharacteristic
227C8×Dic3C22×C311yescharacteristic
228#810C22×C311yescharacteristic
229#810C22×C311yescharacteristic
230#810C22×C311yescharacteristic
231#809C22×C311yescharacteristic
232#808C22×C311yescharacteristic
233#808C22×C311yescharacteristic
234C4⋊(C3⋊C8)C22×C311yescharacteristic
235C22×C3×D3—21no—
236C22×C3×D3C2×D411yescharacteristic
237C32×Q8—21no—
238C32×Q8—81no—
239C32×Q8#4112yes—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4C2×D411yescharacteristic
245C2×C32×C4C2×D411yescharacteristic
246C2×C32×C4C2411yescharacteristic
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3C2×D411yescharacteristic
251C2×C3×Dic3C2×D411yescharacteristic
252C2×C3×Dic3C2×D411yescharacteristic
253C3×D12—21no—
254C3×D12—21no—
255C3×D12—81no—
256C3×C4×D3—24no—
257C3×C4×D3—21no—
258C3×C4×D3—21no—
259C3×C4×D3—81no—
260C3×Dic6—24no—
261C3×Dic6—21no—
262C3×Dic6—21no—
263C3×Dic6—21no—
264C3×Dic6#4112yes—
265C32×C8—21no—
266C32×C8—21no—
267C3×C3⋊C8—21no—
268C3×C3⋊C8—21no—
269#542—31no—
270#519—31no—
271#485—31no—
272#482—31no—
273#477C3×D311yescharacteristic, complemented
274#475—31no—
275#464—31no—
276#464—31no—
277#451—31no—
278#448—31no—
279#441—31no—
280#440—31no—
281C4×Q16—31no—
282C4×SD16—31no—
283#433—31no—
284C2×C3×Q8—21no—
285C2×C3×Q8—21no—
286C2×C3×Q8—21no—
287C2×C3×Q8—31no—
288C2×C3×Q8—31no—
289C2×C3×Q8—41no—
290C2×C3×Q8—61no—
291C2×C3×Q8—62no—
292C2×C3×Q8—62no—
293C2×C3×Q8C22×D311yescharacteristic
294C2×C3×Q8C23×C311yescharacteristic
295C2×C3×D4—31no—
296C2×C3×D4—61no—
297C22×C3×C4—31no—
298C22×C3×C4—61no—
299C22×C3×C4—61no—
300D3×Q8—22no—
301D3×Q8—22no—
302C2×D12—21no—
303C2×D12C23×C311yescharacteristic
304C2×C4×D3—21no—
305C2×C4×D3—21no—
306C2×C4×D3C23×C311yescharacteristic
307C2×Dic6—21no—
308C2×Dic6C23×C311yescharacteristic
309C2×Dic6C23×C311yescharacteristic
310C3×Q16—62no—
311C3×Q16—62no—
312C3×SD16—62no—
313C3×SD16—62no—
314C2×C3×C8—21no—
315C2×C3×C8—21no—
316C2×C3×C8—31no—
317C2×C3×C8—31no—
318C2×C3×C8C22×D311yescharacteristic
319C2×C3×C8C22×D311yescharacteristic
320C2×C3×C8C23×C311yescharacteristic
321C2×C3×C8C23×C311yescharacteristic
322C3×C4⋊C4—21no—
323C3×C4⋊C4—21no—
324C3×C4⋊C4—21no—
325C3×C4⋊C4—21no—
326C3×C4⋊C4—21no—
327C3×C4⋊C4—21no—
328C3×C4⋊C4—21no—
329C3×C4⋊C4—31no—
330C3×C4⋊C4—31no—
331C3×C4⋊C4—31no—
332C3×C4⋊C4—41no—
333C3×C4⋊C4—41no—
334C3×C4⋊C4—61no—
335C3×C4⋊C4—61no—
336C3×C4⋊C4—61no—
337C3×C4⋊C4—61no—
338C3×C4⋊C4—61no—
339C3×C4⋊C4C22×D311yescharacteristic
340C3×C4⋊C4C22×D311yescharacteristic
341C3×C4⋊C4C22×D311yescharacteristic
342C3×C4⋊C4C23×C311yescharacteristic
343C3×C4⋊C4C23×C311yescharacteristic
344C3×C4⋊C4C23×C311yescharacteristic
345C3×C22⋊C4—31no—
346C3×C22⋊C4—31no—
347C3×C22⋊C4—61no—
348C3×C22⋊C4—61no—
349C3×C22⋊C4—61no—
350C3×C22⋊C4—61no—
351C3×C22⋊C4—61no—
352C3×C22⋊C4—61no—
353C3×C42—21no—
354C3×C42—21no—
355C3×C42—21no—
356C3×C42—31no—
357C3×C42—41no—
358C3×C42—61no—
359C3×C42—61no—
360C3×C42—61no—
361C3×C42—61no—
362C3×C42—61no—
363C3×C42C22×D311yescharacteristic
364C3×C42C23×C311yescharacteristic
365#216—22no—
366#215—22no—
367(C2×D3)⋊C4—21no—
368(C2×D3)⋊C4—21no—
369(C2×D3)⋊C4—21no—
370(C2×D3)⋊C4—21no—
371(C2×D3)⋊C4—21no—
372(C2×D3)⋊C4—21no—
373(C2×D3)⋊C4C3×D411yescharacteristic
374(C2×D3)⋊C4C3×D411yescharacteristic
375C4⋊Dic3—21no—
376C4⋊Dic3—21no—
377C4⋊Dic3C23×C311yescharacteristic
378Dic3⋊C4—21no—
379Dic3⋊C4—21no—
380Dic3⋊C4—21no—
381Dic3⋊C4C3×D411yescharacteristic
382Dic3⋊C4C3×D411yescharacteristic
383C4×Dic3—21no—
384C4×Dic3—21no—
385C4×Dic3—21no—
386C4×Dic3—21no—
387C4×Dic3—21no—
388C4×Dic3C23×C311yescharacteristic
389C2×C3⋊C8C23×C311yescharacteristic
390C2×C3⋊C8C23×C311yescharacteristic
391Dic12—22no—
392#204—22no—
393C22×C32C22×D411yescharacteristic
394C2×C3×D3—21no—
395C2×C3×D3—21no—
396C2×C3×D3—21no—
397C2×C3×D3—41no—
398C2×C3×D3—41no—
399C2×C3×D3—41no—
400C32×C4—21no—
401C32×C4—22no—
402C32×C4—21no—
403C32×C4—41no—
404C32×C4—41no—
405C32×C4—41no—
406C32×C4C2×#4111yescharacteristic
407C32×C4C2×#4111yescharacteristic
408C3×Dic3—21no—
409C3×Dic3—22no—
410C3×Dic3—21no—
411C3×Dic3—21no—
412C3×Dic3—41no—
413C3×Dic3—41no—
414C22×Q8—31no—
415C2×Q16—31no—
416C2×Q16—31no—
417C2×SD16—31no—
418C2×SD16—31no—
419C4⋊Q8C2×C3×D311yescharacteristic
420#126—61no—
421#124—31no—
422#124—61no—
423#123—61no—
424C22⋊Q8—31no—
425C22⋊Q8—61no—
426#121—31no—
427C4×Q8—31no—
428C4×Q8—31no—
429C4×Q8—31no—
430C4×Q8—31no—
431C4×Q8—61no—
432C4×Q8—61no—
433C4×Q8C2×C3×D311yescharacteristic
434C4×D4—31no—
435#117—31no—
436#117—31no—
437#117—61no—
438#117—61no—
439#107C2×C3×D311yescharacteristic
440#107C2×C3×D311yescharacteristic
441#106—31no—
442#106—31no—
443C4⋊C8—31no—
444C4⋊C8C2×C3×D311yescharacteristic
445#103—31no—
446#103—31no—
447#103—31no—
448#103—31no—
449#103C2×C3×D311yescharacteristic
450#103C2×C3×D311yescharacteristic
451#102—31no—
452#102—31no—
453C22⋊C8—31no—
454C22⋊C8—31no—
455#97—31no—
456C4×C8—31no—
457C23×C3—31no—
458C23×C3—61no—
459C22×D3—21no—
460C22×D3C2×C3×D411yescharacteristic
461C3×Q8—21no—
462C3×Q8—21no—
463C3×Q8—22no—
464C3×Q8—32no—
465C3×Q8—41no—
466C3×Q8—64no—
467C3×Q8—61no—
468C3×Q8—61no—
469C3×Q8—61no—
470C3×Q8—81no—
471C3×Q8—81no—
472C3×Q8—82no—
473C3×Q8#23912yes—
474C3×Q8C3×#4112yes—
475C3×D4—61no—
476C3×D4—61no—
477C3×D4—241no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—31no—
490C2×C3×C4—31no—
491C2×C3×C4—31no—
492C2×C3×C4—41no—
493C2×C3×C4—41no—
494C2×C3×C4—41no—
495C2×C3×C4—41no—
496C2×C3×C4—64no—
497C2×C3×C4—61no—
498C2×C3×C4—61no—
499C2×C3×C4—61no—
500C2×C3×C4—61no—
501C2×C3×C4—61no—
502C2×C3×C4—241no—
503C2×C3×C4D3×D411yescharacteristic
504C2×C3×C4D3×D411yescharacteristic
505C2×C3×C4C2×C3×D411yescharacteristic
506C2×C3×C4C2×C3×D411yescharacteristic
507C2×C3×C4C23×D311yescharacteristic
508C2×C3×C4C24×C311yescharacteristic
509C2×Dic3—21no—
510C2×Dic3—21no—
511C2×Dic3—21no—
512C2×Dic3C2×C3×D411yescharacteristic
513C2×Dic3C2×C3×D411yescharacteristic
514C2×Dic3C2×C3×D411yescharacteristic
515D12—21no—
516D12—21no—
517D12—81no—
518C4×D3—24no—
519C4×D3—21no—
520C4×D3—21no—
521C4×D3—81no—
522Dic6—24no—
523Dic6—21no—
524Dic6—21no—
525Dic6—21no—
526Dic6C3×#4112yes—
527C3×C8—21no—
528C3×C8—21no—
529C3×C8—21no—
530C3×C8—21no—
531C3×C8—41no—
532C3×C8—41no—
533C3×C8—61no—
534C3×C8—61no—
535C3⋊C8—21no—
536C3⋊C8—21no—
537C2×C32#52511yescharacteristic
538C2×C32#57711yescharacteristic
539C2×C32#57811yescharacteristic
540C3×D3—41no—
541C3×D3—81no—
542C2×Q8—21no—
543C2×Q8—31no—
544C2×Q8—31no—
545C2×Q8—61no—
546C2×Q8—62no—
547C2×Q8—62no—
548C2×Q8C22×C3×D311yescharacteristic
549C2×D4—31no—
550C2×D4—61no—
551C22×C4—31no—
552C22×C4—61no—
553C22×C4—61no—
554Q16—62no—
555Q16—62no—
556SD16—62no—
557SD16—62no—
558C2×C8—31no—
559C2×C8—31no—
560C2×C8C22×C3×D311yescharacteristic
561C2×C8C22×C3×D311yescharacteristic
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—31no—
565C4⋊C4—31no—
566C4⋊C4—31no—
567C4⋊C4—61no—
568C4⋊C4—61no—
569C4⋊C4—61no—
570C4⋊C4—61no—
571C4⋊C4—61no—
572C4⋊C4C22×C3×D311yescharacteristic
573C4⋊C4C22×C3×D311yescharacteristic
574C4⋊C4C22×C3×D311yescharacteristic
575C22⋊C4—31no—
576C22⋊C4—31no—
577C22⋊C4—61no—
578C22⋊C4—61no—
579C22⋊C4—61no—
580C22⋊C4—61no—
581C22⋊C4—61no—
582C22⋊C4—61no—
583C42—21no—
584C42—31no—
585C42—61no—
586C42—61no—
587C42—61no—
588C42—61no—
589C42—61no—
590C42C22×C3×D311yescharacteristic
591C22×C3—21no—
592C22×C3—61no—
593C22×C3—61no—
594C22×C3—61no—
595C22×C3—121no—
596C22×C3—121no—
597C22×C3—121no—
598C22×C3C2×D3×D411yescharacteristic
599C22×C3C22×C3×D411yescharacteristic
600C2×D3—21no—
601C2×D3—21no—
602C2×D3—21no—
603C2×D3—41no—
604C2×D3—41no—
605C2×D3—41no—
606C3×C4—22no—
607C3×C4—21no—
608C3×C4—21no—
609C3×C4—21no—
610C3×C4—21no—
611C3×C4—22no—
612C3×C4—22no—
613C3×C4—21no—
614C3×C4—21no—
615C3×C4—41no—
616C3×C4—42no—
617C3×C4—41no—
618C3×C4—41no—
619C3×C4—41no—
620C3×C4—41no—
621C3×C4—41no—
622C3×C4—41no—
623C3×C4—61no—
624C3×C4—61no—
625C3×C4—61no—
626C3×C4—62no—
627C3×C4—81no—
628C3×C4—81no—
629C3×C4—81no—
630C3×C4—121no—
631C3×C4—121no—
632C3×C4C2×#23911yescharacteristic
633C3×C4D3×#4111yescharacteristic
634C3×C4C2×C3×#4111yescharacteristic
635C3×C4C2×C3×#4111yescharacteristic
636Dic3—21no—
637Dic3—21no—
638Dic3—21no—
639Dic3—22no—
640Dic3—41no—
641Dic3—41no—
642C32#312111yescharacteristic, complemented, Sylow
643C23—31no—
644C23—61no—
645Q8—21no—
646Q8—32no—
647Q8—64no—
648Q8—61no—
649Q8—61no—
650Q8—61no—
651Q8—81no—
652Q8C3×#23912yes—
653D4—61no—
654D4—61no—
655D4—241no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—31no—
661C2×C4—31no—
662C2×C4—31no—
663C2×C4—64no—
664C2×C4—61no—
665C2×C4—61no—
666C2×C4—61no—
667C2×C4—61no—
668C2×C4—61no—
669C2×C4—241no—
670C2×C4C3×D3×D411yescharacteristic
671C2×C4C3×D3×D411yescharacteristic
672C2×C4C23×C3×D311yescharacteristic
673C8—21no—
674C8—21no—
675C8—61no—
676C8—61no—
677C2×C3—21no—
678C2×C3—21no—
679C2×C3—21no—
680C2×C3—121no—
681C2×C3—241no—
682C2×C3#562711yescharacteristic
683C2×C3#576611yescharacteristic
684C2×C3#577511yescharacteristic
685C2×C3C3×#52511yescharacteristic
686C2×C3C3×#57711yescharacteristic
687C2×C3C3×#57811yescharacteristic
688D3—41no—
689D3—81no—
690C22—61no—
691C22—61no—
692C22—61no—
693C22—121no—
694C22—121no—
695C22—121no—
696C22C2×C3×D3×D411yescharacteristic
697C4—21no—
698C4—21no—
699C4—22no—
700C4—41no—
701C4—41no—
702C4—41no—
703C4—61no—
704C4—61no—
705C4—61no—
706C4—62no—
707C4—121no—
708C4—121no—
709C4C2×C3×#23911yescharacteristic
710C4C3×D3×#4111yescharacteristic
711C3—21no—
712C3#8109611yescharacteristic, direct product factor
713C3C3×#312111yescharacteristic, complemented
714C2—121no—
715C2—241no—
716C2C3×#562711yescharacteristic
717C2C3×#576611yescharacteristic
718C2C3×#577511yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#477C2
socleC22×C32C22×D4
prime radicalC3×#895C22
hypercenterC3×#477D3
hypocenterC3C3×#3121
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#477

Complements

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

NH ≅ G/Ntype
2. C3×#5572C2semidirect
3. C32×#477C2semidirect
4. C3×#5094C2semidirect
5. C3×#5028C2semidirect
6. C3×#4889C2semidirect
7. C3×#4888C2semidirect
9. C3×#4873C2semidirect
10. C3×#4845C2semidirect
11. C3×#4840C2semidirect
12. C3×#4809C2semidirect
14. C3×#4789C2semidirect
15. C3×#4788C2semidirect
17. #81096C3direct (N × H)
64. #5572C2×C3semidirect
68. C3×#477D3semidirect
69. C3×#477C2×C3semidirect
80. #5094C2×C3semidirect
81. #5028C2×C3semidirect
82. #4889C2×C3semidirect
83. #4888C2×C3semidirect
85. #4873C2×C3semidirect
86. #4845C2×C3semidirect
87. #4840C2×C3semidirect
88. #4809C2×C3semidirect
90. #4789C2×C3semidirect
91. #4788C2×C3semidirect
273. #477C3×D3semidirect
642. C32#3121semidirect
712. C3#81096direct (N × H)
713. C3C3×#3121semidirect

Maximal subgroups

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

subgroupindex
C3×#57332
C3×#55722
C32×#4772
C3×#50942
C3×#50282
C3×#48892
C3×#48882
C3×#48852
C3×#48732
C3×#48452
C3×#48402
C3×#48092
C3×#48062
C3×#47892
C3×#47882
C3×#31213
#810963