Finite Group Databasebeta

← C3×#81233 #11869028

Subgroups — C3×#81233 #11869028

Order 1152.

769 conjugacy classes of subgroups.

The subgroup lattice has 683 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5689C211yesmaximal, characteristic
2C3×#5572C211yesmaximal, characteristic
3C32×#479C211yesmaximal, characteristic, complemented
4C3×#5063C211yesmaximal, characteristic, complemented
5C3×#5021C211yesmaximal, characteristic, complemented
6C3×#4881C211yesmaximal, characteristic
7C3×#4875C211yesmaximal, characteristic, complemented
8C3×#4860C211yesmaximal, characteristic
9C3×#4857C211yesmaximal, characteristic, complemented
10C3×#4851C211yesmaximal, characteristic, complemented
11C3×#4839C211yesmaximal, characteristic
12C3×#4802C211yesmaximal, characteristic
13C3×D3×#103C211yesmaximal, characteristic
14C3×#4799C211yesmaximal, characteristic, complemented
15C3×#4791C211yesmaximal, characteristic, complemented
16C3×#3082—31nomaximal
17#81233C311yesmaximal, characteristic, direct product factor
18C2×C3×D3×Q8C2211yescharacteristic
19C32×#125C2211yescharacteristic
20C32×C4×Q8C2211yescharacteristic
21C3×Q8×Dic3C2211yescharacteristic
22C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
23C2×C3×D3×C8C2211yescharacteristic
24C3×#897—21no—
25C3×#896—21no—
26C3×#892—21no—
27C3×#892C2211yescharacteristic
28C3×#892C2211yescharacteristic
29C3×D3×C4⋊C4C2211yescharacteristic
30C3×#890C2211yescharacteristic
31C3×#889—21no—
32C3×#888—21no—
33C3×#888C2211yescharacteristic
34C3×#887—21no—
35C3×#887C2211yescharacteristic
36C3×#872—21no—
37C3×#872C2211yescharacteristic
38C3×#869C2211yescharacteristic
39C3×C4×Dic6—21no—
40C3×C4×Dic6C2211yescharacteristic
41C32×#107C2211yescharacteristic
42C32×#106C2211yescharacteristic
43C32×C4⋊C8C2211yescharacteristic
44C32×#103C2211yescharacteristic
45C32×#103C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#817C2211yescharacteristic
49C3×#817C2211yescharacteristic
50C3×#816C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×Dic3⋊C8C2211yescharacteristic
53C3×Dic3⋊C8C2211yescharacteristic
54C3×#810C2211yescharacteristic
55C3×#810C2211yescharacteristic
56C3×#808C2211yescharacteristic
57C3×#807C2211yescharacteristic
58C3×#807C2211yescharacteristic
59C3×#807C2211yescharacteristic
60C3×C4⋊(C3⋊C8)C2211yescharacteristic
61C3×#544—31no—
62C3×#519—31no—
63#5689C2×C311yescharacteristic
64#5572C2×C311yescharacteristic
65C3×#479—21no—
66C3×#479—31no—
67C3×#479—31no—
68C3×#479—31no—
69C3×#479D311yescharacteristic, complemented
70C3×#479C2×C311yescharacteristic, complemented
71C3×#477—31no—
72C3×#477—31no—
73C3×#475—31no—
74C3×#475—31no—
75C3×#428—31no—
76C3×#427—31no—
77C3×#424—31no—
78C3×#419—31no—
79C2×C3×#103—31no—
80#5063C2×C311yescharacteristic, complemented
81#5021C2×C311yescharacteristic, complemented
82#4881C2×C311yescharacteristic
83#4875C2×C311yescharacteristic, complemented
84#4860C2×C311yescharacteristic
85#4857C2×C311yescharacteristic, complemented
86#4851C2×C311yescharacteristic, complemented
87#4839C2×C311yescharacteristic
88#4802C2×C311yescharacteristic
89D3×#103C2×C311yescharacteristic
90#4799C2×C311yescharacteristic, complemented
91#4791C2×C311yescharacteristic, complemented
92C2×C32×Q8C2311yescharacteristic
93C3×D3×Q8—22no—
94C3×D3×Q8Q814yescomplemented
95C2×C3×C4×D3—21no—
96C2×C3×C4×D3—21no—
97C2×C3×C4×D3C2311yescharacteristic
98C2×C3×Dic6—21no—
99C2×C3×Dic6—21no—
100C2×C3×Dic6—21no—
101C2×C3×Dic6C2311yescharacteristic
102C2×C32×C8C2311yescharacteristic
103C2×C32×C8C2311yescharacteristic
104C32×C4⋊C4—21no—
105C32×C4⋊C4—21no—
106C32×C4⋊C4—21no—
107C32×C4⋊C4C2311yescharacteristic
108C32×C4⋊C4C2311yescharacteristic
109C32×C4⋊C4C2311yescharacteristic
110C32×C42—21no—
111C32×C42C2311yescharacteristic
112C3×(C2×D3)⋊C4—21no—
113C3×(C2×D3)⋊C4—21no—
114C3×(C2×D3)⋊C4D411yescharacteristic
115C3×(C2×D3)⋊C4D411yescharacteristic
116C3×C4⋊Dic3—21no—
117C3×C4⋊Dic3—21no—
118C3×C4⋊Dic3—21no—
119C3×C4⋊Dic3C2311yescharacteristic
120C3×C4⋊Dic3C2311yescharacteristic
121C3×C4⋊Dic3C2311yescharacteristic
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×Dic3—21no—
133C3×C4×Dic3—21no—
134C3×C4×Dic3C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C3×ΓL(1,𝔽25)—22no—
138C3×D3×C8—22no—
139#3082—31noSylow
140C22×C3×Q8—31no—
141C2×D3×Q8C22×C311yescharacteristic
142C2×C3×M16—31no—
143C22×C3×C8—31no—
144C3×C4⋊Q8—31no—
145C3×C4⋊Q8—31no—
146C3×C4⋊Q8—61no—
147C3×#125—21no—
148C3×#125—31no—
149C3×#125—61no—
150C3×#125C2×D311yescharacteristic
151C3×#125C22×C311yescharacteristic
152C3×C22⋊Q8—61no—
153C3×C22⋊Q8—61no—
154C3×C4×Q8—21no—
155C3×C4×Q8—31no—
156C3×C4×Q8—31no—
157C3×C4×Q8—31no—
158C3×C4×Q8—61no—
159C3×C4×Q8—61no—
160C3×C4×Q8C2×D311yescharacteristic
161C3×C4×Q8C22×C311yescharacteristic
162C3×#117—31no—
163C3×#117—31no—
164C3×#117—31no—
165C3×#117—61no—
166C3×#117—61no—
167C2×C3×C4⋊C4—31no—
168Q8×Dic3C22×C311yescharacteristic
169C2×ΓL(1,𝔽25)C22×C311yescharacteristic
170C2×D3×C8C22×C311yescharacteristic
171#897—21no—
172#896—21no—
173#892—21no—
174#892C22×C311yescharacteristic
175#892C22×C311yescharacteristic
176D3×C4⋊C4C22×C311yescharacteristic
177#890C22×C311yescharacteristic
178#889—21no—
179#888—21no—
180#888C22×C311yescharacteristic
181#887—21no—
182#887C22×C311yescharacteristic
183#872—21no—
184#872C22×C311yescharacteristic
185#869C22×C311yescharacteristic
186C4×Dic6—21no—
187C4×Dic6C22×C311yescharacteristic
188C3×#107—21no—
189C3×#107—31no—
190C3×#107—31no—
191C3×#107—31no—
192C3×#107C2×D311yescharacteristic
193C3×#107C22×C311yescharacteristic
194C3×#106—21no—
195C3×#106—31no—
196C3×#106—31no—
197C3×#106—31no—
198C3×#106C2×D311yescharacteristic
199C3×#106C22×C311yescharacteristic
200C3×C4⋊C8—21no—
201C3×C4⋊C8—31no—
202C3×C4⋊C8—31no—
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×#103—31no—
213C3×#103—31no—
214C3×#103C2×D311yescharacteristic
215C3×#103C2×D311yescharacteristic
216C3×#103C22×C311yescharacteristic
217C3×#103C22×C311yescharacteristic
218#835C22×C311yescharacteristic
219#835C22×C311yescharacteristic
220#817C22×C311yescharacteristic
221#817C22×C311yescharacteristic
222#816C22×C311yescharacteristic
223#816C22×C311yescharacteristic
224Dic3⋊C8C22×C311yescharacteristic
225Dic3⋊C8C22×C311yescharacteristic
226#810C22×C311yescharacteristic
227#810C22×C311yescharacteristic
228#808C22×C311yescharacteristic
229#807C22×C311yescharacteristic
230#807C22×C311yescharacteristic
231#807C22×C311yescharacteristic
232C4⋊(C3⋊C8)C22×C311yescharacteristic
233C22×C3×D3C2×D411yescharacteristic
234C32×Q8—21no—
235C32×Q8C2×Q812yes—
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×Dic3—21no—
247C2×C3×Dic3C2×D411yescharacteristic
248C2×C3×Dic3C2×D411yescharacteristic
249C2×C3×Dic3C2×D411yescharacteristic
250C3×C4×D3—24no—
251C3×C4×D3—81no—
252C3×C4×D3C2×Q812yes—
253C3×C4×D3#4112yes—
254C3×Dic6—21no—
255C3×Dic6—24no—
256C3×Dic6—81no—
257C3×Dic6—81no—
258C3×Dic6C2×Q812yes—
259C32×C8—21no—
260C32×C8—21no—
261C3×C3⋊C8—21no—
262C3×C3⋊C8—21no—
263#544—31no—
264#519—31no—
265#479—31no—
266#479—31no—
267#479—31no—
268#479C3×D311yescharacteristic, complemented
269#477—31no—
270#477—31no—
271#475—31no—
272#475—31no—
273#428—31no—
274#427—31no—
275#424—31no—
276#419—31no—
277C2×#103—31no—
278C2×C3×Q8—21no—
279C2×C3×Q8—34no—
280C2×C3×Q8—31no—
281C2×C3×Q8—61no—
282C2×C3×Q8—61no—
283C2×C3×Q8—62no—
284C2×C3×Q8—61no—
285C2×C3×Q8C22×D311yescharacteristic
286C2×C3×Q8C23×C311yescharacteristic
287C22×C3×C4—31no—
288C22×C3×C4—61no—
289C22×C3×C4—61no—
290D3×Q8—22no—
291D3×Q8C3×Q814yescomplemented
292C2×C4×D3—21no—
293C2×C4×D3—21no—
294C2×C4×D3C23×C311yescharacteristic
295C2×Dic6—21no—
296C2×Dic6—21no—
297C2×Dic6—21no—
298C2×Dic6C23×C311yescharacteristic
299C3×M16—62no—
300C2×C3×C8—21no—
301C2×C3×C8—21no—
302C2×C3×C8—31no—
303C2×C3×C8—31no—
304C2×C3×C8—62no—
305C2×C3×C8C22×D311yescharacteristic
306C2×C3×C8C22×D311yescharacteristic
307C2×C3×C8C23×C311yescharacteristic
308C2×C3×C8C23×C311yescharacteristic
309C3×C4⋊C4—21no—
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—21no—
318C3×C4⋊C4—31no—
319C3×C4⋊C4—31no—
320C3×C4⋊C4—31no—
321C3×C4⋊C4—31no—
322C3×C4⋊C4—31no—
323C3×C4⋊C4—41no—
324C3×C4⋊C4—41no—
325C3×C4⋊C4—41no—
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⋊C4C22×D311yescharacteristic
336C3×C4⋊C4C22×D311yescharacteristic
337C3×C4⋊C4C23×C311yescharacteristic
338C3×C4⋊C4C23×C311yescharacteristic
339C3×C4⋊C4C23×C311yescharacteristic
340C3×C22⋊C4—31no—
341C3×C22⋊C4—31no—
342C3×C22⋊C4—61no—
343C3×C22⋊C4—61no—
344C3×C42—21no—
345C3×C42—21no—
346C3×C42—21no—
347C3×C42—31no—
348C3×C42—41no—
349C3×C42—61no—
350C3×C42—61no—
351C3×C42—61no—
352C3×C42—61no—
353C3×C42—61no—
354C3×C42C22×D311yescharacteristic
355C3×C42C23×C311yescharacteristic
356(C2×D3)⋊C4—21no—
357(C2×D3)⋊C4—21no—
358(C2×D3)⋊C4C3×D411yescharacteristic
359(C2×D3)⋊C4C3×D411yescharacteristic
360C4⋊Dic3—21no—
361C4⋊Dic3—21no—
362C4⋊Dic3—21no—
363C4⋊Dic3C23×C311yescharacteristic
364C4⋊Dic3C23×C311yescharacteristic
365C4⋊Dic3C23×C311yescharacteristic
366Dic3⋊C4—21no—
367Dic3⋊C4—21no—
368Dic3⋊C4—21no—
369Dic3⋊C4—21no—
370Dic3⋊C4—21no—
371Dic3⋊C4C3×D411yescharacteristic
372Dic3⋊C4C3×D411yescharacteristic
373C4×Dic3—21no—
374C4×Dic3—21no—
375C4×Dic3—21no—
376C4×Dic3—21no—
377C4×Dic3—21no—
378C4×Dic3C23×C311yescharacteristic
379C2×C3⋊C8C23×C311yescharacteristic
380C2×C3⋊C8C23×C311yescharacteristic
381ΓL(1,𝔽25)—22no—
382D3×C8—22no—
383C22×C32C22×D411yescharacteristic
384C2×C3×D3—21no—
385C2×C3×D3—21no—
386C2×C3×D3C22⋊Q812yes—
387C32×C4—22no—
388C32×C4—21no—
389C32×C4—21no—
390C32×C4—41no—
391C32×C4—41no—
392C32×C4—41no—
393C32×C4C22×Q811yescharacteristic
394C32×C4C2×#4111yescharacteristic
395C3×Dic3—22no—
396C3×Dic3—21no—
397C3×Dic3—21no—
398C3×Dic3—41no—
399C3×Dic3—41no—
400C3×Dic3—41no—
401C3×Dic3C22⋊Q812yes—
402C22×Q8—31no—
403C2×M16—31no—
404C22×C8—31no—
405C4⋊Q8—31no—
406C4⋊Q8—31no—
407C4⋊Q8—61no—
408#125—31no—
409#125—61no—
410#125C2×C3×D311yescharacteristic
411C22⋊Q8—61no—
412C22⋊Q8—61no—
413C4×Q8—31no—
414C4×Q8—31no—
415C4×Q8—31no—
416C4×Q8—61no—
417C4×Q8—61no—
418C4×Q8C2×C3×D311yescharacteristic
419#117—31no—
420#117—31no—
421#117—31no—
422#117—61no—
423#117—61no—
424C2×C4⋊C4—31no—
425#107—31no—
426#107—31no—
427#107—31no—
428#107C2×C3×D311yescharacteristic
429#106—31no—
430#106—31no—
431#106—31no—
432#106C2×C3×D311yescharacteristic
433C4⋊C8—31no—
434C4⋊C8—31no—
435C4⋊C8—31no—
436C4⋊C8C2×C3×D311yescharacteristic
437#103—31no—
438#103—31no—
439#103—31no—
440#103—31no—
441#103—31no—
442#103—31no—
443#103C2×C3×D311yescharacteristic
444#103C2×C3×D311yescharacteristic
445C23×C3—31no—
446C22×D3C2×C3×D411yescharacteristic
447C3×Q8—21no—
448C3×Q8—21no—
449C3×Q8—22no—
450C3×Q8—32no—
451C3×Q8—41no—
452C3×Q8—64no—
453C3×Q8—61no—
454C3×Q8—241no—
455C3×Q8—241no—
456C3×Q8D3×Q812yes—
457C3×Q8C2×C3×Q812yes—
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—21no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—31no—
470C2×C3×C4—32no—
471C2×C3×C4—32no—
472C2×C3×C4—31no—
473C2×C3×C4—31no—
474C2×C3×C4—41no—
475C2×C3×C4—41no—
476C2×C3×C4—41no—
477C2×C3×C4—41no—
478C2×C3×C4—64no—
479C2×C3×C4—61no—
480C2×C3×C4—61no—
481C2×C3×C4—61no—
482C2×C3×C4—61no—
483C2×C3×C4—241no—
484C2×C3×C4D3×D411yescharacteristic
485C2×C3×C4D3×D411yescharacteristic
486C2×C3×C4C2×C3×D411yescharacteristic
487C2×C3×C4C2×C3×D411yescharacteristic
488C2×C3×C4C23×D311yescharacteristic
489C2×C3×C4C24×C311yescharacteristic
490C2×Dic3—21no—
491C2×Dic3—21no—
492C2×Dic3—21no—
493C2×Dic3—21no—
494C2×Dic3C2×C3×D411yescharacteristic
495C2×Dic3C2×C3×D411yescharacteristic
496C2×Dic3C2×C3×D411yescharacteristic
497C4×D3—24no—
498C4×D3—81no—
499C4×D3C2×C3×Q812yes—
500C4×D3C3×#4112yes—
501Dic6—21no—
502Dic6—24no—
503Dic6—81no—
504Dic6—81no—
505Dic6C2×C3×Q812yes—
506C3×C8—21no—
507C3×C8—21no—
508C3×C8—21no—
509C3×C8—21no—
510C3×C8—41no—
511C3×C8—41no—
512C3×C8—61no—
513C3×C8—61no—
514C3⋊C8—21no—
515C3⋊C8—21no—
516C2×C32C2×C22⋊Q811yescharacteristic
517C2×C32#57711yescharacteristic
518C2×C32#57811yescharacteristic
519C3×D3—22no—
520C2×Q8—34no—
521C2×Q8—31no—
522C2×Q8—61no—
523C2×Q8—61no—
524C2×Q8—62no—
525C2×Q8—61no—
526C2×Q8C22×C3×D311yescharacteristic
527C22×C4—31no—
528C22×C4—61no—
529C22×C4—61no—
530M16—62no—
531C2×C8—31no—
532C2×C8—31no—
533C2×C8—62no—
534C2×C8C22×C3×D311yescharacteristic
535C2×C8C22×C3×D311yescharacteristic
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—31no—
540C4⋊C4—31no—
541C4⋊C4—31no—
542C4⋊C4—31no—
543C4⋊C4—31no—
544C4⋊C4—61no—
545C4⋊C4—61no—
546C4⋊C4—61no—
547C4⋊C4—61no—
548C4⋊C4—61no—
549C4⋊C4—61no—
550C4⋊C4—61no—
551C4⋊C4—61no—
552C4⋊C4C22×C3×D311yescharacteristic
553C4⋊C4C22×C3×D311yescharacteristic
554C4⋊C4C22×C3×D311yescharacteristic
555C22⋊C4—31no—
556C22⋊C4—31no—
557C22⋊C4—61no—
558C22⋊C4—61no—
559C42—21no—
560C42—31no—
561C42—61no—
562C42—61no—
563C42—61no—
564C42—61no—
565C42—61no—
566C42C22×C3×D311yescharacteristic
567C22×C3—21no—
568C22×C3—32no—
569C22×C3—61no—
570C22×C3—61no—
571C22×C3C2×D3×D411yescharacteristic
572C22×C3C22×C3×D411yescharacteristic
573C2×D3—21no—
574C2×D3—21no—
575C2×D3C3×C22⋊Q812yes—
576C3×C4—21no—
577C3×C4—21no—
578C3×C4—21no—
579C3×C4—21no—
580C3×C4—22no—
581C3×C4—22no—
582C3×C4—21no—
583C3×C4—21no—
584C3×C4—32no—
585C3×C4—41no—
586C3×C4—41no—
587C3×C4—42no—
588C3×C4—41no—
589C3×C4—41no—
590C3×C4—41no—
591C3×C4—41no—
592C3×C4—41no—
593C3×C4—41no—
594C3×C4—61no—
595C3×C4—61no—
596C3×C4—62no—
597C3×C4—81no—
598C3×C4—81no—
599C3×C4—81no—
600C3×C4—121no—
601C3×C4—121no—
602C3×C4—121no—
603C3×C4C2×D3×Q811yescharacteristic
604C3×C4D3×#4111yescharacteristic
605C3×C4C22×C3×Q811yescharacteristic
606C3×C4C2×C3×#4111yescharacteristic
607Dic3—21no—
608Dic3—21no—
609Dic3—22no—
610Dic3—41no—
611Dic3—41no—
612Dic3—41no—
613Dic3C3×C22⋊Q812yes—
614C32#308211yescharacteristic, complemented, Sylow
615C23—31no—
616Q8—21no—
617Q8—32no—
618Q8—64no—
619Q8—61no—
620Q8—241no—
621Q8—241no—
622Q8C3×D3×Q812yes—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—31no—
628C2×C4—32no—
629C2×C4—32no—
630C2×C4—31no—
631C2×C4—31no—
632C2×C4—64no—
633C2×C4—61no—
634C2×C4—61no—
635C2×C4—61no—
636C2×C4—61no—
637C2×C4—241no—
638C2×C4C3×D3×D411yescharacteristic
639C2×C4C3×D3×D411yescharacteristic
640C2×C4C23×C3×D311yescharacteristic
641C8—21no—
642C8—21no—
643C8—61no—
644C8—61no—
645C2×C3—21no—
646C2×C3—21no—
647C2×C3—21no—
648C2×C3—62no—
649C2×C3D3×C22⋊Q811yescharacteristic
650C2×C3#577011yescharacteristic
651C2×C3#577911yescharacteristic
652C2×C3C2×C3×C22⋊Q811yescharacteristic
653C2×C3C3×#57711yescharacteristic
654C2×C3C3×#57811yescharacteristic
655D3—22no—
656C22—32no—
657C22—61no—
658C22—61no—
659C22C2×C3×D3×D411yescharacteristic
660C4—21no—
661C4—21no—
662C4—22no—
663C4—32no—
664C4—41no—
665C4—41no—
666C4—41no—
667C4—61no—
668C4—61no—
669C4—62no—
670C4—121no—
671C4—121no—
672C4—121no—
673C4C2×C3×D3×Q811yescharacteristic
674C4C3×D3×#4111yescharacteristic
675C3—21no—
676C3#8123311yescharacteristic, direct product factor
677C3C3×#308211yescharacteristic, complemented
678C2—62no—
679C2C3×D3×C22⋊Q811yescharacteristic
680C2C3×#577011yescharacteristic
681C2C3×#577911yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#479C2
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
hypercenterC3×#479D3
hypocenterC3C3×#3082
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#479

Complements

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

NH ≅ G/Ntype
3. C32×#479C2semidirect
4. C3×#5063C2semidirect
5. C3×#5021C2semidirect
7. C3×#4875C2semidirect
9. C3×#4857C2semidirect
10. C3×#4851C2semidirect
14. C3×#4799C2semidirect
15. C3×#4791C2semidirect
17. #81233C3direct (N × H)
69. C3×#479D3semidirect
70. C3×#479C2×C3semidirect
80. #5063C2×C3semidirect
81. #5021C2×C3semidirect
83. #4875C2×C3semidirect
85. #4857C2×C3semidirect
86. #4851C2×C3semidirect
90. #4799C2×C3semidirect
91. #4791C2×C3semidirect
94. C3×D3×Q8Q8semidirect
268. #479C3×D3semidirect
291. D3×Q8C3×Q8semidirect
614. C32#3082semidirect
676. C3#81233direct (N × H)
677. C3C3×#3082semidirect

Maximal subgroups

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

subgroupindex
C3×#56892
C3×#55722
C32×#4792
C3×#50632
C3×#50212
C3×#48812
C3×#48752
C3×#48602
C3×#48572
C3×#48512
C3×#48392
C3×#48022
C3×D3×#1032
C3×#47992
C3×#47912
C3×#30823
#812333