Finite Group Databasebeta

← C3×#81013 #11869016

Subgroups — C3×#81013 #11869016

Order 1152.

772 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5729C211yesmaximal, characteristic
2C3×#5572C211yesmaximal, characteristic
3C32×#475C211yesmaximal, characteristic, complemented
4C3×#5091C211yesmaximal, characteristic, complemented
5C3×#5022C211yesmaximal, characteristic, complemented
6C3×#4861C211yesmaximal, characteristic
7C3×#4860C211yesmaximal, characteristic
8C3×#4857C211yesmaximal, characteristic, complemented
9C3×#4854C211yesmaximal, characteristic, complemented
10C3×#4839C211yesmaximal, characteristic
11C3×#4829C211yesmaximal, characteristic, complemented
12C3×#4802C211yesmaximal, characteristic
13C3×D3×#103C211yesmaximal, characteristic
14C3×#4799C211yesmaximal, characteristic, complemented
15C3×#4793C211yesmaximal, characteristic, complemented
16C3×#3082—31nomaximal
17#81013C311yesmaximal, characteristic, direct product factor
18C2×C3×D3×Q8C2211yescharacteristic
19C32×C4⋊Q8C2211yescharacteristic
20C32×C4×Q8C2211yescharacteristic
21C3×#946—21no—
22C3×Q8×Dic3C2211yescharacteristic
23C3×#944—21no—
24C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
25C2×C3×D3×C8C2211yescharacteristic
26C3×#896—21no—
27C3×#892—21no—
28C3×#892C2211yescharacteristic
29C3×#892C2211yescharacteristic
30C3×D3×C4⋊C4C2211yescharacteristic
31C3×#890C2211yescharacteristic
32C3×#889—21no—
33C3×#888C2211yescharacteristic
34C3×#887—21no—
35C3×#887C2211yescharacteristic
36C3×#872—21no—
37C3×#872C2211yescharacteristic
38C3×#870C2211yescharacteristic
39C3×C4×Dic6—21no—
40C3×C4×Dic6C2211yescharacteristic
41C32×#106C2211yescharacteristic
42C32×#106C2211yescharacteristic
43C32×C4⋊C8C2211yescharacteristic
44C32×#103C2211yescharacteristic
45C32×#103C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#818C2211yescharacteristic
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#5729C2×C311yescharacteristic
64#5572C2×C311yescharacteristic
65C3×#479—31no—
66C3×#479—31no—
67C3×#479—31no—
68C3×#479—31no—
69C3×#477—31no—
70C3×#477—31no—
71C3×#475—21no—
72C3×#475—31no—
73C3×#475D311yescharacteristic, complemented
74C3×#475C2×C311yescharacteristic, complemented
75C3×#428—31no—
76C3×#427—31no—
77C3×#424—31no—
78C3×#419—31no—
79C2×C3×#103—31no—
80#5091C2×C311yescharacteristic, complemented
81#5022C2×C311yescharacteristic, complemented
82#4861C2×C311yescharacteristic
83#4860C2×C311yescharacteristic
84#4857C2×C311yescharacteristic, complemented
85#4854C2×C311yescharacteristic, complemented
86#4839C2×C311yescharacteristic
87#4829C2×C311yescharacteristic, complemented
88#4802C2×C311yescharacteristic
89D3×#103C2×C311yescharacteristic
90#4799C2×C311yescharacteristic, complemented
91#4793C2×C311yescharacteristic, complemented
92C2×C32×Q8—21no—
93C2×C32×Q8C2311yescharacteristic
94C3×D3×Q8—22no—
95C3×D3×Q8Q814yescomplemented
96C2×C3×C4×D3—21no—
97C2×C3×C4×D3—21no—
98C2×C3×C4×D3C2311yescharacteristic
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⋊C4C2311yescharacteristic
107C32×C4⋊C4C2311yescharacteristic
108C32×C4⋊C4C2311yescharacteristic
109C32×C42—21no—
110C32×C42C2311yescharacteristic
111C3×(C2×D3)⋊C4—21no—
112C3×(C2×D3)⋊C4—21no—
113C3×(C2×D3)⋊C4D411yescharacteristic
114C3×(C2×D3)⋊C4D411yescharacteristic
115C3×C4⋊Dic3—21no—
116C3×C4⋊Dic3—21no—
117C3×C4⋊Dic3C2311yescharacteristic
118C3×C4⋊Dic3C2311yescharacteristic
119C3×C4⋊Dic3C2311yescharacteristic
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×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—21no—
145C3×C4⋊Q8—31no—
146C3×C4⋊Q8—61no—
147C3×C4⋊Q8C2×D311yescharacteristic
148C3×C4⋊Q8C22×C311yescharacteristic
149C3×#125—31no—
150C3×#125—31no—
151C3×#125—61no—
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—
168#946—21no—
169Q8×Dic3C22×C311yescharacteristic
170#944—21no—
171C2×ΓL(1,𝔽25)C22×C311yescharacteristic
172C2×D3×C8C22×C311yescharacteristic
173#896—21no—
174#892—21no—
175#892C22×C311yescharacteristic
176#892C22×C311yescharacteristic
177D3×C4⋊C4C22×C311yescharacteristic
178#890C22×C311yescharacteristic
179#889—21no—
180#888C22×C311yescharacteristic
181#887—21no—
182#887C22×C311yescharacteristic
183#872—21no—
184#872C22×C311yescharacteristic
185#870C22×C311yescharacteristic
186C4×Dic6—21no—
187C4×Dic6C22×C311yescharacteristic
188C3×#107—31no—
189C3×#107—31no—
190C3×#107—31no—
191C3×#107—31no—
192C3×#106—21no—
193C3×#106—21no—
194C3×#106—31no—
195C3×#106—31no—
196C3×#106C2×D311yescharacteristic
197C3×#106C2×D311yescharacteristic
198C3×#106C22×C311yescharacteristic
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#818C22×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×Q8—81no—
236C32×Q8C2×Q812yes—
237C2×C32×C4—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×Dic3C2×D411yescharacteristic
249C2×C3×Dic3C2×D411yescharacteristic
250C2×C3×Dic3C2×D411yescharacteristic
251C3×C4×D3—24no—
252C3×C4×D3—81no—
253C3×C4×D3C2×Q812yes—
254C3×C4×D3#4112yes—
255C3×Dic6—21no—
256C3×Dic6—24no—
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#479—31no—
269#477—31no—
270#477—31no—
271#475—31no—
272#475C3×D311yescharacteristic, complemented
273#428—31no—
274#427—31no—
275#424—31no—
276#419—31no—
277C2×#103—31no—
278C2×C3×Q8—21no—
279C2×C3×Q8—21no—
280C2×C3×Q8—21no—
281C2×C3×Q8—34no—
282C2×C3×Q8—31no—
283C2×C3×Q8—41no—
284C2×C3×Q8—61no—
285C2×C3×Q8—61no—
286C2×C3×Q8—62no—
287C2×C3×Q8C22×D311yescharacteristic
288C2×C3×Q8C23×C311yescharacteristic
289C22×C3×C4—31no—
290C22×C3×C4—61no—
291C22×C3×C4—61no—
292D3×Q8—22no—
293D3×Q8C3×Q814yescomplemented
294C2×C4×D3—21no—
295C2×C4×D3—21no—
296C2×C4×D3C23×C311yescharacteristic
297C2×Dic6—21no—
298C2×Dic6—21no—
299C2×Dic6C23×C311yescharacteristic
300C3×M16—62no—
301C2×C3×C8—21no—
302C2×C3×C8—21no—
303C2×C3×C8—31no—
304C2×C3×C8—31no—
305C2×C3×C8—62no—
306C2×C3×C8C22×D311yescharacteristic
307C2×C3×C8C22×D311yescharacteristic
308C2×C3×C8C23×C311yescharacteristic
309C2×C3×C8C23×C311yescharacteristic
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—31no—
318C3×C4⋊C4—31no—
319C3×C4⋊C4—31no—
320C3×C4⋊C4—31no—
321C3×C4⋊C4—31no—
322C3×C4⋊C4—41no—
323C3×C4⋊C4—41no—
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⋊C4—61no—
331C3×C4⋊C4—61no—
332C3×C4⋊C4—61no—
333C3×C4⋊C4C22×D311yescharacteristic
334C3×C4⋊C4C22×D311yescharacteristic
335C3×C4⋊C4C22×D311yescharacteristic
336C3×C4⋊C4C23×C311yescharacteristic
337C3×C4⋊C4C23×C311yescharacteristic
338C3×C4⋊C4C23×C311yescharacteristic
339C3×C22⋊C4—31no—
340C3×C22⋊C4—31no—
341C3×C22⋊C4—61no—
342C3×C22⋊C4—61no—
343C3×C42—21no—
344C3×C42—21no—
345C3×C42—21no—
346C3×C42—31no—
347C3×C42—41no—
348C3×C42—61no—
349C3×C42—61no—
350C3×C42—61no—
351C3×C42—61no—
352C3×C42—61no—
353C3×C42C22×D311yescharacteristic
354C3×C42C23×C311yescharacteristic
355(C2×D3)⋊C4—21no—
356(C2×D3)⋊C4—21no—
357(C2×D3)⋊C4C3×D411yescharacteristic
358(C2×D3)⋊C4C3×D411yescharacteristic
359C4⋊Dic3—21no—
360C4⋊Dic3—21no—
361C4⋊Dic3C23×C311yescharacteristic
362C4⋊Dic3C23×C311yescharacteristic
363C4⋊Dic3C23×C311yescharacteristic
364Dic3⋊C4—21no—
365Dic3⋊C4—21no—
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—21no—
388C32×C4—22no—
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—61no—
407C4⋊Q8C2×C3×D311yescharacteristic
408#125—31no—
409#125—31no—
410#125—61no—
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#107—31no—
429#106—31no—
430#106—31no—
431#106C2×C3×D311yescharacteristic
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—81no—
455C3×Q8—81no—
456C3×Q8—82no—
457C3×Q8—241no—
458C3×Q8D3×Q812yes—
459C3×Q8C2×C3×Q812yes—
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—21no—
470C2×C3×C4—21no—
471C2×C3×C4—31no—
472C2×C3×C4—32no—
473C2×C3×C4—32no—
474C2×C3×C4—31no—
475C2×C3×C4—31no—
476C2×C3×C4—41no—
477C2×C3×C4—41no—
478C2×C3×C4—41no—
479C2×C3×C4—41no—
480C2×C3×C4—64no—
481C2×C3×C4—61no—
482C2×C3×C4—61no—
483C2×C3×C4—61no—
484C2×C3×C4—61no—
485C2×C3×C4—241no—
486C2×C3×C4D3×D411yescharacteristic
487C2×C3×C4D3×D411yescharacteristic
488C2×C3×C4C2×C3×D411yescharacteristic
489C2×C3×C4C2×C3×D411yescharacteristic
490C2×C3×C4C23×D311yescharacteristic
491C2×C3×C4C24×C311yescharacteristic
492C2×Dic3—21no—
493C2×Dic3—21no—
494C2×Dic3—21no—
495C2×Dic3—21no—
496C2×Dic3C2×C3×D411yescharacteristic
497C2×Dic3C2×C3×D411yescharacteristic
498C2×Dic3C2×C3×D411yescharacteristic
499C4×D3—24no—
500C4×D3—81no—
501C4×D3C2×C3×Q812yes—
502C4×D3C3×#4112yes—
503Dic6—21no—
504Dic6—24no—
505Dic6—81no—
506Dic6C2×C3×Q812yes—
507C3×C8—21no—
508C3×C8—21no—
509C3×C8—21no—
510C3×C8—21no—
511C3×C8—41no—
512C3×C8—41no—
513C3×C8—61no—
514C3×C8—61no—
515C3⋊C8—21no—
516C3⋊C8—21no—
517C2×C32C2×C22⋊Q811yescharacteristic
518C2×C32#57711yescharacteristic
519C2×C32#57811yescharacteristic
520C3×D3—22no—
521C2×Q8—21no—
522C2×Q8—34no—
523C2×Q8—31no—
524C2×Q8—61no—
525C2×Q8—61no—
526C2×Q8—62no—
527C2×Q8C22×C3×D311yescharacteristic
528C22×C4—31no—
529C22×C4—61no—
530C22×C4—61no—
531M16—62no—
532C2×C8—31no—
533C2×C8—31no—
534C2×C8—62no—
535C2×C8C22×C3×D311yescharacteristic
536C2×C8C22×C3×D311yescharacteristic
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⋊C4—61no—
553C4⋊C4C22×C3×D311yescharacteristic
554C4⋊C4C22×C3×D311yescharacteristic
555C4⋊C4C22×C3×D311yescharacteristic
556C22⋊C4—31no—
557C22⋊C4—31no—
558C22⋊C4—61no—
559C22⋊C4—61no—
560C42—21no—
561C42—31no—
562C42—61no—
563C42—61no—
564C42—61no—
565C42—61no—
566C42—61no—
567C42C22×C3×D311yescharacteristic
568C22×C3—21no—
569C22×C3—32no—
570C22×C3—61no—
571C22×C3—61no—
572C22×C3C2×D3×D411yescharacteristic
573C22×C3C22×C3×D411yescharacteristic
574C2×D3—21no—
575C2×D3—21no—
576C2×D3C3×C22⋊Q812yes—
577C3×C4—22no—
578C3×C4—21no—
579C3×C4—21no—
580C3×C4—21no—
581C3×C4—21no—
582C3×C4—22no—
583C3×C4—22no—
584C3×C4—21no—
585C3×C4—21no—
586C3×C4—32no—
587C3×C4—41no—
588C3×C4—42no—
589C3×C4—41no—
590C3×C4—41no—
591C3×C4—41no—
592C3×C4—41no—
593C3×C4—41no—
594C3×C4—41no—
595C3×C4—61no—
596C3×C4—61no—
597C3×C4—62no—
598C3×C4—81no—
599C3×C4—81no—
600C3×C4—81no—
601C3×C4—121no—
602C3×C4—121no—
603C3×C4—121no—
604C3×C4C2×D3×Q811yescharacteristic
605C3×C4D3×#4111yescharacteristic
606C3×C4C22×C3×Q811yescharacteristic
607C3×C4C2×C3×#4111yescharacteristic
608Dic3—21no—
609Dic3—21no—
610Dic3—22no—
611Dic3—41no—
612Dic3—41no—
613Dic3—41no—
614Dic3C3×C22⋊Q812yes—
615C32#308211yescharacteristic, complemented, Sylow
616C23—31no—
617Q8—21no—
618Q8—32no—
619Q8—64no—
620Q8—61no—
621Q8—81no—
622Q8—241no—
623Q8C3×D3×Q812yes—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—31no—
629C2×C4—32no—
630C2×C4—32no—
631C2×C4—31no—
632C2×C4—31no—
633C2×C4—64no—
634C2×C4—61no—
635C2×C4—61no—
636C2×C4—61no—
637C2×C4—61no—
638C2×C4—241no—
639C2×C4C3×D3×D411yescharacteristic
640C2×C4C3×D3×D411yescharacteristic
641C2×C4C23×C3×D311yescharacteristic
642C8—21no—
643C8—21no—
644C8—61no—
645C8—61no—
646C2×C3—21no—
647C2×C3—21no—
648C2×C3—21no—
649C2×C3—62no—
650C2×C3D3×C22⋊Q811yescharacteristic
651C2×C3#576211yescharacteristic
652C2×C3#577911yescharacteristic
653C2×C3C2×C3×C22⋊Q811yescharacteristic
654C2×C3C3×#57711yescharacteristic
655C2×C3C3×#57811yescharacteristic
656D3—22no—
657C22—32no—
658C22—61no—
659C22—61no—
660C22C2×C3×D3×D411yescharacteristic
661C4—21no—
662C4—21no—
663C4—22no—
664C4—32no—
665C4—41no—
666C4—41no—
667C4—41no—
668C4—61no—
669C4—61no—
670C4—62no—
671C4—121no—
672C4—121no—
673C4—121no—
674C4C2×C3×D3×Q811yescharacteristic
675C4C3×D3×#4111yescharacteristic
676C3—21no—
677C3#8101311yescharacteristic, direct product factor
678C3C3×#308211yescharacteristic, complemented
679C2—62no—
680C2C3×D3×C22⋊Q811yescharacteristic
681C2C3×#576211yescharacteristic
682C2C3×#577911yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#475C2
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
hypercenterC3×#475D3
hypocenterC3C3×#3082
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#475

Complements

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

NH ≅ G/Ntype
3. C32×#475C2semidirect
4. C3×#5091C2semidirect
5. C3×#5022C2semidirect
8. C3×#4857C2semidirect
9. C3×#4854C2semidirect
11. C3×#4829C2semidirect
14. C3×#4799C2semidirect
15. C3×#4793C2semidirect
17. #81013C3direct (N × H)
73. C3×#475D3semidirect
74. C3×#475C2×C3semidirect
80. #5091C2×C3semidirect
81. #5022C2×C3semidirect
84. #4857C2×C3semidirect
85. #4854C2×C3semidirect
87. #4829C2×C3semidirect
90. #4799C2×C3semidirect
91. #4793C2×C3semidirect
95. C3×D3×Q8Q8semidirect
272. #475C3×D3semidirect
293. D3×Q8C3×Q8semidirect
615. C32#3082semidirect
677. C3#81013direct (N × H)
678. C3C3×#3082semidirect

Maximal subgroups

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

subgroupindex
C3×#57292
C3×#55722
C32×#4752
C3×#50912
C3×#50222
C3×#48612
C3×#48602
C3×#48572
C3×#48542
C3×#48392
C3×#48292
C3×#48022
C3×D3×#1032
C3×#47992
C3×#47932
C3×#30823
#810133