Finite Group Databasebeta

← C3×#80703 #11882289

Subgroups — C3×#80703 #11882289

Order 1152.

863 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5600C211yesmaximal, characteristic, complemented
2C3×#5596C211yesmaximal, characteristic, complemented
3C32×#466C211yesmaximal, characteristic, complemented
4C3×#5153C211yesmaximal, characteristic, complemented
5C3×#5150C211yesmaximal, characteristic, complemented
6C3×#5114C211yesmaximal, characteristic, complemented
7C2×C3×Dic3⋊C8C211yesmaximal, characteristic, complemented
8C3×#5041C211yesmaximal, characteristic, complemented
9C3×#5038C211yesmaximal, characteristic, complemented
10C3×#4891C211yesmaximal, characteristic, complemented
11C3×#4875C211yesmaximal, characteristic, complemented
12C3×#4787C211yesmaximal, characteristic, complemented
13C3×#4763C211yesmaximal, characteristic, complemented
14C3×#4762C211yesmaximal, characteristic, complemented
15C3×#4761C211yesmaximal, characteristic, complemented
16C3×#3247—31nomaximal
17#80703C311yesmaximal, characteristic, direct product factor
18C2×C3×#237—21no—
19C2×C32×D8C2211yescharacteristic
20C22×C32×C8C2211yescharacteristic
21C32×#121C2211yescharacteristic
22C32×#121C2211yescharacteristic
23C3×#940C2211yescharacteristic
24C3×#939—21no—
25C3×#936C2211yescharacteristic
26C3×#935—21no—
27C3×D4×Dic3—21no—
28C3×D4×Dic3C2211yescharacteristic
29C3×D4×Dic3C2211yescharacteristic
30C2×C3×#214C2211yescharacteristic
31C2×C3×#213C2211yescharacteristic
32C3×#930C2211yescharacteristic
33C3×#924C2211yescharacteristic
34C2×C3×C4×Dic3C2211yescharacteristic
35C22×C3×C3⋊C8C2211yescharacteristic
36C2×C3×#204C2211yescharacteristic
37C3×#893C2211yescharacteristic
38C3×#890C2211yescharacteristic
39C3×#888C2211yescharacteristic
40C3×#887C2211yescharacteristic
41C3×#885—21no—
42C3×#67⋊C4—21no—
43C3×#879—21no—
44C3×#877—21no—
45C32×#107C2211yescharacteristic
46C32×#102C2211yescharacteristic
47C32×#102C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×#817C2211yescharacteristic
52C3×#816C2211yescharacteristic
53C3×Dic3⋊C8C2211yescharacteristic
54C3×Dic3⋊C8C2211yescharacteristic
55C3×Dic3⋊C8C2211yescharacteristic
56C3×Dic3⋊C8C2211yescharacteristic
57C3×#810C2211yescharacteristic
58C3×#809C2211yescharacteristic
59C3×#808C2211yescharacteristic
60C3×#807C2211yescharacteristic
61C3×#532—31no—
62C3×#529—31no—
63#5600C2×C311yescharacteristic, complemented
64#5596C2×C311yescharacteristic, complemented
65C3×#478—31no—
66C3×#478—31no—
67C3×#477—31no—
68C3×#476—31no—
69C3×#466—21no—
70C3×#466—31no—
71C3×#466D311yescharacteristic, complemented
72C3×#466C2×C311yescharacteristic, complemented
73C3×#465—31no—
74C3×#465—31no—
75C3×#463—31no—
76C3×#463—31no—
77C3×#460—31no—
78C3×#459—31no—
79C2×C3×C4⋊C8—31no—
80#5153C2×C311yescharacteristic, complemented
81#5150C2×C311yescharacteristic, complemented
82#5114C2×C311yescharacteristic, complemented
83C2×Dic3⋊C8C2×C311yescharacteristic, complemented
84#5041C2×C311yescharacteristic, complemented
85#5038C2×C311yescharacteristic, complemented
86#4891C2×C311yescharacteristic, complemented
87#4875C2×C311yescharacteristic, complemented
88#4787C2×C311yescharacteristic, complemented
89#4763C2×C311yescharacteristic, complemented
90#4762C2×C311yescharacteristic, complemented
91#4761C2×C311yescharacteristic, complemented
92C2×C32×D4—21no—
93C2×C32×D4—21no—
94C2×C32×D4C2311yescharacteristic
95C2×C32×D4C2311yescharacteristic
96C22×C32×C4C2311yescharacteristic
97C2×C3×#67—21no—
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C22×C3×Dic3—21no—
101C22×C3×Dic3—21no—
102C22×C3×Dic3D411yescharacteristic
103C22×C3×Dic3D411yescharacteristic
104C3×#237—44no—
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3—21no—
107C2×C3×Dic6—21no—
108C2×C3×Dic6C2311yescharacteristic
109C32×D8—41no—
110C2×C32×C8—41no—
111C2×C32×C8C2311yescharacteristic
112C2×C32×C8C2311yescharacteristic
113C32×C4⋊C4C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115C32×C22⋊C4—21no—
116C32×C22⋊C4—21no—
117C3×#217—21no—
118C3×#217—21no—
119C3×#217—21no—
120C3×#217—21no—
121C3×#217—21no—
122C3×#214—41no—
123C3×#213—41no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C3×C4×Dic3—21no—
134C3×C4×Dic3D411yescharacteristic
135C3×C4×Dic3D411yescharacteristic
136C3×C4×Dic3C2311yescharacteristic
137C3×C4×Dic3C2311yescharacteristic
138C2×C3×C3⋊C8—41no—
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C3×#204—41no—
142#3247—31noSylow
143C2×C3×#41—61no—
144C2×#237—21no—
145C2×C3×SD16—31no—
146C2×C3×SD16—31no—
147C2×C3×D8—21no—
148C2×C3×D8—31no—
149C2×C3×D8C2×D311yescharacteristic
150C2×C3×D8C22×C311yescharacteristic
151C22×C3×C8—21no—
152C22×C3×C8—31no—
153C22×C3×C8C2×D311yescharacteristic
154C22×C3×C8C22×C311yescharacteristic
155C3×C4⋊Q8—31no—
156C3×#127—31no—
157C3×#126—61no—
158C3×#125—31no—
159C3×#124—31no—
160C3×#124—61no—
161C3×#123—61no—
162C3×C22⋊Q8—31no—
163C3×#121—21no—
164C3×#121—21no—
165C3×#121—31no—
166C3×#121—61no—
167C3×#121C2×D311yescharacteristic
168C3×#121C2×D311yescharacteristic
169C3×#121C22×C311yescharacteristic
170C3×#121C22×C311yescharacteristic
171C3×C4×Q8—31no—
172C3×C4×D4—31no—
173C3×C4×D4—31no—
174C3×C4×D4—31no—
175C3×C4×D4—61no—
176C3×C4×D4—61no—
177C3×#117—61no—
178C2×C3×C42—31no—
179#940C22×C311yescharacteristic
180#939—21no—
181#936C22×C311yescharacteristic
182#935—21no—
183D4×Dic3—21no—
184D4×Dic3C22×C311yescharacteristic
185D4×Dic3C22×C311yescharacteristic
186C2×#214C22×C311yescharacteristic
187C2×#213C22×C311yescharacteristic
188#930C22×C311yescharacteristic
189#924C22×C311yescharacteristic
190C2×C4×Dic3C22×C311yescharacteristic
191C22×C3⋊C8C22×C311yescharacteristic
192C2×#204C22×C311yescharacteristic
193#893C22×C311yescharacteristic
194#890C22×C311yescharacteristic
195#888C22×C311yescharacteristic
196#887C22×C311yescharacteristic
197#885—21no—
198#67⋊C4—21no—
199#879—21no—
200#877—21no—
201C3×#107—21no—
202C3×#107—31no—
203C3×#107C2×D311yescharacteristic
204C3×#107C22×C311yescharacteristic
205C3×#106—31no—
206C3×#106—31no—
207C3×C4⋊C8—31no—
208C3×C4⋊C8—31no—
209C3×C4⋊C8—31no—
210C3×C4⋊C8—31no—
211C3×#103—31no—
212C3×#103—31no—
213C3×#102—21no—
214C3×#102—21no—
215C3×#102—31no—
216C3×#102—31no—
217C3×#102—31no—
218C3×#102—31no—
219C3×#102C2×D311yescharacteristic
220C3×#102C2×D311yescharacteristic
221C3×#102C22×C311yescharacteristic
222C3×#102C22×C311yescharacteristic
223#832C22×C311yescharacteristic
224#832C22×C311yescharacteristic
225#821C22×C311yescharacteristic
226#817C22×C311yescharacteristic
227#816C22×C311yescharacteristic
228Dic3⋊C8C22×C311yescharacteristic
229Dic3⋊C8C22×C311yescharacteristic
230Dic3⋊C8C22×C311yescharacteristic
231Dic3⋊C8C22×C311yescharacteristic
232#810C22×C311yescharacteristic
233#809C22×C311yescharacteristic
234#808C22×C311yescharacteristic
235#807C22×C311yescharacteristic
236C23×C32—21no—
237C23×C32—21no—
238C23×C32C2×D411yescharacteristic
239C22×C3×D3—21no—
240C32×D4—21no—
241C32×D4—21no—
242C32×D4—21no—
243C32×D4—21no—
244C32×D4—42no—
245C32×D4—42no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2411yescharacteristic
252C3×#67—42no—
253C3×#67—42no—
254C3×#67—42no—
255C2×C3×Dic3—22no—
256C2×C3×Dic3—22no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—42no—
261C2×C3×Dic3—42no—
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C3×D12—21no—
267C3×D12—21no—
268C3×C4×D3—42no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271C3×Dic6—42no—
272C32×C8—21no—
273C32×C8—21no—
274C3×C3⋊C8—21no—
275C3×C3⋊C8—21no—
276#532—31no—
277#529—31no—
278#478—31no—
279#478—31no—
280#477—31no—
281#476—31no—
282#466—31no—
283#466C3×D311yescharacteristic, complemented
284#465—31no—
285#465—31no—
286#463—31no—
287#463—31no—
288#460—31no—
289#459—31no—
290C2×C4⋊C8—31no—
291C3×#41—124no—
292C2×C3×Q8—31no—
293C2×C3×Q8—61no—
294C2×C3×D4—21no—
295C2×C3×D4—21no—
296C2×C3×D4—21no—
297C2×C3×D4—21no—
298C2×C3×D4—21no—
299C2×C3×D4—21no—
300C2×C3×D4—31no—
301C2×C3×D4—41no—
302C2×C3×D4—41no—
303C2×C3×D4—61no—
304C2×C3×D4—61no—
305C2×C3×D4—61no—
306C2×C3×D4C22×D311yescharacteristic
307C2×C3×D4C22×D311yescharacteristic
308C2×C3×D4C23×C311yescharacteristic
309C2×C3×D4C23×C311yescharacteristic
310C22×C3×C4—21no—
311C22×C3×C4—31no—
312C22×C3×C4—31no—
313C22×C3×C4—61no—
314C22×C3×C4—61no—
315C22×C3×C4—61no—
316C22×C3×C4C22×D311yescharacteristic
317C22×C3×C4C23×C311yescharacteristic
318C2×#67—21no—
319C2×#67—21no—
320C2×#67—21no—
321C22×Dic3—21no—
322C22×Dic3—21no—
323C22×Dic3C3×D411yescharacteristic
324C22×Dic3C3×D411yescharacteristic
325#237—44no—
326C2×D12C23×C311yescharacteristic
327C2×C4×D3—21no—
328C2×Dic6—21no—
329C2×Dic6C23×C311yescharacteristic
330C3×SD16—121no—
331C3×SD16—121no—
332C3×D8—41no—
333C3×D8—41no—
334C3×D8—42no—
335C3×D8—121no—
336C2×C3×C8—21no—
337C2×C3×C8—21no—
338C2×C3×C8—31no—
339C2×C3×C8—31no—
340C2×C3×C8—41no—
341C2×C3×C8—41no—
342C2×C3×C8—42no—
343C2×C3×C8—121no—
344C2×C3×C8C22×D311yescharacteristic
345C2×C3×C8C22×D311yescharacteristic
346C2×C3×C8C23×C311yescharacteristic
347C2×C3×C8C23×C311yescharacteristic
348C3×C4⋊C4—21no—
349C3×C4⋊C4—21no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4—61no—
355C3×C4⋊C4—61no—
356C3×C4⋊C4—61no—
357C3×C4⋊C4C22×D311yescharacteristic
358C3×C4⋊C4C22×D311yescharacteristic
359C3×C4⋊C4C23×C311yescharacteristic
360C3×C4⋊C4C23×C311yescharacteristic
361C3×C22⋊C4—21no—
362C3×C22⋊C4—21no—
363C3×C22⋊C4—21no—
364C3×C22⋊C4—21no—
365C3×C22⋊C4—41no—
366C3×C22⋊C4—41no—
367C3×C22⋊C4—61no—
368C3×C22⋊C4—61no—
369C3×C22⋊C4—61no—
370C3×C22⋊C4—61no—
371C3×C22⋊C4—61no—
372C3×C22⋊C4—61no—
373C3×C22⋊C4—61no—
374C3×C42—31no—
375C3×C42—31no—
376C3×C42—31no—
377C3×C42—31no—
378C3×C42—61no—
379#217—21no—
380#217—21no—
381#217—21no—
382#217—21no—
383#217—21no—
384#214—41no—
385#213—41no—
386(C2×D3)⋊C4—21no—
387(C2×D3)⋊C4—21no—
388C4⋊Dic3—21no—
389C4⋊Dic3C23×C311yescharacteristic
390C4⋊Dic3C23×C311yescharacteristic
391Dic3⋊C4—21no—
392Dic3⋊C4—21no—
393Dic3⋊C4—21no—
394Dic3⋊C4—21no—
395C4×Dic3—21no—
396C4×Dic3C3×D411yescharacteristic
397C4×Dic3C3×D411yescharacteristic
398C4×Dic3C23×C311yescharacteristic
399C4×Dic3C23×C311yescharacteristic
400C2×C3⋊C8—41no—
401C2×C3⋊C8C23×C311yescharacteristic
402C2×C3⋊C8C23×C311yescharacteristic
403#204—41no—
404C22×C32—21no—
405C22×C32—21no—
406C22×C32—41no—
407C22×C32—41no—
408C22×C32—41no—
409C22×C32—41no—
410C22×C32—41no—
411C22×C32—41no—
412C22×C32AGL(1,ℤ/8)12yes—
413C22×C32C22×D411yescharacteristic
414C2×C3×D3—41no—
415C2×C3×D3—41no—
416C2×C3×D3—41no—
417C32×C4—21no—
418C32×C4—41no—
419C32×C4—41no—
420C32×C4H(5,𝔽2)11yescharacteristic
421C32×C42−1+411yescharacteristic
422C3×Dic3—21no—
423C3×Dic3—21no—
424C3×Dic3—21no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C3×Dic3—41no—
428C3×Dic3#13512yes—
429C2×#41—61no—
430C2×SD16—31no—
431C2×SD16—31no—
432C2×D8—31no—
433C2×D8C2×C3×D311yescharacteristic
434C22×C8—31no—
435C22×C8C2×C3×D311yescharacteristic
436C4⋊Q8—31no—
437#127—31no—
438#126—61no—
439#125—31no—
440#124—31no—
441#124—61no—
442#123—61no—
443C22⋊Q8—31no—
444#121—31no—
445#121—61no—
446#121C2×C3×D311yescharacteristic
447#121C2×C3×D311yescharacteristic
448C4×Q8—31no—
449C4×D4—31no—
450C4×D4—31no—
451C4×D4—31no—
452C4×D4—61no—
453C4×D4—61no—
454#117—61no—
455C2×C42—31no—
456#107—31no—
457#107C2×C3×D311yescharacteristic
458#106—31no—
459#106—31no—
460C4⋊C8—31no—
461C4⋊C8—31no—
462C4⋊C8—31no—
463C4⋊C8—31no—
464#103—31no—
465#103—31no—
466#102—31no—
467#102—31no—
468#102—31no—
469#102—31no—
470#102C2×C3×D311yescharacteristic
471#102C2×C3×D311yescharacteristic
472C23×C3—21no—
473C23×C3—21no—
474C23×C3—21no—
475C23×C3—21no—
476C23×C3—21no—
477C23×C3—41no—
478C23×C3—41no—
479C23×C3—61no—
480C23×C3D3×D411yescharacteristic
481C23×C3C2×C3×D411yescharacteristic
482C22×D3—21no—
483C3×Q8—61no—
484C3×Q8—61no—
485C3×Q8—122no—
486C3×D4—21no—
487C3×D4—21no—
488C3×D4—21no—
489C3×D4—21no—
490C3×D4—21no—
491C3×D4—21no—
492C3×D4—21no—
493C3×D4—21no—
494C3×D4—41no—
495C3×D4—41no—
496C3×D4—41no—
497C3×D4—41no—
498C3×D4—42no—
499C3×D4—42no—
500C3×D4—42no—
501C3×D4—42no—
502C3×D4—61no—
503C3×D4—61no—
504C3×D4—82no—
505C3×D4—82no—
506C3×D4—122no—
507C3×D4—122no—
508C3×D4—122no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—31no—
520C2×C3×C4—31no—
521C2×C3×C4—31no—
522C2×C3×C4—31no—
523C2×C3×C4—41no—
524C2×C3×C4—41no—
525C2×C3×C4—41no—
526C2×C3×C4—41no—
527C2×C3×C4—62no—
528C2×C3×C4—62no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—122no—
533C2×C3×C4—122no—
534C2×C3×C4—122no—
535C2×C3×C4D3×D411yescharacteristic
536C2×C3×C4C2×C3×D411yescharacteristic
537C2×C3×C4C23×D311yescharacteristic
538C2×C3×C4C24×C311yescharacteristic
539#67—42no—
540#67—42no—
541#67—42no—
542C2×Dic3—22no—
543C2×Dic3—22no—
544C2×Dic3—21no—
545C2×Dic3—21no—
546C2×Dic3—21no—
547C2×Dic3—42no—
548C2×Dic3—42no—
549C2×Dic3C2×C3×D411yescharacteristic
550C2×Dic3C2×C3×D411yescharacteristic
551C2×Dic3C2×C3×D411yescharacteristic
552C2×Dic3C2×C3×D411yescharacteristic
553D12—21no—
554D12—21no—
555C4×D3—42no—
556Dic6—21no—
557Dic6—21no—
558Dic6—42no—
559C3×C8—22no—
560C3×C8—21no—
561C3×C8—21no—
562C3×C8—21no—
563C3×C8—21no—
564C3×C8—41no—
565C3×C8—61no—
566C3×C8—61no—
567C3⋊C8—21no—
568C3⋊C8—21no—
569C2×C32—22no—
570C2×C32—81no—
571C2×C32—81no—
572C2×C32#53711yescharacteristic
573C2×C32C2×#13511yescharacteristic
574C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
575C3×D3—81no—
576#41—124no—
577C2×Q8—31no—
578C2×Q8—61no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—31no—
582C2×D4—61no—
583C2×D4—61no—
584C2×D4—61no—
585C2×D4C22×C3×D311yescharacteristic
586C2×D4C22×C3×D311yescharacteristic
587C22×C4—31no—
588C22×C4—31no—
589C22×C4—61no—
590C22×C4—61no—
591C22×C4—61no—
592C22×C4C22×C3×D311yescharacteristic
593SD16—121no—
594SD16—121no—
595D8—41no—
596D8—121no—
597C2×C8—31no—
598C2×C8—31no—
599C2×C8—41no—
600C2×C8—121no—
601C2×C8C22×C3×D311yescharacteristic
602C2×C8C22×C3×D311yescharacteristic
603C4⋊C4—31no—
604C4⋊C4—31no—
605C4⋊C4—61no—
606C4⋊C4—61no—
607C4⋊C4—61no—
608C4⋊C4—61no—
609C4⋊C4—61no—
610C4⋊C4C22×C3×D311yescharacteristic
611C4⋊C4C22×C3×D311yescharacteristic
612C22⋊C4—21no—
613C22⋊C4—21no—
614C22⋊C4—61no—
615C22⋊C4—61no—
616C22⋊C4—61no—
617C22⋊C4—61no—
618C22⋊C4—61no—
619C22⋊C4—61no—
620C22⋊C4—61no—
621C42—31no—
622C42—31no—
623C42—31no—
624C42—31no—
625C42—61no—
626C22×C3—21no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—22no—
631C22×C3—21no—
632C22×C3—41no—
633C22×C3—41no—
634C22×C3—41no—
635C22×C3—41no—
636C22×C3—41no—
637C22×C3—41no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—41no—
642C22×C3—41no—
643C22×C3—41no—
644C22×C3—41no—
645C22×C3—41no—
646C22×C3—81no—
647C22×C3—81no—
648C22×C3—81no—
649C22×C3—81no—
650C22×C3—81no—
651C22×C3—81no—
652C22×C3—121no—
653C22×C3—121no—
654C22×C3—121no—
655C22×C3#91112yes—
656C22×C3C3×AGL(1,ℤ/8)12yes—
657C22×C3C2×D3×D411yescharacteristic
658C22×C3C22×C3×D411yescharacteristic
659C2×D3—41no—
660C2×D3—41no—
661C2×D3—41no—
662C3×C4—21no—
663C3×C4—21no—
664C3×C4—21no—
665C3×C4—21no—
666C3×C4—32no—
667C3×C4—41no—
668C3×C4—41no—
669C3×C4—41no—
670C3×C4—41no—
671C3×C4—41no—
672C3×C4—61no—
673C3×C4—61no—
674C3×C4—61no—
675C3×C4—81no—
676C3×C4—81no—
677C3×C4—121no—
678C3×C4—121no—
679C3×C4—121no—
680C3×C4#100411yescharacteristic
681C3×C4#101011yescharacteristic
682C3×C4C3×H(5,𝔽2)11yescharacteristic
683C3×C4C3×2−1+411yescharacteristic
684Dic3—21no—
685Dic3—21no—
686Dic3—21no—
687Dic3—41no—
688Dic3—41no—
689Dic3—41no—
690Dic3C3×#13512yes—
691C32#324711yescharacteristic, complemented, Sylow
692C23—21no—
693C23—21no—
694C23—61no—
695C23C3×D3×D411yescharacteristic
696Q8—61no—
697Q8—61no—
698Q8—122no—
699D4—21no—
700D4—21no—
701D4—21no—
702D4—21no—
703D4—42no—
704D4—42no—
705D4—61no—
706D4—61no—
707D4—122no—
708D4—122no—
709D4—122no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—31no—
715C2×C4—31no—
716C2×C4—31no—
717C2×C4—31no—
718C2×C4—62no—
719C2×C4—62no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—122no—
724C2×C4—122no—
725C2×C4—122no—
726C2×C4C3×D3×D411yescharacteristic
727C2×C4C23×C3×D311yescharacteristic
728C8—21no—
729C8—21no—
730C8—61no—
731C8—61no—
732C2×C3—22no—
733C2×C3—22no—
734C2×C3—21no—
735C2×C3—21no—
736C2×C3—21no—
737C2×C3—42no—
738C2×C3—81no—
739C2×C3—81no—
740C2×C3—81no—
741C2×C3—81no—
742C2×C3—161no—
743C2×C3—161no—
744C2×C3—241no—
745C2×C3#559711yescharacteristic
746C2×C3C2×#91111yescharacteristic
747C2×C3D3×#13511yescharacteristic
748C2×C3C3×#53711yescharacteristic
749C2×C3C2×C3×#13511yescharacteristic
750C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
751D3—81no—
752C22—21no—
753C22—21no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—121no—
761C22—121no—
762C22—121no—
763C22C3×#91112yes—
764C22C2×C3×D3×D411yescharacteristic
765C4—21no—
766C4—32no—
767C4—41no—
768C4—41no—
769C4—61no—
770C4—61no—
771C4—61no—
772C4—121no—
773C4—121no—
774C4—121no—
775C4C3×#100411yescharacteristic
776C4C3×#101011yescharacteristic
777C3—21no—
778C3#8070311yescharacteristic, direct product factor
779C3C3×#324711yescharacteristic, complemented
780C2—22no—
781C2—81no—
782C2—81no—
783C2—241no—
784C2C3×#559711yescharacteristic
785C2C2×C3×#91111yescharacteristic
786C2C3×D3×#13511yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#466C2
socleC22×C32C22×D4
hypercenterC3×#466D3
hypocenterC3C3×#3247
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#466

Complements

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

NH ≅ G/Ntype
1. C3×#5600C2semidirect
2. C3×#5596C2semidirect
3. C32×#466C2semidirect
4. C3×#5153C2semidirect
5. C3×#5150C2semidirect
6. C3×#5114C2semidirect
7. C2×C3×Dic3⋊C8C2semidirect
8. C3×#5041C2semidirect
9. C3×#5038C2semidirect
10. C3×#4891C2semidirect
11. C3×#4875C2semidirect
12. C3×#4787C2semidirect
13. C3×#4763C2semidirect
14. C3×#4762C2semidirect
15. C3×#4761C2semidirect
17. #80703C3direct (N × H)
63. #5600C2×C3semidirect
64. #5596C2×C3semidirect
71. C3×#466D3semidirect
72. C3×#466C2×C3semidirect
80. #5153C2×C3semidirect
81. #5150C2×C3semidirect
82. #5114C2×C3semidirect
83. C2×Dic3⋊C8C2×C3semidirect
84. #5041C2×C3semidirect
85. #5038C2×C3semidirect
86. #4891C2×C3semidirect
87. #4875C2×C3semidirect
88. #4787C2×C3semidirect
89. #4763C2×C3semidirect
90. #4762C2×C3semidirect
91. #4761C2×C3semidirect
283. #466C3×D3semidirect
691. C32#3247semidirect
778. C3#80703direct (N × H)
779. C3C3×#3247semidirect

Maximal subgroups

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

subgroupindex
C3×#56002
C3×#55962
C32×#4662
C3×#51532
C3×#51502
C3×#51142
C2×C3×Dic3⋊C82
C3×#50412
C3×#50382
C3×#48912
C3×#48752
C3×#47872
C3×#47632
C3×#47622
C3×#47612
C3×#32473
#807033