Finite Group Databasebeta

← C3×#78996 #11865088

Subgroups — C3×#78996 #11865088

Order 1152.

1473 conjugacy classes of subgroups.

The subgroup lattice has 801 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1010C211yesmaximal, characteristic, complemented
2C3×#5822C211yesmaximal, characteristic, complemented
3C3×#5748C211yesmaximal, characteristic, complemented
4C3×#5526C211yesmaximal, characteristic, complemented
5C32×#421C211yesmaximal, characteristic, complemented
6C2×C3×#824C211yesmaximal, characteristic, complemented
7C3×#5005C211yesmaximal, characteristic, complemented
8C3×#4827C214yesmaximal, complemented
9C3×#4826C214yesmaximal, complemented
10C3×#3020—31nomaximal
11#78996C311yesmaximal, characteristic, direct product factor
12C2×C32×#41C2211yescharacteristic
13C3×#1010—22no—
14C3×#1010—22no—
15C3×#1010—22no—
16C3×#1010C2214yes—
17C2×C3×D3×Q8—21no—
18C2×C3×#237—21no—
19C2×C3×#237—22no—
20C2×C3×#235—21no—
21C2×C3×#235C2211yescharacteristic
22C2×C3×#235C2211yescharacteristic
23C22×C3×Dic6—21no—
24C22×C3×Dic6C2211yescharacteristic
25C2×C32×M16C2211yescharacteristic
26C32×#117C2211yescharacteristic
27C3×#951C2212yescomplemented
28C3×#950—22no—
29C3×#949C2212yescomplemented
30C3×#942—21no—
31C3×#932—21no—
32C2×C3×#208C2211yescharacteristic
33C3×#909—21no—
34C3×#909C2212yescomplemented
35C3×#908—21no—
36C3×#908C2212yescomplemented
37C3×#904—22no—
38C3×#897—22no—
39C3×#886—22no—
40C3×#875C2212yescomplemented
41C3×#869C2212yescomplemented
42C32×#104C2214yescomplemented
43C3×#824C2214yescomplemented
44C3×#805C2214yescomplemented
45C2×C3×2−1+4—31no—
46C2×#1010C2×C311yescharacteristic, complemented
47C3×#575—31no—
48C3×#575—31no—
49C3×#536—31no—
50#5822C2×C311yescharacteristic, complemented
51#5748C2×C311yescharacteristic, complemented
52#5526C2×C311yescharacteristic, complemented
53C3×#456—34no—
54C3×#454—34no—
55C3×#421—21no—
56C3×#421—31no—
57C3×#421D311yescharacteristic, complemented
58C3×#421C2×C311yescharacteristic, complemented
59C2×C3×#101—31no—
60C2×#824C2×C311yescharacteristic, complemented
61#5005C2×C311yescharacteristic, complemented
62#4827C2×C314yescomplemented
63#4826C2×C314yescomplemented
64C32×#41—21no—
65C32×#41—21no—
66C32×#41D412yes—
67C32×#41C2312yes—
68C2×C32×Q8D411yescharacteristic
69C2×C32×D4—21no—
70C2×C32×D4D411yescharacteristic
71C22×C32×C4—21no—
72C22×C32×C4C2311yescharacteristic
73C2×C3×#67—22no—
74C2×C3×#67—21no—
75C2×C3×#67—21no—
76C22×C3×Dic3—22no—
77C22×C3×Dic3D412yes—
78C3×D3×Q8—24no—
79C3×D3×Q8—24no—
80C3×#237—28no—
81C3×#237—24no—
82C3×#237—24no—
83C3×#237—28no—
84C3×#235—24no—
85C3×#235—21no—
86C3×#235—21no—
87C3×#235—24no—
88C3×#235—21no—
89C3×#235—21no—
90C3×#235—21no—
91C3×#235—21no—
92C3×#235D412yes—
93C3×#235C2312yes—
94C2×C3×D12D411yescharacteristic
95C2×C3×D12C2311yescharacteristic
96C2×C3×C4×D3—22no—
97C2×C3×C4×D3—21no—
98C2×C3×C4×D3—21no—
99C2×C3×Dic6—22no—
100C2×C3×Dic6—24no—
101C2×C3×Dic6—21no—
102C2×C3×Dic6—21no—
103C2×C3×Dic6—21no—
104C2×C3×Dic6—21no—
105C2×C3×Dic6—24no—
106C2×C3×Dic6D412yes—
107C2×C3×Dic6D411yescharacteristic
108C2×C3×Dic6C2311yescharacteristic
109C2×C3×Dic6C2312yes—
110C32×M16—21no—
111C32×M16C2312yes—
112C2×C32×C8—21no—
113C32×C4⋊C4—21no—
114C32×C22⋊C4—21no—
115C32×C42C2312yes—
116C3×#216—22no—
117C3×#215—22no—
118C3×#214—22no—
119C3×#213—22no—
120C3×(C2×D3)⋊C4—24no—
121C3×C4⋊Dic3—24no—
122C3×#208—21no—
123C3×#208C2312yes—
124C2×C3×C3⋊C8—21no—
125C3×Dic12—22no—
126C3×D24—22no—
127C3×#204—22no—
128C3×#204—22no—
129#3020—31noSylow
130C3×2−1+4—34no—
131C3×2−1+4—62no—
132C3×2−1+4—62no—
133C3×2−1+4—62no—
134C2×C3×#41—21no—
135C2×C3×#41—31no—
136C2×C3×#41—31no—
137C2×C3×#41—61no—
138C2×C3×#41—62no—
139C2×C3×#41—61no—
140C2×C3×#41C2×D311yescharacteristic
141C2×C3×#41C22×C311yescharacteristic
142C22×C3×Q8—31no—
143C22×C3×Q8—61no—
144C22×C3×Q8—61no—
145#1010—22no—
146#1010—22no—
147#1010—22no—
148#1010C22×C314yes—
149C2×D3×Q8—21no—
150C2×#237—21no—
151C2×#237—22no—
152C2×#235—21no—
153C2×#235C22×C311yescharacteristic
154C2×#235C22×C311yescharacteristic
155C22×Dic6—21no—
156C22×Dic6C22×C311yescharacteristic
157C3×#137—32no—
158C3×#137—32no—
159C3×#137—61no—
160C3×#137—61no—
161C3×AGL(1,ℤ/8)—32no—
162C3×AGL(1,ℤ/8)—32no—
163C3×AGL(1,ℤ/8)—61no—
164C3×AGL(1,ℤ/8)—61no—
165C3×#135—62no—
166C3×#135—62no—
167C2×C3×M16—21no—
168C2×C3×M16—31no—
169C2×C3×M16C2×D311yescharacteristic
170C2×C3×M16C22×C311yescharacteristic
171C3×C4⋊Q8—32no—
172C3×#124—32no—
173C3×#123—62no—
174C3×C22⋊Q8—62no—
175C3×#117—21no—
176C3×#117C2×D311yescharacteristic
177C3×#117C22×C311yescharacteristic
178#951C22×C312yescomplemented
179#950—22no—
180#949C22×C312yescomplemented
181#942—21no—
182#932—21no—
183C2×#208C22×C311yescharacteristic
184#909—21no—
185#909C22×C312yescomplemented
186#908—21no—
187#908C22×C312yescomplemented
188#904—22no—
189#897—22no—
190#886—22no—
191#875C22×C312yescomplemented
192#869C22×C312yescomplemented
193C3×#104—24no—
194C3×#104—34no—
195C3×#104C2×D314yescomplemented
196C3×#104C22×C314yescomplemented
197C3×#101—34no—
198#824C22×C314yescomplemented
199#805C22×C314yescomplemented
200C23×C32—21no—
201C23×C32C2×D411yescharacteristic
202C22×C3×D3—21no—
203C22×C3×D3—21no—
204C32×Q8—21no—
205C32×Q8C2×D412yes—
206C32×D4—22no—
207C32×D4—22no—
208C32×D4—21no—
209C32×D4C2×D412yes—
210C2×C32×C4—21no—
211C2×C32×C4—22no—
212C2×C32×C4—22no—
213C2×C32×C4—22no—
214C2×C32×C4C2×D411yescharacteristic
215C2×C32×C4C2×D411yescharacteristic
216C2×C32×C4C2×D411yescharacteristic
217C2×C32×C4C2×D411yescharacteristic
218C2×C32×C4C2×D411yescharacteristic
219C2×C32×C4C2411yescharacteristic
220C3×#67—28no—
221C3×#67—22no—
222C3×#67—22no—
223C3×#67—41no—
224C3×#67—41no—
225C2×C3×Dic3—28no—
226C2×C3×Dic3—22no—
227C2×C3×Dic3—21no—
228C2×C3×Dic3—22no—
229C2×C3×Dic3—21no—
230C2×C3×Dic3C2×D414yes—
231C3×D12—21no—
232C3×D12—21no—
233C3×D12—21no—
234C3×D12C2×D412yes—
235C3×C4×D3—28no—
236C3×C4×D3—22no—
237C3×C4×D3—22no—
238C3×C4×D3—41no—
239C3×C4×D3—41no—
240C3×Dic6—28no—
241C3×Dic6—22no—
242C3×Dic6—21no—
243C3×Dic6—22no—
244C3×Dic6—22no—
245C3×Dic6—22no—
246C3×Dic6—21no—
247C3×Dic6—21no—
248C3×Dic6C2×D412yes—
249C32×C8—22no—
250C3×C3⋊C8—22no—
251C2×2−1+4—31no—
252#575—31no—
253#575—31no—
254#536—31no—
255#456—34no—
256#454—34no—
257#421—31no—
258#421C3×D311yescharacteristic, complemented
259C2×#101—31no—
260C3×#41—21no—
261C3×#41—21no—
262C3×#41—21no—
263C3×#41—21no—
264C3×#41—22no—
265C3×#41—22no—
266C3×#41—32no—
267C3×#41—32no—
268C3×#41—41no—
269C3×#41—41no—
270C3×#41—64no—
271C3×#41—64no—
272C3×#41—68no—
273C3×#41—68no—
274C3×#41—64no—
275C3×#41—64no—
276C3×#41—61no—
277C3×#41—61no—
278C3×#41—61no—
279C3×#41—61no—
280C3×#41—61no—
281C3×#41—61no—
282C3×#41D1212yes—
283C3×#41C3×D412yes—
284C3×#41C22×D312yes—
285C3×#41C23×C312yes—
286C2×C3×Q8—21no—
287C2×C3×Q8—32no—
288C2×C3×Q8—32no—
289C2×C3×Q8—31no—
290C2×C3×Q8—31no—
291C2×C3×Q8—64no—
292C2×C3×Q8—62no—
293C2×C3×Q8—64no—
294C2×C3×Q8—64no—
295C2×C3×Q8—64no—
296C2×C3×Q8—61no—
297C2×C3×Q8—61no—
298C2×C3×Q8—61no—
299C2×C3×Q8—61no—
300C2×C3×Q8D1211yescharacteristic
301C2×C3×Q8C3×D411yescharacteristic
302C2×C3×D4—21no—
303C2×C3×D4—21no—
304C2×C3×D4—21no—
305C2×C3×D4—31no—
306C2×C3×D4—31no—
307C2×C3×D4—41no—
308C2×C3×D4—62no—
309C2×C3×D4—61no—
310C2×C3×D4—61no—
311C2×C3×D4D1211yescharacteristic
312C2×C3×D4C3×D411yescharacteristic
313C22×C3×C4—21no—
314C22×C3×C4—21no—
315C22×C3×C4—21no—
316C22×C3×C4—32no—
317C22×C3×C4—41no—
318C22×C3×C4—62no—
319C22×C3×C4—62no—
320C22×C3×C4—61no—
321C22×C3×C4—61no—
322C22×C3×C4C22×D311yescharacteristic
323C22×C3×C4C23×C311yescharacteristic
324C2×#67—22no—
325C2×#67—21no—
326C2×#67—21no—
327C22×Dic3—22no—
328C22×Dic3C3×D412yes—
329D3×Q8—24no—
330D3×Q8—24no—
331#237—28no—
332#237—24no—
333#237—24no—
334#237—28no—
335#235—24no—
336#235—21no—
337#235—21no—
338#235—24no—
339#235—21no—
340#235—21no—
341#235—21no—
342#235—21no—
343#235C3×D412yes—
344#235C23×C312yes—
345C2×D12C3×D411yescharacteristic
346C2×D12C23×C311yescharacteristic
347C2×C4×D3—22no—
348C2×C4×D3—21no—
349C2×C4×D3—21no—
350C2×Dic6—22no—
351C2×Dic6—24no—
352C2×Dic6—21no—
353C2×Dic6—21no—
354C2×Dic6—21no—
355C2×Dic6—21no—
356C2×Dic6—24no—
357C2×Dic6C3×D412yes—
358C2×Dic6C3×D411yescharacteristic
359C2×Dic6C23×C311yescharacteristic
360C2×Dic6C23×C312yes—
361C3×Q16—62no—
362C3×Q16—62no—
363C3×SD16—62no—
364C3×SD16—62no—
365C3×SD16—62no—
366C3×SD16—62no—
367C3×D8—62no—
368C3×D8—62no—
369C3×M16—21no—
370C3×M16—21no—
371C3×M16—22no—
372C3×M16—32no—
373C3×M16—41no—
374C3×M16—61no—
375C3×M16C22×D312yes—
376C3×M16C23×C312yes—
377C2×C3×C8—21no—
378C2×C3×C8—21no—
379C2×C3×C8—41no—
380C2×C3×C8—61no—
381C3×C4⋊C4—21no—
382C3×C4⋊C4—21no—
383C3×C4⋊C4—41no—
384C3×C4⋊C4—64no—
385C3×C22⋊C4—21no—
386C3×C22⋊C4—21no—
387C3×C22⋊C4—41no—
388C3×C22⋊C4—64no—
389C3×C42—22no—
390C3×C42C22×D312yes—
391C3×C42C23×C312yes—
392#216—22no—
393#215—22no—
394#214—22no—
395#213—22no—
396(C2×D3)⋊C4—24no—
397C4⋊Dic3—24no—
398#208—21no—
399#208C23×C312yes—
400C2×C3⋊C8—21no—
401Dic12—22no—
402D24—22no—
403#204—22no—
404#204—22no—
405C22×C32—22no—
406C22×C32—41no—
407C22×C32—42no—
408C22×C32#12011yescharacteristic
409C22×C32#12011yescharacteristic
410C22×C32C22×D411yescharacteristic
411C2×C3×D3—22no—
412C2×C3×D3—42no—
413C2×C3×D3—42no—
414C2×C3×D3—41no—
415C32×C4—22no—
416C32×C4—42no—
417C32×C4#12011yescharacteristic
418C32×C4#12011yescharacteristic
419C32×C4C22×D411yescharacteristic
420C32×C4C22×D411yescharacteristic
421C3×Dic3—24no—
422C3×Dic3—22no—
423C3×Dic3—41no—
4242−1+4—34no—
4252−1+4—62no—
4262−1+4—62no—
4272−1+4—62no—
428C2×#41—31no—
429C2×#41—31no—
430C2×#41—61no—
431C2×#41—62no—
432C2×#41—61no—
433C2×#41C2×C3×D311yescharacteristic
434C22×Q8—31no—
435C22×Q8—61no—
436C22×Q8—61no—
437#137—32no—
438#137—32no—
439#137—61no—
440#137—61no—
441AGL(1,ℤ/8)—32no—
442AGL(1,ℤ/8)—32no—
443AGL(1,ℤ/8)—61no—
444AGL(1,ℤ/8)—61no—
445#135—62no—
446#135—62no—
447C2×M16—31no—
448C2×M16C2×C3×D311yescharacteristic
449C4⋊Q8—32no—
450#124—32no—
451#123—62no—
452C22⋊Q8—62no—
453#117C2×C3×D311yescharacteristic
454#104—34no—
455#104C2×C3×D314yescomplemented
456#101—34no—
457C23×C3—21no—
458C23×C3—21no—
459C23×C3—21no—
460C23×C3—41no—
461C23×C3—61no—
462C23×C3—61no—
463C23×C3D3×D411yescharacteristic
464C23×C3C2×C3×D411yescharacteristic
465C22×D3—21no—
466C22×D3—21no—
467C3×Q8—21no—
468C3×Q8—21no—
469C3×Q8—22no—
470C3×Q8—32no—
471C3×Q8—41no—
472C3×Q8—68no—
473C3×Q8—62no—
474C3×Q8—62no—
475C3×Q8—61no—
476C3×Q8—62no—
477C3×Q8—62no—
478C3×Q8—61no—
479C3×Q8—61no—
480C3×Q8C2×D1212yes—
481C3×Q8C2×C3×D412yes—
482C3×D4—22no—
483C3×D4—22no—
484C3×D4—22no—
485C3×D4—22no—
486C3×D4—21no—
487C3×D4—21no—
488C3×D4—22no—
489C3×D4—32no—
490C3×D4—41no—
491C3×D4—42no—
492C3×D4—42no—
493C3×D4—68no—
494C3×D4—62no—
495C3×D4—62no—
496C3×D4—61no—
497C3×D4—61no—
498C3×D4—61no—
499C3×D4—121no—
500C3×D4—121no—
501C3×D4C2×D1212yes—
502C3×D4C2×C3×D412yes—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—22no—
506C2×C3×C4—22no—
507C2×C3×C4—22no—
508C2×C3×C4—22no—
509C2×C3×C4—22no—
510C2×C3×C4—22no—
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—34no—
518C2×C3×C4—42no—
519C2×C3×C4—42no—
520C2×C3×C4—41no—
521C2×C3×C4—42no—
522C2×C3×C4—68no—
523C2×C3×C4—68no—
524C2×C3×C4—62no—
525C2×C3×C4—62no—
526C2×C3×C4—61no—
527C2×C3×C4—62no—
528C2×C3×C4—62no—
529C2×C3×C4—61no—
530C2×C3×C4—121no—
531C2×C3×C4—121no—
532C2×C3×C4C2×D1211yescharacteristic
533C2×C3×C4C2×D1211yescharacteristic
534C2×C3×C4D3×D411yescharacteristic
535C2×C3×C4D3×D411yescharacteristic
536C2×C3×C4D3×D411yescharacteristic
537C2×C3×C4C2×C3×D411yescharacteristic
538C2×C3×C4C2×C3×D411yescharacteristic
539C2×C3×C4C2×C3×D411yescharacteristic
540C2×C3×C4C2×C3×D411yescharacteristic
541C2×C3×C4C2×C3×D411yescharacteristic
542C2×C3×C4C23×D311yescharacteristic
543C2×C3×C4C24×C311yescharacteristic
544#67—28no—
545#67—22no—
546#67—22no—
547#67—41no—
548#67—41no—
549C2×Dic3—28no—
550C2×Dic3—22no—
551C2×Dic3—21no—
552C2×Dic3—22no—
553C2×Dic3—21no—
554C2×Dic3C2×C3×D414yes—
555D12—21no—
556D12—21no—
557D12—21no—
558D12C2×C3×D412yes—
559C4×D3—28no—
560C4×D3—22no—
561C4×D3—22no—
562C4×D3—41no—
563C4×D3—41no—
564Dic6—28no—
565Dic6—22no—
566Dic6—21no—
567Dic6—22no—
568Dic6—22no—
569Dic6—22no—
570Dic6—21no—
571Dic6—21no—
572Dic6C2×C3×D412yes—
573C3×C8—22no—
574C3×C8—22no—
575C3×C8—42no—
576C3×C8—62no—
577C3⋊C8—22no—
578C2×C32—21no—
579C2×C32—21no—
580C2×C32—21no—
581C2×C32—42no—
582C2×C32C2×#12011yescharacteristic
583C3×D3—42no—
584C3×D3—81no—
585#41—21no—
586#41—21no—
587#41—32no—
588#41—32no—
589#41—64no—
590#41—64no—
591#41—68no—
592#41—68no—
593#41—64no—
594#41—64no—
595#41—61no—
596#41—61no—
597#41—61no—
598#41—61no—
599#41—61no—
600#41—61no—
601#41C3×D1212yes—
602#41C22×C3×D312yes—
603C2×Q8—32no—
604C2×Q8—32no—
605C2×Q8—31no—
606C2×Q8—31no—
607C2×Q8—64no—
608C2×Q8—62no—
609C2×Q8—64no—
610C2×Q8—64no—
611C2×Q8—64no—
612C2×Q8—61no—
613C2×Q8—61no—
614C2×Q8—61no—
615C2×Q8—61no—
616C2×Q8C3×D1211yescharacteristic
617C2×D4—21no—
618C2×D4—31no—
619C2×D4—31no—
620C2×D4—62no—
621C2×D4—61no—
622C2×D4—61no—
623C2×D4C3×D1211yescharacteristic
624C22×C4—21no—
625C22×C4—32no—
626C22×C4—62no—
627C22×C4—62no—
628C22×C4—61no—
629C22×C4—61no—
630C22×C4C22×C3×D311yescharacteristic
631Q16—62no—
632Q16—62no—
633SD16—62no—
634SD16—62no—
635SD16—62no—
636SD16—62no—
637D8—62no—
638D8—62no—
639M16—21no—
640M16—32no—
641M16—61no—
642M16C22×C3×D312yes—
643C2×C8—21no—
644C2×C8—61no—
645C4⋊C4—21no—
646C4⋊C4—64no—
647C22⋊C4—21no—
648C22⋊C4—64no—
649C42C22×C3×D312yes—
650C22×C3—22no—
651C22×C3—22no—
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—21no—
655C22×C3—42no—
656C22×C3—41no—
657C22×C3—41no—
658C22×C3—42no—
659C22×C3—42no—
660C22×C3—62no—
661C22×C3—81no—
662C22×C3—82no—
663C22×C3—122no—
664C22×C3—122no—
665C22×C3—121no—
666C22×C3#88211yescharacteristic
667C22×C3#88211yescharacteristic
668C22×C3C3×#12011yescharacteristic
669C22×C3C3×#12011yescharacteristic
670C22×C3C2×D3×D411yescharacteristic
671C22×C3C22×C3×D411yescharacteristic
672C2×D3—22no—
673C2×D3—42no—
674C2×D3—42no—
675C2×D3—41no—
676C3×C4—22no—
677C3×C4—22no—
678C3×C4—21no—
679C3×C4—21no—
680C3×C4—21no—
681C3×C4—21no—
682C3×C4—42no—
683C3×C4—42no—
684C3×C4—42no—
685C3×C4—64no—
686C3×C4—62no—
687C3×C4—82no—
688C3×C4—121no—
689C3×C4#88211yescharacteristic
690C3×C4#88211yescharacteristic
691C3×C4C3×#12011yescharacteristic
692C3×C4C3×#12011yescharacteristic
693C3×C4C22×D1211yescharacteristic
694C3×C4C2×D3×D411yescharacteristic
695C3×C4C22×C3×D411yescharacteristic
696C3×C4C22×C3×D411yescharacteristic
697Dic3—24no—
698Dic3—22no—
699Dic3—41no—
700C32#302011yescharacteristic, complemented, Sylow
701C23—21no—
702C23—61no—
703C23—61no—
704C23C3×D3×D411yescharacteristic
705Q8—21no—
706Q8—32no—
707Q8—68no—
708Q8—62no—
709Q8—62no—
710Q8—61no—
711Q8—62no—
712Q8—62no—
713Q8—61no—
714Q8—61no—
715Q8C2×C3×D1212yes—
716D4—22no—
717D4—22no—
718D4—21no—
719D4—32no—
720D4—68no—
721D4—62no—
722D4—62no—
723D4—61no—
724D4—61no—
725D4—61no—
726D4—121no—
727D4—121no—
728D4C2×C3×D1212yes—
729C2×C4—21no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—34no—
734C2×C4—68no—
735C2×C4—68no—
736C2×C4—62no—
737C2×C4—62no—
738C2×C4—61no—
739C2×C4—62no—
740C2×C4—62no—
741C2×C4—61no—
742C2×C4—121no—
743C2×C4—121no—
744C2×C4C2×C3×D1211yescharacteristic
745C2×C4C2×C3×D1211yescharacteristic
746C2×C4C3×D3×D411yescharacteristic
747C2×C4C3×D3×D411yescharacteristic
748C2×C4C3×D3×D411yescharacteristic
749C2×C4C23×C3×D311yescharacteristic
750C8—22no—
751C8—62no—
752C2×C3—21no—
753C2×C3—21no—
754C2×C3—21no—
755C2×C3—21no—
756C2×C3—21no—
757C2×C3—21no—
758C2×C3—21no—
759C2×C3—41no—
760C2×C3—41no—
761C2×C3—41no—
762C2×C3—42no—
763C2×C3—42no—
764C2×C3—82no—
765C2×C3—122no—
766C2×C3—241no—
767C2×C3C2×#88211yescharacteristic
768C2×C3C2×C3×#12011yescharacteristic
769D3—42no—
770D3—81no—
771C22—22no—
772C22—41no—
773C22—42no—
774C22—62no—
775C22—122no—
776C22—122no—
777C22—121no—
778C22C3×#88211yescharacteristic
779C22C3×#88211yescharacteristic
780C22C2×C3×D3×D411yescharacteristic
781C4—22no—
782C4—42no—
783C4—64no—
784C4—62no—
785C4—121no—
786C4C3×#88211yescharacteristic
787C4C3×#88211yescharacteristic
788C4C22×C3×D1211yescharacteristic
789C4C2×C3×D3×D411yescharacteristic
790C3—21no—
791C3#7899611yescharacteristic, direct product factor
792C3C3×#302011yescharacteristic, complemented
793C2—21no—
794C2—21no—
795C2—21no—
796C2—42no—
797C2—122no—
798C2—241no—
799C2C2×C3×#88211yescharacteristic
subgroupG/H
centerC2×C3C2×#882
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#421C2
socleC2×C32C2×#120
hypercenterC3×#421D3
hypocenterC3C3×#3020
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C22×C3×C4 ◁ C3×#421

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1010C2semidirect
2. C3×#5822C2semidirect
3. C3×#5748C2semidirect
4. C3×#5526C2semidirect
5. C32×#421C2semidirect
6. C2×C3×#824C2semidirect
7. C3×#5005C2semidirect
8. C3×#4827C2semidirect
9. C3×#4826C2semidirect
11. #78996C3direct (N × H)
27. C3×#951C22semidirect
29. C3×#949C22semidirect
34. C3×#909C22semidirect
36. C3×#908C22semidirect
40. C3×#875C22semidirect
41. C3×#869C22semidirect
42. C32×#104C22semidirect
43. C3×#824C22semidirect
44. C3×#805C22semidirect
46. C2×#1010C2×C3semidirect
50. #5822C2×C3semidirect
51. #5748C2×C3semidirect
52. #5526C2×C3semidirect
57. C3×#421D3semidirect
58. C3×#421C2×C3semidirect
60. C2×#824C2×C3semidirect
61. #5005C2×C3semidirect
62. #4827C2×C3semidirect
63. #4826C2×C3semidirect
178. #951C22×C3semidirect
180. #949C22×C3semidirect
185. #909C22×C3semidirect
187. #908C22×C3semidirect
191. #875C22×C3semidirect
192. #869C22×C3semidirect
195. C3×#104C2×D3semidirect
196. C3×#104C22×C3semidirect
198. #824C22×C3semidirect
199. #805C22×C3semidirect
258. #421C3×D3semidirect
455. #104C2×C3×D3semidirect
700. C32#3020semidirect
791. C3#78996direct (N × H)
792. C3C3×#3020semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10102
C3×#58222
C3×#57482
C3×#55262
C32×#4212
C2×C3×#8242
C3×#50052
C3×#48272
C3×#48262
C3×#30203
#789963