Finite Group Databasebeta

← C3×#82525 #11865748

Subgroups — C3×#82525 #11865748

Order 1152.

1147 conjugacy classes of subgroups.

The subgroup lattice has 687 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C4×#41C211yesmaximal, characteristic, complemented
2C2×C3×#950C212yesmaximal, complemented
3C3×#5477C211yesmaximal, characteristic, complemented
4C3×#5031C211yesmaximal, characteristic, complemented
5C3×#5028C212yesmaximal, complemented
6C3×#5027C211yesmaximal, characteristic, complemented
7C3×#5019C211yesmaximal, characteristic, complemented
8C3×#5016C212yesmaximal, complemented
9C3×#5015C211yesmaximal, characteristic, complemented
10C3×#5002C212yesmaximal, complemented
11C2×C3×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
12C3×#3035—31nomaximal
13#82525C311yesmaximal, characteristic, direct product factor
14C2×C32×#41C2211yescharacteristic
15C2×C3×#235C2212yes—
16C32×C4×Q8C2211yescharacteristic
17C32×C4×Q8C2211yescharacteristic
18C32×C4×D4—21no—
19C32×C4×D4—21no—
20C32×C4×D4C2211yescharacteristic
21C32×C4×D4C2211yescharacteristic
22C32×#117—21no—
23C32×#117C2211yescharacteristic
24C2×C32×C42—21no—
25C2×C32×C42C2211yescharacteristic
26C3×#950—28no—
27C2×C3×#216C2212yes—
28C2×C3×#215C2212yes—
29C2×C3×#214C2212yes—
30C2×C3×#213C2212yes—
31C3×#930—21no—
32C3×#930—21no—
33C22×C3×C3⋊C8C2212yes—
34C3×#875C2212yes—
35C3×#874C2211yescharacteristic
36C3×C4×D12—21no—
37C3×C4×D12—21no—
38C3×#869C2211yescharacteristic
39C3×#810C2212yes—
40C3×#810C2212yes—
41C3×#809C2212yes—
42C3×#809C2212yes—
43C3×C4⋊(C3⋊C8)C2211yescharacteristic
44C3×C4⋊(C3⋊C8)C2212yes—
45C3×C4⋊(C3⋊C8)C2211yescharacteristic
46C2×C3×#135—32no—
47C3×#532—31no—
48C3×C4×#41—21no—
49C3×C4×#41D311yescharacteristic, complemented
50C3×C4×#41C2×C311yescharacteristic, complemented
51C2×#950C2×C312yescomplemented
52#5477C2×C311yescharacteristic, complemented
53C3×#464—32no—
54C3×#463—32no—
55C3×#462—31no—
56C3×#461—31no—
57C3×#460—31no—
58C3×#459—31no—
59C2×C3×C4⋊C8—31no—
60C3×#416—32no—
61#5031C2×C311yescharacteristic, complemented
62#5028C2×C312yescomplemented
63#5027C2×C311yescharacteristic, complemented
64#5019C2×C311yescharacteristic, complemented
65#5016C2×C312yescomplemented
66#5015C2×C311yescharacteristic, complemented
67#5002C2×C312yescomplemented
68C2×C4⋊(C3⋊C8)C2×C311yescharacteristic, complemented
69C32×#41—22no—
70C32×#41D414yescomplemented
71C2×C32×Q8C2311yescharacteristic
72C2×C32×D4—21no—
73C2×C32×D4C2311yescharacteristic
74C22×C32×C4—21no—
75C22×C32×C4—21no—
76C22×C32×C4—21no—
77C22×C32×C4D411yescharacteristic
78C22×C32×C4D411yescharacteristic
79C22×C32×C4C2311yescharacteristic
80C2×C3×#67—22no—
81C3×#235—24no—
82C3×#235—24no—
83C2×C3×D12—21no—
84C2×C3×D12—21no—
85C2×C3×D12C2312yes—
86C2×C3×C4×D3—22no—
87C2×C3×Dic6C2312yes—
88C32×C4⋊C4—21no—
89C32×C4⋊C4—21no—
90C32×C4⋊C4C2311yescharacteristic
91C32×C4⋊C4C2311yescharacteristic
92C32×C22⋊C4—21no—
93C32×C22⋊C4—21no—
94C32×C22⋊C4—21no—
95C32×C42—21no—
96C32×C42—21no—
97C32×C42—21no—
98C32×C42D411yescharacteristic
99C32×C42D411yescharacteristic
100C32×C42C2311yescharacteristic
101C32×C42C2311yescharacteristic
102C3×#216—24no—
103C3×#215—24no—
104C3×#214—24no—
105C3×#213—24no—
106C3×(C2×D3)⋊C4—22no—
107C3×(C2×D3)⋊C4—22no—
108C3×C4⋊Dic3—21no—
109C3×C4⋊Dic3—21no—
110C2×C3×C3⋊C8—24no—
111C2×C3×C3⋊C8C2312yes—
112C2×C3×C3⋊C8C2312yes—
113#3035—31noSylow
114C2×C3×#41—21no—
115C2×C3×#41—32no—
116C2×C3×#41C2×D311yescharacteristic
117C2×C3×#41C22×C311yescharacteristic
118C2×#235C22×C312yes—
119C3×#135—68no—
120C2×C3×Q16—32no—
121C2×C3×SD16—32no—
122C2×C3×SD16—32no—
123C2×C3×D8—32no—
124C22×C3×C8—32no—
125C3×C4⋊Q8—31no—
126C3×#127—31no—
127C3×#124—32no—
128C3×#121—61no—
129C3×#121—61no—
130C3×C4×Q8—21no—
131C3×C4×Q8—21no—
132C3×C4×Q8C2×D311yescharacteristic
133C3×C4×Q8C2×D311yescharacteristic
134C3×C4×Q8C22×C311yescharacteristic
135C3×C4×Q8C22×C311yescharacteristic
136C3×C4×D4—22no—
137C3×C4×D4—22no—
138C3×C4×D4—21no—
139C3×C4×D4—21no—
140C3×C4×D4—21no—
141C3×C4×D4—21no—
142C3×C4×D4—21no—
143C3×C4×D4—21no—
144C3×C4×D4—61no—
145C3×C4×D4—61no—
146C3×C4×D4C2×D311yescharacteristic
147C3×C4×D4C2×D311yescharacteristic
148C3×C4×D4C22×C311yescharacteristic
149C3×C4×D4C22×C311yescharacteristic
150C3×#117—22no—
151C3×#117—21no—
152C3×#117—21no—
153C3×#117—21no—
154C3×#117C2×D311yescharacteristic
155C3×#117C22×C311yescharacteristic
156C2×C3×C42—22no—
157C2×C3×C42—21no—
158C2×C3×C42—21no—
159C2×C3×C42—21no—
160C2×C3×C42C2×D311yescharacteristic
161C2×C3×C42C22×C311yescharacteristic
162#950—28no—
163C2×#216C22×C312yes—
164C2×#215C22×C312yes—
165C2×#214C22×C312yes—
166C2×#213C22×C312yes—
167#930—21no—
168#930—21no—
169C22×C3⋊C8C22×C312yes—
170#875C22×C312yes—
171#874C22×C311yescharacteristic
172C4×D12—21no—
173C4×D12—21no—
174#869C22×C311yescharacteristic
175C3×C4⋊C8—31no—
176C3×C4⋊C8—31no—
177C3×C4⋊C8—32no—
178C3×#103—32no—
179C3×#103—32no—
180C3×#102—32no—
181C3×#102—32no—
182#810C22×C312yes—
183#810C22×C312yes—
184#809C22×C312yes—
185#809C22×C312yes—
186C4⋊(C3⋊C8)C22×C311yescharacteristic
187C4⋊(C3⋊C8)C22×C312yes—
188C4⋊(C3⋊C8)C22×C311yescharacteristic
189C23×C32—21no—
190C23×C32C2×D411yescharacteristic
191C22×C3×D3—22no—
192C32×Q8—21no—
193C32×Q8C2×D412yes—
194C32×D4—24no—
195C32×D4—21no—
196C32×D4C2×D412yes—
197C2×C32×C4—21no—
198C2×C32×C4—24no—
199C2×C32×C4—21no—
200C2×C32×C4—21no—
201C2×C32×C4—22no—
202C2×C32×C4—41no—
203C2×C32×C4—42no—
204C2×C32×C4—42no—
205C2×C32×C4C2×D412yes—
206C2×C32×C4C2×D411yescharacteristic
207C2×C32×C4C2×D411yescharacteristic
208C2×C32×C4C2×D411yescharacteristic
209C2×C32×C4C2×D411yescharacteristic
210C2×C32×C4C2×D411yescharacteristic
211C2×C32×C4#4112yes—
212C2×C32×C4C2411yescharacteristic
213C3×#67—44no—
214C2×C3×Dic3—22no—
215C3×D12—22no—
216C3×D12—22no—
217C3×D12—42no—
218C3×D12—42no—
219C3×C4×D3—44no—
220C3×Dic6—22no—
221C3×Dic6—22no—
222C3×C3⋊C8—22no—
223C3×C3⋊C8—22no—
224C2×#135—32no—
225#532—31no—
226C4×#41C3×D311yescharacteristic, complemented
227#464—32no—
228#463—32no—
229#462—31no—
230#461—31no—
231#460—31no—
232#459—31no—
233C2×C4⋊C8—31no—
234#416—32no—
235C3×#41—24no—
236C3×#41—22no—
237C3×#41—22no—
238C3×#41—24no—
239C3×#41—64no—
240C3×#41—64no—
241C3×#41D1214yescomplemented
242C3×#41C3×D414yescomplemented
243C2×C3×Q8—21no—
244C2×C3×Q8—32no—
245C2×C3×Q8C22×D311yescharacteristic
246C2×C3×Q8C23×C311yescharacteristic
247C2×C3×D4—22no—
248C2×C3×D4—21no—
249C2×C3×D4—21no—
250C2×C3×D4—21no—
251C2×C3×D4—32no—
252C2×C3×D4—62no—
253C2×C3×D4—61no—
254C2×C3×D4—61no—
255C2×C3×D4C22×D311yescharacteristic
256C2×C3×D4C23×C311yescharacteristic
257C22×C3×C4—22no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—22no—
261C22×C3×C4—22no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—62no—
270C22×C3×C4#6711yescharacteristic
271C22×C3×C4#6711yescharacteristic
272C22×C3×C4C3×D411yescharacteristic
273C22×C3×C4C3×D411yescharacteristic
274C22×C3×C4C22×D311yescharacteristic
275C22×C3×C4C23×C311yescharacteristic
276C2×#67—22no—
277#235—24no—
278#235—24no—
279C2×D12—21no—
280C2×D12—21no—
281C2×D12C23×C312yes—
282C2×C4×D3—22no—
283C2×Dic6C23×C312yes—
284C3×Q16—64no—
285C3×SD16—64no—
286C3×SD16—64no—
287C3×D8—64no—
288C2×C3×C8—32no—
289C2×C3×C8—32no—
290C2×C3×C8—64no—
291C3×C4⋊C4—22no—
292C3×C4⋊C4—22no—
293C3×C4⋊C4—21no—
294C3×C4⋊C4—21no—
295C3×C4⋊C4—21no—
296C3×C4⋊C4—21no—
297C3×C4⋊C4—21no—
298C3×C4⋊C4—21no—
299C3×C4⋊C4—61no—
300C3×C4⋊C4—61no—
301C3×C4⋊C4C22×D311yescharacteristic
302C3×C4⋊C4C22×D311yescharacteristic
303C3×C4⋊C4C23×C311yescharacteristic
304C3×C4⋊C4C23×C311yescharacteristic
305C3×C22⋊C4—22no—
306C3×C22⋊C4—22no—
307C3×C22⋊C4—22no—
308C3×C22⋊C4—21no—
309C3×C22⋊C4—21no—
310C3×C22⋊C4—21no—
311C3×C22⋊C4—21no—
312C3×C22⋊C4—21no—
313C3×C22⋊C4—21no—
314C3×C22⋊C4—62no—
315C3×C22⋊C4—62no—
316C3×C42—22no—
317C3×C42—22no—
318C3×C42—22no—
319C3×C42—21no—
320C3×C42—21no—
321C3×C42—21no—
322C3×C42—21no—
323C3×C42—21no—
324C3×C42—21no—
325C3×C42—21no—
326C3×C42—21no—
327C3×C42—21no—
328C3×C42—21no—
329C3×C42#6711yescharacteristic
330C3×C42#6711yescharacteristic
331C3×C42C3×D411yescharacteristic
332C3×C42C3×D411yescharacteristic
333C3×C42C22×D311yescharacteristic
334C3×C42C22×D311yescharacteristic
335C3×C42C23×C311yescharacteristic
336C3×C42C23×C311yescharacteristic
337#216—24no—
338#215—24no—
339#214—24no—
340#213—24no—
341(C2×D3)⋊C4—22no—
342(C2×D3)⋊C4—22no—
343C4⋊Dic3—21no—
344C4⋊Dic3—21no—
345C2×C3⋊C8—24no—
346C2×C3⋊C8C23×C312yes—
347C2×C3⋊C8C23×C312yes—
348C22×C32—22no—
349C22×C32—21no—
350C22×C32—21no—
351C22×C32—41no—
352C22×C32—41no—
353C22×C32#12112yes—
354C22×C32C22×D411yescharacteristic
355C2×C3×D3—42no—
356C2×C3×D3—42no—
357C2×C3×D3—42no—
358C32×C4—22no—
359C32×C4—21no—
360C32×C4—21no—
361C32×C4—21no—
362C32×C4—41no—
363C32×C4—41no—
364C32×C4#12112yes—
365C32×C4#13512yescomplemented
366C32×C4C22×D411yescharacteristic
367C32×C4C2×#4111yescharacteristic
368C3×Dic3—42no—
369C2×#41—32no—
370C2×#41C2×C3×D311yescharacteristic
371#135—68no—
372C2×Q16—32no—
373C2×SD16—32no—
374C2×SD16—32no—
375C2×D8—32no—
376C22×C8—32no—
377C4⋊Q8—31no—
378#127—31no—
379#124—32no—
380#121—61no—
381#121—61no—
382C4×Q8C2×C3×D311yescharacteristic
383C4×Q8C2×C3×D311yescharacteristic
384C4×D4—21no—
385C4×D4—21no—
386C4×D4—61no—
387C4×D4—61no—
388C4×D4C2×C3×D311yescharacteristic
389C4×D4C2×C3×D311yescharacteristic
390#117—21no—
391#117C2×C3×D311yescharacteristic
392C2×C42—21no—
393C2×C42C2×C3×D311yescharacteristic
394C4⋊C8—31no—
395C4⋊C8—31no—
396C4⋊C8—32no—
397#103—32no—
398#103—32no—
399#102—32no—
400#102—32no—
401C23×C3—22no—
402C23×C3—21no—
403C23×C3—21no—
404C23×C3—21no—
405C23×C3—62no—
406C23×C3C2×#6711yescharacteristic
407C23×C3C2×C3×D411yescharacteristic
408C22×D3—22no—
409C3×Q8—22no—
410C3×Q8—21no—
411C3×Q8—21no—
412C3×Q8—22no—
413C3×Q8—62no—
414C3×Q8—62no—
415C3×Q8C2×D1212yes—
416C3×Q8C2×C3×D412yes—
417C3×D4—28no—
418C3×D4—22no—
419C3×D4—24no—
420C3×D4—24no—
421C3×D4—21no—
422C3×D4—21no—
423C3×D4—22no—
424C3×D4—62no—
425C3×D4—62no—
426C3×D4—122no—
427C3×D4—124no—
428C3×D4—122no—
429C3×D4C2×D1212yes—
430C3×D4C2×C3×D412yes—
431C2×C3×C4—22no—
432C2×C3×C4—28no—
433C2×C3×C4—21no—
434C2×C3×C4—21no—
435C2×C3×C4—24no—
436C2×C3×C4—22no—
437C2×C3×C4—24no—
438C2×C3×C4—22no—
439C2×C3×C4—22no—
440C2×C3×C4—22no—
441C2×C3×C4—21no—
442C2×C3×C4—21no—
443C2×C3×C4—21no—
444C2×C3×C4—21no—
445C2×C3×C4—21no—
446C2×C3×C4—22no—
447C2×C3×C4—22no—
448C2×C3×C4—21no—
449C2×C3×C4—21no—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
452C2×C3×C4—21no—
453C2×C3×C4—42no—
454C2×C3×C4—41no—
455C2×C3×C4—41no—
456C2×C3×C4—42no—
457C2×C3×C4—44no—
458C2×C3×C4—42no—
459C2×C3×C4—42no—
460C2×C3×C4—44no—
461C2×C3×C4—42no—
462C2×C3×C4—42no—
463C2×C3×C4—62no—
464C2×C3×C4—124no—
465C2×C3×C4C2×D1212yes—
466C2×C3×C4#23512yes—
467C2×C3×C4C2×#6711yescharacteristic
468C2×C3×C4C2×#6711yescharacteristic
469C2×C3×C4C2×#6711yescharacteristic
470C2×C3×C4C2×#6711yescharacteristic
471C2×C3×C4C2×#6711yescharacteristic
472C2×C3×C4C2×C3×D412yes—
473C2×C3×C4C2×C3×D411yescharacteristic
474C2×C3×C4C2×C3×D411yescharacteristic
475C2×C3×C4C2×C3×D411yescharacteristic
476C2×C3×C4C2×C3×D411yescharacteristic
477C2×C3×C4C2×C3×D411yescharacteristic
478C2×C3×C4C3×#4112yes—
479C2×C3×C4C23×D311yescharacteristic
480C2×C3×C4C24×C311yescharacteristic
481#67—44no—
482C2×Dic3—22no—
483D12—22no—
484D12—22no—
485D12—42no—
486D12—42no—
487C4×D3—44no—
488Dic6—22no—
489Dic6—22no—
490C3×C8—62no—
491C3×C8—62no—
492C3⋊C8—22no—
493C3⋊C8—22no—
494C2×C32—22no—
495C2×C32—42no—
496C2×C32C2×#12111yescharacteristic
497C2×C32C2×#13511yescharacteristic
498C2×C32#57511yescharacteristic
499C3×D3—82no—
500#41—22no—
501#41—64no—
502#41—64no—
503#41C3×D1214yescomplemented
504C2×Q8—32no—
505C2×Q8C22×C3×D311yescharacteristic
506C2×D4—21no—
507C2×D4—32no—
508C2×D4—62no—
509C2×D4—61no—
510C2×D4—61no—
511C2×D4C22×C3×D311yescharacteristic
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—62no—
516C22×C4C3×#6711yescharacteristic
517C22×C4C3×#6711yescharacteristic
518C22×C4C22×C3×D311yescharacteristic
519Q16—64no—
520SD16—64no—
521SD16—64no—
522D8—64no—
523C2×C8—32no—
524C2×C8—32no—
525C2×C8—64no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—61no—
529C4⋊C4—61no—
530C4⋊C4C22×C3×D311yescharacteristic
531C4⋊C4C22×C3×D311yescharacteristic
532C22⋊C4—21no—
533C22⋊C4—21no—
534C22⋊C4—21no—
535C22⋊C4—62no—
536C22⋊C4—62no—
537C42—21no—
538C42—21no—
539C42—21no—
540C42C3×#6711yescharacteristic
541C42C3×#6711yescharacteristic
542C42C22×C3×D311yescharacteristic
543C42C22×C3×D311yescharacteristic
544C22×C3—21no—
545C22×C3—21no—
546C22×C3—21no—
547C22×C3—21no—
548C22×C3—24no—
549C22×C3—22no—
550C22×C3—22no—
551C22×C3—22no—
552C22×C3—21no—
553C22×C3—41no—
554C22×C3—41no—
555C22×C3—42no—
556C22×C3—42no—
557C22×C3—41no—
558C22×C3—41no—
559C22×C3—41no—
560C22×C3—41no—
561C22×C3—122no—
562C22×C3—122no—
563C22×C3—122no—
564C22×C3#93012yes—
565C22×C3C3×#12112yes—
566C22×C3C22×#6711yescharacteristic
567C22×C3C22×C3×D411yescharacteristic
568C2×D3—42no—
569C2×D3—42no—
570C2×D3—42no—
571C3×C4—24no—
572C3×C4—22no—
573C3×C4—21no—
574C3×C4—21no—
575C3×C4—21no—
576C3×C4—22no—
577C3×C4—21no—
578C3×C4—21no—
579C3×C4—21no—
580C3×C4—22no—
581C3×C4—22no—
582C3×C4—22no—
583C3×C4—21no—
584C3×C4—21no—
585C3×C4—41no—
586C3×C4—41no—
587C3×C4—42no—
588C3×C4—42no—
589C3×C4—41no—
590C3×C4—41no—
591C3×C4—41no—
592C3×C4—41no—
593C3×C4—122no—
594C3×C4#93012yes—
595C3×C4#95012yescomplemented
596C3×C4C3×#12112yes—
597C3×C4C3×#13512yescomplemented
598C3×C4C22×D1211yescharacteristic
599C3×C4C2×#23511yescharacteristic
600C3×C4C22×C3×D411yescharacteristic
601C3×C4C2×C3×#4111yescharacteristic
602Dic3—42no—
603C32#303511yescharacteristic, complemented, Sylow
604C23—21no—
605C23—62no—
606C23C2×C3×#6711yescharacteristic
607Q8—21no—
608Q8—62no—
609Q8—62no—
610Q8C2×C3×D1212yes—
611D4—24no—
612D4—21no—
613D4—62no—
614D4—62no—
615D4—122no—
616D4—124no—
617D4—122no—
618D4C2×C3×D1212yes—
619C2×C4—21no—
620C2×C4—24no—
621C2×C4—22no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—41no—
625C2×C4—42no—
626C2×C4—42no—
627C2×C4—62no—
628C2×C4—124no—
629C2×C4C2×C3×D1212yes—
630C2×C4C3×#23512yes—
631C2×C4C2×C3×#6711yescharacteristic
632C2×C4C2×C3×#6711yescharacteristic
633C2×C4C2×C3×#6711yescharacteristic
634C2×C4C2×C3×#6711yescharacteristic
635C2×C4C2×C3×#6711yescharacteristic
636C2×C4C23×C3×D311yescharacteristic
637C8—62no—
638C8—62no—
639C2×C3—22no—
640C2×C3—22no—
641C2×C3—21no—
642C2×C3—21no—
643C2×C3—21no—
644C2×C3—42no—
645C2×C3—44no—
646C2×C3—42no—
647C2×C3—42no—
648C2×C3—242no—
649C2×C3C2×#93011yescharacteristic
650C2×C3C2×#95011yescharacteristic
651C2×C3#582211yescharacteristic
652C2×C3C2×C3×#12111yescharacteristic
653C2×C3C2×C3×#13511yescharacteristic
654C2×C3C3×#57511yescharacteristic
655D3—82no—
656C22—21no—
657C22—21no—
658C22—22no—
659C22—41no—
660C22—41no—
661C22—122no—
662C22—122no—
663C22—122no—
664C22C3×#93012yes—
665C22C22×C3×#6711yescharacteristic
666C4—22no—
667C4—21no—
668C4—21no—
669C4—21no—
670C4—41no—
671C4—41no—
672C4—122no—
673C4C3×#93012yes—
674C4C3×#95012yescomplemented
675C4C22×C3×D1211yescharacteristic
676C4C2×C3×#23511yescharacteristic
677C3—21no—
678C3#8252511yescharacteristic, direct product factor
679C3C3×#303511yescharacteristic, complemented
680C2—22no—
681C2—42no—
682C2—242no—
683C2C2×C3×#93011yescharacteristic
684C2C2×C3×#95011yescharacteristic
685C2C3×#582211yescharacteristic
subgroupG/H
centerC2×C3×C4C2×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×C4×#41C2
socleC22×C32C22×D4
hypercenterC3×C4×#41D3
hypocenterC3C3×#3035
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C2×C3×C42 ◁ C3×C4×#41

Complements

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

NH ≅ G/Ntype
1. C32×C4×#41C2semidirect
2. C2×C3×#950C2semidirect
3. C3×#5477C2semidirect
4. C3×#5031C2semidirect
5. C3×#5028C2semidirect
6. C3×#5027C2semidirect
7. C3×#5019C2semidirect
8. C3×#5016C2semidirect
9. C3×#5015C2semidirect
10. C3×#5002C2semidirect
11. C2×C3×C4⋊(C3⋊C8)C2semidirect
13. #82525C3direct (N × H)
49. C3×C4×#41D3semidirect
50. C3×C4×#41C2×C3semidirect
51. C2×#950C2×C3semidirect
52. #5477C2×C3semidirect
61. #5031C2×C3semidirect
62. #5028C2×C3semidirect
63. #5027C2×C3semidirect
64. #5019C2×C3semidirect
65. #5016C2×C3semidirect
66. #5015C2×C3semidirect
67. #5002C2×C3semidirect
68. C2×C4⋊(C3⋊C8)C2×C3semidirect
70. C32×#41D4semidirect
226. C4×#41C3×D3semidirect
241. C3×#41D12semidirect
242. C3×#41C3×D4semidirect
365. C32×C4#135semidirect
503. #41C3×D12semidirect
595. C3×C4#950semidirect
597. C3×C4C3×#135semidirect
603. C32#3035semidirect
674. C4C3×#950semidirect
678. C3#82525direct (N × H)
679. C3C3×#3035semidirect

Maximal subgroups

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

subgroupindex
C32×C4×#412
C2×C3×#9502
C3×#54772
C3×#50312
C3×#50282
C3×#50272
C3×#50192
C3×#50162
C3×#50152
C3×#50022
C2×C3×C4⋊(C3⋊C8)2
C3×#30353
#825253