Finite Group Databasebeta

← C3×#87264 #11904735

Subgroups — C3×#87264 #11904735

Order 1152.

3489 conjugacy classes of subgroups.

The subgroup lattice has 695 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×#41C211yesmaximal, characteristic, complemented
2C2×C3×#1010C211yesmaximal, characteristic, complemented
3C3×#5833C213yesmaximal, complemented
4C3×#5831C212yesmaximal, complemented
5C3×#5827C211yesmaximal, characteristic, complemented
6C3×#5825C213yesmaximal, complemented
7C3×#5824C216yesmaximal, complemented
8C3×Q8×#67C212yesmaximal, complemented
9C3×#5806C216yesmaximal, complemented
10C3×#5791C213yesmaximal, complemented
11C2×C3×#924C213yesmaximal, complemented
12C3×#3489—31nomaximal
13#87264C311yesmaximal, characteristic, direct product factor
14C2×C32×#41—28no—
15C2×C32×#41C2213yes—
16C2×C32×#41C2213yes—
17C2×C32×#41C2211yescharacteristic
18C2×C32×#41C2211yescharacteristic
19C22×C32×Q8C2211yescharacteristic
20C22×C32×D4C2213yes—
21C23×C32×C4C2213yes—
22C3×#1010—28no—
23C2×C3×D3×Q8C2212yescomplemented
24C2×C3×#237C2216yescomplemented
25C2×C3×#235C2213yescomplemented
26C22×C3×Dic6C2213yescomplemented
27C3×#953C2216yes—
28C2×C3×#217C2216yes—
29C3×#946C2216yescomplemented
30C3×Q8×Dic3C2212yescomplemented
31C3×#944C2216yescomplemented
32C3×#939C22112yescomplemented
33C3×#938C2216yescomplemented
34C3×#936C2216yescomplemented
35C3×#935C22112yescomplemented
36C3×D4×Dic3C2216yescomplemented
37C3×#930C2211yescharacteristic
38C3×#930C2213yescomplemented
39C3×#929C2216yescomplemented
40C3×C4×#67C2216yes—
41C3×C4×#67C2216yescomplemented
42C3×#926C2213yescomplemented
43C2×C3×C4⋊Dic3C2213yescomplemented
44C3×#924C2213yes—
45C3×#924C2216yes—
46C3×#924C2216yescomplemented
47C3×#924C2216yescomplemented
48C3×#924C2213yescomplemented
49C2×C3×Dic3⋊C4C2216yescomplemented
50C2×C3×2−1+4—31no—
51C22×C3×#41—21no—
52C22×C3×#41D311yescharacteristic, complemented
53C22×C3×#41C2×C311yescharacteristic, complemented
54C2×#1010C2×C311yescharacteristic, complemented
55C3×D4×Q8—32no—
56C3×#548—32no—
57C3×#547—36no—
58C3×#546—36no—
59C3×#537—33no—
60C3×#536—33no—
61C3×#525—33no—
62C2×C3×C22⋊Q8—33no—
63C3×#520—31no—
64#5833C2×C313yescomplemented
65#5831C2×C312yescomplemented
66#5827C2×C311yescharacteristic, complemented
67#5825C2×C313yescomplemented
68#5824C2×C316yescomplemented
69Q8×#67C2×C312yescomplemented
70#5806C2×C316yescomplemented
71#5791C2×C313yescomplemented
72C2×#924C2×C313yescomplemented
73C24×C32C2313yes—
74C32×#41—24no—
75C32×#41—212no—
76C32×#41—212no—
77C32×#41D418yescomplemented
78C2×C32×Q8—24no—
79C2×C32×Q8C2313yes—
80C2×C32×Q8C2311yescharacteristic
81C2×C32×D4—212no—
82C2×C32×D4C2316yes—
83C2×C32×D4C2313yes—
84C2×C32×D4C2313yes—
85C22×C32×C4—212no—
86C22×C32×C4C2313yes—
87C22×C32×C4C2311yescharacteristic
88C22×C32×C4C2313yes—
89C22×C32×C4C2313yes—
90C22×C32×C4C2313yes—
91C22×C32×C4C2313yes—
92C2×C3×#67C2312yes—
93C2×C3×#67C2316yes—
94C2×C3×#67C2316yes—
95C22×C3×Dic3C2316yes—
96C22×C3×Dic3C2316yes—
97C3×D3×Q8—28no—
98C3×#237—224no—
99C3×#235—212no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3C2316yes—
102C2×C3×Dic6—212no—
103C2×C3×Dic6C2313yes—
104C2×C3×Dic6C2316yes—
105C3×#217C2316yes—
106C3×#217C23112yes—
107C3×#217C2316yes—
108C3×#217C2316yes—
109C3×(C2×D3)⋊C4C2316yes—
110C3×(C2×D3)⋊C4C2312yes—
111C3×C4⋊Dic3C2313yes—
112C3×C4⋊Dic3C2316yes—
113C3×C4⋊Dic3C2311yescharacteristic
114C3×Dic3⋊C4C2316yes—
115C3×Dic3⋊C4C23112yes—
116C3×Dic3⋊C4C2316yes—
117C3×C4×Dic3C2316yes—
118#3489—31noSylow
119C3×2−1+4—68no—
120C2×C3×#41—216no—
121C2×C3×#41—28no—
122C2×C3×#41—28no—
123C2×C3×#41—23no—
124C2×C3×#41—23no—
125C2×C3×#41—21no—
126C2×C3×#41—21no—
127C2×C3×#41—36no—
128C2×C3×#41—33no—
129C2×C3×#41C2×D313yes—
130C2×C3×#41C2×D313yes—
131C2×C3×#41C2×D311yescharacteristic
132C2×C3×#41C2×D311yescharacteristic
133C2×C3×#41C22×C313yes—
134C2×C3×#41C22×C313yes—
135C2×C3×#41C22×C311yescharacteristic
136C2×C3×#41C22×C311yescharacteristic
137C22×C3×Q8—21no—
138C22×C3×Q8—32no—
139C22×C3×Q8—33no—
140C22×C3×Q8C2×D311yescharacteristic
141C22×C3×Q8C22×C311yescharacteristic
142C22×C3×D4—23no—
143C22×C3×D4C2×D313yes—
144C22×C3×D4C22×C313yes—
145C23×C3×C4—23no—
146C23×C3×C4C2×D313yes—
147C23×C3×C4C22×C313yes—
148#1010—28no—
149C2×D3×Q8C22×C312yescomplemented
150C2×#237C22×C316yescomplemented
151C2×#235C22×C313yescomplemented
152C22×Dic6C22×C313yescomplemented
153C3×C4⋊Q8—36no—
154C3×#124—36no—
155C3×#123—312no—
156C3×#123—36no—
157C3×C22⋊Q8—36no—
158C3×C22⋊Q8—33no—
159C3×C22⋊Q8—36no—
160C3×C22⋊Q8—36no—
161C3×C22⋊Q8—36no—
162C3×C22⋊Q8—33no—
163C3×#121—36no—
164C3×#121—312no—
165C3×#121—31no—
166C3×#121—33no—
167C3×#120—36no—
168C3×C4×Q8—32no—
169C3×C4×D4—36no—
170C3×C4×D4—36no—
171C3×C4×D4—36no—
172C3×#117—33no—
173C2×C3×C4⋊C4—36no—
174C2×C3×C4⋊C4—33no—
175C2×C3×C22⋊C4—36no—
176#953C22×C316yes—
177C2×#217C22×C316yes—
178#946C22×C316yescomplemented
179Q8×Dic3C22×C312yescomplemented
180#944C22×C316yescomplemented
181#939C22×C3112yescomplemented
182#938C22×C316yescomplemented
183#936C22×C316yescomplemented
184#935C22×C3112yescomplemented
185D4×Dic3C22×C316yescomplemented
186#930C22×C311yescharacteristic
187#930C22×C313yescomplemented
188#929C22×C316yescomplemented
189C4×#67C22×C316yes—
190C4×#67C22×C316yescomplemented
191#926C22×C313yescomplemented
192C2×C4⋊Dic3C22×C313yescomplemented
193#924C22×C313yes—
194#924C22×C316yes—
195#924C22×C316yescomplemented
196#924C22×C316yescomplemented
197#924C22×C313yescomplemented
198C2×Dic3⋊C4C22×C316yescomplemented
199C23×C32—26no—
200C23×C32—26no—
201C23×C32—43no—
202C23×C32C2413yes—
203C23×C32C2413yes—
204C23×C32C2411yescharacteristic
205C22×C3×D3C2412yes—
206C32×Q8—26no—
207C32×Q8C2×D414yes—
208C32×D4—212no—
209C32×D4—26no—
210C32×D4C2×D4112yes—
211C2×C32×C4—26no—
212C2×C32×C4—22no—
213C2×C32×C4—26no—
214C2×C32×C4—26no—
215C2×C32×C4—26no—
216C2×C32×C4C2×D4112yes—
217C2×C32×C4C2411yescharacteristic
218C2×C32×C4C2413yes—
219C2×C32×C4C2413yes—
220C2×C32×C4C2411yescharacteristic
221C3×#67—212no—
222C3×#67—24no—
223C3×#67—46no—
224C2×C3×Dic3—212no—
225C2×C3×Dic3—46no—
226C2×C3×Dic3C2412yes—
227C2×C3×Dic3C2416yes—
228C2×C3×Dic3C2416yes—
229C3×D12—22no—
230C3×C4×D3—212no—
231C3×Dic6—26no—
232C3×Dic6—212no—
233C2×2−1+4—31no—
234C22×#41C3×D311yescharacteristic, complemented
235D4×Q8—32no—
236#548—32no—
237#547—36no—
238#546—36no—
239#537—33no—
240#536—33no—
241#525—33no—
242C2×C22⋊Q8—33no—
243#520—31no—
244C24×C3—23no—
245C24×C3C22×D313yes—
246C24×C3C23×C313yes—
247C3×#41—28no—
248C3×#41—224no—
249C3×#41—224no—
250C3×#41—24no—
251C3×#41—24no—
252C3×#41—212no—
253C3×#41—212no—
254C3×#41—212no—
255C3×#41—212no—
256C3×#41—28no—
257C3×#41—624no—
258C3×#41—612no—
259C3×#41#6718yescomplemented
260C3×#41C3×D418yescomplemented
261C2×C3×Q8—28no—
262C2×C3×Q8—24no—
263C2×C3×Q8—24no—
264C2×C3×Q8—23no—
265C2×C3×Q8—21no—
266C2×C3×Q8—33no—
267C2×C3×Q8—36no—
268C2×C3×Q8—68no—
269C2×C3×Q8—612no—
270C2×C3×Q8C22×D313yes—
271C2×C3×Q8C22×D311yescharacteristic
272C2×C3×Q8C23×C313yes—
273C2×C3×Q8C23×C311yescharacteristic
274C2×C3×D4—224no—
275C2×C3×D4—212no—
276C2×C3×D4—212no—
277C2×C3×D4—26no—
278C2×C3×D4—23no—
279C2×C3×D4—23no—
280C2×C3×D4—32no—
281C2×C3×D4—36no—
282C2×C3×D4—36no—
283C2×C3×D4—31no—
284C2×C3×D4C22×D316yes—
285C2×C3×D4C22×D313yes—
286C2×C3×D4C22×D313yes—
287C2×C3×D4C23×C316yes—
288C2×C3×D4C23×C313yes—
289C2×C3×D4C23×C313yes—
290C22×C3×C4—224no—
291C22×C3×C4—212no—
292C22×C3×C4—212no—
293C22×C3×C4—21no—
294C22×C3×C4—23no—
295C22×C3×C4—23no—
296C22×C3×C4—23no—
297C22×C3×C4—23no—
298C22×C3×C4—23no—
299C22×C3×C4—36no—
300C22×C3×C4—36no—
301C22×C3×C4—36no—
302C22×C3×C4C22×D313yes—
303C22×C3×C4C22×D313yes—
304C22×C3×C4C22×D313yes—
305C22×C3×C4C22×D311yescharacteristic
306C22×C3×C4C22×D313yes—
307C22×C3×C4C22×D313yes—
308C22×C3×C4C23×C313yes—
309C22×C3×C4C23×C311yescharacteristic
310C22×C3×C4C23×C313yes—
311C22×C3×C4C23×C313yes—
312C22×C3×C4C23×C313yes—
313C22×C3×C4C23×C313yes—
314C2×#67C23×C312yes—
315C2×#67C23×C316yes—
316C2×#67C23×C316yes—
317C22×Dic3C23×C316yes—
318C22×Dic3C23×C316yes—
319D3×Q8—28no—
320#237—224no—
321#235—212no—
322C2×D12C23×C311yescharacteristic
323C2×C4×D3C23×C316yes—
324C2×Dic6—212no—
325C2×Dic6C23×C313yes—
326C2×Dic6C23×C316yes—
327C3×C4⋊C4—36no—
328C3×C4⋊C4—312no—
329C3×C4⋊C4—36no—
330C3×C4⋊C4—33no—
331C3×C4⋊C4—36no—
332C3×C4⋊C4—31no—
333C3×C22⋊C4—36no—
334C3×C22⋊C4—312no—
335C3×C22⋊C4—36no—
336C3×C22⋊C4—36no—
337C3×C22⋊C4—32no—
338C3×C22⋊C4—36no—
339C3×C42—36no—
340#217C23×C316yes—
341#217C23×C3112yes—
342#217C23×C316yes—
343#217C23×C316yes—
344(C2×D3)⋊C4C23×C316yes—
345(C2×D3)⋊C4C23×C312yes—
346C4⋊Dic3C23×C313yes—
347C4⋊Dic3C23×C316yes—
348C4⋊Dic3C23×C311yescharacteristic
349Dic3⋊C4C23×C316yes—
350Dic3⋊C4C23×C3112yes—
351Dic3⋊C4C23×C316yes—
352C4×Dic3C23×C316yes—
353C22×C32—21no—
354C22×C32—21no—
355C22×C32—23no—
356C22×C32—23no—
357C22×C32—23no—
358C22×C32—23no—
359C22×C32—23no—
360C22×C32—412no—
361C22×C32C22×D416yes—
362C22×C322−1+412yescomplemented
363C22×C32C2511yescharacteristic
364C2×C3×D3—22no—
365C2×C3×D3—22no—
366C2×C3×D3—22no—
367C32×C4—21no—
368C32×C4—23no—
369C32×C4C22×D412yes—
370C32×C4C22×D416yes—
371C3×Dic3—26no—
372C3×Dic3—22no—
373C3×Dic3—26no—
3742−1+4—68no—
375C2×#41—28no—
376C2×#41—36no—
377C2×#41—33no—
378C2×#41C2×C3×D313yes—
379C2×#41C2×C3×D313yes—
380C2×#41C2×C3×D311yescharacteristic
381C2×#41C2×C3×D311yescharacteristic
382C22×Q8—32no—
383C22×Q8—33no—
384C22×Q8C2×C3×D311yescharacteristic
385C22×D4C2×C3×D313yes—
386C23×C4C2×C3×D313yes—
387C4⋊Q8—36no—
388#124—36no—
389#123—312no—
390#123—36no—
391C22⋊Q8—36no—
392C22⋊Q8—33no—
393C22⋊Q8—36no—
394C22⋊Q8—36no—
395C22⋊Q8—36no—
396C22⋊Q8—33no—
397#121—312no—
398#121—36no—
399#121—31no—
400#121—33no—
401#120—36no—
402C4×Q8—32no—
403C4×D4—36no—
404C4×D4—36no—
405C4×D4—36no—
406#117—33no—
407C2×C4⋊C4—33no—
408C2×C4⋊C4—36no—
409C2×C22⋊C4—36no—
410C23×C3—212no—
411C23×C3—26no—
412C23×C3—26no—
413C23×C3—26no—
414C23×C3—26no—
415C23×C3—21no—
416C23×C3—23no—
417C23×C3—23no—
418C23×C3—32no—
419C23×C3—46no—
420C23×C3—43no—
421C23×C3—43no—
422C23×C3—46no—
423C23×C3C23×D313yes—
424C23×C3C23×D311yescharacteristic
425C23×C3C23×D313yes—
426C23×C3C24×C313yes—
427C23×C3C24×C313yes—
428C23×C3C24×C311yescharacteristic
429C22×D3C24×C312yes—
430C3×Q8—212no—
431C3×Q8—26no—
432C3×Q8—26no—
433C3×Q8—24no—
434C3×Q8—66no—
435C3×Q8—612no—
436C3×Q8C2×#6714yes—
437C3×Q8C2×C3×D414yes—
438C3×D4—224no—
439C3×D4—212no—
440C3×D4—212no—
441C3×D4—212no—
442C3×D4—26no—
443C3×D4—26no—
444C3×D4—212no—
445C3×D4—64no—
446C3×D4—612no—
447C3×D4—62no—
448C3×D4—126no—
449C3×D4C2×#67112yes—
450C3×D4C2×C3×D4112yes—
451C2×C3×C4—24no—
452C2×C3×C4—212no—
453C2×C3×C4—212no—
454C2×C3×C4—212no—
455C2×C3×C4—212no—
456C2×C3×C4—26no—
457C2×C3×C4—26no—
458C2×C3×C4—22no—
459C2×C3×C4—26no—
460C2×C3×C4—26no—
461C2×C3×C4—26no—
462C2×C3×C4—22no—
463C2×C3×C4—26no—
464C2×C3×C4—26no—
465C2×C3×C4—26no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—23no—
469C2×C3×C4—23no—
470C2×C3×C4—212no—
471C2×C3×C4—32no—
472C2×C3×C4—36no—
473C2×C3×C4—36no—
474C2×C3×C4—612no—
475C2×C3×C4—612no—
476C2×C3×C4—126no—
477C2×C3×C4C2×#67112yes—
478C2×C3×C4C2×C3×D4112yes—
479C2×C3×C4C23×D311yescharacteristic
480C2×C3×C4C23×D313yes—
481C2×C3×C4C23×D313yes—
482C2×C3×C4C23×D311yescharacteristic
483C2×C3×C4C24×C311yescharacteristic
484C2×C3×C4C24×C313yes—
485C2×C3×C4C24×C313yes—
486C2×C3×C4C24×C311yescharacteristic
487#67—212no—
488#67—24no—
489#67—46no—
490C2×Dic3—212no—
491C2×Dic3—46no—
492C2×Dic3C24×C312yes—
493C2×Dic3C24×C316yes—
494C2×Dic3C24×C316yes—
495D12—22no—
496C4×D3—212no—
497Dic6—26no—
498Dic6—212no—
499C2×C32—22no—
500C2×C32—26no—
501C2×C32—43no—
502C2×C32C23×D411yescharacteristic
503C2×C32C2×2−1+411yescharacteristic
504C2×C32#58511yescharacteristic
505C3×D3—42no—
506C24C22×C3×D313yes—
507#41—24no—
508#41—212no—
509#41—212no—
510#41—624no—
511#41—612no—
512#41C3×#6718yescomplemented
513C2×Q8—24no—
514C2×Q8—33no—
515C2×Q8—36no—
516C2×Q8—68no—
517C2×Q8—612no—
518C2×Q8C22×C3×D313yes—
519C2×Q8C22×C3×D311yescharacteristic
520C2×D4—212no—
521C2×D4—32no—
522C2×D4—36no—
523C2×D4—36no—
524C2×D4—31no—
525C2×D4C22×C3×D316yes—
526C2×D4C22×C3×D313yes—
527C2×D4C22×C3×D313yes—
528C22×C4—212no—
529C22×C4—36no—
530C22×C4—36no—
531C22×C4—36no—
532C22×C4C22×C3×D313yes—
533C22×C4C22×C3×D313yes—
534C22×C4C22×C3×D313yes—
535C22×C4C22×C3×D311yescharacteristic
536C22×C4C22×C3×D313yes—
537C22×C4C22×C3×D313yes—
538C4⋊C4—33no—
539C4⋊C4—36no—
540C4⋊C4—36no—
541C4⋊C4—312no—
542C4⋊C4—31no—
543C4⋊C4—36no—
544C22⋊C4—36no—
545C22⋊C4—312no—
546C22⋊C4—36no—
547C22⋊C4—36no—
548C22⋊C4—32no—
549C22⋊C4—36no—
550C42—36no—
551C22×C3—22no—
552C22×C3—22no—
553C22×C3—23no—
554C22×C3—23no—
555C22×C3—21no—
556C22×C3—21no—
557C22×C3—21no—
558C22×C3—23no—
559C22×C3—23no—
560C22×C3—21no—
561C22×C3—26no—
562C22×C3—23no—
563C22×C3—23no—
564C22×C3—23no—
565C22×C3—23no—
566C22×C3—23no—
567C22×C3—23no—
568C22×C3—22no—
569C22×C3—26no—
570C22×C3—21no—
571C22×C3—43no—
572C22×C3—43no—
573C22×C3—43no—
574C22×C3—43no—
575C22×C3—412no—
576C22×C3—412no—
577C22×C3—424no—
578C22×C3—62no—
579C22×C3—62no—
580C22×C3—62no—
581C22×C3#101012yescomplemented
582C22×C3C22×#6716yes—
583C22×C3C22×C3×D416yes—
584C22×C3C3×2−1+412yescomplemented
585C22×C3C24×D311yescharacteristic
586C22×C3C25×C311yescharacteristic
587C2×D3—22no—
588C2×D3—22no—
589C2×D3—22no—
590C3×C4—22no—
591C3×C4—26no—
592C3×C4—21no—
593C3×C4—23no—
594C3×C4—21no—
595C3×C4—23no—
596C3×C4—22no—
597C3×C4—26no—
598C3×C4—62no—
599C3×C4—66no—
600C3×C4—66no—
601C3×C4C22×#6712yes—
602C3×C4C22×#6716yes—
603C3×C4C22×C3×D412yes—
604C3×C4C22×C3×D416yes—
605Dic3—26no—
606Dic3—22no—
607Dic3—26no—
608C32#348911yescharacteristic, complemented, Sylow
609C23—26no—
610C23—26no—
611C23—32no—
612C23—43no—
613C23C23×C3×D313yes—
614C23C23×C3×D311yescharacteristic
615C23C23×C3×D313yes—
616Q8—26no—
617Q8—66no—
618Q8—612no—
619Q8C2×C3×#6714yes—
620D4—212no—
621D4—26no—
622D4—64no—
623D4—612no—
624D4—62no—
625D4—126no—
626D4C2×C3×#67112yes—
627C2×C4—26no—
628C2×C4—22no—
629C2×C4—26no—
630C2×C4—26no—
631C2×C4—26no—
632C2×C4—32no—
633C2×C4—36no—
634C2×C4—36no—
635C2×C4—612no—
636C2×C4—612no—
637C2×C4—126no—
638C2×C4C2×C3×#67112yes—
639C2×C4C23×C3×D311yescharacteristic
640C2×C4C23×C3×D313yes—
641C2×C4C23×C3×D313yes—
642C2×C4C23×C3×D311yescharacteristic
643C2×C3—24no—
644C2×C3—22no—
645C2×C3—26no—
646C2×C3—22no—
647C2×C3—26no—
648C2×C3—21no—
649C2×C3—21no—
650C2×C3—21no—
651C2×C3—46no—
652C2×C3—46no—
653C2×C3—43no—
654C2×C3—43no—
655C2×C3—122no—
656C2×C3C2×#101011yescharacteristic
657C2×C3#596411yescharacteristic
658C2×C3C23×#6711yescharacteristic
659C2×C3C23×C3×D411yescharacteristic
660C2×C3C2×C3×2−1+411yescharacteristic
661C2×C3C3×#58511yescharacteristic
662D3—42no—
663C22—23no—
664C22—23no—
665C22—21no—
666C22—21no—
667C22—23no—
668C22—23no—
669C22—23no—
670C22—412no—
671C22—62no—
672C22—62no—
673C22—62no—
674C22C3×#101012yescomplemented
675C22C22×C3×#6716yes—
676C22C24×C3×D311yescharacteristic
677C4—21no—
678C4—23no—
679C4—62no—
680C4—66no—
681C4—66no—
682C4C22×C3×#6712yes—
683C4C22×C3×#6716yes—
684C3—21no—
685C3#8726411yescharacteristic, direct product factor
686C3C3×#348911yescharacteristic, complemented
687C2—22no—
688C2—26no—
689C2—43no—
690C2—122no—
691C2C2×C3×#101011yescharacteristic
692C2C3×#596411yescharacteristic
693C2C23×C3×#6711yescharacteristic
subgroupG/H
centerC22×C3C24×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC22×C32×#41C2
socleC22×C32C25
hypercenterC22×C3×#41D3
hypocenterC3C3×#3489
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×#41

Complements

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

NH ≅ G/Ntype
1. C22×C32×#41C2semidirect
2. C2×C3×#1010C2semidirect
3. C3×#5833C2semidirect
4. C3×#5831C2semidirect
5. C3×#5827C2semidirect
6. C3×#5825C2semidirect
7. C3×#5824C2semidirect
8. C3×Q8×#67C2semidirect
9. C3×#5806C2semidirect
10. C3×#5791C2semidirect
11. C2×C3×#924C2semidirect
13. #87264C3direct (N × H)
23. C2×C3×D3×Q8C22semidirect
24. C2×C3×#237C22semidirect
25. C2×C3×#235C22semidirect
26. C22×C3×Dic6C22semidirect
29. C3×#946C22semidirect
30. C3×Q8×Dic3C22semidirect
31. C3×#944C22semidirect
32. C3×#939C22semidirect
33. C3×#938C22semidirect
34. C3×#936C22semidirect
35. C3×#935C22semidirect
36. C3×D4×Dic3C22semidirect
38. C3×#930C22semidirect
39. C3×#929C22semidirect
41. C3×C4×#67C22semidirect
42. C3×#926C22semidirect
43. C2×C3×C4⋊Dic3C22semidirect
46. C3×#924C22semidirect
47. C3×#924C22semidirect
48. C3×#924C22semidirect
49. C2×C3×Dic3⋊C4C22semidirect
52. C22×C3×#41D3semidirect
53. C22×C3×#41C2×C3semidirect
54. C2×#1010C2×C3semidirect
64. #5833C2×C3semidirect
65. #5831C2×C3semidirect
66. #5827C2×C3semidirect
67. #5825C2×C3semidirect
68. #5824C2×C3semidirect
69. Q8×#67C2×C3semidirect
70. #5806C2×C3semidirect
71. #5791C2×C3semidirect
72. C2×#924C2×C3semidirect
77. C32×#41D4semidirect
149. C2×D3×Q8C22×C3semidirect
150. C2×#237C22×C3semidirect
151. C2×#235C22×C3semidirect
152. C22×Dic6C22×C3semidirect
178. #946C22×C3semidirect
179. Q8×Dic3C22×C3semidirect
180. #944C22×C3semidirect
181. #939C22×C3semidirect
182. #938C22×C3semidirect
183. #936C22×C3semidirect
184. #935C22×C3semidirect
185. D4×Dic3C22×C3semidirect
187. #930C22×C3semidirect
188. #929C22×C3semidirect
190. C4×#67C22×C3semidirect
191. #926C22×C3semidirect
192. C2×C4⋊Dic3C22×C3semidirect
195. #924C22×C3semidirect
196. #924C22×C3semidirect
197. #924C22×C3semidirect
198. C2×Dic3⋊C4C22×C3semidirect
234. C22×#41C3×D3semidirect
259. C3×#41#67semidirect
260. C3×#41C3×D4semidirect
362. C22×C322−1+4semidirect
512. #41C3×#67semidirect
581. C22×C3#1010semidirect
584. C22×C3C3×2−1+4semidirect
608. C32#3489semidirect
674. C22C3×#1010semidirect
685. C3#87264direct (N × H)
686. C3C3×#3489semidirect

Maximal subgroups

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

subgroupindex
C22×C32×#412
C2×C3×#10102
C3×#58332
C3×#58312
C3×#58272
C3×#58252
C3×#58242
C3×Q8×#672
C3×#58062
C3×#57912
C2×C3×#9242
C3×#34893
#872643