Finite Group Databasebeta

← C3×#87285 #11904591

Subgroups — C3×#87285 #11904591

Order 1152.

3765 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×H(5,𝔽2)C211yesmaximal, characteristic, complemented
2C2×C3×D3×#41C211yesmaximal, characteristic, complemented
3C3×#5834C212yesmaximal, complemented
4C3×#5833C213yesmaximal, complemented
5C3×#5831C212yesmaximal, complemented
6C3×#5828C213yesmaximal, complemented
7C3×#5827C211yesmaximal, characteristic, complemented
8C3×#5806C216yesmaximal, complemented
9C3×#5805C213yesmaximal, complemented
10C3×D4×#67C216yesmaximal, complemented
11C2×C3×#938C213yesmaximal, complemented
12C3×#3488—31nomaximal
13#87285C311yesmaximal, characteristic, direct product factor
14C32×H(5,𝔽2)—28no—
15C2×C32×#41C2211yescharacteristic
16C2×C32×#41C2213yescomplemented
17C2×C32×#41C2212yescomplemented
18C22×C32×D4C2213yescomplemented
19C22×C32×D4C2216yescomplemented
20C22×C3×#67C2216yescomplemented
21C3×D3×#41—28no—
22C2×C3×#239C2211yescharacteristic, complemented
23C2×C3×D3×Q8C2211yescharacteristic, complemented
24C2×C3×#237C2213yescomplemented
25C2×C3×D3×D4C2213yescomplemented
26C2×C3×#235C2213yescomplemented
27C22×C3×C4×D3C2213yescomplemented
28C3×#953C22112yescomplemented
29C2×C3×#217C2216yescomplemented
30C3×#946C2211yescharacteristic, complemented
31C3×#946C2213yescomplemented
32C3×Q8×Dic3C2212yescomplemented
33C3×#940C2216yescomplemented
34C3×#939C22112yescomplemented
35C3×#938C2213yescomplemented
36C3×#938C2216yescomplemented
37C3×#938C2216yescomplemented
38C3×#938C2216yescomplemented
39C3×#938C2213yescomplemented
40C3×#937C2216yescomplemented
41C3×#936C2216yescomplemented
42C3×#935C2216yescomplemented
43C3×D4×Dic3C2216yescomplemented
44C3×#930C2216yescomplemented
45C3×C4×#67C2216yescomplemented
46C3×C4×#67C2216yescomplemented
47C3×#926C2213yescomplemented
48C2×C3×C4⋊Dic3C2213yescomplemented
49C3×#924C2216yescomplemented
50C2×C3×H(5,𝔽2)—21no—
51C2×C3×H(5,𝔽2)D311yescharacteristic, complemented
52C2×C3×H(5,𝔽2)C2×C311yescharacteristic, complemented
53C22×C3×#41—31no—
54C2×D3×#41C2×C311yescharacteristic, complemented
55C3×#550—32no—
56C3×#548—32no—
57C3×#546—36no—
58C3×D42—36no—
59C3×#537—33no—
60C3×#535—33no—
61C3×#525—33no—
62C2×C3×#121—33no—
63C3×#520—31no—
64#5834C2×C312yescomplemented
65#5833C2×C313yescomplemented
66#5831C2×C312yescomplemented
67#5828C2×C313yescomplemented
68#5827C2×C311yescharacteristic, complemented
69#5806C2×C316yescomplemented
70#5805C2×C313yescomplemented
71D4×#67C2×C316yescomplemented
72C2×#938C2×C313yescomplemented
73C24×C32C2316yes—
74C23×C3×D3C2313yes—
75C32×#41—28no—
76C32×#41—212no—
77C32×#41D418yescomplemented
78C2×C32×Q8C2311yescharacteristic
79C2×C32×Q8C2311yescharacteristic
80C2×C32×D4—224no—
81C2×C32×D4—212no—
82C2×C32×D4C2316yes—
83C2×C32×D4C2316yes—
84C2×C32×D4C2313yes—
85C2×C32×D4C2313yes—
86C22×C32×C4C2316yes—
87C22×C32×C4C2313yes—
88C2×C3×#67—412no—
89C2×C3×#67C2316yes—
90C2×C3×#67C2316yes—
91C2×C3×#67C2316yes—
92C2×C3×#67C23112yes—
93C22×C3×Dic3C2313yes—
94C22×C3×Dic3C2316yes—
95C3×#239—24no—
96C3×D3×Q8—24no—
97C3×#237—212no—
98C3×D3×D4—212no—
99C3×#235—212no—
100C2×C3×D12C2313yes—
101C2×C3×C4×D3—212no—
102C2×C3×C4×D3C2313yes—
103C2×C3×C4×D3C2313yes—
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×C4×D3C2313yes—
106C2×C3×Dic6C2313yes—
107C3×#217C23112yes—
108C3×#217C2316yes—
109C3×#217C2316yes—
110C3×#217C2316yes—
111C3×(C2×D3)⋊C4C2312yes—
112C3×(C2×D3)⋊C4C2316yes—
113C3×C4⋊Dic3C2316yes—
114C3×C4⋊Dic3C2313yes—
115C3×C4⋊Dic3C2311yescharacteristic
116C3×Dic3⋊C4C2316yes—
117C3×Dic3⋊C4C2312yes—
118C3×C4×Dic3C2316yes—
119#3488—31noSylow
120C3×H(5,𝔽2)—216no—
121C3×H(5,𝔽2)—28no—
122C3×H(5,𝔽2)—28no—
123C2×C3×#41—21no—
124C2×C3×#41—23no—
125C2×C3×#41—22no—
126C2×C3×#41—31no—
127C2×C3×#41—33no—
128C2×C3×#41—33no—
129C2×C3×#41—68no—
130C2×C3×#41C2×D311yescharacteristic
131C2×C3×#41C2×D313yescomplemented
132C2×C3×#41C2×D312yescomplemented
133C2×C3×#41C22×C311yescharacteristic
134C2×C3×#41C22×C313yescomplemented
135C2×C3×#41C22×C312yescomplemented
136C22×C3×Q8—31no—
137C22×C3×D4—23no—
138C22×C3×D4—26no—
139C22×C3×D4—36no—
140C22×C3×D4—33no—
141C22×C3×D4C2×D313yescomplemented
142C22×C3×D4C2×D316yescomplemented
143C22×C3×D4C22×C313yescomplemented
144C22×C3×D4C22×C316yescomplemented
145C23×C3×C4—33no—
146C22×#67C22×C316yescomplemented
147D3×#41—28no—
148C2×#239C22×C311yescharacteristic, complemented
149C2×D3×Q8C22×C311yescharacteristic, complemented
150C2×#237C22×C313yescomplemented
151C2×D3×D4C22×C313yescomplemented
152C2×#235C22×C313yescomplemented
153C22×C4×D3C22×C313yescomplemented
154C3×#127—36no—
155C3×#124—36no—
156C3×#123—36no—
157C3×C22⋊Q8—31no—
158C3×C22⋊Q8—33no—
159C3×C22⋊Q8—36no—
160C3×#121—33no—
161C3×#121—36no—
162C3×#121—36no—
163C3×#121—36no—
164C3×#121—33no—
165C3×#121—312no—
166C3×#121—36no—
167C3×#120—312no—
168C3×#120—36no—
169C3×C4×Q8—32no—
170C3×C4×D4—36no—
171C3×C4×D4—36no—
172C3×C4×D4—36no—
173C3×#117—33no—
174C2×C3×C4⋊C4—33no—
175C2×C3×C22⋊C4—36no—
176#953C22×C3112yescomplemented
177C2×#217C22×C316yescomplemented
178#946C22×C311yescharacteristic, complemented
179#946C22×C313yescomplemented
180Q8×Dic3C22×C312yescomplemented
181#940C22×C316yescomplemented
182#939C22×C3112yescomplemented
183#938C22×C313yescomplemented
184#938C22×C316yescomplemented
185#938C22×C316yescomplemented
186#938C22×C316yescomplemented
187#938C22×C313yescomplemented
188#937C22×C316yescomplemented
189#936C22×C316yescomplemented
190#935C22×C316yescomplemented
191D4×Dic3C22×C316yescomplemented
192#930C22×C316yescomplemented
193C4×#67C22×C316yescomplemented
194C4×#67C22×C316yescomplemented
195#926C22×C313yescomplemented
196C2×C4⋊Dic3C22×C313yescomplemented
197#924C22×C316yescomplemented
198C23×C32—212no—
199C23×C32—46no—
200C23×C32—46no—
201C23×C32C2416yes—
202C23×C32C2413yes—
203C22×C3×D3—26no—
204C22×C3×D3—26no—
205C22×C3×D3—43no—
206C22×C3×D3C2413yes—
207C22×C3×D3C2411yescharacteristic
208C32×Q8—22no—
209C32×Q8C2×D414yescomplemented
210C32×D4—212no—
211C32×D4—212no—
212C32×D4—26no—
213C32×D4C2×D4112yescomplemented
214C2×C32×C4—212no—
215C2×C32×C4C2×D4112yescomplemented
216C2×C32×C4C2412yes—
217C2×C32×C4C2413yes—
218C2×C32×C4C2411yescharacteristic
219C3×#67—212no—
220C3×#67—212no—
221C3×#67—412no—
222C3×#67—46no—
223C2×C3×Dic3—26no—
224C2×C3×Dic3—46no—
225C2×C3×Dic3C2412yes—
226C2×C3×Dic3C2416yes—
227C2×C3×Dic3C2413yes—
228C2×C3×Dic3C2411yescharacteristic
229C3×D12—26no—
230C3×C4×D3—22no—
231C3×C4×D3—26no—
232C3×C4×D3—26no—
233C3×C4×D3—26no—
234C3×Dic6—26no—
235C2×H(5,𝔽2)C3×D311yescharacteristic, complemented
236C22×#41—31no—
237#550—32no—
238#548—32no—
239#546—36no—
240D42—36no—
241#537—33no—
242#535—33no—
243#525—33no—
244C2×#121—33no—
245#520—31no—
246C24×C3—26no—
247C24×C3—33no—
248C24×C3C22×D316yes—
249C24×C3C23×C316yes—
250C23×D3C23×C313yes—
251C3×#41—216no—
252C3×#41—224no—
253C3×#41—28no—
254C3×#41—28no—
255C3×#41—212no—
256C3×#41—212no—
257C3×#41—28no—
258C3×#41—64no—
259C3×#41—612no—
260C3×#41—612no—
261C3×#41#6718yescomplemented
262C3×#41C3×D418yescomplemented
263C2×C3×Q8—21no—
264C2×C3×Q8—21no—
265C2×C3×Q8—33no—
266C2×C3×Q8—64no—
267C2×C3×Q8C22×D311yescharacteristic
268C2×C3×Q8C22×D311yescharacteristic
269C2×C3×Q8C23×C311yescharacteristic
270C2×C3×Q8C23×C311yescharacteristic
271C2×C3×D4—248no—
272C2×C3×D4—224no—
273C2×C3×D4—224no—
274C2×C3×D4—224no—
275C2×C3×D4—212no—
276C2×C3×D4—212no—
277C2×C3×D4—26no—
278C2×C3×D4—23no—
279C2×C3×D4—26no—
280C2×C3×D4—23no—
281C2×C3×D4—36no—
282C2×C3×D4—36no—
283C2×C3×D4—36no—
284C2×C3×D4—312no—
285C2×C3×D4—33no—
286C2×C3×D4—612no—
287C2×C3×D4—1212no—
288C2×C3×D4C22×D316yes—
289C2×C3×D4C22×D313yes—
290C2×C3×D4C22×D316yes—
291C2×C3×D4C22×D313yes—
292C2×C3×D4C23×C316yes—
293C2×C3×D4C23×C316yes—
294C2×C3×D4C23×C313yes—
295C2×C3×D4C23×C313yes—
296C22×C3×C4—26no—
297C22×C3×C4—23no—
298C22×C3×C4—33no—
299C22×C3×C4—36no—
300C22×C3×C4—33no—
301C22×C3×C4—33no—
302C22×C3×C4—31no—
303C22×C3×C4—33no—
304C22×C3×C4—612no—
305C22×C3×C4C22×D316yes—
306C22×C3×C4C22×D313yes—
307C22×C3×C4C23×C316yes—
308C22×C3×C4C23×C313yes—
309C2×#67—412no—
310C2×#67C23×C316yes—
311C2×#67C23×C316yes—
312C2×#67C23×C316yes—
313C2×#67C23×C3112yes—
314C22×Dic3C23×C313yes—
315C22×Dic3C23×C316yes—
316#239—24no—
317D3×Q8—24no—
318#237—212no—
319D3×D4—212no—
320#235—212no—
321C2×D12C23×C313yes—
322C2×C4×D3—212no—
323C2×C4×D3C23×C313yes—
324C2×C4×D3C23×C313yes—
325C2×C4×D3C23×C311yescharacteristic
326C2×C4×D3C23×C313yes—
327C2×Dic6C23×C313yes—
328C3×C4⋊C4—32no—
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×C3112yes—
341#217C23×C316yes—
342#217C23×C316yes—
343#217C23×C316yes—
344(C2×D3)⋊C4C23×C312yes—
345(C2×D3)⋊C4C23×C316yes—
346C4⋊Dic3C23×C316yes—
347C4⋊Dic3C23×C313yes—
348C4⋊Dic3C23×C311yescharacteristic
349Dic3⋊C4C23×C316yes—
350Dic3⋊C4C23×C312yes—
351C4×Dic3C23×C316yes—
352C22×C32—26no—
353C22×C32—23no—
354C22×C32—23no—
355C22×C32—26no—
356C22×C32—26no—
357C22×C32—812no—
358C22×C32C22×D416yes—
359C22×C32C2511yescharacteristic
360C2×C3×D3—21no—
361C2×C3×D3—21no—
362C2×C3×D3—23no—
363C2×C3×D3—23no—
364C2×C3×D3—23no—
365C2×C3×D3—412no—
366C2×C3×D3H(5,𝔽2)12yescomplemented
367C32×C4—22no—
368C32×C4C22×D416yes—
369C32×C4C22×D412yes—
370C3×Dic3—23no—
371C3×Dic3—21no—
372C3×Dic3—26no—
373C3×Dic3—22no—
374H(5,𝔽2)—28no—
375C2×#41—31no—
376C2×#41—33no—
377C2×#41—33no—
378C2×#41—68no—
379C2×#41C2×C3×D311yescharacteristic
380C2×#41C2×C3×D313yescomplemented
381C2×#41C2×C3×D312yescomplemented
382C22×Q8—31no—
383C22×D4—36no—
384C22×D4—33no—
385C22×D4C2×C3×D313yescomplemented
386C22×D4C2×C3×D316yescomplemented
387C23×C4—33no—
388#127—36no—
389#124—36no—
390#123—36no—
391C22⋊Q8—31no—
392C22⋊Q8—33no—
393C22⋊Q8—36no—
394#121—33no—
395#121—36no—
396#121—36no—
397#121—36no—
398#121—33no—
399#121—312no—
400#121—36no—
401#120—312no—
402#120—36no—
403C4×Q8—32no—
404C4×D4—36no—
405C4×D4—36no—
406C4×D4—36no—
407#117—33no—
408C2×C4⋊C4—33no—
409C2×C22⋊C4—36no—
410C23×C3—224no—
411C23×C3—212no—
412C23×C3—212no—
413C23×C3—26no—
414C23×C3—23no—
415C23×C3—31no—
416C23×C3—33no—
417C23×C3—46no—
418C23×C3—46no—
419C23×C3—46no—
420C23×C3—46no—
421C23×C3—66no—
422C23×C3—66no—
423C23×C3—86no—
424C23×C3—86no—
425C23×C3—123no—
426C23×C3C23×D316yes—
427C23×C3C23×D313yes—
428C23×C3C24×C316yes—
429C23×C3C24×C313yes—
430C22×D3—26no—
431C22×D3—26no—
432C22×D3—43no—
433C22×D3C24×C313yes—
434C22×D3C24×C311yescharacteristic
435C3×Q8—24no—
436C3×Q8—22no—
437C3×Q8—22no—
438C3×Q8—24no—
439C3×Q8—66no—
440C3×Q8C2×#6714yescomplemented
441C3×Q8C2×C3×D414yescomplemented
442C3×D4—224no—
443C3×D4—224no—
444C3×D4—212no—
445C3×D4—212no—
446C3×D4—212no—
447C3×D4—212no—
448C3×D4—26no—
449C3×D4—212no—
450C3×D4—26no—
451C3×D4—212no—
452C3×D4—612no—
453C3×D4—612no—
454C3×D4—66no—
455C3×D4—126no—
456C3×D4—1212no—
457C3×D4C2×#67112yescomplemented
458C3×D4C2×C3×D4112yescomplemented
459C2×C3×C4—224no—
460C2×C3×C4—212no—
461C2×C3×C4—212no—
462C2×C3×C4—22no—
463C2×C3×C4—23no—
464C2×C3×C4—21no—
465C2×C3×C4—212no—
466C2×C3×C4—32no—
467C2×C3×C4—36no—
468C2×C3×C4—31no—
469C2×C3×C4—33no—
470C2×C3×C4—66no—
471C2×C3×C4—62no—
472C2×C3×C4—66no—
473C2×C3×C4—66no—
474C2×C3×C4—66no—
475C2×C3×C4—126no—
476C2×C3×C4C2×#67112yescomplemented
477C2×C3×C4C2×C3×D4112yescomplemented
478C2×C3×C4C23×D312yes—
479C2×C3×C4C23×D313yes—
480C2×C3×C4C23×D311yescharacteristic
481C2×C3×C4C24×C312yes—
482C2×C3×C4C24×C313yes—
483C2×C3×C4C24×C311yescharacteristic
484#67—212no—
485#67—212no—
486#67—412no—
487#67—46no—
488C2×Dic3—26no—
489C2×Dic3—46no—
490C2×Dic3C24×C312yes—
491C2×Dic3C24×C316yes—
492C2×Dic3C24×C313yes—
493C2×Dic3C24×C311yescharacteristic
494D12—26no—
495C4×D3—22no—
496C4×D3—26no—
497C4×D3—26no—
498C4×D3—26no—
499Dic6—26no—
500C2×C32—26no—
501C2×C32—46no—
502C2×C32C23×D411yescharacteristic
503C2×C32C2×H(5,𝔽2)11yescharacteristic
504C2×C32#58511yescharacteristic
505C3×D3—22no—
506C3×D3—43no—
507C24—33no—
508C24C22×C3×D316yes—
509#41—28no—
510#41—212no—
511#41—64no—
512#41—612no—
513#41—612no—
514#41C3×#6718yescomplemented
515C2×Q8—33no—
516C2×Q8—64no—
517C2×Q8C22×C3×D311yescharacteristic
518C2×Q8C22×C3×D311yescharacteristic
519C2×D4—224no—
520C2×D4—212no—
521C2×D4—36no—
522C2×D4—36no—
523C2×D4—36no—
524C2×D4—312no—
525C2×D4—33no—
526C2×D4—612no—
527C2×D4—1212no—
528C2×D4C22×C3×D316yes—
529C2×D4C22×C3×D313yes—
530C2×D4C22×C3×D316yes—
531C2×D4C22×C3×D313yes—
532C22×C4—33no—
533C22×C4—36no—
534C22×C4—33no—
535C22×C4—33no—
536C22×C4—31no—
537C22×C4—33no—
538C22×C4—612no—
539C22×C4C22×C3×D316yes—
540C22×C4C22×C3×D313yes—
541C4⋊C4—33no—
542C4⋊C4—36no—
543C4⋊C4—31no—
544C4⋊C4—32no—
545C4⋊C4—36no—
546C22⋊C4—36no—
547C22⋊C4—312no—
548C22⋊C4—36no—
549C22⋊C4—36no—
550C22⋊C4—32no—
551C22⋊C4—36no—
552C42—36no—
553C22×C3—23no—
554C22×C3—23no—
555C22×C3—23no—
556C22×C3—23no—
557C22×C3—212no—
558C22×C3—26no—
559C22×C3—26no—
560C22×C3—26no—
561C22×C3—26no—
562C22×C3—26no—
563C22×C3—26no—
564C22×C3—26no—
565C22×C3—21no—
566C22×C3—32no—
567C22×C3—43no—
568C22×C3—43no—
569C22×C3—46no—
570C22×C3—46no—
571C22×C3—61no—
572C22×C3—61no—
573C22×C3—63no—
574C22×C3—63no—
575C22×C3—63no—
576C22×C3—812no—
577C22×C3—812no—
578C22×C3—824no—
579C22×C3—1212no—
580C22×C3C22×#6716yes—
581C22×C3C22×C3×D416yes—
582C22×C3C24×D311yescharacteristic
583C22×C3C25×C311yescharacteristic
584C2×D3—21no—
585C2×D3—21no—
586C2×D3—23no—
587C2×D3—23no—
588C2×D3—23no—
589C2×D3—412no—
590C2×D3C3×H(5,𝔽2)12yescomplemented
591C3×C4—24no—
592C3×C4—22no—
593C3×C4—22no—
594C3×C4—26no—
595C3×C4—22no—
596C3×C4—66no—
597C3×C4—62no—
598C3×C4—61no—
599C3×C4—63no—
600C3×C4C22×#6716yes—
601C3×C4C22×#6712yes—
602C3×C4C22×C3×D416yes—
603C3×C4C22×C3×D412yes—
604Dic3—23no—
605Dic3—21no—
606Dic3—26no—
607Dic3—22no—
608C32#348811yescharacteristic, complemented, Sylow
609C23—212no—
610C23—31no—
611C23—33no—
612C23—46no—
613C23—46no—
614C23—66no—
615C23—66no—
616C23—123no—
617C23C23×C3×D316yes—
618C23C23×C3×D313yes—
619Q8—22no—
620Q8—66no—
621Q8C2×C3×#6714yescomplemented
622D4—212no—
623D4—212no—
624D4—26no—
625D4—612no—
626D4—612no—
627D4—66no—
628D4—1212no—
629D4—126no—
630D4C2×C3×#67112yescomplemented
631C2×C4—212no—
632C2×C4—32no—
633C2×C4—36no—
634C2×C4—31no—
635C2×C4—33no—
636C2×C4—66no—
637C2×C4—62no—
638C2×C4—66no—
639C2×C4—66no—
640C2×C4—66no—
641C2×C4—126no—
642C2×C4C2×C3×#67112yescomplemented
643C2×C4C23×C3×D312yes—
644C2×C4C23×C3×D313yes—
645C2×C4C23×C3×D311yescharacteristic
646C2×C3—26no—
647C2×C3—26no—
648C2×C3—21no—
649C2×C3—21no—
650C2×C3—21no—
651C2×C3—46no—
652C2×C3—412no—
653C2×C3—46no—
654C2×C3—46no—
655C2×C3—62no—
656C2×C3—123no—
657C2×C3D3×H(5,𝔽2)11yescharacteristic
658C2×C3#596611yescharacteristic
659C2×C3C23×#6711yescharacteristic
660C2×C3C23×C3×D411yescharacteristic
661C2×C3C2×C3×H(5,𝔽2)11yescharacteristic
662C2×C3C3×#58511yescharacteristic
663D3—22no—
664D3—43no—
665C22—23no—
666C22—23no—
667C22—26no—
668C22—26no—
669C22—26no—
670C22—32no—
671C22—61no—
672C22—61no—
673C22—63no—
674C22—63no—
675C22—63no—
676C22—812no—
677C22—1212no—
678C22C22×C3×#6716yes—
679C22C24×C3×D311yescharacteristic
680C4—22no—
681C4—66no—
682C4—62no—
683C4—61no—
684C4—63no—
685C4C22×C3×#6716yes—
686C4C22×C3×#6712yes—
687C3—21no—
688C3#8728511yescharacteristic, direct product factor
689C3C3×#348811yescharacteristic, complemented
690C2—26no—
691C2—46no—
692C2—62no—
693C2—123no—
694C2C3×D3×H(5,𝔽2)11yescharacteristic
695C2C3×#596611yescharacteristic
696C2C23×C3×#6711yescharacteristic
subgroupG/H
centerC22×C3C24×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC2×C32×H(5,𝔽2)C2
socleC22×C32C25
hypercenterC2×C3×H(5,𝔽2)D3
hypocenterC3C3×#3488
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C2×C3×H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. C2×C32×H(5,𝔽2)C2semidirect
2. C2×C3×D3×#41C2semidirect
3. C3×#5834C2semidirect
4. C3×#5833C2semidirect
5. C3×#5831C2semidirect
6. C3×#5828C2semidirect
7. C3×#5827C2semidirect
8. C3×#5806C2semidirect
9. C3×#5805C2semidirect
10. C3×D4×#67C2semidirect
11. C2×C3×#938C2semidirect
13. #87285C3direct (N × H)
16. C2×C32×#41C22semidirect
17. C2×C32×#41C22semidirect
18. C22×C32×D4C22semidirect
19. C22×C32×D4C22semidirect
20. C22×C3×#67C22semidirect
22. C2×C3×#239C22semidirect
23. C2×C3×D3×Q8C22semidirect
24. C2×C3×#237C22semidirect
25. C2×C3×D3×D4C22semidirect
26. C2×C3×#235C22semidirect
27. C22×C3×C4×D3C22semidirect
28. C3×#953C22semidirect
29. C2×C3×#217C22semidirect
30. C3×#946C22semidirect
31. C3×#946C22semidirect
32. C3×Q8×Dic3C22semidirect
33. C3×#940C22semidirect
34. C3×#939C22semidirect
35. C3×#938C22semidirect
36. C3×#938C22semidirect
37. C3×#938C22semidirect
38. C3×#938C22semidirect
39. C3×#938C22semidirect
40. C3×#937C22semidirect
41. C3×#936C22semidirect
42. C3×#935C22semidirect
43. C3×D4×Dic3C22semidirect
44. C3×#930C22semidirect
45. C3×C4×#67C22semidirect
46. C3×C4×#67C22semidirect
47. C3×#926C22semidirect
48. C2×C3×C4⋊Dic3C22semidirect
49. C3×#924C22semidirect
51. C2×C3×H(5,𝔽2)D3semidirect
52. C2×C3×H(5,𝔽2)C2×C3semidirect
54. C2×D3×#41C2×C3semidirect
64. #5834C2×C3semidirect
65. #5833C2×C3semidirect
66. #5831C2×C3semidirect
67. #5828C2×C3semidirect
68. #5827C2×C3semidirect
69. #5806C2×C3semidirect
70. #5805C2×C3semidirect
71. D4×#67C2×C3semidirect
72. C2×#938C2×C3semidirect
77. C32×#41D4semidirect
131. C2×C3×#41C2×D3semidirect
132. C2×C3×#41C2×D3semidirect
134. C2×C3×#41C22×C3semidirect
135. C2×C3×#41C22×C3semidirect
141. C22×C3×D4C2×D3semidirect
142. C22×C3×D4C2×D3semidirect
143. C22×C3×D4C22×C3semidirect
144. C22×C3×D4C22×C3semidirect
146. C22×#67C22×C3semidirect
148. C2×#239C22×C3semidirect
149. C2×D3×Q8C22×C3semidirect
150. C2×#237C22×C3semidirect
151. C2×D3×D4C22×C3semidirect
152. C2×#235C22×C3semidirect
153. C22×C4×D3C22×C3semidirect
176. #953C22×C3semidirect
177. C2×#217C22×C3semidirect
178. #946C22×C3semidirect
179. #946C22×C3semidirect
180. Q8×Dic3C22×C3semidirect
181. #940C22×C3semidirect
182. #939C22×C3semidirect
183. #938C22×C3semidirect
184. #938C22×C3semidirect
185. #938C22×C3semidirect
186. #938C22×C3semidirect
187. #938C22×C3semidirect
188. #937C22×C3semidirect
189. #936C22×C3semidirect
190. #935C22×C3semidirect
191. D4×Dic3C22×C3semidirect
192. #930C22×C3semidirect
193. C4×#67C22×C3semidirect
194. C4×#67C22×C3semidirect
195. #926C22×C3semidirect
196. C2×C4⋊Dic3C22×C3semidirect
197. #924C22×C3semidirect
209. C32×Q8C2×D4semidirect
213. C32×D4C2×D4semidirect
215. C2×C32×C4C2×D4semidirect
235. C2×H(5,𝔽2)C3×D3semidirect
261. C3×#41#67semidirect
262. C3×#41C3×D4semidirect
366. C2×C3×D3H(5,𝔽2)semidirect
380. C2×#41C2×C3×D3semidirect
381. C2×#41C2×C3×D3semidirect
385. C22×D4C2×C3×D3semidirect
386. C22×D4C2×C3×D3semidirect
440. C3×Q8C2×#67semidirect
441. C3×Q8C2×C3×D4semidirect
457. C3×D4C2×#67semidirect
458. C3×D4C2×C3×D4semidirect
476. C2×C3×C4C2×#67semidirect
477. C2×C3×C4C2×C3×D4semidirect
514. #41C3×#67semidirect
590. C2×D3C3×H(5,𝔽2)semidirect
608. C32#3488semidirect
621. Q8C2×C3×#67semidirect
630. D4C2×C3×#67semidirect
642. C2×C4C2×C3×#67semidirect
688. C3#87285direct (N × H)
689. C3C3×#3488semidirect

Maximal subgroups

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

subgroupindex
C2×C32×H(5,𝔽2)2
C2×C3×D3×#412
C3×#58342
C3×#58332
C3×#58312
C3×#58282
C3×#58272
C3×#58062
C3×#58052
C3×D4×#672
C2×C3×#9382
C3×#34883
#872853