Finite Group Databasebeta

← C3×#86769 #11904609

Subgroups — C3×#86769 #11904609

Order 1152.

3472 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1009C211yesmaximal, characteristic, complemented
2C2×C3×D3×#41C211yesmaximal, characteristic, complemented
3C32×#550C211yesmaximal, characteristic, complemented
4C3×#5834C211yesmaximal, characteristic, complemented
5C3×#5831C211yesmaximal, characteristic, complemented
6C3×#5717C213yesmaximal, complemented
7C3×#5715C213yesmaximal, complemented
8C3×#5612C213yesmaximal, complemented
9C3×#5609C213yesmaximal, complemented
10C3×#5608C213yesmaximal, complemented
11C3×D3×#121C213yesmaximal, complemented
12C3×#5576C211yesmaximal, characteristic, complemented
13C3×#5574C211yesmaximal, characteristic, complemented
14C3×#5550C213yesmaximal, complemented
15C3×#5547C213yesmaximal, complemented
16C3×#3488—31nomaximal
17#86769C311yesmaximal, characteristic, direct product factor
18C2×C32×#41C2211yescharacteristic, complemented
19C2×C32×#41C2211yescharacteristic, complemented
20C3×#1009—28no—
21C3×D3×#41—28no—
22C2×C3×#239C2211yescharacteristic
23C2×C3×#239C2211yescharacteristic, complemented
24C2×C3×D3×Q8C2211yescharacteristic, complemented
25C2×C3×#237C2213yescomplemented
26C2×C3×D3×D4C2213yescomplemented
27C2×C3×D3×D4C2213yescomplemented
28C2×C3×D3×D4C2213yescomplemented
29C2×C3×D3×D4C2216yescomplemented
30C2×C3×#235C2213yescomplemented
31C2×C3×#235C2213yescomplemented
32C22×C3×D12C2213yescomplemented
33C22×C3×C4×D3C2213yescomplemented
34C32×#127C2213yescomplemented
35C32×#121C2213yescomplemented
36C32×#121C2213yescomplemented
37C32×C4×Q8C2211yescharacteristic, complemented
38C32×C4×D4C2213yescomplemented
39C3×Q8×Dic3C2211yescharacteristic, complemented
40C3×#940C2213yescomplemented
41C3×#939C2213yescomplemented
42C3×#939C2216yescomplemented
43C3×#938C2213yescomplemented
44C3×#938C2213yescomplemented
45C3×#938C2216yescomplemented
46C3×#937C2213yescomplemented
47C3×#937C2216yescomplemented
48C3×#937C2216yescomplemented
49C3×#936C2213yescomplemented
50C3×#930C2213yescomplemented
51C3×C4×#67C2213yescomplemented
52C3×C4×#67C2213yescomplemented
53C3×#924C2213yescomplemented
54C3×#897C2213yescomplemented
55C3×#896C2211yescharacteristic, complemented
56C3×#895C2213yescomplemented
57C3×#894C2213yescomplemented
58C3×#893C2213yescomplemented
59C3×D3×C4⋊C4C2213yescomplemented
60C3×#884C2213yescomplemented
61C3×#884C2216yescomplemented
62C3×#883C2213yescomplemented
63C3×#882C2213yescomplemented
64C3×D3×C22⋊C4C2216yescomplemented
65C3×#878C2213yescomplemented
66C3×#875C2213yescomplemented
67C3×C4×D12C2213yescomplemented
68C3×C4×D12C2213yescomplemented
69C3×#872C2213yescomplemented
70C2×C3×H(5,𝔽2)—31no—
71C22×C3×#41—31no—
72C2×#1009C2×C311yescharacteristic, complemented
73C2×D3×#41C2×C311yescharacteristic, complemented
74C3×#550—21no—
75C3×#550—31no—
76C3×#550D311yescharacteristic, complemented
77C3×#550C2×C311yescharacteristic, complemented
78C3×#548—31no—
79C3×#548—31no—
80C3×#546—33no—
81C3×#546—33no—
82C3×D42—33no—
83C3×D42—33no—
84C3×#537—33no—
85C3×#535—33no—
86C3×#525—33no—
87C2×C3×#121—33no—
88C3×#520—31no—
89#5834C2×C311yescharacteristic, complemented
90#5831C2×C311yescharacteristic, complemented
91#5717C2×C313yescomplemented
92#5715C2×C313yescomplemented
93#5612C2×C313yescomplemented
94#5609C2×C313yescomplemented
95#5608C2×C313yescomplemented
96D3×#121C2×C313yescomplemented
97#5576C2×C311yescharacteristic, complemented
98#5574C2×C311yescharacteristic, complemented
99#5550C2×C313yescomplemented
100#5547C2×C313yescomplemented
101C23×C3×D3C2313yes—
102C23×C3×D3C2316yes—
103C32×#41—24no—
104C32×#41—24no—
105C2×C32×Q8C2311yescharacteristic
106C2×C32×D4C2313yes—
107C2×C32×D4C2313yes—
108C2×C32×D4C2313yes—
109C2×C32×D4C2316yes—
110C22×C32×C4C2313yes—
111C22×C32×C4C2313yes—
112C2×C3×#67C2313yes—
113C2×C3×#67C2313yes—
114C2×C3×#67C2316yes—
115C2×C3×#67C2313yes—
116C2×C3×#67C2313yes—
117C2×C3×#67C2316yes—
118C22×C3×Dic3C2313yes—
119C3×#239—24no—
120C3×#239D418yescomplemented
121C3×D3×Q8—24no—
122C3×#237—212no—
123C3×D3×D4—212no—
124C3×D3×D4—212no—
125C3×D3×D4—212no—
126C3×D3×D4—412no—
127C3×#235—212no—
128C3×#235—212no—
129C2×C3×D12—212no—
130C2×C3×D12C2313yes—
131C2×C3×D12C2313yes—
132C2×C3×D12C2313yes—
133C2×C3×D12C2313yes—
134C2×C3×C4×D3—212no—
135C2×C3×C4×D3C2313yes—
136C2×C3×C4×D3C2311yescharacteristic
137C2×C3×C4×D3C2313yes—
138C2×C3×C4×D3C2313yes—
139C2×C3×C4×D3C2316yes—
140C2×C3×C4×D3C2313yes—
141C2×C3×Dic6C2311yescharacteristic
142C2×C3×Dic6C2313yes—
143C32×C4⋊C4C2313yes—
144C32×C4⋊C4C2311yescharacteristic
145C32×C22⋊C4C2313yes—
146C32×C22⋊C4C2313yes—
147C32×C42C2313yes—
148C3×#217C2313yes—
149C3×#217C2316yes—
150C3×#217C2313yes—
151C3×(C2×D3)⋊C4C2313yes—
152C3×(C2×D3)⋊C4C2316yes—
153C3×(C2×D3)⋊C4C2311yescharacteristic
154C3×(C2×D3)⋊C4C2313yes—
155C3×(C2×D3)⋊C4C2313yes—
156C3×(C2×D3)⋊C4C2313yes—
157C3×(C2×D3)⋊C4C2311yescharacteristic
158C3×C4⋊Dic3C2313yes—
159C3×C4⋊Dic3C2313yes—
160C3×Dic3⋊C4C2313yes—
161C3×Dic3⋊C4C2313yes—
162C3×Dic3⋊C4C2311yescharacteristic
163C3×Dic3⋊C4C2311yescharacteristic
164C3×C4×Dic3C2313yes—
165#3488—31noSylow
166C3×H(5,𝔽2)—68no—
167C2×C3×#41—21no—
168C2×C3×#41—21no—
169C2×C3×#41—31no—
170C2×C3×#41—31no—
171C2×C3×#41—33no—
172C2×C3×#41—33no—
173C2×C3×#41—33no—
174C2×C3×#41—68no—
175C2×C3×#41C2×D311yescharacteristic, complemented
176C2×C3×#41C2×D311yescharacteristic, complemented
177C2×C3×#41C22×C311yescharacteristic, complemented
178C2×C3×#41C22×C311yescharacteristic, complemented
179C22×C3×Q8—31no—
180C22×C3×D4—33no—
181C22×C3×D4—33no—
182C22×C3×D4—33no—
183C22×C3×D4—36no—
184C22×C3×D4—33no—
185C23×C3×C4—33no—
186#1009—28no—
187D3×#41—28no—
188C2×#239C22×C311yescharacteristic
189C2×#239C22×C311yescharacteristic, complemented
190C2×D3×Q8C22×C311yescharacteristic, complemented
191C2×#237C22×C313yescomplemented
192C2×D3×D4C22×C313yescomplemented
193C2×D3×D4C22×C313yescomplemented
194C2×D3×D4C22×C313yescomplemented
195C2×D3×D4C22×C316yescomplemented
196C2×#235C22×C313yescomplemented
197C2×#235C22×C313yescomplemented
198C22×D12C22×C313yescomplemented
199C22×C4×D3C22×C313yescomplemented
200C3×#127—23no—
201C3×#127—33no—
202C3×#127C2×D313yescomplemented
203C3×#127C22×C313yescomplemented
204C3×#124—33no—
205C3×#124—33no—
206C3×#123—33no—
207C3×#123—33no—
208C3×C22⋊Q8—33no—
209C3×C22⋊Q8—31no—
210C3×C22⋊Q8—33no—
211C3×C22⋊Q8—33no—
212C3×#121—23no—
213C3×#121—23no—
214C3×#121—33no—
215C3×#121—36no—
216C3×#121—33no—
217C3×#121—36no—
218C3×#121—33no—
219C3×#121—33no—
220C3×#121—33no—
221C3×#121—33no—
222C3×#121—36no—
223C3×#121C2×D313yescomplemented
224C3×#121C2×D313yescomplemented
225C3×#121C22×C313yescomplemented
226C3×#121C22×C313yescomplemented
227C3×#120—33no—
228C3×#120—36no—
229C3×#120—36no—
230C3×#120—33no—
231C3×C4×Q8—21no—
232C3×C4×Q8—31no—
233C3×C4×Q8C2×D311yescharacteristic, complemented
234C3×C4×Q8C22×C311yescharacteristic, complemented
235C3×C4×D4—23no—
236C3×C4×D4—33no—
237C3×C4×D4—33no—
238C3×C4×D4—33no—
239C3×C4×D4—33no—
240C3×C4×D4—33no—
241C3×C4×D4C2×D313yescomplemented
242C3×C4×D4C22×C313yescomplemented
243C3×#117—33no—
244C2×C3×C4⋊C4—33no—
245C2×C3×C22⋊C4—36no—
246Q8×Dic3C22×C311yescharacteristic, complemented
247#940C22×C313yescomplemented
248#939C22×C313yescomplemented
249#939C22×C316yescomplemented
250#938C22×C313yescomplemented
251#938C22×C313yescomplemented
252#938C22×C316yescomplemented
253#937C22×C316yescomplemented
254#937C22×C316yescomplemented
255#937C22×C313yescomplemented
256#936C22×C313yescomplemented
257#930C22×C313yescomplemented
258C4×#67C22×C313yescomplemented
259C4×#67C22×C313yescomplemented
260#924C22×C313yescomplemented
261#897C22×C313yescomplemented
262#896C22×C311yescharacteristic, complemented
263#895C22×C313yescomplemented
264#894C22×C313yescomplemented
265#893C22×C313yescomplemented
266D3×C4⋊C4C22×C313yescomplemented
267#884C22×C313yescomplemented
268#884C22×C316yescomplemented
269#883C22×C313yescomplemented
270#882C22×C313yescomplemented
271D3×C22⋊C4C22×C316yescomplemented
272#878C22×C313yescomplemented
273#875C22×C313yescomplemented
274C4×D12C22×C313yescomplemented
275C4×D12C22×C313yescomplemented
276#872C22×C313yescomplemented
277C23×C32C2413yes—
278C23×C32C2413yes—
279C22×C3×D3—26no—
280C22×C3×D3—26no—
281C22×C3×D3—212no—
282C22×C3×D3—43no—
283C22×C3×D3—46no—
284C22×C3×D3—46no—
285C22×C3×D3C2413yes—
286C22×C3×D3C2413yes—
287C22×C3×D3C2411yescharacteristic
288C32×Q8C2×D414yescomplemented
289C32×D4—26no—
290C32×D4—26no—
291C32×D4—43no—
292C32×D4—46no—
293C2×C32×C4—26no—
294C2×C32×C4—26no—
295C2×C32×C4C2411yescharacteristic
296C2×C32×C4C2413yes—
297C2×C32×C4C2411yescharacteristic
298C2×C32×C4C2411yescharacteristic
299C2×C32×C4C2413yes—
300C3×#67—26no—
301C3×#67—212no—
302C3×#67—26no—
303C3×#67—26no—
304C3×#67—46no—
305C3×#67—43no—
306C2×C3×Dic3—26no—
307C2×C3×Dic3C2411yescharacteristic
308C2×C3×Dic3C2413yes—
309C2×C3×Dic3C2411yescharacteristic
310C2×C3×Dic3C2413yes—
311C2×C3×Dic3C2411yescharacteristic
312C3×D12—26no—
313C3×D12—26no—
314C3×D12—26no—
315C3×D12C2×D4112yescomplemented
316C3×C4×D3—26no—
317C3×C4×D3—26no—
318C3×C4×D3—26no—
319C3×C4×D3—22no—
320C3×C4×D3—46no—
321C3×C4×D3C2×D4112yescomplemented
322C3×Dic6—26no—
323C3×Dic6—22no—
324C2×H(5,𝔽2)—31no—
325C22×#41—31no—
326#550—31no—
327#550C3×D311yescharacteristic, complemented
328#548—31no—
329#548—31no—
330#546—33no—
331#546—33no—
332D42—33no—
333D42—33no—
334#537—33no—
335#535—33no—
336#525—33no—
337C2×#121—33no—
338#520—31no—
339C24×C3—33no—
340C24×C3—36no—
341C23×D3C23×C313yes—
342C23×D3C23×C316yes—
343C3×#41—24no—
344C3×#41—24no—
345C3×#41—24no—
346C3×#41—24no—
347C3×#41—38no—
348C3×#41—44no—
349C3×#41—44no—
350C3×#41—612no—
351C3×#41—612no—
352C3×#41—612no—
353C3×#41—64no—
354C2×C3×Q8—21no—
355C2×C3×Q8—31no—
356C2×C3×Q8—33no—
357C2×C3×Q8—64no—
358C2×C3×Q8C22×D311yescharacteristic
359C2×C3×Q8C23×C311yescharacteristic
360C2×C3×D4—23no—
361C2×C3×D4—23no—
362C2×C3×D4—23no—
363C2×C3×D4—26no—
364C2×C3×D4—33no—
365C2×C3×D4—36no—
366C2×C3×D4—33no—
367C2×C3×D4—33no—
368C2×C3×D4—33no—
369C2×C3×D4—36no—
370C2×C3×D4—33no—
371C2×C3×D4—33no—
372C2×C3×D4—33no—
373C2×C3×D4—33no—
374C2×C3×D4—612no—
375C2×C3×D4—612no—
376C2×C3×D4—612no—
377C2×C3×D4—612no—
378C2×C3×D4—1212no—
379C2×C3×D4C22×D313yes—
380C2×C3×D4C22×D313yes—
381C2×C3×D4C22×D313yes—
382C2×C3×D4C22×D316yes—
383C2×C3×D4C23×C313yes—
384C2×C3×D4C23×C313yes—
385C2×C3×D4C23×C313yes—
386C2×C3×D4C23×C316yes—
387C22×C3×C4—23no—
388C22×C3×C4—23no—
389C22×C3×C4—33no—
390C22×C3×C4—33no—
391C22×C3×C4—33no—
392C22×C3×C4—33no—
393C22×C3×C4—33no—
394C22×C3×C4—31no—
395C22×C3×C4—36no—
396C22×C3×C4—612no—
397C22×C3×C4C22×D313yes—
398C22×C3×C4C22×D313yes—
399C22×C3×C4C23×C313yes—
400C22×C3×C4C23×C313yes—
401C2×#67C23×C313yes—
402C2×#67C23×C313yes—
403C2×#67C23×C316yes—
404C2×#67C23×C313yes—
405C2×#67C23×C313yes—
406C2×#67C23×C316yes—
407C22×Dic3C23×C313yes—
408#239—24no—
409#239C3×D418yescomplemented
410D3×Q8—24no—
411#237—212no—
412D3×D4—212no—
413D3×D4—212no—
414D3×D4—212no—
415D3×D4—412no—
416#235—212no—
417#235—212no—
418C2×D12—212no—
419C2×D12C23×C313yes—
420C2×D12C23×C313yes—
421C2×D12C23×C313yes—
422C2×D12C23×C313yes—
423C2×C4×D3—212no—
424C2×C4×D3C23×C313yes—
425C2×C4×D3C23×C313yes—
426C2×C4×D3C23×C313yes—
427C2×C4×D3C23×C311yescharacteristic
428C2×C4×D3C23×C316yes—
429C2×C4×D3C23×C313yes—
430C2×Dic6C23×C313yes—
431C2×Dic6C23×C311yescharacteristic
432C3×C4⋊C4—21no—
433C3×C4⋊C4—23no—
434C3×C4⋊C4—33no—
435C3×C4⋊C4—31no—
436C3×C4⋊C4—31no—
437C3×C4⋊C4—33no—
438C3×C4⋊C4—33no—
439C3×C4⋊C4—33no—
440C3×C4⋊C4C22×D313yes—
441C3×C4⋊C4C22×D311yescharacteristic
442C3×C4⋊C4C23×C313yes—
443C3×C4⋊C4C23×C311yescharacteristic
444C3×C22⋊C4—23no—
445C3×C22⋊C4—23no—
446C3×C22⋊C4—36no—
447C3×C22⋊C4—33no—
448C3×C22⋊C4—33no—
449C3×C22⋊C4—33no—
450C3×C22⋊C4—36no—
451C3×C22⋊C4—33no—
452C3×C22⋊C4—33no—
453C3×C22⋊C4—31no—
454C3×C22⋊C4—31no—
455C3×C22⋊C4—33no—
456C3×C22⋊C4C22×D313yes—
457C3×C22⋊C4C22×D313yes—
458C3×C22⋊C4C23×C313yes—
459C3×C22⋊C4C23×C313yes—
460C3×C42—23no—
461C3×C42—33no—
462C3×C42C22×D313yes—
463C3×C42C23×C313yes—
464#217C23×C313yes—
465#217C23×C316yes—
466#217C23×C313yes—
467(C2×D3)⋊C4C23×C313yes—
468(C2×D3)⋊C4C23×C313yes—
469(C2×D3)⋊C4C23×C311yescharacteristic
470(C2×D3)⋊C4C23×C313yes—
471(C2×D3)⋊C4C23×C316yes—
472(C2×D3)⋊C4C23×C313yes—
473(C2×D3)⋊C4C23×C311yescharacteristic
474C4⋊Dic3C23×C313yes—
475C4⋊Dic3C23×C313yes—
476Dic3⋊C4C23×C311yescharacteristic
477Dic3⋊C4C23×C313yes—
478Dic3⋊C4C23×C313yes—
479Dic3⋊C4C23×C311yescharacteristic
480C4×Dic3C23×C313yes—
481C22×C32—23no—
482C22×C32—23no—
483C22×C32—23no—
484C22×C32—23no—
485C22×C32—23no—
486C22×C32—23no—
487C22×C32C2511yescharacteristic
488C2×C3×D3—21no—
489C2×C3×D3—23no—
490C2×C3×D3—21no—
491C2×C3×D3—23no—
492C2×C3×D3—23no—
493C2×C3×D3—23no—
494C2×C3×D3—23no—
495C2×C3×D3—412no—
496C2×C3×D3—812no—
497C2×C3×D3C22×D416yes—
498C2×C3×D3H(5,𝔽2)12yescomplemented
499C32×C4—21no—
500C32×C4—21no—
501C32×C4—21no—
502C32×C4—23no—
503C32×C4C22×D416yes—
504C3×Dic3—23no—
505C3×Dic3—21no—
506C3×Dic3—23no—
507C3×Dic3—21no—
508C3×Dic3C22×D412yes—
509H(5,𝔽2)—68no—
510C2×#41—31no—
511C2×#41—31no—
512C2×#41—33no—
513C2×#41—33no—
514C2×#41—33no—
515C2×#41—68no—
516C2×#41C2×C3×D311yescharacteristic, complemented
517C2×#41C2×C3×D311yescharacteristic, complemented
518C22×Q8—31no—
519C22×D4—33no—
520C22×D4—33no—
521C22×D4—33no—
522C22×D4—36no—
523C22×D4—33no—
524C23×C4—33no—
525#127—33no—
526#127C2×C3×D313yescomplemented
527#124—33no—
528#124—33no—
529#123—33no—
530#123—33no—
531C22⋊Q8—33no—
532C22⋊Q8—31no—
533C22⋊Q8—33no—
534C22⋊Q8—33no—
535#121—36no—
536#121—33no—
537#121—33no—
538#121—36no—
539#121—33no—
540#121—33no—
541#121—33no—
542#121—33no—
543#121—36no—
544#121C2×C3×D313yescomplemented
545#121C2×C3×D313yescomplemented
546#120—33no—
547#120—36no—
548#120—36no—
549#120—33no—
550C4×Q8—31no—
551C4×Q8C2×C3×D311yescharacteristic, complemented
552C4×D4—33no—
553C4×D4—33no—
554C4×D4—33no—
555C4×D4—33no—
556C4×D4—33no—
557C4×D4C2×C3×D313yescomplemented
558#117—33no—
559C2×C4⋊C4—33no—
560C2×C22⋊C4—36no—
561C23×C3—23no—
562C23×C3—23no—
563C23×C3—33no—
564C23×C3—31no—
565C23×C3—33no—
566C23×C3—66no—
567C23×C3—66no—
568C23×C3—612no—
569C23×C3—123no—
570C23×C3—126no—
571C23×C3—126no—
572C23×C3C23×D313yes—
573C23×C3C23×D313yes—
574C23×C3C24×C313yes—
575C23×C3C24×C313yes—
576C22×D3—26no—
577C22×D3—26no—
578C22×D3—212no—
579C22×D3—43no—
580C22×D3—46no—
581C22×D3—46no—
582C22×D3C24×C313yes—
583C22×D3C24×C313yes—
584C22×D3C24×C311yescharacteristic
585C3×Q8—24no—
586C3×Q8—62no—
587C3×Q8—66no—
588C3×Q8D3×D414yescomplemented
589C3×Q8C2×C3×D414yescomplemented
590C3×D4—26no—
591C3×D4—26no—
592C3×D4—26no—
593C3×D4—26no—
594C3×D4—312no—
595C3×D4—46no—
596C3×D4—46no—
597C3×D4—46no—
598C3×D4—46no—
599C3×D4—43no—
600C3×D4—43no—
601C3×D4—46no—
602C3×D4—66no—
603C3×D4—66no—
604C3×D4—66no—
605C3×D4—66no—
606C3×D4—612no—
607C3×D4—66no—
608C3×D4—66no—
609C3×D4—86no—
610C3×D4—123no—
611C3×D4—126no—
612C2×C3×C4—26no—
613C2×C3×C4—26no—
614C2×C3×C4—26no—
615C2×C3×C4—26no—
616C2×C3×C4—21no—
617C2×C3×C4—23no—
618C2×C3×C4—23no—
619C2×C3×C4—21no—
620C2×C3×C4—21no—
621C2×C3×C4—31no—
622C2×C3×C4—312no—
623C2×C3×C4—31no—
624C2×C3×C4—33no—
625C2×C3×C4—33no—
626C2×C3×C4—31no—
627C2×C3×C4—46no—
628C2×C3×C4—46no—
629C2×C3×C4—62no—
630C2×C3×C4—66no—
631C2×C3×C4—66no—
632C2×C3×C4—66no—
633C2×C3×C4—66no—
634C2×C3×C4—126no—
635C2×C3×C4C23×D311yescharacteristic
636C2×C3×C4C23×D313yes—
637C2×C3×C4C23×D311yescharacteristic
638C2×C3×C4C23×D311yescharacteristic
639C2×C3×C4C23×D313yes—
640C2×C3×C4C24×C311yescharacteristic
641C2×C3×C4C24×C313yes—
642C2×C3×C4C24×C311yescharacteristic
643C2×C3×C4C24×C311yescharacteristic
644C2×C3×C4C24×C313yes—
645#67—26no—
646#67—212no—
647#67—26no—
648#67—26no—
649#67—46no—
650#67—43no—
651C2×Dic3—26no—
652C2×Dic3C24×C311yescharacteristic
653C2×Dic3C24×C313yes—
654C2×Dic3C24×C311yescharacteristic
655C2×Dic3C24×C313yes—
656C2×Dic3C24×C311yescharacteristic
657D12—26no—
658D12—26no—
659D12—26no—
660D12C2×C3×D4112yescomplemented
661C4×D3—26no—
662C4×D3—26no—
663C4×D3—26no—
664C4×D3—22no—
665C4×D3—46no—
666C4×D3C2×C3×D4112yescomplemented
667Dic6—26no—
668Dic6—22no—
669C2×C32—43no—
670C2×C32—43no—
671C2×C32C23×D411yescharacteristic
672C2×C32C2×H(5,𝔽2)11yescharacteristic
673C2×C32#58511yescharacteristic
674C3×D3—22no—
675C3×D3—26no—
676C3×D3—43no—
677C24—33no—
678C24—36no—
679#41—24no—
680#41—24no—
681#41—38no—
682#41—612no—
683#41—612no—
684#41—612no—
685#41—64no—
686C2×Q8—31no—
687C2×Q8—33no—
688C2×Q8—64no—
689C2×Q8C22×C3×D311yescharacteristic
690C2×D4—33no—
691C2×D4—36no—
692C2×D4—33no—
693C2×D4—33no—
694C2×D4—33no—
695C2×D4—36no—
696C2×D4—33no—
697C2×D4—33no—
698C2×D4—33no—
699C2×D4—33no—
700C2×D4—612no—
701C2×D4—612no—
702C2×D4—612no—
703C2×D4—612no—
704C2×D4—1212no—
705C2×D4C22×C3×D313yes—
706C2×D4C22×C3×D313yes—
707C2×D4C22×C3×D313yes—
708C2×D4C22×C3×D316yes—
709C22×C4—33no—
710C22×C4—33no—
711C22×C4—33no—
712C22×C4—33no—
713C22×C4—33no—
714C22×C4—31no—
715C22×C4—36no—
716C22×C4—612no—
717C22×C4C22×C3×D313yes—
718C22×C4C22×C3×D313yes—
719C4⋊C4—33no—
720C4⋊C4—33no—
721C4⋊C4—31no—
722C4⋊C4—31no—
723C4⋊C4—33no—
724C4⋊C4—33no—
725C4⋊C4C22×C3×D313yes—
726C4⋊C4C22×C3×D311yescharacteristic
727C22⋊C4—36no—
728C22⋊C4—33no—
729C22⋊C4—33no—
730C22⋊C4—33no—
731C22⋊C4—36no—
732C22⋊C4—33no—
733C22⋊C4—33no—
734C22⋊C4—31no—
735C22⋊C4—31no—
736C22⋊C4—33no—
737C22⋊C4C22×C3×D313yes—
738C22⋊C4C22×C3×D313yes—
739C42—33no—
740C42C22×C3×D313yes—
741C22×C3—23no—
742C22×C3—23no—
743C22×C3—23no—
744C22×C3—23no—
745C22×C3—23no—
746C22×C3—23no—
747C22×C3—23no—
748C22×C3—23no—
749C22×C3—23no—
750C22×C3—23no—
751C22×C3—23no—
752C22×C3—23no—
753C22×C3—21no—
754C22×C3—36no—
755C22×C3—32no—
756C22×C3—43no—
757C22×C3—43no—
758C22×C3—43no—
759C22×C3—43no—
760C22×C3—43no—
761C22×C3—43no—
762C22×C3—61no—
763C22×C3—61no—
764C22×C3—63no—
765C22×C3—63no—
766C22×C3—63no—
767C22×C3—63no—
768C22×C3—63no—
769C22×C3—1212no—
770C22×C3—2412no—
771C22×C3C24×D311yescharacteristic
772C22×C3C25×C311yescharacteristic
773C2×D3—21no—
774C2×D3—23no—
775C2×D3—21no—
776C2×D3—23no—
777C2×D3—23no—
778C2×D3—23no—
779C2×D3—23no—
780C2×D3—412no—
781C2×D3—812no—
782C2×D3C22×C3×D416yes—
783C2×D3C3×H(5,𝔽2)12yescomplemented
784C3×C4—22no—
785C3×C4—21no—
786C3×C4—21no—
787C3×C4—21no—
788C3×C4—23no—
789C3×C4—21no—
790C3×C4—21no—
791C3×C4—23no—
792C3×C4—21no—
793C3×C4—26no—
794C3×C4—32no—
795C3×C4—41no—
796C3×C4—41no—
797C3×C4—43no—
798C3×C4—61no—
799C3×C4—63no—
800C3×C4—61no—
801C3×C4—63no—
802C3×C4C2×D3×D416yes—
803C3×C4C22×C3×D416yes—
804Dic3—23no—
805Dic3—21no—
806Dic3—23no—
807Dic3—21no—
808Dic3C22×C3×D412yes—
809C32#348811yescharacteristic, complemented, Sylow
810C23—33no—
811C23—31no—
812C23—33no—
813C23—66no—
814C23—66no—
815C23—612no—
816C23—123no—
817C23—126no—
818C23—126no—
819C23C23×C3×D313yes—
820C23C23×C3×D313yes—
821Q8—62no—
822Q8—66no—
823Q8C3×D3×D414yescomplemented
824D4—26no—
825D4—26no—
826D4—312no—
827D4—46no—
828D4—43no—
829D4—66no—
830D4—66no—
831D4—66no—
832D4—66no—
833D4—612no—
834D4—66no—
835D4—66no—
836D4—126no—
837D4—123no—
838C2×C4—26no—
839C2×C4—26no—
840C2×C4—31no—
841C2×C4—312no—
842C2×C4—31no—
843C2×C4—33no—
844C2×C4—33no—
845C2×C4—31no—
846C2×C4—62no—
847C2×C4—66no—
848C2×C4—66no—
849C2×C4—66no—
850C2×C4—66no—
851C2×C4—126no—
852C2×C4C23×C3×D311yescharacteristic
853C2×C4C23×C3×D313yes—
854C2×C4C23×C3×D311yescharacteristic
855C2×C4C23×C3×D311yescharacteristic
856C2×C4C23×C3×D313yes—
857C2×C3—21no—
858C2×C3—21no—
859C2×C3—21no—
860C2×C3—43no—
861C2×C3—43no—
862C2×C3—43no—
863C2×C3—43no—
864C2×C3—62no—
865C2×C3—66no—
866C2×C3—83no—
867C2×C3—83no—
868C2×C3—123no—
869C2×C3C22×D3×D411yescharacteristic
870C2×C3#596411yescharacteristic
871C2×C3D3×H(5,𝔽2)11yescharacteristic
872C2×C3C23×C3×D411yescharacteristic
873C2×C3C2×C3×H(5,𝔽2)11yescharacteristic
874C2×C3C3×#58511yescharacteristic
875D3—22no—
876D3—26no—
877D3—43no—
878C22—23no—
879C22—23no—
880C22—23no—
881C22—23no—
882C22—23no—
883C22—23no—
884C22—36no—
885C22—32no—
886C22—61no—
887C22—61no—
888C22—63no—
889C22—63no—
890C22—63no—
891C22—63no—
892C22—63no—
893C22—1212no—
894C22—2412no—
895C22C24×C3×D311yescharacteristic
896C4—21no—
897C4—21no—
898C4—21no—
899C4—23no—
900C4—32no—
901C4—61no—
902C4—63no—
903C4—61no—
904C4—63no—
905C4C2×C3×D3×D416yes—
906C3—21no—
907C3#8676911yescharacteristic, direct product factor
908C3C3×#348811yescharacteristic, complemented
909C2—43no—
910C2—43no—
911C2—62no—
912C2—66no—
913C2—123no—
914C2C22×C3×D3×D411yescharacteristic
915C2C3×#596411yescharacteristic
916C2C3×D3×H(5,𝔽2)11yescharacteristic
subgroupG/H
centerC22×C3C24×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC32×#550C2
socleC22×C32C25
hypercenterC3×#550D3
hypocenterC3C3×#3488
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×#550

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1009C2semidirect
2. C2×C3×D3×#41C2semidirect
3. C32×#550C2semidirect
4. C3×#5834C2semidirect
5. C3×#5831C2semidirect
6. C3×#5717C2semidirect
7. C3×#5715C2semidirect
8. C3×#5612C2semidirect
9. C3×#5609C2semidirect
10. C3×#5608C2semidirect
11. C3×D3×#121C2semidirect
12. C3×#5576C2semidirect
13. C3×#5574C2semidirect
14. C3×#5550C2semidirect
15. C3×#5547C2semidirect
17. #86769C3direct (N × H)
18. C2×C32×#41C22semidirect
19. C2×C32×#41C22semidirect
23. C2×C3×#239C22semidirect
24. C2×C3×D3×Q8C22semidirect
25. C2×C3×#237C22semidirect
26. C2×C3×D3×D4C22semidirect
27. C2×C3×D3×D4C22semidirect
28. C2×C3×D3×D4C22semidirect
29. C2×C3×D3×D4C22semidirect
30. C2×C3×#235C22semidirect
31. C2×C3×#235C22semidirect
32. C22×C3×D12C22semidirect
33. C22×C3×C4×D3C22semidirect
34. C32×#127C22semidirect
35. C32×#121C22semidirect
36. C32×#121C22semidirect
37. C32×C4×Q8C22semidirect
38. C32×C4×D4C22semidirect
39. C3×Q8×Dic3C22semidirect
40. C3×#940C22semidirect
41. C3×#939C22semidirect
42. C3×#939C22semidirect
43. C3×#938C22semidirect
44. C3×#938C22semidirect
45. C3×#938C22semidirect
46. C3×#937C22semidirect
47. C3×#937C22semidirect
48. C3×#937C22semidirect
49. C3×#936C22semidirect
50. C3×#930C22semidirect
51. C3×C4×#67C22semidirect
52. C3×C4×#67C22semidirect
53. C3×#924C22semidirect
54. C3×#897C22semidirect
55. C3×#896C22semidirect
56. C3×#895C22semidirect
57. C3×#894C22semidirect
58. C3×#893C22semidirect
59. C3×D3×C4⋊C4C22semidirect
60. C3×#884C22semidirect
61. C3×#884C22semidirect
62. C3×#883C22semidirect
63. C3×#882C22semidirect
64. C3×D3×C22⋊C4C22semidirect
65. C3×#878C22semidirect
66. C3×#875C22semidirect
67. C3×C4×D12C22semidirect
68. C3×C4×D12C22semidirect
69. C3×#872C22semidirect
72. C2×#1009C2×C3semidirect
73. C2×D3×#41C2×C3semidirect
76. C3×#550D3semidirect
77. C3×#550C2×C3semidirect
89. #5834C2×C3semidirect
90. #5831C2×C3semidirect
91. #5717C2×C3semidirect
92. #5715C2×C3semidirect
93. #5612C2×C3semidirect
94. #5609C2×C3semidirect
95. #5608C2×C3semidirect
96. D3×#121C2×C3semidirect
97. #5576C2×C3semidirect
98. #5574C2×C3semidirect
99. #5550C2×C3semidirect
100. #5547C2×C3semidirect
120. C3×#239D4semidirect
175. C2×C3×#41C2×D3semidirect
176. C2×C3×#41C2×D3semidirect
177. C2×C3×#41C22×C3semidirect
178. C2×C3×#41C22×C3semidirect
189. C2×#239C22×C3semidirect
190. C2×D3×Q8C22×C3semidirect
191. C2×#237C22×C3semidirect
192. C2×D3×D4C22×C3semidirect
193. C2×D3×D4C22×C3semidirect
194. C2×D3×D4C22×C3semidirect
195. C2×D3×D4C22×C3semidirect
196. C2×#235C22×C3semidirect
197. C2×#235C22×C3semidirect
198. C22×D12C22×C3semidirect
199. C22×C4×D3C22×C3semidirect
202. C3×#127C2×D3semidirect
203. C3×#127C22×C3semidirect
223. C3×#121C2×D3semidirect
224. C3×#121C2×D3semidirect
225. C3×#121C22×C3semidirect
226. C3×#121C22×C3semidirect
233. C3×C4×Q8C2×D3semidirect
234. C3×C4×Q8C22×C3semidirect
241. C3×C4×D4C2×D3semidirect
242. C3×C4×D4C22×C3semidirect
246. Q8×Dic3C22×C3semidirect
247. #940C22×C3semidirect
248. #939C22×C3semidirect
249. #939C22×C3semidirect
250. #938C22×C3semidirect
251. #938C22×C3semidirect
252. #938C22×C3semidirect
253. #937C22×C3semidirect
254. #937C22×C3semidirect
255. #937C22×C3semidirect
256. #936C22×C3semidirect
257. #930C22×C3semidirect
258. C4×#67C22×C3semidirect
259. C4×#67C22×C3semidirect
260. #924C22×C3semidirect
261. #897C22×C3semidirect
262. #896C22×C3semidirect
263. #895C22×C3semidirect
264. #894C22×C3semidirect
265. #893C22×C3semidirect
266. D3×C4⋊C4C22×C3semidirect
267. #884C22×C3semidirect
268. #884C22×C3semidirect
269. #883C22×C3semidirect
270. #882C22×C3semidirect
271. D3×C22⋊C4C22×C3semidirect
272. #878C22×C3semidirect
273. #875C22×C3semidirect
274. C4×D12C22×C3semidirect
275. C4×D12C22×C3semidirect
276. #872C22×C3semidirect
288. C32×Q8C2×D4semidirect
315. C3×D12C2×D4semidirect
321. C3×C4×D3C2×D4semidirect
327. #550C3×D3semidirect
409. #239C3×D4semidirect
498. C2×C3×D3H(5,𝔽2)semidirect
516. C2×#41C2×C3×D3semidirect
517. C2×#41C2×C3×D3semidirect
526. #127C2×C3×D3semidirect
544. #121C2×C3×D3semidirect
545. #121C2×C3×D3semidirect
551. C4×Q8C2×C3×D3semidirect
557. C4×D4C2×C3×D3semidirect
588. C3×Q8D3×D4semidirect
589. C3×Q8C2×C3×D4semidirect
660. D12C2×C3×D4semidirect
666. C4×D3C2×C3×D4semidirect
783. C2×D3C3×H(5,𝔽2)semidirect
809. C32#3488semidirect
823. Q8C3×D3×D4semidirect
907. C3#86769direct (N × H)
908. C3C3×#3488semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10092
C2×C3×D3×#412
C32×#5502
C3×#58342
C3×#58312
C3×#57172
C3×#57152
C3×#56122
C3×#56092
C3×#56082
C3×D3×#1212
C3×#55762
C3×#55742
C3×#55502
C3×#55472
C3×#34883
#867693