Finite Group Databasebeta

← #13168116

Subgroups — #13168116

Order 1728.

1624 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3802C211yesmaximal, characteristic, complemented
2C2×C3×#3796C211yesmaximal, characteristic, complemented
3C4×#6295C211yesmaximal, characteristic, complemented
4#11723522C211yesmaximal, characteristic, complemented
5D12×C3⋊Dic3C211yesmaximal, characteristic, complemented
6#11723435C211yesmaximal, characteristic, complemented
7C3×#63863C211yesmaximal, characteristic, complemented
8#11722985C212yesmaximal, complemented
9#11722954C212yesmaximal, complemented
10#11722947C212yesmaximal, complemented
11D3×(C2×D3)⋊Dic3C212yesmaximal, complemented
12#10595428—31nomaximal
13#10595244—31nomaximal
14#10595229—31nomaximal
15C22×C3×D32C2212yes—
16C2×C3×C4×C3⋊D3C2211yescharacteristic
17C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
18C2×C32×D12C2211yescharacteristic
19C2×C32×D12C2211yescharacteristic
20C2×C32×Dic6C2211yescharacteristic, complemented
21C2×#6295C2211yescharacteristic
22C2×#6290C2212yescomplemented
23C2×D3×C3⋊Dic3C2212yescomplemented
24C2×C3×#626C2212yescomplemented
25C2×C3×#625C2212yes—
26C2×C3×D3×Dic3C2212yescomplemented
27C3×#3802—24no—
28C3×#3796—24no—
29C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic, complemented
30C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
31#88815C2211yescharacteristic, complemented
32#88814C2211yescharacteristic
33#88814C2211yescharacteristic, complemented
34#88806C2212yescomplemented
35#88803C2212yes—
36(C2×D3)⋊(C3⋊Dic3)C2212yescomplemented
37(C2×D3)⋊(C3⋊Dic3)C2212yescomplemented
38C3×(C2×D3)⋊Dic3C2212yescomplemented
39C3×(C2×D3)⋊Dic3C2212yescomplemented
40C2×C3×#239—31no—
41C2×C3×#237—31no—
42C2×C3×D3×D4—31no—
43C2×C3×D3×D4—31no—
44C2×#3802D311yescharacteristic, complemented
45C2×#3796D311yescharacteristic, complemented
46#64155—31no—
47#64147—31no—
48D4×C3⋊Dic3—31no—
49C3×#947—31no—
50C3×#936—31no—
51#63980—32no—
52#63977—32no—
53#63976—32no—
54#63971—32no—
55#63969—32no—
56D3×#217—32no—
57#63961—32no—
58C2×(C2×D3)⋊Dic3—32no—
59#63922—32no—
60D3×(C2×D3)⋊C4—32no—
61#63908—31no—
62#63908—31no—
63#63908—61no—
64#63905—32no—
65C4×#626—31no—
66C4×#626—31no—
67C4×#625—31no—
68Dic3×D12—31no—
69Dic3×D12—31no—
70Dic3×D12—61no—
71#63885—32no—
72#63863D311yescharacteristic, complemented
73#63856—31no—
74#63856—31no—
75#63856—61no—
76C22×C3×C3⋊D3C2311yescharacteristic
77C22×C3×C3⋊D3C2311yescharacteristic
78C22×C32×D3C2312yes—
79C22×C32×D3C2312yes—
80C2×C3×D32—24no—
81C2×C3×D32—24no—
82C2×C3×D32—42no—
83C2×C33×C4C2311yescharacteristic
84C2×C3⋊(C3⋊Dic3)C2312yes—
85C2×C3×C3⋊Dic3C2311yescharacteristic
86C2×C3×C3⋊Dic3C2311yescharacteristic
87C2×C3×C3⋊Dic3C2311yescharacteristic
88C2×C3×C3⋊Dic3C2311yescharacteristic
89C3×C4×C3⋊D3—22no—
90C3×C4×C3⋊D3—22no—
91C2×C32×Dic3C2312yes—
92C32×D12—22no—
93C32×D12D414yescomplemented
94C32×Dic6—22no—
95#6295—22no—
96#6290—42no—
97D3×C3⋊Dic3—42no—
98C3×#626—24no—
99C3×#625—24no—
100C3×D3×Dic3—24no—
101#5829—91no—
102#5806—91no—
103#5676—91no—
104C23×C3×D3—32no—
105C23×C3×D3—32no—
106C22×D32C2×D312yes—
107C2×C32×Q8—31no—
108C2×C32×D4—31no—
109C2×C32×D4—31no—
110C2×#638—32no—
111C22×C3⋊Dic3—32no—
112C2×C4×C3⋊D3C2×D311yescharacteristic
113C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
114C2×C3×#67—32no—
115C2×C3×#67—32no—
116C2×C3×#67—32no—
117C22×C3×Dic3—32no—
118C3×#239—64no—
119C3×#237—64no—
120C3×D3×D4—64no—
121C3×D3×D4—64no—
122C2×C3×D12—21no—
123C2×C3×D12—21no—
124C2×C3×D12—32no—
125C2×C3×D12C2×D311yescharacteristic
126C2×C3×D12C2×D311yescharacteristic
127C2×C3×D12C2×D311yescharacteristic
128C2×C3×D12C2×D311yescharacteristic
129C2×C3×C4×D3—32no—
130C2×C3×C4×D3—31no—
131C2×C3×C4×D3—31no—
132C2×C3×C4×D3—31no—
133C2×C3×C4×D3—31no—
134C2×C3×C4×D3—61no—
135C2×C3×C4×D3—61no—
136C2×C3×Dic6—21no—
137C2×C3×Dic6C2×D311yescharacteristic, complemented
138C2×C3×Dic6C2×D311yescharacteristic, complemented
139C2×#626—31no—
140C2×#626—31no—
141C2×#626C2×D312yescomplemented
142C2×#625—31no—
143C2×#625—32no—
144C2×#625—32no—
145C2×#625—62no—
146C2×#625C2×D312yes—
147C2×D3×Dic3—32no—
148C2×D3×Dic3—32no—
149C2×D3×Dic3—62no—
150C2×D3×Dic3C2×D312yescomplemented
151#3802—24no—
152#3796—24no—
153#3757—32no—
154#3757—32no—
155#3752—32no—
156C4⋊(C3⋊Dic3)—31no—
157C4⋊(C3⋊Dic3)—31no—
158C4⋊(C3⋊Dic3)—31no—
159C4⋊(C3⋊Dic3)—61no—
160C4⋊(C3⋊Dic3)—61no—
161C4⋊(C3⋊Dic3)—61no—
162C4⋊(C3⋊Dic3)—121no—
163#3750—32no—
164C4×C3⋊Dic3C2×D311yescharacteristic, complemented
165C3×#217—32no—
166C3×#217—32no—
167C3×(C2×D3)⋊C4—32no—
168C3×(C2×D3)⋊C4—32no—
169C3×C4×Dic3—31no—
170C3×C4×Dic3—31no—
171C3×C4×Dic3—61no—
172#3724—31no—
173#3724—32no—
174#3724—32no—
175#3724—62no—
176Dic3⋊Dic3—31no—
177Dic3⋊Dic3—31no—
178#3722—31no—
179#3722—31no—
180(C2×D3)⋊Dic3—32no—
181(C2×D3)⋊Dic3—32no—
182(C2×D3)⋊Dic3—32no—
183(C2×D3)⋊Dic3—32no—
184(C2×D3)⋊Dic3—31no—
185(C2×D3)⋊Dic3—31no—
186(C2×D3)⋊Dic3—31no—
187(C2×D3)⋊Dic3—31no—
188(C2×D3)⋊Dic3—32no—
189(C2×D3)⋊Dic3—32no—
190(C2×D3)⋊Dic3—62no—
191(C2×D3)⋊Dic3—62no—
192(C2×D3)⋊Dic3—62no—
193(C2×D3)⋊Dic3C2×D312yescomplemented
194(C2×D3)⋊Dic3C2×D312yescomplemented
195C22×C33C2411yescharacteristic
196C2×C3×C3⋊D3—21no—
197C2×C3×C3⋊D3—21no—
198C2×C3×C3⋊D3—21no—
199C2×C3×C3⋊D3—21no—
200C2×C3×C3⋊D3—21no—
201C2×C3×C3⋊D3#4112yescomplemented
202C2×C32×D3—22no—
203C2×C32×D3—22no—
204C2×C32×D3—22no—
205C2×C32×D3—22no—
206C2×C32×D3—22no—
207C2×C32×D3C2×D414yes—
208C3×D32—48no—
209C33×C4C2×D412yes—
210C3⋊(C3⋊Dic3)—22no—
211C3×C3⋊Dic3—21no—
212C3×C3⋊Dic3—21no—
213C3×C3⋊Dic3—21no—
214C3×C3⋊Dic3—21no—
215C32×Dic3—22no—
216C2×C3×#41—91no—
217C22×C3×D4—91no—
218C2×#239—31no—
219C2×#237—31no—
220C2×D3×D4—31no—
221C2×D3×D4—31no—
222C3×#124—91no—
223#953—92no—
224C2×#217—92no—
225#947—31no—
226#946—91no—
227#946—91no—
228#946—181no—
229#939—92no—
230#939—92no—
231#938—91no—
232#938—91no—
233#938—181no—
234#937—92no—
235#936—31no—
236#935—92no—
237D4×Dic3—91no—
238D4×Dic3—91no—
239D4×Dic3—181no—
240#930—91no—
241#929—92no—
242C4×#67—91no—
243C4×#67—91no—
244C2×(C2×D3)⋊C4—92no—
245#924—91no—
246#884—92no—
247#883—92no—
248#882—92no—
249D3×C22⋊C4—92no—
250C4×D12—91no—
251C4×D12—91no—
252C23×C32—32no—
253C23×C32—32no—
254C22×C3⋊D3C22×D311yescharacteristic
255C22×C3⋊D3C22×D311yescharacteristic
256C22×C3×D3—22no—
257C22×C3×D3—22no—
258C22×C3×D3—31no—
259C22×C3×D3—31no—
260C22×C3×D3—31no—
261C22×C3×D3—31no—
262C22×C3×D3—61no—
263C22×C3×D3—61no—
264C22×C3×D3—64no—
265C22×C3×D3—64no—
266C22×C3×D3—64no—
267C22×C3×D3—64no—
268C22×C3×D3—122no—
269C22×C3×D3—122no—
270C22×C3×D3C22×D312yes—
271C22×C3×D3C22×D312yes—
272C22×C3×D3C22×D312yes—
273C22×C3×D3C22×D312yes—
274C2×D32—24no—
275C2×D32—24no—
276C2×D32—42no—
277C32×Q8—62no—
278C32×D4—34no—
279C32×D4—62no—
280C2×C32×C4—21no—
281C2×C32×C4—21no—
282C2×C32×C4—21no—
283C2×C32×C4—32no—
284C2×C32×C4—41no—
285C2×C32×C4C22×D311yescharacteristic
286C2×C32×C4C22×D311yescharacteristic
287C2×C32×C4C22×D311yescharacteristic
288#638—122no—
289C2×C3⋊Dic3—32no—
290C2×C3⋊Dic3—32no—
291C2×C3⋊Dic3—32no—
292C2×C3⋊Dic3—62no—
293C2×C3⋊Dic3—62no—
294C2×C3⋊Dic3—62no—
295C2×C3⋊Dic3—122no—
296C2×C3⋊Dic3—122no—
297C2×C3⋊Dic3C22×D311yescharacteristic
298C2×C3⋊Dic3C22×D311yescharacteristic
299C2×C3⋊Dic3C22×D311yescharacteristic
300C2×C3⋊Dic3C22×D311yescharacteristic
301C4×C3⋊D3—22no—
302C4×C3⋊D3—22no—
303C3×#67—64no—
304C3×#67—64no—
305C3×#67—64no—
306C2×C3×Dic3—22no—
307C2×C3×Dic3—31no—
308C2×C3×Dic3—31no—
309C2×C3×Dic3—31no—
310C2×C3×Dic3—31no—
311C2×C3×Dic3—31no—
312C2×C3×Dic3—31no—
313C2×C3×Dic3—31no—
314C2×C3×Dic3—31no—
315C2×C3×Dic3—61no—
316C2×C3×Dic3—61no—
317C2×C3×Dic3—61no—
318C2×C3×Dic3—61no—
319C2×C3×Dic3—64no—
320C2×C3×Dic3C22×D312yes—
321C2×C3×Dic3C22×D312yes—
322C3×D12—22no—
323C3×D12—22no—
324C3×D12—24no—
325C3×D12—42no—
326C3×D12—64no—
327C3×D12#6714yescomplemented
328C3×D12#6714yescomplemented
329C3×C4×D3—64no—
330C3×C4×D3—62no—
331C3×C4×D3—62no—
332C3×C4×D3—62no—
333C3×C4×D3—62no—
334C3×C4×D3—122no—
335C3×C4×D3—122no—
336C3×Dic6—22no—
337C3×Dic6—22no—
338C3×Dic6—42no—
339#626—24no—
340#626—62no—
341#626—62no—
342#625—24no—
343#625—62no—
344#625—122no—
345#625—122no—
346#625—124no—
347D3×Dic3—24no—
348D3×Dic3—122no—
349D3×Dic3—122no—
350D3×Dic3—124no—
351#546—271noSylow
352C2×C33C22×D411yescharacteristic
353C2×C33C2×#4111yescharacteristic
354C2×C33H(5,𝔽2)11yescharacteristic
355C3×C3⋊D3—22no—
356C3×C3⋊D3—41no—
357C32×D3—24no—
358C32×D3—42no—
359C24×C3—92no—
360C23×D3—32no—
361C23×D3—32no—
362C3×#41—184no—
363C2×C3×Q8—31no—
364C2×C3×Q8—31no—
365C2×C3×Q8—61no—
366C2×C3×D4—31no—
367C2×C3×D4—31no—
368C2×C3×D4—31no—
369C2×C3×D4—31no—
370C2×C3×D4—61no—
371C2×C3×D4—61no—
372C2×C3×D4—92no—
373C2×C3×D4—92no—
374C2×C3×D4—184no—
375C22×C3×C4—92no—
376C22×C3×C4—91no—
377C22×C3×C4—91no—
378C2×#67—32no—
379C2×#67—32no—
380C2×#67—32no—
381C2×#67—91no—
382C2×#67—91no—
383C2×#67—92no—
384C2×#67—92no—
385C2×#67—92no—
386C2×#67—182no—
387C22×Dic3—32no—
388C22×Dic3—92no—
389C22×Dic3—92no—
390C22×Dic3—182no—
391#239—64no—
392#237—64no—
393D3×D4—64no—
394D3×D4—64no—
395C2×D12—32no—
396C2×D12—91no—
397C2×D12D3211yescharacteristic
398C2×D12D3211yescharacteristic
399C2×C4×D3—32no—
400C2×C4×D3—31no—
401C2×C4×D3—31no—
402C2×C4×D3—31no—
403C2×C4×D3—31no—
404C2×C4×D3—61no—
405C2×C4×D3—61no—
406C2×C4×D3—92no—
407C2×Dic6D3211yescharacteristic, complemented
408C3×C22⋊C4—92no—
409C3×C22⋊C4—92no—
410C3×C42—91no—
411#217—32no—
412#217—32no—
413#217—91no—
414#217—91no—
415#217—92no—
416#217—92no—
417#217—92no—
418#217—92no—
419#217—92no—
420#217—182no—
421#217—182no—
422(C2×D3)⋊C4—32no—
423(C2×D3)⋊C4—32no—
424(C2×D3)⋊C4—91no—
425(C2×D3)⋊C4—91no—
426(C2×D3)⋊C4—91no—
427(C2×D3)⋊C4—91no—
428(C2×D3)⋊C4—92no—
429(C2×D3)⋊C4—92no—
430(C2×D3)⋊C4—92no—
431(C2×D3)⋊C4—92no—
432(C2×D3)⋊C4—182no—
433C4⋊Dic3—91no—
434C4⋊Dic3—91no—
435C4⋊Dic3—91no—
436C4⋊Dic3—91no—
437C4⋊Dic3—181no—
438C4⋊Dic3—181no—
439C4⋊Dic3—181no—
440C4⋊Dic3—361no—
441Dic3⋊C4—91no—
442Dic3⋊C4—91no—
443Dic3⋊C4—92no—
444Dic3⋊C4—92no—
445Dic3⋊C4—92no—
446Dic3⋊C4—182no—
447C4×Dic3—31no—
448C4×Dic3—31no—
449C4×Dic3—61no—
450C22×C32—21no—
451C22×C32—21no—
452C22×C32—21no—
453C22×C32—34no—
454C22×C32—41no—
455C22×C32—62no—
456C22×C32—62no—
457C22×C32—62no—
458C22×C32—62no—
459C22×C32—62no—
460C22×C32C23×D311yescharacteristic
461C22×C32C23×D311yescharacteristic
462C22×C32C23×D311yescharacteristic
463C2×C3⋊D3—21no—
464C2×C3⋊D3—21no—
465C2×C3⋊D3—21no—
466C2×C3⋊D3—21no—
467C2×C3⋊D3—21no—
468C2×C3⋊D3#23712yescomplemented
469C2×C3×D3—22no—
470C2×C3×D3—22no—
471C2×C3×D3—22no—
472C2×C3×D3—22no—
473C2×C3×D3—22no—
474C2×C3×D3—22no—
475C2×C3×D3—22no—
476C2×C3×D3—22no—
477C2×C3×D3—22no—
478C2×C3×D3—22no—
479C2×C3×D3—24no—
480C2×C3×D3—32no—
481C2×C3×D3—32no—
482C2×C3×D3—42no—
483C2×C3×D3—42no—
484C2×C3×D3—42no—
485C2×C3×D3—42no—
486C2×C3×D3—42no—
487C2×C3×D3—62no—
488C2×C3×D3—61no—
489C2×C3×D3—61no—
490C2×C3×D3—61no—
491C2×C3×D3—61no—
492C2×C3×D3—62no—
493C2×C3×D3—61no—
494C2×C3×D3—61no—
495C2×C3×D3—61no—
496C2×C3×D3—61no—
497C2×C3×D3—61no—
498C2×C3×D3—61no—
499C2×C3×D3—121no—
500C2×C3×D3—121no—
501C2×C3×D3—121no—
502C2×C3×D3—121no—
503C2×C3×D3—128no—
504C2×C3×D3—128no—
505C2×C3×D3C2×#6714yes—
506C2×C3×D3C2×#6714yes—
507D32—48no—
508C32×C4—22no—
509C32×C4—22no—
510C32×C4—22no—
511C32×C4—42no—
512C32×C4—62no—
513C32×C4D3×D412yes—
514C32×C4C2×#6712yes—
515C32×C4C2×#6712yes—
516C3⋊Dic3—21no—
517C3⋊Dic3—21no—
518C3⋊Dic3—21no—
519C3⋊Dic3—21no—
520C3⋊Dic3—62no—
521C3⋊Dic3—62no—
522C3⋊Dic3—62no—
523C3⋊Dic3—122no—
524C3⋊Dic3—122no—
525C3⋊Dic3—122no—
526C3⋊Dic3—242no—
527C3×Dic3—22no—
528C3×Dic3—22no—
529C3×Dic3—42no—
530C3×Dic3—62no—
531C3×Dic3—61no—
532C3×Dic3—61no—
533C3×Dic3—61no—
534C3×Dic3—61no—
535C3×Dic3—61no—
536C3×Dic3—61no—
537C3×Dic3—61no—
538C3×Dic3—61no—
539C3×Dic3—121no—
540C3×Dic3—121no—
541C3×Dic3—121no—
542C2×#41—91no—
543C22×D4—91no—
544#124—91no—
545#123—272no—
546C22⋊Q8—271no—
547#121—272no—
548#121—271no—
549#120—272no—
550C4×D4—271no—
551C4×D4—271no—
552C2×C22⋊C4—272no—
553C33#54611yescharacteristic, complemented, Sylow
554C23×C3—32no—
555C23×C3—32no—
556C23×C3—32no—
557C23×C3—32no—
558C23×C3—62no—
559C23×C3—62no—
560C23×C3—91no—
561C23×C3—91no—
562C23×C3—184no—
563C23×C3—184no—
564C23×C3—362no—
565C22×D3—31no—
566C22×D3—31no—
567C22×D3—31no—
568C22×D3—31no—
569C22×D3—61no—
570C22×D3—61no—
571C22×D3—64no—
572C22×D3—64no—
573C22×D3—64no—
574C22×D3—64no—
575C22×D3—122no—
576C22×D3—122no—
577C22×D3C2×D3212yes—
578C22×D3C2×D3212yes—
579C3×Q8—62no—
580C3×Q8—62no—
581C3×Q8—122no—
582C3×D4—34no—
583C3×D4—34no—
584C3×D4—64no—
585C3×D4—62no—
586C3×D4—62no—
587C3×D4—122no—
588C3×D4—184no—
589C3×D4—184no—
590C2×C3×C4—21no—
591C2×C3×C4—21no—
592C2×C3×C4—21no—
593C2×C3×C4—32no—
594C2×C3×C4—32no—
595C2×C3×C4—41no—
596C2×C3×C4—62no—
597C2×C3×C4—91no—
598C2×C3×C4—91no—
599C2×C3×C4—91no—
600C2×C3×C4—91no—
601C2×C3×C4—184no—
602C2×C3×C4—182no—
603C2×C3×C4—182no—
604C2×C3×C4C2×D3211yescharacteristic
605C2×C3×C4C2×D3211yescharacteristic
606C2×C3×C4C2×D3211yescharacteristic
607#67—64no—
608#67—64no—
609#67—64no—
610#67—182no—
611#67—182no—
612#67—362no—
613#67—362no—
614#67—362no—
615#67—364no—
616C2×Dic3—31no—
617C2×Dic3—31no—
618C2×Dic3—31no—
619C2×Dic3—31no—
620C2×Dic3—31no—
621C2×Dic3—31no—
622C2×Dic3—31no—
623C2×Dic3—31no—
624C2×Dic3—61no—
625C2×Dic3—61no—
626C2×Dic3—61no—
627C2×Dic3—61no—
628C2×Dic3—64no—
629C2×Dic3—92no—
630C2×Dic3—92no—
631C2×Dic3—92no—
632C2×Dic3—182no—
633C2×Dic3—182no—
634C2×Dic3—182no—
635C2×Dic3—362no—
636C2×Dic3—362no—
637C2×Dic3—362no—
638C2×Dic3—364no—
639C2×Dic3C2×D3212yes—
640D12—22no—
641D12—64no—
642D12—182no—
643D12#62514yescomplemented
644C4×D3—64no—
645C4×D3—62no—
646C4×D3—62no—
647C4×D3—62no—
648C4×D3—62no—
649C4×D3—122no—
650C4×D3—122no—
651C4×D3—362no—
652Dic6—22no—
653C2×C32—21no—
654C2×C32—21no—
655C2×C32—21no—
656C2×C32—21no—
657C2×C32—21no—
658C2×C32—21no—
659C2×C32—21no—
660C2×C32—21no—
661C2×C32—21no—
662C2×C32—41no—
663C2×C32—41no—
664C2×C32—41no—
665C2×C32—64no—
666C2×C32—122no—
667C2×C32C2×D3×D411yescharacteristic
668C2×C32C2×#23711yescharacteristic
669C2×C32#100411yescharacteristic
670C2×C32D3×#4111yescharacteristic
671C2×C32D3×#4111yescharacteristic
672C2×C32#100911yescharacteristic
673C2×C32#100911yescharacteristic
674C2×C32C22×#6711yescharacteristic
675C2×C32C22×#6711yescharacteristic
676C3⋊D3—22no—
677C3⋊D3—41no—
678C3×D3—24no—
679C3×D3—24no—
680C3×D3—44no—
681C3×D3—42no—
682C3×D3—42no—
683C3×D3—62no—
684C3×D3—62no—
685C3×D3—82no—
686C3×D3—122no—
687C3×D3—122no—
688C3×D3—121no—
689C3×D3—121no—
690C24—92no—
691#41—184no—
692C2×Q8—31no—
693C2×D4—31no—
694C2×D4—31no—
695C2×D4—92no—
696C2×D4—92no—
697C2×D4—184no—
698C2×D4—271no—
699C2×D4—272no—
700C22×C4—92no—
701C22×C4—91no—
702C22×C4—91no—
703C22×C4—272no—
704C4⋊C4—272no—
705C4⋊C4—271no—
706C4⋊C4—271no—
707C22⋊C4—92no—
708C22⋊C4—92no—
709C22⋊C4—272no—
710C22⋊C4—271no—
711C22⋊C4—271no—
712C22⋊C4—272no—
713C22⋊C4—272no—
714C42—91no—
715C22×C3—21no—
716C22×C3—21no—
717C22×C3—21no—
718C22×C3—34no—
719C22×C3—34no—
720C22×C3—41no—
721C22×C3—64no—
722C22×C3—62no—
723C22×C3—62no—
724C22×C3—62no—
725C22×C3—62no—
726C22×C3—62no—
727C22×C3—62no—
728C22×C3—62no—
729C22×C3—62no—
730C22×C3—62no—
731C22×C3—62no—
732C22×C3—92no—
733C22×C3—122no—
734C22×C3—122no—
735C22×C3—122no—
736C22×C3—122no—
737C22×C3—122no—
738C22×C3—181no—
739C22×C3—181no—
740C22×C3—181no—
741C22×C3—181no—
742C22×C3—181no—
743C22×C3—368no—
744C22×C3C22×D3211yescharacteristic
745C22×C3C22×D3211yescharacteristic
746C22×C3C22×D3211yescharacteristic
747C2×D3—22no—
748C2×D3—22no—
749C2×D3—22no—
750C2×D3—22no—
751C2×D3—22no—
752C2×D3—32no—
753C2×D3—32no—
754C2×D3—62no—
755C2×D3—61no—
756C2×D3—61no—
757C2×D3—61no—
758C2×D3—61no—
759C2×D3—62no—
760C2×D3—61no—
761C2×D3—61no—
762C2×D3—61no—
763C2×D3—61no—
764C2×D3—61no—
765C2×D3—61no—
766C2×D3—121no—
767C2×D3—121no—
768C2×D3—121no—
769C2×D3—121no—
770C2×D3—128no—
771C2×D3—128no—
772C2×D3C2×#62514yes—
773C3×C4—22no—
774C3×C4—22no—
775C3×C4—22no—
776C3×C4—42no—
777C3×C4—62no—
778C3×C4—62no—
779C3×C4—122no—
780C3×C4—181no—
781C3×C4—181no—
782C3×C4—181no—
783C3×C4—181no—
784C3×C4C2×#62512yes—
785C3×C4D3×#6712yes—
786C3×C4D3×#6712yes—
787Dic3—22no—
788Dic3—62no—
789Dic3—61no—
790Dic3—61no—
791Dic3—61no—
792Dic3—61no—
793Dic3—61no—
794Dic3—61no—
795Dic3—61no—
796Dic3—61no—
797Dic3—121no—
798Dic3—121no—
799Dic3—121no—
800Dic3—182no—
801Dic3—182no—
802Dic3—182no—
803Dic3—362no—
804Dic3—362no—
805Dic3—362no—
806Dic3—722no—
807C32—21no—
808C32—21no—
809C32—21no—
810C32—41no—
811C32#567611yescharacteristic, complemented
812C32#580611yescharacteristic, complemented
813C32#582911yescharacteristic, complemented
814C23—32no—
815C23—32no—
816C23—91no—
817C23—91no—
818C23—184no—
819C23—184no—
820C23—362no—
821Q8—62no—
822D4—34no—
823D4—62no—
824D4—184no—
825D4—184no—
826D4—542no—
827D4—1082no—
828C2×C4—32no—
829C2×C4—91no—
830C2×C4—91no—
831C2×C4—91no—
832C2×C4—91no—
833C2×C4—184no—
834C2×C4—182no—
835C2×C4—182no—
836C2×C4—272no—
837C2×C4—1082no—
838C2×C4D3311yescharacteristic
839C2×C3—21no—
840C2×C3—21no—
841C2×C3—21no—
842C2×C3—21no—
843C2×C3—21no—
844C2×C3—21no—
845C2×C3—21no—
846C2×C3—21no—
847C2×C3—21no—
848C2×C3—41no—
849C2×C3—41no—
850C2×C3—41no—
851C2×C3—64no—
852C2×C3—64no—
853C2×C3—124no—
854C2×C3—122no—
855C2×C3—122no—
856C2×C3—182no—
857C2×C3—242no—
858C2×C3—361no—
859C2×C3D3×#23711yescharacteristic
860C2×C3D3×#23711yescharacteristic
861C2×C3#6431411yescharacteristic
862C2×C3#6431411yescharacteristic
863C2×C3#6431911yescharacteristic
864C2×C3#6432011yescharacteristic
865C2×C3C22×#62511yescharacteristic
866C2×C3C2×D3×#6711yescharacteristic
867C2×C3C2×D3×#6711yescharacteristic
868D3—24no—
869D3—42no—
870D3—62no—
871D3—62no—
872D3—122no—
873D3—122no—
874D3—121no—
875D3—121no—
876C22—34no—
877C22—62no—
878C22—62no—
879C22—62no—
880C22—62no—
881C22—62no—
882C22—92no—
883C22—181no—
884C22—181no—
885C22—181no—
886C22—181no—
887C22—181no—
888C22—368no—
889C22C2×D3311yescharacteristic
890C4—62no—
891C4—181no—
892C4—181no—
893C4—181no—
894C4—181no—
895C4—542no—
896C4D3×#62512yes—
897C3—21no—
898C3—21no—
899C3—21no—
900C3—41no—
901C3#1059522911yescharacteristic, complemented
902C3#1059524411yescharacteristic, complemented
903C3#1059542811yescharacteristic, complemented
904C2—64no—
905C2—122no—
906C2—182no—
907C2—361no—
908C2#1172437411yescharacteristic
909C2#1172438611yescharacteristic
910C2C2×D3×#62511yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
hypercenterC2×C4D33
hypocenterC33#546
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#3802C2semidirect
2. C2×C3×#3796C2semidirect
3. C4×#6295C2semidirect
4. #11723522C2semidirect
5. D12×C3⋊Dic3C2semidirect
6. #11723435C2semidirect
7. C3×#63863C2semidirect
8. #11722985C2semidirect
9. #11722954C2semidirect
10. #11722947C2semidirect
11. D3×(C2×D3)⋊Dic3C2semidirect
17. C2×C3×C4×C3⋊D3C22semidirect
20. C2×C32×Dic6C22semidirect
22. C2×#6290C22semidirect
23. C2×D3×C3⋊Dic3C22semidirect
24. C2×C3×#626C22semidirect
26. C2×C3×D3×Dic3C22semidirect
29. C4⋊(C3⋊(C3⋊Dic3))C22semidirect
30. C3×C4×C3⋊Dic3C22semidirect
31. #88815C22semidirect
33. #88814C22semidirect
34. #88806C22semidirect
36. (C2×D3)⋊(C3⋊Dic3)C22semidirect
37. (C2×D3)⋊(C3⋊Dic3)C22semidirect
38. C3×(C2×D3)⋊Dic3C22semidirect
39. C3×(C2×D3)⋊Dic3C22semidirect
44. C2×#3802D3semidirect
45. C2×#3796D3semidirect
72. #63863D3semidirect
93. C32×D12D4semidirect
113. C2×C4×C3⋊D3C2×D3semidirect
137. C2×C3×Dic6C2×D3semidirect
138. C2×C3×Dic6C2×D3semidirect
141. C2×#626C2×D3semidirect
150. C2×D3×Dic3C2×D3semidirect
164. C4×C3⋊Dic3C2×D3semidirect
193. (C2×D3)⋊Dic3C2×D3semidirect
194. (C2×D3)⋊Dic3C2×D3semidirect
201. C2×C3×C3⋊D3#41semidirect
327. C3×D12#67semidirect
328. C3×D12#67semidirect
407. C2×Dic6D32semidirect
468. C2×C3⋊D3#237semidirect
553. C33#546semidirect
643. D12#625semidirect
811. C32#5676semidirect
812. C32#5806semidirect
813. C32#5829semidirect
901. C3#10595229semidirect
902. C3#10595244semidirect
903. C3#10595428semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#38022
C2×C3×#37962
C4×#62952
#117235222
D12×C3⋊Dic32
#117234352
C3×#638632
#117229852
#117229542
#117229472
D3×(C2×D3)⋊Dic32
#105954283
#105952443
#105952293