Finite Group Databasebeta

← #13178633

Subgroups — #13178633

Order 1728.

1746 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3830C211yesmaximal, characteristic, complemented
2C22×#6294C211yesmaximal, characteristic, complemented
3C3×#64146C211yesmaximal, characteristic, complemented
4C3×#64144C211yesmaximal, characteristic, complemented
5#11723727C211yesmaximal, characteristic, complemented
6#11723726C212yesmaximal, complemented
7#11723725C212yesmaximal, complemented
8#11723720C211yesmaximal, characteristic, complemented
9#11723715C211yesmaximal, characteristic, complemented
10#11723688C212yesmaximal, complemented
11#11723684C212yesmaximal, complemented
12#10595160—31nomaximal
13#10595159—31nomaximal
14#10595154—31nomaximal
15C23×C3×C3⋊D3C2211yescharacteristic
16C2×C33×D4C2211yescharacteristic
17C2×C3×#638C2212yes—
18C2×C3×#638C2211yescharacteristic
19C2×C3×#638C2211yescharacteristic, complemented
20C22×C3×C3⋊Dic3C2211yescharacteristic
21C22×C3×C3⋊Dic3C2211yescharacteristic
22C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
23C3×#3830—24no—
24C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
25C2×C3×#634C2211yescharacteristic, complemented
26C2×#6295C2212yes—
27C2×#6294—24no—
28C2×#6294C2212yes—
29C2×#6294C2212yes—
30C3×#3757C2211yescharacteristic
31C3×#3757C2211yescharacteristic
32C3×#3757C2212yescomplemented
33C3×#3752C2212yes—
34C3×#3750C2212yescomplemented
35#88815C2212yescomplemented
36#88815C2212yescomplemented
37#88814C2212yes—
38#88814C2212yescomplemented
39#88813C2212yescomplemented
40C2×#3830D311yescharacteristic, complemented
41C2×C3×#237—31no—
42C2×C3×#237—31no—
43C2×C3×#237—61no—
44C22×#624—31no—
45C22×D3×Dic3—31no—
46C22×D3×Dic3—31no—
47#64146D311yescharacteristic, complemented
48#64144D311yescharacteristic, complemented
49C3×#937—31no—
50C3×#937—31no—
51C3×#937—61no—
52C3×#935—31no—
53C3×#935—31no—
54C3×#935—61no—
55#63981—31no—
56#63977—31no—
57#63976—31no—
58#67⋊Dic3—32no—
59Dic3×#67—32no—
60#63971—32no—
61#63970—32no—
62#63966—31no—
63#63962—31no—
64#63961—31no—
65#63958—32no—
66#63957—31no—
67#63955—31no—
68#63955—31no—
69#63952—32no—
70#63904—32no—
71#63896—32no—
72#63888—32no—
73#63887—32no—
74#63881—32no—
75#63879—32no—
76C23×C33C2311yescharacteristic
77C23×C33C2311yescharacteristic
78C22×C3×C3⋊D3—22no—
79C22×C3×C3⋊D3—24no—
80C22×C3×C3⋊D3C2311yescharacteristic
81C22×C3×C3⋊D3C2312yes—
82C33×D4—22no—
83C2×C33×C4C2311yescharacteristic
84C3×#638—22no—
85C3×#638—24no—
86C3×#638—22no—
87C2×C3×C3⋊Dic3—22no—
88C2×C3×C3⋊Dic3—22no—
89C2×C3×C3⋊Dic3D414yescomplemented
90C2×C3×C3⋊Dic3C2312yes—
91C2×C3×C3⋊Dic3C2312yes—
92C2×C3×C3⋊Dic3C2312yes—
93C2×C3×C3⋊Dic3C2311yescharacteristic
94C2×C3×C3⋊Dic3C2311yescharacteristic
95C2×C3×C3⋊Dic3C2311yescharacteristic
96C3×C4×C3⋊D3—22no—
97C3×#634—22no—
98#6295—24no—
99#6294—24no—
100#6294—24no—
101#5828—91no—
102#5656—91no—
103#5586—91no—
104C23×C3⋊D3C2×D311yescharacteristic
105C23×C3×D3—31no—
106C23×C3×D3—31no—
107C23×C3×D3—61no—
108C2×C32×D4—21no—
109C2×C32×D4—21no—
110C2×C32×D4—21no—
111C2×C32×D4—41no—
112C2×C32×D4C2×D311yescharacteristic
113C2×C32×D4C2×D311yescharacteristic
114C2×C32×D4C2×D311yescharacteristic
115C2×#638C2×D311yescharacteristic
116C2×#638C2×D312yes—
117C2×#638C2×D311yescharacteristic, complemented
118C22×C3⋊Dic3C2×D311yescharacteristic
119C22×C3⋊Dic3C2×D311yescharacteristic
120C22×C3⋊Dic3C2×D311yescharacteristic, complemented
121#3830—24no—
122C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
123C2×#634C2×D311yescharacteristic, complemented
124C2×C3×#67—32no—
125C2×C3×#67—32no—
126C2×C3×#67—31no—
127C2×C3×#67—31no—
128C2×C3×#67—31no—
129C2×C3×#67—31no—
130C2×C3×#67—61no—
131C2×C3×#67—61no—
132C2×C3×#67—62no—
133C22×C3×Dic3—31no—
134C22×C3×Dic3—31no—
135C22×C3×Dic3—31no—
136C22×C3×Dic3—31no—
137C22×C3×Dic3—31no—
138C22×C3×Dic3—31no—
139C22×C3×Dic3—61no—
140C22×C3×Dic3—61no—
141C22×C3×Dic3—61no—
142C3×#237—64no—
143C3×#237—64no—
144C3×#237—68no—
145C2×C3×C4×D3—31no—
146C2×C3×C4×D3—31no—
147C2×C3×C4×D3—61no—
148C2×C3×Dic6—31no—
149C2×C3×Dic6—31no—
150C2×C3×Dic6—61no—
151C2×#626—32no—
152C2×#626—32no—
153C2×#625—32no—
154C2×#624—32no—
155C2×#624—32no—
156C2×#624—64no—
157C2×D3×Dic3—32no—
158C2×D3×Dic3—32no—
159C2×D3×Dic3—32no—
160C2×D3×Dic3—32no—
161C2×D3×Dic3—64no—
162C2×D3×Dic3—64no—
163#3757C2×D311yescharacteristic
164#3757C2×D311yescharacteristic
165#3757C2×D312yescomplemented
166#3752C2×D312yes—
167#3750C2×D312yescomplemented
168C3×#217—31no—
169C3×#217—31no—
170C3×#217—31no—
171C3×#217—31no—
172C3×#217—32no—
173C3×#217—32no—
174C3×#217—61no—
175C3×#217—61no—
176C3×#217—62no—
177C3×(C2×D3)⋊C4—32no—
178C3×(C2×D3)⋊C4—32no—
179C3×(C2×D3)⋊C4—62no—
180C3×Dic3⋊C4—32no—
181C3×Dic3⋊C4—32no—
182C3×Dic3⋊C4—62no—
183#3724—32no—
184#3724—32no—
185Dic3⋊Dic3—32no—
186Dic3⋊Dic3—32no—
187Dic3⋊Dic3—32no—
188Dic3⋊Dic3—32no—
189#3722—32no—
190#3722—32no—
191(C2×D3)⋊Dic3—32no—
192(C2×D3)⋊Dic3—32no—
193(C2×D3)⋊Dic3—32no—
194(C2×D3)⋊Dic3—32no—
195Dic32—32no—
196Dic32—32no—
197Dic32—32no—
198C22×C33—22no—
199C22×C33—21no—
200C22×C33—22no—
201C22×C33C2×D412yes—
202C22×C33C2411yescharacteristic
203C2×C3×C3⋊D3—28no—
204C2×C3×C3⋊D3—22no—
205C2×C3×C3⋊D3—22no—
206C2×C3×C3⋊D3—21no—
207C2×C3×C3⋊D3—22no—
208C2×C3×C3⋊D3#4114yescomplemented
209C33×C4—21no—
210C3×C3⋊Dic3—21no—
211C3×C3⋊Dic3—22no—
212C3×C3⋊Dic3—22no—
213C3×C3⋊Dic3—22no—
214C3×C3⋊Dic3C2×D412yes—
215C3×C3⋊Dic3C2×D412yes—
216C2×C3×#41—91no—
217C23×Dic3—91no—
218C2×#237—31no—
219C2×#237—31no—
220C2×#237—61no—
221C22×C4×D3—91no—
222C22×C4×D3—91no—
223C3×#123—91no—
224C3×#120—91no—
225#953—91no—
226#946—92no—
227#939—92no—
228#938—92no—
229#937—31no—
230#937—31no—
231#937—61no—
232#937—91no—
233#935—31no—
234#935—31no—
235#935—61no—
236#935—91no—
237D4×Dic3—92no—
238#929—91no—
239C4×#67—92no—
240C4×#67—92no—
241#926—91no—
242#896—92no—
243#893—92no—
244#886—91no—
245#884—92no—
246#882—91no—
247#67⋊C4—92no—
248#67⋊C4—92no—
249#878—92no—
250#877—91no—
251#877—91no—
252C23×C32—21no—
253C23×C32—21no—
254C23×C32—21no—
255C23×C32—21no—
256C23×C32—21no—
257C23×C32—21no—
258C23×C32—41no—
259C23×C32—41no—
260C23×C32C22×D311yescharacteristic
261C23×C32C22×D311yescharacteristic
262C23×C32C22×D311yescharacteristic
263C23×C32C22×D311yescharacteristic
264C23×C32C22×D311yescharacteristic
265C23×C32C22×D311yescharacteristic
266C22×C3⋊D3—22no—
267C22×C3⋊D3—24no—
268C22×C3⋊D3C22×D311yescharacteristic
269C22×C3⋊D3C22×D312yes—
270C22×C3×D3—32no—
271C22×C3×D3—32no—
272C22×C3×D3—31no—
273C22×C3×D3—31no—
274C22×C3×D3—62no—
275C22×C3×D3—61no—
276C22×C3×D3—64no—
277C22×C3×D3—64no—
278C22×C3×D3—62no—
279C22×C3×D3—62no—
280C22×C3×D3—124no—
281C22×C3×D3—122no—
282C32×D4—22no—
283C32×D4—24no—
284C32×D4—22no—
285C32×D4—22no—
286C32×D4—42no—
287C32×D4—42no—
288C32×D4—44no—
289C2×C32×C4—21no—
290C2×C32×C4—21no—
291C2×C32×C4—21no—
292C2×C32×C4—41no—
293C2×C32×C4C22×D311yescharacteristic
294C2×C32×C4C22×D311yescharacteristic
295C2×C32×C4C22×D311yescharacteristic
296#638—22no—
297#638—22no—
298#638—24no—
299C2×C3⋊Dic3—22no—
300C2×C3⋊Dic3—22no—
301C2×C3⋊Dic3#6714yescomplemented
302C2×C3⋊Dic3C22×D312yes—
303C2×C3⋊Dic3C22×D312yes—
304C2×C3⋊Dic3C22×D311yescharacteristic
305C2×C3⋊Dic3C22×D312yes—
306C2×C3⋊Dic3C22×D311yescharacteristic
307C2×C3⋊Dic3C22×D311yescharacteristic
308C4×C3⋊D3—22no—
309#634—22no—
310C3×#67—62no—
311C3×#67—62no—
312C3×#67—64no—
313C3×#67—64no—
314C3×#67—64no—
315C3×#67—64no—
316C3×#67—62no—
317C3×#67—62no—
318C3×#67—124no—
319C2×C3×Dic3—34no—
320C2×C3×Dic3—34no—
321C2×C3×Dic3—31no—
322C2×C3×Dic3—31no—
323C2×C3×Dic3—31no—
324C2×C3×Dic3—31no—
325C2×C3×Dic3—32no—
326C2×C3×Dic3—32no—
327C2×C3×Dic3—32no—
328C2×C3×Dic3—32no—
329C2×C3×Dic3—31no—
330C2×C3×Dic3—32no—
331C2×C3×Dic3—31no—
332C2×C3×Dic3—32no—
333C2×C3×Dic3—64no—
334C2×C3×Dic3—61no—
335C2×C3×Dic3—61no—
336C2×C3×Dic3—61no—
337C2×C3×Dic3—62no—
338C2×C3×Dic3—62no—
339C2×C3×Dic3—62no—
340C2×C3×Dic3—62no—
341C2×C3×Dic3—62no—
342C2×C3×Dic3—64no—
343C2×C3×Dic3—62no—
344C2×C3×Dic3—62no—
345C2×C3×Dic3—122no—
346C3×C4×D3—62no—
347C3×C4×D3—62no—
348C3×C4×D3—64no—
349C3×Dic6—62no—
350C3×Dic6—62no—
351C3×Dic6—64no—
352#626—64no—
353#626—64no—
354#625—64no—
355#624—64no—
356#624—64no—
357D3×Dic3—64no—
358D3×Dic3—64no—
359D3×Dic3—64no—
360D3×Dic3—64no—
361#525—271noSylow
362C2×C33—22no—
363C2×C33—41no—
364C2×C33C22×D411yescharacteristic
365C2×C33C2×#4112yes—
366C3×C3⋊D3—24no—
367C3×C3⋊D3—41no—
368C24×C3—91no—
369C23×D3—31no—
370C23×D3—31no—
371C23×D3—61no—
372C3×#41—184no—
373C2×C3×Q8—91no—
374C2×C3×D4—21no—
375C2×C3×D4—21no—
376C2×C3×D4—21no—
377C2×C3×D4—41no—
378C2×C3×D4—92no—
379C2×C3×D4—91no—
380C2×C3×D4—91no—
381C2×C3×D4D3211yescharacteristic
382C2×C3×D4D3211yescharacteristic
383C2×C3×D4D3211yescharacteristic
384C22×C3×C4—91no—
385C22×C3×C4—91no—
386C22×C3×C4—91no—
387C22×C3×C4—91no—
388C2×#67—32no—
389C2×#67—31no—
390C2×#67—31no—
391C2×#67—31no—
392C2×#67—32no—
393C2×#67—31no—
394C2×#67—61no—
395C2×#67—61no—
396C2×#67—62no—
397C2×#67—92no—
398C2×#67—92no—
399C22×Dic3—31no—
400C22×Dic3—31no—
401C22×Dic3—31no—
402C22×Dic3—31no—
403C22×Dic3—31no—
404C22×Dic3—31no—
405C22×Dic3—61no—
406C22×Dic3—61no—
407C22×Dic3—61no—
408C22×Dic3—92no—
409C22×Dic3—92no—
410C22×Dic3—184no—
411#237—64no—
412#237—64no—
413#237—68no—
414C2×D12—92no—
415C2×C4×D3—31no—
416C2×C4×D3—31no—
417C2×C4×D3—61no—
418C2×C4×D3—92no—
419C2×C4×D3—92no—
420C2×C4×D3—92no—
421C2×C4×D3—92no—
422C2×C4×D3—184no—
423C2×C4×D3—184no—
424C2×Dic6—31no—
425C2×Dic6—31no—
426C2×Dic6—61no—
427C3×C4⋊C4—92no—
428C3×C22⋊C4—91no—
429C3×C22⋊C4—91no—
430C3×C22⋊C4—92no—
431C3×C22⋊C4—92no—
432#217—31no—
433#217—31no—
434#217—31no—
435#217—31no—
436#217—32no—
437#217—32no—
438#217—61no—
439#217—62no—
440#217—61no—
441#217—92no—
442#217—92no—
443(C2×D3)⋊C4—32no—
444(C2×D3)⋊C4—32no—
445(C2×D3)⋊C4—62no—
446(C2×D3)⋊C4—92no—
447(C2×D3)⋊C4—92no—
448(C2×D3)⋊C4—92no—
449(C2×D3)⋊C4—92no—
450C4⋊Dic3—92no—
451C4⋊Dic3—92no—
452Dic3⋊C4—32no—
453Dic3⋊C4—32no—
454Dic3⋊C4—62no—
455Dic3⋊C4—92no—
456Dic3⋊C4—92no—
457Dic3⋊C4—92no—
458Dic3⋊C4—92no—
459C4×Dic3—92no—
460C4×Dic3—92no—
461C4×Dic3—92no—
462C22×C32—21no—
463C22×C32—22no—
464C22×C32—22no—
465C22×C32—22no—
466C22×C32—22no—
467C22×C32—21no—
468C22×C32—21no—
469C22×C32—22no—
470C22×C32—22no—
471C22×C32—22no—
472C22×C32—21no—
473C22×C32—21no—
474C22×C32—21no—
475C22×C32—22no—
476C22×C32—22no—
477C22×C32—22no—
478C22×C32—41no—
479C22×C32—42no—
480C22×C32—41no—
481C22×C32—41no—
482C22×C32—42no—
483C22×C32—42no—
484C22×C32—42no—
485C22×C32—42no—
486C22×C32—42no—
487C22×C32—42no—
488C22×C32—42no—
489C22×C32—82no—
490C22×C32—82no—
491C22×C32D3×D412yes—
492C22×C32D3×D412yes—
493C22×C32C2×#6712yes—
494C22×C32C23×D311yescharacteristic
495C22×C32C23×D311yescharacteristic
496C22×C32C23×D311yescharacteristic
497C2×C3⋊D3—21no—
498C2×C3⋊D3—28no—
499C2×C3⋊D3—22no—
500C2×C3⋊D3—22no—
501C2×C3⋊D3—22no—
502C2×C3⋊D3#23714yescomplemented
503C2×C3×D3—34no—
504C2×C3×D3—34no—
505C2×C3×D3—64no—
506C2×C3×D3—68no—
507C2×C3×D3—68no—
508C2×C3×D3—62no—
509C2×C3×D3—62no—
510C2×C3×D3—62no—
511C2×C3×D3—62no—
512C2×C3×D3—62no—
513C2×C3×D3—61no—
514C2×C3×D3—61no—
515C2×C3×D3—62no—
516C2×C3×D3—62no—
517C2×C3×D3—122no—
518C2×C3×D3—122no—
519C2×C3×D3—122no—
520C2×C3×D3—128no—
521C32×C4—21no—
522C32×C4—22no—
523C32×C4—21no—
524C32×C4—21no—
525C32×C4—41no—
526C32×C4—41no—
527C32×C4—42no—
528C3⋊Dic3—21no—
529C3⋊Dic3—22no—
530C3⋊Dic3—22no—
531C3⋊Dic3—22no—
532C3⋊Dic3C2×#6712yes—
533C3⋊Dic3C2×#6712yes—
534C3×Dic3—32no—
535C3×Dic3—32no—
536C3×Dic3—32no—
537C3×Dic3—32no—
538C3×Dic3—62no—
539C3×Dic3—62no—
540C3×Dic3—62no—
541C3×Dic3—62no—
542C3×Dic3—61no—
543C3×Dic3—61no—
544C3×Dic3—62no—
545C3×Dic3—62no—
546C3×Dic3—62no—
547C3×Dic3—62no—
548C3×Dic3—62no—
549C3×Dic3—122no—
550C3×Dic3—122no—
551C3×Dic3—122no—
552C2×#41—91no—
553C23×C4—271no—
554#123—91no—
555#123—271no—
556C22⋊Q8—272no—
557#121—272no—
558#120—91no—
559#120—271no—
560C4×D4—272no—
561C4×D4—272no—
562#117—271no—
563C33#52511yescharacteristic, complemented, Sylow
564C23×C3—21no—
565C23×C3—21no—
566C23×C3—21no—
567C23×C3—21no—
568C23×C3—21no—
569C23×C3—21no—
570C23×C3—41no—
571C23×C3—41no—
572C23×C3—92no—
573C23×C3—91no—
574C23×C3—184no—
575C23×C3—182no—
576C23×C3C2×D3211yescharacteristic
577C23×C3C2×D3211yescharacteristic
578C23×C3C2×D3211yescharacteristic
579C23×C3C2×D3211yescharacteristic
580C23×C3C2×D3211yescharacteristic
581C23×C3C2×D3211yescharacteristic
582C22×D3—32no—
583C22×D3—32no—
584C22×D3—31no—
585C22×D3—31no—
586C22×D3—62no—
587C22×D3—61no—
588C22×D3—64no—
589C22×D3—64no—
590C22×D3—62no—
591C22×D3—62no—
592C22×D3—124no—
593C22×D3—122no—
594C3×Q8—182no—
595C3×D4—24no—
596C3×D4—22no—
597C3×D4—22no—
598C3×D4—22no—
599C3×D4—42no—
600C3×D4—42no—
601C3×D4—44no—
602C3×D4—182no—
603C3×D4—184no—
604C3×D4—182no—
605C2×C3×C4—21no—
606C2×C3×C4—21no—
607C2×C3×C4—21no—
608C2×C3×C4—41no—
609C2×C3×C4—91no—
610C2×C3×C4—91no—
611C2×C3×C4—94no—
612C2×C3×C4—92no—
613C2×C3×C4—92no—
614C2×C3×C4—91no—
615C2×C3×C4—92no—
616C2×C3×C4—182no—
617C2×C3×C4—182no—
618C2×C3×C4—182no—
619C2×C3×C4C2×D3211yescharacteristic
620C2×C3×C4C2×D3211yescharacteristic
621C2×C3×C4C2×D3211yescharacteristic
622#67—62no—
623#67—62no—
624#67—64no—
625#67—64no—
626#67—64no—
627#67—64no—
628#67—62no—
629#67—62no—
630#67—124no—
631#67—184no—
632#67—184no—
633C2×Dic3—31no—
634C2×Dic3—31no—
635C2×Dic3—31no—
636C2×Dic3—31no—
637C2×Dic3—34no—
638C2×Dic3—34no—
639C2×Dic3—32no—
640C2×Dic3—32no—
641C2×Dic3—32no—
642C2×Dic3—32no—
643C2×Dic3—32no—
644C2×Dic3—32no—
645C2×Dic3—31no—
646C2×Dic3—31no—
647C2×Dic3—64no—
648C2×Dic3—61no—
649C2×Dic3—61no—
650C2×Dic3—61no—
651C2×Dic3—62no—
652C2×Dic3—62no—
653C2×Dic3—62no—
654C2×Dic3—62no—
655C2×Dic3—62no—
656C2×Dic3—64no—
657C2×Dic3—62no—
658C2×Dic3—62no—
659C2×Dic3—122no—
660C2×Dic3—184no—
661C2×Dic3—184no—
662D12—184no—
663C4×D3—62no—
664C4×D3—62no—
665C4×D3—64no—
666C4×D3—184no—
667C4×D3—184no—
668C4×D3—184no—
669C4×D3—184no—
670Dic6—62no—
671Dic6—62no—
672Dic6—64no—
673C2×C32—22no—
674C2×C32—22no—
675C2×C32—22no—
676C2×C32—22no—
677C2×C32—22no—
678C2×C32—22no—
679C2×C32—21no—
680C2×C32—21no—
681C2×C32—21no—
682C2×C32—41no—
683C2×C32—42no—
684C2×C32—42no—
685C2×C32—42no—
686C2×C32—42no—
687C2×C32—41no—
688C2×C32—42no—
689C2×C32—41no—
690C2×C32—41no—
691C2×C32—82no—
692C2×C32—81no—
693C2×C32—81no—
694C2×C32—82no—
695C2×C32C2×D3×D411yescharacteristic
696C2×C32C2×D3×D411yescharacteristic
697C2×C32C2×#23712yes—
698C2×C32D3×#4112yes—
699C2×C32D3×#4112yes—
700C2×C32C22×#6711yescharacteristic
701C3⋊D3—24no—
702C3⋊D3—41no—
703C3×D3—64no—
704C3×D3—64no—
705C3×D3—124no—
706C3×D3—122no—
707C3×D3—121no—
708C3×D3—121no—
709C24—91no—
710#41—184no—
711C2×Q8—91no—
712C2×D4—92no—
713C2×D4—91no—
714C2×D4—91no—
715C2×D4—272no—
716C2×D4#111311yescharacteristic
717C22×C4—91no—
718C22×C4—91no—
719C22×C4—91no—
720C22×C4—91no—
721C22×C4—272no—
722C22×C4—272no—
723C22×C4—544no—
724C4⋊C4—92no—
725C4⋊C4—272no—
726C4⋊C4—272no—
727C22⋊C4—91no—
728C22⋊C4—91no—
729C22⋊C4—92no—
730C22⋊C4—92no—
731C22⋊C4—272no—
732C22⋊C4—272no—
733C42—272no—
734C22×C3—22no—
735C22×C3—22no—
736C22×C3—22no—
737C22×C3—22no—
738C22×C3—22no—
739C22×C3—22no—
740C22×C3—22no—
741C22×C3—21no—
742C22×C3—21no—
743C22×C3—21no—
744C22×C3—21no—
745C22×C3—21no—
746C22×C3—21no—
747C22×C3—22no—
748C22×C3—22no—
749C22×C3—22no—
750C22×C3—42no—
751C22×C3—42no—
752C22×C3—42no—
753C22×C3—42no—
754C22×C3—42no—
755C22×C3—41no—
756C22×C3—41no—
757C22×C3—42no—
758C22×C3—42no—
759C22×C3—41no—
760C22×C3—42no—
761C22×C3—82no—
762C22×C3—82no—
763C22×C3—94no—
764C22×C3—188no—
765C22×C3—182no—
766C22×C3—182no—
767C22×C3—182no—
768C22×C3—181no—
769C22×C3D3×#6712yes—
770C22×C3D3×#6712yes—
771C22×C3#381112yes—
772C22×C3C22×D3211yescharacteristic
773C22×C3C22×D3211yescharacteristic
774C22×C3C22×D3211yescharacteristic
775C2×D3—34no—
776C2×D3—34no—
777C2×D3—64no—
778C2×D3—68no—
779C2×D3—68no—
780C2×D3—62no—
781C2×D3—62no—
782C2×D3—62no—
783C2×D3—62no—
784C2×D3—62no—
785C2×D3—62no—
786C2×D3—62no—
787C2×D3—61no—
788C2×D3—61no—
789C2×D3—122no—
790C2×D3—122no—
791C2×D3—122no—
792C2×D3—128no—
793C3×C4—22no—
794C3×C4—21no—
795C3×C4—21no—
796C3×C4—21no—
797C3×C4—41no—
798C3×C4—41no—
799C3×C4—42no—
800C3×C4—92no—
801C3×C4—92no—
802C3×C4—182no—
803C3×C4—182no—
804C3×C4—182no—
805C3×C4—181no—
806Dic3—32no—
807Dic3—32no—
808Dic3—32no—
809Dic3—32no—
810Dic3—62no—
811Dic3—62no—
812Dic3—62no—
813Dic3—62no—
814Dic3—62no—
815Dic3—62no—
816Dic3—62no—
817Dic3—61no—
818Dic3—61no—
819Dic3—62no—
820Dic3—62no—
821Dic3—122no—
822Dic3—122no—
823Dic3—122no—
824C32—21no—
825C32—21no—
826C32—21no—
827C32—41no—
828C32#558611yescharacteristic, complemented
829C32#565611yescharacteristic, complemented
830C32#582811yescharacteristic, complemented
831C23—92no—
832C23—91no—
833C23—184no—
834C23—182no—
835C23C2×#111311yescharacteristic
836C23C2×#111311yescharacteristic
837Q8—182no—
838D4—22no—
839D4—182no—
840D4—184no—
841D4—182no—
842D4—544no—
843C2×C4—91no—
844C2×C4—91no—
845C2×C4—94no—
846C2×C4—92no—
847C2×C4—92no—
848C2×C4—92no—
849C2×C4—91no—
850C2×C4—182no—
851C2×C4—182no—
852C2×C4—182no—
853C2×C4—544no—
854C2×C4—544no—
855C2×C4C2×#111311yescharacteristic
856C2×C3—22no—
857C2×C3—22no—
858C2×C3—22no—
859C2×C3—22no—
860C2×C3—22no—
861C2×C3—22no—
862C2×C3—21no—
863C2×C3—21no—
864C2×C3—21no—
865C2×C3—42no—
866C2×C3—42no—
867C2×C3—42no—
868C2×C3—42no—
869C2×C3—41no—
870C2×C3—41no—
871C2×C3—41no—
872C2×C3—42no—
873C2×C3—41no—
874C2×C3—82no—
875C2×C3—81no—
876C2×C3—81no—
877C2×C3—82no—
878C2×C3—184no—
879C2×C3—361no—
880C2×C3D3×#23712yes—
881C2×C3D3×#23712yes—
882C2×C3#6431212yes—
883C2×C3C2×D3×#6711yescharacteristic
884C2×C3C2×D3×#6711yescharacteristic
885C2×C3C2×#381111yescharacteristic
886D3—64no—
887D3—64no—
888D3—124no—
889D3—122no—
890D3—121no—
891D3—121no—
892C22—22no—
893C22—22no—
894C22—21no—
895C22—94no—
896C22—188no—
897C22—182no—
898C22—182no—
899C22—182no—
900C22—181no—
901C22#8904912yes—
902C22C22×#111311yescharacteristic
903C4—21no—
904C4—92no—
905C4—92no—
906C4—182no—
907C4—182no—
908C4—182no—
909C4—181no—
910C3—21no—
911C3—21no—
912C3—21no—
913C3—41no—
914C3#1059515411yescharacteristic, complemented
915C3#1059515911yescharacteristic, complemented
916C3#1059516011yescharacteristic, complemented
917C2—22no—
918C2—41no—
919C2—184no—
920C2—361no—
921C2#1172462212yes—
922C2C2×#8904911yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC2×C33×D4C22
hypercenterC2×D4#1113
hypocenterC33#525
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#3830C2semidirect
2. C22×#6294C2semidirect
3. C3×#64146C2semidirect
4. C3×#64144C2semidirect
5. #11723727C2semidirect
6. #11723726C2semidirect
7. #11723725C2semidirect
8. #11723720C2semidirect
9. #11723715C2semidirect
10. #11723688C2semidirect
11. #11723684C2semidirect
19. C2×C3×#638C22semidirect
22. C22×C3×C3⋊Dic3C22semidirect
24. C2×C3×C4×C3⋊D3C22semidirect
25. C2×C3×#634C22semidirect
32. C3×#3757C22semidirect
34. C3×#3750C22semidirect
35. #88815C22semidirect
36. #88815C22semidirect
38. #88814C22semidirect
39. #88813C22semidirect
40. C2×#3830D3semidirect
47. #64146D3semidirect
48. #64144D3semidirect
89. C2×C3×C3⋊Dic3D4semidirect
117. C2×#638C2×D3semidirect
120. C22×C3⋊Dic3C2×D3semidirect
122. C2×C4×C3⋊D3C2×D3semidirect
123. C2×#634C2×D3semidirect
165. #3757C2×D3semidirect
167. #3750C2×D3semidirect
208. C2×C3×C3⋊D3#41semidirect
301. C2×C3⋊Dic3#67semidirect
502. C2×C3⋊D3#237semidirect
563. C33#525semidirect
828. C32#5586semidirect
829. C32#5656semidirect
830. C32#5828semidirect
914. C3#10595154semidirect
915. C3#10595159semidirect
916. C3#10595160semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#38302
C22×#62942
C3×#641462
C3×#641442
#117237272
#117237262
#117237252
#117237202
#117237152
#117236882
#117236842
#105951603
#105951593
#105951543