Finite Group Databasebeta

← #13178624

Subgroups — #13178624

Order 1728.

1722 conjugacy classes of subgroups.

The subgroup lattice has 1388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89049C211yesmaximal, characteristic, complemented
2C2×#89046C211yesmaximal, characteristic, complemented
3C3×#64149C211yesmaximal, characteristic, complemented
4C3×#64148C211yesmaximal, characteristic, complemented
5C3×#64146C211yesmaximal, characteristic, complemented
6#11723729C211yesmaximal, characteristic, complemented
7#11723728C211yesmaximal, characteristic, complemented
8#11723727C211yesmaximal, characteristic, complemented
9#11723725C211yesmaximal, characteristic, complemented
10#11723718C211yesmaximal, characteristic, complemented
11#11723717C211yesmaximal, characteristic, complemented
12#11723701C211yesmaximal, characteristic, complemented
13#11723687C211yesmaximal, characteristic, complemented
14#11723683C211yesmaximal, characteristic, complemented
15#11723672C211yesmaximal, characteristic, complemented
16#10595299—31nomaximal
17#10595286—31nomaximal
18#10595285—31nomaximal
19C23×C3×C3⋊D3C2211yescharacteristic
20C22×#1113C2211yescharacteristic
21C2×C33×D4C2211yescharacteristic, complemented
22C2×C3×#638C2211yescharacteristic
23C2×C3×#638C2211yescharacteristic
24C2×C3×#638C2211yescharacteristic
25C2×C3×#638C2211yescharacteristic, complemented
26C2×C3×#638C2211yescharacteristic, complemented
27C2×C3×#638C2211yescharacteristic, complemented
28C2×C3×#638C2211yescharacteristic, complemented
29C2×C3×#638C2211yescharacteristic, complemented
30C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
31C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
32#89049—24no—
33C2×#6296C2211yescharacteristic, complemented
34C2×#6295C2211yescharacteristic
35C2×#6295C2211yescharacteristic
36C2×#6295C2211yescharacteristic
37C2×#6295C2211yescharacteristic, complemented
38C2×#6295C2211yescharacteristic, complemented
39#89046—24no—
40C2×#6294C2211yescharacteristic
41C2×#6294C2211yescharacteristic, complemented
42C3×#3757C2211yescharacteristic, complemented
43C3×#3757C2211yescharacteristic, complemented
44C3×#3752C2211yescharacteristic
45C3×#3752C2211yescharacteristic, complemented
46C3×#3752C2211yescharacteristic, complemented
47C3×#3750C2211yescharacteristic, complemented
48C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
49#88815C2211yescharacteristic, complemented
50#88814C2211yescharacteristic
51#88814C2211yescharacteristic, complemented
52#88814C2211yescharacteristic, complemented
53#88814C2211yescharacteristic, complemented
54#88814C2211yescharacteristic, complemented
55#88813C2211yescharacteristic, complemented
56C2×#3811—31no—
57C2×D3×#67—31no—
58C2×D3×#67—31no—
59C2×#3805—31no—
60C2×#3804—31no—
61C2×#3804—31no—
62#64149D311yescharacteristic, complemented
63#64148D311yescharacteristic, complemented
64#64146D311yescharacteristic, complemented
65C3×#940—31no—
66C3×#940—31no—
67C3×#940—61no—
68C3×#939—31no—
69C3×#939—31no—
70C3×#939—61no—
71C3×#937—31no—
72C3×#937—31no—
73C3×#937—61no—
74#63983—31no—
75#63983—31no—
76#63983—31no—
77#63981—31no—
78#63980—31no—
79#63979—31no—
80#63979—31no—
81#63979—31no—
82#63978—31no—
83#63978—31no—
84#63977—31no—
85#63976—31no—
86#63971—31no—
87#63970—31no—
88#63959—31no—
89#63959—31no—
90#63958—31no—
91#63953—31no—
92#63923—31no—
93#63922—31no—
94#63922—31no—
95#63915—31no—
96#63910—31no—
97#63886—31no—
98#63885—31no—
99#63878—31no—
100#63877—31no—
101#63852—31no—
102#63852—31no—
103#63836—31no—
104C23×C33C2311yescharacteristic
105C23×C33C2311yescharacteristic
106C22×C3×C3⋊D3—22no—
107C22×C3×C3⋊D3—41no—
108C22×C3×C3⋊D3—41no—
109C22×C3×C3⋊D3C2311yescharacteristic
110C22×C3×C3⋊D3C2311yescharacteristic
111C22×C3×C3⋊D3C2311yescharacteristic
112C22×C3×C3⋊D3C2311yescharacteristic
113C22×C3×C3⋊D3C2311yescharacteristic
114C2×#1113—22no—
115C2×#1113—41no—
116C2×#1113—41no—
117C33×D4—41no—
118C2×C33×C4C2311yescharacteristic
119C3×#638—22no—
120C3×#638—22no—
121C3×#638—22no—
122C3×#638—22no—
123C3×#638—41no—
124C3×#638—41no—
125C3×#638—41no—
126C3×#638—41no—
127C2×C3×C3⋊Dic3—22no—
128C2×C3×C3⋊Dic3C2311yescharacteristic
129C2×C3×C3⋊Dic3C2311yescharacteristic
130C2×C3×C3⋊Dic3C2311yescharacteristic
131C2×C3×C3⋊Dic3C2311yescharacteristic
132C2×C3×C3⋊Dic3C2311yescharacteristic
133C2×C3×C3⋊Dic3C2311yescharacteristic
134C2×C3×C3⋊Dic3C2311yescharacteristic
135C3×C4⋊(C3⋊D3)—41no—
136#6296—22no—
137#6295—22no—
138#6295—22no—
139#6295—22no—
140#6295—41no—
141#6295—41no—
142#6294—22no—
143#6294D414yescomplemented
144#5715—91no—
145#5607—91no—
146#5592—91no—
147C23×C3⋊D3C2×D311yescharacteristic
148C23×C3×D3—31no—
149C23×C3×D3—31no—
150C23×C3×D3—61no—
151C22×D32—31no—
152C22×D32—31no—
153C22×D32—31no—
154C2×C32×D4—21no—
155C2×C32×D4—21no—
156C2×C32×D4—21no—
157C2×C32×D4—41no—
158C2×C32×D4C2×D311yescharacteristic, complemented
159C2×C32×D4C2×D311yescharacteristic, complemented
160C2×C32×D4C2×D311yescharacteristic, complemented
161C2×#638C2×D311yescharacteristic
162C2×#638C2×D311yescharacteristic
163C2×#638C2×D311yescharacteristic
164C2×#638C2×D311yescharacteristic, complemented
165C2×#638C2×D311yescharacteristic, complemented
166C2×#638C2×D311yescharacteristic, complemented
167C2×#638C2×D311yescharacteristic, complemented
168C2×#638C2×D311yescharacteristic, complemented
169C22×C3⋊Dic3C2×D311yescharacteristic, complemented
170C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
171C2×C3×#67—31no—
172C2×C3×#67—31no—
173C2×C3×#67—31no—
174C2×C3×#67—31no—
175C2×C3×#67—31no—
176C2×C3×#67—31no—
177C2×C3×#67—31no—
178C2×C3×#67—31no—
179C2×C3×#67—31no—
180C2×C3×#67—31no—
181C2×C3×#67—31no—
182C2×C3×#67—31no—
183C2×C3×#67—31no—
184C2×C3×#67—31no—
185C2×C3×#67—31no—
186C2×C3×#67—31no—
187C2×C3×#67—61no—
188C2×C3×#67—61no—
189C2×C3×#67—61no—
190C2×C3×#67—61no—
191C2×C3×#67—61no—
192C2×C3×#67—61no—
193C2×C3×#67—61no—
194C2×C3×#67—61no—
195C22×C3×Dic3—31no—
196C22×C3×Dic3—31no—
197C22×C3×Dic3—61no—
198C2×C3×D12—31no—
199C2×C3×D12—31no—
200C2×C3×D12—61no—
201#3811—64no—
202D3×#67—64no—
203D3×#67—64no—
204C2×#627—31no—
205C2×#627—31no—
206C2×#627—31no—
207C2×#626—31no—
208C2×#626—31no—
209C2×#626—31no—
210C2×#626—31no—
211C2×#626—31no—
212C2×#626—31no—
213C2×#626—31no—
214C2×#626—31no—
215C2×#626—31no—
216C2×#626—31no—
217C2×#625—31no—
218C2×#625—31no—
219C2×#625—31no—
220C2×#625—31no—
221C2×#625—31no—
222C2×#624—31no—
223C2×#624—31no—
224#3805—64no—
225#3804—64no—
226#3804—64no—
227C2×D3×Dic3—31no—
228C2×D3×Dic3—31no—
229C2×D3×Dic3—31no—
230C2×D3×Dic3—31no—
231#3757C2×D311yescharacteristic, complemented
232#3757C2×D311yescharacteristic, complemented
233#3752C2×D311yescharacteristic
234#3752C2×D311yescharacteristic, complemented
235#3752C2×D311yescharacteristic, complemented
236#3750C2×D311yescharacteristic, complemented
237C4×C3⋊Dic3C2×D311yescharacteristic, complemented
238C3×#217—31no—
239C3×#217—31no—
240C3×#217—31no—
241C3×#217—31no—
242C3×#217—61no—
243C3×#217—61no—
244C3×(C2×D3)⋊C4—31no—
245C3×(C2×D3)⋊C4—31no—
246C3×(C2×D3)⋊C4—31no—
247C3×(C2×D3)⋊C4—31no—
248C3×(C2×D3)⋊C4—31no—
249C3×(C2×D3)⋊C4—31no—
250C3×(C2×D3)⋊C4—61no—
251C3×(C2×D3)⋊C4—61no—
252C3×(C2×D3)⋊C4—61no—
253C3×Dic3⋊C4—31no—
254C3×Dic3⋊C4—31no—
255C3×Dic3⋊C4—61no—
256C3×C4×Dic3—31no—
257C3×C4×Dic3—31no—
258C3×C4×Dic3—61no—
259#3724—31no—
260Dic3⋊Dic3—31no—
261Dic3⋊Dic3—31no—
262#3722—31no—
263#3722—31no—
264#3722—31no—
265#3722—31no—
266#3722—31no—
267(C2×D3)⋊Dic3—31no—
268(C2×D3)⋊Dic3—31no—
269(C2×D3)⋊Dic3—31no—
270(C2×D3)⋊Dic3—31no—
271(C2×D3)⋊Dic3—31no—
272(C2×D3)⋊Dic3—31no—
273(C2×D3)⋊Dic3—31no—
274(C2×D3)⋊Dic3—31no—
275(C2×D3)⋊Dic3—31no—
276(C2×D3)⋊Dic3—31no—
277Dic32—31no—
278Dic32—31no—
279Dic32—31no—
280C22×C33—21no—
281C22×C33—21no—
282C22×C33—21no—
283C22×C33—21no—
284C22×C33—21no—
285C22×C33—21no—
286C22×C33C2411yescharacteristic
287C2×C3×C3⋊D3—21no—
288C2×C3×C3⋊D3—21no—
289C2×C3×C3⋊D3—21no—
290C2×C3×C3⋊D3—21no—
291C2×C3×C3⋊D3—21no—
292C2×C3×C3⋊D3—21no—
293C2×C3×C3⋊D3—21no—
294C2×C3×C3⋊D3—21no—
295C2×C3×C3⋊D3—21no—
296C2×C3×C3⋊D3—21no—
297C2×C3×C3⋊D3—21no—
298C2×C3×C3⋊D3—21no—
299C2×C3×C3⋊D3—21no—
300C2×C3×C3⋊D3—21no—
301C2×C3×C3⋊D3—44no—
302C2×C3×C3⋊D3C2×D412yes—
303#1113—44no—
304C33×C4—21no—
305C3×C3⋊Dic3—21no—
306C3×C3⋊Dic3—21no—
307C3×C3⋊Dic3—21no—
308C3×C3⋊Dic3—21no—
309C3×C3⋊Dic3—21no—
310C3×C3⋊Dic3C2×D412yes—
311C3×C3⋊Dic3C2×D412yes—
312C22×#67—91no—
313C2×#237—91no—
314C2×#237—91no—
315C2×D3×D4—91no—
316C2×D3×D4—91no—
317C2×#235—91no—
318C3×#127—91no—
319C3×#121—91no—
320C3×#120—91no—
321#953—91no—
322#940—31no—
323#940—31no—
324#940—61no—
325#940—91no—
326#940—91no—
327#940—91no—
328#939—31no—
329#939—31no—
330#939—61no—
331#939—91no—
332#939—91no—
333#939—91no—
334#939—91no—
335#938—91no—
336#937—31no—
337#937—31no—
338#937—61no—
339#937—91no—
340#937—91no—
341#937—91no—
342#937—91no—
343#937—91no—
344#936—91no—
345#930—91no—
346#895—91no—
347#892—91no—
348#885—91no—
349#885—91no—
350#885—91no—
351#885—91no—
352#884—91no—
353#884—91no—
354#882—91no—
355#882—91no—
356#882—91no—
357#877—91no—
358#875—91no—
359#872—91no—
360C23×C32—21no—
361C23×C32—21no—
362C23×C32—21no—
363C23×C32—21no—
364C23×C32—21no—
365C23×C32—21no—
366C23×C32—41no—
367C23×C32—41no—
368C23×C32C22×D311yescharacteristic
369C23×C32C22×D311yescharacteristic
370C23×C32C22×D311yescharacteristic
371C23×C32C22×D311yescharacteristic
372C23×C32C22×D311yescharacteristic
373C23×C32C22×D311yescharacteristic
374C22×C3⋊D3—22no—
375C22×C3⋊D3—41no—
376C22×C3⋊D3—41no—
377C22×C3⋊D3C22×D311yescharacteristic
378C22×C3⋊D3C22×D311yescharacteristic
379C22×C3⋊D3C22×D311yescharacteristic
380C22×C3⋊D3C22×D311yescharacteristic
381C22×C3⋊D3C22×D311yescharacteristic
382C22×C3×D3—31no—
383C22×C3×D3—31no—
384C22×C3×D3—31no—
385C22×C3×D3—31no—
386C22×C3×D3—31no—
387C22×C3×D3—31no—
388C22×C3×D3—31no—
389C22×C3×D3—31no—
390C22×C3×D3—31no—
391C22×C3×D3—31no—
392C22×C3×D3—61no—
393C22×C3×D3—61no—
394C22×C3×D3—61no—
395C22×C3×D3—61no—
396C22×C3×D3—61no—
397C22×C3×D3—62no—
398C22×C3×D3—62no—
399C22×C3×D3—122no—
400C22×C3×D3—121no—
401C22×C3×D3—121no—
402C22×C3×D3—121no—
403C22×C3×D3—121no—
404C22×C3×D3—122no—
405C22×C3×D3—122no—
406C2×D32—62no—
407C2×D32—62no—
408C2×D32—62no—
409C2×D32—121no—
410C2×D32—121no—
411C2×D32—121no—
412C2×D32—121no—
413C2×D32—121no—
414C2×D32—121no—
415C32×D4—41no—
416C32×D4—41no—
417C32×D4—41no—
418C32×D4—42no—
419C32×D4—42no—
420C32×D4—42no—
421C32×D4—44no—
422C2×C32×C4—21no—
423C2×C32×C4—21no—
424C2×C32×C4—21no—
425C2×C32×C4—41no—
426C2×C32×C4C22×D311yescharacteristic
427C2×C32×C4C22×D311yescharacteristic
428C2×C32×C4C22×D311yescharacteristic
429#638—22no—
430#638—22no—
431#638—22no—
432#638—22no—
433#638—41no—
434#638—41no—
435#638—41no—
436#638—41no—
437C2×C3⋊Dic3—22no—
438C2×C3⋊Dic3C22×D311yescharacteristic
439C2×C3⋊Dic3C22×D311yescharacteristic
440C2×C3⋊Dic3C22×D311yescharacteristic
441C2×C3⋊Dic3C22×D311yescharacteristic
442C2×C3⋊Dic3C22×D311yescharacteristic
443C2×C3⋊Dic3C22×D311yescharacteristic
444C2×C3⋊Dic3C22×D311yescharacteristic
445C4⋊(C3⋊D3)—41no—
446C3×#67—62no—
447C3×#67—62no—
448C3×#67—62no—
449C3×#67—62no—
450C3×#67—62no—
451C3×#67—62no—
452C3×#67—62no—
453C3×#67—62no—
454C3×#67—122no—
455C3×#67—122no—
456C3×#67—122no—
457C3×#67—122no—
458C3×#67—121no—
459C3×#67—121no—
460C3×#67—121no—
461C3×#67—121no—
462C3×#67—121no—
463C3×#67—121no—
464C3×#67—121no—
465C3×#67—121no—
466C3×#67—122no—
467C3×#67—122no—
468C3×#67—122no—
469C3×#67—122no—
470C2×C3×Dic3—31no—
471C2×C3×Dic3—31no—
472C2×C3×Dic3—31no—
473C2×C3×Dic3—31no—
474C2×C3×Dic3—31no—
475C2×C3×Dic3—31no—
476C2×C3×Dic3—31no—
477C2×C3×Dic3—31no—
478C2×C3×Dic3—31no—
479C2×C3×Dic3—31no—
480C2×C3×Dic3—31no—
481C2×C3×Dic3—31no—
482C2×C3×Dic3—31no—
483C2×C3×Dic3—31no—
484C2×C3×Dic3—61no—
485C2×C3×Dic3—61no—
486C2×C3×Dic3—61no—
487C2×C3×Dic3—61no—
488C2×C3×Dic3—61no—
489C2×C3×Dic3—61no—
490C2×C3×Dic3—61no—
491C2×C3×Dic3—62no—
492C2×C3×Dic3—62no—
493C2×C3×Dic3—122no—
494C3×D12—121no—
495C3×D12—121no—
496C3×D12—122no—
497#627—62no—
498#627—62no—
499#627—62no—
500#626—62no—
501#626—62no—
502#626—62no—
503#626—62no—
504#626—62no—
505#626—62no—
506#626—121no—
507#626—121no—
508#626—121no—
509#626—121no—
510#625—62no—
511#625—62no—
512#625—62no—
513#625—121no—
514#625—121no—
515#624—34no—
516#624—62no—
517D3×Dic3—34no—
518D3×Dic3—34no—
519D3×Dic3—62no—
520D3×Dic3—62no—
521#535—271noSylow
522C2×C33—41no—
523C2×C33—41no—
524C2×C33C22×D411yescharacteristic
525C2×C33H(5,𝔽2)11yescharacteristic
526C2×C33H(5,𝔽2)11yescharacteristic
527C3×C3⋊D3—22no—
528C3×C3⋊D3—41no—
529C3×C3⋊D3—41no—
530C3×C3⋊D3—41no—
531C3×C3⋊D3—41no—
532C24×C3—91no—
533C23×D3—31no—
534C23×D3—31no—
535C23×D3—61no—
536C23×D3—91no—
537C23×D3—91no—
538C23×D3—91no—
539C2×C3×D4—21no—
540C2×C3×D4—21no—
541C2×C3×D4—21no—
542C2×C3×D4—41no—
543C2×C3×D4—91no—
544C2×C3×D4—91no—
545C2×C3×D4—91no—
546C2×C3×D4—91no—
547C2×C3×D4—91no—
548C2×C3×D4—91no—
549C2×C3×D4—91no—
550C2×C3×D4—91no—
551C2×C3×D4—91no—
552C2×C3×D4D3211yescharacteristic, complemented
553C2×C3×D4D3211yescharacteristic, complemented
554C2×C3×D4D3211yescharacteristic, complemented
555C22×C3×C4—91no—
556C2×#67—31no—
557C2×#67—31no—
558C2×#67—31no—
559C2×#67—31no—
560C2×#67—31no—
561C2×#67—31no—
562C2×#67—31no—
563C2×#67—31no—
564C2×#67—31no—
565C2×#67—31no—
566C2×#67—31no—
567C2×#67—31no—
568C2×#67—31no—
569C2×#67—31no—
570C2×#67—31no—
571C2×#67—31no—
572C2×#67—61no—
573C2×#67—61no—
574C2×#67—61no—
575C2×#67—61no—
576C2×#67—61no—
577C2×#67—61no—
578C2×#67—61no—
579C2×#67—61no—
580C2×#67—91no—
581C2×#67—91no—
582C2×#67—91no—
583C2×#67—91no—
584C2×#67—91no—
585C2×#67—91no—
586C2×#67—91no—
587C2×#67—91no—
588C2×#67—91no—
589C2×#67—91no—
590C2×#67—184no—
591C22×Dic3—31no—
592C22×Dic3—31no—
593C22×Dic3—61no—
594C22×Dic3—91no—
595C22×Dic3—91no—
596#237—184no—
597#237—184no—
598D3×D4—184no—
599D3×D4—184no—
600#235—184no—
601C2×D12—31no—
602C2×D12—31no—
603C2×D12—61no—
604C2×D12—91no—
605C2×D12—91no—
606C2×D12—91no—
607C2×D12—91no—
608C2×D12—91no—
609C2×C4×D3—91no—
610C2×C4×D3—91no—
611C2×C4×D3—91no—
612C2×C4×D3—91no—
613C2×Dic6—91no—
614C2×Dic6—91no—
615C2×Dic6—91no—
616C3×C4⋊C4—91no—
617C3×C22⋊C4—91no—
618C3×C22⋊C4—91no—
619C3×C22⋊C4—91no—
620C3×C22⋊C4—91no—
621C3×C22⋊C4—91no—
622C3×C42—91no—
623#217—31no—
624#217—31no—
625#217—31no—
626#217—31no—
627#217—61no—
628#217—61no—
629#217—91no—
630#217—91no—
631#217—91no—
632#217—91no—
633#217—91no—
634(C2×D3)⋊C4—31no—
635(C2×D3)⋊C4—31no—
636(C2×D3)⋊C4—31no—
637(C2×D3)⋊C4—31no—
638(C2×D3)⋊C4—31no—
639(C2×D3)⋊C4—31no—
640(C2×D3)⋊C4—61no—
641(C2×D3)⋊C4—61no—
642(C2×D3)⋊C4—61no—
643(C2×D3)⋊C4—91no—
644(C2×D3)⋊C4—91no—
645(C2×D3)⋊C4—91no—
646(C2×D3)⋊C4—91no—
647(C2×D3)⋊C4—91no—
648(C2×D3)⋊C4—91no—
649(C2×D3)⋊C4—91no—
650(C2×D3)⋊C4—91no—
651(C2×D3)⋊C4—91no—
652(C2×D3)⋊C4—91no—
653C4⋊Dic3—91no—
654Dic3⋊C4—31no—
655Dic3⋊C4—31no—
656Dic3⋊C4—61no—
657Dic3⋊C4—91no—
658Dic3⋊C4—91no—
659C4×Dic3—31no—
660C4×Dic3—31no—
661C4×Dic3—61no—
662C4×Dic3—91no—
663C4×Dic3—91no—
664C4×Dic3—91no—
665C22×C32—21no—
666C22×C32—21no—
667C22×C32—22no—
668C22×C32—22no—
669C22×C32—21no—
670C22×C32—21no—
671C22×C32—21no—
672C22×C32—21no—
673C22×C32—21no—
674C22×C32—21no—
675C22×C32—21no—
676C22×C32—21no—
677C22×C32—21no—
678C22×C32—21no—
679C22×C32—21no—
680C22×C32—21no—
681C22×C32—21no—
682C22×C32—21no—
683C22×C32—21no—
684C22×C32—21no—
685C22×C32—21no—
686C22×C32—21no—
687C22×C32—21no—
688C22×C32—41no—
689C22×C32—41no—
690C22×C32—41no—
691C22×C32—41no—
692C22×C32—41no—
693C22×C32—42no—
694C22×C32—42no—
695C22×C32—41no—
696C22×C32—41no—
697C22×C32—41no—
698C22×C32—41no—
699C22×C32—41no—
700C22×C32—41no—
701C22×C32—41no—
702C22×C32—41no—
703C22×C32—41no—
704C22×C32—41no—
705C22×C32—41no—
706C22×C32—41no—
707C22×C32—81no—
708C22×C32—81no—
709C22×C32—81no—
710C22×C32—81no—
711C22×C32C23×D311yescharacteristic
712C22×C32C23×D311yescharacteristic
713C22×C32C23×D311yescharacteristic
714C2×C3⋊D3—21no—
715C2×C3⋊D3—21no—
716C2×C3⋊D3—21no—
717C2×C3⋊D3—21no—
718C2×C3⋊D3—21no—
719C2×C3⋊D3—21no—
720C2×C3⋊D3—21no—
721C2×C3⋊D3—21no—
722C2×C3⋊D3—21no—
723C2×C3⋊D3—21no—
724C2×C3⋊D3—21no—
725C2×C3⋊D3—21no—
726C2×C3⋊D3—21no—
727C2×C3⋊D3—21no—
728C2×C3⋊D3—44no—
729C2×C3⋊D3D3×D412yes—
730C2×C3×D3—32no—
731C2×C3×D3—32no—
732C2×C3×D3—62no—
733C2×C3×D3—61no—
734C2×C3×D3—61no—
735C2×C3×D3—61no—
736C2×C3×D3—61no—
737C2×C3×D3—62no—
738C2×C3×D3—61no—
739C2×C3×D3—61no—
740C2×C3×D3—61no—
741C2×C3×D3—61no—
742C2×C3×D3—61no—
743C2×C3×D3—61no—
744C2×C3×D3—61no—
745C2×C3×D3—61no—
746C2×C3×D3—61no—
747C2×C3×D3—61no—
748C2×C3×D3—61no—
749C2×C3×D3—61no—
750C2×C3×D3—61no—
751C2×C3×D3—61no—
752C2×C3×D3—61no—
753C2×C3×D3—61no—
754C2×C3×D3—61no—
755C2×C3×D3—61no—
756C2×C3×D3—61no—
757C2×C3×D3—61no—
758C2×C3×D3—61no—
759C2×C3×D3—61no—
760C2×C3×D3—61no—
761C2×C3×D3—61no—
762C2×C3×D3—121no—
763C2×C3×D3—121no—
764C2×C3×D3—121no—
765C2×C3×D3—121no—
766C2×C3×D3—121no—
767C2×C3×D3—121no—
768C2×C3×D3—121no—
769C2×C3×D3—121no—
770C2×C3×D3—121no—
771C2×C3×D3—121no—
772C2×C3×D3—121no—
773C2×C3×D3—121no—
774C2×C3×D3—121no—
775C2×C3×D3—124no—
776C2×C3×D3—124no—
777C2×C3×D3—128no—
778D32—124no—
779D32—124no—
780D32—124no—
781C32×C4—21no—
782C32×C4—22no—
783C32×C4—21no—
784C32×C4—21no—
785C32×C4—41no—
786C32×C4—41no—
787C32×C4—42no—
788C3⋊Dic3—21no—
789C3⋊Dic3—21no—
790C3⋊Dic3—21no—
791C3⋊Dic3—21no—
792C3⋊Dic3—21no—
793C3⋊Dic3D3×D412yes—
794C3⋊Dic3D3×D412yes—
795C3×Dic3—32no—
796C3×Dic3—32no—
797C3×Dic3—32no—
798C3×Dic3—32no—
799C3×Dic3—62no—
800C3×Dic3—62no—
801C3×Dic3—62no—
802C3×Dic3—61no—
803C3×Dic3—61no—
804C3×Dic3—61no—
805C3×Dic3—61no—
806C3×Dic3—61no—
807C3×Dic3—61no—
808C3×Dic3—61no—
809C3×Dic3—61no—
810C3×Dic3—61no—
811C3×Dic3—61no—
812C3×Dic3—121no—
813C3×Dic3—121no—
814C3×Dic3—121no—
815C3×Dic3—121no—
816C2×#41—271no—
817C22×D4—271no—
818#127—91no—
819#127—271no—
820#124—271no—
821#124—271no—
822#121—91no—
823#121—271no—
824#121—271no—
825#121—271no—
826#120—91no—
827#120—271no—
828#120—271no—
829#120—271no—
830#117—271no—
831C33#53511yescharacteristic, complemented, Sylow
832C23×C3—21no—
833C23×C3—21no—
834C23×C3—21no—
835C23×C3—21no—
836C23×C3—21no—
837C23×C3—21no—
838C23×C3—41no—
839C23×C3—41no—
840C23×C3—91no—
841C23×C3—91no—
842C23×C3—91no—
843C23×C3—91no—
844C23×C3—91no—
845C23×C3—182no—
846C23×C3—361no—
847C23×C3—361no—
848C23×C3C2×D3211yescharacteristic
849C23×C3C2×D3211yescharacteristic
850C23×C3C2×D3211yescharacteristic
851C23×C3C2×D3211yescharacteristic
852C23×C3C2×D3211yescharacteristic
853C23×C3C2×D3211yescharacteristic
854C22×D3—31no—
855C22×D3—31no—
856C22×D3—31no—
857C22×D3—31no—
858C22×D3—31no—
859C22×D3—31no—
860C22×D3—31no—
861C22×D3—31no—
862C22×D3—31no—
863C22×D3—31no—
864C22×D3—61no—
865C22×D3—61no—
866C22×D3—61no—
867C22×D3—61no—
868C22×D3—61no—
869C22×D3—62no—
870C22×D3—62no—
871C22×D3—122no—
872C22×D3—121no—
873C22×D3—121no—
874C22×D3—121no—
875C22×D3—121no—
876C22×D3—122no—
877C22×D3—122no—
878C22×D3—182no—
879C22×D3—182no—
880C22×D3—182no—
881C22×D3—361no—
882C22×D3—361no—
883C22×D3—361no—
884C22×D3—361no—
885C22×D3—361no—
886C22×D3—361no—
887C3×D4—41no—
888C3×D4—41no—
889C3×D4—41no—
890C3×D4—42no—
891C3×D4—42no—
892C3×D4—42no—
893C3×D4—44no—
894C3×D4—182no—
895C3×D4—182no—
896C3×D4—182no—
897C3×D4—182no—
898C3×D4—361no—
899C3×D4—361no—
900C3×D4—361no—
901C3×D4—361no—
902C3×D4—361no—
903C2×C3×C4—21no—
904C2×C3×C4—21no—
905C2×C3×C4—21no—
906C2×C3×C4—41no—
907C2×C3×C4—91no—
908C2×C3×C4—91no—
909C2×C3×C4—91no—
910C2×C3×C4—91no—
911C2×C3×C4—91no—
912C2×C3×C4—91no—
913C2×C3×C4—91no—
914C2×C3×C4—182no—
915C2×C3×C4C2×D3211yescharacteristic
916C2×C3×C4C2×D3211yescharacteristic
917C2×C3×C4C2×D3211yescharacteristic
918#67—62no—
919#67—62no—
920#67—62no—
921#67—62no—
922#67—62no—
923#67—62no—
924#67—62no—
925#67—62no—
926#67—122no—
927#67—122no—
928#67—122no—
929#67—122no—
930#67—121no—
931#67—121no—
932#67—121no—
933#67—121no—
934#67—121no—
935#67—121no—
936#67—121no—
937#67—121no—
938#67—122no—
939#67—122no—
940#67—122no—
941#67—122no—
942#67—182no—
943#67—182no—
944#67—182no—
945#67—182no—
946#67—182no—
947#67—182no—
948#67—361no—
949#67—361no—
950#67—361no—
951#67—361no—
952C2×Dic3—31no—
953C2×Dic3—31no—
954C2×Dic3—31no—
955C2×Dic3—31no—
956C2×Dic3—31no—
957C2×Dic3—31no—
958C2×Dic3—31no—
959C2×Dic3—31no—
960C2×Dic3—31no—
961C2×Dic3—31no—
962C2×Dic3—31no—
963C2×Dic3—31no—
964C2×Dic3—31no—
965C2×Dic3—31no—
966C2×Dic3—61no—
967C2×Dic3—61no—
968C2×Dic3—61no—
969C2×Dic3—61no—
970C2×Dic3—61no—
971C2×Dic3—61no—
972C2×Dic3—61no—
973C2×Dic3—62no—
974C2×Dic3—62no—
975C2×Dic3—94no—
976C2×Dic3—122no—
977C2×Dic3—182no—
978D12—121no—
979D12—121no—
980D12—122no—
981D12—182no—
982D12—182no—
983D12—182no—
984D12—361no—
985D12—361no—
986C4×D3—94no—
987C4×D3—94no—
988C4×D3—182no—
989C4×D3—182no—
990Dic6—182no—
991Dic6—182no—
992Dic6—182no—
993C2×C32—21no—
994C2×C32—21no—
995C2×C32—21no—
996C2×C32—21no—
997C2×C32—21no—
998C2×C32—21no—
999C2×C32—21no—
1000C2×C32—21no—
1001C2×C32—21no—
1002C2×C32—41no—
1003C2×C32—41no—
1004C2×C32—41no—
1005C2×C32—41no—
1006C2×C32—41no—
1007C2×C32—42no—
1008C2×C32—42no—
1009C2×C32—41no—
1010C2×C32—41no—
1011C2×C32—41no—
1012C2×C32—41no—
1013C2×C32—81no—
1014C2×C32—81no—
1015C2×C32—81no—
1016C2×C32—81no—
1017C2×C32—82no—
1018C2×C32—82no—
1019C2×C32C2×D3×D411yescharacteristic
1020C2×C32C2×D3×D411yescharacteristic
1021C2×C32C2×D3×D411yescharacteristic
1022C2×C32#100411yescharacteristic
1023C2×C32#100411yescharacteristic
1024C2×C32#100411yescharacteristic
1025C2×C32#100411yescharacteristic
1026C2×C32#100411yescharacteristic
1027C2×C32#100911yescharacteristic
1028C3⋊D3—22no—
1029C3⋊D3—41no—
1030C3⋊D3—41no—
1031C3⋊D3—41no—
1032C3⋊D3—41no—
1033C3×D3—62no—
1034C3×D3—62no—
1035C3×D3—122no—
1036C3×D3—122no—
1037C3×D3—121no—
1038C3×D3—121no—
1039C3×D3—121no—
1040C3×D3—121no—
1041C3×D3—121no—
1042C3×D3—121no—
1043C3×D3—121no—
1044C3×D3—121no—
1045C3×D3—241no—
1046C3×D3—241no—
1047C3×D3—241no—
1048C24—91no—
1049C24—271no—
1050#41—544no—
1051C2×Q8—271no—
1052C2×D4—91no—
1053C2×D4—91no—
1054C2×D4—91no—
1055C2×D4—91no—
1056C2×D4—91no—
1057C2×D4—91no—
1058C2×D4—91no—
1059C2×D4—91no—
1060C2×D4—91no—
1061C2×D4—271no—
1062C2×D4—271no—
1063C2×D4—271no—
1064C2×D4—271no—
1065C2×D4—271no—
1066C2×D4—544no—
1067C2×D4#111311yescharacteristic, complemented
1068C22×C4—91no—
1069C22×C4—271no—
1070C22×C4—271no—
1071C4⋊C4—91no—
1072C4⋊C4—271no—
1073C22⋊C4—91no—
1074C22⋊C4—91no—
1075C22⋊C4—91no—
1076C22⋊C4—91no—
1077C22⋊C4—91no—
1078C22⋊C4—271no—
1079C22⋊C4—271no—
1080C22⋊C4—271no—
1081C22⋊C4—271no—
1082C22⋊C4—271no—
1083C42—91no—
1084C42—271no—
1085C22×C3—22no—
1086C22×C3—22no—
1087C22×C3—21no—
1088C22×C3—21no—
1089C22×C3—21no—
1090C22×C3—21no—
1091C22×C3—21no—
1092C22×C3—21no—
1093C22×C3—21no—
1094C22×C3—21no—
1095C22×C3—21no—
1096C22×C3—21no—
1097C22×C3—21no—
1098C22×C3—21no—
1099C22×C3—21no—
1100C22×C3—21no—
1101C22×C3—21no—
1102C22×C3—21no—
1103C22×C3—21no—
1104C22×C3—21no—
1105C22×C3—21no—
1106C22×C3—21no—
1107C22×C3—21no—
1108C22×C3—41no—
1109C22×C3—41no—
1110C22×C3—41no—
1111C22×C3—41no—
1112C22×C3—41no—
1113C22×C3—41no—
1114C22×C3—41no—
1115C22×C3—41no—
1116C22×C3—41no—
1117C22×C3—41no—
1118C22×C3—41no—
1119C22×C3—41no—
1120C22×C3—41no—
1121C22×C3—41no—
1122C22×C3—41no—
1123C22×C3—41no—
1124C22×C3—42no—
1125C22×C3—42no—
1126C22×C3—41no—
1127C22×C3—81no—
1128C22×C3—81no—
1129C22×C3—81no—
1130C22×C3—81no—
1131C22×C3—92no—
1132C22×C3—181no—
1133C22×C3—181no—
1134C22×C3—181no—
1135C22×C3—181no—
1136C22×C3—181no—
1137C22×C3—181no—
1138C22×C3—181no—
1139C22×C3—181no—
1140C22×C3—181no—
1141C22×C3—181no—
1142C22×C3—181no—
1143C22×C3—181no—
1144C22×C3—181no—
1145C22×C3—181no—
1146C22×C3—364no—
1147C22×C3C22×D3211yescharacteristic
1148C22×C3C22×D3211yescharacteristic
1149C22×C3C22×D3211yescharacteristic
1150C2×D3—32no—
1151C2×D3—32no—
1152C2×D3—62no—
1153C2×D3—61no—
1154C2×D3—61no—
1155C2×D3—61no—
1156C2×D3—61no—
1157C2×D3—62no—
1158C2×D3—61no—
1159C2×D3—61no—
1160C2×D3—61no—
1161C2×D3—61no—
1162C2×D3—61no—
1163C2×D3—61no—
1164C2×D3—61no—
1165C2×D3—61no—
1166C2×D3—61no—
1167C2×D3—61no—
1168C2×D3—61no—
1169C2×D3—61no—
1170C2×D3—61no—
1171C2×D3—61no—
1172C2×D3—61no—
1173C2×D3—61no—
1174C2×D3—61no—
1175C2×D3—61no—
1176C2×D3—61no—
1177C2×D3—61no—
1178C2×D3—61no—
1179C2×D3—61no—
1180C2×D3—61no—
1181C2×D3—61no—
1182C2×D3—121no—
1183C2×D3—121no—
1184C2×D3—121no—
1185C2×D3—121no—
1186C2×D3—121no—
1187C2×D3—121no—
1188C2×D3—121no—
1189C2×D3—121no—
1190C2×D3—121no—
1191C2×D3—121no—
1192C2×D3—121no—
1193C2×D3—121no—
1194C2×D3—121no—
1195C2×D3—124no—
1196C2×D3—124no—
1197C2×D3—128no—
1198C2×D3—364no—
1199C2×D3—364no—
1200C2×D3—364no—
1201C3×C4—22no—
1202C3×C4—21no—
1203C3×C4—21no—
1204C3×C4—21no—
1205C3×C4—41no—
1206C3×C4—41no—
1207C3×C4—42no—
1208C3×C4—92no—
1209C3×C4—92no—
1210C3×C4—181no—
1211C3×C4—181no—
1212C3×C4—181no—
1213C3×C4—181no—
1214C3×C4—181no—
1215Dic3—32no—
1216Dic3—32no—
1217Dic3—32no—
1218Dic3—32no—
1219Dic3—62no—
1220Dic3—62no—
1221Dic3—62no—
1222Dic3—61no—
1223Dic3—61no—
1224Dic3—61no—
1225Dic3—61no—
1226Dic3—61no—
1227Dic3—61no—
1228Dic3—61no—
1229Dic3—61no—
1230Dic3—61no—
1231Dic3—61no—
1232Dic3—121no—
1233Dic3—121no—
1234Dic3—121no—
1235Dic3—121no—
1236C32—21no—
1237C32—21no—
1238C32—21no—
1239C32—41no—
1240C32#559211yescharacteristic, complemented
1241C32#560711yescharacteristic, complemented
1242C32#571511yescharacteristic, complemented
1243C23—91no—
1244C23—91no—
1245C23—91no—
1246C23—91no—
1247C23—91no—
1248C23—182no—
1249C23—361no—
1250C23—361no—
1251C23—542no—
1252C23—1081no—
1253C23—1081no—
1254C23C2×#111311yescharacteristic
1255C23C2×#111311yescharacteristic
1256Q8—542no—
1257D4—41no—
1258D4—182no—
1259D4—182no—
1260D4—182no—
1261D4—182no—
1262D4—361no—
1263D4—361no—
1264D4—361no—
1265D4—361no—
1266D4—361no—
1267D4—542no—
1268D4—542no—
1269D4—542no—
1270D4—1081no—
1271D4—1081no—
1272C2×C4—91no—
1273C2×C4—91no—
1274C2×C4—91no—
1275C2×C4—91no—
1276C2×C4—91no—
1277C2×C4—91no—
1278C2×C4—91no—
1279C2×C4—182no—
1280C2×C4—274no—
1281C2×C4—542no—
1282C2×C4C2×#111311yescharacteristic
1283C2×C3—21no—
1284C2×C3—21no—
1285C2×C3—21no—
1286C2×C3—21no—
1287C2×C3—21no—
1288C2×C3—21no—
1289C2×C3—21no—
1290C2×C3—21no—
1291C2×C3—21no—
1292C2×C3—42no—
1293C2×C3—42no—
1294C2×C3—41no—
1295C2×C3—41no—
1296C2×C3—41no—
1297C2×C3—41no—
1298C2×C3—41no—
1299C2×C3—41no—
1300C2×C3—41no—
1301C2×C3—41no—
1302C2×C3—41no—
1303C2×C3—81no—
1304C2×C3—81no—
1305C2×C3—81no—
1306C2×C3—81no—
1307C2×C3—82no—
1308C2×C3—82no—
1309C2×C3—182no—
1310C2×C3—361no—
1311C2×C3—361no—
1312C2×C3—361no—
1313C2×C3—361no—
1314C2×C3D32×D411yescharacteristic
1315C2×C3D32×D411yescharacteristic
1316C2×C3D32×D411yescharacteristic
1317C2×C3#6431311yescharacteristic
1318C2×C3#6431411yescharacteristic
1319C2×C3#6431411yescharacteristic
1320C2×C3#6433011yescharacteristic
1321C2×C3#6433011yescharacteristic
1322C2×C3#6433011yescharacteristic
1323D3—62no—
1324D3—62no—
1325D3—122no—
1326D3—122no—
1327D3—121no—
1328D3—121no—
1329D3—121no—
1330D3—121no—
1331D3—121no—
1332D3—121no—
1333D3—121no—
1334D3—121no—
1335D3—241no—
1336D3—241no—
1337D3—241no—
1338C22—21no—
1339C22—21no—
1340C22—21no—
1341C22—21no—
1342C22—21no—
1343C22—21no—
1344C22—92no—
1345C22—181no—
1346C22—181no—
1347C22—181no—
1348C22—181no—
1349C22—181no—
1350C22—181no—
1351C22—181no—
1352C22—181no—
1353C22—181no—
1354C22—181no—
1355C22—181no—
1356C22—181no—
1357C22—181no—
1358C22—181no—
1359C22—364no—
1360C22—1084no—
1361C22C22×#111311yescharacteristic
1362C4—21no—
1363C4—92no—
1364C4—92no—
1365C4—181no—
1366C4—181no—
1367C4—181no—
1368C4—181no—
1369C4—181no—
1370C3—21no—
1371C3—21no—
1372C3—21no—
1373C3—41no—
1374C3#1059528511yescharacteristic, complemented
1375C3#1059528611yescharacteristic, complemented
1376C3#1059529911yescharacteristic, complemented
1377C2—41no—
1378C2—41no—
1379C2—182no—
1380C2—361no—
1381C2—361no—
1382C2—361no—
1383C2—361no—
1384C2D4×#111311yescharacteristic
1385C2#1172462311yescharacteristic
1386C2#1172463311yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC2×C33×D4C22
hypercenterC2×D4#1113
hypocenterC33#535
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×#89049C2semidirect
2. C2×#89046C2semidirect
3. C3×#64149C2semidirect
4. C3×#64148C2semidirect
5. C3×#64146C2semidirect
6. #11723729C2semidirect
7. #11723728C2semidirect
8. #11723727C2semidirect
9. #11723725C2semidirect
10. #11723718C2semidirect
11. #11723717C2semidirect
12. #11723701C2semidirect
13. #11723687C2semidirect
14. #11723683C2semidirect
15. #11723672C2semidirect
21. C2×C33×D4C22semidirect
25. C2×C3×#638C22semidirect
26. C2×C3×#638C22semidirect
27. C2×C3×#638C22semidirect
28. C2×C3×#638C22semidirect
29. C2×C3×#638C22semidirect
30. C22×C3×C3⋊Dic3C22semidirect
31. C2×C3×C4⋊(C3⋊D3)C22semidirect
33. C2×#6296C22semidirect
37. C2×#6295C22semidirect
38. C2×#6295C22semidirect
41. C2×#6294C22semidirect
42. C3×#3757C22semidirect
43. C3×#3757C22semidirect
45. C3×#3752C22semidirect
46. C3×#3752C22semidirect
47. C3×#3750C22semidirect
48. C3×C4×C3⋊Dic3C22semidirect
49. #88815C22semidirect
51. #88814C22semidirect
52. #88814C22semidirect
53. #88814C22semidirect
54. #88814C22semidirect
55. #88813C22semidirect
62. #64149D3semidirect
63. #64148D3semidirect
64. #64146D3semidirect
143. #6294D4semidirect
158. C2×C32×D4C2×D3semidirect
159. C2×C32×D4C2×D3semidirect
160. C2×C32×D4C2×D3semidirect
164. C2×#638C2×D3semidirect
165. C2×#638C2×D3semidirect
166. C2×#638C2×D3semidirect
167. C2×#638C2×D3semidirect
168. C2×#638C2×D3semidirect
169. C22×C3⋊Dic3C2×D3semidirect
170. C2×C4⋊(C3⋊D3)C2×D3semidirect
231. #3757C2×D3semidirect
232. #3757C2×D3semidirect
234. #3752C2×D3semidirect
235. #3752C2×D3semidirect
236. #3750C2×D3semidirect
237. C4×C3⋊Dic3C2×D3semidirect
552. C2×C3×D4D32semidirect
553. C2×C3×D4D32semidirect
554. C2×C3×D4D32semidirect
831. C33#535semidirect
1067. C2×D4#1113semidirect
1240. C32#5592semidirect
1241. C32#5607semidirect
1242. C32#5715semidirect
1374. C3#10595285semidirect
1375. C3#10595286semidirect
1376. C3#10595299semidirect

Maximal subgroups

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

subgroupindex
C2×#890492
C2×#890462
C3×#641492
C3×#641482
C3×#641462
#117237292
#117237282
#117237272
#117237252
#117237182
#117237172
#117237012
#117236872
#117236832
#117236722
#105952993
#105952863
#105952853