Finite Group Databasebeta

← #13178708

Subgroups — #13178708

Order 1728.

1778 conjugacy classes of subgroups.

The subgroup lattice has 1338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3830C211yesmaximal, characteristic, complemented
2C2×#89049C211yesmaximal, characteristic, complemented
3C3×#64148C211yesmaximal, characteristic, complemented
4C3×#64146C211yesmaximal, characteristic, complemented
5#11723729C211yesmaximal, characteristic, complemented
6#11723726C211yesmaximal, characteristic, complemented
7#11723726C211yesmaximal, characteristic, complemented
8#11723725C211yesmaximal, characteristic, complemented
9#11723720C211yesmaximal, characteristic, complemented
10C2×#88814C211yesmaximal, characteristic, complemented
11#11723717C211yesmaximal, characteristic, complemented
12#11723700C211yesmaximal, characteristic, complemented
13#11723694C211yesmaximal, characteristic, complemented
14#11723688C211yesmaximal, characteristic, complemented
15#11723670C211yesmaximal, characteristic, complemented
16#10595307—31nomaximal
17#10595305—31nomaximal
18#10595304—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
28C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
29C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
30C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
31C3×#3830—24no—
32C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
33C2×C3×#634C2211yescharacteristic, complemented
34#89049—24no—
35C2×#6295C2211yescharacteristic
36C2×#6295C2211yescharacteristic
37C2×#6294C2211yescharacteristic
38C2×#6294C2211yescharacteristic, complemented
39C3×#3757C2211yescharacteristic, complemented
40C3×#3757C2211yescharacteristic, complemented
41C3×#3752C2211yescharacteristic
42C3×#3752C2211yescharacteristic, complemented
43C3×#3752C2211yescharacteristic, complemented
44C3×#3750C2211yescharacteristic, complemented
45#88815C2211yescharacteristic, complemented
46#88815C2211yescharacteristic, complemented
47#88815C2211yescharacteristic, complemented
48#88814C2211yescharacteristic
49#88814C2211yescharacteristic
50#88814C2211yescharacteristic, complemented
51#88814C2211yescharacteristic, complemented
52#88814C2211yescharacteristic, complemented
53#88814C2211yescharacteristic, complemented
54#88814C2211yescharacteristic, complemented
55#88813C2211yescharacteristic, complemented
56C2×#3830D311yescharacteristic, complemented
57C2×C3×#237—31no—
58C2×C3×#237—31no—
59C2×C3×#237—61no—
60C2×#3811—31no—
61C2×D3×#67—31no—
62C2×D3×#67—31no—
63#64148D311yescharacteristic, complemented
64#64146D311yescharacteristic, complemented
65C3×#939—31no—
66C3×#939—31no—
67C3×#939—61no—
68C3×#937—31no—
69C3×#937—31no—
70C3×#937—61no—
71#63983—31no—
72#63983—31no—
73#63983—31no—
74#63980—31no—
75#63978—31no—
76#63978—31no—
77#67⋊Dic3—31no—
78#67⋊Dic3—31no—
79Dic3×#67—31no—
80Dic3×#67—31no—
81#63971—31no—
82#63970—31no—
83#63966—31no—
84C2×#3722—31no—
85#63962—31no—
86#63961—31no—
87C2×(C2×D3)⋊Dic3—31no—
88C2×(C2×D3)⋊Dic3—31no—
89#63958—31no—
90#63952—31no—
91#63952—31no—
92#63921—31no—
93D3×(C2×D3)⋊C4—31no—
94D3×(C2×D3)⋊C4—31no—
95#63913—31no—
96#63907—31no—
97#63907—31no—
98#63905—31no—
99#63896—31no—
100#63888—31no—
101#63887—31no—
102#63853—31no—
103#63850—31no—
104C23×C33C2311yescharacteristic
105C23×C33C2311yescharacteristic
106C22×C3×C3⋊D3—22no—
107C22×C3×C3⋊D3—22no—
108C22×C3×C3⋊D3—41no—
109C22×C3×C3⋊D3C2311yescharacteristic
110C22×C3×C3⋊D3C2311yescharacteristic
111C22×C3×C3⋊D3C2311yescharacteristic
112C22×C3×C3⋊D3C2311yescharacteristic
113C2×#1113—22no—
114C2×#1113—22no—
115C2×#1113—41no—
116C33×D4—22no—
117C2×C33×C4C2311yescharacteristic
118C3×#638—22no—
119C3×#638—22no—
120C3×#638—22no—
121C3×#638—41no—
122C3×#638—41no—
123C3×#638D414yescomplemented
124C2×C3×C3⋊Dic3—22no—
125C2×C3×C3⋊Dic3—22no—
126C2×C3×C3⋊Dic3—41no—
127C2×C3×C3⋊Dic3C2311yescharacteristic
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—22no—
136C3×#634—22no—
137#6295—22no—
138#6295—22no—
139#6294—22no—
140#6294—41no—
141#5829—91no—
142#5610—91no—
143#5591—91no—
144C23×C3⋊D3C2×D311yescharacteristic
145C23×C3×D3—31no—
146C23×C3×D3—31no—
147C23×C3×D3—61no—
148C22×D32—31no—
149C22×D32—31no—
150C22×D32—31no—
151C2×C32×D4—21no—
152C2×C32×D4—21no—
153C2×C32×D4—21no—
154C2×C32×D4—41no—
155C2×C32×D4C2×D311yescharacteristic, complemented
156C2×C32×D4C2×D311yescharacteristic, complemented
157C2×C32×D4C2×D311yescharacteristic, complemented
158C2×#638C2×D311yescharacteristic
159C2×#638C2×D311yescharacteristic
160C2×#638C2×D311yescharacteristic
161C2×#638C2×D311yescharacteristic, complemented
162C2×#638C2×D311yescharacteristic, complemented
163C2×#638C2×D311yescharacteristic, complemented
164C22×C3⋊Dic3C2×D311yescharacteristic, complemented
165C22×C3⋊Dic3C2×D311yescharacteristic, complemented
166C22×C3⋊Dic3C2×D311yescharacteristic, complemented
167#3830—24no—
168C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
169C2×#634C2×D311yescharacteristic, complemented
170C2×C3×#67—31no—
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—61no—
183C2×C3×#67—61no—
184C2×C3×#67—61no—
185C2×C3×#67—61no—
186C2×C3×#67—61no—
187C2×C3×#67—61no—
188C22×C3×Dic3—31no—
189C22×C3×Dic3—31no—
190C22×C3×Dic3—31no—
191C22×C3×Dic3—31no—
192C22×C3×Dic3—31no—
193C22×C3×Dic3—31no—
194C22×C3×Dic3—61no—
195C22×C3×Dic3—61no—
196C22×C3×Dic3—61no—
197C3×#237—64no—
198C3×#237—64no—
199C3×#237—68no—
200C2×C3×C4×D3—31no—
201C2×C3×C4×D3—31no—
202C2×C3×C4×D3—61no—
203C2×C3×Dic6—31no—
204C2×C3×Dic6—31no—
205C2×C3×Dic6—61no—
206#3811—64no—
207D3×#67—64no—
208D3×#67—64no—
209C2×#626—31no—
210C2×#626—31no—
211C2×#626—31no—
212C2×#626—31no—
213C2×#625—31no—
214C2×#625—31no—
215C2×#624—31no—
216C2×#624—31no—
217C2×D3×Dic3—31no—
218C2×D3×Dic3—31no—
219C2×D3×Dic3—31no—
220C2×D3×Dic3—31no—
221#3757C2×D311yescharacteristic, complemented
222#3757C2×D311yescharacteristic, complemented
223#3752C2×D311yescharacteristic
224#3752C2×D311yescharacteristic, complemented
225#3752C2×D311yescharacteristic, complemented
226#3750C2×D311yescharacteristic, complemented
227C3×#217—31no—
228C3×#217—31no—
229C3×#217—31no—
230C3×#217—31no—
231C3×#217—61no—
232C3×#217—61no—
233C3×(C2×D3)⋊C4—31no—
234C3×(C2×D3)⋊C4—31no—
235C3×(C2×D3)⋊C4—31no—
236C3×(C2×D3)⋊C4—31no—
237C3×(C2×D3)⋊C4—31no—
238C3×(C2×D3)⋊C4—31no—
239C3×(C2×D3)⋊C4—61no—
240C3×(C2×D3)⋊C4—61no—
241C3×(C2×D3)⋊C4—61no—
242C3×Dic3⋊C4—31no—
243C3×Dic3⋊C4—31no—
244C3×Dic3⋊C4—61no—
245#3724—31no—
246#3724—31no—
247#3724—31no—
248Dic3⋊Dic3—31no—
249Dic3⋊Dic3—31no—
250Dic3⋊Dic3—31no—
251Dic3⋊Dic3—31no—
252Dic3⋊Dic3—31no—
253Dic3⋊Dic3—31no—
254#3722—31no—
255#3722—31no—
256#3722—31no—
257#3722—31no—
258#3722—31no—
259#3722—31no—
260#3722—31no—
261(C2×D3)⋊Dic3—31no—
262(C2×D3)⋊Dic3—31no—
263(C2×D3)⋊Dic3—31no—
264(C2×D3)⋊Dic3—31no—
265(C2×D3)⋊Dic3—31no—
266(C2×D3)⋊Dic3—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—
275Dic32—31no—
276Dic32—31no—
277Dic32—31no—
278C22×C33—21no—
279C22×C33—21no—
280C22×C33—21no—
281C22×C33—21no—
282C22×C33—21no—
283C22×C33C2×D412yes—
284C22×C33C2411yescharacteristic
285C2×C3×C3⋊D3—21no—
286C2×C3×C3⋊D3—21no—
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—44no—
296C2×C3×C3⋊D3C2×D412yes—
297C2×C3×C3⋊D3#4112yescomplemented
298#1113—44no—
299C33×C4—21no—
300C3×C3⋊Dic3—21no—
301C3×C3⋊Dic3—21no—
302C3×C3⋊Dic3—21no—
303C3×C3⋊Dic3—21no—
304C3×C3⋊Dic3—21no—
305C3×C3⋊Dic3—21no—
306C3×C3⋊Dic3—21no—
307C3×C3⋊Dic3C2×D412yes—
308C2×C3×#41—91no—
309C22×#67—91no—
310C2×#237—31no—
311C2×#237—31no—
312C2×#237—61no—
313C2×D3×D4—91no—
314C2×D3×D4—91no—
315C3×#121—91no—
316C3×#120—91no—
317C2×#217—91no—
318#947—91no—
319#946—91no—
320#939—31no—
321#939—31no—
322#939—61no—
323#939—91no—
324#939—91no—
325#939—91no—
326#938—91no—
327#937—31no—
328#937—31no—
329#937—61no—
330#937—91no—
331#937—91no—
332#937—91no—
333#935—91no—
334D4×Dic3—91no—
335D4×Dic3—91no—
336#930—91no—
337#929—91no—
338#929—91no—
339C4×#67—91no—
340C4×#67—91no—
341C2×(C2×D3)⋊C4—91no—
342C2×(C2×D3)⋊C4—91no—
343C2×(C2×D3)⋊C4—91no—
344#896—91no—
345#894—91no—
346#886—91no—
347#885—91no—
348#885—91no—
349#884—91no—
350#883—91no—
351#67⋊C4—91no—
352#67⋊C4—91no—
353D3×C22⋊C4—91no—
354D3×C22⋊C4—91no—
355#878—91no—
356C23×C32—21no—
357C23×C32—21no—
358C23×C32—21no—
359C23×C32—21no—
360C23×C32—21no—
361C23×C32—21no—
362C23×C32—41no—
363C23×C32—41no—
364C23×C32C22×D311yescharacteristic
365C23×C32C22×D311yescharacteristic
366C23×C32C22×D311yescharacteristic
367C23×C32C22×D311yescharacteristic
368C23×C32C22×D311yescharacteristic
369C23×C32C22×D311yescharacteristic
370C22×C3⋊D3—22no—
371C22×C3⋊D3—22no—
372C22×C3⋊D3—41no—
373C22×C3⋊D3C22×D311yescharacteristic
374C22×C3⋊D3C22×D311yescharacteristic
375C22×C3⋊D3C22×D311yescharacteristic
376C22×C3⋊D3C22×D311yescharacteristic
377C22×C3×D3—31no—
378C22×C3×D3—31no—
379C22×C3×D3—31no—
380C22×C3×D3—31no—
381C22×C3×D3—31no—
382C22×C3×D3—31no—
383C22×C3×D3—31no—
384C22×C3×D3—31no—
385C22×C3×D3—61no—
386C22×C3×D3—61no—
387C22×C3×D3—61no—
388C22×C3×D3—61no—
389C22×C3×D3—62no—
390C22×C3×D3—62no—
391C22×C3×D3—62no—
392C22×C3×D3—62no—
393C22×C3×D3—122no—
394C22×C3×D3—122no—
395C22×C3×D3—121no—
396C22×C3×D3—121no—
397C22×C3×D3—122no—
398C2×D32—62no—
399C2×D32—62no—
400C2×D32—62no—
401C2×D32—62no—
402C2×D32—62no—
403C2×D32—62no—
404C2×D32—121no—
405C2×D32—121no—
406C2×D32—121no—
407C32×D4—22no—
408C32×D4—24no—
409C32×D4—22no—
410C32×D4—22no—
411C32×D4—42no—
412C32×D4—42no—
413C32×D4—44no—
414C2×C32×C4—21no—
415C2×C32×C4—21no—
416C2×C32×C4—21no—
417C2×C32×C4—41no—
418C2×C32×C4C22×D311yescharacteristic
419C2×C32×C4C22×D311yescharacteristic
420C2×C32×C4C22×D311yescharacteristic
421#638—22no—
422#638—22no—
423#638—22no—
424#638—41no—
425#638—41no—
426#638#6714yescomplemented
427C2×C3⋊Dic3—22no—
428C2×C3⋊Dic3—22no—
429C2×C3⋊Dic3—41no—
430C2×C3⋊Dic3C22×D311yescharacteristic
431C2×C3⋊Dic3C22×D311yescharacteristic
432C2×C3⋊Dic3C22×D311yescharacteristic
433C2×C3⋊Dic3C22×D311yescharacteristic
434C2×C3⋊Dic3C22×D311yescharacteristic
435C2×C3⋊Dic3C22×D311yescharacteristic
436C2×C3⋊Dic3C22×D311yescharacteristic
437C2×C3⋊Dic3C22×D311yescharacteristic
438C4×C3⋊D3—22no—
439#634—22no—
440C3×#67—34no—
441C3×#67—34no—
442C3×#67—64no—
443C3×#67—62no—
444C3×#67—62no—
445C3×#67—62no—
446C3×#67—62no—
447C3×#67—64no—
448C3×#67—62no—
449C3×#67—62no—
450C3×#67—122no—
451C3×#67—122no—
452C3×#67—121no—
453C3×#67—121no—
454C3×#67—121no—
455C3×#67—121no—
456C3×#67—122no—
457C3×#67—122no—
458C2×C3×Dic3—31no—
459C2×C3×Dic3—31no—
460C2×C3×Dic3—31no—
461C2×C3×Dic3—31no—
462C2×C3×Dic3—31no—
463C2×C3×Dic3—31no—
464C2×C3×Dic3—31no—
465C2×C3×Dic3—31no—
466C2×C3×Dic3—31no—
467C2×C3×Dic3—31no—
468C2×C3×Dic3—31no—
469C2×C3×Dic3—31no—
470C2×C3×Dic3—31no—
471C2×C3×Dic3—31no—
472C2×C3×Dic3—31no—
473C2×C3×Dic3—31no—
474C2×C3×Dic3—61no—
475C2×C3×Dic3—61no—
476C2×C3×Dic3—61no—
477C2×C3×Dic3—61no—
478C2×C3×Dic3—61no—
479C2×C3×Dic3—61no—
480C2×C3×Dic3—61no—
481C2×C3×Dic3—61no—
482C2×C3×Dic3—62no—
483C2×C3×Dic3—62no—
484C2×C3×Dic3—64no—
485C2×C3×Dic3—64no—
486C2×C3×Dic3—62no—
487C2×C3×Dic3—62no—
488C2×C3×Dic3—121no—
489C2×C3×Dic3—121no—
490C2×C3×Dic3—122no—
491C3×C4×D3—62no—
492C3×C4×D3—62no—
493C3×C4×D3—64no—
494C3×Dic6—62no—
495C3×Dic6—62no—
496C3×Dic6—64no—
497#626—62no—
498#626—62no—
499#626—62no—
500#626—62no—
501#625—62no—
502#625—62no—
503#624—62no—
504#624—121no—
505D3×Dic3—62no—
506D3×Dic3—62no—
507D3×Dic3—121no—
508D3×Dic3—121no—
509#546—271noSylow
510C2×C33—22no—
511C2×C33—41no—
512C2×C33C22×D411yescharacteristic
513C2×C33C2×#4111yescharacteristic
514C2×C33H(5,𝔽2)11yescharacteristic
515C3×C3⋊D3—22no—
516C3×C3⋊D3—22no—
517C3×C3⋊D3—41no—
518C3×C3⋊D3—41no—
519C24×C3—91no—
520C23×D3—31no—
521C23×D3—31no—
522C23×D3—61no—
523C23×D3—91no—
524C23×D3—91no—
525C23×D3—91no—
526C3×#41—184no—
527C2×C3×Q8—91no—
528C2×C3×D4—21no—
529C2×C3×D4—21no—
530C2×C3×D4—21no—
531C2×C3×D4—41no—
532C2×C3×D4—91no—
533C2×C3×D4—91no—
534C2×C3×D4—91no—
535C2×C3×D4—91no—
536C2×C3×D4—91no—
537C2×C3×D4—91no—
538C2×C3×D4D3211yescharacteristic, complemented
539C2×C3×D4D3211yescharacteristic, complemented
540C2×C3×D4D3211yescharacteristic, complemented
541C22×C3×C4—91no—
542C22×C3×C4—91no—
543C22×C3×C4—91no—
544C22×C3×C4—91no—
545C2×#67—31no—
546C2×#67—31no—
547C2×#67—31no—
548C2×#67—31no—
549C2×#67—31no—
550C2×#67—31no—
551C2×#67—31no—
552C2×#67—31no—
553C2×#67—31no—
554C2×#67—31no—
555C2×#67—31no—
556C2×#67—31no—
557C2×#67—61no—
558C2×#67—61no—
559C2×#67—61no—
560C2×#67—61no—
561C2×#67—61no—
562C2×#67—61no—
563C2×#67—91no—
564C2×#67—91no—
565C2×#67—91no—
566C2×#67—91no—
567C2×#67—184no—
568C22×Dic3—31no—
569C22×Dic3—31no—
570C22×Dic3—31no—
571C22×Dic3—31no—
572C22×Dic3—31no—
573C22×Dic3—31no—
574C22×Dic3—61no—
575C22×Dic3—61no—
576C22×Dic3—61no—
577C22×Dic3—91no—
578C22×Dic3—91no—
579#237—64no—
580#237—64no—
581#237—68no—
582D3×D4—184no—
583D3×D4—184no—
584C2×D12—91no—
585C2×D12—91no—
586C2×C4×D3—31no—
587C2×C4×D3—31no—
588C2×C4×D3—61no—
589C2×C4×D3—91no—
590C2×C4×D3—91no—
591C2×C4×D3—91no—
592C2×C4×D3—91no—
593C2×Dic6—31no—
594C2×Dic6—31no—
595C2×Dic6—61no—
596C3×C4⋊C4—91no—
597C3×C22⋊C4—91no—
598C3×C22⋊C4—91no—
599C3×C22⋊C4—91no—
600C3×C22⋊C4—91no—
601C3×C22⋊C4—91no—
602#217—31no—
603#217—31no—
604#217—31no—
605#217—31no—
606#217—61no—
607#217—61no—
608#217—91no—
609#217—91no—
610#217—91no—
611#217—91no—
612#217—91no—
613#217—91no—
614#217—91no—
615(C2×D3)⋊C4—31no—
616(C2×D3)⋊C4—31no—
617(C2×D3)⋊C4—31no—
618(C2×D3)⋊C4—31no—
619(C2×D3)⋊C4—31no—
620(C2×D3)⋊C4—31no—
621(C2×D3)⋊C4—61no—
622(C2×D3)⋊C4—61no—
623(C2×D3)⋊C4—61no—
624(C2×D3)⋊C4—91no—
625(C2×D3)⋊C4—91no—
626(C2×D3)⋊C4—91no—
627(C2×D3)⋊C4—91no—
628(C2×D3)⋊C4—91no—
629(C2×D3)⋊C4—91no—
630(C2×D3)⋊C4—91no—
631(C2×D3)⋊C4—91no—
632(C2×D3)⋊C4—91no—
633(C2×D3)⋊C4—91no—
634(C2×D3)⋊C4—91no—
635(C2×D3)⋊C4—91no—
636(C2×D3)⋊C4—91no—
637(C2×D3)⋊C4—91no—
638C4⋊Dic3—91no—
639C4⋊Dic3—91no—
640C4⋊Dic3—91no—
641Dic3⋊C4—31no—
642Dic3⋊C4—31no—
643Dic3⋊C4—61no—
644Dic3⋊C4—91no—
645Dic3⋊C4—91no—
646Dic3⋊C4—91no—
647Dic3⋊C4—91no—
648Dic3⋊C4—91no—
649Dic3⋊C4—91no—
650C4×Dic3—91no—
651C4×Dic3—91no—
652C4×Dic3—91no—
653C22×C32—21no—
654C22×C32—21no—
655C22×C32—21no—
656C22×C32—21no—
657C22×C32—21no—
658C22×C32—21no—
659C22×C32—21no—
660C22×C32—22no—
661C22×C32—21no—
662C22×C32—21no—
663C22×C32—21no—
664C22×C32—21no—
665C22×C32—21no—
666C22×C32—21no—
667C22×C32—21no—
668C22×C32—21no—
669C22×C32—21no—
670C22×C32—21no—
671C22×C32—21no—
672C22×C32—22no—
673C22×C32—22no—
674C22×C32—22no—
675C22×C32—41no—
676C22×C32—42no—
677C22×C32—41no—
678C22×C32—41no—
679C22×C32—42no—
680C22×C32—41no—
681C22×C32—41no—
682C22×C32—41no—
683C22×C32—41no—
684C22×C32—41no—
685C22×C32—41no—
686C22×C32—41no—
687C22×C32—41no—
688C22×C32—41no—
689C22×C32—41no—
690C22×C32—41no—
691C22×C32—41no—
692C22×C32—81no—
693C22×C32—81no—
694C22×C32—81no—
695C22×C32—81no—
696C22×C32D3×D412yes—
697C22×C32D3×D412yes—
698C22×C32C2×#6712yes—
699C22×C32C23×D311yescharacteristic
700C22×C32C23×D311yescharacteristic
701C22×C32C23×D311yescharacteristic
702C2×C3⋊D3—21no—
703C2×C3⋊D3—21no—
704C2×C3⋊D3—21no—
705C2×C3⋊D3—21no—
706C2×C3⋊D3—21no—
707C2×C3⋊D3—21no—
708C2×C3⋊D3—21no—
709C2×C3⋊D3—21no—
710C2×C3⋊D3—21no—
711C2×C3⋊D3—21no—
712C2×C3⋊D3—44no—
713C2×C3⋊D3#23712yescomplemented
714C2×C3⋊D3C2×#6712yes—
715C2×C3×D3—32no—
716C2×C3×D3—32no—
717C2×C3×D3—32no—
718C2×C3×D3—32no—
719C2×C3×D3—62no—
720C2×C3×D3—62no—
721C2×C3×D3—61no—
722C2×C3×D3—61no—
723C2×C3×D3—61no—
724C2×C3×D3—61no—
725C2×C3×D3—61no—
726C2×C3×D3—61no—
727C2×C3×D3—61no—
728C2×C3×D3—61no—
729C2×C3×D3—62no—
730C2×C3×D3—61no—
731C2×C3×D3—61no—
732C2×C3×D3—61no—
733C2×C3×D3—61no—
734C2×C3×D3—61no—
735C2×C3×D3—61no—
736C2×C3×D3—61no—
737C2×C3×D3—61no—
738C2×C3×D3—61no—
739C2×C3×D3—61no—
740C2×C3×D3—61no—
741C2×C3×D3—61no—
742C2×C3×D3—121no—
743C2×C3×D3—121no—
744C2×C3×D3—121no—
745C2×C3×D3—121no—
746C2×C3×D3—121no—
747C2×C3×D3—121no—
748C2×C3×D3—121no—
749C2×C3×D3—121no—
750C2×C3×D3—121no—
751C2×C3×D3—124no—
752C2×C3×D3—124no—
753C2×C3×D3—128no—
754D32—124no—
755D32—124no—
756D32—124no—
757C32×C4—21no—
758C32×C4—22no—
759C32×C4—21no—
760C32×C4—21no—
761C32×C4—41no—
762C32×C4—41no—
763C32×C4—42no—
764C3⋊Dic3—21no—
765C3⋊Dic3—21no—
766C3⋊Dic3—21no—
767C3⋊Dic3—21no—
768C3⋊Dic3—21no—
769C3⋊Dic3—21no—
770C3⋊Dic3—21no—
771C3⋊Dic3C2×#6712yes—
772C3×Dic3—32no—
773C3×Dic3—32no—
774C3×Dic3—62no—
775C3×Dic3—62no—
776C3×Dic3—62no—
777C3×Dic3—62no—
778C3×Dic3—61no—
779C3×Dic3—61no—
780C3×Dic3—61no—
781C3×Dic3—61no—
782C3×Dic3—61no—
783C3×Dic3—61no—
784C3×Dic3—61no—
785C3×Dic3—61no—
786C3×Dic3—61no—
787C3×Dic3—61no—
788C3×Dic3—61no—
789C3×Dic3—61no—
790C3×Dic3—61no—
791C3×Dic3—61no—
792C3×Dic3—121no—
793C3×Dic3—121no—
794C3×Dic3—121no—
795C3×Dic3—121no—
796C2×#41—91no—
797C22×D4—271no—
798#124—271no—
799#123—271no—
800#123—271no—
801C22⋊Q8—271no—
802#121—91no—
803#121—271no—
804#121—271no—
805#120—91no—
806#120—271no—
807C4×D4—271no—
808C4×D4—271no—
809C2×C22⋊C4—271no—
810C2×C22⋊C4—271no—
811C33#54611yescharacteristic, complemented, Sylow
812C23×C3—21no—
813C23×C3—21no—
814C23×C3—21no—
815C23×C3—21no—
816C23×C3—21no—
817C23×C3—21no—
818C23×C3—41no—
819C23×C3—41no—
820C23×C3—91no—
821C23×C3—91no—
822C23×C3—91no—
823C23×C3—91no—
824C23×C3—182no—
825C23×C3—182no—
826C23×C3—361no—
827C23×C3C2×D3211yescharacteristic
828C23×C3C2×D3211yescharacteristic
829C23×C3C2×D3211yescharacteristic
830C23×C3C2×D3211yescharacteristic
831C23×C3C2×D3211yescharacteristic
832C23×C3C2×D3211yescharacteristic
833C22×D3—31no—
834C22×D3—31no—
835C22×D3—31no—
836C22×D3—31no—
837C22×D3—31no—
838C22×D3—31no—
839C22×D3—31no—
840C22×D3—31no—
841C22×D3—61no—
842C22×D3—61no—
843C22×D3—61no—
844C22×D3—61no—
845C22×D3—62no—
846C22×D3—62no—
847C22×D3—62no—
848C22×D3—62no—
849C22×D3—122no—
850C22×D3—122no—
851C22×D3—121no—
852C22×D3—121no—
853C22×D3—122no—
854C22×D3—182no—
855C22×D3—182no—
856C22×D3—182no—
857C22×D3—182no—
858C22×D3—182no—
859C22×D3—182no—
860C22×D3—361no—
861C22×D3—361no—
862C22×D3—361no—
863C3×Q8—182no—
864C3×D4—24no—
865C3×D4—22no—
866C3×D4—22no—
867C3×D4—22no—
868C3×D4—42no—
869C3×D4—42no—
870C3×D4—44no—
871C3×D4—94no—
872C3×D4—182no—
873C3×D4—182no—
874C3×D4—182no—
875C3×D4—361no—
876C3×D4—361no—
877C2×C3×C4—21no—
878C2×C3×C4—21no—
879C2×C3×C4—21no—
880C2×C3×C4—41no—
881C2×C3×C4—91no—
882C2×C3×C4—91no—
883C2×C3×C4—91no—
884C2×C3×C4—91no—
885C2×C3×C4—91no—
886C2×C3×C4—91no—
887C2×C3×C4—91no—
888C2×C3×C4—91no—
889C2×C3×C4—182no—
890C2×C3×C4—182no—
891C2×C3×C4—182no—
892C2×C3×C4—361no—
893C2×C3×C4C2×D3211yescharacteristic
894C2×C3×C4C2×D3211yescharacteristic
895C2×C3×C4C2×D3211yescharacteristic
896#67—34no—
897#67—34no—
898#67—64no—
899#67—62no—
900#67—62no—
901#67—62no—
902#67—62no—
903#67—64no—
904#67—62no—
905#67—62no—
906#67—122no—
907#67—122no—
908#67—121no—
909#67—121no—
910#67—121no—
911#67—121no—
912#67—122no—
913#67—122no—
914#67—182no—
915#67—182no—
916#67—182no—
917#67—182no—
918C2×Dic3—31no—
919C2×Dic3—31no—
920C2×Dic3—31no—
921C2×Dic3—31no—
922C2×Dic3—31no—
923C2×Dic3—31no—
924C2×Dic3—31no—
925C2×Dic3—31no—
926C2×Dic3—31no—
927C2×Dic3—31no—
928C2×Dic3—31no—
929C2×Dic3—31no—
930C2×Dic3—31no—
931C2×Dic3—31no—
932C2×Dic3—31no—
933C2×Dic3—31no—
934C2×Dic3—61no—
935C2×Dic3—61no—
936C2×Dic3—61no—
937C2×Dic3—61no—
938C2×Dic3—61no—
939C2×Dic3—61no—
940C2×Dic3—61no—
941C2×Dic3—61no—
942C2×Dic3—62no—
943C2×Dic3—62no—
944C2×Dic3—64no—
945C2×Dic3—64no—
946C2×Dic3—62no—
947C2×Dic3—62no—
948C2×Dic3—121no—
949C2×Dic3—121no—
950C2×Dic3—122no—
951C2×Dic3—182no—
952C2×Dic3—361no—
953D12—182no—
954D12—182no—
955C4×D3—62no—
956C4×D3—62no—
957C4×D3—64no—
958C4×D3—182no—
959C4×D3—182no—
960C4×D3—361no—
961C4×D3—361no—
962Dic6—62no—
963Dic6—62no—
964Dic6—64no—
965C2×C32—22no—
966C2×C32—22no—
967C2×C32—22no—
968C2×C32—21no—
969C2×C32—21no—
970C2×C32—21no—
971C2×C32—21no—
972C2×C32—21no—
973C2×C32—21no—
974C2×C32—21no—
975C2×C32—21no—
976C2×C32—21no—
977C2×C32—41no—
978C2×C32—41no—
979C2×C32—41no—
980C2×C32—42no—
981C2×C32—42no—
982C2×C32—42no—
983C2×C32—41no—
984C2×C32—42no—
985C2×C32—41no—
986C2×C32—41no—
987C2×C32—82no—
988C2×C32—81no—
989C2×C32—81no—
990C2×C32—82no—
991C2×C32C2×D3×D411yescharacteristic
992C2×C32C2×D3×D411yescharacteristic
993C2×C32C2×#23711yescharacteristic
994C2×C32#100411yescharacteristic
995C2×C32#100411yescharacteristic
996C2×C32D3×#4111yescharacteristic
997C2×C32D3×#4111yescharacteristic
998C2×C32#100911yescharacteristic
999C2×C32C22×#6711yescharacteristic
1000C3⋊D3—22no—
1001C3⋊D3—22no—
1002C3⋊D3—41no—
1003C3⋊D3—41no—
1004C3×D3—62no—
1005C3×D3—62no—
1006C3×D3—62no—
1007C3×D3—62no—
1008C3×D3—122no—
1009C3×D3—122no—
1010C3×D3—122no—
1011C3×D3—121no—
1012C3×D3—121no—
1013C3×D3—121no—
1014C3×D3—121no—
1015C3×D3—241no—
1016C24—91no—
1017C24—271no—
1018#41—184no—
1019C2×Q8—91no—
1020C2×D4—91no—
1021C2×D4—91no—
1022C2×D4—91no—
1023C2×D4—91no—
1024C2×D4—91no—
1025C2×D4—91no—
1026C2×D4—271no—
1027C2×D4—271no—
1028C2×D4—544no—
1029C2×D4#111311yescharacteristic, complemented
1030C22×C4—91no—
1031C22×C4—91no—
1032C22×C4—91no—
1033C22×C4—91no—
1034C22×C4—271no—
1035C22×C4—271no—
1036C4⋊C4—91no—
1037C4⋊C4—271no—
1038C4⋊C4—271no—
1039C4⋊C4—271no—
1040C22⋊C4—91no—
1041C22⋊C4—91no—
1042C22⋊C4—91no—
1043C22⋊C4—91no—
1044C22⋊C4—91no—
1045C22⋊C4—271no—
1046C22⋊C4—271no—
1047C22⋊C4—271no—
1048C22⋊C4—271no—
1049C22⋊C4—271no—
1050C22⋊C4—271no—
1051C22⋊C4—271no—
1052C42—271no—
1053C22×C3—21no—
1054C22×C3—21no—
1055C22×C3—21no—
1056C22×C3—21no—
1057C22×C3—21no—
1058C22×C3—21no—
1059C22×C3—22no—
1060C22×C3—21no—
1061C22×C3—21no—
1062C22×C3—21no—
1063C22×C3—21no—
1064C22×C3—21no—
1065C22×C3—21no—
1066C22×C3—21no—
1067C22×C3—21no—
1068C22×C3—21no—
1069C22×C3—21no—
1070C22×C3—21no—
1071C22×C3—21no—
1072C22×C3—22no—
1073C22×C3—22no—
1074C22×C3—22no—
1075C22×C3—41no—
1076C22×C3—41no—
1077C22×C3—41no—
1078C22×C3—41no—
1079C22×C3—41no—
1080C22×C3—41no—
1081C22×C3—41no—
1082C22×C3—41no—
1083C22×C3—41no—
1084C22×C3—41no—
1085C22×C3—41no—
1086C22×C3—41no—
1087C22×C3—41no—
1088C22×C3—41no—
1089C22×C3—42no—
1090C22×C3—41no—
1091C22×C3—42no—
1092C22×C3—81no—
1093C22×C3—81no—
1094C22×C3—81no—
1095C22×C3—81no—
1096C22×C3—92no—
1097C22×C3—92no—
1098C22×C3—181no—
1099C22×C3—181no—
1100C22×C3—181no—
1101C22×C3—181no—
1102C22×C3—181no—
1103C22×C3—181no—
1104C22×C3—181no—
1105C22×C3—181no—
1106C22×C3—181no—
1107C22×C3—181no—
1108C22×C3—364no—
1109C22×C3D3×#6712yes—
1110C22×C3D3×#6712yes—
1111C22×C3#381112yes—
1112C22×C3C22×D3211yescharacteristic
1113C22×C3C22×D3211yescharacteristic
1114C22×C3C22×D3211yescharacteristic
1115C2×D3—32no—
1116C2×D3—32no—
1117C2×D3—32no—
1118C2×D3—32no—
1119C2×D3—62no—
1120C2×D3—62no—
1121C2×D3—61no—
1122C2×D3—61no—
1123C2×D3—61no—
1124C2×D3—61no—
1125C2×D3—61no—
1126C2×D3—61no—
1127C2×D3—61no—
1128C2×D3—61no—
1129C2×D3—62no—
1130C2×D3—61no—
1131C2×D3—61no—
1132C2×D3—61no—
1133C2×D3—61no—
1134C2×D3—61no—
1135C2×D3—61no—
1136C2×D3—61no—
1137C2×D3—61no—
1138C2×D3—61no—
1139C2×D3—61no—
1140C2×D3—61no—
1141C2×D3—61no—
1142C2×D3—121no—
1143C2×D3—121no—
1144C2×D3—121no—
1145C2×D3—121no—
1146C2×D3—121no—
1147C2×D3—121no—
1148C2×D3—121no—
1149C2×D3—121no—
1150C2×D3—121no—
1151C2×D3—124no—
1152C2×D3—124no—
1153C2×D3—128no—
1154C2×D3—364no—
1155C2×D3—364no—
1156C2×D3—364no—
1157C3×C4—22no—
1158C3×C4—21no—
1159C3×C4—21no—
1160C3×C4—21no—
1161C3×C4—41no—
1162C3×C4—41no—
1163C3×C4—42no—
1164C3×C4—92no—
1165C3×C4—181no—
1166C3×C4—181no—
1167C3×C4—181no—
1168C3×C4—181no—
1169C3×C4—181no—
1170C3×C4—181no—
1171C3×C4—181no—
1172Dic3—32no—
1173Dic3—32no—
1174Dic3—62no—
1175Dic3—62no—
1176Dic3—62no—
1177Dic3—62no—
1178Dic3—61no—
1179Dic3—61no—
1180Dic3—61no—
1181Dic3—61no—
1182Dic3—61no—
1183Dic3—61no—
1184Dic3—61no—
1185Dic3—61no—
1186Dic3—61no—
1187Dic3—61no—
1188Dic3—61no—
1189Dic3—61no—
1190Dic3—61no—
1191Dic3—61no—
1192Dic3—121no—
1193Dic3—121no—
1194Dic3—121no—
1195Dic3—121no—
1196C32—21no—
1197C32—21no—
1198C32—21no—
1199C32—41no—
1200C32#559111yescharacteristic, complemented
1201C32#561011yescharacteristic, complemented
1202C32#582911yescharacteristic, complemented
1203C23—91no—
1204C23—91no—
1205C23—91no—
1206C23—91no—
1207C23—182no—
1208C23—182no—
1209C23—361no—
1210C23—542no—
1211C23—542no—
1212C23—1081no—
1213C23C2×#111311yescharacteristic
1214C23C2×#111311yescharacteristic
1215Q8—182no—
1216D4—22no—
1217D4—94no—
1218D4—182no—
1219D4—182no—
1220D4—182no—
1221D4—361no—
1222D4—361no—
1223D4—542no—
1224D4—542no—
1225C2×C4—91no—
1226C2×C4—91no—
1227C2×C4—91no—
1228C2×C4—91no—
1229C2×C4—91no—
1230C2×C4—91no—
1231C2×C4—91no—
1232C2×C4—91no—
1233C2×C4—182no—
1234C2×C4—182no—
1235C2×C4—182no—
1236C2×C4—361no—
1237C2×C4—542no—
1238C2×C4—1081no—
1239C2×C4C2×#111311yescharacteristic
1240C2×C3—22no—
1241C2×C3—22no—
1242C2×C3—22no—
1243C2×C3—21no—
1244C2×C3—21no—
1245C2×C3—21no—
1246C2×C3—21no—
1247C2×C3—21no—
1248C2×C3—21no—
1249C2×C3—21no—
1250C2×C3—21no—
1251C2×C3—21no—
1252C2×C3—42no—
1253C2×C3—42no—
1254C2×C3—42no—
1255C2×C3—42no—
1256C2×C3—41no—
1257C2×C3—41no—
1258C2×C3—41no—
1259C2×C3—41no—
1260C2×C3—41no—
1261C2×C3—41no—
1262C2×C3—82no—
1263C2×C3—81no—
1264C2×C3—81no—
1265C2×C3—82no—
1266C2×C3—182no—
1267C2×C3—182no—
1268C2×C3—361no—
1269C2×C3—361no—
1270C2×C3D3×#23711yescharacteristic
1271C2×C3D3×#23711yescharacteristic
1272C2×C3#6431211yescharacteristic
1273C2×C3#6431311yescharacteristic
1274C2×C3#6431411yescharacteristic
1275C2×C3#6431411yescharacteristic
1276C2×C3C2×D3×#6711yescharacteristic
1277C2×C3C2×D3×#6711yescharacteristic
1278C2×C3C2×#381111yescharacteristic
1279D3—62no—
1280D3—62no—
1281D3—62no—
1282D3—62no—
1283D3—122no—
1284D3—122no—
1285D3—122no—
1286D3—121no—
1287D3—121no—
1288D3—121no—
1289D3—121no—
1290D3—241no—
1291C22—21no—
1292C22—21no—
1293C22—21no—
1294C22—21no—
1295C22—21no—
1296C22—92no—
1297C22—92no—
1298C22—181no—
1299C22—181no—
1300C22—181no—
1301C22—181no—
1302C22—181no—
1303C22—181no—
1304C22—181no—
1305C22—181no—
1306C22—181no—
1307C22—181no—
1308C22—364no—
1309C22—1084no—
1310C22#8904912yes—
1311C22C22×#111311yescharacteristic
1312C4—21no—
1313C4—92no—
1314C4—181no—
1315C4—181no—
1316C4—181no—
1317C4—181no—
1318C4—181no—
1319C4—181no—
1320C4—181no—
1321C3—21no—
1322C3—21no—
1323C3—21no—
1324C3—41no—
1325C3#1059530411yescharacteristic, complemented
1326C3#1059530511yescharacteristic, complemented
1327C3#1059530711yescharacteristic, complemented
1328C2—22no—
1329C2—41no—
1330C2—182no—
1331C2—182no—
1332C2—361no—
1333C2—361no—
1334C2#1172462211yescharacteristic
1335C2#1172462311yescharacteristic
1336C2C2×#8904911yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC2×C33×D4C22
hypercenterC2×D4#1113
hypocenterC33#546
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. C2×#89049C2semidirect
3. C3×#64148C2semidirect
4. C3×#64146C2semidirect
5. #11723729C2semidirect
6. #11723726C2semidirect
7. #11723726C2semidirect
8. #11723725C2semidirect
9. #11723720C2semidirect
10. C2×#88814C2semidirect
11. #11723717C2semidirect
12. #11723700C2semidirect
13. #11723694C2semidirect
14. #11723688C2semidirect
15. #11723670C2semidirect
21. C2×C33×D4C22semidirect
25. C2×C3×#638C22semidirect
26. C2×C3×#638C22semidirect
27. C2×C3×#638C22semidirect
28. C22×C3×C3⋊Dic3C22semidirect
29. C22×C3×C3⋊Dic3C22semidirect
30. C22×C3×C3⋊Dic3C22semidirect
32. C2×C3×C4×C3⋊D3C22semidirect
33. C2×C3×#634C22semidirect
38. C2×#6294C22semidirect
39. C3×#3757C22semidirect
40. C3×#3757C22semidirect
42. C3×#3752C22semidirect
43. C3×#3752C22semidirect
44. C3×#3750C22semidirect
45. #88815C22semidirect
46. #88815C22semidirect
47. #88815C22semidirect
50. #88814C22semidirect
51. #88814C22semidirect
52. #88814C22semidirect
53. #88814C22semidirect
54. #88814C22semidirect
55. #88813C22semidirect
56. C2×#3830D3semidirect
63. #64148D3semidirect
64. #64146D3semidirect
123. C3×#638D4semidirect
155. C2×C32×D4C2×D3semidirect
156. C2×C32×D4C2×D3semidirect
157. C2×C32×D4C2×D3semidirect
161. C2×#638C2×D3semidirect
162. C2×#638C2×D3semidirect
163. C2×#638C2×D3semidirect
164. C22×C3⋊Dic3C2×D3semidirect
165. C22×C3⋊Dic3C2×D3semidirect
166. C22×C3⋊Dic3C2×D3semidirect
168. C2×C4×C3⋊D3C2×D3semidirect
169. C2×#634C2×D3semidirect
221. #3757C2×D3semidirect
222. #3757C2×D3semidirect
224. #3752C2×D3semidirect
225. #3752C2×D3semidirect
226. #3750C2×D3semidirect
297. C2×C3×C3⋊D3#41semidirect
426. #638#67semidirect
538. C2×C3×D4D32semidirect
539. C2×C3×D4D32semidirect
540. C2×C3×D4D32semidirect
713. C2×C3⋊D3#237semidirect
811. C33#546semidirect
1029. C2×D4#1113semidirect
1200. C32#5591semidirect
1201. C32#5610semidirect
1202. C32#5829semidirect
1325. C3#10595304semidirect
1326. C3#10595305semidirect
1327. C3#10595307semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#38302
C2×#890492
C3×#641482
C3×#641462
#117237292
#117237262
#117237252
#117237202
C2×#888142
#117237172
#117237002
#117236942
#117236882
#117236702
#105953073
#105953053
#105953043