Finite Group Databasebeta

← #13172044

Subgroups — #13172044

Order 1728.

1884 conjugacy classes of subgroups.

The subgroup lattice has 1350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#638C211yesmaximal, characteristic, complemented
2C2×#89031C211yesmaximal, characteristic, complemented
3#11723717C211yesmaximal, characteristic, complemented
4#11723622C211yesmaximal, characteristic, complemented
5C3×#63977C211yesmaximal, characteristic, complemented
6C3×#63966C211yesmaximal, characteristic, complemented
7C2×C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
8#11723009C211yesmaximal, characteristic, complemented
9#11722996C211yesmaximal, characteristic, complemented
10#11722980C211yesmaximal, characteristic, complemented
11#11722967C211yesmaximal, characteristic, complemented
12#11722963C211yesmaximal, characteristic, complemented
13#11722950C211yesmaximal, characteristic, complemented
14#11722929C211yesmaximal, characteristic, complemented
15#11722906C211yesmaximal, characteristic, complemented
16#10595500—31nomaximal
17#10595077—31nomaximal
18#10594294—31nomaximal
19C23×C32×D3C2211yescharacteristic
20C22×D3×C3⋊D3C2211yescharacteristic
21C2×#6312C2211yescharacteristic
22C2×C3×#638C2211yescharacteristic
23C2×C3×#638C2211yescharacteristic, complemented
24C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
25C22×C32×Dic3C2211yescharacteristic, complemented
26C2×#6295C2211yescharacteristic, complemented
27D3×#638—24no—
28C2×#6293C2211yescharacteristic, complemented
29C2×#6292C2211yescharacteristic, complemented
30C2×#6291C2211yescharacteristic
31C2×#6290C2211yescharacteristic
32C2×#6289C2211yescharacteristic, complemented
33C2×#6289C2211yescharacteristic, complemented
34#89031—24no—
35C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
36C2×D3×C3⋊Dic3C2211yescharacteristic
37C2×C3×#626C2211yescharacteristic
38C2×C3×#626C2211yescharacteristic, complemented
39C32×#217C2211yescharacteristic, complemented
40#88815C2211yescharacteristic, complemented
41#88814C2211yescharacteristic, complemented
42#88814C2211yescharacteristic, complemented
43#88806C2211yescharacteristic, complemented
44#88804C2211yescharacteristic, complemented
45Dic3×C3⋊Dic3C2211yescharacteristic, complemented
46C3×Dic3⋊Dic3C2211yescharacteristic, complemented
47C3×Dic3⋊Dic3C2211yescharacteristic, complemented
48C3×#3722C2211yescharacteristic, complemented
49C3×#3722C2211yescharacteristic, complemented
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
54C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
55C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
56C22×#638—31no—
57C2×#3828—31no—
58C2×D3×#67—31no—
59C2×D3×#67—31no—
60C2×D3×#67—61no—
61C2×#3804—31no—
62C2×#3804—31no—
63C2×#3804—61no—
64#64090—31no—
65C3×#953—31no—
66C2×C3×#217—31no—
67C3×#929—31no—
68C2×C3×(C2×D3)⋊C4—31no—
69C3×#886—31no—
70C3×#882—31no—
71#63982—31no—
72#63981—31no—
73#63980—31no—
74#63978—31no—
75#63978—31no—
76#63977D311yescharacteristic, complemented
77#63975—31no—
78#63974—31no—
79#67⋊Dic3—31no—
80#63971—31no—
81#63966D311yescharacteristic, complemented
82C2×(C2×D3)⋊Dic3D311yescharacteristic, complemented
83#63958—31no—
84#63953—31no—
85#63952—31no—
86#63952—31no—
87#63952—61no—
88#63923—31no—
89#63922—31no—
90#63921—31no—
91#63921—31no—
92#63916—31no—
93#63915—31no—
94#63913—31no—
95#63912—31no—
96#63910—31no—
97#63899—31no—
98#63898—31no—
99#63896—31no—
100#63885—31no—
101#63881—31no—
102#63854—31no—
103#63853—31no—
104C23×C33C2311yescharacteristic
105C22×C3⋊(C3⋊D3)C2311yescharacteristic
106C22×C3×C3⋊D3C2311yescharacteristic
107C22×C3×C3⋊D3C2311yescharacteristic
108C22×C32×D3—22no—
109C22×C32×D3—22no—
110C22×C32×D3—41no—
111C22×C32×D3C2311yescharacteristic
112C22×C32×D3C2311yescharacteristic
113C2×D3×C3⋊D3—22no—
114C2×D3×C3⋊D3—22no—
115C2×D3×C3⋊D3—41no—
116#6312D414yescomplemented
117C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
118C3×#638—22no—
119C3×#638—22no—
120C2×C3×C3⋊Dic3—41no—
121C2×C3×C3⋊Dic3C2311yescharacteristic
122C2×C3×C3⋊Dic3C2311yescharacteristic
123C2×C3×C3⋊Dic3C2311yescharacteristic
124C2×C3×C3⋊Dic3C2311yescharacteristic
125C2×C32×Dic3—22no—
126C2×C32×Dic3C2311yescharacteristic
127C2×C32×Dic3C2311yescharacteristic
128C2×C32×Dic3C2311yescharacteristic
129C2×C32×Dic3C2311yescharacteristic
130#6295—41no—
131#6293—22no—
132#6292—22no—
133#6291—22no—
134#6290—22no—
135#6289—22no—
136#6289—41no—
137Dic3×C3⋊D3—22no—
138D3×C3⋊Dic3—22no—
139C3×#626—22no—
140C3×#626—41no—
141#5654—91no—
142#5591—91no—
143#5490—91no—
144C24×C32—31no—
145C23×C3⋊D3—31no—
146C23×C3×D3—21no—
147C23×C3×D3C2×D311yescharacteristic
148C23×C3×D3C2×D311yescharacteristic
149C22×D32—31no—
150C22×D32—31no—
151C22×D32—61no—
152C22×C32×C4—31no—
153C2×#638—31no—
154C2×#638—31no—
155C2×#638—31no—
156C2×#638—31no—
157C2×#638—31no—
158C2×#638—64no—
159C2×#638—61no—
160C2×#638—61no—
161C2×#638—61no—
162C2×#638—121no—
163C2×#638C2×D311yescharacteristic
164C2×#638C2×D311yescharacteristic, complemented
165C22×C3⋊Dic3—31no—
166C22×C3⋊Dic3C2×D311yescharacteristic, complemented
167#3828—64no—
168C2×C4⋊(C3⋊D3)—31no—
169C2×C4×C3⋊D3—31no—
170C2×C4×C3⋊D3—31no—
171C2×C4×C3⋊D3—31no—
172C2×#634—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—61no—
180C2×C3×#67—61no—
181C22×C3×Dic3—21no—
182C22×C3×Dic3—31no—
183C22×C3×Dic3—31no—
184C22×C3×Dic3—61no—
185C22×C3×Dic3C2×D311yescharacteristic, complemented
186C22×C3×Dic3C2×D311yescharacteristic, complemented
187C2×C3×D12—31no—
188C2×C3×D12—31no—
189D3×#67—64no—
190D3×#67—64no—
191D3×#67—68no—
192C2×#627—31no—
193C2×#627—31no—
194C2×#627—61no—
195C2×#626—31no—
196C2×#626—31no—
197C2×#626—31no—
198C2×#626—31no—
199C2×#626—31no—
200C2×#626—31no—
201C2×#626—61no—
202C2×#626—61no—
203C2×#626C2×D311yescharacteristic
204C2×#626C2×D311yescharacteristic, complemented
205C2×#625—31no—
206C2×#625—31no—
207C2×#625—31no—
208C2×#625—61no—
209C2×#624—31no—
210C2×#624—31no—
211C2×#624—31no—
212C2×#624—31no—
213C2×#624—61no—
214C2×#624—61no—
215#3804—64no—
216#3804—64no—
217#3804—68no—
218C2×D3×Dic3—31no—
219C2×D3×Dic3—31no—
220C2×D3×Dic3—31no—
221C2×D3×Dic3—31no—
222C2×D3×Dic3—61no—
223C2×D3×Dic3—61no—
224C32×C22⋊C4—31no—
225#3752—31no—
226#3750—31no—
227C4×C3⋊Dic3—31no—
228C3×#217—21no—
229C3×#217—31no—
230C3×#217—31no—
231C3×#217—31no—
232C3×#217—31no—
233C3×#217—31no—
234C3×#217—31no—
235C3×#217C2×D311yescharacteristic, complemented
236C3×#217C2×D311yescharacteristic, complemented
237C3×(C2×D3)⋊C4—31no—
238C3×(C2×D3)⋊C4—31no—
239C3×(C2×D3)⋊C4—31no—
240C3×(C2×D3)⋊C4—31no—
241C3×(C2×D3)⋊C4—31no—
242C3×(C2×D3)⋊C4—31no—
243C3×(C2×D3)⋊C4—31no—
244C3×(C2×D3)⋊C4—31no—
245C3×(C2×D3)⋊C4—31no—
246C3×(C2×D3)⋊C4—31no—
247C3×C4⋊Dic3—31no—
248C3×C4⋊Dic3—31no—
249C3×Dic3⋊C4—31no—
250C3×Dic3⋊C4—31no—
251#3724—31no—
252#3724—31no—
253#3724—31no—
254#3724—61no—
255Dic3⋊Dic3—31no—
256Dic3⋊Dic3—31no—
257Dic3⋊Dic3C2×D311yescharacteristic, complemented
258Dic3⋊Dic3C2×D311yescharacteristic, complemented
259#3722—31no—
260#3722—31no—
261#3722—31no—
262#3722—31no—
263#3722—61no—
264#3722C2×D311yescharacteristic, complemented
265#3722C2×D311yescharacteristic, complemented
266(C2×D3)⋊Dic3—31no—
267(C2×D3)⋊Dic3—31no—
268(C2×D3)⋊Dic3—31no—
269(C2×D3)⋊Dic3—31no—
270(C2×D3)⋊Dic3C2×D311yescharacteristic
271(C2×D3)⋊Dic3C2×D311yescharacteristic
272(C2×D3)⋊Dic3C2×D311yescharacteristic
273(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
274(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
275(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
276Dic32—31no—
277Dic32—31no—
278Dic32—61no—
279C22×C33—21no—
280C22×C33—21no—
281C22×C33C2×D412yes—
282C22×C33C2411yescharacteristic
283C2×C3⋊(C3⋊D3)—21no—
284C2×C3⋊(C3⋊D3)—21no—
285C2×C3⋊(C3⋊D3)C2×D412yes—
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×C32×D3—21no—
293C2×C32×D3—21no—
294C2×C32×D3—21no—
295C2×C32×D3—21no—
296C2×C32×D3—21no—
297C2×C32×D3—44no—
298C2×C32×D3#4112yescomplemented
299D3×C3⋊D3—44no—
300C3⋊(C3⋊Dic3)C2×D412yes—
301C3×C3⋊Dic3—21no—
302C3×C3⋊Dic3—21no—
303C3×C3⋊Dic3—21no—
304C3×C3⋊Dic3—21no—
305C32×Dic3—21no—
306C32×Dic3—21no—
307C32×Dic3—21no—
308C32×Dic3—21no—
309C22×#67—91no—
310C22×#67—91no—
311C22×#67—181no—
312C2×#237—91no—
313C2×D3×D4—91no—
314C2×#235—91no—
315C2×#235—91no—
316C2×#235—181no—
317C3×#123—91no—
318C3×#120—91no—
319C2×C3×C22⋊C4—91no—
320#953—31no—
321C2×#217—31no—
322#939—91no—
323#939—91no—
324#939—91no—
325#938—91no—
326#937—91no—
327D4×Dic3—91no—
328#930—91no—
329#929—31no—
330C4×#67—91no—
331C2×(C2×D3)⋊C4—31no—
332#896—91no—
333#895—91no—
334#894—91no—
335#893—91no—
336#886—31no—
337#885—91no—
338#885—91no—
339#885—91no—
340#884—91no—
341#884—91no—
342#884—91no—
343#883—91no—
344#883—91no—
345#882—31no—
346#882—91no—
347#882—91no—
348#67⋊C4—91no—
349#67⋊C4—91no—
350#67⋊C4—91no—
351#67⋊C4—181no—
352D3×C22⋊C4—91no—
353D3×C22⋊C4—91no—
354D3×C22⋊C4—91no—
355#878—91no—
356#878—91no—
357C23×C32—21no—
358C23×C32—21no—
359C23×C32—21no—
360C23×C32—31no—
361C23×C32—31no—
362C23×C32—41no—
363C23×C32—62no—
364C23×C32—62no—
365C23×C32—121no—
366C23×C32C22×D311yescharacteristic
367C23×C32C22×D311yescharacteristic
368C23×C32C22×D311yescharacteristic
369C22×C3⋊D3—31no—
370C22×C3⋊D3—31no—
371C22×C3⋊D3—31no—
372C22×C3⋊D3—61no—
373C22×C3⋊D3—61no—
374C22×C3⋊D3—61no—
375C22×C3⋊D3—62no—
376C22×C3⋊D3—62no—
377C22×C3⋊D3—121no—
378C22×C3⋊D3—121no—
379C22×C3⋊D3C22×D311yescharacteristic
380C22×C3⋊D3C22×D311yescharacteristic
381C22×C3×D3—24no—
382C22×C3×D3—22no—
383C22×C3×D3—22no—
384C22×C3×D3—22no—
385C22×C3×D3—22no—
386C22×C3×D3—21no—
387C22×C3×D3—21no—
388C22×C3×D3—31no—
389C22×C3×D3—31no—
390C22×C3×D3—31no—
391C22×C3×D3—31no—
392C22×C3×D3—42no—
393C22×C3×D3—41no—
394C22×C3×D3—41no—
395C22×C3×D3—42no—
396C22×C3×D3—61no—
397C22×C3×D3—61no—
398C22×C3×D3C22×D311yescharacteristic
399C22×C3×D3C22×D311yescharacteristic
400C22×C3×D3C22×D311yescharacteristic
401C22×C3×D3C22×D311yescharacteristic
402C2×D32—62no—
403C2×D32—62no—
404C2×D32—64no—
405C2×D32—62no—
406C2×D32—62no—
407C2×D32—122no—
408C2×D32—121no—
409C2×D32—121no—
410C2×D32—122no—
411C2×C32×C4—31no—
412C2×C32×C4—31no—
413C2×C32×C4—31no—
414C2×C32×C4—31no—
415C2×C32×C4—62no—
416#638—22no—
417#638—22no—
418#638—34no—
419#638—34no—
420#638—34no—
421#638—64no—
422#638—64no—
423#638—64no—
424#638—62no—
425#638—62no—
426#638—124no—
427C2×C3⋊Dic3—31no—
428C2×C3⋊Dic3—31no—
429C2×C3⋊Dic3—31no—
430C2×C3⋊Dic3—41no—
431C2×C3⋊Dic3—61no—
432C2×C3⋊Dic3—61no—
433C2×C3⋊Dic3—61no—
434C2×C3⋊Dic3—62no—
435C2×C3⋊Dic3—121no—
436C2×C3⋊Dic3C22×D311yescharacteristic
437C2×C3⋊Dic3C22×D311yescharacteristic
438C2×C3⋊Dic3C22×D311yescharacteristic
439C2×C3⋊Dic3C22×D311yescharacteristic
440C4⋊(C3⋊D3)—62no—
441C4×C3⋊D3—62no—
442C4×C3⋊D3—62no—
443C4×C3⋊D3—121no—
444#634—62no—
445C3×#67—62no—
446C3×#67—64no—
447C3×#67—64no—
448C3×#67—62no—
449C3×#67—62no—
450C3×#67—62no—
451C3×#67—62no—
452C3×#67—121no—
453C2×C3×Dic3—24no—
454C2×C3×Dic3—22no—
455C2×C3×Dic3—22no—
456C2×C3×Dic3—21no—
457C2×C3×Dic3—21no—
458C2×C3×Dic3—21no—
459C2×C3×Dic3—21no—
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—61no—
469C2×C3×Dic3—61no—
470C2×C3×Dic3—61no—
471C2×C3×Dic3—61no—
472C2×C3×Dic3—121no—
473C2×C3×Dic3—121no—
474C2×C3×Dic3—122no—
475C2×C3×Dic3C22×D311yescharacteristic
476C2×C3×Dic3C22×D311yescharacteristic
477C2×C3×Dic3C22×D311yescharacteristic
478C2×C3×Dic3C22×D311yescharacteristic
479C2×C3×Dic3C22×D311yescharacteristic
480C2×C3×Dic3C22×D311yescharacteristic
481C2×C3×Dic3C22×D311yescharacteristic
482C2×C3×Dic3C22×D311yescharacteristic
483C3×D12—62no—
484C3×D12—121no—
485#627—62no—
486#627—62no—
487#627—64no—
488#626—22no—
489#626—41no—
490#626—62no—
491#626—62no—
492#626—64no—
493#626—62no—
494#626—62no—
495#626—64no—
496#626—121no—
497#626—121no—
498#625—62no—
499#625—62no—
500#625—64no—
501#625—121no—
502#624—62no—
503#624—62no—
504#624—64no—
505#624—121no—
506#624—121no—
507#624—122no—
508D3×Dic3—62no—
509D3×Dic3—62no—
510D3×Dic3—64no—
511D3×Dic3—62no—
512D3×Dic3—62no—
513D3×Dic3—64no—
514#546—271noSylow
515C2×C33—22no—
516C2×C33C22×D411yescharacteristic
517C2×C33C2×#4111yescharacteristic
518C2×C33H(5,𝔽2)11yescharacteristic
519C3⋊(C3⋊D3)—22no—
520C3×C3⋊D3—41no—
521C3×C3⋊D3—41no—
522C32×D3—22no—
523C32×D3—41no—
524C24×C3—31no—
525C24×C3—31no—
526C24×C3—61no—
527C23×D3—91no—
528C23×D3—91no—
529C23×D3—91no—
530C23×D3—181no—
531C23×D3D3211yescharacteristic
532C2×C3×D4—91no—
533C2×C3×D4—91no—
534C2×C3×D4—91no—
535C2×C3×D4—91no—
536C22×C3×C4—31no—
537C22×C3×C4—31no—
538C22×C3×C4—61no—
539C22×C3×C4—91no—
540C2×#67—31no—
541C2×#67—31no—
542C2×#67—31no—
543C2×#67—31no—
544C2×#67—31no—
545C2×#67—31no—
546C2×#67—61no—
547C2×#67—61no—
548C2×#67—91no—
549C2×#67—91no—
550C2×#67—91no—
551C2×#67—91no—
552C2×#67—91no—
553C2×#67—91no—
554C2×#67—91no—
555C2×#67—91no—
556C2×#67—91no—
557C2×#67—91no—
558C2×#67—91no—
559C2×#67—181no—
560C2×#67—181no—
561C2×#67—181no—
562C2×#67—181no—
563C2×#67—181no—
564C2×#67—184no—
565C2×#67—184no—
566C2×#67—188no—
567C2×#67—361no—
568C22×Dic3—31no—
569C22×Dic3—31no—
570C22×Dic3—61no—
571C22×Dic3—91no—
572C22×Dic3—91no—
573C22×Dic3—91no—
574C22×Dic3—181no—
575C22×Dic3D3211yescharacteristic, complemented
576#237—184no—
577D3×D4—184no—
578#235—184no—
579#235—184no—
580#235—188no—
581C2×D12—31no—
582C2×D12—31no—
583C2×D12—91no—
584C2×D12—91no—
585C2×D12—91no—
586C2×D12—91no—
587C2×D12—181no—
588C2×C4×D3—91no—
589C2×C4×D3—91no—
590C2×C4×D3—91no—
591C2×C4×D3—91no—
592C2×C4×D3—91no—
593C2×C4×D3—91no—
594C2×C4×D3—91no—
595C2×C4×D3—91no—
596C2×C4×D3—91no—
597C2×C4×D3—181no—
598C2×C4×D3—181no—
599C2×C4×D3—181no—
600C2×Dic6—91no—
601C2×Dic6—91no—
602C2×Dic6—91no—
603C2×Dic6—181no—
604C3×C4⋊C4—91no—
605C3×C4⋊C4—91no—
606C3×C22⋊C4—31no—
607C3×C22⋊C4—31no—
608C3×C22⋊C4—61no—
609C3×C22⋊C4—91no—
610C3×C22⋊C4—91no—
611C3×C22⋊C4—91no—
612C3×C22⋊C4—91no—
613C3×C22⋊C4—91no—
614C3×C22⋊C4—91no—
615C3×C22⋊C4—91no—
616C3×C22⋊C4—91no—
617#217—31no—
618#217—31no—
619#217—31no—
620#217—31no—
621#217—31no—
622#217—31no—
623#217—91no—
624#217—91no—
625#217D3211yescharacteristic, complemented
626(C2×D3)⋊C4—31no—
627(C2×D3)⋊C4—31no—
628(C2×D3)⋊C4—31no—
629(C2×D3)⋊C4—31no—
630(C2×D3)⋊C4—31no—
631(C2×D3)⋊C4—31no—
632(C2×D3)⋊C4—31no—
633(C2×D3)⋊C4—31no—
634(C2×D3)⋊C4—31no—
635(C2×D3)⋊C4—31no—
636(C2×D3)⋊C4—91no—
637(C2×D3)⋊C4—91no—
638(C2×D3)⋊C4—91no—
639(C2×D3)⋊C4—91no—
640(C2×D3)⋊C4—91no—
641(C2×D3)⋊C4—91no—
642(C2×D3)⋊C4—91no—
643(C2×D3)⋊C4—181no—
644C4⋊Dic3—31no—
645C4⋊Dic3—31no—
646C4⋊Dic3—91no—
647Dic3⋊C4—31no—
648Dic3⋊C4—31no—
649Dic3⋊C4—91no—
650Dic3⋊C4—91no—
651Dic3⋊C4—91no—
652Dic3⋊C4—91no—
653Dic3⋊C4—91no—
654Dic3⋊C4—181no—
655C4×Dic3—91no—
656C4×Dic3—91no—
657C4×Dic3—91no—
658C4×Dic3—181no—
659C22×C32—21no—
660C22×C32—21no—
661C22×C32—21no—
662C22×C32—21no—
663C22×C32—21no—
664C22×C32—21no—
665C22×C32—21no—
666C22×C32—21no—
667C22×C32—21no—
668C22×C32—22no—
669C22×C32—22no—
670C22×C32—22no—
671C22×C32—32no—
672C22×C32—41no—
673C22×C32—42no—
674C22×C32—41no—
675C22×C32—41no—
676C22×C32—41no—
677C22×C32—41no—
678C22×C32—41no—
679C22×C32—41no—
680C22×C32—61no—
681C22×C32—61no—
682C22×C32—61no—
683C22×C32—61no—
684C22×C32—61no—
685C22×C32—81no—
686C22×C32—81no—
687C22×C32—124no—
688C22×C32D3×D412yes—
689C22×C32D3×D412yes—
690C22×C32D3×D412yes—
691C22×C32C23×D311yescharacteristic
692C22×C32C23×D311yescharacteristic
693C22×C32C23×D311yescharacteristic
694C2×C3⋊D3—21no—
695C2×C3⋊D3—21no—
696C2×C3⋊D3—21no—
697C2×C3⋊D3—21no—
698C2×C3⋊D3—21no—
699C2×C3⋊D3—21no—
700C2×C3⋊D3—32no—
701C2×C3⋊D3—32no—
702C2×C3⋊D3—32no—
703C2×C3⋊D3—62no—
704C2×C3⋊D3—62no—
705C2×C3⋊D3—62no—
706C2×C3⋊D3—61no—
707C2×C3⋊D3—61no—
708C2×C3⋊D3—61no—
709C2×C3⋊D3—61no—
710C2×C3⋊D3—61no—
711C2×C3⋊D3—61no—
712C2×C3⋊D3—122no—
713C2×C3⋊D3—121no—
714C2×C3⋊D3—121no—
715C2×C3⋊D3—121no—
716C2×C3⋊D3—121no—
717C2×C3⋊D3—121no—
718C2×C3⋊D3—121no—
719C2×C3⋊D3—124no—
720C2×C3⋊D3—241no—
721C2×C3⋊D3—241no—
722C2×C3×D3—22no—
723C2×C3×D3—22no—
724C2×C3×D3—21no—
725C2×C3×D3—21no—
726C2×C3×D3—21no—
727C2×C3×D3—21no—
728C2×C3×D3—22no—
729C2×C3×D3—21no—
730C2×C3×D3—21no—
731C2×C3×D3—21no—
732C2×C3×D3—21no—
733C2×C3×D3—21no—
734C2×C3×D3—21no—
735C2×C3×D3—22no—
736C2×C3×D3—41no—
737C2×C3×D3—41no—
738C2×C3×D3—44no—
739C2×C3×D3—44no—
740C2×C3×D3—48no—
741C2×C3×D3—62no—
742C2×C3×D3—62no—
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—121no—
756C2×C3×D3—121no—
757C2×C3×D3—121no—
758C2×C3×D3—121no—
759C2×C3×D3#23512yescomplemented
760C2×C3×D3#23712yescomplemented
761D32—124no—
762D32—124no—
763D32—128no—
764C32×C4—61no—
765C32×C4—61no—
766C32×C4—61no—
767C32×C4—61no—
768C3⋊Dic3—21no—
769C3⋊Dic3—21no—
770C3⋊Dic3—21no—
771C3⋊Dic3—21no—
772C3⋊Dic3—32no—
773C3⋊Dic3—32no—
774C3⋊Dic3—32no—
775C3⋊Dic3—62no—
776C3⋊Dic3—62no—
777C3⋊Dic3—62no—
778C3⋊Dic3—122no—
779C3×Dic3—22no—
780C3×Dic3—22no—
781C3×Dic3—21no—
782C3×Dic3—21no—
783C3×Dic3—21no—
784C3×Dic3—21no—
785C3×Dic3—21no—
786C3×Dic3—21no—
787C3×Dic3—21no—
788C3×Dic3—21no—
789C3×Dic3—41no—
790C3×Dic3—41no—
791C3×Dic3—62no—
792C3×Dic3—62no—
793C3×Dic3—62no—
794C3×Dic3—61no—
795C3×Dic3—61no—
796C3×Dic3—61no—
797C3×Dic3—61no—
798C3×Dic3—61no—
799C3×Dic3—61no—
800C3×Dic3—61no—
801C3×Dic3—61no—
802C3×Dic3—121no—
803C2×#41—271no—
804C22×D4—271no—
805#124—271no—
806#123—91no—
807#123—271no—
808C22⋊Q8—271no—
809#121—271no—
810#121—271no—
811#121—271no—
812#120—91no—
813#120—271no—
814C4×D4—271no—
815C4×D4—271no—
816C2×C22⋊C4—91no—
817C2×C22⋊C4—271no—
818C33#54611yescharacteristic, complemented, Sylow
819C23×C3—21no—
820C23×C3—21no—
821C23×C3—21no—
822C23×C3—31no—
823C23×C3—31no—
824C23×C3—31no—
825C23×C3—31no—
826C23×C3—41no—
827C23×C3—61no—
828C23×C3—61no—
829C23×C3—62no—
830C23×C3—62no—
831C23×C3—64no—
832C23×C3—62no—
833C23×C3—62no—
834C23×C3—91no—
835C23×C3—91no—
836C23×C3—122no—
837C23×C3—121no—
838C23×C3—121no—
839C23×C3—122no—
840C23×C3C2×D3211yescharacteristic
841C23×C3C2×D3211yescharacteristic
842C23×C3C2×D3211yescharacteristic
843C22×D3—22no—
844C22×D3—22no—
845C22×D3—31no—
846C22×D3—31no—
847C22×D3—31no—
848C22×D3—31no—
849C22×D3—41no—
850C22×D3—61no—
851C22×D3—61no—
852C22×D3—91no—
853C22×D3—91no—
854C22×D3—91no—
855C22×D3—181no—
856C22×D3—181no—
857C22×D3—181no—
858C22×D3—182no—
859C22×D3—182no—
860C22×D3—182no—
861C22×D3—182no—
862C22×D3—182no—
863C22×D3—184no—
864C22×D3—182no—
865C22×D3—361no—
866C22×D3—362no—
867C22×D3—361no—
868C22×D3—361no—
869C22×D3—361no—
870C22×D3—362no—
871C22×D3C2×D3211yescharacteristic
872C22×D3C2×D3211yescharacteristic
873C3×D4—182no—
874C3×D4—182no—
875C3×D4—182no—
876C3×D4—361no—
877C2×C3×C4—31no—
878C2×C3×C4—31no—
879C2×C3×C4—31no—
880C2×C3×C4—31no—
881C2×C3×C4—31no—
882C2×C3×C4—31no—
883C2×C3×C4—31no—
884C2×C3×C4—31no—
885C2×C3×C4—61no—
886C2×C3×C4—61no—
887C2×C3×C4—61no—
888C2×C3×C4—61no—
889C2×C3×C4—64no—
890C2×C3×C4—62no—
891C2×C3×C4—62no—
892C2×C3×C4—91no—
893C2×C3×C4—91no—
894C2×C3×C4—91no—
895C2×C3×C4—91no—
896C2×C3×C4—361no—
897#67—62no—
898#67—64no—
899#67—64no—
900#67—62no—
901#67—62no—
902#67—62no—
903#67—62no—
904#67—94no—
905#67—94no—
906#67—94no—
907#67—121no—
908#67—184no—
909#67—184no—
910#67—184no—
911#67—182no—
912#67—182no—
913#67—182no—
914#67—184no—
915#67—182no—
916#67—182no—
917#67—182no—
918#67—184no—
919#67—364no—
920#67—361no—
921#67—361no—
922C2×Dic3—22no—
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—61no—
932C2×Dic3—61no—
933C2×Dic3—61no—
934C2×Dic3—61no—
935C2×Dic3—91no—
936C2×Dic3—91no—
937C2×Dic3—91no—
938C2×Dic3—121no—
939C2×Dic3—121no—
940C2×Dic3—122no—
941C2×Dic3—181no—
942C2×Dic3—181no—
943C2×Dic3—181no—
944C2×Dic3—182no—
945C2×Dic3—182no—
946C2×Dic3—182no—
947C2×Dic3—184no—
948C2×Dic3—361no—
949C2×Dic3C2×D3211yescharacteristic
950C2×Dic3C2×D3211yescharacteristic
951C2×Dic3C2×D3211yescharacteristic
952C2×Dic3C2×D3211yescharacteristic
953D12—62no—
954D12—121no—
955D12—182no—
956D12—182no—
957D12—184no—
958D12—182no—
959D12—361no—
960C4×D3—182no—
961C4×D3—182no—
962C4×D3—182no—
963C4×D3—184no—
964C4×D3—182no—
965C4×D3—182no—
966C4×D3—182no—
967C4×D3—184no—
968C4×D3—361no—
969C4×D3—361no—
970C4×D3—361no—
971C4×D3—362no—
972Dic6—182no—
973Dic6—182no—
974Dic6—182no—
975Dic6—184no—
976C2×C32—22no—
977C2×C32—22no—
978C2×C32—22no—
979C2×C32—21no—
980C2×C32—21no—
981C2×C32—21no—
982C2×C32—21no—
983C2×C32—21no—
984C2×C32—21no—
985C2×C32—21no—
986C2×C32—21no—
987C2×C32—21no—
988C2×C32—41no—
989C2×C32—41no—
990C2×C32—41no—
991C2×C32—42no—
992C2×C32—42no—
993C2×C32—42no—
994C2×C32—62no—
995C2×C32—82no—
996C2×C32—121no—
997C2×C32C2×#23511yescharacteristic
998C2×C32C2×D3×D411yescharacteristic
999C2×C32C2×D3×D411yescharacteristic
1000C2×C32C2×D3×D411yescharacteristic
1001C2×C32C2×#23711yescharacteristic
1002C2×C32#100411yescharacteristic
1003C2×C32#100411yescharacteristic
1004C2×C32D3×#4111yescharacteristic
1005C2×C32#100911yescharacteristic
1006C3⋊D3—41no—
1007C3⋊D3—41no—
1008C3⋊D3—62no—
1009C3⋊D3—62no—
1010C3⋊D3—62no—
1011C3⋊D3—122no—
1012C3⋊D3—122no—
1013C3⋊D3—122no—
1014C3⋊D3—242no—
1015C3×D3—24no—
1016C3×D3—22no—
1017C3×D3—22no—
1018C3×D3—42no—
1019C3×D3—41no—
1020C3×D3—41no—
1021C3×D3—122no—
1022C3×D3—122no—
1023C3×D3—121no—
1024C3×D3—121no—
1025C3×D3—121no—
1026C3×D3—121no—
1027C24—31no—
1028C24—271no—
1029#41—544no—
1030C2×Q8—271no—
1031C2×D4—91no—
1032C2×D4—91no—
1033C2×D4—91no—
1034C2×D4—91no—
1035C2×D4—271no—
1036C2×D4—271no—
1037C2×D4—271no—
1038C2×D4—271no—
1039C2×D4—271no—
1040C2×D4—544no—
1041C22×C4—31no—
1042C22×C4—91no—
1043C22×C4—271no—
1044C22×C4—271no—
1045C22×C4—271no—
1046C22×C4—271no—
1047C4⋊C4—91no—
1048C4⋊C4—91no—
1049C4⋊C4—271no—
1050C4⋊C4—271no—
1051C22⋊C4—31no—
1052C22⋊C4—91no—
1053C22⋊C4—91no—
1054C22⋊C4—91no—
1055C22⋊C4—91no—
1056C22⋊C4—91no—
1057C22⋊C4—91no—
1058C22⋊C4—91no—
1059C22⋊C4—91no—
1060C22⋊C4—271no—
1061C22⋊C4—271no—
1062C22⋊C4—271no—
1063C42—271no—
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—21no—
1073C22×C3—22no—
1074C22×C3—22no—
1075C22×C3—22no—
1076C22×C3—32no—
1077C22×C3—32no—
1078C22×C3—41no—
1079C22×C3—41no—
1080C22×C3—41no—
1081C22×C3—41no—
1082C22×C3—41no—
1083C22×C3—41no—
1084C22×C3—41no—
1085C22×C3—42no—
1086C22×C3—62no—
1087C22×C3—62no—
1088C22×C3—62no—
1089C22×C3—62no—
1090C22×C3—61no—
1091C22×C3—61no—
1092C22×C3—61no—
1093C22×C3—61no—
1094C22×C3—61no—
1095C22×C3—61no—
1096C22×C3—61no—
1097C22×C3—61no—
1098C22×C3—61no—
1099C22×C3—61no—
1100C22×C3—81no—
1101C22×C3—81no—
1102C22×C3—121no—
1103C22×C3—121no—
1104C22×C3—124no—
1105C22×C3—124no—
1106C22×C3—128no—
1107C22×C3—181no—
1108C22×C3—181no—
1109C22×C3—181no—
1110C22×C3—181no—
1111C22×C3—181no—
1112C22×C3—181no—
1113C22×C3#380212yes—
1114C22×C3#381112yes—
1115C22×C3#381112yes—
1116C22×C3C22×D3211yescharacteristic
1117C22×C3C22×D3211yescharacteristic
1118C22×C3C22×D3211yescharacteristic
1119C2×D3—21no—
1120C2×D3—21no—
1121C2×D3—21no—
1122C2×D3—21no—
1123C2×D3—21no—
1124C2×D3—44no—
1125C2×D3—62no—
1126C2×D3—62no—
1127C2×D3—61no—
1128C2×D3—61no—
1129C2×D3—61no—
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—92no—
1140C2×D3—92no—
1141C2×D3—92no—
1142C2×D3—121no—
1143C2×D3—121no—
1144C2×D3—121no—
1145C2×D3—121no—
1146C2×D3—182no—
1147C2×D3—182no—
1148C2×D3—182no—
1149C2×D3—181no—
1150C2×D3—181no—
1151C2×D3—181no—
1152C2×D3—181no—
1153C2×D3—181no—
1154C2×D3—181no—
1155C2×D3—362no—
1156C2×D3—361no—
1157C2×D3—361no—
1158C2×D3—361no—
1159C2×D3—361no—
1160C2×D3—361no—
1161C2×D3—361no—
1162C2×D3—364no—
1163C2×D3—364no—
1164C2×D3—364no—
1165C2×D3—368no—
1166C2×D3—721no—
1167C2×D3—721no—
1168C2×D3#380412yescomplemented
1169C3×C4—62no—
1170C3×C4—62no—
1171C3×C4—61no—
1172C3×C4—61no—
1173C3×C4—61no—
1174C3×C4—61no—
1175C3×C4—61no—
1176C3×C4—61no—
1177C3×C4—61no—
1178C3×C4—61no—
1179C3×C4—121no—
1180C3×C4—121no—
1181C3×C4—181no—
1182C3×C4—181no—
1183C3×C4—181no—
1184C3×C4—181no—
1185Dic3—21no—
1186Dic3—21no—
1187Dic3—21no—
1188Dic3—21no—
1189Dic3—62no—
1190Dic3—62no—
1191Dic3—62no—
1192Dic3—61no—
1193Dic3—61no—
1194Dic3—61no—
1195Dic3—61no—
1196Dic3—61no—
1197Dic3—61no—
1198Dic3—61no—
1199Dic3—61no—
1200Dic3—92no—
1201Dic3—92no—
1202Dic3—92no—
1203Dic3—121no—
1204Dic3—182no—
1205Dic3—182no—
1206Dic3—182no—
1207Dic3—362no—
1208C32—21no—
1209C32—21no—
1210C32—21no—
1211C32—41no—
1212C32#549011yescharacteristic, complemented
1213C32#559111yescharacteristic, complemented
1214C32#565411yescharacteristic, complemented
1215C23—31no—
1216C23—31no—
1217C23—62no—
1218C23—62no—
1219C23—91no—
1220C23—91no—
1221C23—121no—
1222C23—271no—
1223C23—542no—
1224C23—542no—
1225C23—1081no—
1226C23D3311yescharacteristic
1227Q8—542no—
1228D4—182no—
1229D4—182no—
1230D4—182no—
1231D4—274no—
1232D4—361no—
1233D4—542no—
1234D4—542no—
1235D4—542no—
1236D4—1081no—
1237C2×C4—31no—
1238C2×C4—31no—
1239C2×C4—31no—
1240C2×C4—31no—
1241C2×C4—62no—
1242C2×C4—91no—
1243C2×C4—91no—
1244C2×C4—91no—
1245C2×C4—91no—
1246C2×C4—271no—
1247C2×C4—361no—
1248C2×C4—542no—
1249C2×C4—542no—
1250C2×C4—542no—
1251C2×C4—1081no—
1252C2×C3—22no—
1253C2×C3—22no—
1254C2×C3—22no—
1255C2×C3—21no—
1256C2×C3—21no—
1257C2×C3—21no—
1258C2×C3—21no—
1259C2×C3—21no—
1260C2×C3—21no—
1261C2×C3—21no—
1262C2×C3—21no—
1263C2×C3—21no—
1264C2×C3—42no—
1265C2×C3—42no—
1266C2×C3—42no—
1267C2×C3—41no—
1268C2×C3—41no—
1269C2×C3—41no—
1270C2×C3—64no—
1271C2×C3—62no—
1272C2×C3—62no—
1273C2×C3—82no—
1274C2×C3—122no—
1275C2×C3—121no—
1276C2×C3—121no—
1277C2×C3—361no—
1278C2×C3—361no—
1279C2×C3C2×#380211yescharacteristic
1280C2×C3D3×#23511yescharacteristic
1281C2×C3#6430711yescharacteristic
1282C2×C3D3×#23711yescharacteristic
1283C2×C3#6431411yescharacteristic
1284C2×C3C2×#380411yescharacteristic
1285C2×C3C2×#381111yescharacteristic
1286C2×C3C2×#381111yescharacteristic
1287C2×C3#6433011yescharacteristic
1288D3—22no—
1289D3—41no—
1290D3—122no—
1291D3—122no—
1292D3—121no—
1293D3—121no—
1294D3—121no—
1295D3—121no—
1296D3—182no—
1297D3—182no—
1298D3—182no—
1299D3—362no—
1300D3—362no—
1301D3—362no—
1302D3—722no—
1303C22—21no—
1304C22—21no—
1305C22—32no—
1306C22—61no—
1307C22—61no—
1308C22—61no—
1309C22—61no—
1310C22—61no—
1311C22—124no—
1312C22—181no—
1313C22—181no—
1314C22—181no—
1315C22—181no—
1316C22—181no—
1317C22—181no—
1318C22—272no—
1319C22—541no—
1320C22—541no—
1321C22—1084no—
1322C22#8895412yes—
1323C22C2×D3311yescharacteristic
1324C4—61no—
1325C4—61no—
1326C4—61no—
1327C4—61no—
1328C4—181no—
1329C4—181no—
1330C4—181no—
1331C4—181no—
1332C4—272no—
1333C3—21no—
1334C3—21no—
1335C3—21no—
1336C3—41no—
1337C3#1059429411yescharacteristic, complemented
1338C3#1059507711yescharacteristic, complemented
1339C3#1059550011yescharacteristic, complemented
1340C2—22no—
1341C2—62no—
1342C2—121no—
1343C2—361no—
1344C2—361no—
1345C2—542no—
1346C2D3×#380411yescharacteristic
1347C2#1172441811yescharacteristic
1348C2C2×#8895411yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
hypercenterC23D33
hypocenterC33#546
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C2×D3×#638C2semidirect
2. C2×#89031C2semidirect
3. #11723717C2semidirect
4. #11723622C2semidirect
5. C3×#63977C2semidirect
6. C3×#63966C2semidirect
7. C2×C3×(C2×D3)⋊Dic3C2semidirect
8. #11723009C2semidirect
9. #11722996C2semidirect
10. #11722980C2semidirect
11. #11722967C2semidirect
12. #11722963C2semidirect
13. #11722950C2semidirect
14. #11722929C2semidirect
15. #11722906C2semidirect
23. C2×C3×#638C22semidirect
24. C22×C3×C3⋊Dic3C22semidirect
25. C22×C32×Dic3C22semidirect
26. C2×#6295C22semidirect
28. C2×#6293C22semidirect
29. C2×#6292C22semidirect
32. C2×#6289C22semidirect
33. C2×#6289C22semidirect
35. C2×Dic3×C3⋊D3C22semidirect
38. C2×C3×#626C22semidirect
39. C32×#217C22semidirect
40. #88815C22semidirect
41. #88814C22semidirect
42. #88814C22semidirect
43. #88806C22semidirect
44. #88804C22semidirect
45. Dic3×C3⋊Dic3C22semidirect
46. C3×Dic3⋊Dic3C22semidirect
47. C3×Dic3⋊Dic3C22semidirect
48. C3×#3722C22semidirect
49. C3×#3722C22semidirect
53. C3×(C2×D3)⋊Dic3C22semidirect
54. C3×(C2×D3)⋊Dic3C22semidirect
55. C3×(C2×D3)⋊Dic3C22semidirect
76. #63977D3semidirect
81. #63966D3semidirect
82. C2×(C2×D3)⋊Dic3D3semidirect
116. #6312D4semidirect
164. C2×#638C2×D3semidirect
166. C22×C3⋊Dic3C2×D3semidirect
185. C22×C3×Dic3C2×D3semidirect
186. C22×C3×Dic3C2×D3semidirect
204. C2×#626C2×D3semidirect
235. C3×#217C2×D3semidirect
236. C3×#217C2×D3semidirect
257. Dic3⋊Dic3C2×D3semidirect
258. Dic3⋊Dic3C2×D3semidirect
264. #3722C2×D3semidirect
265. #3722C2×D3semidirect
273. (C2×D3)⋊Dic3C2×D3semidirect
274. (C2×D3)⋊Dic3C2×D3semidirect
275. (C2×D3)⋊Dic3C2×D3semidirect
298. C2×C32×D3#41semidirect
575. C22×Dic3D32semidirect
625. #217D32semidirect
759. C2×C3×D3#235semidirect
760. C2×C3×D3#237semidirect
818. C33#546semidirect
1168. C2×D3#3804semidirect
1212. C32#5490semidirect
1213. C32#5591semidirect
1214. C32#5654semidirect
1337. C3#10594294semidirect
1338. C3#10595077semidirect
1339. C3#10595500semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#6382
C2×#890312
#117237172
#117236222
C3×#639772
C3×#639662
C2×C3×(C2×D3)⋊Dic32
#117230092
#117229962
#117229802
#117229672
#117229632
#117229502
#117229292
#117229062
#105955003
#105950773
#105942943