Finite Group Databasebeta

← #13172310

Subgroups — #13172310

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×C3⋊D3×#67C211yesmaximal, characteristic, complemented
2C2×#89031C211yesmaximal, characteristic, complemented
3#11723727C211yesmaximal, characteristic, complemented
4#11723618C211yesmaximal, characteristic, complemented
5C3×#63978C211yesmaximal, characteristic, complemented
6C2×C3×#3722C211yesmaximal, characteristic, complemented
7C3×#63961C211yesmaximal, characteristic, complemented
8#11723009C211yesmaximal, characteristic, complemented
9#11723000C211yesmaximal, characteristic, complemented
10#11722983C211yesmaximal, characteristic, complemented
11#11722968C211yesmaximal, characteristic, complemented
12#11722967C211yesmaximal, characteristic, complemented
13#11722950C211yesmaximal, characteristic, complemented
14#11722938C211yesmaximal, characteristic, complemented
15#11722906C211yesmaximal, characteristic, complemented
16#10595163—31nomaximal
17#10595083—31nomaximal
18#10595077—31nomaximal
19C23×C3×C3⋊D3C2211yescharacteristic
20C22×D3×C3⋊D3C2211yescharacteristic
21C2×#6312C2211yescharacteristic
22C2×C3×#638C2211yescharacteristic, complemented
23C2×C32×#67C2211yescharacteristic
24C22×C32×Dic3C2211yescharacteristic, complemented
25C22×C32×Dic3C2211yescharacteristic, complemented
26C2×#6295C2211yescharacteristic
27C2×#6295C2211yescharacteristic, complemented
28C3⋊D3×#67—24no—
29C2×#6293C2211yescharacteristic, complemented
30C2×#6292C2211yescharacteristic
31C2×#6292C2211yescharacteristic, complemented
32C2×#6290C2211yescharacteristic
33C2×#6289C2211yescharacteristic, complemented
34C2×#6289C2211yescharacteristic, complemented
35#89031—24no—
36C2×Dic3×C3⋊D3C2211yescharacteristic
37C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
38C2×C3×#626C2211yescharacteristic, complemented
39C3×#3757C2211yescharacteristic, complemented
40#88814C2211yescharacteristic
41#88814C2211yescharacteristic, complemented
42#88806C2211yescharacteristic, complemented
43#88804C2211yescharacteristic, complemented
44Dic3×C3⋊Dic3C2211yescharacteristic, complemented
45C3×#3724C2211yescharacteristic, complemented
46C3×#3724C2211yescharacteristic, complemented
47C3×Dic3⋊Dic3C2211yescharacteristic, complemented
48C3×#3722C2211yescharacteristic
49C3×#3722C2211yescharacteristic
50C3×#3722C2211yescharacteristic, complemented
51C3×#3722C2211yescharacteristic, complemented
52C3×#3722C2211yescharacteristic, complemented
53C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
54C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
55C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
56C2×D4×C3⋊D3—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—
64C4×#638—31no—
65C3×#939—31no—
66C3×#935—31no—
67C3×#930—31no—
68C3×#929—31no—
69C2×C3×(C2×D3)⋊C4—31no—
70C2×C3×(C2×D3)⋊C4—31no—
71#63981—31no—
72#63981—31no—
73#63978D311yescharacteristic, complemented
74#63977—31no—
75#63976—31no—
76#63974—31no—
77#63971—31no—
78C2×#3722D311yescharacteristic, complemented
79#63961D311yescharacteristic, complemented
80#63953—31no—
81#63952—31no—
82#63952—31no—
83#63952—61no—
84#63923—31no—
85#63922—31no—
86#63921—31no—
87#63921—31no—
88#63915—31no—
89#63913—31no—
90#63912—31no—
91#63912—31no—
92#63910—31no—
93#63910—31no—
94#63902—31no—
95#63899—31no—
96#63897—31no—
97#63896—31no—
98#63885—31no—
99#63881—31no—
100#63881—31no—
101#63865—31no—
102#63854—31no—
103#63853—31no—
104C23×C33C2311yescharacteristic
105C22×C3⋊(C3⋊D3)C2311yescharacteristic
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×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—
119C2×C3×C3⋊Dic3C2311yescharacteristic
120C2×C3×C3⋊Dic3C2311yescharacteristic
121C2×C3×C3⋊Dic3C2311yescharacteristic
122C32×#67—22no—
123C2×C32×Dic3—22no—
124C2×C32×Dic3—41no—
125C2×C32×Dic3C2311yescharacteristic
126C2×C32×Dic3C2311yescharacteristic
127C2×C32×Dic3C2311yescharacteristic
128C2×C32×Dic3C2311yescharacteristic
129C2×C32×Dic3C2311yescharacteristic
130#6295—22no—
131#6295—41no—
132#6293—22no—
133#6292—22no—
134#6292—22no—
135#6290—22no—
136#6289—22no—
137#6289—41no—
138Dic3×C3⋊D3—22no—
139Dic3×C3⋊D3—22no—
140C3×#626—41no—
141#5654—91no—
142#5610—91no—
143#5490—91no—
144C23×C3⋊D3—31no—
145C23×C3⋊D3C2×D311yescharacteristic
146C23×C3×D3—31no—
147C23×C3×D3—31no—
148C23×C3×D3—61no—
149C22×D32—31no—
150C22×D32—31no—
151C22×D32—61no—
152C2×C32×D4—31no—
153C22×C32×C4—31no—
154C22×C32×C4—31no—
155C2×#638—31no—
156C2×#638—31no—
157C2×#638—31no—
158C2×#638—31no—
159C2×#638—61no—
160C2×#638—61no—
161C2×#638—61no—
162C2×#638—121no—
163C2×#638C2×D311yescharacteristic, complemented
164D4×C3⋊D3—64no—
165#3828—64no—
166C2×C4⋊(C3⋊D3)—31no—
167C2×C4⋊(C3⋊D3)—31no—
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—21no—
174C2×C3×#67—31no—
175C2×C3×#67—31no—
176C2×C3×#67—31no—
177C2×C3×#67—61no—
178C2×C3×#67C2×D311yescharacteristic
179C2×C3×#67C2×D311yescharacteristic
180C22×C3×Dic3—21no—
181C22×C3×Dic3—21no—
182C22×C3×Dic3C2×D311yescharacteristic, complemented
183C22×C3×Dic3C2×D311yescharacteristic, complemented
184C22×C3×Dic3C2×D311yescharacteristic, complemented
185C22×C3×Dic3C2×D311yescharacteristic, complemented
186C2×C3×D12—31no—
187D3×#67—64no—
188D3×#67—64no—
189D3×#67—68no—
190C2×#627—31no—
191C2×#627—31no—
192C2×#627—61no—
193C2×#626—31no—
194C2×#626—31no—
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, complemented
204C2×#625—31no—
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—
224#3757C2×D311yescharacteristic, complemented
225#3752—31no—
226#3750—31no—
227C4×C3⋊Dic3—31no—
228C3×#217—31no—
229C3×#217—31no—
230C3×#217—31no—
231C3×#217—31no—
232C3×#217—31no—
233C3×#217—61no—
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—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×Dic3⋊C4—31no—
249C3×Dic3⋊C4—31no—
250C3×Dic3⋊C4—31no—
251C3×Dic3⋊C4—31no—
252C3×Dic3⋊C4—31no—
253#3724—31no—
254#3724—31no—
255#3724—61no—
256#3724C2×D311yescharacteristic, complemented
257#3724C2×D311yescharacteristic, complemented
258Dic3⋊Dic3C2×D311yescharacteristic, complemented
259#3722—31no—
260#3722—31no—
261#3722—31no—
262#3722—31no—
263#3722—61no—
264#3722C2×D311yescharacteristic
265#3722C2×D311yescharacteristic
266#3722C2×D311yescharacteristic, complemented
267#3722C2×D311yescharacteristic, complemented
268#3722C2×D311yescharacteristic, complemented
269(C2×D3)⋊Dic3—31no—
270(C2×D3)⋊Dic3—31no—
271(C2×D3)⋊Dic3—31no—
272(C2×D3)⋊Dic3—31no—
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×C3×C3⋊D3—21no—
293C2×C3×C3⋊D3—21no—
294C2×C3×C3⋊D3—44no—
295C2×C3×C3⋊D3#4112yescomplemented
296C2×C32×D3—21no—
297C2×C32×D3—21no—
298C2×C32×D3—21no—
299D3×C3⋊D3—44no—
300C3⋊(C3⋊Dic3)C2×D412yes—
301C3×C3⋊Dic3—21no—
302C3×C3⋊Dic3—21no—
303C3×C3⋊Dic3—21no—
304C32×Dic3—21no—
305C32×Dic3—21no—
306C32×Dic3—21no—
307C32×Dic3—21no—
308C32×Dic3—21no—
309C22×#67—91no—
310C2×#237—91no—
311C2×D3×D4—91no—
312C2×D3×D4—91no—
313C2×D3×D4—181no—
314C2×#235—91no—
315C2×#235—91no—
316C2×#235—181no—
317C3×#123—91no—
318C3×#121—91no—
319C2×C3×C22⋊C4—91no—
320#953—91no—
321#939—31no—
322#939—91no—
323#937—91no—
324#937—91no—
325#935—31no—
326#930—31no—
327#929—31no—
328C4×#67—91no—
329C4×#67—91no—
330C4×#67—181no—
331C2×(C2×D3)⋊C4—31no—
332C2×(C2×D3)⋊C4—31no—
333#896—91no—
334#896—91no—
335#895—91no—
336#894—91no—
337#894—91no—
338#893—91no—
339#885—91no—
340#885—91no—
341#885—91no—
342#884—91no—
343#884—91no—
344#884—91no—
345#884—91no—
346#883—91no—
347#882—91no—
348#882—91no—
349#882—91no—
350#67⋊C4—91no—
351#67⋊C4—91no—
352#67⋊C4—91no—
353D3×C22⋊C4—91no—
354D3×C22⋊C4—91no—
355D3×C22⋊C4—91no—
356#878—91no—
357C23×C32—21no—
358C23×C32—21no—
359C23×C32—21no—
360C23×C32—31no—
361C23×C32—41no—
362C23×C32C22×D311yescharacteristic
363C23×C32C22×D311yescharacteristic
364C23×C32C22×D311yescharacteristic
365C22×C3⋊D3—22no—
366C22×C3⋊D3—22no—
367C22×C3⋊D3—31no—
368C22×C3⋊D3—31no—
369C22×C3⋊D3—31no—
370C22×C3⋊D3—41no—
371C22×C3⋊D3—61no—
372C22×C3⋊D3—61no—
373C22×C3⋊D3—61no—
374C22×C3⋊D3—62no—
375C22×C3⋊D3—62no—
376C22×C3⋊D3—121no—
377C22×C3⋊D3—121no—
378C22×C3⋊D3C22×D311yescharacteristic
379C22×C3⋊D3C22×D311yescharacteristic
380C22×C3⋊D3C22×D311yescharacteristic
381C22×C3×D3—21no—
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—61no—
389C22×C3×D3—61no—
390C22×C3×D3—61no—
391C22×C3×D3—62no—
392C22×C3×D3—62no—
393C22×C3×D3—64no—
394C22×C3×D3—62no—
395C22×C3×D3—62no—
396C22×C3×D3—122no—
397C22×C3×D3—121no—
398C22×C3×D3—121no—
399C22×C3×D3—122no—
400C22×C3×D3C22×D311yescharacteristic
401C22×C3×D3C22×D311yescharacteristic
402C2×D32—62no—
403C2×D32—62no—
404C2×D32—62no—
405C2×D32—62no—
406C2×D32—64no—
407C2×D32—122no—
408C2×D32—121no—
409C2×D32—121no—
410C2×D32—122no—
411C32×D4—62no—
412C2×C32×C4—31no—
413C2×C32×C4—31no—
414C2×C32×C4—31no—
415C2×C32×C4—31no—
416C2×C32×C4—31no—
417C2×C32×C4—62no—
418C2×C32×C4—121no—
419#638—22no—
420#638—34no—
421#638—34no—
422#638—34no—
423#638—64no—
424#638—64no—
425#638—64no—
426#638—62no—
427#638—124no—
428C2×C3⋊Dic3—31no—
429C2×C3⋊Dic3—31no—
430C2×C3⋊Dic3—31no—
431C2×C3⋊Dic3—61no—
432C2×C3⋊Dic3—61no—
433C2×C3⋊Dic3—61no—
434C2×C3⋊Dic3—121no—
435C2×C3⋊Dic3C22×D311yescharacteristic
436C2×C3⋊Dic3C22×D311yescharacteristic
437C2×C3⋊Dic3C22×D311yescharacteristic
438C4⋊(C3⋊D3)—62no—
439C4⋊(C3⋊D3)—62no—
440C4×C3⋊D3—62no—
441C4×C3⋊D3—62no—
442C4×C3⋊D3—62no—
443C4×C3⋊D3—121no—
444#634—62no—
445C3×#67—24no—
446C3×#67—22no—
447C3×#67—22no—
448C3×#67—64no—
449C3×#67—62no—
450C3×#67—62no—
451C3×#67—121no—
452C2×C3×Dic3—24no—
453C2×C3×Dic3—22no—
454C2×C3×Dic3—22no—
455C2×C3×Dic3—21no—
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—41no—
467C2×C3×Dic3—41no—
468C2×C3×Dic3—42no—
469C2×C3×Dic3—61no—
470C2×C3×Dic3—61no—
471C2×C3×Dic3—61no—
472C2×C3×Dic3C22×D311yescharacteristic
473C2×C3×Dic3C22×D311yescharacteristic
474C2×C3×Dic3C22×D311yescharacteristic
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
482C3×D12—121no—
483#627—62no—
484#627—62no—
485#627—64no—
486#626—41no—
487#626—62no—
488#626—62no—
489#626—62no—
490#626—62no—
491#626—64no—
492#626—64no—
493#626—62no—
494#626—62no—
495#626—121no—
496#626—121no—
497#625—62no—
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—62no—
511D3×Dic3—62no—
512D3×Dic3—64no—
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—22no—
521C3×C3⋊D3—41no—
522C3×C3⋊D3—41no—
523C32×D3—41no—
524C24×C3—91no—
525C23×D3—31no—
526C23×D3—31no—
527C23×D3—61no—
528C23×D3—91no—
529C23×D3—91no—
530C23×D3—91no—
531C23×D3—181no—
532C2×C3×D4—31no—
533C2×C3×D4—31no—
534C2×C3×D4—61no—
535C2×C3×D4—91no—
536C2×C3×D4—91no—
537C22×C3×C4—31no—
538C22×C3×C4—31no—
539C22×C3×C4—31no—
540C22×C3×C4—31no—
541C22×C3×C4—61no—
542C22×C3×C4—61no—
543C2×#67—31no—
544C2×#67—31no—
545C2×#67—31no—
546C2×#67—61no—
547C2×#67—91no—
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—184no—
564C2×#67—361no—
565C2×#67D3211yescharacteristic
566C22×Dic3—91no—
567C22×Dic3—91no—
568C22×Dic3D3211yescharacteristic, complemented
569C22×Dic3D3211yescharacteristic, complemented
570#237—184no—
571D3×D4—184no—
572D3×D4—184no—
573D3×D4—188no—
574#235—184no—
575#235—184no—
576#235—188no—
577C2×D12—31no—
578C2×D12—91no—
579C2×D12—91no—
580C2×D12—91no—
581C2×D12—91no—
582C2×D12—91no—
583C2×D12—91no—
584C2×D12—181no—
585C2×D12—181no—
586C2×C4×D3—91no—
587C2×C4×D3—91no—
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—181no—
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×C4⋊C4—91no—
607C3×C22⋊C4—91no—
608C3×C22⋊C4—91no—
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—
616#217—31no—
617#217—31no—
618#217—31no—
619#217—31no—
620#217—31no—
621#217—61no—
622#217—91no—
623#217—91no—
624(C2×D3)⋊C4—31no—
625(C2×D3)⋊C4—31no—
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—31no—
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—91no—
644(C2×D3)⋊C4—181no—
645C4⋊Dic3—31no—
646Dic3⋊C4—31no—
647Dic3⋊C4—31no—
648Dic3⋊C4—31no—
649Dic3⋊C4—31no—
650Dic3⋊C4—31no—
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—41no—
672C22×C32—42no—
673C22×C32—41no—
674C22×C32—41no—
675C22×C32—41no—
676C22×C32—41no—
677C22×C32—41no—
678C22×C32—41no—
679C22×C32—61no—
680C22×C32—61no—
681C22×C32—61no—
682C22×C32—81no—
683C22×C32—81no—
684C22×C32D3×D412yes—
685C22×C32D3×D412yes—
686C22×C32D3×D412yes—
687C22×C32C23×D311yescharacteristic
688C22×C32C23×D311yescharacteristic
689C22×C32C23×D311yescharacteristic
690C2×C3⋊D3—21no—
691C2×C3⋊D3—21no—
692C2×C3⋊D3—21no—
693C2×C3⋊D3—21no—
694C2×C3⋊D3—21no—
695C2×C3⋊D3—21no—
696C2×C3⋊D3—21no—
697C2×C3⋊D3—21no—
698C2×C3⋊D3—32no—
699C2×C3⋊D3—32no—
700C2×C3⋊D3—32no—
701C2×C3⋊D3—44no—
702C2×C3⋊D3—62no—
703C2×C3⋊D3—62no—
704C2×C3⋊D3—62no—
705C2×C3⋊D3—61no—
706C2×C3⋊D3—61no—
707C2×C3⋊D3—61no—
708C2×C3⋊D3—61no—
709C2×C3⋊D3—61no—
710C2×C3⋊D3—61no—
711C2×C3⋊D3—122no—
712C2×C3⋊D3—121no—
713C2×C3⋊D3—121no—
714C2×C3⋊D3—121no—
715C2×C3⋊D3—121no—
716C2×C3⋊D3—121no—
717C2×C3⋊D3—121no—
718C2×C3⋊D3—124no—
719C2×C3⋊D3—241no—
720C2×C3⋊D3—241no—
721C2×C3⋊D3#23512yescomplemented
722C2×C3×D3—22no—
723C2×C3×D3—21no—
724C2×C3×D3—21no—
725C2×C3×D3—21no—
726C2×C3×D3—21no—
727C2×C3×D3—21no—
728C2×C3×D3—21no—
729C2×C3×D3—32no—
730C2×C3×D3—32no—
731C2×C3×D3—41no—
732C2×C3×D3—41no—
733C2×C3×D3—62no—
734C2×C3×D3—62no—
735C2×C3×D3—62no—
736C2×C3×D3—61no—
737C2×C3×D3—61no—
738C2×C3×D3—61no—
739C2×C3×D3—61no—
740C2×C3×D3—62no—
741C2×C3×D3—62no—
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—121no—
755C2×C3×D3—121no—
756C2×C3×D3—121no—
757C2×C3×D3—121no—
758C2×C3×D3—124no—
759C2×C3×D3—124no—
760C2×C3×D3—128no—
761D32—124no—
762D32—124no—
763D32—128no—
764C32×C4—61no—
765C32×C4—61no—
766C32×C4—61no—
767C32×C4—61no—
768C32×C4—61no—
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—22no—
782C3×Dic3—22no—
783C3×Dic3—21no—
784C3×Dic3—21no—
785C3×Dic3—21no—
786C3×Dic3—21no—
787C3×Dic3—21no—
788C3×Dic3—21no—
789C3×Dic3—21no—
790C3×Dic3—21no—
791C3×Dic3—21no—
792C3×Dic3—21no—
793C3×Dic3—41no—
794C3×Dic3—62no—
795C3×Dic3—61no—
796C3×Dic3—61no—
797C3×Dic3—61no—
798C3×Dic3—61no—
799C3×Dic3—61no—
800C3×Dic3—61no—
801C3×Dic3—121no—
802C3×Dic3—121no—
803C2×#41—271no—
804C22×D4—271no—
805#124—271no—
806#123—91no—
807#123—271no—
808C22⋊Q8—271no—
809#121—91no—
810#121—271no—
811#121—271no—
812#120—271no—
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—41no—
825C23×C3—61no—
826C23×C3—91no—
827C23×C3—91no—
828C23×C3—91no—
829C23×C3—182no—
830C23×C3—182no—
831C23×C3—361no—
832C23×C3C2×D3211yescharacteristic
833C23×C3C2×D3211yescharacteristic
834C23×C3C2×D3211yescharacteristic
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—62no—
845C22×D3—62no—
846C22×D3—64no—
847C22×D3—62no—
848C22×D3—62no—
849C22×D3—91no—
850C22×D3—91no—
851C22×D3—91no—
852C22×D3—122no—
853C22×D3—121no—
854C22×D3—121no—
855C22×D3—122no—
856C22×D3—181no—
857C22×D3—181no—
858C22×D3—181no—
859C22×D3—182no—
860C22×D3—182no—
861C22×D3—182no—
862C22×D3—182no—
863C22×D3—182no—
864C22×D3—182no—
865C22×D3—184no—
866C22×D3—361no—
867C22×D3—362no—
868C22×D3—361no—
869C22×D3—361no—
870C22×D3—361no—
871C22×D3—362no—
872C22×D3C2×D3211yescharacteristic
873C3×D4—64no—
874C3×D4—62no—
875C3×D4—62no—
876C3×D4—182no—
877C3×D4—361no—
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—31no—
886C2×C3×C4—31no—
887C2×C3×C4—31no—
888C2×C3×C4—61no—
889C2×C3×C4—61no—
890C2×C3×C4—61no—
891C2×C3×C4—61no—
892C2×C3×C4—61no—
893C2×C3×C4—64no—
894C2×C3×C4—62no—
895C2×C3×C4—62no—
896C2×C3×C4—91no—
897C2×C3×C4—91no—
898C2×C3×C4—91no—
899C2×C3×C4—121no—
900C2×C3×C4—121no—
901C2×C3×C4—122no—
902#67—22no—
903#67—64no—
904#67—62no—
905#67—62no—
906#67—94no—
907#67—94no—
908#67—94no—
909#67—121no—
910#67—184no—
911#67—184no—
912#67—184no—
913#67—182no—
914#67—182no—
915#67—182no—
916#67—182no—
917#67—182no—
918#67—182no—
919#67—182no—
920#67—184no—
921#67—364no—
922#67—361no—
923#67—361no—
924C2×Dic3—22no—
925C2×Dic3—31no—
926C2×Dic3—31no—
927C2×Dic3—31no—
928C2×Dic3—31no—
929C2×Dic3—31no—
930C2×Dic3—31no—
931C2×Dic3—41no—
932C2×Dic3—61no—
933C2×Dic3—61no—
934C2×Dic3—61no—
935C2×Dic3—91no—
936C2×Dic3—91no—
937C2×Dic3—91no—
938C2×Dic3—181no—
939C2×Dic3—181no—
940C2×Dic3—181no—
941C2×Dic3—182no—
942C2×Dic3—182no—
943C2×Dic3—361no—
944C2×Dic3C2×D3211yescharacteristic
945C2×Dic3C2×D3211yescharacteristic
946C2×Dic3C2×D3211yescharacteristic
947C2×Dic3C2×D3211yescharacteristic
948C2×Dic3C2×D3211yescharacteristic
949D12—121no—
950D12—182no—
951D12—182no—
952D12—182no—
953D12—182no—
954D12—184no—
955D12—184no—
956D12—182no—
957D12—361no—
958C4×D3—182no—
959C4×D3—182no—
960C4×D3—182no—
961C4×D3—184no—
962C4×D3—182no—
963C4×D3—182no—
964C4×D3—182no—
965C4×D3—182no—
966C4×D3—184no—
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—82no—
995C2×C32—121no—
996C2×C32C2×#23511yescharacteristic
997C2×C32C2×D3×D411yescharacteristic
998C2×C32C2×D3×D411yescharacteristic
999C2×C32C2×D3×D411yescharacteristic
1000C2×C32#100411yescharacteristic
1001C2×C32#100411yescharacteristic
1002C2×C32D3×#4111yescharacteristic
1003C2×C32D3×#4111yescharacteristic
1004C2×C32#100911yescharacteristic
1005C3⋊D3—22no—
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—42no—
1016C3×D3—41no—
1017C3×D3—41no—
1018C3×D3—64no—
1019C3×D3—62no—
1020C3×D3—62no—
1021C3×D3—122no—
1022C3×D3—122no—
1023C3×D3—121no—
1024C3×D3—121no—
1025C3×D3—121no—
1026C3×D3—121no—
1027C24—91no—
1028C24—271no—
1029#41—544no—
1030C2×Q8—271no—
1031C2×D4—31no—
1032C2×D4—91no—
1033C2×D4—91no—
1034C2×D4—271no—
1035C2×D4—271no—
1036C2×D4—271no—
1037C2×D4—271no—
1038C2×D4—271no—
1039C2×D4—271no—
1040C2×D4—544no—
1041C22×C4—31no—
1042C22×C4—31no—
1043C22×C4—271no—
1044C22×C4—271no—
1045C22×C4—271no—
1046C22×C4—271no—
1047C4⋊C4—91no—
1048C4⋊C4—91no—
1049C4⋊C4—91no—
1050C4⋊C4—271no—
1051C22⋊C4—91no—
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—41no—
1077C22×C3—41no—
1078C22×C3—41no—
1079C22×C3—41no—
1080C22×C3—41no—
1081C22×C3—41no—
1082C22×C3—41no—
1083C22×C3—42no—
1084C22×C3—62no—
1085C22×C3—61no—
1086C22×C3—61no—
1087C22×C3—61no—
1088C22×C3—61no—
1089C22×C3—61no—
1090C22×C3—61no—
1091C22×C3—81no—
1092C22×C3—81no—
1093C22×C3—92no—
1094C22×C3—121no—
1095C22×C3—121no—
1096C22×C3—181no—
1097C22×C3—181no—
1098C22×C3—181no—
1099C22×C3—181no—
1100C22×C3—181no—
1101C22×C3—181no—
1102C22×C3—181no—
1103C22×C3—181no—
1104C22×C3—364no—
1105C22×C3#380212yes—
1106C22×C3#381112yes—
1107C22×C3#381112yes—
1108C22×C3C22×D3211yescharacteristic
1109C22×C3C22×D3211yescharacteristic
1110C22×C3C22×D3211yescharacteristic
1111C2×D3—21no—
1112C2×D3—21no—
1113C2×D3—21no—
1114C2×D3—32no—
1115C2×D3—32no—
1116C2×D3—62no—
1117C2×D3—62no—
1118C2×D3—62no—
1119C2×D3—61no—
1120C2×D3—61no—
1121C2×D3—61no—
1122C2×D3—61no—
1123C2×D3—62no—
1124C2×D3—62no—
1125C2×D3—61no—
1126C2×D3—61no—
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—92no—
1138C2×D3—92no—
1139C2×D3—92no—
1140C2×D3—121no—
1141C2×D3—121no—
1142C2×D3—121no—
1143C2×D3—121no—
1144C2×D3—124no—
1145C2×D3—124no—
1146C2×D3—128no—
1147C2×D3—182no—
1148C2×D3—182no—
1149C2×D3—182no—
1150C2×D3—181no—
1151C2×D3—181no—
1152C2×D3—181no—
1153C2×D3—181no—
1154C2×D3—181no—
1155C2×D3—181no—
1156C2×D3—362no—
1157C2×D3—361no—
1158C2×D3—361no—
1159C2×D3—361no—
1160C2×D3—361no—
1161C2×D3—361no—
1162C2×D3—361no—
1163C2×D3—364no—
1164C2×D3—364no—
1165C2×D3—364no—
1166C2×D3—368no—
1167C2×D3—721no—
1168C2×D3—721no—
1169C3×C4—62no—
1170C3×C4—62no—
1171C3×C4—62no—
1172C3×C4—62no—
1173C3×C4—61no—
1174C3×C4—61no—
1175C3×C4—61no—
1176C3×C4—61no—
1177C3×C4—61no—
1178C3×C4—61no—
1179C3×C4—61no—
1180C3×C4—61no—
1181C3×C4—61no—
1182C3×C4—61no—
1183C3×C4—121no—
1184C3×C4—181no—
1185C3×C4—181no—
1186C3×C4—181no—
1187Dic3—21no—
1188Dic3—21no—
1189Dic3—21no—
1190Dic3—21no—
1191Dic3—21no—
1192Dic3—62no—
1193Dic3—61no—
1194Dic3—61no—
1195Dic3—61no—
1196Dic3—61no—
1197Dic3—61no—
1198Dic3—61no—
1199Dic3—92no—
1200Dic3—92no—
1201Dic3—92no—
1202Dic3—121no—
1203Dic3—121no—
1204Dic3—182no—
1205Dic3—182no—
1206Dic3—182no—
1207Dic3—362no—
1208C32—21no—
1209C32—21no—
1210C32—21no—
1211C32—41no—
1212C32#549011yescharacteristic, complemented
1213C32#561011yescharacteristic, complemented
1214C32#565411yescharacteristic, complemented
1215C23—31no—
1216C23—91no—
1217C23—91no—
1218C23—91no—
1219C23—182no—
1220C23—182no—
1221C23—271no—
1222C23—361no—
1223C23—542no—
1224C23—542no—
1225C23—1081no—
1226C23D3311yescharacteristic
1227Q8—542no—
1228D4—62no—
1229D4—182no—
1230D4—274no—
1231D4—361no—
1232D4—542no—
1233D4—542no—
1234D4—542no—
1235D4—542no—
1236D4—1081no—
1237C2×C4—31no—
1238C2×C4—31no—
1239C2×C4—31no—
1240C2×C4—31no—
1241C2×C4—31no—
1242C2×C4—62no—
1243C2×C4—91no—
1244C2×C4—91no—
1245C2×C4—91no—
1246C2×C4—121no—
1247C2×C4—271no—
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—82no—
1271C2×C3—122no—
1272C2×C3—121no—
1273C2×C3—121no—
1274C2×C3—182no—
1275C2×C3—361no—
1276C2×C3—361no—
1277C2×C3C2×#380211yescharacteristic
1278C2×C3D3×#23511yescharacteristic
1279C2×C3D3×#23511yescharacteristic
1280C2×C3#6430711yescharacteristic
1281C2×C3#6431211yescharacteristic
1282C2×C3#6431411yescharacteristic
1283C2×C3C2×#381111yescharacteristic
1284C2×C3C2×#381111yescharacteristic
1285C2×C3#6433011yescharacteristic
1286D3—41no—
1287D3—64no—
1288D3—62no—
1289D3—62no—
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—61no—
1306C22—61no—
1307C22—61no—
1308C22—92no—
1309C22—181no—
1310C22—181no—
1311C22—181no—
1312C22—181no—
1313C22—181no—
1314C22—181no—
1315C22—181no—
1316C22—181no—
1317C22—272no—
1318C22—364no—
1319C22—541no—
1320C22—541no—
1321C22—1084no—
1322C22#8895412yes—
1323C22C2×D3311yescharacteristic
1324C4—61no—
1325C4—61no—
1326C4—61no—
1327C4—61no—
1328C4—61no—
1329C4—181no—
1330C4—181no—
1331C4—181no—
1332C4—272no—
1333C3—21no—
1334C3—21no—
1335C3—21no—
1336C3—41no—
1337C3#1059507711yescharacteristic, complemented
1338C3#1059508311yescharacteristic, complemented
1339C3#1059516311yescharacteristic, complemented
1340C2—22no—
1341C2—121no—
1342C2—182no—
1343C2—361no—
1344C2—361no—
1345C2—542no—
1346C2#1172441011yescharacteristic
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×C3⋊D3×#67C2semidirect
2. C2×#89031C2semidirect
3. #11723727C2semidirect
4. #11723618C2semidirect
5. C3×#63978C2semidirect
6. C2×C3×#3722C2semidirect
7. C3×#63961C2semidirect
8. #11723009C2semidirect
9. #11723000C2semidirect
10. #11722983C2semidirect
11. #11722968C2semidirect
12. #11722967C2semidirect
13. #11722950C2semidirect
14. #11722938C2semidirect
15. #11722906C2semidirect
22. C2×C3×#638C22semidirect
24. C22×C32×Dic3C22semidirect
25. C22×C32×Dic3C22semidirect
27. C2×#6295C22semidirect
29. C2×#6293C22semidirect
31. C2×#6292C22semidirect
33. C2×#6289C22semidirect
34. C2×#6289C22semidirect
37. C2×Dic3×C3⋊D3C22semidirect
38. C2×C3×#626C22semidirect
39. C3×#3757C22semidirect
41. #88814C22semidirect
42. #88806C22semidirect
43. #88804C22semidirect
44. Dic3×C3⋊Dic3C22semidirect
45. C3×#3724C22semidirect
46. C3×#3724C22semidirect
47. C3×Dic3⋊Dic3C22semidirect
50. C3×#3722C22semidirect
51. C3×#3722C22semidirect
52. C3×#3722C22semidirect
53. C3×(C2×D3)⋊Dic3C22semidirect
54. C3×(C2×D3)⋊Dic3C22semidirect
55. C3×(C2×D3)⋊Dic3C22semidirect
73. #63978D3semidirect
78. C2×#3722D3semidirect
79. #63961D3semidirect
116. #6312D4semidirect
163. C2×#638C2×D3semidirect
182. C22×C3×Dic3C2×D3semidirect
183. C22×C3×Dic3C2×D3semidirect
184. C22×C3×Dic3C2×D3semidirect
185. C22×C3×Dic3C2×D3semidirect
203. C2×#626C2×D3semidirect
224. #3757C2×D3semidirect
256. #3724C2×D3semidirect
257. #3724C2×D3semidirect
258. Dic3⋊Dic3C2×D3semidirect
266. #3722C2×D3semidirect
267. #3722C2×D3semidirect
268. #3722C2×D3semidirect
273. (C2×D3)⋊Dic3C2×D3semidirect
274. (C2×D3)⋊Dic3C2×D3semidirect
275. (C2×D3)⋊Dic3C2×D3semidirect
295. C2×C3×C3⋊D3#41semidirect
568. C22×Dic3D32semidirect
569. C22×Dic3D32semidirect
721. C2×C3⋊D3#235semidirect
818. C33#546semidirect
1212. C32#5490semidirect
1213. C32#5610semidirect
1214. C32#5654semidirect
1337. C3#10595077semidirect
1338. C3#10595083semidirect
1339. C3#10595163semidirect

Maximal subgroups

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

subgroupindex
C2×C3⋊D3×#672
C2×#890312
#117237272
#117236182
C3×#639782
C2×C3×#37222
C3×#639612
#117230092
#117230002
#117229832
#117229682
#117229672
#117229502
#117229382
#117229062
#105951633
#105950833
#105950773