Finite Group Databasebeta

← #13172145

Subgroups — #13172145

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×#89028C211yesmaximal, characteristic, complemented
3C2×#88814C211yesmaximal, characteristic, complemented
4#11723622C211yesmaximal, characteristic, complemented
5C3×#63981C211yesmaximal, characteristic, complemented
6C3×#63980C211yesmaximal, characteristic, complemented
7C3×#63962C211yesmaximal, characteristic, complemented
8#11723009C211yesmaximal, characteristic, complemented
9#11723000C211yesmaximal, characteristic, complemented
10#11722983C211yesmaximal, characteristic, complemented
11#11722963C211yesmaximal, characteristic, complemented
12#11722954C211yesmaximal, characteristic, complemented
13#11722949C211yesmaximal, characteristic, complemented
14#11722929C211yesmaximal, characteristic, complemented
15#11722906C211yesmaximal, characteristic, complemented
16#10595307—31nomaximal
17#10595163—31nomaximal
18#10594294—31nomaximal
19C23×C3×C3⋊D3C2211yescharacteristic
20C22×D3×C3⋊D3C2211yescharacteristic
21C2×#6312C2211yescharacteristic
22C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
23C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
24C2×C32×#67C2211yescharacteristic
25C2×C32×#67C2211yescharacteristic, complemented
26C3⋊D3×#67—24no—
27C2×#6293C2211yescharacteristic, complemented
28C2×#6292C2211yescharacteristic
29C2×#6291C2211yescharacteristic, complemented
30C2×#6290C2211yescharacteristic
31C2×#6289C2211yescharacteristic, complemented
32C2×#6289C2211yescharacteristic, complemented
33C2×Dic3×C3⋊D3C2211yescharacteristic
34#89028—24no—
35C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
36C2×C3×#626C2211yescharacteristic
37C2×C3×#626C2211yescharacteristic, complemented
38C2×C3×#625C2211yescharacteristic, complemented
39C32×#217C2211yescharacteristic, complemented
40#88814C2211yescharacteristic
41#88814C2211yescharacteristic
42#88814C2211yescharacteristic, complemented
43#88814C2211yescharacteristic, complemented
44#88806C2211yescharacteristic, complemented
45#88804C2211yescharacteristic, complemented
46Dic3×C3⋊Dic3C2211yescharacteristic, complemented
47C3×#3724C2211yescharacteristic, complemented
48C3×Dic3⋊Dic3C2211yescharacteristic, complemented
49C3×Dic3⋊Dic3C2211yescharacteristic, complemented
50C3×#3722C2211yescharacteristic
51C3×#3722C2211yescharacteristic, complemented
52C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
53C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
54C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
55C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
56C2×#3830—31no—
57C2×D4×C3⋊D3—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×#939—31no—
66C3×#939—31no—
67C3×#937—31no—
68C3×#935—31no—
69C3×#886—31no—
70C3×#882—31no—
71#63983—31no—
72#63981—31no—
73#63981D311yescharacteristic, complemented
74#63980—31no—
75#63980D311yescharacteristic, complemented
76#63974—31no—
77#67⋊Dic3—31no—
78#63971—31no—
79C2×#3722—31no—
80#63962D311yescharacteristic, complemented
81C2×(C2×D3)⋊Dic3—31no—
82C2×(C2×D3)⋊Dic3—31no—
83#63958—31no—
84#63953—31no—
85#63952—31no—
86#63952—31no—
87#63952—61no—
88#63922—31no—
89#63921—31no—
90#63921—31no—
91#63916—31no—
92#63915—31no—
93#63913—31no—
94#63910—31no—
95#63899—31no—
96#63898—31no—
97#63897—31no—
98#63896—31no—
99#63885—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×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
118C2×C3×C3⋊Dic3—22no—
119C2×C3×C3⋊Dic3—41no—
120C2×C3×C3⋊Dic3C2311yescharacteristic
121C2×C3×C3⋊Dic3C2311yescharacteristic
122C2×C3×C3⋊Dic3C2311yescharacteristic
123C2×C3×C3⋊Dic3C2311yescharacteristic
124C32×#67—22no—
125C32×#67—22no—
126C2×C32×Dic3C2311yescharacteristic
127C2×C32×Dic3C2311yescharacteristic
128C2×C32×Dic3C2311yescharacteristic
129C2×C32×Dic3C2311yescharacteristic
130#6293—22no—
131#6292—22no—
132#6291—22no—
133#6290—22no—
134#6289—22no—
135#6289—41no—
136Dic3×C3⋊D3—22no—
137D3×C3⋊Dic3—22no—
138C3×#626—22no—
139C3×#626—41no—
140C3×#625—41no—
141#5654—91no—
142#5610—91no—
143#5591—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—
153C2×C32×D4—31no—
154C2×#638—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—
163C22×C3⋊Dic3—31no—
164C22×C3⋊Dic3C2×D311yescharacteristic, complemented
165C22×C3⋊Dic3C2×D311yescharacteristic, complemented
166#3830—64no—
167D4×C3⋊D3—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—21no—
174C2×C3×#67—21no—
175C2×C3×#67—31no—
176C2×C3×#67—31no—
177C2×C3×#67—31no—
178C2×C3×#67—31no—
179C2×C3×#67C2×D311yescharacteristic
180C2×C3×#67C2×D311yescharacteristic
181C2×C3×#67C2×D311yescharacteristic, complemented
182C2×C3×#67C2×D311yescharacteristic, complemented
183C22×C3×Dic3—31no—
184C22×C3×Dic3—31no—
185C22×C3×Dic3—31no—
186C22×C3×Dic3—31no—
187C22×C3×Dic3—61no—
188C22×C3×Dic3—61no—
189C2×C3×D12—31no—
190C2×C3×D12—31no—
191D3×#67—64no—
192D3×#67—64no—
193D3×#67—68no—
194C2×#627—31no—
195C2×#627—31no—
196C2×#627—61no—
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—61no—
208C2×#625C2×D311yescharacteristic, complemented
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×#217C2×D311yescharacteristic, complemented
234C3×#217C2×D311yescharacteristic, complemented
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×C4⋊Dic3—31no—
244C3×C4⋊Dic3—31no—
245C3×Dic3⋊C4—31no—
246C3×Dic3⋊C4—31no—
247C3×Dic3⋊C4—31no—
248C3×Dic3⋊C4—31no—
249#3724—31no—
250#3724—31no—
251#3724—61no—
252#3724C2×D311yescharacteristic, complemented
253Dic3⋊Dic3C2×D311yescharacteristic, complemented
254Dic3⋊Dic3C2×D311yescharacteristic, complemented
255#3722—31no—
256#3722—31no—
257#3722—31no—
258#3722—31no—
259#3722—31no—
260#3722—31no—
261#3722—61no—
262#3722C2×D311yescharacteristic
263#3722C2×D311yescharacteristic, complemented
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)⋊Dic3C2×D311yescharacteristic, complemented
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—44no—
292C2×C3×C3⋊D3#4112yescomplemented
293C2×C32×D3—21no—
294C2×C32×D3—21no—
295C2×C32×D3—21no—
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—
304C3×C3⋊Dic3—21no—
305C32×Dic3—21no—
306C32×Dic3—21no—
307C32×Dic3—21no—
308C32×Dic3—21no—
309C22×#67—91no—
310C2×#237—91no—
311C2×#237—91no—
312C2×#237—181no—
313C2×D3×D4—91no—
314C2×D3×D4—91no—
315C2×D3×D4—181no—
316C2×#235—91no—
317C3×#123—91no—
318C3×#121—91no—
319C3×#120—91no—
320C2×#217—91no—
321#939—31no—
322#939—31no—
323#939—91no—
324#939—91no—
325#938—91no—
326#937—31no—
327#937—91no—
328#937—91no—
329#935—31no—
330D4×Dic3—91no—
331C4×#67—91no—
332C2×(C2×D3)⋊C4—91no—
333C2×(C2×D3)⋊C4—91no—
334#896—91no—
335#896—91no—
336#895—91no—
337#894—91no—
338#894—91no—
339#893—91no—
340#886—31no—
341#885—91no—
342#885—91no—
343#885—91no—
344#884—91no—
345#884—91no—
346#883—91no—
347#882—31no—
348#882—91no—
349#67⋊C4—91no—
350#67⋊C4—91no—
351#67⋊C4—91no—
352#67⋊C4—181no—
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—31no—
362C23×C32—41no—
363C23×C32C22×D311yescharacteristic
364C23×C32C22×D311yescharacteristic
365C23×C32C22×D311yescharacteristic
366C22×C3⋊D3—22no—
367C22×C3⋊D3—22no—
368C22×C3⋊D3—31no—
369C22×C3⋊D3—31no—
370C22×C3⋊D3—31no—
371C22×C3⋊D3—41no—
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—21no—
382C22×C3×D3—21no—
383C22×C3×D3—31no—
384C22×C3×D3—31no—
385C22×C3×D3—31no—
386C22×C3×D3—31no—
387C22×C3×D3—61no—
388C22×C3×D3—61no—
389C22×C3×D3—62no—
390C22×C3×D3—62no—
391C22×C3×D3—64no—
392C22×C3×D3—62no—
393C22×C3×D3—62no—
394C22×C3×D3—122no—
395C22×C3×D3—121no—
396C22×C3×D3—121no—
397C22×C3×D3—122no—
398C22×C3×D3C22×D311yescharacteristic
399C22×C3×D3C22×D311yescharacteristic
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—
412C32×D4—62no—
413C2×C32×C4—31no—
414C2×C32×C4—31no—
415C2×C32×C4—31no—
416C2×C32×C4—31no—
417#638—34no—
418#638—34no—
419#638—34no—
420#638—64no—
421#638—64no—
422#638—64no—
423#638—62no—
424#638—62no—
425#638—124no—
426C2×C3⋊Dic3—22no—
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—24no—
446C3×#67—24no—
447C3×#67—22no—
448C3×#67—22no—
449C3×#67—22no—
450C3×#67—22no—
451C3×#67—62no—
452C3×#67—121no—
453C3×#67—121no—
454C3×#67—121no—
455C2×C3×Dic3—21no—
456C2×C3×Dic3—21no—
457C2×C3×Dic3—21no—
458C2×C3×Dic3—21no—
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—61no—
468C2×C3×Dic3—61no—
469C2×C3×Dic3—61no—
470C2×C3×Dic3—61no—
471C2×C3×Dic3—64no—
472C2×C3×Dic3—62no—
473C2×C3×Dic3—62no—
474C2×C3×Dic3—121no—
475C2×C3×Dic3—121no—
476C2×C3×Dic3—122no—
477C2×C3×Dic3C22×D311yescharacteristic
478C2×C3×Dic3C22×D311yescharacteristic
479C2×C3×Dic3C22×D311yescharacteristic
480C2×C3×Dic3C22×D311yescharacteristic
481C2×C3×Dic3C22×D311yescharacteristic
482C2×C3×Dic3C22×D311yescharacteristic
483C2×C3×Dic3C22×D311yescharacteristic
484C2×C3×Dic3C22×D311yescharacteristic
485C3×D12—62no—
486C3×D12—121no—
487#627—62no—
488#627—62no—
489#627—64no—
490#626—22no—
491#626—41no—
492#626—62no—
493#626—62no—
494#626—64no—
495#626—62no—
496#626—62no—
497#626—64no—
498#625—41no—
499#625—62no—
500#625—62no—
501#625—64no—
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—22no—
521C3×C3⋊D3—41no—
522C32×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—31no—
535C2×C3×D4—31no—
536C2×C3×D4—61no—
537C2×C3×D4—61no—
538C2×C3×D4—91no—
539C2×C3×D4—91no—
540C2×C3×D4—91no—
541C22×C3×C4—91no—
542C22×C3×C4—91no—
543C2×#67—31no—
544C2×#67—31no—
545C2×#67—31no—
546C2×#67—31no—
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—181no—
557C2×#67—181no—
558C2×#67—181no—
559C2×#67—181no—
560C2×#67—181no—
561C2×#67—184no—
562C2×#67—361no—
563C2×#67D3211yescharacteristic
564C2×#67D3211yescharacteristic, complemented
565C22×Dic3—31no—
566C22×Dic3—31no—
567C22×Dic3—31no—
568C22×Dic3—31no—
569C22×Dic3—61no—
570C22×Dic3—61no—
571C22×Dic3—91no—
572C22×Dic3—91no—
573C22×Dic3—91no—
574C22×Dic3—181no—
575#237—184no—
576#237—184no—
577#237—188no—
578D3×D4—184no—
579D3×D4—184no—
580D3×D4—188no—
581#235—184no—
582C2×D12—31no—
583C2×D12—31no—
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×C4⋊C4—91no—
607C3×C22⋊C4—31no—
608C3×C22⋊C4—31no—
609C3×C22⋊C4—61no—
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—91no—
621#217—91no—
622#217—91no—
623#217—91no—
624#217D3211yescharacteristic, complemented
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—91no—
634(C2×D3)⋊C4—91no—
635(C2×D3)⋊C4—91no—
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—91no—
644(C2×D3)⋊C4—181no—
645C4⋊Dic3—31no—
646C4⋊Dic3—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—61no—
683C22×C32—61no—
684C22×C32—61no—
685C22×C32—81no—
686C22×C32—81no—
687C22×C32D3×D412yes—
688C22×C32D3×D412yes—
689C22×C32D3×D412yes—
690C22×C32C23×D311yescharacteristic
691C22×C32C23×D311yescharacteristic
692C22×C32C23×D311yescharacteristic
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#23712yescomplemented
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—21no—
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—21no—
736C2×C3×D3—32no—
737C2×C3×D3—32no—
738C2×C3×D3—41no—
739C2×C3×D3—41no—
740C2×C3×D3—41no—
741C2×C3×D3—41no—
742C2×C3×D3—62no—
743C2×C3×D3—62no—
744C2×C3×D3—62no—
745C2×C3×D3—61no—
746C2×C3×D3—61no—
747C2×C3×D3—61no—
748C2×C3×D3—61no—
749C2×C3×D3—62no—
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—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—
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—91no—
810#121—271no—
811#121—271no—
812#120—91no—
813#120—271no—
814C4×D4—271no—
815C4×D4—271no—
816C2×C22⋊C4—271no—
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—91no—
830C23×C3—91no—
831C23×C3—182no—
832C23×C3—182no—
833C23×C3—361no—
834C23×C3C2×D3211yescharacteristic
835C23×C3C2×D3211yescharacteristic
836C23×C3C2×D3211yescharacteristic
837C22×D3—31no—
838C22×D3—31no—
839C22×D3—31no—
840C22×D3—31no—
841C22×D3—61no—
842C22×D3—61no—
843C22×D3—62no—
844C22×D3—62no—
845C22×D3—64no—
846C22×D3—62no—
847C22×D3—62no—
848C22×D3—91no—
849C22×D3—91no—
850C22×D3—91no—
851C22×D3—122no—
852C22×D3—121no—
853C22×D3—121no—
854C22×D3—122no—
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—182no—
864C22×D3—184no—
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—64no—
874C3×D4—64no—
875C3×D4—62no—
876C3×D4—62no—
877C3×D4—62no—
878C3×D4—62no—
879C3×D4—182no—
880C3×D4—361no—
881C3×D4—361no—
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—31no—
889C2×C3×C4—31no—
890C2×C3×C4—61no—
891C2×C3×C4—61no—
892C2×C3×C4—61no—
893C2×C3×C4—61no—
894C2×C3×C4—91no—
895C2×C3×C4—91no—
896C2×C3×C4—91no—
897C2×C3×C4—91no—
898C2×C3×C4—182no—
899C2×C3×C4—361no—
900#67—22no—
901#67—22no—
902#67—62no—
903#67—94no—
904#67—94no—
905#67—94no—
906#67—121no—
907#67—121no—
908#67—121no—
909#67—184no—
910#67—184no—
911#67—184no—
912#67—182no—
913#67—182no—
914#67—182no—
915#67—184no—
916#67—182no—
917#67—182no—
918#67—182no—
919#67—184no—
920#67—364no—
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—61no—
930C2×Dic3—61no—
931C2×Dic3—61no—
932C2×Dic3—61no—
933C2×Dic3—64no—
934C2×Dic3—62no—
935C2×Dic3—62no—
936C2×Dic3—91no—
937C2×Dic3—91no—
938C2×Dic3—91no—
939C2×Dic3—121no—
940C2×Dic3—121no—
941C2×Dic3—122no—
942C2×Dic3—181no—
943C2×Dic3—181no—
944C2×Dic3—181no—
945C2×Dic3—182no—
946C2×Dic3—182no—
947C2×Dic3—182no—
948C2×Dic3—184no—
949C2×Dic3—361no—
950C2×Dic3C2×D3211yescharacteristic
951C2×Dic3C2×D3211yescharacteristic
952C2×Dic3C2×D3211yescharacteristic
953C2×Dic3C2×D3211yescharacteristic
954D12—62no—
955D12—121no—
956D12—182no—
957D12—182no—
958D12—184no—
959D12—182no—
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—82no—
995C2×C32—121no—
996C2×C32—121no—
997C2×C32C2×D3×D411yescharacteristic
998C2×C32C2×D3×D411yescharacteristic
999C2×C32C2×D3×D411yescharacteristic
1000C2×C32C2×#23711yescharacteristic
1001C2×C32#100411yescharacteristic
1002C2×C32#100411yescharacteristic
1003C2×C32D3×#4111yescharacteristic
1004C2×C32D3×#4111yescharacteristic
1005C2×C32#100911yescharacteristic
1006C3⋊D3—22no—
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—42no—
1017C3×D3—41no—
1018C3×D3—41no—
1019C3×D3—41no—
1020C3×D3—41no—
1021C3×D3—64no—
1022C3×D3—62no—
1023C3×D3—62no—
1024C3×D3—122no—
1025C3×D3—121no—
1026C3×D3—121no—
1027C24—91no—
1028C24—271no—
1029#41—544no—
1030C2×Q8—271no—
1031C2×D4—31no—
1032C2×D4—31no—
1033C2×D4—91no—
1034C2×D4—91no—
1035C2×D4—91no—
1036C2×D4—271no—
1037C2×D4—271no—
1038C2×D4—271no—
1039C2×D4—271no—
1040C2×D4—544no—
1041C22×C4—91no—
1042C22×C4—91no—
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—31no—
1052C22⋊C4—91no—
1053C22⋊C4—91no—
1054C22⋊C4—91no—
1055C22⋊C4—91no—
1056C22⋊C4—91no—
1057C22⋊C4—91no—
1058C22⋊C4—271no—
1059C22⋊C4—271no—
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—62no—
1086C22×C3—61no—
1087C22×C3—61no—
1088C22×C3—61no—
1089C22×C3—61no—
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—81no—
1099C22×C3—81no—
1100C22×C3—92no—
1101C22×C3—121no—
1102C22×C3—121no—
1103C22×C3—121no—
1104C22×C3—121no—
1105C22×C3—181no—
1106C22×C3—181no—
1107C22×C3—181no—
1108C22×C3—181no—
1109C22×C3—181no—
1110C22×C3—364no—
1111C22×C3#380212yes—
1112C22×C3#381112yes—
1113C22×C3#381112yes—
1114C22×C3C22×D3211yescharacteristic
1115C22×C3C22×D3211yescharacteristic
1116C22×C3C22×D3211yescharacteristic
1117C2×D3—21no—
1118C2×D3—21no—
1119C2×D3—21no—
1120C2×D3—21no—
1121C2×D3—21no—
1122C2×D3—21no—
1123C2×D3—32no—
1124C2×D3—32no—
1125C2×D3—62no—
1126C2×D3—62no—
1127C2×D3—62no—
1128C2×D3—61no—
1129C2×D3—61no—
1130C2×D3—61no—
1131C2×D3—61no—
1132C2×D3—62no—
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—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—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#559111yescharacteristic, complemented
1213C32#561011yescharacteristic, complemented
1214C32#565411yescharacteristic, complemented
1215C23—31no—
1216C23—31no—
1217C23—91no—
1218C23—91no—
1219C23—182no—
1220C23—182no—
1221C23—271no—
1222C23—361no—
1223C23—542no—
1224C23—542no—
1225C23—1081no—
1226C23D3311yescharacteristic
1227Q8—542no—
1228D4—62no—
1229D4—62no—
1230D4—182no—
1231D4—274no—
1232D4—361no—
1233D4—361no—
1234D4—542no—
1235D4—542no—
1236D4—542no—
1237C2×C4—31no—
1238C2×C4—31no—
1239C2×C4—31no—
1240C2×C4—31no—
1241C2×C4—91no—
1242C2×C4—91no—
1243C2×C4—91no—
1244C2×C4—91no—
1245C2×C4—182no—
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—82no—
1271C2×C3—122no—
1272C2×C3—122no—
1273C2×C3—121no—
1274C2×C3—121no—
1275C2×C3—121no—
1276C2×C3—121no—
1277C2×C3—182no—
1278C2×C3—361no—
1279C2×C3C2×#380211yescharacteristic
1280C2×C3D3×#23711yescharacteristic
1281C2×C3D3×#23711yescharacteristic
1282C2×C3#6431211yescharacteristic
1283C2×C3#6431311yescharacteristic
1284C2×C3#6431411yescharacteristic
1285C2×C3#6431411yescharacteristic
1286C2×C3C2×#381111yescharacteristic
1287C2×C3C2×#381111yescharacteristic
1288D3—41no—
1289D3—41no—
1290D3—64no—
1291D3—62no—
1292D3—62no—
1293D3—122no—
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—61no—
1309C22—61no—
1310C22—61no—
1311C22—92no—
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—181no—
1329C4—181no—
1330C4—181no—
1331C4—181no—
1332C4—272no—
1333C3—21no—
1334C3—21no—
1335C3—21no—
1336C3—41no—
1337C3#1059429411yescharacteristic, complemented
1338C3#1059516311yescharacteristic, complemented
1339C3#1059530711yescharacteristic, complemented
1340C2—22no—
1341C2—121no—
1342C2—121no—
1343C2—182no—
1344C2—361no—
1345C2—542no—
1346C2#1172440811yescharacteristic
1347C2#1172441611yescharacteristic
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×#89028C2semidirect
3. C2×#88814C2semidirect
4. #11723622C2semidirect
5. C3×#63981C2semidirect
6. C3×#63980C2semidirect
7. C3×#63962C2semidirect
8. #11723009C2semidirect
9. #11723000C2semidirect
10. #11722983C2semidirect
11. #11722963C2semidirect
12. #11722954C2semidirect
13. #11722949C2semidirect
14. #11722929C2semidirect
15. #11722906C2semidirect
22. C22×C3×C3⋊Dic3C22semidirect
23. C22×C3×C3⋊Dic3C22semidirect
25. C2×C32×#67C22semidirect
27. C2×#6293C22semidirect
29. C2×#6291C22semidirect
31. C2×#6289C22semidirect
32. C2×#6289C22semidirect
35. C2×D3×C3⋊Dic3C22semidirect
37. C2×C3×#626C22semidirect
38. C2×C3×#625C22semidirect
39. C32×#217C22semidirect
42. #88814C22semidirect
43. #88814C22semidirect
44. #88806C22semidirect
45. #88804C22semidirect
46. Dic3×C3⋊Dic3C22semidirect
47. C3×#3724C22semidirect
48. C3×Dic3⋊Dic3C22semidirect
49. C3×Dic3⋊Dic3C22semidirect
51. C3×#3722C22semidirect
52. C3×(C2×D3)⋊Dic3C22semidirect
53. C3×(C2×D3)⋊Dic3C22semidirect
54. C3×(C2×D3)⋊Dic3C22semidirect
55. C3×(C2×D3)⋊Dic3C22semidirect
73. #63981D3semidirect
75. #63980D3semidirect
80. #63962D3semidirect
116. #6312D4semidirect
164. C22×C3⋊Dic3C2×D3semidirect
165. C22×C3⋊Dic3C2×D3semidirect
181. C2×C3×#67C2×D3semidirect
182. C2×C3×#67C2×D3semidirect
204. C2×#626C2×D3semidirect
208. C2×#625C2×D3semidirect
233. C3×#217C2×D3semidirect
234. C3×#217C2×D3semidirect
252. #3724C2×D3semidirect
253. Dic3⋊Dic3C2×D3semidirect
254. Dic3⋊Dic3C2×D3semidirect
263. #3722C2×D3semidirect
272. (C2×D3)⋊Dic3C2×D3semidirect
273. (C2×D3)⋊Dic3C2×D3semidirect
274. (C2×D3)⋊Dic3C2×D3semidirect
275. (C2×D3)⋊Dic3C2×D3semidirect
292. C2×C3×C3⋊D3#41semidirect
564. C2×#67D32semidirect
624. #217D32semidirect
721. C2×C3⋊D3#237semidirect
818. C33#546semidirect
1212. C32#5591semidirect
1213. C32#5610semidirect
1214. C32#5654semidirect
1337. C3#10594294semidirect
1338. C3#10595163semidirect
1339. C3#10595307semidirect

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×#890282
C2×#888142
#117236222
C3×#639812
C3×#639802
C3×#639622
#117230092
#117230002
#117229832
#117229632
#117229542
#117229492
#117229292
#117229062
#105953073
#105951633
#105942943