Finite Group Databasebeta

← #13172674

Subgroups — #13172674

Order 1728.

1708 conjugacy classes of subgroups.

The subgroup lattice has 1330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3804C211yesmaximal, characteristic, complemented
2C2×D3×#626C211yesmaximal, characteristic, complemented
3#11723725C211yesmaximal, characteristic, complemented
4#11723643C211yesmaximal, characteristic, complemented
5#11723632C211yesmaximal, characteristic, complemented
6#11723616C211yesmaximal, characteristic, complemented
7C3×#63983C211yesmaximal, characteristic, complemented
8C3×Dic3×#67C211yesmaximal, characteristic, complemented
9#11723003C211yesmaximal, characteristic, complemented
10#11722995C211yesmaximal, characteristic, complemented
11#11722987C211yesmaximal, characteristic, complemented
12#11722969C211yesmaximal, characteristic, complemented
13#11722928C211yesmaximal, characteristic, complemented
14#11722904C211yesmaximal, characteristic, complemented
15D3×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
16#10595304—31nomaximal
17#10595135—31nomaximal
18#10595067—31nomaximal
19C22×D3×C3⋊D3C2211yescharacteristic
20C22×C3×D32C2211yescharacteristic
21C2×#6312C2211yescharacteristic, complemented
22C2×C3×#638C2211yescharacteristic, complemented
23C2×C3×#638C2211yescharacteristic, complemented
24C2×C32×#67C2211yescharacteristic
25C2×C32×#67C2211yescharacteristic, complemented
26C22×C32×Dic3C2211yescharacteristic, complemented
27C2×#6295C2211yescharacteristic
28C2×#6294C2211yescharacteristic, complemented
29C2×#6292C2211yescharacteristic
30C2×#6291C2211yescharacteristic
31C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
32C2×C3×#627C2211yescharacteristic, complemented
33C2×C3×#626C2211yescharacteristic
34C2×C3×#624C2211yescharacteristic, complemented
35C3×#3804—24no—
36C2×C3×D3×Dic3C2211yescharacteristic
37C2×C3×D3×Dic3C2211yescharacteristic, complemented
38D3×#626—24no—
39C3×#3757C2211yescharacteristic, complemented
40#88815C2211yescharacteristic, complemented
41#88814C2211yescharacteristic, complemented
42#88806C2211yescharacteristic, complemented
43Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
44#88804C2211yescharacteristic, complemented
45#88804C2211yescharacteristic, complemented
46#88804C2211yescharacteristic, complemented
47#88803C2211yescharacteristic, complemented
48#88803C2211yescharacteristic, complemented
49(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
50C3×Dic3⋊Dic3C2211yescharacteristic, complemented
51C3×#3722C2211yescharacteristic, complemented
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×(C2×D3)⋊Dic3C2211yescharacteristic
54C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
55C3×Dic32C2211yescharacteristic, complemented
56C2×C3×#237—31no—
57C2×C3×#235—31no—
58C2×D3×#67—31no—
59C22×#626—31no—
60C2×#3804D311yescharacteristic, complemented
61C2×D3×D12—31no—
62#64148—31no—
63#64146—31no—
64#64139—31no—
65C3×#937—31no—
66C3×#937—31no—
67C3×D4×Dic3—31no—
68C3×C4×#67—31no—
69#63983—31no—
70#63983—31no—
71#63983—61no—
72#63983D311yescharacteristic, complemented
73#63978—31no—
74#63978—31no—
75#63978—61no—
76#63974—31no—
77#67⋊Dic3—31no—
78Dic3×#67D311yescharacteristic, complemented
79#63971—31no—
80#63971—31no—
81#63971—31no—
82#63971—61no—
83#63970—31no—
84D3×#217—31no—
85#63966—31no—
86#63964—31no—
87C2×(C2×D3)⋊Dic3—31no—
88#63958—31no—
89D3×(C2×D3)⋊C4—31no—
90D3×(C2×D3)⋊C4—31no—
91D3×(C2×D3)⋊C4—31no—
92#63907—31no—
93#63905—31no—
94Dic3×D12—31no—
95#63890—31no—
96#63887—31no—
97#63880—31no—
98#63864—31no—
99#63856—31no—
100#63854—31no—
101#63852—31no—
102#63850—31no—
103#63850—31no—
104C23×C33C2311yescharacteristic
105C22×C3⋊(C3⋊D3)C2311yescharacteristic
106C22×C3×C3⋊D3C2311yescharacteristic
107C22×C3×C3⋊D3C2311yescharacteristic
108C22×C32×D3C2311yescharacteristic
109C22×C32×D3C2311yescharacteristic
110C2×D3×C3⋊D3—22no—
111C2×D3×C3⋊D3—22no—
112C2×D3×C3⋊D3—41no—
113C2×C3×D32—22no—
114C2×C3×D32—22no—
115C2×C3×D32—41no—
116#6312—41no—
117C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
118C3×#638—22no—
119C3×#638—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×Dic3—22no—
127C2×C32×Dic3C2311yescharacteristic
128C2×C32×Dic3C2311yescharacteristic
129C2×C32×Dic3C2311yescharacteristic
130C2×C32×Dic3C2311yescharacteristic
131#6295—22no—
132#6294—41no—
133#6292—22no—
134#6291—22no—
135D3×C3⋊Dic3—41no—
136C3×#627—22no—
137C3×#626D414yescomplemented
138C3×#624—22no—
139C3×D3×Dic3—22no—
140C3×D3×Dic3—22no—
141#5829—91no—
142#5591—91no—
143#5550—91no—
144C23×C3⋊D3—31no—
145C23×C3×D3—31no—
146C23×C3×D3—31no—
147C22×D32—31no—
148C22×D32—31no—
149C22×D32—61no—
150C22×D32C2×D311yescharacteristic
151C2×C32×D4—31no—
152C2×C32×D4—31no—
153C22×C32×C4—31no—
154C2×#638—31no—
155C2×#638—31no—
156C2×#638—31no—
157C2×#638—31no—
158C2×#638—61no—
159C2×#638—61no—
160C2×#638—61no—
161C2×#638—121no—
162C2×#638C2×D311yescharacteristic, complemented
163C2×#638C2×D311yescharacteristic, complemented
164C22×C3⋊Dic3—31no—
165C2×C4⋊(C3⋊D3)—31no—
166C2×C3×#67—21no—
167C2×C3×#67—21no—
168C2×C3×#67—31no—
169C2×C3×#67—31no—
170C2×C3×#67—31no—
171C2×C3×#67—31no—
172C2×C3×#67—31no—
173C2×C3×#67—61no—
174C2×C3×#67—61no—
175C2×C3×#67C2×D311yescharacteristic
176C2×C3×#67C2×D311yescharacteristic
177C2×C3×#67C2×D311yescharacteristic, complemented
178C2×C3×#67C2×D311yescharacteristic, complemented
179C22×C3×Dic3—21no—
180C22×C3×Dic3—31no—
181C22×C3×Dic3—31no—
182C22×C3×Dic3C2×D311yescharacteristic, complemented
183C22×C3×Dic3C2×D311yescharacteristic, complemented
184C3×#237—64no—
185C3×#235—64no—
186C2×C3×D12—31no—
187C2×C3×C4×D3—31no—
188C2×C3×C4×D3—31no—
189C2×C3×C4×D3—31no—
190C2×C3×C4×D3—31no—
191C2×C3×Dic6—31no—
192C2×C3×Dic6—31no—
193D3×#67—64no—
194C2×#627C2×D311yescharacteristic, complemented
195C2×#626—31no—
196C2×#626—31no—
197C2×#626—31no—
198C2×#626—31no—
199C2×#626—31no—
200C2×#626—31no—
201C2×#626—64no—
202C2×#626—61no—
203C2×#626—61no—
204C2×#626C2×D311yescharacteristic
205C2×#625—31no—
206C2×#624—31no—
207C2×#624C2×D311yescharacteristic, complemented
208#3804—24no—
209C2×D3×Dic3—31no—
210C2×D3×Dic3—31no—
211C2×D3×Dic3—31no—
212C2×D3×Dic3—31no—
213C2×D3×Dic3—61no—
214C2×D3×Dic3C2×D311yescharacteristic
215C2×D3×Dic3C2×D311yescharacteristic, complemented
216D3×D12—64no—
217#3757—31no—
218#3757C2×D311yescharacteristic, complemented
219#3752—31no—
220#3752—31no—
221#3752—31no—
222#3752—31no—
223#3752—31no—
224C4⋊(C3⋊Dic3)—31no—
225#3750—31no—
226C3×#217—31no—
227C3×#217—31no—
228C3×#217—31no—
229C3×#217—31no—
230C3×#217—31no—
231C3×#217—61no—
232C3×(C2×D3)⋊C4—31no—
233C3×(C2×D3)⋊C4—31no—
234C3×(C2×D3)⋊C4—31no—
235C3×(C2×D3)⋊C4—31no—
236C3×(C2×D3)⋊C4—31no—
237C3×C4⋊Dic3—31no—
238C3×Dic3⋊C4—31no—
239C3×C4×Dic3—31no—
240C3×C4×Dic3—31no—
241#3724—31no—
242#3724—31no—
243#3724—31no—
244#3724—61no—
245Dic3⋊Dic3—31no—
246Dic3⋊Dic3—31no—
247Dic3⋊Dic3—31no—
248Dic3⋊Dic3—31no—
249Dic3⋊Dic3—61no—
250Dic3⋊Dic3C2×D311yescharacteristic, complemented
251#3722—31no—
252#3722—31no—
253#3722—31no—
254#3722—31no—
255#3722—31no—
256#3722—31no—
257#3722—31no—
258#3722—61no—
259#3722—61no—
260#3722—61no—
261#3722C2×D311yescharacteristic, complemented
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—61no—
271(C2×D3)⋊Dic3—61no—
272(C2×D3)⋊Dic3—61no—
273(C2×D3)⋊Dic3C2×D311yescharacteristic
274(C2×D3)⋊Dic3C2×D311yescharacteristic
275(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
276Dic32C2×D311yescharacteristic, complemented
277C22×C33—21no—
278C22×C33—21no—
279C22×C33—21no—
280C22×C33C2411yescharacteristic
281C2×C3⋊(C3⋊D3)—21no—
282C2×C3⋊(C3⋊D3)—21no—
283C2×C3⋊(C3⋊D3)—21no—
284C2×C3×C3⋊D3—21no—
285C2×C3×C3⋊D3—21no—
286C2×C3×C3⋊D3—21no—
287C2×C3×C3⋊D3—21no—
288C2×C3×C3⋊D3—21no—
289C2×C3×C3⋊D3C2×D412yes—
290C2×C32×D3—21no—
291C2×C32×D3—21no—
292C2×C32×D3—21no—
293C2×C32×D3—21no—
294C2×C32×D3C2×D412yes—
295C2×C32×D3#4112yescomplemented
296D3×C3⋊D3—44no—
297C3×D32—44no—
298C3⋊(C3⋊Dic3)—21no—
299C3×C3⋊Dic3—21no—
300C3×C3⋊Dic3—21no—
301C3×C3⋊Dic3—21no—
302C3×C3⋊Dic3—21no—
303C32×Dic3—21no—
304C32×Dic3—21no—
305C32×Dic3—21no—
306C32×Dic3C2×D412yes—
307C2×C3×#41—91no—
308C22×#67—91no—
309C2×#237—31no—
310C2×D3×D4—91no—
311C2×#235—31no—
312C22×D12—91no—
313C3×#120—91no—
314C3×C4×D4—91no—
315C2×#217—91no—
316#947—91no—
317#946—91no—
318#939—91no—
319#939—91no—
320#939—91no—
321#939—91no—
322#939—181no—
323#938—91no—
324#937—31no—
325#937—31no—
326#937—91no—
327#937—91no—
328#937—91no—
329#937—181no—
330D4×Dic3—31no—
331D4×Dic3—91no—
332#930—91no—
333#930—91no—
334#930—181no—
335#929—91no—
336#929—91no—
337C4×#67—31no—
338C2×(C2×D3)⋊C4—91no—
339C2×(C2×D3)⋊C4—91no—
340#924—91no—
341#894—91no—
342#894—91no—
343#886—91no—
344#885—91no—
345#884—91no—
346#884—91no—
347#883—91no—
348#67⋊C4—91no—
349D3×C22⋊C4—91no—
350D3×C22⋊C4—91no—
351D3×C22⋊C4—91no—
352#878—91no—
353#875—91no—
354C4×D12—91no—
355C23×C32—21no—
356C23×C32—21no—
357C23×C32—21no—
358C23×C32—31no—
359C23×C32—31no—
360C23×C32—41no—
361C23×C32C22×D311yescharacteristic
362C23×C32C22×D311yescharacteristic
363C23×C32C22×D311yescharacteristic
364C22×C3⋊D3—31no—
365C22×C3⋊D3—31no—
366C22×C3⋊D3—31no—
367C22×C3⋊D3—61no—
368C22×C3⋊D3—61no—
369C22×C3⋊D3—61no—
370C22×C3⋊D3—62no—
371C22×C3⋊D3—62no—
372C22×C3⋊D3—121no—
373C22×C3⋊D3—121no—
374C22×C3⋊D3C22×D311yescharacteristic
375C22×C3⋊D3C22×D311yescharacteristic
376C22×C3×D3—21no—
377C22×C3×D3—21no—
378C22×C3×D3—31no—
379C22×C3×D3—31no—
380C22×C3×D3—31no—
381C22×C3×D3—31no—
382C22×C3×D3—61no—
383C22×C3×D3—61no—
384C22×C3×D3—62no—
385C22×C3×D3—62no—
386C22×C3×D3—62no—
387C22×C3×D3—62no—
388C22×C3×D3—121no—
389C22×C3×D3—121no—
390C22×C3×D3C22×D311yescharacteristic
391C22×C3×D3C22×D311yescharacteristic
392C22×C3×D3C22×D311yescharacteristic
393C22×C3×D3C22×D311yescharacteristic
394C2×D32—22no—
395C2×D32—22no—
396C2×D32—41no—
397C2×D32—62no—
398C2×D32—62no—
399C2×D32—62no—
400C2×D32—62no—
401C2×D32—122no—
402C2×D32—122no—
403C2×D32—121no—
404C2×D32—121no—
405C2×D32—122no—
406C32×D4—62no—
407C32×D4—62no—
408C2×C32×C4—31no—
409C2×C32×C4—31no—
410C2×C32×C4—31no—
411C2×C32×C4—31no—
412C2×C32×C4—62no—
413#638—22no—
414#638—41no—
415#638—62no—
416#638—121no—
417#638—121no—
418#638—121no—
419#638—122no—
420#638—122no—
421#638—122no—
422#638—124no—
423C2×C3⋊Dic3—31no—
424C2×C3⋊Dic3—31no—
425C2×C3⋊Dic3—31no—
426C2×C3⋊Dic3—61no—
427C2×C3⋊Dic3—61no—
428C2×C3⋊Dic3—61no—
429C2×C3⋊Dic3—121no—
430C2×C3⋊Dic3—121no—
431C2×C3⋊Dic3C22×D311yescharacteristic
432C2×C3⋊Dic3C22×D311yescharacteristic
433C2×C3⋊Dic3C22×D311yescharacteristic
434C2×C3⋊Dic3C22×D311yescharacteristic
435C4⋊(C3⋊D3)—62no—
436C3×#67—22no—
437C3×#67—22no—
438C3×#67—22no—
439C3×#67—22no—
440C3×#67—34no—
441C3×#67—42no—
442C3×#67—42no—
443C3×#67—62no—
444C3×#67—62no—
445C3×#67—122no—
446C3×#67—121no—
447C3×#67—121no—
448C3×#67—122no—
449C2×C3×Dic3—22no—
450C2×C3×Dic3—22no—
451C2×C3×Dic3—21no—
452C2×C3×Dic3—21no—
453C2×C3×Dic3—21no—
454C2×C3×Dic3—21no—
455C2×C3×Dic3—31no—
456C2×C3×Dic3—31no—
457C2×C3×Dic3—31no—
458C2×C3×Dic3—31no—
459C2×C3×Dic3—31no—
460C2×C3×Dic3—31no—
461C2×C3×Dic3—31no—
462C2×C3×Dic3—31no—
463C2×C3×Dic3—42no—
464C2×C3×Dic3—61no—
465C2×C3×Dic3—61no—
466C2×C3×Dic3—61no—
467C2×C3×Dic3—61no—
468C2×C3×Dic3—62no—
469C2×C3×Dic3—62no—
470C2×C3×Dic3C22×D311yescharacteristic
471C2×C3×Dic3C22×D311yescharacteristic
472C2×C3×Dic3C22×D311yescharacteristic
473C2×C3×Dic3C22×D311yescharacteristic
474C2×C3×Dic3C22×D311yescharacteristic
475C2×C3×Dic3C22×D311yescharacteristic
476C2×C3×Dic3C22×D311yescharacteristic
477C2×C3×Dic3C22×D311yescharacteristic
478C3×D12—34no—
479C3×C4×D3—62no—
480C3×C4×D3—62no—
481C3×C4×D3—62no—
482C3×C4×D3—62no—
483C3×Dic6—62no—
484C3×Dic6—62no—
485#627—22no—
486#626—62no—
487#626—62no—
488#626—62no—
489#626—62no—
490#626—62no—
491#626—62no—
492#626—122no—
493#626—122no—
494#626#6714yescomplemented
495#625—62no—
496#624—22no—
497#624—121no—
498D3×Dic3—22no—
499D3×Dic3—22no—
500D3×Dic3—121no—
501D3×Dic3—121no—
502D3×Dic3—121no—
503D3×Dic3—121no—
504D3×Dic3—122no—
505#546—271noSylow
506C2×C33—41no—
507C2×C33C22×D411yescharacteristic
508C2×C33C2×#4111yescharacteristic
509C2×C33H(5,𝔽2)11yescharacteristic
510C3⋊(C3⋊D3)—41no—
511C3×C3⋊D3—22no—
512C3×C3⋊D3—41no—
513C32×D3—22no—
514C32×D3—22no—
515C24×C3—91no—
516C23×D3—31no—
517C23×D3—31no—
518C23×D3—91no—
519C23×D3—91no—
520C23×D3—91no—
521C23×D3—181no—
522C3×#41—184no—
523C2×C3×Q8—91no—
524C2×C3×D4—31no—
525C2×C3×D4—31no—
526C2×C3×D4—31no—
527C2×C3×D4—31no—
528C2×C3×D4—61no—
529C2×C3×D4—61no—
530C2×C3×D4—91no—
531C2×C3×D4—91no—
532C2×C3×D4—91no—
533C22×C3×C4—31no—
534C22×C3×C4—31no—
535C22×C3×C4—61no—
536C22×C3×C4—91no—
537C22×C3×C4—91no—
538C22×C3×C4—91no—
539C2×#67—31no—
540C2×#67—31no—
541C2×#67—31no—
542C2×#67—31no—
543C2×#67—31no—
544C2×#67—61no—
545C2×#67—61no—
546C2×#67—91no—
547C2×#67—91no—
548C2×#67—91no—
549C2×#67—91no—
550C2×#67—91no—
551C2×#67—91no—
552C2×#67—91no—
553C2×#67—91no—
554C2×#67—181no—
555C2×#67—181no—
556C2×#67—181no—
557C2×#67—181no—
558C2×#67—184no—
559C2×#67—361no—
560C2×#67D3211yescharacteristic
561C2×#67D3211yescharacteristic, complemented
562C22×Dic3—31no—
563C22×Dic3—31no—
564C22×Dic3—91no—
565C22×Dic3—91no—
566C22×Dic3—91no—
567C22×Dic3—181no—
568C22×Dic3D3211yescharacteristic, complemented
569#237—64no—
570D3×D4—184no—
571#235—64no—
572C2×D12—31no—
573C2×D12—91no—
574C2×D12—91no—
575C2×D12—91no—
576C2×D12—91no—
577C2×D12—181no—
578C2×D12—184no—
579C2×C4×D3—31no—
580C2×C4×D3—31no—
581C2×C4×D3—31no—
582C2×C4×D3—31no—
583C2×C4×D3—91no—
584C2×C4×D3—91no—
585C2×C4×D3—91no—
586C2×Dic6—31no—
587C2×Dic6—31no—
588C3×C4⋊C4—91no—
589C3×C22⋊C4—91no—
590C3×C22⋊C4—91no—
591C3×C22⋊C4—91no—
592C3×C22⋊C4—91no—
593C3×C22⋊C4—91no—
594C3×C42—91no—
595#217—31no—
596#217—31no—
597#217—31no—
598#217—31no—
599#217—31no—
600#217—61no—
601#217—91no—
602#217—91no—
603#217—91no—
604#217—91no—
605#217—91no—
606#217—181no—
607(C2×D3)⋊C4—31no—
608(C2×D3)⋊C4—31no—
609(C2×D3)⋊C4—31no—
610(C2×D3)⋊C4—31no—
611(C2×D3)⋊C4—31no—
612(C2×D3)⋊C4—91no—
613(C2×D3)⋊C4—91no—
614(C2×D3)⋊C4—91no—
615(C2×D3)⋊C4—91no—
616(C2×D3)⋊C4—91no—
617(C2×D3)⋊C4—91no—
618(C2×D3)⋊C4—91no—
619(C2×D3)⋊C4—91no—
620(C2×D3)⋊C4—91no—
621(C2×D3)⋊C4—91no—
622(C2×D3)⋊C4—91no—
623(C2×D3)⋊C4—91no—
624(C2×D3)⋊C4—91no—
625(C2×D3)⋊C4—91no—
626(C2×D3)⋊C4—91no—
627(C2×D3)⋊C4—91no—
628(C2×D3)⋊C4—181no—
629(C2×D3)⋊C4—181no—
630(C2×D3)⋊C4—181no—
631(C2×D3)⋊C4—181no—
632(C2×D3)⋊C4—181no—
633C4⋊Dic3—31no—
634C4⋊Dic3—91no—
635C4⋊Dic3—91no—
636C4⋊Dic3—91no—
637C4⋊Dic3—181no—
638Dic3⋊C4—31no—
639Dic3⋊C4—91no—
640Dic3⋊C4—91no—
641Dic3⋊C4—91no—
642Dic3⋊C4—91no—
643Dic3⋊C4—91no—
644Dic3⋊C4—91no—
645Dic3⋊C4—181no—
646C4×Dic3—31no—
647C4×Dic3—31no—
648C22×C32—21no—
649C22×C32—22no—
650C22×C32—21no—
651C22×C32—21no—
652C22×C32—21no—
653C22×C32—21no—
654C22×C32—21no—
655C22×C32—21no—
656C22×C32—21no—
657C22×C32—21no—
658C22×C32—21no—
659C22×C32—21no—
660C22×C32—21no—
661C22×C32—32no—
662C22×C32—32no—
663C22×C32—41no—
664C22×C32—41no—
665C22×C32—41no—
666C22×C32—42no—
667C22×C32—41no—
668C22×C32—41no—
669C22×C32—41no—
670C22×C32—41no—
671C22×C32—41no—
672C22×C32—41no—
673C22×C32—61no—
674C22×C32—61no—
675C22×C32—61no—
676C22×C32—61no—
677C22×C32—81no—
678C22×C32—81no—
679C22×C32C23×D311yescharacteristic
680C22×C32C23×D311yescharacteristic
681C22×C32C23×D311yescharacteristic
682C2×C3⋊D3—21no—
683C2×C3⋊D3—21no—
684C2×C3⋊D3—21no—
685C2×C3⋊D3—21no—
686C2×C3⋊D3—21no—
687C2×C3⋊D3—61no—
688C2×C3⋊D3—62no—
689C2×C3⋊D3—61no—
690C2×C3⋊D3—61no—
691C2×C3⋊D3—61no—
692C2×C3⋊D3—61no—
693C2×C3⋊D3—61no—
694C2×C3⋊D3—61no—
695C2×C3⋊D3—61no—
696C2×C3⋊D3—61no—
697C2×C3⋊D3—121no—
698C2×C3⋊D3—121no—
699C2×C3⋊D3—122no—
700C2×C3⋊D3—121no—
701C2×C3⋊D3—121no—
702C2×C3⋊D3—121no—
703C2×C3⋊D3—121no—
704C2×C3⋊D3—121no—
705C2×C3⋊D3—121no—
706C2×C3⋊D3—124no—
707C2×C3⋊D3—241no—
708C2×C3⋊D3—241no—
709C2×C3⋊D3C2×#6712yes—
710C2×C3×D3—21no—
711C2×C3×D3—21no—
712C2×C3×D3—21no—
713C2×C3×D3—21no—
714C2×C3×D3—21no—
715C2×C3×D3—21no—
716C2×C3×D3—21no—
717C2×C3×D3—21no—
718C2×C3×D3—22no—
719C2×C3×D3—22no—
720C2×C3×D3—32no—
721C2×C3×D3—32no—
722C2×C3×D3—41no—
723C2×C3×D3—41no—
724C2×C3×D3—41no—
725C2×C3×D3—41no—
726C2×C3×D3—62no—
727C2×C3×D3—61no—
728C2×C3×D3—61no—
729C2×C3×D3—61no—
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—121no—
738C2×C3×D3—121no—
739C2×C3×D3—121no—
740C2×C3×D3—121no—
741C2×C3×D3—121no—
742C2×C3×D3—124no—
743C2×C3×D3—124no—
744C2×C3×D3#23512yescomplemented
745C2×C3×D3D3×D412yes—
746C2×C3×D3#23712yescomplemented
747C2×C3×D3C2×#6712yes—
748D32—44no—
749D32—124no—
750D32—124no—
751D32—128no—
752C32×C4—32no—
753C32×C4—61no—
754C32×C4—61no—
755C32×C4—61no—
756C3⋊Dic3—21no—
757C3⋊Dic3—21no—
758C3⋊Dic3—21no—
759C3⋊Dic3—21no—
760C3⋊Dic3—61no—
761C3⋊Dic3—62no—
762C3⋊Dic3—61no—
763C3⋊Dic3—61no—
764C3⋊Dic3—121no—
765C3⋊Dic3—121no—
766C3⋊Dic3—122no—
767C3×Dic3—21no—
768C3×Dic3—21no—
769C3×Dic3—21no—
770C3×Dic3—21no—
771C3×Dic3—21no—
772C3×Dic3—21no—
773C3×Dic3—22no—
774C3×Dic3—41no—
775C3×Dic3—41no—
776C3×Dic3—41no—
777C3×Dic3—61no—
778C3×Dic3—61no—
779C3×Dic3—61no—
780C3×Dic3—61no—
781C3×Dic3—61no—
782C3×Dic3—61no—
783C3×Dic3—61no—
784C3×Dic3—61no—
785C3×Dic3—121no—
786C3×Dic3—121no—
787C3×Dic3—121no—
788C3×Dic3—121no—
789C3×Dic3D3×D412yes—
790C3×Dic3C2×#6712yes—
791C2×#41—91no—
792C22×D4—271no—
793#124—271no—
794#123—271no—
795#123—271no—
796C22⋊Q8—271no—
797#121—271no—
798#121—271no—
799#121—271no—
800#120—91no—
801#120—271no—
802C4×D4—91no—
803C4×D4—271no—
804C2×C22⋊C4—271no—
805C2×C22⋊C4—271no—
806C33#54611yescharacteristic, complemented, Sylow
807C23×C3—21no—
808C23×C3—21no—
809C23×C3—21no—
810C23×C3—31no—
811C23×C3—31no—
812C23×C3—31no—
813C23×C3—31no—
814C23×C3—41no—
815C23×C3—61no—
816C23×C3—61no—
817C23×C3—91no—
818C23×C3—91no—
819C23×C3—182no—
820C23×C3—182no—
821C23×C3—361no—
822C23×C3C2×D3211yescharacteristic
823C23×C3C2×D3211yescharacteristic
824C23×C3C2×D3211yescharacteristic
825C22×D3—31no—
826C22×D3—31no—
827C22×D3—31no—
828C22×D3—31no—
829C22×D3—61no—
830C22×D3—61no—
831C22×D3—62no—
832C22×D3—62no—
833C22×D3—62no—
834C22×D3—62no—
835C22×D3—91no—
836C22×D3—91no—
837C22×D3—91no—
838C22×D3—121no—
839C22×D3—121no—
840C22×D3—181no—
841C22×D3—181no—
842C22×D3—181no—
843C22×D3—182no—
844C22×D3—182no—
845C22×D3—182no—
846C22×D3—182no—
847C22×D3—182no—
848C22×D3—182no—
849C22×D3—361no—
850C22×D3—362no—
851C22×D3—362no—
852C22×D3—361no—
853C22×D3—361no—
854C22×D3—361no—
855C22×D3—362no—
856C22×D3C2×D3211yescharacteristic
857C22×D3C2×D3211yescharacteristic
858C3×Q8—182no—
859C3×D4—62no—
860C3×D4—62no—
861C3×D4—62no—
862C3×D4—62no—
863C3×D4—94no—
864C3×D4—122no—
865C3×D4—122no—
866C3×D4—182no—
867C3×D4—361no—
868C2×C3×C4—31no—
869C2×C3×C4—31no—
870C2×C3×C4—31no—
871C2×C3×C4—31no—
872C2×C3×C4—31no—
873C2×C3×C4—31no—
874C2×C3×C4—31no—
875C2×C3×C4—31no—
876C2×C3×C4—61no—
877C2×C3×C4—61no—
878C2×C3×C4—61no—
879C2×C3×C4—61no—
880C2×C3×C4—62no—
881C2×C3×C4—62no—
882C2×C3×C4—91no—
883C2×C3×C4—91no—
884C2×C3×C4—91no—
885C2×C3×C4—91no—
886C2×C3×C4—122no—
887C2×C3×C4—182no—
888C2×C3×C4—182no—
889C2×C3×C4—182no—
890#67—22no—
891#67—22no—
892#67—34no—
893#67—62no—
894#67—62no—
895#67—122no—
896#67—121no—
897#67—121no—
898#67—122no—
899#67—182no—
900#67—182no—
901#67—182no—
902#67—182no—
903#67—182no—
904#67—362no—
905#67—361no—
906#67—361no—
907#67—361no—
908#67—362no—
909#67—362no—
910#67—362no—
911#67—364no—
912C2×Dic3—22no—
913C2×Dic3—31no—
914C2×Dic3—31no—
915C2×Dic3—31no—
916C2×Dic3—31no—
917C2×Dic3—31no—
918C2×Dic3—31no—
919C2×Dic3—31no—
920C2×Dic3—31no—
921C2×Dic3—61no—
922C2×Dic3—61no—
923C2×Dic3—61no—
924C2×Dic3—61no—
925C2×Dic3—62no—
926C2×Dic3—62no—
927C2×Dic3—91no—
928C2×Dic3—91no—
929C2×Dic3—91no—
930C2×Dic3—181no—
931C2×Dic3—181no—
932C2×Dic3—181no—
933C2×Dic3—361no—
934C2×Dic3—361no—
935C2×Dic3—361no—
936C2×Dic3—361no—
937C2×Dic3—362no—
938C2×Dic3C2×D3211yescharacteristic
939C2×Dic3C2×D3211yescharacteristic
940C2×Dic3C2×D3211yescharacteristic
941C2×Dic3C2×D3211yescharacteristic
942D12—34no—
943D12—182no—
944D12—182no—
945D12—182no—
946D12—182no—
947D12—362no—
948C4×D3—62no—
949C4×D3—62no—
950C4×D3—62no—
951C4×D3—62no—
952C4×D3—361no—
953C4×D3—361no—
954C4×D3—361no—
955Dic6—62no—
956Dic6—62no—
957C2×C32—21no—
958C2×C32—21no—
959C2×C32—21no—
960C2×C32—21no—
961C2×C32—21no—
962C2×C32—21no—
963C2×C32—21no—
964C2×C32—21no—
965C2×C32—21no—
966C2×C32—41no—
967C2×C32—41no—
968C2×C32—41no—
969C2×C32—41no—
970C2×C32—42no—
971C2×C32—41no—
972C2×C32—41no—
973C2×C32—62no—
974C2×C32—62no—
975C2×C32—81no—
976C2×C32—81no—
977C2×C32—82no—
978C2×C32C2×#23511yescharacteristic
979C2×C32C2×D3×D411yescharacteristic
980C2×C32C2×D3×D411yescharacteristic
981C2×C32C2×#23711yescharacteristic
982C2×C32#100411yescharacteristic
983C2×C32D3×#4111yescharacteristic
984C2×C32#100911yescharacteristic
985C2×C32#100911yescharacteristic
986C2×C32C22×#6711yescharacteristic
987C3⋊D3—22no—
988C3⋊D3—41no—
989C3⋊D3—121no—
990C3⋊D3—122no—
991C3⋊D3—121no—
992C3⋊D3—121no—
993C3⋊D3—241no—
994C3⋊D3—241no—
995C3⋊D3—242no—
996C3×D3—22no—
997C3×D3—22no—
998C3×D3—22no—
999C3×D3—22no—
1000C3×D3—42no—
1001C3×D3—42no—
1002C3×D3—62no—
1003C3×D3—62no—
1004C3×D3—122no—
1005C3×D3—121no—
1006C3×D3—121no—
1007C3×D3—241no—
1008C24—91no—
1009C24—271no—
1010#41—184no—
1011C2×Q8—91no—
1012C2×D4—31no—
1013C2×D4—31no—
1014C2×D4—91no—
1015C2×D4—91no—
1016C2×D4—91no—
1017C2×D4—271no—
1018C2×D4—271no—
1019C2×D4—271no—
1020C2×D4—271no—
1021C2×D4—544no—
1022C22×C4—31no—
1023C22×C4—91no—
1024C22×C4—91no—
1025C22×C4—91no—
1026C22×C4—271no—
1027C22×C4—271no—
1028C4⋊C4—91no—
1029C4⋊C4—271no—
1030C4⋊C4—271no—
1031C4⋊C4—271no—
1032C22⋊C4—91no—
1033C22⋊C4—91no—
1034C22⋊C4—91no—
1035C22⋊C4—91no—
1036C22⋊C4—91no—
1037C22⋊C4—271no—
1038C22⋊C4—271no—
1039C22⋊C4—271no—
1040C22⋊C4—271no—
1041C22⋊C4—271no—
1042C22⋊C4—271no—
1043C22⋊C4—271no—
1044C42—91no—
1045C22×C3—22no—
1046C22×C3—21no—
1047C22×C3—21no—
1048C22×C3—21no—
1049C22×C3—21no—
1050C22×C3—21no—
1051C22×C3—21no—
1052C22×C3—21no—
1053C22×C3—21no—
1054C22×C3—21no—
1055C22×C3—21no—
1056C22×C3—21no—
1057C22×C3—21no—
1058C22×C3—32no—
1059C22×C3—32no—
1060C22×C3—32no—
1061C22×C3—32no—
1062C22×C3—41no—
1063C22×C3—41no—
1064C22×C3—41no—
1065C22×C3—41no—
1066C22×C3—41no—
1067C22×C3—41no—
1068C22×C3—41no—
1069C22×C3—41no—
1070C22×C3—42no—
1071C22×C3—41no—
1072C22×C3—62no—
1073C22×C3—62no—
1074C22×C3—61no—
1075C22×C3—61no—
1076C22×C3—61no—
1077C22×C3—61no—
1078C22×C3—61no—
1079C22×C3—61no—
1080C22×C3—61no—
1081C22×C3—61no—
1082C22×C3—81no—
1083C22×C3—81no—
1084C22×C3—92no—
1085C22×C3—121no—
1086C22×C3—121no—
1087C22×C3—121no—
1088C22×C3—121no—
1089C22×C3—181no—
1090C22×C3—181no—
1091C22×C3—181no—
1092C22×C3—181no—
1093C22×C3—181no—
1094C22×C3—364no—
1095C22×C3C22×D3211yescharacteristic
1096C22×C3C22×D3211yescharacteristic
1097C22×C3C22×D3211yescharacteristic
1098C2×D3—21no—
1099C2×D3—21no—
1100C2×D3—21no—
1101C2×D3—21no—
1102C2×D3—32no—
1103C2×D3—32no—
1104C2×D3—62no—
1105C2×D3—61no—
1106C2×D3—61no—
1107C2×D3—61no—
1108C2×D3—61no—
1109C2×D3—61no—
1110C2×D3—61no—
1111C2×D3—61no—
1112C2×D3—61no—
1113C2×D3—61no—
1114C2×D3—61no—
1115C2×D3—121no—
1116C2×D3—121no—
1117C2×D3—121no—
1118C2×D3—121no—
1119C2×D3—121no—
1120C2×D3—124no—
1121C2×D3—124no—
1122C2×D3—182no—
1123C2×D3—181no—
1124C2×D3—181no—
1125C2×D3—181no—
1126C2×D3—181no—
1127C2×D3—181no—
1128C2×D3—181no—
1129C2×D3—181no—
1130C2×D3—181no—
1131C2×D3—181no—
1132C2×D3—361no—
1133C2×D3—361no—
1134C2×D3—361no—
1135C2×D3—361no—
1136C2×D3—361no—
1137C2×D3—361no—
1138C2×D3—361no—
1139C2×D3—361no—
1140C2×D3—362no—
1141C2×D3—364no—
1142C2×D3—364no—
1143C2×D3—364no—
1144C2×D3—368no—
1145C2×D3—721no—
1146C2×D3—721no—
1147C2×D3#380412yescomplemented
1148C2×D3D3×#6712yes—
1149C3×C4—32no—
1150C3×C4—32no—
1151C3×C4—62no—
1152C3×C4—61no—
1153C3×C4—61no—
1154C3×C4—61no—
1155C3×C4—61no—
1156C3×C4—61no—
1157C3×C4—61no—
1158C3×C4—121no—
1159C3×C4—121no—
1160C3×C4—121no—
1161C3×C4—181no—
1162C3×C4—181no—
1163C3×C4—181no—
1164C3×C4—181no—
1165Dic3—21no—
1166Dic3—21no—
1167Dic3—21no—
1168Dic3—61no—
1169Dic3—61no—
1170Dic3—61no—
1171Dic3—61no—
1172Dic3—61no—
1173Dic3—61no—
1174Dic3—61no—
1175Dic3—61no—
1176Dic3—121no—
1177Dic3—121no—
1178Dic3—121no—
1179Dic3—121no—
1180Dic3—182no—
1181Dic3—181no—
1182Dic3—181no—
1183Dic3—181no—
1184Dic3—361no—
1185Dic3—361no—
1186Dic3—362no—
1187Dic3D3×#6712yes—
1188C32—21no—
1189C32—21no—
1190C32—21no—
1191C32—41no—
1192C32#555011yescharacteristic, complemented
1193C32#559111yescharacteristic, complemented
1194C32#582911yescharacteristic, complemented
1195C23—31no—
1196C23—31no—
1197C23—91no—
1198C23—91no—
1199C23—182no—
1200C23—182no—
1201C23—271no—
1202C23—361no—
1203C23—542no—
1204C23—542no—
1205C23—1081no—
1206C23D3311yescharacteristic
1207Q8—182no—
1208D4—62no—
1209D4—62no—
1210D4—94no—
1211D4—182no—
1212D4—361no—
1213D4—542no—
1214D4—542no—
1215D4—542no—
1216D4—1081no—
1217C2×C4—31no—
1218C2×C4—31no—
1219C2×C4—31no—
1220C2×C4—31no—
1221C2×C4—62no—
1222C2×C4—91no—
1223C2×C4—91no—
1224C2×C4—91no—
1225C2×C4—91no—
1226C2×C4—182no—
1227C2×C4—182no—
1228C2×C4—182no—
1229C2×C4—271no—
1230C2×C4—1081no—
1231C2×C4—1081no—
1232C2×C3—21no—
1233C2×C3—21no—
1234C2×C3—21no—
1235C2×C3—21no—
1236C2×C3—21no—
1237C2×C3—21no—
1238C2×C3—21no—
1239C2×C3—21no—
1240C2×C3—21no—
1241C2×C3—42no—
1242C2×C3—41no—
1243C2×C3—41no—
1244C2×C3—41no—
1245C2×C3—41no—
1246C2×C3—41no—
1247C2×C3—41no—
1248C2×C3—62no—
1249C2×C3—62no—
1250C2×C3—62no—
1251C2×C3—62no—
1252C2×C3—81no—
1253C2×C3—81no—
1254C2×C3—82no—
1255C2×C3—122no—
1256C2×C3—122no—
1257C2×C3—182no—
1258C2×C3—361no—
1259C2×C3D3×#23511yescharacteristic
1260C2×C3#6430811yescharacteristic
1261C2×C3D32×D411yescharacteristic
1262C2×C3D3×#23711yescharacteristic
1263C2×C3#6431411yescharacteristic
1264C2×C3#6431411yescharacteristic
1265C2×C3C2×#380411yescharacteristic
1266C2×C3C2×D3×#6711yescharacteristic
1267C2×C3C2×D3×#6711yescharacteristic
1268D3—22no—
1269D3—22no—
1270D3—62no—
1271D3—62no—
1272D3—122no—
1273D3—121no—
1274D3—121no—
1275D3—241no—
1276D3—362no—
1277D3—361no—
1278D3—361no—
1279D3—361no—
1280D3—721no—
1281D3—721no—
1282D3—722no—
1283C22—21no—
1284C22—21no—
1285C22—21no—
1286C22—32no—
1287C22—32no—
1288C22—61no—
1289C22—61no—
1290C22—61no—
1291C22—61no—
1292C22—92no—
1293C22—181no—
1294C22—181no—
1295C22—181no—
1296C22—181no—
1297C22—181no—
1298C22—364no—
1299C22—541no—
1300C22—541no—
1301C22—541no—
1302C22—1084no—
1303C22C2×D3311yescharacteristic
1304C4—32no—
1305C4—61no—
1306C4—61no—
1307C4—61no—
1308C4—181no—
1309C4—181no—
1310C4—181no—
1311C4—181no—
1312C4—541no—
1313C3—21no—
1314C3—21no—
1315C3—21no—
1316C3—41no—
1317C3#1059506711yescharacteristic, complemented
1318C3#1059513511yescharacteristic, complemented
1319C3#1059530411yescharacteristic, complemented
1320C2—41no—
1321C2—62no—
1322C2—62no—
1323C2—182no—
1324C2—361no—
1325C2—1081no—
1326C2D3×#380411yescharacteristic
1327C2#1172442011yescharacteristic
1328C2D32×#6711yescharacteristic
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×#3804C2semidirect
2. C2×D3×#626C2semidirect
3. #11723725C2semidirect
4. #11723643C2semidirect
5. #11723632C2semidirect
6. #11723616C2semidirect
7. C3×#63983C2semidirect
8. C3×Dic3×#67C2semidirect
9. #11723003C2semidirect
10. #11722995C2semidirect
11. #11722987C2semidirect
12. #11722969C2semidirect
13. #11722928C2semidirect
14. #11722904C2semidirect
15. D3×(C2×D3)⋊Dic3C2semidirect
21. C2×#6312C22semidirect
22. C2×C3×#638C22semidirect
23. C2×C3×#638C22semidirect
25. C2×C32×#67C22semidirect
26. C22×C32×Dic3C22semidirect
28. C2×#6294C22semidirect
31. C2×D3×C3⋊Dic3C22semidirect
32. C2×C3×#627C22semidirect
34. C2×C3×#624C22semidirect
37. C2×C3×D3×Dic3C22semidirect
39. C3×#3757C22semidirect
40. #88815C22semidirect
41. #88814C22semidirect
42. #88806C22semidirect
43. Dic3⋊(C3⋊Dic3)C22semidirect
44. #88804C22semidirect
45. #88804C22semidirect
46. #88804C22semidirect
47. #88803C22semidirect
48. #88803C22semidirect
50. C3×Dic3⋊Dic3C22semidirect
51. C3×#3722C22semidirect
54. C3×(C2×D3)⋊Dic3C22semidirect
55. C3×Dic32C22semidirect
60. C2×#3804D3semidirect
72. #63983D3semidirect
78. Dic3×#67D3semidirect
137. C3×#626D4semidirect
162. C2×#638C2×D3semidirect
163. C2×#638C2×D3semidirect
177. C2×C3×#67C2×D3semidirect
178. C2×C3×#67C2×D3semidirect
182. C22×C3×Dic3C2×D3semidirect
183. C22×C3×Dic3C2×D3semidirect
194. C2×#627C2×D3semidirect
207. C2×#624C2×D3semidirect
215. C2×D3×Dic3C2×D3semidirect
218. #3757C2×D3semidirect
250. Dic3⋊Dic3C2×D3semidirect
261. #3722C2×D3semidirect
275. (C2×D3)⋊Dic3C2×D3semidirect
276. Dic32C2×D3semidirect
295. C2×C32×D3#41semidirect
494. #626#67semidirect
561. C2×#67D32semidirect
568. C22×Dic3D32semidirect
744. C2×C3×D3#235semidirect
746. C2×C3×D3#237semidirect
806. C33#546semidirect
1147. C2×D3#3804semidirect
1192. C32#5550semidirect
1193. C32#5591semidirect
1194. C32#5829semidirect
1317. C3#10595067semidirect
1318. C3#10595135semidirect
1319. C3#10595304semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#38042
C2×D3×#6262
#117237252
#117236432
#117236322
#117236162
C3×#639832
C3×Dic3×#672
#117230032
#117229952
#117229872
#117229692
#117229282
#117229042
D3×(C2×D3)⋊Dic32
#105953043
#105951353
#105950673