Finite Group Databasebeta

← #13172720

Subgroups — #13172720

Order 1728.

1778 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89031C211yesmaximal, characteristic, complemented
2C2×D3×#626C211yesmaximal, characteristic, complemented
3#11723725C211yesmaximal, characteristic, complemented
4#11723643C211yesmaximal, characteristic, complemented
5#11723599C211yesmaximal, characteristic, complemented
6C3×#63983C211yesmaximal, characteristic, complemented
7C3×#63978C211yesmaximal, characteristic, complemented
8C3×Dic3×#67C211yesmaximal, characteristic, complemented
9#11723002C211yesmaximal, characteristic, complemented
10#11722997C211yesmaximal, characteristic, complemented
11#11722996C211yesmaximal, characteristic, complemented
12#11722971C211yesmaximal, characteristic, complemented
13#11722937C211yesmaximal, characteristic, complemented
14#11722906C211yesmaximal, characteristic, complemented
15#11722902C211yesmaximal, characteristic, complemented
16#10595294—31nomaximal
17#10595135—31nomaximal
18#10595078—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×#6293C2211yescharacteristic, complemented
30C2×#6292C2211yescharacteristic
31C2×#6291C2211yescharacteristic
32C2×#6289C2211yescharacteristic, complemented
33C2×#6289C2211yescharacteristic, complemented
34#89031—24no—
35C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
36C2×C3×#626C2211yescharacteristic
37C2×C3×D3×Dic3C2211yescharacteristic
38D3×#626—24no—
39C3×#3757C2211yescharacteristic, complemented
40#88815C2211yescharacteristic, complemented
41#88814C2211yescharacteristic, complemented
42Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
43#88804C2211yescharacteristic, complemented
44#88803C2211yescharacteristic, complemented
45(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
46(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
47C3×Dic3⋊Dic3C2211yescharacteristic, complemented
48C3×Dic3⋊Dic3C2211yescharacteristic, complemented
49C3×#3722C2211yescharacteristic, complemented
50C3×#3722C2211yescharacteristic, complemented
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
54C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
55C3×Dic32C2211yescharacteristic, complemented
56C2×#3828—31no—
57C2×D3×#67—31no—
58C22×#626—31no—
59C2×#3804—31no—
60C2×#3804—31no—
61C2×#3804—61no—
62C2×D3×D12—31no—
63#64147—31no—
64#64146—31no—
65C3×#939—31no—
66C3×#937—31no—
67C3×#937—31no—
68C3×D4×Dic3—31no—
69C3×#930—31no—
70C3×C4×#67—31no—
71#63983—31no—
72#63983—31no—
73#63983—61no—
74#63983D311yescharacteristic, complemented
75#63978D311yescharacteristic, complemented
76#63975—31no—
77#63974—31no—
78Dic3×#67D311yescharacteristic, complemented
79#63971—31no—
80#63970—31no—
81D3×#217—31no—
82D3×#217—31no—
83#63964—31no—
84#63959—31no—
85#63958—31no—
86#63958—31no—
87#63958—31no—
88#63958—61no—
89#63921—31no—
90#63921—31no—
91#63921—31no—
92#63894—31no—
93#63893—31no—
94#63891—31no—
95#63890—31no—
96#63881—31no—
97#63880—31no—
98#63860—31no—
99#63857—31no—
100#63854—31no—
101#63853—31no—
102#63853—31no—
103#63852—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—22no—
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—41no—
126C2×C32×Dic3—22no—
127C2×C32×Dic3C2311yescharacteristic
128C2×C32×Dic3C2311yescharacteristic
129C2×C32×Dic3C2311yescharacteristic
130C2×C32×Dic3C2311yescharacteristic
131#6295—22no—
132#6294—41no—
133#6293—22no—
134#6292D414yescomplemented
135#6291—22no—
136#6289—22no—
137#6289—41no—
138Dic3×C3⋊D3—22no—
139C3×#626—22no—
140C3×D3×Dic3—22no—
141#5612—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
164#3828—64no—
165C2×C4⋊(C3⋊D3)—31no—
166C2×C4×C3⋊D3—31no—
167C2×C4×C3⋊D3—31no—
168C2×C4×C3⋊D3—31no—
169C2×#634—31no—
170C2×C3×#67—21no—
171C2×C3×#67—21no—
172C2×C3×#67—31no—
173C2×C3×#67—31no—
174C2×C3×#67—31no—
175C2×C3×#67—31no—
176C2×C3×#67—31no—
177C2×C3×#67—61no—
178C2×C3×#67—61no—
179C2×C3×#67C2×D311yescharacteristic
180C2×C3×#67C2×D311yescharacteristic
181C2×C3×#67C2×D311yescharacteristic, complemented
182C2×C3×#67C2×D311yescharacteristic, complemented
183C22×C3×Dic3—21no—
184C22×C3×Dic3—31no—
185C22×C3×Dic3C2×D311yescharacteristic, complemented
186C22×C3×Dic3C2×D311yescharacteristic, complemented
187C2×C3×D12—31no—
188C2×C3×C4×D3—31no—
189D3×#67—64no—
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—64no—
200C2×#626—61no—
201C2×#626—61no—
202C2×#626C2×D311yescharacteristic
203C2×#625—31no—
204C2×#624—31no—
205C2×#624—31no—
206C2×#624—31no—
207C2×#624—31no—
208C2×#624—31no—
209C2×#624—61no—
210C2×#624—61no—
211#3804—64no—
212#3804—64no—
213#3804—68no—
214C2×D3×Dic3—31no—
215C2×D3×Dic3—31no—
216C2×D3×Dic3—31no—
217C2×D3×Dic3—31no—
218C2×D3×Dic3—61no—
219C2×D3×Dic3C2×D311yescharacteristic
220D3×D12—64no—
221#3757—31no—
222#3757—31no—
223#3757C2×D311yescharacteristic, complemented
224#3752—31no—
225#3752—31no—
226C4⋊(C3⋊Dic3)—31no—
227C3×#217—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×C4⋊Dic3—31no—
243C3×C4⋊Dic3—31no—
244C3×Dic3⋊C4—31no—
245C3×Dic3⋊C4—31no—
246C3×C4×Dic3—31no—
247C3×C4×Dic3—31no—
248#3724—31no—
249Dic3⋊Dic3—31no—
250Dic3⋊Dic3—31no—
251Dic3⋊Dic3—31no—
252Dic3⋊Dic3—31no—
253Dic3⋊Dic3—61no—
254Dic3⋊Dic3C2×D311yescharacteristic, complemented
255Dic3⋊Dic3C2×D311yescharacteristic, complemented
256#3722—31no—
257#3722—31no—
258#3722—31no—
259#3722—61no—
260#3722C2×D311yescharacteristic, complemented
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
276(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
277Dic32C2×D311yescharacteristic, complemented
278C22×C33—21no—
279C22×C33—21no—
280C22×C33—21no—
281C22×C33C2411yescharacteristic
282C2×C3⋊(C3⋊D3)—21no—
283C2×C3⋊(C3⋊D3)—21no—
284C2×C3⋊(C3⋊D3)C2×D412yes—
285C2×C3×C3⋊D3—21no—
286C2×C3×C3⋊D3—21no—
287C2×C3×C3⋊D3—21no—
288C2×C3×C3⋊D3—21no—
289C2×C3×C3⋊D3—21no—
290C2×C3×C3⋊D3C2×D412yes—
291C2×C32×D3—21no—
292C2×C32×D3—21no—
293C2×C32×D3—21no—
294C2×C32×D3—21no—
295C2×C32×D3—21no—
296C2×C32×D3#4112yescomplemented
297D3×C3⋊D3—44no—
298C3×D32—44no—
299C3⋊(C3⋊Dic3)—21no—
300C3×C3⋊Dic3—21no—
301C3×C3⋊Dic3—21no—
302C3×C3⋊Dic3—21no—
303C3×C3⋊Dic3—21no—
304C32×Dic3—21no—
305C32×Dic3—21no—
306C32×Dic3—21no—
307C32×Dic3C2×D412yes—
308C22×#67—91no—
309C2×#237—91no—
310C2×D3×D4—91no—
311C2×#235—91no—
312C2×#235—91no—
313C2×#235—181no—
314C22×D12—91no—
315C3×#121—91no—
316C3×#120—91no—
317C3×C4×D4—91no—
318C2×#217—91no—
319#939—31no—
320#939—91no—
321#938—91no—
322#938—91no—
323#938—91no—
324#938—181no—
325#937—31no—
326#937—31no—
327#937—91no—
328#937—91no—
329#937—91no—
330#937—181no—
331#936—91no—
332D4×Dic3—31no—
333#930—31no—
334C4×#67—31no—
335#924—91no—
336#897—91no—
337#894—91no—
338#894—91no—
339#893—91no—
340#886—91no—
341#885—91no—
342#884—91no—
343#884—91no—
344#883—91no—
345#883—91no—
346#883—91no—
347#67⋊C4—91no—
348D3×C22⋊C4—91no—
349D3×C22⋊C4—91no—
350D3×C22⋊C4—91no—
351D3×C22⋊C4—91no—
352D3×C22⋊C4—91no—
353#878—91no—
354#875—91no—
355C4×D12—91no—
356C23×C32—21no—
357C23×C32—21no—
358C23×C32—21no—
359C23×C32—31no—
360C23×C32—31no—
361C23×C32—41no—
362C23×C32C22×D311yescharacteristic
363C23×C32C22×D311yescharacteristic
364C23×C32C22×D311yescharacteristic
365C22×C3⋊D3—31no—
366C22×C3⋊D3—31no—
367C22×C3⋊D3—31no—
368C22×C3⋊D3—61no—
369C22×C3⋊D3—61no—
370C22×C3⋊D3—61no—
371C22×C3⋊D3—62no—
372C22×C3⋊D3—62no—
373C22×C3⋊D3—121no—
374C22×C3⋊D3—121no—
375C22×C3⋊D3C22×D311yescharacteristic
376C22×C3⋊D3C22×D311yescharacteristic
377C22×C3×D3—21no—
378C22×C3×D3—21no—
379C22×C3×D3—31no—
380C22×C3×D3—31no—
381C22×C3×D3—31no—
382C22×C3×D3—31no—
383C22×C3×D3—61no—
384C22×C3×D3—61no—
385C22×C3×D3—62no—
386C22×C3×D3—62no—
387C22×C3×D3—62no—
388C22×C3×D3—62no—
389C22×C3×D3—121no—
390C22×C3×D3—121no—
391C22×C3×D3C22×D311yescharacteristic
392C22×C3×D3C22×D311yescharacteristic
393C22×C3×D3C22×D311yescharacteristic
394C22×C3×D3C22×D311yescharacteristic
395C2×D32—22no—
396C2×D32—22no—
397C2×D32—41no—
398C2×D32—62no—
399C2×D32—62no—
400C2×D32—62no—
401C2×D32—62no—
402C2×D32—122no—
403C2×D32—122no—
404C2×D32—121no—
405C2×D32—121no—
406C2×D32—122no—
407C32×D4—62no—
408C32×D4—121no—
409C2×C32×C4—31no—
410C2×C32×C4—31no—
411C2×C32×C4—31no—
412C2×C32×C4—31no—
413C2×C32×C4—62no—
414#638—22no—
415#638—41no—
416#638—62no—
417#638—62no—
418#638—62no—
419#638—62no—
420#638—64no—
421#638—122no—
422#638—122no—
423#638—124no—
424C2×C3⋊Dic3—31no—
425C2×C3⋊Dic3—31no—
426C2×C3⋊Dic3—31no—
427C2×C3⋊Dic3—61no—
428C2×C3⋊Dic3—61no—
429C2×C3⋊Dic3—61no—
430C2×C3⋊Dic3—121no—
431C2×C3⋊Dic3C22×D311yescharacteristic
432C2×C3⋊Dic3C22×D311yescharacteristic
433C2×C3⋊Dic3C22×D311yescharacteristic
434C2×C3⋊Dic3C22×D311yescharacteristic
435C4⋊(C3⋊D3)—34no—
436C4×C3⋊D3—62no—
437C4×C3⋊D3—62no—
438C4×C3⋊D3—121no—
439#634—62no—
440C3×#67—22no—
441C3×#67—22no—
442C3×#67—42no—
443C3×#67—41no—
444C3×#67—41no—
445C3×#67—42no—
446C3×#67—62no—
447C3×#67—62no—
448C3×#67—64no—
449C3×#67—62no—
450C3×#67—121no—
451C3×#67—121no—
452C3×#67—122no—
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—62no—
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
481C3×D12—62no—
482C3×C4×D3—62no—
483#627—64no—
484#627—62no—
485#627—62no—
486#626—22no—
487#626—34no—
488#626—34no—
489#626—64no—
490#626—62no—
491#626—62no—
492#626—62no—
493#626—62no—
494#626—122no—
495#625—62no—
496#624—62no—
497#624—62no—
498#624—64no—
499#624—121no—
500#624—121no—
501#624—122no—
502#624—121no—
503D3×Dic3—22no—
504D3×Dic3—62no—
505D3×Dic3—62no—
506D3×Dic3—64no—
507D3×Dic3—121no—
508D3×Dic3—121no—
509#546—271noSylow
510C2×C33—41no—
511C2×C33C22×D411yescharacteristic
512C2×C33C2×#4111yescharacteristic
513C2×C33H(5,𝔽2)11yescharacteristic
514C3⋊(C3⋊D3)—22no—
515C3×C3⋊D3—22no—
516C3×C3⋊D3—41no—
517C32×D3—22no—
518C32×D3—41no—
519C24×C3—91no—
520C23×D3—31no—
521C23×D3—31no—
522C23×D3—91no—
523C23×D3—91no—
524C23×D3—91no—
525C23×D3—181no—
526C2×C3×D4—31no—
527C2×C3×D4—31no—
528C2×C3×D4—31no—
529C2×C3×D4—31no—
530C2×C3×D4—61no—
531C2×C3×D4—61no—
532C2×C3×D4—91no—
533C2×C3×D4—91no—
534C2×C3×D4—91no—
535C22×C3×C4—31no—
536C22×C3×C4—31no—
537C22×C3×C4—61no—
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—91no—
564C22×Dic3—91no—
565C22×Dic3D3211yescharacteristic, complemented
566#237—184no—
567D3×D4—184no—
568#235—184no—
569#235—184no—
570#235—188no—
571C2×D12—31no—
572C2×D12—91no—
573C2×D12—91no—
574C2×D12—91no—
575C2×D12—91no—
576C2×D12—181no—
577C2×D12—184no—
578C2×C4×D3—31no—
579C2×C4×D3—91no—
580C2×C4×D3—91no—
581C2×C4×D3—91no—
582C2×C4×D3—91no—
583C2×C4×D3—91no—
584C2×C4×D3—91no—
585C2×C4×D3—91no—
586C2×C4×D3—91no—
587C2×C4×D3—91no—
588C2×C4×D3—91no—
589C2×C4×D3—181no—
590C2×C4×D3—181no—
591C2×C4×D3—181no—
592C2×Dic6—91no—
593C2×Dic6—91no—
594C2×Dic6—91no—
595C2×Dic6—181no—
596C3×C4⋊C4—91no—
597C3×C4⋊C4—91no—
598C3×C22⋊C4—91no—
599C3×C22⋊C4—91no—
600C3×C22⋊C4—91no—
601C3×C22⋊C4—91no—
602C3×C22⋊C4—91no—
603C3×C22⋊C4—91no—
604C3×C22⋊C4—91no—
605C3×C42—91no—
606#217—31no—
607#217—31no—
608#217—31no—
609#217—31no—
610#217—31no—
611#217—31no—
612#217—61no—
613#217—91no—
614#217—91no—
615#217—91no—
616#217—91no—
617#217—91no—
618#217—91no—
619#217—181no—
620#217—181no—
621(C2×D3)⋊C4—31no—
622(C2×D3)⋊C4—31no—
623(C2×D3)⋊C4—31no—
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—91no—
630(C2×D3)⋊C4—91no—
631(C2×D3)⋊C4—91no—
632(C2×D3)⋊C4—91no—
633(C2×D3)⋊C4—91no—
634(C2×D3)⋊C4—91no—
635(C2×D3)⋊C4—91no—
636(C2×D3)⋊C4—91no—
637(C2×D3)⋊C4—91no—
638(C2×D3)⋊C4—181no—
639(C2×D3)⋊C4—181no—
640C4⋊Dic3—31no—
641C4⋊Dic3—31no—
642C4⋊Dic3—91no—
643C4⋊Dic3—91no—
644C4⋊Dic3—91no—
645C4⋊Dic3—181no—
646Dic3⋊C4—31no—
647Dic3⋊C4—31no—
648Dic3⋊C4—91no—
649Dic3⋊C4—91no—
650Dic3⋊C4—91no—
651C4×Dic3—31no—
652C4×Dic3—31no—
653C22×C32—21no—
654C22×C32—22no—
655C22×C32—21no—
656C22×C32—21no—
657C22×C32—21no—
658C22×C32—21no—
659C22×C32—21no—
660C22×C32—21no—
661C22×C32—21no—
662C22×C32—21no—
663C22×C32—21no—
664C22×C32—21no—
665C22×C32—21no—
666C22×C32—32no—
667C22×C32—41no—
668C22×C32—41no—
669C22×C32—41no—
670C22×C32—42no—
671C22×C32—41no—
672C22×C32—41no—
673C22×C32—41no—
674C22×C32—41no—
675C22×C32—41no—
676C22×C32—41no—
677C22×C32—61no—
678C22×C32—61no—
679C22×C32—61no—
680C22×C32—61no—
681C22×C32—61no—
682C22×C32—81no—
683C22×C32—81no—
684C22×C32C23×D311yescharacteristic
685C22×C32C23×D311yescharacteristic
686C22×C32C23×D311yescharacteristic
687C2×C3⋊D3—21no—
688C2×C3⋊D3—21no—
689C2×C3⋊D3—21no—
690C2×C3⋊D3—21no—
691C2×C3⋊D3—21no—
692C2×C3⋊D3—32no—
693C2×C3⋊D3—32no—
694C2×C3⋊D3—32no—
695C2×C3⋊D3—62no—
696C2×C3⋊D3—62no—
697C2×C3⋊D3—62no—
698C2×C3⋊D3—61no—
699C2×C3⋊D3—61no—
700C2×C3⋊D3—61no—
701C2×C3⋊D3—61no—
702C2×C3⋊D3—61no—
703C2×C3⋊D3—61no—
704C2×C3⋊D3—122no—
705C2×C3⋊D3—121no—
706C2×C3⋊D3—121no—
707C2×C3⋊D3—121no—
708C2×C3⋊D3—121no—
709C2×C3⋊D3—121no—
710C2×C3⋊D3—121no—
711C2×C3⋊D3—124no—
712C2×C3⋊D3—241no—
713C2×C3⋊D3—241no—
714C2×C3⋊D3D3×D412yes—
715C2×C3×D3—21no—
716C2×C3×D3—21no—
717C2×C3×D3—21no—
718C2×C3×D3—21no—
719C2×C3×D3—21no—
720C2×C3×D3—21no—
721C2×C3×D3—21no—
722C2×C3×D3—21no—
723C2×C3×D3—21no—
724C2×C3×D3—21no—
725C2×C3×D3—22no—
726C2×C3×D3—32no—
727C2×C3×D3—32no—
728C2×C3×D3—41no—
729C2×C3×D3—41no—
730C2×C3×D3—41no—
731C2×C3×D3—41no—
732C2×C3×D3—41no—
733C2×C3×D3—62no—
734C2×C3×D3—61no—
735C2×C3×D3—61no—
736C2×C3×D3—61no—
737C2×C3×D3—61no—
738C2×C3×D3—62no—
739C2×C3×D3—61no—
740C2×C3×D3—61no—
741C2×C3×D3—61no—
742C2×C3×D3—61no—
743C2×C3×D3—61no—
744C2×C3×D3—61no—
745C2×C3×D3—121no—
746C2×C3×D3—121no—
747C2×C3×D3—121no—
748C2×C3×D3—121no—
749C2×C3×D3—124no—
750C2×C3×D3—124no—
751C2×C3×D3#23512yescomplemented
752C2×C3×D3#23712yescomplemented
753D32—44no—
754D32—124no—
755D32—124no—
756D32—128no—
757C32×C4—32no—
758C32×C4—61no—
759C32×C4—61no—
760C32×C4—61no—
761C3⋊Dic3—21no—
762C3⋊Dic3—21no—
763C3⋊Dic3—21no—
764C3⋊Dic3—21no—
765C3⋊Dic3—61no—
766C3⋊Dic3—62no—
767C3⋊Dic3—61no—
768C3⋊Dic3—61no—
769C3⋊Dic3—121no—
770C3⋊Dic3—121no—
771C3⋊Dic3—122no—
772C3×Dic3—22no—
773C3×Dic3—22no—
774C3×Dic3—21no—
775C3×Dic3—21no—
776C3×Dic3—21no—
777C3×Dic3—21no—
778C3×Dic3—21no—
779C3×Dic3—21no—
780C3×Dic3—22no—
781C3×Dic3—41no—
782C3×Dic3—62no—
783C3×Dic3—61no—
784C3×Dic3—61no—
785C3×Dic3—61no—
786C3×Dic3—61no—
787C3×Dic3—61no—
788C3×Dic3—61no—
789C3×Dic3—61no—
790C3×Dic3—61no—
791C3×Dic3—121no—
792C3×Dic3—121no—
793C3×Dic3—121no—
794C3×Dic3D3×D412yes—
795C3×Dic3D3×D412yes—
796C2×#41—271no—
797C22×D4—271no—
798#124—271no—
799#123—271no—
800#123—271no—
801C22⋊Q8—271no—
802#121—91no—
803#121—271no—
804#121—271no—
805#120—91no—
806#120—271no—
807C4×D4—91no—
808C4×D4—271no—
809C2×C22⋊C4—271no—
810C2×C22⋊C4—271no—
811C33#54611yescharacteristic, complemented, Sylow
812C23×C3—21no—
813C23×C3—21no—
814C23×C3—21no—
815C23×C3—31no—
816C23×C3—31no—
817C23×C3—31no—
818C23×C3—31no—
819C23×C3—41no—
820C23×C3—61no—
821C23×C3—61no—
822C23×C3—91no—
823C23×C3—91no—
824C23×C3—182no—
825C23×C3—182no—
826C23×C3—361no—
827C23×C3C2×D3211yescharacteristic
828C23×C3C2×D3211yescharacteristic
829C23×C3C2×D3211yescharacteristic
830C22×D3—31no—
831C22×D3—31no—
832C22×D3—31no—
833C22×D3—31no—
834C22×D3—61no—
835C22×D3—61no—
836C22×D3—62no—
837C22×D3—62no—
838C22×D3—62no—
839C22×D3—62no—
840C22×D3—91no—
841C22×D3—91no—
842C22×D3—91no—
843C22×D3—121no—
844C22×D3—121no—
845C22×D3—181no—
846C22×D3—181no—
847C22×D3—181no—
848C22×D3—182no—
849C22×D3—182no—
850C22×D3—182no—
851C22×D3—182no—
852C22×D3—182no—
853C22×D3—182no—
854C22×D3—361no—
855C22×D3—362no—
856C22×D3—362no—
857C22×D3—361no—
858C22×D3—361no—
859C22×D3—361no—
860C22×D3—362no—
861C22×D3C2×D3211yescharacteristic
862C22×D3C2×D3211yescharacteristic
863C3×D4—62no—
864C3×D4—62no—
865C3×D4—122no—
866C3×D4—121no—
867C3×D4—121no—
868C3×D4—122no—
869C3×D4—182no—
870C3×D4—182no—
871C3×D4—361no—
872C2×C3×C4—31no—
873C2×C3×C4—31no—
874C2×C3×C4—31no—
875C2×C3×C4—31no—
876C2×C3×C4—31no—
877C2×C3×C4—31no—
878C2×C3×C4—31no—
879C2×C3×C4—31no—
880C2×C3×C4—61no—
881C2×C3×C4—61no—
882C2×C3×C4—61no—
883C2×C3×C4—61no—
884C2×C3×C4—62no—
885C2×C3×C4—62no—
886C2×C3×C4—64no—
887C2×C3×C4—91no—
888C2×C3×C4—91no—
889C2×C3×C4—91no—
890C2×C3×C4—91no—
891C2×C3×C4—182no—
892#67—22no—
893#67—41no—
894#67—62no—
895#67—62no—
896#67—64no—
897#67—62no—
898#67—94no—
899#67—121no—
900#67—121no—
901#67—122no—
902#67—182no—
903#67—182no—
904#67—182no—
905#67—182no—
906#67—182no—
907#67—182no—
908#67—182no—
909#67—184no—
910#67—362no—
911#67—362no—
912#67—362no—
913#67—364no—
914C2×Dic3—22no—
915C2×Dic3—31no—
916C2×Dic3—31no—
917C2×Dic3—31no—
918C2×Dic3—31no—
919C2×Dic3—31no—
920C2×Dic3—31no—
921C2×Dic3—31no—
922C2×Dic3—31no—
923C2×Dic3—61no—
924C2×Dic3—61no—
925C2×Dic3—61no—
926C2×Dic3—61no—
927C2×Dic3—62no—
928C2×Dic3—91no—
929C2×Dic3—91no—
930C2×Dic3—91no—
931C2×Dic3—181no—
932C2×Dic3—181no—
933C2×Dic3—181no—
934C2×Dic3—182no—
935C2×Dic3—361no—
936C2×Dic3—361no—
937C2×Dic3C2×D3211yescharacteristic
938C2×Dic3C2×D3211yescharacteristic
939C2×Dic3C2×D3211yescharacteristic
940C2×Dic3C2×D3211yescharacteristic
941D12—62no—
942D12—94no—
943D12—94no—
944D12—184no—
945D12—182no—
946D12—182no—
947C4×D3—62no—
948C4×D3—182no—
949C4×D3—182no—
950C4×D3—182no—
951C4×D3—184no—
952C4×D3—182no—
953C4×D3—182no—
954C4×D3—184no—
955C4×D3—361no—
956C4×D3—361no—
957C4×D3—361no—
958C4×D3—361no—
959C4×D3—361no—
960C4×D3—362no—
961Dic6—182no—
962Dic6—182no—
963Dic6—184no—
964Dic6—182no—
965C2×C32—21no—
966C2×C32—21no—
967C2×C32—21no—
968C2×C32—21no—
969C2×C32—21no—
970C2×C32—21no—
971C2×C32—21no—
972C2×C32—21no—
973C2×C32—21no—
974C2×C32—41no—
975C2×C32—41no—
976C2×C32—41no—
977C2×C32—41no—
978C2×C32—42no—
979C2×C32—41no—
980C2×C32—41no—
981C2×C32—62no—
982C2×C32—81no—
983C2×C32—81no—
984C2×C32—82no—
985C2×C32—121no—
986C2×C32C2×#23511yescharacteristic
987C2×C32C2×D3×D411yescharacteristic
988C2×C32C2×D3×D411yescharacteristic
989C2×C32C2×D3×D411yescharacteristic
990C2×C32C2×#23711yescharacteristic
991C2×C32#100411yescharacteristic
992C2×C32#100411yescharacteristic
993C2×C32D3×#4111yescharacteristic
994C2×C32#100911yescharacteristic
995C3⋊D3—22no—
996C3⋊D3—41no—
997C3⋊D3—62no—
998C3⋊D3—62no—
999C3⋊D3—62no—
1000C3⋊D3—122no—
1001C3⋊D3—122no—
1002C3⋊D3—122no—
1003C3⋊D3—242no—
1004C3×D3—22no—
1005C3×D3—22no—
1006C3×D3—42no—
1007C3×D3—41no—
1008C3×D3—41no—
1009C3×D3—62no—
1010C3×D3—62no—
1011C3×D3—81no—
1012C3×D3—122no—
1013C3×D3—122no—
1014C3×D3—121no—
1015C3×D3—121no—
1016C24—91no—
1017C24—271no—
1018#41—544no—
1019C2×Q8—271no—
1020C2×D4—31no—
1021C2×D4—31no—
1022C2×D4—91no—
1023C2×D4—91no—
1024C2×D4—91no—
1025C2×D4—271no—
1026C2×D4—271no—
1027C2×D4—271no—
1028C2×D4—271no—
1029C2×D4—544no—
1030C22×C4—31no—
1031C22×C4—91no—
1032C22×C4—271no—
1033C22×C4—271no—
1034C22×C4—271no—
1035C22×C4—271no—
1036C4⋊C4—91no—
1037C4⋊C4—91no—
1038C4⋊C4—271no—
1039C4⋊C4—271no—
1040C22⋊C4—91no—
1041C22⋊C4—91no—
1042C22⋊C4—91no—
1043C22⋊C4—91no—
1044C22⋊C4—91no—
1045C22⋊C4—91no—
1046C22⋊C4—91no—
1047C22⋊C4—271no—
1048C22⋊C4—271no—
1049C22⋊C4—271no—
1050C22⋊C4—271no—
1051C22⋊C4—271no—
1052C42—91no—
1053C22×C3—22no—
1054C22×C3—21no—
1055C22×C3—21no—
1056C22×C3—21no—
1057C22×C3—21no—
1058C22×C3—21no—
1059C22×C3—21no—
1060C22×C3—21no—
1061C22×C3—21no—
1062C22×C3—21no—
1063C22×C3—21no—
1064C22×C3—21no—
1065C22×C3—21no—
1066C22×C3—32no—
1067C22×C3—32no—
1068C22×C3—41no—
1069C22×C3—41no—
1070C22×C3—41no—
1071C22×C3—41no—
1072C22×C3—41no—
1073C22×C3—41no—
1074C22×C3—41no—
1075C22×C3—41no—
1076C22×C3—42no—
1077C22×C3—41no—
1078C22×C3—62no—
1079C22×C3—61no—
1080C22×C3—61no—
1081C22×C3—61no—
1082C22×C3—61no—
1083C22×C3—61no—
1084C22×C3—61no—
1085C22×C3—61no—
1086C22×C3—61no—
1087C22×C3—61no—
1088C22×C3—61no—
1089C22×C3—81no—
1090C22×C3—81no—
1091C22×C3—92no—
1092C22×C3—121no—
1093C22×C3—121no—
1094C22×C3—121no—
1095C22×C3—121no—
1096C22×C3—121no—
1097C22×C3—181no—
1098C22×C3—181no—
1099C22×C3—181no—
1100C22×C3—181no—
1101C22×C3—181no—
1102C22×C3—364no—
1103C22×C3C22×D3211yescharacteristic
1104C22×C3C22×D3211yescharacteristic
1105C22×C3C22×D3211yescharacteristic
1106C2×D3—21no—
1107C2×D3—21no—
1108C2×D3—21no—
1109C2×D3—21no—
1110C2×D3—21no—
1111C2×D3—32no—
1112C2×D3—32no—
1113C2×D3—62no—
1114C2×D3—61no—
1115C2×D3—61no—
1116C2×D3—61no—
1117C2×D3—61no—
1118C2×D3—62no—
1119C2×D3—61no—
1120C2×D3—61no—
1121C2×D3—61no—
1122C2×D3—61no—
1123C2×D3—61no—
1124C2×D3—61no—
1125C2×D3—92no—
1126C2×D3—92no—
1127C2×D3—92no—
1128C2×D3—121no—
1129C2×D3—121no—
1130C2×D3—121no—
1131C2×D3—121no—
1132C2×D3—124no—
1133C2×D3—124no—
1134C2×D3—182no—
1135C2×D3—182no—
1136C2×D3—182no—
1137C2×D3—181no—
1138C2×D3—181no—
1139C2×D3—181no—
1140C2×D3—181no—
1141C2×D3—181no—
1142C2×D3—181no—
1143C2×D3—362no—
1144C2×D3—361no—
1145C2×D3—361no—
1146C2×D3—361no—
1147C2×D3—361no—
1148C2×D3—361no—
1149C2×D3—361no—
1150C2×D3—364no—
1151C2×D3—364no—
1152C2×D3—364no—
1153C2×D3—368no—
1154C2×D3—721no—
1155C2×D3—721no—
1156C2×D3#380412yescomplemented
1157C3×C4—32no—
1158C3×C4—32no—
1159C3×C4—62no—
1160C3×C4—62no—
1161C3×C4—62no—
1162C3×C4—61no—
1163C3×C4—61no—
1164C3×C4—61no—
1165C3×C4—61no—
1166C3×C4—61no—
1167C3×C4—61no—
1168C3×C4—121no—
1169C3×C4—181no—
1170C3×C4—181no—
1171C3×C4—181no—
1172C3×C4—181no—
1173Dic3—21no—
1174Dic3—21no—
1175Dic3—21no—
1176Dic3—62no—
1177Dic3—61no—
1178Dic3—61no—
1179Dic3—61no—
1180Dic3—61no—
1181Dic3—61no—
1182Dic3—61no—
1183Dic3—61no—
1184Dic3—61no—
1185Dic3—121no—
1186Dic3—121no—
1187Dic3—121no—
1188Dic3—182no—
1189Dic3—181no—
1190Dic3—181no—
1191Dic3—181no—
1192Dic3—361no—
1193Dic3—361no—
1194Dic3—362no—
1195Dic3#381112yes—
1196C32—21no—
1197C32—21no—
1198C32—21no—
1199C32—41no—
1200C32#555011yescharacteristic, complemented
1201C32#559111yescharacteristic, complemented
1202C32#561211yescharacteristic, complemented
1203C23—31no—
1204C23—31no—
1205C23—91no—
1206C23—91no—
1207C23—182no—
1208C23—182no—
1209C23—271no—
1210C23—361no—
1211C23—542no—
1212C23—542no—
1213C23—1081no—
1214C23D3311yescharacteristic
1215Q8—542no—
1216D4—62no—
1217D4—121no—
1218D4—182no—
1219D4—182no—
1220D4—274no—
1221D4—361no—
1222D4—542no—
1223D4—542no—
1224D4—542no—
1225C2×C4—31no—
1226C2×C4—31no—
1227C2×C4—31no—
1228C2×C4—31no—
1229C2×C4—62no—
1230C2×C4—91no—
1231C2×C4—91no—
1232C2×C4—91no—
1233C2×C4—91no—
1234C2×C4—182no—
1235C2×C4—271no—
1236C2×C4—542no—
1237C2×C4—542no—
1238C2×C4—1081no—
1239C2×C4—1081no—
1240C2×C3—21no—
1241C2×C3—21no—
1242C2×C3—21no—
1243C2×C3—21no—
1244C2×C3—21no—
1245C2×C3—21no—
1246C2×C3—21no—
1247C2×C3—21no—
1248C2×C3—21no—
1249C2×C3—42no—
1250C2×C3—41no—
1251C2×C3—41no—
1252C2×C3—41no—
1253C2×C3—41no—
1254C2×C3—41no—
1255C2×C3—41no—
1256C2×C3—62no—
1257C2×C3—62no—
1258C2×C3—81no—
1259C2×C3—81no—
1260C2×C3—82no—
1261C2×C3—122no—
1262C2×C3—121no—
1263C2×C3—121no—
1264C2×C3—182no—
1265C2×C3—241no—
1266C2×C3—361no—
1267C2×C3D3×#23511yescharacteristic
1268C2×C3#6430711yescharacteristic
1269C2×C3D32×D411yescharacteristic
1270C2×C3D32×D411yescharacteristic
1271C2×C3D3×#23711yescharacteristic
1272C2×C3#6431411yescharacteristic
1273C2×C3C2×#380411yescharacteristic
1274C2×C3C2×#381111yescharacteristic
1275C2×C3#6433011yescharacteristic
1276D3—22no—
1277D3—41no—
1278D3—62no—
1279D3—62no—
1280D3—122no—
1281D3—122no—
1282D3—121no—
1283D3—121no—
1284D3—182no—
1285D3—182no—
1286D3—182no—
1287D3—362no—
1288D3—362no—
1289D3—362no—
1290D3—722no—
1291C22—21no—
1292C22—21no—
1293C22—21no—
1294C22—32no—
1295C22—61no—
1296C22—61no—
1297C22—61no—
1298C22—61no—
1299C22—61no—
1300C22—92no—
1301C22—181no—
1302C22—181no—
1303C22—181no—
1304C22—181no—
1305C22—181no—
1306C22—272no—
1307C22—364no—
1308C22—541no—
1309C22—541no—
1310C22—1084no—
1311C22C2×D3311yescharacteristic
1312C4—32no—
1313C4—61no—
1314C4—61no—
1315C4—61no—
1316C4—181no—
1317C4—181no—
1318C4—181no—
1319C4—181no—
1320C4—541no—
1321C3—21no—
1322C3—21no—
1323C3—21no—
1324C3—41no—
1325C3#1059507811yescharacteristic, complemented
1326C3#1059513511yescharacteristic, complemented
1327C3#1059529411yescharacteristic, complemented
1328C2—41no—
1329C2—62no—
1330C2—121no—
1331C2—182no—
1332C2—361no—
1333C2—542no—
1334C2D3×#380411yescharacteristic
1335C2#1172441811yescharacteristic
1336C2D3×#381111yescharacteristic
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×#89031C2semidirect
2. C2×D3×#626C2semidirect
3. #11723725C2semidirect
4. #11723643C2semidirect
5. #11723599C2semidirect
6. C3×#63983C2semidirect
7. C3×#63978C2semidirect
8. C3×Dic3×#67C2semidirect
9. #11723002C2semidirect
10. #11722997C2semidirect
11. #11722996C2semidirect
12. #11722971C2semidirect
13. #11722937C2semidirect
14. #11722906C2semidirect
15. #11722902C2semidirect
21. C2×#6312C22semidirect
22. C2×C3×#638C22semidirect
23. C2×C3×#638C22semidirect
25. C2×C32×#67C22semidirect
26. C22×C32×Dic3C22semidirect
28. C2×#6294C22semidirect
29. C2×#6293C22semidirect
32. C2×#6289C22semidirect
33. C2×#6289C22semidirect
35. C2×Dic3×C3⋊D3C22semidirect
39. C3×#3757C22semidirect
40. #88815C22semidirect
41. #88814C22semidirect
42. Dic3⋊(C3⋊Dic3)C22semidirect
43. #88804C22semidirect
44. #88803C22semidirect
46. (C2×D3)⋊(C3⋊Dic3)C22semidirect
47. C3×Dic3⋊Dic3C22semidirect
48. C3×Dic3⋊Dic3C22semidirect
49. C3×#3722C22semidirect
50. C3×#3722C22semidirect
53. C3×(C2×D3)⋊Dic3C22semidirect
54. C3×(C2×D3)⋊Dic3C22semidirect
55. C3×Dic32C22semidirect
74. #63983D3semidirect
75. #63978D3semidirect
78. Dic3×#67D3semidirect
134. #6292D4semidirect
162. C2×#638C2×D3semidirect
163. C2×#638C2×D3semidirect
181. C2×C3×#67C2×D3semidirect
182. C2×C3×#67C2×D3semidirect
185. C22×C3×Dic3C2×D3semidirect
186. C22×C3×Dic3C2×D3semidirect
223. #3757C2×D3semidirect
254. Dic3⋊Dic3C2×D3semidirect
255. Dic3⋊Dic3C2×D3semidirect
260. #3722C2×D3semidirect
261. #3722C2×D3semidirect
275. (C2×D3)⋊Dic3C2×D3semidirect
276. (C2×D3)⋊Dic3C2×D3semidirect
277. Dic32C2×D3semidirect
296. C2×C32×D3#41semidirect
561. C2×#67D32semidirect
565. C22×Dic3D32semidirect
751. C2×C3×D3#235semidirect
752. C2×C3×D3#237semidirect
811. C33#546semidirect
1156. C2×D3#3804semidirect
1200. C32#5550semidirect
1201. C32#5591semidirect
1202. C32#5612semidirect
1325. C3#10595078semidirect
1326. C3#10595135semidirect
1327. C3#10595294semidirect

Maximal subgroups

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

subgroupindex
C2×#890312
C2×D3×#6262
#117237252
#117236432
#117235992
C3×#639832
C3×#639782
C3×Dic3×#672
#117230022
#117229972
#117229962
#117229712
#117229372
#117229062
#117229022
#105952943
#105951353
#105950783