Finite Group Databasebeta

← #13172700

Subgroups — #13172700

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×#89028C211yesmaximal, characteristic, complemented
2C2×D3×#626C211yesmaximal, characteristic, complemented
3#11723717C211yesmaximal, characteristic, complemented
4#11723643C211yesmaximal, characteristic, complemented
5#11723623C211yesmaximal, characteristic, complemented
6C3×#63983C211yesmaximal, characteristic, complemented
7C3×#67⋊Dic3C211yesmaximal, characteristic, complemented
8C3×#63971C211yesmaximal, characteristic, complemented
9#11723010C211yesmaximal, characteristic, complemented
10#11723000C211yesmaximal, characteristic, complemented
11#11722990C211yesmaximal, characteristic, complemented
12#11722975C211yesmaximal, characteristic, complemented
13#11722932C211yesmaximal, characteristic, complemented
14#11722906C211yesmaximal, characteristic, complemented
15D3×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
16#10595307—31nomaximal
17#10595135—31nomaximal
18#10594283—31nomaximal
19C22×D3×C3⋊D3C2211yescharacteristic
20C22×C3×D32C2211yescharacteristic
21C2×#6312C2211yescharacteristic, complemented
22C2×C3×#638C2211yescharacteristic, complemented
23C2×C3×#638C2211yescharacteristic, complemented
24C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
25C2×C32×#67C2211yescharacteristic
26C2×C32×#67C2211yescharacteristic, complemented
27C2×#6295C2211yescharacteristic
28C2×#6293C2211yescharacteristic, complemented
29C2×#6292C2211yescharacteristic
30C2×#6291C2211yescharacteristic
31C2×#6289C2211yescharacteristic, complemented
32C2×#6289C2211yescharacteristic, complemented
33#89028—24no—
34C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
35C2×C3×#626C2211yescharacteristic
36C2×C3×D3×Dic3C2211yescharacteristic
37C2×C3×D3×Dic3C2211yescharacteristic, complemented
38D3×#626—24no—
39C32×#217C2211yescharacteristic, complemented
40#88815C2211yescharacteristic, complemented
41#88814C2211yescharacteristic, complemented
42#88814C2211yescharacteristic, complemented
43#88807C2211yescharacteristic, complemented
44#88804C2211yescharacteristic, complemented
45#88803C2211yescharacteristic, complemented
46#88803C2211yescharacteristic, complemented
47(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
48C3×#3724C2211yescharacteristic, complemented
49C3×Dic3⋊Dic3C2211yescharacteristic, complemented
50C3×#3722C2211yescharacteristic, complemented
51C3×#3722C2211yescharacteristic, complemented
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×(C2×D3)⋊Dic3C2211yescharacteristic
54C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
55C3×Dic32C2211yescharacteristic, complemented
56C2×#3830—31no—
57C2×D3×#67—31no—
58C22×#626—31no—
59C2×#3804—31no—
60C2×#3804—31no—
61C2×#3804—61no—
62C2×D3×D12—31no—
63#64146—31no—
64#64093—31no—
65C3×#939—31no—
66C3×#937—31no—
67C3×#937—31no—
68C3×D4×Dic3—31no—
69C3×#884—31no—
70C3×#67⋊C4—31no—
71#63983—31no—
72#63983—31no—
73#63983—61no—
74#63983D311yescharacteristic, complemented
75#63980—31no—
76#63978—31no—
77#63978—31no—
78#63974—31no—
79#67⋊Dic3D311yescharacteristic, complemented
80#63971D311yescharacteristic, complemented
81D3×#217—31no—
82#63964—31no—
83#63962—31no—
84C2×(C2×D3)⋊Dic3—31no—
85#63958—31no—
86#63958—31no—
87#63958—61no—
88#63952—31no—
89#63921—31no—
90#63921—31no—
91D3×(C2×D3)⋊C4—31no—
92#63913—31no—
93C4×#626—31no—
94#63897—31no—
95#63896—31no—
96#63890—31no—
97#63884—31no—
98#63880—31no—
99#63854—31no—
100#63853—31no—
101#63852—31no—
102#63852—31no—
103#63851—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—41no—
119C3×#638—41no—
120C2×C3×C3⋊Dic3—22no—
121C2×C3×C3⋊Dic3C2311yescharacteristic
122C2×C3×C3⋊Dic3C2311yescharacteristic
123C2×C3×C3⋊Dic3C2311yescharacteristic
124C2×C3×C3⋊Dic3C2311yescharacteristic
125C32×#67—22no—
126C32×#67—22no—
127C2×C32×Dic3C2311yescharacteristic
128C2×C32×Dic3C2311yescharacteristic
129C2×C32×Dic3C2311yescharacteristic
130C2×C32×Dic3C2311yescharacteristic
131#6295—22no—
132#6293—22no—
133#6292—22no—
134#6291D414yescomplemented
135#6289—22no—
136#6289—41no—
137D3×C3⋊Dic3—22no—
138C3×#626—22no—
139C3×D3×Dic3—22no—
140C3×D3×Dic3—41no—
141#5610—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—
153C2×#638—31no—
154C2×#638—31no—
155C2×#638—31no—
156C2×#638—31no—
157C2×#638—61no—
158C2×#638—61no—
159C2×#638—61no—
160C2×#638—121no—
161C2×#638C2×D311yescharacteristic, complemented
162C2×#638C2×D311yescharacteristic, complemented
163C22×C3⋊Dic3—31no—
164C22×C3⋊Dic3C2×D311yescharacteristic, complemented
165#3830—64no—
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—31no—
184C22×C3×Dic3—31no—
185C22×C3×Dic3—31no—
186C22×C3×Dic3—31no—
187C22×C3×Dic3—61no—
188C2×C3×D12—31no—
189C2×C3×C4×D3—31no—
190C2×C3×C4×D3—31no—
191D3×#67—64no—
192C2×#627—31no—
193C2×#627—31no—
194C2×#627—61no—
195C2×#626—31no—
196C2×#626—31no—
197C2×#626—31no—
198C2×#626—31no—
199C2×#626—31no—
200C2×#626—31no—
201C2×#626—64no—
202C2×#626—61no—
203C2×#626—61no—
204C2×#626C2×D311yescharacteristic
205C2×#625—31no—
206C2×#624—31no—
207C2×#624—31no—
208C2×#624—31no—
209C2×#624—31no—
210C2×#624—61no—
211C2×#624—61no—
212#3804—64no—
213#3804—64no—
214#3804—68no—
215C2×D3×Dic3—31no—
216C2×D3×Dic3—31no—
217C2×D3×Dic3—61no—
218C2×D3×Dic3C2×D311yescharacteristic
219C2×D3×Dic3C2×D311yescharacteristic, complemented
220D3×D12—64no—
221C32×C22⋊C4—31no—
222#3757—31no—
223#3752—31no—
224#3752—31no—
225#3752—31no—
226#3750—31no—
227C3×#217—21no—
228C3×#217—31no—
229C3×#217—31no—
230C3×#217—31no—
231C3×#217C2×D311yescharacteristic, complemented
232C3×#217C2×D311yescharacteristic, complemented
233C3×(C2×D3)⋊C4—31no—
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×C4⋊Dic3—31no—
241C3×Dic3⋊C4—31no—
242C3×Dic3⋊C4—31no—
243C3×Dic3⋊C4—31no—
244C3×C4×Dic3—31no—
245C3×C4×Dic3—31no—
246#3724—31no—
247#3724C2×D311yescharacteristic, complemented
248Dic3⋊Dic3—31no—
249Dic3⋊Dic3—31no—
250Dic3⋊Dic3—31no—
251Dic3⋊Dic3—31no—
252Dic3⋊Dic3—61no—
253Dic3⋊Dic3C2×D311yescharacteristic, complemented
254#3722—31no—
255#3722—31no—
256#3722—31no—
257#3722—31no—
258#3722—61no—
259#3722C2×D311yescharacteristic, complemented
260#3722C2×D311yescharacteristic, complemented
261(C2×D3)⋊Dic3—31no—
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—31no—
271(C2×D3)⋊Dic3—61no—
272(C2×D3)⋊Dic3—61no—
273(C2×D3)⋊Dic3—61no—
274(C2×D3)⋊Dic3C2×D311yescharacteristic
275(C2×D3)⋊Dic3C2×D311yescharacteristic
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⋊D3—21no—
291C2×C32×D3—21no—
292C2×C32×D3—21no—
293C2×C32×D3—21no—
294C2×C32×D3—21no—
295C2×C32×D3C2×D412yes—
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⋊Dic3C2×D412yes—
304C32×Dic3—21no—
305C32×Dic3—21no—
306C32×Dic3—21no—
307C32×Dic3—21no—
308C22×#67—91no—
309C2×#237—91no—
310C2×#237—91no—
311C2×#237—181no—
312C2×D3×D4—91no—
313C2×#235—91no—
314C22×D12—91no—
315C3×#121—91no—
316C3×#120—91no—
317C3×C4×D4—91no—
318C2×#217—91no—
319#939—31no—
320#939—91no—
321#939—91no—
322#938—91no—
323#937—31no—
324#937—31no—
325#937—91no—
326#937—91no—
327#937—91no—
328#937—181no—
329#935—91no—
330D4×Dic3—31no—
331#930—91no—
332C4×#67—91no—
333C2×(C2×D3)⋊C4—91no—
334#924—91no—
335#896—91no—
336#894—91no—
337#894—91no—
338#894—91no—
339#886—91no—
340#885—91no—
341#885—91no—
342#884—31no—
343#884—91no—
344#884—91no—
345#884—181no—
346#883—91no—
347#67⋊C4—31no—
348#67⋊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—62no—
409C2×C32×C4—31no—
410C2×C32×C4—31no—
411C2×C32×C4—31no—
412C2×C32×C4—31no—
413#638—34no—
414#638—41no—
415#638—41no—
416#638—62no—
417#638—62no—
418#638—62no—
419#638—64no—
420#638—122no—
421#638—122no—
422#638—124no—
423C2×C3⋊Dic3—22no—
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—62no—
431C2×C3⋊Dic3—121no—
432C2×C3⋊Dic3C22×D311yescharacteristic
433C2×C3⋊Dic3C22×D311yescharacteristic
434C2×C3⋊Dic3C22×D311yescharacteristic
435C2×C3⋊Dic3C22×D311yescharacteristic
436C4⋊(C3⋊D3)—62no—
437C4×C3⋊D3—62no—
438C4×C3⋊D3—121no—
439#634—62no—
440C3×#67—24no—
441C3×#67—22no—
442C3×#67—22no—
443C3×#67—22no—
444C3×#67—22no—
445C3×#67—42no—
446C3×#67—62no—
447C3×#67—121no—
448C3×#67—121no—
449C3×#67—121no—
450C3×#67—121no—
451C3×#67—122no—
452C3×#67—122no—
453C2×C3×Dic3—21no—
454C2×C3×Dic3—21no—
455C2×C3×Dic3—21no—
456C2×C3×Dic3—21no—
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—31no—
464C2×C3×Dic3—31no—
465C2×C3×Dic3—61no—
466C2×C3×Dic3—61no—
467C2×C3×Dic3—61no—
468C2×C3×Dic3—61no—
469C2×C3×Dic3—62no—
470C2×C3×Dic3—62no—
471C2×C3×Dic3—62no—
472C2×C3×Dic3—64no—
473C2×C3×Dic3—121no—
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—62no—
483C3×C4×D3—62no—
484C3×C4×D3—121no—
485#627—62no—
486#627—62no—
487#627—64no—
488#626—22no—
489#626—34no—
490#626—34no—
491#626—64no—
492#626—62no—
493#626—62no—
494#626—62no—
495#626—62no—
496#626—122no—
497#625—62no—
498#624—62no—
499#624—62no—
500#624—64no—
501#624—121no—
502#624—121no—
503#624—122no—
504D3×Dic3—22no—
505D3×Dic3—41no—
506D3×Dic3—64no—
507D3×Dic3—62no—
508D3×Dic3—62no—
509#546—271noSylow
510C2×C33—41no—
511C2×C33C22×D411yescharacteristic
512C2×C33C2×#4111yescharacteristic
513C2×C33H(5,𝔽2)11yescharacteristic
514C3⋊(C3⋊D3)—22no—
515C3×C3⋊D3—41no—
516C3×C3⋊D3—41no—
517C32×D3—22no—
518C32×D3—22no—
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—91no—
536C22×C3×C4—91no—
537C22×C3×C4—91no—
538C2×#67—31no—
539C2×#67—31no—
540C2×#67—31no—
541C2×#67—31no—
542C2×#67—31no—
543C2×#67—61no—
544C2×#67—61no—
545C2×#67—91no—
546C2×#67—91no—
547C2×#67—91no—
548C2×#67—91no—
549C2×#67—91no—
550C2×#67—91no—
551C2×#67—91no—
552C2×#67—91no—
553C2×#67—181no—
554C2×#67—181no—
555C2×#67—181no—
556C2×#67—181no—
557C2×#67—184no—
558C2×#67—361no—
559C2×#67D3211yescharacteristic
560C2×#67D3211yescharacteristic, complemented
561C22×Dic3—31no—
562C22×Dic3—31no—
563C22×Dic3—31no—
564C22×Dic3—31no—
565C22×Dic3—61no—
566C22×Dic3—91no—
567C22×Dic3—91no—
568C22×Dic3—181no—
569#237—184no—
570#237—184no—
571#237—188no—
572D3×D4—184no—
573#235—184no—
574C2×D12—31no—
575C2×D12—91no—
576C2×D12—91no—
577C2×D12—91no—
578C2×D12—91no—
579C2×D12—181no—
580C2×D12—184no—
581C2×C4×D3—31no—
582C2×C4×D3—31no—
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—91no—
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—31no—
599C3×C22⋊C4—31no—
600C3×C22⋊C4—61no—
601C3×C22⋊C4—91no—
602C3×C22⋊C4—91no—
603C3×C22⋊C4—91no—
604C3×C22⋊C4—91no—
605C3×C22⋊C4—91no—
606C3×C42—91no—
607#217—31no—
608#217—31no—
609#217—31no—
610#217—91no—
611#217—91no—
612#217—91no—
613#217—91no—
614#217—91no—
615#217—91no—
616#217—181no—
617#217D3211yescharacteristic, complemented
618(C2×D3)⋊C4—31no—
619(C2×D3)⋊C4—31no—
620(C2×D3)⋊C4—31no—
621(C2×D3)⋊C4—31no—
622(C2×D3)⋊C4—31no—
623(C2×D3)⋊C4—31no—
624(C2×D3)⋊C4—31no—
625(C2×D3)⋊C4—91no—
626(C2×D3)⋊C4—91no—
627(C2×D3)⋊C4—91no—
628(C2×D3)⋊C4—91no—
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—181no—
638(C2×D3)⋊C4—181no—
639(C2×D3)⋊C4—181no—
640C4⋊Dic3—31no—
641C4⋊Dic3—91no—
642C4⋊Dic3—91no—
643Dic3⋊C4—31no—
644Dic3⋊C4—31no—
645Dic3⋊C4—31no—
646Dic3⋊C4—91no—
647Dic3⋊C4—91no—
648Dic3⋊C4—91no—
649Dic3⋊C4—91no—
650Dic3⋊C4—181no—
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—32no—
668C22×C32—41no—
669C22×C32—41no—
670C22×C32—41no—
671C22×C32—42no—
672C22×C32—41no—
673C22×C32—41no—
674C22×C32—41no—
675C22×C32—41no—
676C22×C32—41no—
677C22×C32—41no—
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—21no—
693C2×C3⋊D3—32no—
694C2×C3⋊D3—32no—
695C2×C3⋊D3—32no—
696C2×C3⋊D3—62no—
697C2×C3⋊D3—62no—
698C2×C3⋊D3—62no—
699C2×C3⋊D3—61no—
700C2×C3⋊D3—61no—
701C2×C3⋊D3—61no—
702C2×C3⋊D3—61no—
703C2×C3⋊D3—61no—
704C2×C3⋊D3—61no—
705C2×C3⋊D3—122no—
706C2×C3⋊D3—121no—
707C2×C3⋊D3—121no—
708C2×C3⋊D3—121no—
709C2×C3⋊D3—121no—
710C2×C3⋊D3—121no—
711C2×C3⋊D3—121no—
712C2×C3⋊D3—124no—
713C2×C3⋊D3—241no—
714C2×C3⋊D3—241no—
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—22no—
724C2×C3×D3—22no—
725C2×C3×D3—41no—
726C2×C3×D3—41no—
727C2×C3×D3—41no—
728C2×C3×D3—41no—
729C2×C3×D3—62no—
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—61no—
738C2×C3×D3—61no—
739C2×C3×D3—61no—
740C2×C3×D3—61no—
741C2×C3×D3—61no—
742C2×C3×D3—121no—
743C2×C3×D3—121no—
744C2×C3×D3—121no—
745C2×C3×D3—121no—
746C2×C3×D3—121no—
747C2×C3×D3—124no—
748C2×C3×D3—124no—
749C2×C3×D3#23512yescomplemented
750C2×C3×D3D3×D412yes—
751C2×C3×D3D3×D412yes—
752C2×C3×D3#23712yescomplemented
753D32—44no—
754D32—124no—
755D32—124no—
756D32—128no—
757C32×C4—61no—
758C32×C4—61no—
759C32×C4—61no—
760C32×C4—61no—
761C3⋊Dic3—21no—
762C3⋊Dic3—21no—
763C3⋊Dic3—21no—
764C3⋊Dic3—61no—
765C3⋊Dic3—62no—
766C3⋊Dic3—61no—
767C3⋊Dic3—61no—
768C3⋊Dic3—121no—
769C3⋊Dic3—121no—
770C3⋊Dic3—122no—
771C3⋊Dic3D3×D412yes—
772C3×Dic3—22no—
773C3×Dic3—21no—
774C3×Dic3—21no—
775C3×Dic3—21no—
776C3×Dic3—21no—
777C3×Dic3—21no—
778C3×Dic3—21no—
779C3×Dic3—21no—
780C3×Dic3—21no—
781C3×Dic3—32no—
782C3×Dic3—32no—
783C3×Dic3—41no—
784C3×Dic3—41no—
785C3×Dic3—41no—
786C3×Dic3—62no—
787C3×Dic3—62no—
788C3×Dic3—62no—
789C3×Dic3—61no—
790C3×Dic3—61no—
791C3×Dic3—61no—
792C3×Dic3—61no—
793C3×Dic3—61no—
794C3×Dic3—61no—
795C3×Dic3—121no—
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—62no—
866C3×D4—62no—
867C3×D4—64no—
868C3×D4—122no—
869C3×D4—182no—
870C3×D4—361no—
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—91no—
885C2×C3×C4—91no—
886C2×C3×C4—91no—
887C2×C3×C4—91no—
888C2×C3×C4—182no—
889C2×C3×C4—182no—
890C2×C3×C4—361no—
891#67—22no—
892#67—22no—
893#67—62no—
894#67—94no—
895#67—94no—
896#67—121no—
897#67—121no—
898#67—121no—
899#67—121no—
900#67—122no—
901#67—122no—
902#67—184no—
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—364no—
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—62no—
928C2×Dic3—64no—
929C2×Dic3—91no—
930C2×Dic3—91no—
931C2×Dic3—91no—
932C2×Dic3—121no—
933C2×Dic3—181no—
934C2×Dic3—181no—
935C2×Dic3—181no—
936C2×Dic3—182no—
937C2×Dic3—182no—
938C2×Dic3—184no—
939C2×Dic3—361no—
940C2×Dic3C2×D3211yescharacteristic
941C2×Dic3C2×D3211yescharacteristic
942C2×Dic3C2×D3211yescharacteristic
943C2×Dic3C2×D3211yescharacteristic
944D12—62no—
945D12—94no—
946D12—182no—
947D12—182no—
948D12—182no—
949D12—362no—
950C4×D3—62no—
951C4×D3—121no—
952C4×D3—182no—
953C4×D3—182no—
954C4×D3—182no—
955C4×D3—184no—
956C4×D3—182no—
957C4×D3—361no—
958C4×D3—361no—
959C4×D3—361no—
960C4×D3—362no—
961Dic6—182no—
962Dic6—182no—
963Dic6—182no—
964Dic6—184no—
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—62no—
983C2×C32—81no—
984C2×C32—81no—
985C2×C32—82no—
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—41no—
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—22no—
1007C3×D3—22no—
1008C3×D3—42no—
1009C3×D3—42no—
1010C3×D3—122no—
1011C3×D3—121no—
1012C3×D3—121no—
1013C3×D3—121no—
1014C3×D3—121no—
1015C3×D3—241no—
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—91no—
1031C22×C4—91no—
1032C22×C4—91no—
1033C22×C4—271no—
1034C22×C4—271no—
1035C22×C4—271no—
1036C4⋊C4—91no—
1037C4⋊C4—91no—
1038C4⋊C4—271no—
1039C4⋊C4—271no—
1040C22⋊C4—31no—
1041C22⋊C4—91no—
1042C22⋊C4—91no—
1043C22⋊C4—91no—
1044C22⋊C4—91no—
1045C22⋊C4—91no—
1046C22⋊C4—271no—
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—32no—
1069C22×C3—32no—
1070C22×C3—41no—
1071C22×C3—41no—
1072C22×C3—41no—
1073C22×C3—41no—
1074C22×C3—41no—
1075C22×C3—41no—
1076C22×C3—41no—
1077C22×C3—41no—
1078C22×C3—42no—
1079C22×C3—41no—
1080C22×C3—62no—
1081C22×C3—62no—
1082C22×C3—61no—
1083C22×C3—61no—
1084C22×C3—61no—
1085C22×C3—61no—
1086C22×C3—61no—
1087C22×C3—61no—
1088C22×C3—61no—
1089C22×C3—61no—
1090C22×C3—81no—
1091C22×C3—81no—
1092C22×C3—121no—
1093C22×C3—121no—
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—364no—
1103C22×C3C22×D3211yescharacteristic
1104C22×C3C22×D3211yescharacteristic
1105C22×C3C22×D3211yescharacteristic
1106C2×D3—21no—
1107C2×D3—21no—
1108C2×D3—21no—
1109C2×D3—21no—
1110C2×D3—62no—
1111C2×D3—61no—
1112C2×D3—61no—
1113C2×D3—61no—
1114C2×D3—61no—
1115C2×D3—61no—
1116C2×D3—61no—
1117C2×D3—61no—
1118C2×D3—61no—
1119C2×D3—61no—
1120C2×D3—61no—
1121C2×D3—61no—
1122C2×D3—61no—
1123C2×D3—92no—
1124C2×D3—92no—
1125C2×D3—92no—
1126C2×D3—121no—
1127C2×D3—121no—
1128C2×D3—121no—
1129C2×D3—121no—
1130C2×D3—121no—
1131C2×D3—124no—
1132C2×D3—124no—
1133C2×D3—182no—
1134C2×D3—182no—
1135C2×D3—182no—
1136C2×D3—181no—
1137C2×D3—181no—
1138C2×D3—181no—
1139C2×D3—181no—
1140C2×D3—181no—
1141C2×D3—181no—
1142C2×D3—362no—
1143C2×D3—361no—
1144C2×D3—361no—
1145C2×D3—361no—
1146C2×D3—361no—
1147C2×D3—361no—
1148C2×D3—361no—
1149C2×D3—364no—
1150C2×D3—364no—
1151C2×D3—364no—
1152C2×D3—368no—
1153C2×D3—721no—
1154C2×D3—721no—
1155C2×D3#380412yescomplemented
1156C2×D3#381112yes—
1157C3×C4—62no—
1158C3×C4—61no—
1159C3×C4—61no—
1160C3×C4—61no—
1161C3×C4—61no—
1162C3×C4—61no—
1163C3×C4—61no—
1164C3×C4—61no—
1165C3×C4—61no—
1166C3×C4—92no—
1167C3×C4—121no—
1168C3×C4—121no—
1169C3×C4—121no—
1170C3×C4—181no—
1171C3×C4—181no—
1172C3×C4—181no—
1173Dic3—21no—
1174Dic3—21no—
1175Dic3—21no—
1176Dic3—21no—
1177Dic3—32no—
1178Dic3—32no—
1179Dic3—62no—
1180Dic3—62no—
1181Dic3—62no—
1182Dic3—61no—
1183Dic3—61no—
1184Dic3—61no—
1185Dic3—61no—
1186Dic3—61no—
1187Dic3—61no—
1188Dic3—121no—
1189Dic3—182no—
1190Dic3—181no—
1191Dic3—181no—
1192Dic3—181no—
1193Dic3—361no—
1194Dic3—361no—
1195Dic3—362no—
1196C32—21no—
1197C32—21no—
1198C32—21no—
1199C32—41no—
1200C32#555011yescharacteristic, complemented
1201C32#559111yescharacteristic, complemented
1202C32#561011yescharacteristic, 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—62no—
1218D4—182no—
1219D4—274no—
1220D4—361no—
1221D4—361no—
1222D4—542no—
1223D4—542no—
1224D4—542no—
1225C2×C4—31no—
1226C2×C4—31no—
1227C2×C4—31no—
1228C2×C4—31no—
1229C2×C4—91no—
1230C2×C4—91no—
1231C2×C4—91no—
1232C2×C4—91no—
1233C2×C4—182no—
1234C2×C4—182no—
1235C2×C4—271no—
1236C2×C4—361no—
1237C2×C4—542no—
1238C2×C4—542no—
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—62no—
1259C2×C3—62no—
1260C2×C3—81no—
1261C2×C3—81no—
1262C2×C3—82no—
1263C2×C3—122no—
1264C2×C3—122no—
1265C2×C3—361no—
1266C2×C3—361no—
1267C2×C3D3×#23511yescharacteristic
1268C2×C3D32×D411yescharacteristic
1269C2×C3D32×D411yescharacteristic
1270C2×C3D3×#23711yescharacteristic
1271C2×C3#6431311yescharacteristic
1272C2×C3#6431411yescharacteristic
1273C2×C3#6431411yescharacteristic
1274C2×C3C2×#380411yescharacteristic
1275C2×C3C2×#381111yescharacteristic
1276D3—22no—
1277D3—22no—
1278D3—122no—
1279D3—121no—
1280D3—121no—
1281D3—121no—
1282D3—121no—
1283D3—182no—
1284D3—182no—
1285D3—182no—
1286D3—241no—
1287D3—362no—
1288D3—362no—
1289D3—362no—
1290D3—722no—
1291C22—21no—
1292C22—21no—
1293C22—21no—
1294C22—32no—
1295C22—32no—
1296C22—61no—
1297C22—61no—
1298C22—61no—
1299C22—61no—
1300C22—181no—
1301C22—181no—
1302C22—181no—
1303C22—181no—
1304C22—181no—
1305C22—181no—
1306C22—272no—
1307C22—364no—
1308C22—541no—
1309C22—541no—
1310C22—1084no—
1311C22C2×D3311yescharacteristic
1312C4—61no—
1313C4—61no—
1314C4—61no—
1315C4—61no—
1316C4—92no—
1317C4—181no—
1318C4—181no—
1319C4—181no—
1320C4—541no—
1321C3—21no—
1322C3—21no—
1323C3—21no—
1324C3—41no—
1325C3#1059428311yescharacteristic, complemented
1326C3#1059513511yescharacteristic, complemented
1327C3#1059530711yescharacteristic, complemented
1328C2—41no—
1329C2—62no—
1330C2—62no—
1331C2—361no—
1332C2—361no—
1333C2—542no—
1334C2D3×#380411yescharacteristic
1335C2#1172441611yescharacteristic
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×#89028C2semidirect
2. C2×D3×#626C2semidirect
3. #11723717C2semidirect
4. #11723643C2semidirect
5. #11723623C2semidirect
6. C3×#63983C2semidirect
7. C3×#67⋊Dic3C2semidirect
8. C3×#63971C2semidirect
9. #11723010C2semidirect
10. #11723000C2semidirect
11. #11722990C2semidirect
12. #11722975C2semidirect
13. #11722932C2semidirect
14. #11722906C2semidirect
15. D3×(C2×D3)⋊Dic3C2semidirect
21. C2×#6312C22semidirect
22. C2×C3×#638C22semidirect
23. C2×C3×#638C22semidirect
24. C22×C3×C3⋊Dic3C22semidirect
26. C2×C32×#67C22semidirect
28. C2×#6293C22semidirect
31. C2×#6289C22semidirect
32. C2×#6289C22semidirect
34. C2×D3×C3⋊Dic3C22semidirect
37. C2×C3×D3×Dic3C22semidirect
39. C32×#217C22semidirect
40. #88815C22semidirect
41. #88814C22semidirect
42. #88814C22semidirect
43. #88807C22semidirect
44. #88804C22semidirect
45. #88803C22semidirect
46. #88803C22semidirect
48. C3×#3724C22semidirect
49. C3×Dic3⋊Dic3C22semidirect
50. C3×#3722C22semidirect
51. C3×#3722C22semidirect
54. C3×(C2×D3)⋊Dic3C22semidirect
55. C3×Dic32C22semidirect
74. #63983D3semidirect
79. #67⋊Dic3D3semidirect
80. #63971D3semidirect
134. #6291D4semidirect
161. C2×#638C2×D3semidirect
162. C2×#638C2×D3semidirect
164. C22×C3⋊Dic3C2×D3semidirect
181. C2×C3×#67C2×D3semidirect
182. C2×C3×#67C2×D3semidirect
219. C2×D3×Dic3C2×D3semidirect
231. C3×#217C2×D3semidirect
232. C3×#217C2×D3semidirect
247. #3724C2×D3semidirect
253. Dic3⋊Dic3C2×D3semidirect
259. #3722C2×D3semidirect
260. #3722C2×D3semidirect
276. (C2×D3)⋊Dic3C2×D3semidirect
277. Dic32C2×D3semidirect
296. C2×C32×D3#41semidirect
560. C2×#67D32semidirect
617. #217D32semidirect
749. C2×C3×D3#235semidirect
752. C2×C3×D3#237semidirect
811. C33#546semidirect
1155. C2×D3#3804semidirect
1200. C32#5550semidirect
1201. C32#5591semidirect
1202. C32#5610semidirect
1325. C3#10594283semidirect
1326. C3#10595135semidirect
1327. C3#10595307semidirect

Maximal subgroups

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

subgroupindex
C2×#890282
C2×D3×#6262
#117237172
#117236432
#117236232
C3×#639832
C3×#67⋊Dic32
C3×#639712
#117230102
#117230002
#117229902
#117229752
#117229322
#117229062
D3×(C2×D3)⋊Dic32
#105953073
#105951353
#105942833