Finite Group Databasebeta

← #13172735

Subgroups — #13172735

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×#89046C211yesmaximal, characteristic, complemented
2C2×D3×#626C211yesmaximal, characteristic, complemented
3#11723643C211yesmaximal, characteristic, complemented
4#11723635C211yesmaximal, characteristic, complemented
5#11723624C211yesmaximal, characteristic, complemented
6C3×#63983C211yesmaximal, characteristic, complemented
7C3×#67⋊Dic3C211yesmaximal, characteristic, complemented
8C3×#63958C211yesmaximal, characteristic, complemented
9#11723008C211yesmaximal, characteristic, complemented
10#11722999C211yesmaximal, characteristic, complemented
11#11722994C211yesmaximal, characteristic, complemented
12#11722978C211yesmaximal, characteristic, complemented
13#11722934C211yesmaximal, characteristic, complemented
14#11722904C211yesmaximal, characteristic, complemented
15#11722902C211yesmaximal, characteristic, complemented
16#10595290—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×#6296C2211yescharacteristic, complemented
28C2×#6295C2211yescharacteristic
29#89046—24no—
30C2×#6294C2211yescharacteristic, complemented
31C2×#6294C2211yescharacteristic, complemented
32C2×#6292C2211yescharacteristic
33C2×#6291C2211yescharacteristic
34C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
35C2×C3×#626C2211yescharacteristic
36C2×C3×#624C2211yescharacteristic, complemented
37C2×C3×D3×Dic3C2211yescharacteristic
38D3×#626—24no—
39C32×#217C2211yescharacteristic, complemented
40#88807C2211yescharacteristic, complemented
41#88806C2211yescharacteristic, complemented
42#88804C2211yescharacteristic, complemented
43#88804C2211yescharacteristic, complemented
44#88804C2211yescharacteristic, complemented
45#88803C2211yescharacteristic, complemented
46(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
47(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
48C3×Dic3⋊Dic3C2211yescharacteristic, complemented
49C3×Dic3⋊Dic3C2211yescharacteristic, 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×D3×#67—31no—
57C22×#626—31no—
58C2×#3805—31no—
59C2×#3804—31no—
60C2×#3804—31no—
61C2×D3×D12—31no—
62#64148—31no—
63#64146—31no—
64#64093—31no—
65C3×#938—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#63978—31no—
76#63978—31no—
77#63978—61no—
78#63974—31no—
79#67⋊Dic3D311yescharacteristic, complemented
80#63971—31no—
81#63971—31no—
82#63971—61no—
83#63969—31no—
84D3×#217—31no—
85D3×#217—31no—
86#63964—31no—
87#63958D311yescharacteristic, complemented
88#63953—31no—
89#63921—31no—
90D3×(C2×D3)⋊C4—31no—
91D3×(C2×D3)⋊C4—31no—
92C4×#626—31no—
93#63899—31no—
94#63897—31no—
95#63890—31no—
96#63890—31no—
97#63884—31no—
98#63880—31no—
99#63879—31no—
100#63854—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—41no—
117C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
118C3×#638—22no—
119C3×#638—22no—
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—41no—
127C2×C32×Dic3C2311yescharacteristic
128C2×C32×Dic3C2311yescharacteristic
129C2×C32×Dic3C2311yescharacteristic
130C2×C32×Dic3C2311yescharacteristic
131#6296—22no—
132#6295D414yescomplemented
133#6294—22no—
134#6294—22no—
135#6292—22no—
136#6291—22no—
137Dic3×C3⋊D3—41no—
138C3×#626—22no—
139C3×#624—41no—
140C3×D3×Dic3—22no—
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⋊Dic3C2×D311yescharacteristic, complemented
164C2×C4⋊(C3⋊D3)—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—31no—
180C22×C3×Dic3—31no—
181C22×C3×Dic3—31no—
182C22×C3×Dic3—61no—
183C2×C3×D12—31no—
184C2×C3×C4×D3—31no—
185C2×C3×C4×D3—31no—
186C2×C3×C4×D3—31no—
187D3×#67—64no—
188C2×#627—31no—
189C2×#627—31no—
190C2×#627—31no—
191C2×#626—31no—
192C2×#626—31no—
193C2×#626—31no—
194C2×#626—31no—
195C2×#626—31no—
196C2×#626—31no—
197C2×#626—64no—
198C2×#626—61no—
199C2×#626—61no—
200C2×#626C2×D311yescharacteristic
201C2×#625—31no—
202C2×#624—31no—
203C2×#624—31no—
204C2×#624C2×D311yescharacteristic, complemented
205#3805—64no—
206#3804—64no—
207#3804—64no—
208C2×D3×Dic3—31no—
209C2×D3×Dic3—31no—
210C2×D3×Dic3—31no—
211C2×D3×Dic3—31no—
212C2×D3×Dic3—31no—
213C2×D3×Dic3—31no—
214C2×D3×Dic3—61no—
215C2×D3×Dic3C2×D311yescharacteristic
216D3×D12—64no—
217C32×C22⋊C4—31no—
218#3757—31no—
219#3757—31no—
220#3752—31no—
221#3752—31no—
222#3752—31no—
223#3752—31no—
224#3750—31no—
225#3750—31no—
226C3×#217—21no—
227C3×#217—31no—
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×C4⋊Dic3—31no—
240C3×C4⋊Dic3—31no—
241C3×Dic3⋊C4—31no—
242C3×Dic3⋊C4—31no—
243C3×C4×Dic3—31no—
244C3×C4×Dic3—31no—
245#3724—31no—
246#3724—31no—
247#3724—61no—
248Dic3⋊Dic3—31no—
249Dic3⋊Dic3—31no—
250Dic3⋊Dic3—61no—
251Dic3⋊Dic3C2×D311yescharacteristic, complemented
252Dic3⋊Dic3C2×D311yescharacteristic, complemented
253#3722—31no—
254#3722—31no—
255#3722—31no—
256#3722—31no—
257#3722—31no—
258#3722—31no—
259#3722—61no—
260#3722—61no—
261#3722—61no—
262#3722C2×D311yescharacteristic, complemented
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—61no—
270(C2×D3)⋊Dic3—61no—
271(C2×D3)⋊Dic3—61no—
272(C2×D3)⋊Dic3C2×D311yescharacteristic
273(C2×D3)⋊Dic3C2×D311yescharacteristic
274(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
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⋊D3C2×D412yes—
289C2×C3×C3⋊D3C2×D412yes—
290C2×C32×D3—21no—
291C2×C32×D3—21no—
292C2×C32×D3—21no—
293C2×C32×D3—21no—
294C2×C32×D3—21no—
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⋊Dic3C2×D412yes—
303C32×Dic3—21no—
304C32×Dic3—21no—
305C32×Dic3—21no—
306C32×Dic3—21no—
307C22×#67—91no—
308C2×#237—91no—
309C2×#237—91no—
310C2×D3×D4—91no—
311C2×#235—91no—
312C22×D12—91no—
313C3×#121—91no—
314C3×#120—91no—
315C3×C4×D4—91no—
316C2×#217—91no—
317#939—91no—
318#939—91no—
319#939—91no—
320#939—181no—
321#938—31no—
322#937—31no—
323#937—31no—
324#937—91no—
325#937—91no—
326#937—91no—
327#937—181no—
328#935—91no—
329D4×Dic3—31no—
330#930—91no—
331C4×#67—91no—
332C2×(C2×D3)⋊C4—91no—
333#924—91no—
334#896—91no—
335#894—91no—
336#894—91no—
337#894—91no—
338#886—91no—
339#885—91no—
340#885—91no—
341#884—31no—
342#884—91no—
343#884—91no—
344#884—181no—
345#883—91no—
346#67⋊C4—31no—
347#67⋊C4—91no—
348D3×C22⋊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—121no—
408C2×C32×C4—31no—
409C2×C32×C4—31no—
410C2×C32×C4—31no—
411C2×C32×C4—31no—
412#638—22no—
413#638—22no—
414#638—62no—
415#638—121no—
416#638—121no—
417#638—121no—
418#638—122no—
419#638—122no—
420#638—122no—
421#638—124no—
422C2×C3⋊Dic3—22no—
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⋊Dic3C22×D311yescharacteristic
431C2×C3⋊Dic3C22×D311yescharacteristic
432C2×C3⋊Dic3C22×D311yescharacteristic
433C2×C3⋊Dic3C22×D311yescharacteristic
434C4⋊(C3⋊D3)—62no—
435C4×C3⋊D3—121no—
436C3×#67—22no—
437C3×#67—22no—
438C3×#67—42no—
439C3×#67—41no—
440C3×#67—41no—
441C3×#67—42no—
442C3×#67—62no—
443C3×#67—62no—
444C3×#67—62no—
445C3×#67—62no—
446C3×#67—62no—
447C3×#67—122no—
448C3×#67—122no—
449C2×C3×Dic3—21no—
450C2×C3×Dic3—21no—
451C2×C3×Dic3—21no—
452C2×C3×Dic3—21no—
453C2×C3×Dic3—31no—
454C2×C3×Dic3—31no—
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—61no—
462C2×C3×Dic3—61no—
463C2×C3×Dic3—61no—
464C2×C3×Dic3—61no—
465C2×C3×Dic3—62no—
466C2×C3×Dic3—62no—
467C2×C3×Dic3—62no—
468C2×C3×Dic3—122no—
469C2×C3×Dic3C22×D311yescharacteristic
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
477C3×D12—62no—
478C3×C4×D3—62no—
479C3×C4×D3—121no—
480C3×C4×D3—121no—
481#627—62no—
482#627—62no—
483#627—62no—
484#626—22no—
485#626—34no—
486#626—34no—
487#626—62no—
488#626—62no—
489#626—62no—
490#626—62no—
491#626—122no—
492#626—122no—
493#625—34no—
494#624—41no—
495#624—62no—
496#624—62no—
497D3×Dic3—22no—
498D3×Dic3—62no—
499D3×Dic3—62no—
500D3×Dic3—62no—
501D3×Dic3—62no—
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—22no—
513C32×D3—22no—
514C32×D3—41no—
515C24×C3—91no—
516C23×D3—31no—
517C23×D3—31no—
518C23×D3—91no—
519C23×D3—91no—
520C23×D3—91no—
521C23×D3—181no—
522C2×C3×D4—31no—
523C2×C3×D4—31no—
524C2×C3×D4—31no—
525C2×C3×D4—31no—
526C2×C3×D4—61no—
527C2×C3×D4—61no—
528C2×C3×D4—91no—
529C2×C3×D4—91no—
530C2×C3×D4—91no—
531C22×C3×C4—91no—
532C22×C3×C4—91no—
533C22×C3×C4—91no—
534C2×#67—31no—
535C2×#67—31no—
536C2×#67—31no—
537C2×#67—31no—
538C2×#67—31no—
539C2×#67—61no—
540C2×#67—61no—
541C2×#67—91no—
542C2×#67—91no—
543C2×#67—91no—
544C2×#67—91no—
545C2×#67—91no—
546C2×#67—91no—
547C2×#67—91no—
548C2×#67—91no—
549C2×#67—181no—
550C2×#67—181no—
551C2×#67—181no—
552C2×#67—181no—
553C2×#67—184no—
554C2×#67—361no—
555C2×#67D3211yescharacteristic
556C2×#67D3211yescharacteristic, complemented
557C22×Dic3—31no—
558C22×Dic3—31no—
559C22×Dic3—31no—
560C22×Dic3—61no—
561C22×Dic3—91no—
562C22×Dic3—91no—
563C22×Dic3—91no—
564#237—184no—
565#237—184no—
566D3×D4—184no—
567#235—184no—
568C2×D12—31no—
569C2×D12—91no—
570C2×D12—91no—
571C2×D12—91no—
572C2×D12—91no—
573C2×D12—181no—
574C2×D12—184no—
575C2×C4×D3—31no—
576C2×C4×D3—31no—
577C2×C4×D3—31no—
578C2×C4×D3—91no—
579C2×C4×D3—91no—
580C2×C4×D3—91no—
581C2×C4×D3—91no—
582C2×C4×D3—91no—
583C2×C4×D3—91no—
584C2×C4×D3—181no—
585C2×Dic6—91no—
586C2×Dic6—91no—
587C2×Dic6—91no—
588C3×C4⋊C4—91no—
589C3×C4⋊C4—91no—
590C3×C22⋊C4—31no—
591C3×C22⋊C4—31no—
592C3×C22⋊C4—61no—
593C3×C22⋊C4—91no—
594C3×C22⋊C4—91no—
595C3×C22⋊C4—91no—
596C3×C22⋊C4—91no—
597C3×C22⋊C4—91no—
598C3×C42—91no—
599#217—31no—
600#217—31no—
601#217—31no—
602#217—31no—
603#217—91no—
604#217—91no—
605#217—91no—
606#217—91no—
607#217—91no—
608#217—181no—
609#217—181no—
610#217D3211yescharacteristic, complemented
611(C2×D3)⋊C4—31no—
612(C2×D3)⋊C4—31no—
613(C2×D3)⋊C4—31no—
614(C2×D3)⋊C4—31no—
615(C2×D3)⋊C4—31no—
616(C2×D3)⋊C4—31no—
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—91no—
629(C2×D3)⋊C4—91no—
630(C2×D3)⋊C4—181no—
631(C2×D3)⋊C4—181no—
632(C2×D3)⋊C4—181no—
633(C2×D3)⋊C4—181no—
634C4⋊Dic3—31no—
635C4⋊Dic3—31no—
636C4⋊Dic3—91no—
637Dic3⋊C4—31no—
638Dic3⋊C4—31no—
639Dic3⋊C4—91no—
640Dic3⋊C4—91no—
641Dic3⋊C4—91no—
642Dic3⋊C4—91no—
643Dic3⋊C4—91no—
644Dic3⋊C4—181no—
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—41no—
663C22×C32—41no—
664C22×C32—41no—
665C22×C32—42no—
666C22×C32—41no—
667C22×C32—41no—
668C22×C32—41no—
669C22×C32—41no—
670C22×C32—41no—
671C22×C32—41no—
672C22×C32—61no—
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—61no—
687C2×C3⋊D3—62no—
688C2×C3⋊D3—61no—
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—121no—
697C2×C3⋊D3—121no—
698C2×C3⋊D3—122no—
699C2×C3⋊D3—121no—
700C2×C3⋊D3—121no—
701C2×C3⋊D3—121no—
702C2×C3⋊D3—121no—
703C2×C3⋊D3—121no—
704C2×C3⋊D3—121no—
705C2×C3⋊D3—124no—
706C2×C3⋊D3—241no—
707C2×C3⋊D3—241no—
708C2×C3⋊D3D3×D412yes—
709C2×C3⋊D3D3×D412yes—
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—21no—
719C2×C3×D3—21no—
720C2×C3×D3—22no—
721C2×C3×D3—32no—
722C2×C3×D3—32no—
723C2×C3×D3—32no—
724C2×C3×D3—32no—
725C2×C3×D3—41no—
726C2×C3×D3—41no—
727C2×C3×D3—41no—
728C2×C3×D3—41no—
729C2×C3×D3—41no—
730C2×C3×D3—62no—
731C2×C3×D3—62no—
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—121no—
741C2×C3×D3—121no—
742C2×C3×D3—121no—
743C2×C3×D3—121no—
744C2×C3×D3—124no—
745C2×C3×D3—124no—
746C2×C3×D3#23512yescomplemented
747C2×C3×D3#23712yescomplemented
748D32—44no—
749D32—124no—
750D32—124no—
751D32—128no—
752C32×C4—61no—
753C32×C4—61no—
754C32×C4—61no—
755C32×C4—61no—
756C3⋊Dic3—21no—
757C3⋊Dic3—21no—
758C3⋊Dic3—21no—
759C3⋊Dic3—61no—
760C3⋊Dic3—62no—
761C3⋊Dic3—61no—
762C3⋊Dic3—61no—
763C3⋊Dic3—121no—
764C3⋊Dic3—121no—
765C3⋊Dic3—122no—
766C3⋊Dic3D3×D412yes—
767C3×Dic3—21no—
768C3×Dic3—21no—
769C3×Dic3—21no—
770C3×Dic3—21no—
771C3×Dic3—21no—
772C3×Dic3—21no—
773C3×Dic3—21no—
774C3×Dic3—21no—
775C3×Dic3—32no—
776C3×Dic3—32no—
777C3×Dic3—41no—
778C3×Dic3—41no—
779C3×Dic3—41no—
780C3×Dic3—41no—
781C3×Dic3—62no—
782C3×Dic3—61no—
783C3×Dic3—61no—
784C3×Dic3—61no—
785C3×Dic3—61no—
786C3×Dic3—61no—
787C3×Dic3—61no—
788C3×Dic3—121no—
789C3×Dic3—121no—
790C3×Dic3—121no—
791C2×#41—271no—
792C22×D4—271no—
793#124—271no—
794#123—271no—
795#123—271no—
796C22⋊Q8—271no—
797#121—91no—
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×D4—62no—
859C3×D4—62no—
860C3×D4—122no—
861C3×D4—121no—
862C3×D4—121no—
863C3×D4—122no—
864C3×D4—182no—
865C3×D4—182no—
866C3×D4—182no—
867C2×C3×C4—31no—
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—61no—
876C2×C3×C4—61no—
877C2×C3×C4—61no—
878C2×C3×C4—61no—
879C2×C3×C4—91no—
880C2×C3×C4—91no—
881C2×C3×C4—91no—
882C2×C3×C4—91no—
883C2×C3×C4—182no—
884C2×C3×C4—182no—
885C2×C3×C4—361no—
886#67—22no—
887#67—41no—
888#67—62no—
889#67—62no—
890#67—62no—
891#67—62no—
892#67—62no—
893#67—94no—
894#67—94no—
895#67—122no—
896#67—122no—
897#67—182no—
898#67—182no—
899#67—182no—
900#67—362no—
901#67—361no—
902#67—361no—
903#67—361no—
904#67—362no—
905#67—362no—
906#67—362no—
907#67—364no—
908C2×Dic3—31no—
909C2×Dic3—31no—
910C2×Dic3—31no—
911C2×Dic3—31no—
912C2×Dic3—31no—
913C2×Dic3—31no—
914C2×Dic3—31no—
915C2×Dic3—31no—
916C2×Dic3—61no—
917C2×Dic3—61no—
918C2×Dic3—61no—
919C2×Dic3—61no—
920C2×Dic3—62no—
921C2×Dic3—62no—
922C2×Dic3—62no—
923C2×Dic3—91no—
924C2×Dic3—91no—
925C2×Dic3—91no—
926C2×Dic3—122no—
927C2×Dic3—181no—
928C2×Dic3—181no—
929C2×Dic3—181no—
930C2×Dic3—182no—
931C2×Dic3—182no—
932C2×Dic3—361no—
933C2×Dic3—361no—
934C2×Dic3C2×D3211yescharacteristic
935C2×Dic3C2×D3211yescharacteristic
936C2×Dic3C2×D3211yescharacteristic
937C2×Dic3C2×D3211yescharacteristic
938D12—62no—
939D12—94no—
940D12—182no—
941D12—182no—
942D12—182no—
943D12—362no—
944C4×D3—62no—
945C4×D3—121no—
946C4×D3—121no—
947C4×D3—182no—
948C4×D3—182no—
949C4×D3—182no—
950C4×D3—182no—
951C4×D3—361no—
952C4×D3—361no—
953C4×D3—362no—
954Dic6—182no—
955Dic6—182no—
956Dic6—182no—
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—81no—
975C2×C32—81no—
976C2×C32—82no—
977C2×C32—121no—
978C2×C32C2×#23511yescharacteristic
979C2×C32C2×D3×D411yescharacteristic
980C2×C32C2×D3×D411yescharacteristic
981C2×C32C2×D3×D411yescharacteristic
982C2×C32C2×#23711yescharacteristic
983C2×C32#100411yescharacteristic
984C2×C32#100411yescharacteristic
985C2×C32D3×#4111yescharacteristic
986C2×C32#100911yescharacteristic
987C3⋊D3—22no—
988C3⋊D3—22no—
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—42no—
999C3×D3—41no—
1000C3×D3—41no—
1001C3×D3—62no—
1002C3×D3—62no—
1003C3×D3—62no—
1004C3×D3—62no—
1005C3×D3—81no—
1006C3×D3—122no—
1007C3×D3—122no—
1008C24—91no—
1009C24—271no—
1010#41—544no—
1011C2×Q8—271no—
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—91no—
1023C22×C4—91no—
1024C22×C4—91no—
1025C22×C4—271no—
1026C22×C4—271no—
1027C22×C4—271no—
1028C4⋊C4—91no—
1029C4⋊C4—91no—
1030C4⋊C4—271no—
1031C4⋊C4—271no—
1032C22⋊C4—31no—
1033C22⋊C4—91no—
1034C22⋊C4—91no—
1035C22⋊C4—91no—
1036C22⋊C4—91no—
1037C22⋊C4—91no—
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—41no—
1061C22×C3—41no—
1062C22×C3—41no—
1063C22×C3—41no—
1064C22×C3—41no—
1065C22×C3—41no—
1066C22×C3—41no—
1067C22×C3—41no—
1068C22×C3—42no—
1069C22×C3—41no—
1070C22×C3—62no—
1071C22×C3—61no—
1072C22×C3—61no—
1073C22×C3—61no—
1074C22×C3—61no—
1075C22×C3—61no—
1076C22×C3—61no—
1077C22×C3—61no—
1078C22×C3—61no—
1079C22×C3—61no—
1080C22×C3—61no—
1081C22×C3—81no—
1082C22×C3—81no—
1083C22×C3—92no—
1084C22×C3—92no—
1085C22×C3—121no—
1086C22×C3—121no—
1087C22×C3—121no—
1088C22×C3—121no—
1089C22×C3—121no—
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—21no—
1103C2×D3—32no—
1104C2×D3—32no—
1105C2×D3—32no—
1106C2×D3—32no—
1107C2×D3—62no—
1108C2×D3—62no—
1109C2×D3—61no—
1110C2×D3—61no—
1111C2×D3—61no—
1112C2×D3—61no—
1113C2×D3—61no—
1114C2×D3—61no—
1115C2×D3—61no—
1116C2×D3—61no—
1117C2×D3—121no—
1118C2×D3—121no—
1119C2×D3—121no—
1120C2×D3—121no—
1121C2×D3—124no—
1122C2×D3—124no—
1123C2×D3—182no—
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—181no—
1133C2×D3—361no—
1134C2×D3—361no—
1135C2×D3—361no—
1136C2×D3—361no—
1137C2×D3—361no—
1138C2×D3—361no—
1139C2×D3—361no—
1140C2×D3—361no—
1141C2×D3—362no—
1142C2×D3—364no—
1143C2×D3—364no—
1144C2×D3—364no—
1145C2×D3—368no—
1146C2×D3—721no—
1147C2×D3—721no—
1148C2×D3#380412yescomplemented
1149C3×C4—61no—
1150C3×C4—61no—
1151C3×C4—61no—
1152C3×C4—61no—
1153C3×C4—61no—
1154C3×C4—61no—
1155C3×C4—61no—
1156C3×C4—61no—
1157C3×C4—92no—
1158C3×C4—121no—
1159C3×C4—121no—
1160C3×C4—121no—
1161C3×C4—121no—
1162C3×C4—181no—
1163C3×C4—181no—
1164C3×C4—181no—
1165Dic3—21no—
1166Dic3—21no—
1167Dic3—21no—
1168Dic3—21no—
1169Dic3—32no—
1170Dic3—32no—
1171Dic3—62no—
1172Dic3—61no—
1173Dic3—61no—
1174Dic3—61no—
1175Dic3—61no—
1176Dic3—61no—
1177Dic3—61no—
1178Dic3—121no—
1179Dic3—121no—
1180Dic3—121no—
1181Dic3—182no—
1182Dic3—181no—
1183Dic3—181no—
1184Dic3—181no—
1185Dic3—361no—
1186Dic3—361no—
1187Dic3—362no—
1188C32—21no—
1189C32—21no—
1190C32—21no—
1191C32—41no—
1192C32#555011yescharacteristic, complemented
1193C32#559111yescharacteristic, complemented
1194C32#561011yescharacteristic, 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—542no—
1208D4—62no—
1209D4—121no—
1210D4—182no—
1211D4—182no—
1212D4—182no—
1213D4—274no—
1214D4—542no—
1215D4—542no—
1216D4—1081no—
1217C2×C4—31no—
1218C2×C4—31no—
1219C2×C4—31no—
1220C2×C4—31no—
1221C2×C4—91no—
1222C2×C4—91no—
1223C2×C4—91no—
1224C2×C4—91no—
1225C2×C4—182no—
1226C2×C4—182no—
1227C2×C4—271no—
1228C2×C4—361no—
1229C2×C4—542no—
1230C2×C4—542no—
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—81no—
1251C2×C3—81no—
1252C2×C3—82no—
1253C2×C3—122no—
1254C2×C3—121no—
1255C2×C3—121no—
1256C2×C3—182no—
1257C2×C3—182no—
1258C2×C3—241no—
1259C2×C3D3×#23511yescharacteristic
1260C2×C3D32×D411yescharacteristic
1261C2×C3D32×D411yescharacteristic
1262C2×C3D32×D411yescharacteristic
1263C2×C3D3×#23711yescharacteristic
1264C2×C3#6431411yescharacteristic
1265C2×C3#6431411yescharacteristic
1266C2×C3C2×#380411yescharacteristic
1267C2×C3#6433011yescharacteristic
1268D3—22no—
1269D3—41no—
1270D3—62no—
1271D3—62no—
1272D3—62no—
1273D3—62no—
1274D3—122no—
1275D3—122no—
1276D3—362no—
1277D3—361no—
1278D3—361no—
1279D3—361no—
1280D3—721no—
1281D3—721no—
1282D3—722no—
1283C22—21no—
1284C22—21no—
1285C22—21no—
1286C22—32no—
1287C22—61no—
1288C22—61no—
1289C22—61no—
1290C22—61no—
1291C22—61no—
1292C22—92no—
1293C22—92no—
1294C22—181no—
1295C22—181no—
1296C22—181no—
1297C22—181no—
1298C22—364no—
1299C22—541no—
1300C22—541no—
1301C22—541no—
1302C22—1084no—
1303C22C2×D3311yescharacteristic
1304C4—61no—
1305C4—61no—
1306C4—61no—
1307C4—61no—
1308C4—92no—
1309C4—181no—
1310C4—181no—
1311C4—181no—
1312C4—541no—
1313C3—21no—
1314C3—21no—
1315C3—21no—
1316C3—41no—
1317C3#1059428311yescharacteristic, complemented
1318C3#1059513511yescharacteristic, complemented
1319C3#1059529011yescharacteristic, complemented
1320C2—41no—
1321C2—62no—
1322C2—121no—
1323C2—182no—
1324C2—182no—
1325C2—1081no—
1326C2D3×#380411yescharacteristic
1327C2#1172441911yescharacteristic
1328C2#1172444011yescharacteristic
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×#89046C2semidirect
2. C2×D3×#626C2semidirect
3. #11723643C2semidirect
4. #11723635C2semidirect
5. #11723624C2semidirect
6. C3×#63983C2semidirect
7. C3×#67⋊Dic3C2semidirect
8. C3×#63958C2semidirect
9. #11723008C2semidirect
10. #11722999C2semidirect
11. #11722994C2semidirect
12. #11722978C2semidirect
13. #11722934C2semidirect
14. #11722904C2semidirect
15. #11722902C2semidirect
21. C2×#6312C22semidirect
22. C2×C3×#638C22semidirect
23. C2×C3×#638C22semidirect
24. C22×C3×C3⋊Dic3C22semidirect
26. C2×C32×#67C22semidirect
27. C2×#6296C22semidirect
30. C2×#6294C22semidirect
31. C2×#6294C22semidirect
34. C2×Dic3×C3⋊D3C22semidirect
36. C2×C3×#624C22semidirect
39. C32×#217C22semidirect
40. #88807C22semidirect
41. #88806C22semidirect
42. #88804C22semidirect
43. #88804C22semidirect
44. #88804C22semidirect
45. #88803C22semidirect
47. (C2×D3)⋊(C3⋊Dic3)C22semidirect
48. C3×Dic3⋊Dic3C22semidirect
49. C3×Dic3⋊Dic3C22semidirect
50. C3×#3722C22semidirect
53. C3×(C2×D3)⋊Dic3C22semidirect
54. C3×(C2×D3)⋊Dic3C22semidirect
55. C3×Dic32C22semidirect
74. #63983D3semidirect
79. #67⋊Dic3D3semidirect
87. #63958D3semidirect
132. #6295D4semidirect
161. C2×#638C2×D3semidirect
162. C2×#638C2×D3semidirect
163. C22×C3⋊Dic3C2×D3semidirect
177. C2×C3×#67C2×D3semidirect
178. C2×C3×#67C2×D3semidirect
204. C2×#624C2×D3semidirect
231. C3×#217C2×D3semidirect
232. C3×#217C2×D3semidirect
251. Dic3⋊Dic3C2×D3semidirect
252. Dic3⋊Dic3C2×D3semidirect
262. #3722C2×D3semidirect
274. (C2×D3)⋊Dic3C2×D3semidirect
275. (C2×D3)⋊Dic3C2×D3semidirect
276. Dic32C2×D3semidirect
295. C2×C32×D3#41semidirect
556. C2×#67D32semidirect
610. #217D32semidirect
746. C2×C3×D3#235semidirect
747. C2×C3×D3#237semidirect
806. C33#546semidirect
1148. C2×D3#3804semidirect
1192. C32#5550semidirect
1193. C32#5591semidirect
1194. C32#5610semidirect
1317. C3#10594283semidirect
1318. C3#10595135semidirect
1319. C3#10595290semidirect

Maximal subgroups

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

subgroupindex
C2×#890462
C2×D3×#6262
#117236432
#117236352
#117236242
C3×#639832
C3×#67⋊Dic32
C3×#639582
#117230082
#117229992
#117229942
#117229782
#117229342
#117229042
#117229022
#105952903
#105951353
#105942833