Finite Group Databasebeta

← #13172850

Subgroups — #13172850

Order 1728.

1798 conjugacy classes of subgroups.

The subgroup lattice has 1340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#638C211yesmaximal, characteristic, complemented
2C2×#88959C211yesmaximal, characteristic, complemented
3#11723718C211yesmaximal, characteristic, complemented
4#11723628C211yesmaximal, characteristic, complemented
5#11723599C211yesmaximal, characteristic, complemented
6C3×#63976C211yesmaximal, characteristic, complemented
7C3×#63971C211yesmaximal, characteristic, complemented
8C3×D3×#217C211yesmaximal, characteristic, complemented
9#11722988C211yesmaximal, characteristic, complemented
10#11722981C211yesmaximal, characteristic, complemented
11#11722956C211yesmaximal, characteristic, complemented
12#11722949C211yesmaximal, characteristic, complemented
13#11722935C211yesmaximal, characteristic, complemented
14#11722924C211yesmaximal, characteristic, complemented
15#11722906C211yesmaximal, characteristic, complemented
16#10595500—31nomaximal
17#10595294—31nomaximal
18#10594278—31nomaximal
19C23×C32×D3C2211yescharacteristic
20C22×D3×C3⋊D3C2211yescharacteristic
21C2×#6312C2211yescharacteristic
22C2×C3×#638C2211yescharacteristic
23C2×C32×#67C2211yescharacteristic, complemented
24C2×#6296C2211yescharacteristic, complemented
25D3×#638—24no—
26C2×#6291C2211yescharacteristic
27C2×#6291C2211yescharacteristic, complemented
28C2×#6290C2211yescharacteristic
29C2×#6289C2211yescharacteristic, complemented
30C2×#6289C2211yescharacteristic, complemented
31C2×D3×C3⋊Dic3C2211yescharacteristic
32C2×C3×#626C2211yescharacteristic, complemented
33C2×C3×#625C2211yescharacteristic
34C2×C3×#625C2211yescharacteristic, complemented
35C2×C3×D3×Dic3C2211yescharacteristic, complemented
36C2×C3×D3×Dic3C2211yescharacteristic, complemented
37C2×C3×D3×Dic3C2211yescharacteristic, complemented
38#88959—24no—
39C3×#3757C2211yescharacteristic, complemented
40C3×#3757C2211yescharacteristic, complemented
41C32×#217C2211yescharacteristic, complemented
42#88814C2211yescharacteristic, complemented
43#88814C2211yescharacteristic, complemented
44#88813C2211yescharacteristic, complemented
45#88807C2211yescharacteristic, complemented
46Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
47Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
48#88804C2211yescharacteristic, complemented
49(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
50C3×#3724C2211yescharacteristic, complemented
51C3×#3722C2211yescharacteristic, complemented
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×(C2×D3)⋊Dic3C2211yescharacteristic
54C3×(C2×D3)⋊Dic3C2211yescharacteristic
55C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
56C22×#638—31no—
57C2×D3×#67—31no—
58C2×D3×#67—31no—
59C2×D3×#67—61no—
60C2×#3804—31no—
61C2×#3804—31no—
62C2×#3798—31no—
63#64147—31no—
64#64092—31no—
65C3×#953—31no—
66C2×C3×#217—31no—
67C3×#939—31no—
68C3×#937—31no—
69C3×#884—31no—
70C3×D3×C22⋊C4—31no—
71#63983—31no—
72#63982—31no—
73#63981—31no—
74#63978—31no—
75#63976D311yescharacteristic, complemented
76#63975—31no—
77#63975—31no—
78#63975—61no—
79#63974—31no—
80#67⋊Dic3—31no—
81Dic3×#67—31no—
82#63971D311yescharacteristic, complemented
83#63970—31no—
84D3×#217D311yescharacteristic, complemented
85#63966—31no—
86#63959—31no—
87#63959—31no—
88#63958—31no—
89#63958—31no—
90#63958—61no—
91#63953—31no—
92#63952—31no—
93#63922—31no—
94#63921—31no—
95#63921—31no—
96#63908—31no—
97#63905—31no—
98#63904—31no—
99#63893—31no—
100#63893—31no—
101#63891—31no—
102#63881—31no—
103#63879—31no—
104C23×C33C2311yescharacteristic
105C22×C3⋊(C3⋊D3)C2311yescharacteristic
106C22×C3×C3⋊D3C2311yescharacteristic
107C22×C32×D3—22no—
108C22×C32×D3—22no—
109C22×C32×D3—41no—
110C22×C32×D3C2311yescharacteristic
111C22×C32×D3C2311yescharacteristic
112C22×C32×D3C2311yescharacteristic
113C2×D3×C3⋊D3—22no—
114C2×D3×C3⋊D3—22no—
115C2×D3×C3⋊D3—41no—
116#6312—22no—
117C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
118C3×#638—22no—
119C2×C3×C3⋊Dic3C2311yescharacteristic
120C2×C3×C3⋊Dic3C2311yescharacteristic
121C2×C3×C3⋊Dic3C2311yescharacteristic
122C2×C3×C3⋊Dic3C2311yescharacteristic
123C2×C3×C3⋊Dic3C2311yescharacteristic
124C32×#67—41no—
125C2×C32×Dic3C2311yescharacteristic
126C2×C32×Dic3C2311yescharacteristic
127C2×C32×Dic3C2311yescharacteristic
128#6296—22no—
129#6291—22no—
130#6291D414yescomplemented
131#6290—22no—
132#6289—22no—
133#6289—41no—
134D3×C3⋊Dic3—22no—
135C3×#626—41no—
136C3×#625—22no—
137C3×#625—22no—
138C3×D3×Dic3—22no—
139C3×D3×Dic3—22no—
140C3×D3×Dic3—41no—
141#5612—91no—
142#5591—91no—
143#5490—91no—
144C24×C32—31no—
145C23×C3⋊D3—31no—
146C23×C3×D3—21no—
147C23×C3×D3C2×D311yescharacteristic
148C23×C3×D3C2×D311yescharacteristic
149C22×D32—31no—
150C22×D32—31no—
151C22×D32—61no—
152C2×C32×D4—31no—
153C2×#638—31no—
154C2×#638—31no—
155C2×#638—31no—
156C2×#638—31no—
157C2×#638—31no—
158C2×#638—31no—
159C2×#638—64no—
160C2×#638—61no—
161C2×#638—61no—
162C2×#638—61no—
163C2×#638—121no—
164C2×#638C2×D311yescharacteristic
165C22×C3⋊Dic3—31no—
166C2×C4×C3⋊D3—31no—
167C2×C4×C3⋊D3—31no—
168C2×C3×#67—21no—
169C2×C3×#67—31no—
170C2×C3×#67—31no—
171C2×C3×#67—31no—
172C2×C3×#67—31no—
173C2×C3×#67—31no—
174C2×C3×#67—31no—
175C2×C3×#67—31no—
176C2×C3×#67—61no—
177C2×C3×#67C2×D311yescharacteristic, complemented
178C2×C3×#67C2×D311yescharacteristic, complemented
179C22×C3×Dic3—31no—
180C22×C3×Dic3—31no—
181C22×C3×Dic3—31no—
182C2×C3×D12—31no—
183C2×C3×C4×D3—31no—
184C2×C3×C4×D3—31no—
185C2×C3×C4×D3—31no—
186D3×#67—64no—
187D3×#67—64no—
188D3×#67—68no—
189C2×#627—31no—
190C2×#627—31no—
191C2×#627—31no—
192C2×#626—31no—
193C2×#626—31no—
194C2×#626—31no—
195C2×#626—31no—
196C2×#626—61no—
197C2×#626—61no—
198C2×#626C2×D311yescharacteristic, complemented
199C2×#625—31no—
200C2×#625—31no—
201C2×#625—61no—
202C2×#625C2×D311yescharacteristic
203C2×#625C2×D311yescharacteristic, complemented
204C2×#624—31no—
205C2×#624—31no—
206C2×#624—31no—
207C2×#624—31no—
208C2×#624—61no—
209C2×#624—61no—
210#3804—64no—
211#3804—64no—
212C2×D3×Dic3—31no—
213C2×D3×Dic3—31no—
214C2×D3×Dic3—61no—
215C2×D3×Dic3C2×D311yescharacteristic, complemented
216C2×D3×Dic3C2×D311yescharacteristic, complemented
217C2×D3×Dic3C2×D311yescharacteristic, complemented
218#3798—64no—
219C32×C22⋊C4—31no—
220#3757—31no—
221#3757C2×D311yescharacteristic, complemented
222#3757C2×D311yescharacteristic, complemented
223#3752—31no—
224C4⋊(C3⋊Dic3)—31no—
225C4⋊(C3⋊Dic3)—31no—
226#3750—31no—
227C3×#217—21no—
228C3×#217—31no—
229C3×#217—31no—
230C3×#217—31no—
231C3×#217—31no—
232C3×#217—31no—
233C3×#217—31no—
234C3×#217—31no—
235C3×#217—31no—
236C3×#217—61no—
237C3×#217—61no—
238C3×#217C2×D311yescharacteristic, complemented
239C3×#217C2×D311yescharacteristic, complemented
240C3×(C2×D3)⋊C4—31no—
241C3×(C2×D3)⋊C4—31no—
242C3×(C2×D3)⋊C4—31no—
243C3×(C2×D3)⋊C4—31no—
244C3×(C2×D3)⋊C4—31no—
245C3×(C2×D3)⋊C4—31no—
246C3×Dic3⋊C4—31no—
247C3×Dic3⋊C4—31no—
248#3724C2×D311yescharacteristic, complemented
249Dic3⋊Dic3—31no—
250Dic3⋊Dic3—31no—
251Dic3⋊Dic3—31no—
252Dic3⋊Dic3—31no—
253Dic3⋊Dic3—31no—
254Dic3⋊Dic3—31no—
255Dic3⋊Dic3—61no—
256Dic3⋊Dic3—61no—
257Dic3⋊Dic3—61no—
258#3722—31no—
259#3722—31no—
260#3722—31no—
261#3722—31no—
262#3722—61no—
263#3722C2×D311yescharacteristic, complemented
264(C2×D3)⋊Dic3—31no—
265(C2×D3)⋊Dic3—31no—
266(C2×D3)⋊Dic3—31no—
267(C2×D3)⋊Dic3—31no—
268(C2×D3)⋊Dic3—31no—
269(C2×D3)⋊Dic3—31no—
270(C2×D3)⋊Dic3—61no—
271(C2×D3)⋊Dic3C2×D311yescharacteristic
272(C2×D3)⋊Dic3C2×D311yescharacteristic
273(C2×D3)⋊Dic3C2×D311yescharacteristic
274(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
275Dic32—31no—
276Dic32—31no—
277Dic32—31no—
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×C32×D3—21no—
289C2×C32×D3—21no—
290C2×C32×D3—21no—
291C2×C32×D3—21no—
292C2×C32×D3—21no—
293C2×C32×D3—21no—
294C2×C32×D3—21no—
295C2×C32×D3—44no—
296C2×C32×D3C2×D412yes—
297C2×C32×D3#4112yescomplemented
298D3×C3⋊D3—44no—
299C3⋊(C3⋊Dic3)—21no—
300C3×C3⋊Dic3—21no—
301C3×C3⋊Dic3—21no—
302C3×C3⋊Dic3—21no—
303C3×C3⋊Dic3—21no—
304C3×C3⋊Dic3C2×D412yes—
305C32×Dic3—21no—
306C32×Dic3—21no—
307C32×Dic3—21no—
308C22×#67—91no—
309C22×#67—91no—
310C22×#67—181no—
311C2×#237—91no—
312C2×D3×D4—91no—
313C2×#235—91no—
314C2×#235—91no—
315C3×#121—91no—
316C3×#120—91no—
317C2×C3×C22⋊C4—91no—
318#953—31no—
319C2×#217—31no—
320#939—31no—
321#939—91no—
322#938—91no—
323#938—91no—
324#938—91no—
325#938—181no—
326#937—31no—
327#937—91no—
328#937—91no—
329#936—91no—
330D4×Dic3—91no—
331#930—91no—
332#929—91no—
333C4×#67—91no—
334C4×#67—91no—
335#897—91no—
336#893—91no—
337#886—91no—
338#885—91no—
339#885—91no—
340#884—31no—
341#884—91no—
342#883—91no—
343#883—91no—
344#883—91no—
345#883—91no—
346#883—181no—
347#882—91no—
348#67⋊C4—91no—
349#67⋊C4—91no—
350D3×C22⋊C4—31no—
351D3×C22⋊C4—91no—
352D3×C22⋊C4—91no—
353D3×C22⋊C4—91no—
354#878—91no—
355#878—91no—
356C23×C32—21no—
357C23×C32—21no—
358C23×C32—21no—
359C23×C32—31no—
360C23×C32—31no—
361C23×C32—31no—
362C23×C32—41no—
363C23×C32—62no—
364C23×C32—62no—
365C23×C32—121no—
366C23×C32C22×D311yescharacteristic
367C23×C32C22×D311yescharacteristic
368C23×C32C22×D311yescharacteristic
369C22×C3⋊D3—31no—
370C22×C3⋊D3—31no—
371C22×C3⋊D3—31no—
372C22×C3⋊D3—61no—
373C22×C3⋊D3—61no—
374C22×C3⋊D3—61no—
375C22×C3⋊D3—62no—
376C22×C3⋊D3—62no—
377C22×C3⋊D3—121no—
378C22×C3⋊D3—121no—
379C22×C3⋊D3C22×D311yescharacteristic
380C22×C3×D3—24no—
381C22×C3×D3—22no—
382C22×C3×D3—22no—
383C22×C3×D3—22no—
384C22×C3×D3—22no—
385C22×C3×D3—21no—
386C22×C3×D3—21no—
387C22×C3×D3—21no—
388C22×C3×D3—31no—
389C22×C3×D3—31no—
390C22×C3×D3—42no—
391C22×C3×D3—41no—
392C22×C3×D3—41no—
393C22×C3×D3—42no—
394C22×C3×D3—61no—
395C22×C3×D3C22×D311yescharacteristic
396C22×C3×D3C22×D311yescharacteristic
397C22×C3×D3C22×D311yescharacteristic
398C22×C3×D3C22×D311yescharacteristic
399C22×C3×D3C22×D311yescharacteristic
400C22×C3×D3C22×D311yescharacteristic
401C2×D32—62no—
402C2×D32—62no—
403C2×D32—64no—
404C2×D32—62no—
405C2×D32—62no—
406C2×D32—122no—
407C2×D32—121no—
408C2×D32—121no—
409C2×D32—122no—
410C32×D4—121no—
411C2×C32×C4—31no—
412C2×C32×C4—31no—
413C2×C32×C4—31no—
414#638—22no—
415#638—34no—
416#638—62no—
417#638—62no—
418#638—62no—
419#638—62no—
420#638—62no—
421#638—64no—
422#638—122no—
423#638—122no—
424#638—124no—
425C2×C3⋊Dic3—31no—
426C2×C3⋊Dic3—31no—
427C2×C3⋊Dic3—31no—
428C2×C3⋊Dic3—61no—
429C2×C3⋊Dic3—61no—
430C2×C3⋊Dic3—61no—
431C2×C3⋊Dic3—62no—
432C2×C3⋊Dic3—121no—
433C2×C3⋊Dic3C22×D311yescharacteristic
434C2×C3⋊Dic3C22×D311yescharacteristic
435C2×C3⋊Dic3C22×D311yescharacteristic
436C2×C3⋊Dic3C22×D311yescharacteristic
437C2×C3⋊Dic3C22×D311yescharacteristic
438C4×C3⋊D3—62no—
439C4×C3⋊D3—121no—
440C3×#67—41no—
441C3×#67—41no—
442C3×#67—42no—
443C3×#67—62no—
444C3×#67—62no—
445C3×#67—62no—
446C3×#67—62no—
447C3×#67—64no—
448C3×#67—62no—
449C3×#67—62no—
450C3×#67—121no—
451C2×C3×Dic3—21no—
452C2×C3×Dic3—21no—
453C2×C3×Dic3—21no—
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—31no—
462C2×C3×Dic3—31no—
463C2×C3×Dic3—31no—
464C2×C3×Dic3—61no—
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—121no—
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—121no—
479C3×C4×D3—62no—
480C3×C4×D3—62no—
481C3×C4×D3—121no—
482#627—62no—
483#627—62no—
484#627—62no—
485#626—34no—
486#626—34no—
487#626—41no—
488#626—64no—
489#626—62no—
490#626—62no—
491#626—122no—
492#625—22no—
493#625—22no—
494#625—64no—
495#625—62no—
496#625—62no—
497#624—62no—
498#624—62no—
499#624—122no—
500#624—121no—
501#624—121no—
502#624—122no—
503D3×Dic3—22no—
504D3×Dic3—22no—
505D3×Dic3—41no—
506D3×Dic3—62no—
507D3×Dic3—62no—
508D3×Dic3—64no—
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—
516C32×D3—22no—
517C32×D3—22no—
518C32×D3—41no—
519C24×C3—31no—
520C24×C3—31no—
521C24×C3—61no—
522C23×D3—91no—
523C23×D3—91no—
524C23×D3—91no—
525C23×D3—181no—
526C23×D3D3211yescharacteristic
527C2×C3×D4—31no—
528C2×C3×D4—31no—
529C2×C3×D4—61no—
530C2×C3×D4—91no—
531C2×C3×D4—91no—
532C2×C3×D4—91no—
533C2×C3×D4—91no—
534C22×C3×C4—91no—
535C22×C3×C4—91no—
536C22×C3×C4—91no—
537C2×#67—31no—
538C2×#67—31no—
539C2×#67—31no—
540C2×#67—31no—
541C2×#67—31no—
542C2×#67—31no—
543C2×#67—31no—
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—91no—
554C2×#67—91no—
555C2×#67—181no—
556C2×#67—181no—
557C2×#67—181no—
558C2×#67—181no—
559C2×#67—181no—
560C2×#67—181no—
561C2×#67—184no—
562C2×#67—184no—
563C2×#67—188no—
564C2×#67—361no—
565C2×#67D3211yescharacteristic, complemented
566C22×Dic3—31no—
567C22×Dic3—31no—
568C22×Dic3—31no—
569C22×Dic3—91no—
570C22×Dic3—91no—
571C22×Dic3—181no—
572#237—184no—
573D3×D4—184no—
574#235—184no—
575#235—184no—
576C2×D12—31no—
577C2×D12—91no—
578C2×D12—91no—
579C2×C4×D3—31no—
580C2×C4×D3—31no—
581C2×C4×D3—31no—
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×Dic6—91no—
592C2×Dic6—91no—
593C2×Dic6—91no—
594C3×C4⋊C4—91no—
595C3×C22⋊C4—31no—
596C3×C22⋊C4—31no—
597C3×C22⋊C4—61no—
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—
605#217—31no—
606#217—31no—
607#217—31no—
608#217—31no—
609#217—31no—
610#217—31no—
611#217—31no—
612#217—31no—
613#217—61no—
614#217—61no—
615#217—91no—
616#217—91no—
617#217—91no—
618#217—91no—
619#217—181no—
620#217D3211yescharacteristic, complemented
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—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—181no—
636C4⋊Dic3—91no—
637C4⋊Dic3—91no—
638C4⋊Dic3—91no—
639C4⋊Dic3—91no—
640C4⋊Dic3—91no—
641C4⋊Dic3—181no—
642C4⋊Dic3—181no—
643Dic3⋊C4—31no—
644Dic3⋊C4—31no—
645Dic3⋊C4—91no—
646Dic3⋊C4—91no—
647Dic3⋊C4—91no—
648Dic3⋊C4—91no—
649Dic3⋊C4—181no—
650C4×Dic3—91no—
651C4×Dic3—91no—
652C4×Dic3—91no—
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—61no—
683C22×C32—61no—
684C22×C32—61no—
685C22×C32—81no—
686C22×C32—81no—
687C22×C32—124no—
688C22×C32C23×D311yescharacteristic
689C22×C32C23×D311yescharacteristic
690C22×C32C23×D311yescharacteristic
691C2×C3⋊D3—21no—
692C2×C3⋊D3—21no—
693C2×C3⋊D3—21no—
694C2×C3⋊D3—32no—
695C2×C3⋊D3—32no—
696C2×C3⋊D3—32no—
697C2×C3⋊D3—62no—
698C2×C3⋊D3—62no—
699C2×C3⋊D3—62no—
700C2×C3⋊D3—61no—
701C2×C3⋊D3—61no—
702C2×C3⋊D3—61no—
703C2×C3⋊D3—61no—
704C2×C3⋊D3—61no—
705C2×C3⋊D3—61no—
706C2×C3⋊D3—122no—
707C2×C3⋊D3—121no—
708C2×C3⋊D3—121no—
709C2×C3⋊D3—121no—
710C2×C3⋊D3—121no—
711C2×C3⋊D3—121no—
712C2×C3⋊D3—121no—
713C2×C3⋊D3—124no—
714C2×C3⋊D3—241no—
715C2×C3⋊D3—241no—
716C2×C3×D3—22no—
717C2×C3×D3—22no—
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—21no—
726C2×C3×D3—21no—
727C2×C3×D3—21no—
728C2×C3×D3—21no—
729C2×C3×D3—21no—
730C2×C3×D3—21no—
731C2×C3×D3—21no—
732C2×C3×D3—22no—
733C2×C3×D3—22no—
734C2×C3×D3—41no—
735C2×C3×D3—41no—
736C2×C3×D3—41no—
737C2×C3×D3—41no—
738C2×C3×D3—41no—
739C2×C3×D3—44no—
740C2×C3×D3—44no—
741C2×C3×D3—48no—
742C2×C3×D3—62no—
743C2×C3×D3—61no—
744C2×C3×D3—61no—
745C2×C3×D3—61no—
746C2×C3×D3—61no—
747C2×C3×D3—61no—
748C2×C3×D3—61no—
749C2×C3×D3—121no—
750C2×C3×D3—121no—
751C2×C3×D3#23512yescomplemented
752C2×C3×D3D3×D412yes—
753C2×C3×D3D3×D412yes—
754C2×C3×D3#23712yescomplemented
755D32—124no—
756D32—124no—
757D32—128no—
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⋊Dic3D3×D412yes—
773C3×Dic3—22no—
774C3×Dic3—21no—
775C3×Dic3—21no—
776C3×Dic3—21no—
777C3×Dic3—21no—
778C3×Dic3—21no—
779C3×Dic3—21no—
780C3×Dic3—32no—
781C3×Dic3—32no—
782C3×Dic3—41no—
783C3×Dic3—41no—
784C3×Dic3—62no—
785C3×Dic3—61no—
786C3×Dic3—61no—
787C3×Dic3—61no—
788C3×Dic3—61no—
789C3×Dic3—61no—
790C3×Dic3—61no—
791C3×Dic3—61no—
792C3×Dic3—61no—
793C3×Dic3—121no—
794C3×Dic3—121no—
795C3×Dic3—121no—
796C3×Dic3—121no—
797C2×#41—271no—
798C22×D4—271no—
799#124—271no—
800#123—271no—
801#123—271no—
802C22⋊Q8—271no—
803#121—91no—
804#121—271no—
805#121—271no—
806#120—91no—
807#120—271no—
808C4×D4—271no—
809C4×D4—271no—
810C2×C22⋊C4—91no—
811C2×C22⋊C4—271no—
812C33#54611yescharacteristic, complemented, Sylow
813C23×C3—21no—
814C23×C3—21no—
815C23×C3—21no—
816C23×C3—31no—
817C23×C3—31no—
818C23×C3—31no—
819C23×C3—31no—
820C23×C3—31no—
821C23×C3—31no—
822C23×C3—41no—
823C23×C3—61no—
824C23×C3—61no—
825C23×C3—61no—
826C23×C3—62no—
827C23×C3—62no—
828C23×C3—62no—
829C23×C3—62no—
830C23×C3—64no—
831C23×C3—91no—
832C23×C3—122no—
833C23×C3—121no—
834C23×C3—121no—
835C23×C3—122no—
836C23×C3C2×D3211yescharacteristic
837C23×C3C2×D3211yescharacteristic
838C23×C3C2×D3211yescharacteristic
839C22×D3—22no—
840C22×D3—22no—
841C22×D3—31no—
842C22×D3—31no—
843C22×D3—41no—
844C22×D3—61no—
845C22×D3—91no—
846C22×D3—91no—
847C22×D3—91no—
848C22×D3—181no—
849C22×D3—181no—
850C22×D3—181no—
851C22×D3—182no—
852C22×D3—182no—
853C22×D3—182no—
854C22×D3—182no—
855C22×D3—182no—
856C22×D3—184no—
857C22×D3—182no—
858C22×D3—361no—
859C22×D3—362no—
860C22×D3—361no—
861C22×D3—361no—
862C22×D3—361no—
863C22×D3—362no—
864C22×D3C2×D3211yescharacteristic
865C22×D3C2×D3211yescharacteristic
866C22×D3C2×D3211yescharacteristic
867C3×D4—121no—
868C3×D4—121no—
869C3×D4—122no—
870C3×D4—182no—
871C3×D4—182no—
872C3×D4—182no—
873C3×D4—361no—
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—91no—
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—41no—
892#67—62no—
893#67—62no—
894#67—62no—
895#67—62no—
896#67—64no—
897#67—62no—
898#67—62no—
899#67—94no—
900#67—94no—
901#67—121no—
902#67—184no—
903#67—182no—
904#67—182no—
905#67—182no—
906#67—182no—
907#67—184no—
908#67—182no—
909#67—182no—
910#67—182no—
911#67—184no—
912#67—182no—
913#67—362no—
914#67—362no—
915#67—362no—
916#67—364no—
917C2×Dic3—31no—
918C2×Dic3—31no—
919C2×Dic3—31no—
920C2×Dic3—31no—
921C2×Dic3—31no—
922C2×Dic3—31no—
923C2×Dic3—31no—
924C2×Dic3—31no—
925C2×Dic3—31no—
926C2×Dic3—31no—
927C2×Dic3—61no—
928C2×Dic3—61no—
929C2×Dic3—61no—
930C2×Dic3—61no—
931C2×Dic3—61no—
932C2×Dic3—62no—
933C2×Dic3—62no—
934C2×Dic3—91no—
935C2×Dic3—91no—
936C2×Dic3—91no—
937C2×Dic3—121no—
938C2×Dic3—181no—
939C2×Dic3—181no—
940C2×Dic3—181no—
941C2×Dic3—182no—
942C2×Dic3—182no—
943C2×Dic3—184no—
944C2×Dic3—361no—
945C2×Dic3C2×D3211yescharacteristic
946C2×Dic3C2×D3211yescharacteristic
947C2×Dic3C2×D3211yescharacteristic
948D12—94no—
949D12—121no—
950D12—182no—
951C4×D3—62no—
952C4×D3—62no—
953C4×D3—121no—
954C4×D3—182no—
955C4×D3—182no—
956C4×D3—182no—
957C4×D3—182no—
958C4×D3—362no—
959C4×D3—361no—
960C4×D3—361no—
961C4×D3—361no—
962C4×D3—362no—
963Dic6—182no—
964Dic6—182no—
965Dic6—182no—
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—21no—
975C2×C32—41no—
976C2×C32—41no—
977C2×C32—41no—
978C2×C32—41no—
979C2×C32—42no—
980C2×C32—41no—
981C2×C32—41no—
982C2×C32—62no—
983C2×C32—62no—
984C2×C32—81no—
985C2×C32—81no—
986C2×C32—82no—
987C2×C32—121no—
988C2×C32C2×#23511yescharacteristic
989C2×C32C2×D3×D411yescharacteristic
990C2×C32C2×D3×D411yescharacteristic
991C2×C32C2×D3×D411yescharacteristic
992C2×C32C2×#23711yescharacteristic
993C2×C32#100411yescharacteristic
994C2×C32#100411yescharacteristic
995C2×C32#100411yescharacteristic
996C2×C32D3×#4111yescharacteristic
997C3⋊D3—41no—
998C3⋊D3—62no—
999C3⋊D3—62no—
1000C3⋊D3—62no—
1001C3⋊D3—122no—
1002C3⋊D3—122no—
1003C3⋊D3—122no—
1004C3⋊D3—242no—
1005C3×D3—24no—
1006C3×D3—22no—
1007C3×D3—22no—
1008C3×D3—22no—
1009C3×D3—22no—
1010C3×D3—42no—
1011C3×D3—41no—
1012C3×D3—41no—
1013C3×D3—81no—
1014C3×D3—122no—
1015C3×D3—121no—
1016C3×D3—121no—
1017C24—31no—
1018C24—271no—
1019#41—544no—
1020C2×Q8—271no—
1021C2×D4—31no—
1022C2×D4—91no—
1023C2×D4—91no—
1024C2×D4—91no—
1025C2×D4—91no—
1026C2×D4—271no—
1027C2×D4—271no—
1028C2×D4—271no—
1029C2×D4—271no—
1030C2×D4—544no—
1031C22×C4—91no—
1032C22×C4—91no—
1033C22×C4—91no—
1034C22×C4—271no—
1035C22×C4—271no—
1036C22×C4—271no—
1037C4⋊C4—91no—
1038C4⋊C4—271no—
1039C4⋊C4—271no—
1040C4⋊C4—271no—
1041C22⋊C4—31no—
1042C22⋊C4—91no—
1043C22⋊C4—91no—
1044C22⋊C4—91no—
1045C22⋊C4—91no—
1046C22⋊C4—91no—
1047C22⋊C4—91no—
1048C22⋊C4—91no—
1049C22⋊C4—271no—
1050C22⋊C4—271no—
1051C22⋊C4—271no—
1052C22⋊C4—271no—
1053C42—271no—
1054C22×C3—22no—
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—21no—
1067C22×C3—32no—
1068C22×C3—32no—
1069C22×C3—32no—
1070C22×C3—32no—
1071C22×C3—41no—
1072C22×C3—41no—
1073C22×C3—41no—
1074C22×C3—41no—
1075C22×C3—41no—
1076C22×C3—41no—
1077C22×C3—41no—
1078C22×C3—41no—
1079C22×C3—42no—
1080C22×C3—41no—
1081C22×C3—62no—
1082C22×C3—62no—
1083C22×C3—62no—
1084C22×C3—62no—
1085C22×C3—61no—
1086C22×C3—61no—
1087C22×C3—61no—
1088C22×C3—61no—
1089C22×C3—61no—
1090C22×C3—61no—
1091C22×C3—61no—
1092C22×C3—61no—
1093C22×C3—61no—
1094C22×C3—61no—
1095C22×C3—61no—
1096C22×C3—61no—
1097C22×C3—61no—
1098C22×C3—61no—
1099C22×C3—81no—
1100C22×C3—81no—
1101C22×C3—121no—
1102C22×C3—121no—
1103C22×C3—121no—
1104C22×C3—121no—
1105C22×C3—121no—
1106C22×C3—124no—
1107C22×C3—124no—
1108C22×C3—128no—
1109C22×C3—181no—
1110C22×C3—181no—
1111C22×C3—181no—
1112C22×C3C22×D3211yescharacteristic
1113C22×C3C22×D3211yescharacteristic
1114C22×C3C22×D3211yescharacteristic
1115C2×D3—21no—
1116C2×D3—21no—
1117C2×D3—21no—
1118C2×D3—21no—
1119C2×D3—21no—
1120C2×D3—21no—
1121C2×D3—21no—
1122C2×D3—44no—
1123C2×D3—62no—
1124C2×D3—61no—
1125C2×D3—61no—
1126C2×D3—61no—
1127C2×D3—61no—
1128C2×D3—61no—
1129C2×D3—61no—
1130C2×D3—92no—
1131C2×D3—92no—
1132C2×D3—92no—
1133C2×D3—121no—
1134C2×D3—121no—
1135C2×D3—182no—
1136C2×D3—182no—
1137C2×D3—182no—
1138C2×D3—181no—
1139C2×D3—181no—
1140C2×D3—181no—
1141C2×D3—181no—
1142C2×D3—181no—
1143C2×D3—181no—
1144C2×D3—362no—
1145C2×D3—361no—
1146C2×D3—361no—
1147C2×D3—361no—
1148C2×D3—361no—
1149C2×D3—361no—
1150C2×D3—361no—
1151C2×D3—364no—
1152C2×D3—364no—
1153C2×D3—364no—
1154C2×D3—368no—
1155C2×D3—721no—
1156C2×D3—721no—
1157C2×D3#380412yescomplemented
1158C2×D3#381112yes—
1159C3×C4—62no—
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—181no—
1170C3×C4—181no—
1171C3×C4—181no—
1172C3×C4—181no—
1173Dic3—21no—
1174Dic3—21no—
1175Dic3—21no—
1176Dic3—32no—
1177Dic3—32no—
1178Dic3—62no—
1179Dic3—61no—
1180Dic3—61no—
1181Dic3—61no—
1182Dic3—61no—
1183Dic3—61no—
1184Dic3—61no—
1185Dic3—61no—
1186Dic3—61no—
1187Dic3—121no—
1188Dic3—121no—
1189Dic3—121no—
1190Dic3—121no—
1191Dic3—182no—
1192Dic3—181no—
1193Dic3—181no—
1194Dic3—181no—
1195Dic3—361no—
1196Dic3—361no—
1197Dic3—362no—
1198C32—21no—
1199C32—21no—
1200C32—21no—
1201C32—41no—
1202C32#549011yescharacteristic, complemented
1203C32#559111yescharacteristic, complemented
1204C32#561211yescharacteristic, complemented
1205C23—31no—
1206C23—31no—
1207C23—31no—
1208C23—62no—
1209C23—62no—
1210C23—91no—
1211C23—121no—
1212C23—271no—
1213C23—542no—
1214C23—542no—
1215C23—1081no—
1216C23D3311yescharacteristic
1217Q8—542no—
1218D4—121no—
1219D4—182no—
1220D4—182no—
1221D4—182no—
1222D4—274no—
1223D4—361no—
1224D4—542no—
1225D4—542no—
1226D4—542no—
1227C2×C4—31no—
1228C2×C4—31no—
1229C2×C4—31no—
1230C2×C4—91no—
1231C2×C4—91no—
1232C2×C4—91no—
1233C2×C4—91no—
1234C2×C4—91no—
1235C2×C4—182no—
1236C2×C4—182no—
1237C2×C4—271no—
1238C2×C4—361no—
1239C2×C4—542no—
1240C2×C4—542no—
1241C2×C4—1081no—
1242C2×C3—21no—
1243C2×C3—21no—
1244C2×C3—21no—
1245C2×C3—21no—
1246C2×C3—21no—
1247C2×C3—21no—
1248C2×C3—21no—
1249C2×C3—21no—
1250C2×C3—21no—
1251C2×C3—42no—
1252C2×C3—41no—
1253C2×C3—41no—
1254C2×C3—41no—
1255C2×C3—41no—
1256C2×C3—41no—
1257C2×C3—41no—
1258C2×C3—64no—
1259C2×C3—62no—
1260C2×C3—62no—
1261C2×C3—62no—
1262C2×C3—62no—
1263C2×C3—81no—
1264C2×C3—81no—
1265C2×C3—82no—
1266C2×C3—122no—
1267C2×C3—121no—
1268C2×C3—121no—
1269C2×C3—241no—
1270C2×C3—361no—
1271C2×C3D3×#23511yescharacteristic
1272C2×C3D32×D411yescharacteristic
1273C2×C3D32×D411yescharacteristic
1274C2×C3D3×#23711yescharacteristic
1275C2×C3#6431311yescharacteristic
1276C2×C3C2×#380411yescharacteristic
1277C2×C3C2×#381111yescharacteristic
1278C2×C3#6433011yescharacteristic
1279C2×C3#6433011yescharacteristic
1280D3—22no—
1281D3—22no—
1282D3—41no—
1283D3—122no—
1284D3—121no—
1285D3—121no—
1286D3—182no—
1287D3—182no—
1288D3—182no—
1289D3—362no—
1290D3—362no—
1291D3—362no—
1292D3—722no—
1293C22—21no—
1294C22—21no—
1295C22—21no—
1296C22—32no—
1297C22—32no—
1298C22—61no—
1299C22—61no—
1300C22—61no—
1301C22—61no—
1302C22—61no—
1303C22—61no—
1304C22—61no—
1305C22—124no—
1306C22—181no—
1307C22—181no—
1308C22—181no—
1309C22—272no—
1310C22—541no—
1311C22—541no—
1312C22—1084no—
1313C22C2×D3311yescharacteristic
1314C4—61no—
1315C4—61no—
1316C4—61no—
1317C4—92no—
1318C4—181no—
1319C4—181no—
1320C4—181no—
1321C4—181no—
1322C4—541no—
1323C3—21no—
1324C3—21no—
1325C3—21no—
1326C3—41no—
1327C3#1059427811yescharacteristic, complemented
1328C3#1059529411yescharacteristic, complemented
1329C3#1059550011yescharacteristic, complemented
1330C2—41no—
1331C2—62no—
1332C2—62no—
1333C2—121no—
1334C2—361no—
1335C2—542no—
1336C2D3×#380411yescharacteristic
1337C2#1172441411yescharacteristic
1338C2D3×#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×D3×#638C2semidirect
2. C2×#88959C2semidirect
3. #11723718C2semidirect
4. #11723628C2semidirect
5. #11723599C2semidirect
6. C3×#63976C2semidirect
7. C3×#63971C2semidirect
8. C3×D3×#217C2semidirect
9. #11722988C2semidirect
10. #11722981C2semidirect
11. #11722956C2semidirect
12. #11722949C2semidirect
13. #11722935C2semidirect
14. #11722924C2semidirect
15. #11722906C2semidirect
23. C2×C32×#67C22semidirect
24. C2×#6296C22semidirect
27. C2×#6291C22semidirect
29. C2×#6289C22semidirect
30. C2×#6289C22semidirect
32. C2×C3×#626C22semidirect
34. C2×C3×#625C22semidirect
35. C2×C3×D3×Dic3C22semidirect
36. C2×C3×D3×Dic3C22semidirect
37. C2×C3×D3×Dic3C22semidirect
39. C3×#3757C22semidirect
40. C3×#3757C22semidirect
41. C32×#217C22semidirect
42. #88814C22semidirect
43. #88814C22semidirect
44. #88813C22semidirect
45. #88807C22semidirect
46. Dic3⋊(C3⋊Dic3)C22semidirect
47. Dic3⋊(C3⋊Dic3)C22semidirect
48. #88804C22semidirect
49. (C2×D3)⋊(C3⋊Dic3)C22semidirect
50. C3×#3724C22semidirect
51. C3×#3722C22semidirect
55. C3×(C2×D3)⋊Dic3C22semidirect
75. #63976D3semidirect
82. #63971D3semidirect
84. D3×#217D3semidirect
130. #6291D4semidirect
177. C2×C3×#67C2×D3semidirect
178. C2×C3×#67C2×D3semidirect
198. C2×#626C2×D3semidirect
203. C2×#625C2×D3semidirect
215. C2×D3×Dic3C2×D3semidirect
216. C2×D3×Dic3C2×D3semidirect
217. C2×D3×Dic3C2×D3semidirect
221. #3757C2×D3semidirect
222. #3757C2×D3semidirect
238. C3×#217C2×D3semidirect
239. C3×#217C2×D3semidirect
248. #3724C2×D3semidirect
263. #3722C2×D3semidirect
274. (C2×D3)⋊Dic3C2×D3semidirect
297. C2×C32×D3#41semidirect
565. C2×#67D32semidirect
620. #217D32semidirect
751. C2×C3×D3#235semidirect
754. C2×C3×D3#237semidirect
812. C33#546semidirect
1157. C2×D3#3804semidirect
1202. C32#5490semidirect
1203. C32#5591semidirect
1204. C32#5612semidirect
1327. C3#10594278semidirect
1328. C3#10595294semidirect
1329. C3#10595500semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#6382
C2×#889592
#117237182
#117236282
#117235992
C3×#639762
C3×#639712
C3×D3×#2172
#117229882
#117229812
#117229562
#117229492
#117229352
#117229242
#117229062
#105955003
#105952943
#105942783