Finite Group Databasebeta

← #13172339

Subgroups — #13172339

Order 1728.

1326 conjugacy classes of subgroups.

The subgroup lattice has 1246 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723725C211yesmaximal, characteristic, complemented
2#11723629C211yesmaximal, characteristic, complemented
3#11723615C211yesmaximal, characteristic, complemented
4#11723597C211yesmaximal, characteristic, complemented
5C3×#63977C211yesmaximal, characteristic, complemented
6C3×#63976C211yesmaximal, characteristic, complemented
7C3×#63958C211yesmaximal, characteristic, complemented
8#11723029C211yesmaximal, characteristic, complemented
9#11723019C211yesmaximal, characteristic, complemented
10#11722994C211yesmaximal, characteristic, complemented
11#11722992C211yesmaximal, characteristic, complemented
12#11722989C211yesmaximal, characteristic, complemented
13#11722965C211yesmaximal, characteristic, complemented
14#11722957C211yesmaximal, characteristic, complemented
15#11722954C211yesmaximal, characteristic, complemented
16#10595505—31nomaximal
17#10595257—31nomaximal
18#10594234—31nomaximal
19C23×C32×D3C2211yescharacteristic
20C2×C3×#638C2211yescharacteristic
21C2×C3×#638C2211yescharacteristic
22C2×C32×#67C2211yescharacteristic
23C2×#6295C2211yescharacteristic, complemented
24C2×#6294C2211yescharacteristic, complemented
25C2×#6290C2211yescharacteristic
26C2×#6290C2211yescharacteristic
27C2×#6290C2211yescharacteristic, complemented
28C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
29C2×C3×#626C2211yescharacteristic
30C2×C3×#626C2211yescharacteristic
31C2×C3×#626C2211yescharacteristic, complemented
32C2×C3×#625C2211yescharacteristic
33C2×C3×#625C2211yescharacteristic
34C2×C3×#624C2211yescharacteristic, complemented
35#88864C2211yescharacteristic
36C3×#3757C2211yescharacteristic
37C32×#217C2211yescharacteristic
38#88815C2211yescharacteristic, complemented
39#88814C2211yescharacteristic, complemented
40#88807C2211yescharacteristic, complemented
41#88807C2211yescharacteristic, complemented
42#88806C2211yescharacteristic, complemented
43Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
44#88803C2211yescharacteristic, complemented
45(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
46(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
47Dic3×C3⋊Dic3C2211yescharacteristic, complemented
48C3×Dic3⋊Dic3C2211yescharacteristic, complemented
49C3×(C2×D3)⋊Dic3C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
54#64162—31no—
55#64148—31no—
56#64088—31no—
57C3×#953—31no—
58C3×#953—31no—
59C3×#938—31no—
60C3×#937—31no—
61C3×#884—31no—
62C3×#882—31no—
63#63980—31no—
64#63979—31no—
65#63979—31no—
66#63977D311yescharacteristic, complemented
67#63976—31no—
68#63976—31no—
69#63976—61no—
70#63976D311yescharacteristic, complemented
71#63975—31no—
72#63971—31no—
73#63971—31no—
74#63970—31no—
75#63970—31no—
76#63970—31no—
77#63970—31no—
78#63970—61no—
79#63969—31no—
80#63969—31no—
81#63962—31no—
82#63958—31no—
83#63958—31no—
84#63958—31no—
85#63958D311yescharacteristic, complemented
86#63956—31no—
87#63956—31no—
88#63956—31no—
89#63956—61no—
90#63914—31no—
91#63908—31no—
92#63906—31no—
93#63905—31no—
94#63905—31no—
95#63891—31no—
96#63885—31no—
97#63885—31no—
98#63884—31no—
99#63862—31no—
100#63858—31no—
101#63854—31no—
102C23×C33C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C3×C3⋊D3C2311yescharacteristic
105C22×C32×D3—41no—
106C22×C32×D3—41no—
107C22×C32×D3—41no—
108C22×C32×D3C2311yescharacteristic
109C22×C32×D3C2311yescharacteristic
110C22×C32×D3C2311yescharacteristic
111C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
112C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
113C3×#638—41no—
114C3×#638—41no—
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C2×C3×C3⋊Dic3C2311yescharacteristic
118C2×C3×C3⋊Dic3C2311yescharacteristic
119C32×#67—41no—
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122C2×C32×Dic3C2311yescharacteristic
123#6295—41no—
124#6294—41no—
125#6290—41no—
126#6290—41no—
127#6290—41no—
128D3×C3⋊Dic3—41no—
129C3×#626—41no—
130C3×#626—41no—
131C3×#626—41no—
132C3×#625—41no—
133C3×#625—41no—
134C3×#624—41no—
135#5620—91no—
136#5595—91no—
137#5595—91no—
138C24×C32—31no—
139C23×C3×D3—21no—
140C23×C3×D3C2×D311yescharacteristic
141C23×C3×D3C2×D311yescharacteristic
142C2×C32×D4—31no—
143C2×#638—31no—
144C2×#638—31no—
145C2×#638—31no—
146C2×#638C2×D311yescharacteristic
147C2×#638C2×D311yescharacteristic
148C22×C3⋊Dic3—31no—
149C2×C3×#67—21no—
150C2×C3×#67—31no—
151C2×C3×#67—31no—
152C2×C3×#67—31no—
153C2×C3×#67—31no—
154C2×C3×#67—31no—
155C2×C3×#67—31no—
156C2×C3×#67—31no—
157C2×C3×#67—31no—
158C2×C3×#67—31no—
159C2×C3×#67—31no—
160C2×C3×#67—31no—
161C2×C3×#67—61no—
162C2×C3×#67—61no—
163C2×C3×#67C2×D311yescharacteristic
164C2×C3×#67C2×D311yescharacteristic
165C2×C3×D12—31no—
166C2×C3×D12—31no—
167C2×C3×D12—31no—
168C2×C3×C4×D3—31no—
169C2×C3×C4×D3—31no—
170C2×#626—31no—
171C2×#626—31no—
172C2×#626C2×D311yescharacteristic
173C2×#626C2×D311yescharacteristic
174C2×#626C2×D311yescharacteristic, complemented
175C2×#625—31no—
176C2×#625—31no—
177C2×#625—31no—
178C2×#625—31no—
179C2×#625—31no—
180C2×#625—31no—
181C2×#625—31no—
182C2×#625—61no—
183C2×#625—61no—
184C2×#625—61no—
185C2×#625C2×D311yescharacteristic
186C2×#625C2×D311yescharacteristic
187C2×#624—31no—
188C2×#624C2×D311yescharacteristic, complemented
189C2×D3×Dic3—31no—
190C2×D3×Dic3—31no—
191C2×D3×Dic3—31no—
192C2×D3×Dic3—31no—
193C2×D3×Dic3—61no—
194C32×C22⋊C4—31no—
195#3757—31no—
196#3757—31no—
197#3757—31no—
198#3757—31no—
199#3757—31no—
200#3757—61no—
201#3757—61no—
202#3757—61no—
203#3757—121no—
204#3757C2×D311yescharacteristic
205#3752—31no—
206C4⋊(C3⋊Dic3)—31no—
207#3750—31no—
208#3750—31no—
209#3750—31no—
210C4×C3⋊Dic3—31no—
211C3×#217—21no—
212C3×#217—31no—
213C3×#217—31no—
214C3×#217—31no—
215C3×#217—31no—
216C3×#217—31no—
217C3×#217—31no—
218C3×#217—31no—
219C3×#217—61no—
220C3×#217C2×D311yescharacteristic
221C3×#217C2×D311yescharacteristic
222C3×(C2×D3)⋊C4—31no—
223C3×(C2×D3)⋊C4—31no—
224C3×(C2×D3)⋊C4—31no—
225C3×(C2×D3)⋊C4—31no—
226C3×(C2×D3)⋊C4—31no—
227C3×C4⋊Dic3—31no—
228C3×Dic3⋊C4—31no—
229#3724—31no—
230#3724—31no—
231#3724—31no—
232#3724—61no—
233Dic3⋊Dic3—31no—
234Dic3⋊Dic3—31no—
235Dic3⋊Dic3—31no—
236Dic3⋊Dic3—31no—
237Dic3⋊Dic3—31no—
238Dic3⋊Dic3—31no—
239Dic3⋊Dic3—31no—
240Dic3⋊Dic3—31no—
241Dic3⋊Dic3—61no—
242Dic3⋊Dic3—61no—
243Dic3⋊Dic3—61no—
244Dic3⋊Dic3C2×D311yescharacteristic, complemented
245#3722—31no—
246(C2×D3)⋊Dic3—31no—
247(C2×D3)⋊Dic3—31no—
248(C2×D3)⋊Dic3—31no—
249(C2×D3)⋊Dic3—31no—
250(C2×D3)⋊Dic3—31no—
251(C2×D3)⋊Dic3—31no—
252(C2×D3)⋊Dic3—31no—
253(C2×D3)⋊Dic3—31no—
254(C2×D3)⋊Dic3—61no—
255(C2×D3)⋊Dic3—61no—
256(C2×D3)⋊Dic3—61no—
257(C2×D3)⋊Dic3C2×D311yescharacteristic
258(C2×D3)⋊Dic3C2×D311yescharacteristic
259(C2×D3)⋊Dic3C2×D311yescharacteristic
260(C2×D3)⋊Dic3C2×D311yescharacteristic
261(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
262Dic32—31no—
263Dic32—31no—
264Dic32—61no—
265C22×C33—21no—
266C22×C33—21no—
267C22×C33—21no—
268C22×C33C2411yescharacteristic
269C2×C3×C3⋊D3—21no—
270C2×C3×C3⋊D3—21no—
271C2×C3×C3⋊D3—21no—
272C2×C3×C3⋊D3—21no—
273C2×C3×C3⋊D3—21no—
274C2×C3×C3⋊D3—21no—
275C2×C32×D3—21no—
276C2×C32×D3—21no—
277C2×C32×D3—21no—
278C2×C32×D3—21no—
279C2×C32×D3—21no—
280C2×C32×D3—21no—
281C2×C32×D3—21no—
282C2×C32×D3—21no—
283C2×C32×D3—21no—
284C2×C32×D3—44no—
285C3⋊(C3⋊Dic3)—21no—
286C3⋊(C3⋊Dic3)—21no—
287C3×C3⋊Dic3—21no—
288C3×C3⋊Dic3—21no—
289C3×C3⋊Dic3—21no—
290C3×C3⋊Dic3—21no—
291C32×Dic3—21no—
292C32×Dic3—21no—
293C32×Dic3—21no—
294C3×#121—91no—
295C3×#120—91no—
296C3×#120—91no—
297#953—31no—
298#953—31no—
299#953—91no—
300#953—91no—
301#953—181no—
302#940—91no—
303#940—91no—
304#940—91no—
305#939—91no—
306#939—91no—
307#939—91no—
308#939—91no—
309#939—91no—
310#939—91no—
311#939—181no—
312#938—31no—
313#938—91no—
314#938—91no—
315#938—91no—
316#938—91no—
317#937—31no—
318#937—91no—
319#935—91no—
320#935—91no—
321#930—91no—
322#929—91no—
323#898—91no—
324#894—91no—
325#886—91no—
326#884—31no—
327#884—91no—
328#884—91no—
329#884—91no—
330#884—91no—
331#883—91no—
332#883—91no—
333#883—91no—
334#883—91no—
335#882—31no—
336#879—91no—
337#879—91no—
338#879—91no—
339#879—91no—
340#879—91no—
341#879—181no—
342C23×C32—21no—
343C23×C32—21no—
344C23×C32—21no—
345C23×C32—31no—
346C23×C32—31no—
347C23×C32—31no—
348C23×C32—41no—
349C23×C32—121no—
350C23×C32—121no—
351C23×C32—121no—
352C23×C32C22×D311yescharacteristic
353C23×C32C22×D311yescharacteristic
354C23×C32C22×D311yescharacteristic
355C22×C3⋊D3C22×D311yescharacteristic
356C22×C3⋊D3C22×D311yescharacteristic
357C22×C3×D3—21no—
358C22×C3×D3—21no—
359C22×C3×D3—21no—
360C22×C3×D3—31no—
361C22×C3×D3—31no—
362C22×C3×D3—31no—
363C22×C3×D3—31no—
364C22×C3×D3—41no—
365C22×C3×D3—41no—
366C22×C3×D3—41no—
367C22×C3×D3—41no—
368C22×C3×D3—41no—
369C22×C3×D3—41no—
370C22×C3×D3—42no—
371C22×C3×D3—42no—
372C22×C3×D3—42no—
373C22×C3×D3—61no—
374C22×C3×D3—61no—
375C22×C3×D3C22×D311yescharacteristic
376C22×C3×D3C22×D311yescharacteristic
377C22×C3×D3C22×D311yescharacteristic
378C22×C3×D3C22×D311yescharacteristic
379C22×C3×D3C22×D311yescharacteristic
380C22×C3×D3C22×D311yescharacteristic
381C32×D4—121no—
382C2×C32×C4—31no—
383C2×C32×C4—31no—
384C2×C32×C4—31no—
385#638—41no—
386#638—41no—
387#638—121no—
388#638—121no—
389#638—121no—
390C2×C3⋊Dic3—31no—
391C2×C3⋊Dic3—31no—
392C2×C3⋊Dic3—31no—
393C2×C3⋊Dic3—31no—
394C2×C3⋊Dic3—31no—
395C2×C3⋊Dic3—31no—
396C2×C3⋊Dic3—61no—
397C2×C3⋊Dic3—61no—
398C2×C3⋊Dic3—61no—
399C2×C3⋊Dic3—61no—
400C2×C3⋊Dic3—61no—
401C2×C3⋊Dic3—61no—
402C2×C3⋊Dic3—121no—
403C2×C3⋊Dic3—121no—
404C2×C3⋊Dic3—121no—
405C2×C3⋊Dic3C22×D311yescharacteristic
406C2×C3⋊Dic3C22×D311yescharacteristic
407C2×C3⋊Dic3C22×D311yescharacteristic
408C2×C3⋊Dic3C22×D311yescharacteristic
409C3×#67—41no—
410C3×#67—41no—
411C3×#67—42no—
412C3×#67—121no—
413C3×#67—121no—
414C3×#67—121no—
415C3×#67—121no—
416C3×#67—121no—
417C3×#67—121no—
418C3×#67—121no—
419C3×#67—121no—
420C3×#67—121no—
421C3×#67—121no—
422C3×#67—121no—
423C3×#67—122no—
424C3×#67—122no—
425C2×C3×Dic3—21no—
426C2×C3×Dic3—21no—
427C2×C3×Dic3—21no—
428C2×C3×Dic3—31no—
429C2×C3×Dic3—31no—
430C2×C3×Dic3—31no—
431C2×C3×Dic3—31no—
432C2×C3×Dic3—31no—
433C2×C3×Dic3—31no—
434C2×C3×Dic3—31no—
435C2×C3×Dic3—31no—
436C2×C3×Dic3—61no—
437C2×C3×Dic3—61no—
438C2×C3×Dic3—61no—
439C2×C3×Dic3—61no—
440C2×C3×Dic3C22×D311yescharacteristic
441C2×C3×Dic3C22×D311yescharacteristic
442C2×C3×Dic3C22×D311yescharacteristic
443C2×C3×Dic3C22×D311yescharacteristic
444C2×C3×Dic3C22×D311yescharacteristic
445C2×C3×Dic3C22×D311yescharacteristic
446C3×D12—121no—
447C3×D12—121no—
448C3×D12—121no—
449C3×C4×D3—121no—
450C3×C4×D3—121no—
451#626—41no—
452#626—41no—
453#626—41no—
454#626—121no—
455#626—121no—
456#625—41no—
457#625—41no—
458#625—121no—
459#625—121no—
460#625—121no—
461#625—121no—
462#625—121no—
463#625—121no—
464#625—121no—
465#625—122no—
466#625—122no—
467#625—122no—
468#624—41no—
469#624—121no—
470D3×Dic3—121no—
471D3×Dic3—121no—
472D3×Dic3—121no—
473D3×Dic3—121no—
474D3×Dic3—122no—
475#560—271noSylow
476C2×C33—41no—
477C2×C33H(5,𝔽2)11yescharacteristic
478C2×C33H(5,𝔽2)11yescharacteristic
479C2×C33H(5,𝔽2)11yescharacteristic
480C3×C3⋊D3—41no—
481C3×C3⋊D3—41no—
482C32×D3—41no—
483C32×D3—41no—
484C32×D3—41no—
485C24×C3—31no—
486C24×C3—31no—
487C24×C3—61no—
488C23×D3D3211yescharacteristic
489C2×C3×D4—31no—
490C2×C3×D4—31no—
491C2×C3×D4—61no—
492C2×C3×D4—91no—
493C2×C3×D4—91no—
494C2×C3×D4—91no—
495C2×C3×D4—91no—
496C2×C3×D4—91no—
497C2×C3×D4—91no—
498C2×C3×D4—91no—
499C22×C3×C4—91no—
500C2×#67—31no—
501C2×#67—31no—
502C2×#67—31no—
503C2×#67—31no—
504C2×#67—31no—
505C2×#67—31no—
506C2×#67—31no—
507C2×#67—31no—
508C2×#67—31no—
509C2×#67—31no—
510C2×#67—31no—
511C2×#67—61no—
512C2×#67—61no—
513C2×#67—91no—
514C2×#67—91no—
515C2×#67—91no—
516C2×#67—91no—
517C2×#67—91no—
518C2×#67—91no—
519C2×#67—91no—
520C2×#67—91no—
521C2×#67—91no—
522C2×#67—91no—
523C2×#67—91no—
524C2×#67—181no—
525C2×#67—181no—
526C2×#67—181no—
527C2×#67D3211yescharacteristic
528C22×Dic3—91no—
529C22×Dic3—91no—
530C22×Dic3—91no—
531C22×Dic3—181no—
532C2×D12—31no—
533C2×D12—31no—
534C2×D12—31no—
535C2×D12—91no—
536C2×C4×D3—31no—
537C2×C4×D3—31no—
538C2×C4×D3—91no—
539C2×C4×D3—91no—
540C2×C4×D3—91no—
541C3×C4⋊C4—91no—
542C3×C22⋊C4—31no—
543C3×C22⋊C4—31no—
544C3×C22⋊C4—61no—
545C3×C22⋊C4—91no—
546C3×C22⋊C4—91no—
547C3×C22⋊C4—91no—
548C3×C22⋊C4—91no—
549C3×C22⋊C4—91no—
550C3×C22⋊C4—91no—
551#217—31no—
552#217—31no—
553#217—31no—
554#217—31no—
555#217—31no—
556#217—31no—
557#217—31no—
558#217—61no—
559#217—91no—
560#217—91no—
561#217—91no—
562#217—91no—
563#217—91no—
564#217—91no—
565#217—91no—
566#217—91no—
567#217—91no—
568#217—181no—
569#217—181no—
570#217—181no—
571#217—181no—
572#217—181no—
573#217—361no—
574#217D3211yescharacteristic
575(C2×D3)⋊C4—31no—
576(C2×D3)⋊C4—31no—
577(C2×D3)⋊C4—31no—
578(C2×D3)⋊C4—31no—
579(C2×D3)⋊C4—31no—
580(C2×D3)⋊C4—91no—
581(C2×D3)⋊C4—91no—
582(C2×D3)⋊C4—91no—
583(C2×D3)⋊C4—91no—
584(C2×D3)⋊C4—91no—
585(C2×D3)⋊C4—91no—
586(C2×D3)⋊C4—181no—
587C4⋊Dic3—31no—
588C4⋊Dic3—91no—
589C4⋊Dic3—91no—
590C4⋊Dic3—91no—
591C4⋊Dic3—91no—
592C4⋊Dic3—91no—
593C4⋊Dic3—181no—
594Dic3⋊C4—31no—
595Dic3⋊C4—91no—
596Dic3⋊C4—91no—
597Dic3⋊C4—91no—
598Dic3⋊C4—91no—
599Dic3⋊C4—91no—
600Dic3⋊C4—91no—
601Dic3⋊C4—91no—
602Dic3⋊C4—91no—
603Dic3⋊C4—91no—
604Dic3⋊C4—91no—
605Dic3⋊C4—181no—
606Dic3⋊C4—181no—
607Dic3⋊C4—181no—
608C4×Dic3—91no—
609C4×Dic3—91no—
610C4×Dic3—91no—
611C4×Dic3—181no—
612C22×C32—21no—
613C22×C32—22no—
614C22×C32—21no—
615C22×C32—21no—
616C22×C32—21no—
617C22×C32—21no—
618C22×C32—21no—
619C22×C32—21no—
620C22×C32—21no—
621C22×C32—21no—
622C22×C32—21no—
623C22×C32—21no—
624C22×C32—21no—
625C22×C32—41no—
626C22×C32—41no—
627C22×C32—41no—
628C22×C32—42no—
629C22×C32—41no—
630C22×C32—41no—
631C22×C32—41no—
632C22×C32—41no—
633C22×C32—41no—
634C22×C32—41no—
635C22×C32—61no—
636C22×C32—61no—
637C22×C32—61no—
638C22×C32—61no—
639C22×C32—61no—
640C22×C32—61no—
641C22×C32—61no—
642C22×C32—61no—
643C22×C32—61no—
644C22×C32—81no—
645C22×C32—81no—
646C22×C32—124no—
647C22×C32C23×D311yescharacteristic
648C22×C32C23×D311yescharacteristic
649C22×C32C23×D311yescharacteristic
650C2×C3⋊D3—21no—
651C2×C3⋊D3—21no—
652C2×C3⋊D3—21no—
653C2×C3⋊D3—21no—
654C2×C3⋊D3—21no—
655C2×C3⋊D3—21no—
656C2×C3×D3—22no—
657C2×C3×D3—22no—
658C2×C3×D3—22no—
659C2×C3×D3—21no—
660C2×C3×D3—21no—
661C2×C3×D3—21no—
662C2×C3×D3—21no—
663C2×C3×D3—21no—
664C2×C3×D3—21no—
665C2×C3×D3—21no—
666C2×C3×D3—21no—
667C2×C3×D3—21no—
668C2×C3×D3—21no—
669C2×C3×D3—21no—
670C2×C3×D3—21no—
671C2×C3×D3—21no—
672C2×C3×D3—21no—
673C2×C3×D3—21no—
674C2×C3×D3—21no—
675C2×C3×D3—21no—
676C2×C3×D3—21no—
677C2×C3×D3—41no—
678C2×C3×D3—41no—
679C2×C3×D3—41no—
680C2×C3×D3—41no—
681C2×C3×D3—41no—
682C2×C3×D3—41no—
683C2×C3×D3—48no—
684C2×C3×D3—44no—
685C2×C3×D3—44no—
686C2×C3×D3—61no—
687C2×C3×D3—61no—
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—61no—
697C2×C3×D3—61no—
698C2×C3×D3—121no—
699C2×C3×D3—121no—
700C2×C3×D3—121no—
701C2×C3×D3—121no—
702C2×C3×D3—121no—
703C2×C3×D3—121no—
704C32×C4—61no—
705C32×C4—61no—
706C32×C4—61no—
707C3⋊Dic3—21no—
708C3⋊Dic3—21no—
709C3⋊Dic3—21no—
710C3⋊Dic3—21no—
711C3⋊Dic3—61no—
712C3⋊Dic3—61no—
713C3⋊Dic3—61no—
714C3⋊Dic3—61no—
715C3⋊Dic3—61no—
716C3⋊Dic3—61no—
717C3⋊Dic3—121no—
718C3⋊Dic3—121no—
719C3⋊Dic3—121no—
720C3⋊Dic3—121no—
721C3⋊Dic3—121no—
722C3⋊Dic3—121no—
723C3⋊Dic3—241no—
724C3⋊Dic3—241no—
725C3×Dic3—21no—
726C3×Dic3—21no—
727C3×Dic3—21no—
728C3×Dic3—21no—
729C3×Dic3—21no—
730C3×Dic3—21no—
731C3×Dic3—41no—
732C3×Dic3—41no—
733C3×Dic3—41no—
734C3×Dic3—62no—
735C3×Dic3—61no—
736C3×Dic3—61no—
737C3×Dic3—61no—
738C3×Dic3—61no—
739C3×Dic3—61no—
740C3×Dic3—61no—
741C3×Dic3—61no—
742C3×Dic3—61no—
743C3×Dic3—121no—
744C3×Dic3—121no—
745C3×Dic3—121no—
746#127—271no—
747#126—271no—
748#126—271no—
749#123—271no—
750#123—271no—
751#123—271no—
752#121—91no—
753#121—271no—
754#121—271no—
755#121—271no—
756#121—271no—
757#121—271no—
758#120—91no—
759#120—91no—
760#120—271no—
761C33#56011yescharacteristic, complemented, Sylow
762C23×C3—21no—
763C23×C3—21no—
764C23×C3—21no—
765C23×C3—31no—
766C23×C3—31no—
767C23×C3—31no—
768C23×C3—31no—
769C23×C3—31no—
770C23×C3—31no—
771C23×C3—41no—
772C23×C3—61no—
773C23×C3—61no—
774C23×C3—61no—
775C23×C3—91no—
776C23×C3—91no—
777C23×C3—121no—
778C23×C3—121no—
779C23×C3—121no—
780C23×C3—121no—
781C23×C3—121no—
782C23×C3—121no—
783C23×C3—122no—
784C23×C3—122no—
785C23×C3—122no—
786C23×C3C2×D3211yescharacteristic
787C23×C3C2×D3211yescharacteristic
788C23×C3C2×D3211yescharacteristic
789C22×D3—31no—
790C22×D3—31no—
791C22×D3—31no—
792C22×D3—31no—
793C22×D3—41no—
794C22×D3—41no—
795C22×D3—41no—
796C22×D3—61no—
797C22×D3—61no—
798C22×D3C2×D3211yescharacteristic
799C22×D3C2×D3211yescharacteristic
800C22×D3C2×D3211yescharacteristic
801C3×D4—121no—
802C3×D4—121no—
803C3×D4—122no—
804C3×D4—361no—
805C3×D4—361no—
806C3×D4—361no—
807C3×D4—361no—
808C3×D4—361no—
809C3×D4—361no—
810C3×D4—361no—
811C2×C3×C4—31no—
812C2×C3×C4—31no—
813C2×C3×C4—31no—
814C2×C3×C4—31no—
815C2×C3×C4—31no—
816C2×C3×C4—31no—
817C2×C3×C4—61no—
818C2×C3×C4—61no—
819C2×C3×C4—61no—
820C2×C3×C4—91no—
821C2×C3×C4—91no—
822C2×C3×C4—91no—
823C2×C3×C4—91no—
824C2×C3×C4—361no—
825#67—41no—
826#67—121no—
827#67—121no—
828#67—121no—
829#67—121no—
830#67—121no—
831#67—121no—
832#67—121no—
833#67—121no—
834#67—121no—
835#67—121no—
836#67—121no—
837#67—122no—
838#67—122no—
839#67—361no—
840#67—361no—
841#67—361no—
842#67—361no—
843#67—361no—
844#67—361no—
845#67—361no—
846#67—361no—
847#67—361no—
848#67—361no—
849#67—361no—
850#67—362no—
851#67—362no—
852#67—362no—
853C2×Dic3—31no—
854C2×Dic3—31no—
855C2×Dic3—31no—
856C2×Dic3—31no—
857C2×Dic3—31no—
858C2×Dic3—31no—
859C2×Dic3—31no—
860C2×Dic3—31no—
861C2×Dic3—61no—
862C2×Dic3—61no—
863C2×Dic3—61no—
864C2×Dic3—61no—
865C2×Dic3—91no—
866C2×Dic3—91no—
867C2×Dic3—91no—
868C2×Dic3—91no—
869C2×Dic3—91no—
870C2×Dic3—91no—
871C2×Dic3—181no—
872C2×Dic3—181no—
873C2×Dic3—181no—
874C2×Dic3—181no—
875C2×Dic3—181no—
876C2×Dic3—181no—
877C2×Dic3—361no—
878C2×Dic3—361no—
879C2×Dic3—361no—
880C2×Dic3—361no—
881C2×Dic3—361no—
882C2×Dic3—362no—
883C2×Dic3C2×D3211yescharacteristic
884C2×Dic3C2×D3211yescharacteristic
885C2×Dic3C2×D3211yescharacteristic
886D12—121no—
887D12—121no—
888D12—121no—
889D12—361no—
890C4×D3—121no—
891C4×D3—121no—
892C4×D3—361no—
893C4×D3—361no—
894C4×D3—361no—
895C2×C32—21no—
896C2×C32—21no—
897C2×C32—21no—
898C2×C32—21no—
899C2×C32—21no—
900C2×C32—21no—
901C2×C32—21no—
902C2×C32—21no—
903C2×C32—21no—
904C2×C32—41no—
905C2×C32—41no—
906C2×C32—41no—
907C2×C32—41no—
908C2×C32—42no—
909C2×C32—41no—
910C2×C32—41no—
911C2×C32—81no—
912C2×C32—81no—
913C2×C32—82no—
914C2×C32—121no—
915C2×C32—121no—
916C2×C32—121no—
917C2×C32#100411yescharacteristic
918C2×C32#100411yescharacteristic
919C2×C32#100411yescharacteristic
920C2×C32#100411yescharacteristic
921C2×C32#100411yescharacteristic
922C2×C32#100411yescharacteristic
923C2×C32#100411yescharacteristic
924C2×C32#100411yescharacteristic
925C2×C32#100911yescharacteristic
926C3⋊D3—41no—
927C3⋊D3—41no—
928C3×D3—42no—
929C3×D3—42no—
930C3×D3—42no—
931C3×D3—41no—
932C3×D3—41no—
933C3×D3—41no—
934C3×D3—41no—
935C3×D3—41no—
936C3×D3—41no—
937C3×D3—121no—
938C3×D3—121no—
939C3×D3—121no—
940C3×D3—121no—
941C3×D3—241no—
942C3×D3—241no—
943C24—31no—
944C2×D4—31no—
945C2×D4—91no—
946C2×D4—91no—
947C2×D4—91no—
948C2×D4—91no—
949C2×D4—91no—
950C2×D4—91no—
951C2×D4—91no—
952C2×D4—271no—
953C2×D4—271no—
954C2×D4—271no—
955C2×D4—271no—
956C22×C4—91no—
957C22×C4—271no—
958C22×C4—271no—
959C4⋊C4—91no—
960C4⋊C4—271no—
961C4⋊C4—271no—
962C4⋊C4—271no—
963C4⋊C4—271no—
964C4⋊C4—271no—
965C22⋊C4—31no—
966C22⋊C4—91no—
967C22⋊C4—91no—
968C22⋊C4—91no—
969C22⋊C4—91no—
970C22⋊C4—91no—
971C22⋊C4—91no—
972C22⋊C4—271no—
973C22⋊C4—271no—
974C22⋊C4—271no—
975C22⋊C4—271no—
976C22⋊C4—271no—
977C42—271no—
978C22×C3—22no—
979C22×C3—21no—
980C22×C3—21no—
981C22×C3—21no—
982C22×C3—21no—
983C22×C3—21no—
984C22×C3—21no—
985C22×C3—21no—
986C22×C3—21no—
987C22×C3—21no—
988C22×C3—21no—
989C22×C3—21no—
990C22×C3—21no—
991C22×C3—41no—
992C22×C3—41no—
993C22×C3—41no—
994C22×C3—41no—
995C22×C3—41no—
996C22×C3—41no—
997C22×C3—41no—
998C22×C3—41no—
999C22×C3—42no—
1000C22×C3—41no—
1001C22×C3—62no—
1002C22×C3—62no—
1003C22×C3—62no—
1004C22×C3—61no—
1005C22×C3—61no—
1006C22×C3—61no—
1007C22×C3—61no—
1008C22×C3—61no—
1009C22×C3—61no—
1010C22×C3—61no—
1011C22×C3—61no—
1012C22×C3—61no—
1013C22×C3—61no—
1014C22×C3—61no—
1015C22×C3—61no—
1016C22×C3—61no—
1017C22×C3—61no—
1018C22×C3—61no—
1019C22×C3—61no—
1020C22×C3—61no—
1021C22×C3—61no—
1022C22×C3—81no—
1023C22×C3—81no—
1024C22×C3—121no—
1025C22×C3—121no—
1026C22×C3—121no—
1027C22×C3—121no—
1028C22×C3—121no—
1029C22×C3—121no—
1030C22×C3—128no—
1031C22×C3—124no—
1032C22×C3—124no—
1033C22×C3—181no—
1034C22×C3—181no—
1035C22×C3—181no—
1036C22×C3—181no—
1037C22×C3—181no—
1038C22×C3—181no—
1039C22×C3C22×D3211yescharacteristic
1040C22×C3C22×D3211yescharacteristic
1041C22×C3C22×D3211yescharacteristic
1042C2×D3—21no—
1043C2×D3—21no—
1044C2×D3—21no—
1045C2×D3—21no—
1046C2×D3—21no—
1047C2×D3—21no—
1048C2×D3—21no—
1049C2×D3—21no—
1050C2×D3—21no—
1051C2×D3—44no—
1052C2×D3—61no—
1053C2×D3—61no—
1054C2×D3—61no—
1055C2×D3—61no—
1056C2×D3—61no—
1057C2×D3—61no—
1058C2×D3—61no—
1059C2×D3—61no—
1060C2×D3—61no—
1061C2×D3—61no—
1062C2×D3—61no—
1063C2×D3—61no—
1064C2×D3—121no—
1065C2×D3—121no—
1066C2×D3—121no—
1067C2×D3—121no—
1068C2×D3—121no—
1069C2×D3—121no—
1070C3×C4—61no—
1071C3×C4—61no—
1072C3×C4—61no—
1073C3×C4—61no—
1074C3×C4—61no—
1075C3×C4—61no—
1076C3×C4—121no—
1077C3×C4—121no—
1078C3×C4—121no—
1079C3×C4—181no—
1080C3×C4—181no—
1081C3×C4—181no—
1082C3×C4—181no—
1083Dic3—21no—
1084Dic3—21no—
1085Dic3—21no—
1086Dic3—62no—
1087Dic3—61no—
1088Dic3—61no—
1089Dic3—61no—
1090Dic3—61no—
1091Dic3—61no—
1092Dic3—61no—
1093Dic3—61no—
1094Dic3—61no—
1095Dic3—121no—
1096Dic3—121no—
1097Dic3—121no—
1098Dic3—181no—
1099Dic3—181no—
1100Dic3—181no—
1101Dic3—181no—
1102Dic3—181no—
1103Dic3—181no—
1104Dic3—361no—
1105Dic3—361no—
1106Dic3—361no—
1107Dic3—361no—
1108Dic3—361no—
1109Dic3—361no—
1110Dic3—721no—
1111Dic3—721no—
1112C32—21no—
1113C32—21no—
1114C32—21no—
1115C32—41no—
1116C32#559511yescharacteristic, complemented
1117C32#559511yescharacteristic, complemented
1118C32#562011yescharacteristic, complemented
1119C23—31no—
1120C23—31no—
1121C23—31no—
1122C23—91no—
1123C23—91no—
1124C23—121no—
1125C23—121no—
1126C23—121no—
1127C23D3311yescharacteristic
1128D4—121no—
1129D4—361no—
1130D4—361no—
1131D4—361no—
1132D4—361no—
1133D4—361no—
1134D4—361no—
1135D4—361no—
1136D4—1081no—
1137D4—1081no—
1138D4—1081no—
1139D4—1081no—
1140C2×C4—31no—
1141C2×C4—31no—
1142C2×C4—31no—
1143C2×C4—91no—
1144C2×C4—91no—
1145C2×C4—91no—
1146C2×C4—91no—
1147C2×C4—271no—
1148C2×C4—271no—
1149C2×C4—361no—
1150C2×C4—1081no—
1151C2×C4—1081no—
1152C2×C3—21no—
1153C2×C3—21no—
1154C2×C3—21no—
1155C2×C3—21no—
1156C2×C3—21no—
1157C2×C3—21no—
1158C2×C3—21no—
1159C2×C3—21no—
1160C2×C3—21no—
1161C2×C3—42no—
1162C2×C3—41no—
1163C2×C3—41no—
1164C2×C3—41no—
1165C2×C3—41no—
1166C2×C3—41no—
1167C2×C3—41no—
1168C2×C3—81no—
1169C2×C3—81no—
1170C2×C3—82no—
1171C2×C3—122no—
1172C2×C3—122no—
1173C2×C3—122no—
1174C2×C3—121no—
1175C2×C3—121no—
1176C2×C3—121no—
1177C2×C3—121no—
1178C2×C3—121no—
1179C2×C3—121no—
1180C2×C3—361no—
1181C2×C3—361no—
1182C2×C3#6430711yescharacteristic
1183C2×C3#6431311yescharacteristic
1184C2×C3#6431311yescharacteristic
1185C2×C3#6431311yescharacteristic
1186C2×C3#6431411yescharacteristic
1187C2×C3#6433011yescharacteristic
1188C2×C3#6433011yescharacteristic
1189C2×C3#6433011yescharacteristic
1190C2×C3#6433011yescharacteristic
1191D3—41no—
1192D3—41no—
1193D3—41no—
1194D3—121no—
1195D3—121no—
1196D3—121no—
1197D3—121no—
1198D3—241no—
1199D3—241no—
1200C22—21no—
1201C22—21no—
1202C22—21no—
1203C22—61no—
1204C22—61no—
1205C22—61no—
1206C22—61no—
1207C22—61no—
1208C22—61no—
1209C22—61no—
1210C22—61no—
1211C22—61no—
1212C22—124no—
1213C22—181no—
1214C22—181no—
1215C22—181no—
1216C22—181no—
1217C22—181no—
1218C22—181no—
1219C22C2×D3311yescharacteristic
1220C4—61no—
1221C4—61no—
1222C4—61no—
1223C4—181no—
1224C4—181no—
1225C4—181no—
1226C4—181no—
1227C4—541no—
1228C4—541no—
1229C3—21no—
1230C3—21no—
1231C3—21no—
1232C3—41no—
1233C3#1059423411yescharacteristic, complemented
1234C3#1059525711yescharacteristic, complemented
1235C3#1059550511yescharacteristic, complemented
1236C2—41no—
1237C2—121no—
1238C2—121no—
1239C2—121no—
1240C2—361no—
1241C2—361no—
1242C2#1172441411yescharacteristic
1243C2#1172441511yescharacteristic
1244C2#1172441811yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
hypercenterC23D33
hypocenterC33#560
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #11723725C2semidirect
2. #11723629C2semidirect
3. #11723615C2semidirect
4. #11723597C2semidirect
5. C3×#63977C2semidirect
6. C3×#63976C2semidirect
7. C3×#63958C2semidirect
8. #11723029C2semidirect
9. #11723019C2semidirect
10. #11722994C2semidirect
11. #11722992C2semidirect
12. #11722989C2semidirect
13. #11722965C2semidirect
14. #11722957C2semidirect
15. #11722954C2semidirect
23. C2×#6295C22semidirect
24. C2×#6294C22semidirect
27. C2×#6290C22semidirect
28. C2×D3×C3⋊Dic3C22semidirect
31. C2×C3×#626C22semidirect
34. C2×C3×#624C22semidirect
38. #88815C22semidirect
39. #88814C22semidirect
40. #88807C22semidirect
41. #88807C22semidirect
42. #88806C22semidirect
43. Dic3⋊(C3⋊Dic3)C22semidirect
44. #88803C22semidirect
47. Dic3×C3⋊Dic3C22semidirect
48. C3×Dic3⋊Dic3C22semidirect
53. C3×(C2×D3)⋊Dic3C22semidirect
66. #63977D3semidirect
70. #63976D3semidirect
85. #63958D3semidirect
174. C2×#626C2×D3semidirect
188. C2×#624C2×D3semidirect
244. Dic3⋊Dic3C2×D3semidirect
261. (C2×D3)⋊Dic3C2×D3semidirect
761. C33#560semidirect
1116. C32#5595semidirect
1117. C32#5595semidirect
1118. C32#5620semidirect
1233. C3#10594234semidirect
1234. C3#10595257semidirect
1235. C3#10595505semidirect

Maximal subgroups

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

subgroupindex
#117237252
#117236292
#117236152
#117235972
C3×#639772
C3×#639762
C3×#639582
#117230292
#117230192
#117229942
#117229922
#117229892
#117229652
#117229572
#117229542
#105955053
#105952573
#105942343