Finite Group Databasebeta

← #13172341

Subgroups — #13172341

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#11723727C211yesmaximal, characteristic, complemented
2#11723634C211yesmaximal, characteristic, complemented
3#11723615C211yesmaximal, characteristic, complemented
4#11723596C211yesmaximal, characteristic, complemented
5C3×#63981C211yesmaximal, characteristic, complemented
6C3×#63970C211yesmaximal, characteristic, complemented
7C3×#63958C211yesmaximal, characteristic, complemented
8#11723029C211yesmaximal, characteristic, complemented
9#11723025C211yesmaximal, characteristic, complemented
10#11722995C211yesmaximal, characteristic, complemented
11#11722990C211yesmaximal, characteristic, complemented
12#11722988C211yesmaximal, characteristic, complemented
13#11722960C211yesmaximal, characteristic, complemented
14#11722957C211yesmaximal, characteristic, complemented
15#11722954C211yesmaximal, characteristic, complemented
16#10595264—31nomaximal
17#10595257—31nomaximal
18#10594234—31nomaximal
19C23×C3×C3⋊D3C2211yescharacteristic
20C2×C3×#638C2211yescharacteristic
21C2×C32×#67C2211yescharacteristic
22C2×C32×#67C2211yescharacteristic
23C2×#6295C2211yescharacteristic
24C2×#6295C2211yescharacteristic
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, complemented
33C2×C3×#624C2211yescharacteristic, complemented
34C2×C3×D3×Dic3C2211yescharacteristic, complemented
35#88864C2211yescharacteristic
36C3×#3757C2211yescharacteristic
37C32×#217C2211yescharacteristic
38#88814C2211yescharacteristic
39#88814C2211yescharacteristic
40#88807C2211yescharacteristic, complemented
41#88807C2211yescharacteristic, complemented
42#88806C2211yescharacteristic, complemented
43Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
44#88803C2211yescharacteristic
45#88803C2211yescharacteristic
46#88803C2211yescharacteristic, complemented
47Dic3×C3⋊Dic3C2211yescharacteristic, complemented
48C3×Dic3⋊Dic3C2211yescharacteristic, complemented
49C3×Dic3⋊Dic3C2211yescharacteristic, complemented
50C3×#3722C2211yescharacteristic
51C3×#3722C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
53C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
54#64148—31no—
55#64146—31no—
56#64088—31no—
57C3×#939—31no—
58C3×#938—31no—
59C3×#938—31no—
60C3×#937—31no—
61C3×#884—31no—
62C3×#882—31no—
63#63981—31no—
64#63981D311yescharacteristic, complemented
65#63980—31no—
66#63979—31no—
67#63979—31no—
68#63978—31no—
69#63977—31no—
70#63976—31no—
71#63976—31no—
72#63976—31no—
73#63976—61no—
74#63971—31no—
75#63970—31no—
76#63970—31no—
77#63970—61no—
78#63970D311yescharacteristic, complemented
79#63966—31no—
80#63962—31no—
81#63958—31no—
82#63958D311yescharacteristic, complemented
83#63956—31no—
84#63956—31no—
85#63956—61no—
86#63914—31no—
87#63908—31no—
88#63906—31no—
89#63906—31no—
90#63905—31no—
91#63905—31no—
92#63891—31no—
93#63890—31no—
94#63885—31no—
95#63885—31no—
96#63884—31no—
97#63862—31no—
98#63858—31no—
99#63854—31no—
100#63850—31no—
101#63848—31no—
102C23×C33C2311yescharacteristic
103C22×C3×C3⋊D3—41no—
104C22×C3×C3⋊D3—41no—
105C22×C3×C3⋊D3—41no—
106C22×C3×C3⋊D3C2311yescharacteristic
107C22×C3×C3⋊D3C2311yescharacteristic
108C22×C3×C3⋊D3C2311yescharacteristic
109C22×C32×D3C2311yescharacteristic
110C22×C32×D3C2311yescharacteristic
111C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
112C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
113C3×#638—41no—
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C32×#67—41no—
118C32×#67—41no—
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122C2×C32×Dic3C2311yescharacteristic
123#6295—41no—
124#6295—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×#624—41no—
134C3×D3×Dic3—41no—
135#5620—91no—
136#5620—91no—
137#5595—91no—
138C23×C3⋊D3C2×D311yescharacteristic
139C23×C3×D3—31no—
140C23×C3×D3—31no—
141C23×C3×D3—61no—
142C2×C32×D4—31no—
143C2×C32×D4—31no—
144C2×#638—31no—
145C2×#638—31no—
146C2×#638—31no—
147C2×#638C2×D311yescharacteristic
148C22×C3⋊Dic3—31no—
149C2×C3×#67—21no—
150C2×C3×#67—21no—
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—61no—
159C2×C3×#67C2×D311yescharacteristic
160C2×C3×#67C2×D311yescharacteristic
161C2×C3×#67C2×D311yescharacteristic
162C2×C3×#67C2×D311yescharacteristic
163C22×C3×Dic3—31no—
164C2×C3×D12—31no—
165C2×C3×D12—31no—
166C2×C3×D12—31no—
167C2×C3×C4×D3—31no—
168C2×C3×C4×D3—31no—
169C2×C3×C4×D3—31no—
170C2×#626—31no—
171C2×#626—31no—
172C2×#626—31no—
173C2×#626—31no—
174C2×#626C2×D311yescharacteristic
175C2×#626C2×D311yescharacteristic
176C2×#626C2×D311yescharacteristic, complemented
177C2×#625—31no—
178C2×#625—31no—
179C2×#625—31no—
180C2×#625—31no—
181C2×#625—31no—
182C2×#625—31no—
183C2×#625—31no—
184C2×#625—31no—
185C2×#625—61no—
186C2×#625—61no—
187C2×#625—61no—
188C2×#625C2×D311yescharacteristic, complemented
189C2×#624C2×D311yescharacteristic, complemented
190C2×D3×Dic3—31no—
191C2×D3×Dic3—31no—
192C2×D3×Dic3—61no—
193C2×D3×Dic3C2×D311yescharacteristic, complemented
194C32×C22⋊C4—31no—
195#3757—31no—
196#3757—31no—
197#3757—31no—
198#3757—61no—
199#3757—61no—
200#3757—61no—
201#3757—121no—
202#3757C2×D311yescharacteristic
203#3752—31no—
204#3752—31no—
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—61no—
217C3×#217C2×D311yescharacteristic
218C3×#217C2×D311yescharacteristic
219C3×(C2×D3)⋊C4—31no—
220C3×(C2×D3)⋊C4—31no—
221C3×(C2×D3)⋊C4—31no—
222C3×(C2×D3)⋊C4—31no—
223C3×(C2×D3)⋊C4—31no—
224C3×(C2×D3)⋊C4—31no—
225C3×C4⋊Dic3—31no—
226C3×C4⋊Dic3—31no—
227C3×Dic3⋊C4—31no—
228C3×Dic3⋊C4—31no—
229#3724—31no—
230#3724—31no—
231#3724—61no—
232Dic3⋊Dic3—31no—
233Dic3⋊Dic3—31no—
234Dic3⋊Dic3—31no—
235Dic3⋊Dic3—31no—
236Dic3⋊Dic3—31no—
237Dic3⋊Dic3—31no—
238Dic3⋊Dic3—61no—
239Dic3⋊Dic3—61no—
240Dic3⋊Dic3—61no—
241Dic3⋊Dic3C2×D311yescharacteristic, complemented
242Dic3⋊Dic3C2×D311yescharacteristic, complemented
243#3722—31no—
244#3722—31no—
245#3722C2×D311yescharacteristic
246#3722C2×D311yescharacteristic
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—31no—
255(C2×D3)⋊Dic3—31no—
256(C2×D3)⋊Dic3—31no—
257(C2×D3)⋊Dic3—61no—
258(C2×D3)⋊Dic3—61no—
259(C2×D3)⋊Dic3—61no—
260(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
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×C3×C3⋊D3—21no—
276C2×C3×C3⋊D3—21no—
277C2×C3×C3⋊D3—21no—
278C2×C3×C3⋊D3—44no—
279C2×C32×D3—21no—
280C2×C32×D3—21no—
281C2×C32×D3—21no—
282C2×C32×D3—21no—
283C2×C32×D3—21no—
284C2×C32×D3—21no—
285C3⋊(C3⋊Dic3)—21no—
286C3⋊(C3⋊Dic3)—21no—
287C3×C3⋊Dic3—21no—
288C3×C3⋊Dic3—21no—
289C3×C3⋊Dic3—21no—
290C32×Dic3—21no—
291C32×Dic3—21no—
292C32×Dic3—21no—
293C32×Dic3—21no—
294C3×#121—91no—
295C3×#121—91no—
296C3×#120—91no—
297#953—91no—
298#953—91no—
299#940—91no—
300#940—91no—
301#940—91no—
302#939—31no—
303#939—91no—
304#939—91no—
305#939—91no—
306#939—91no—
307#939—91no—
308#939—181no—
309#938—31no—
310#938—31no—
311#938—91no—
312#938—91no—
313#937—31no—
314#937—91no—
315#937—91no—
316#937—91no—
317#937—181no—
318#935—91no—
319#930—91no—
320#930—91no—
321#929—91no—
322#929—91no—
323#898—91no—
324#898—91no—
325#894—91no—
326#894—91no—
327#886—91no—
328#886—91no—
329#884—31no—
330#884—91no—
331#884—91no—
332#884—91no—
333#883—91no—
334#883—91no—
335#882—31no—
336#882—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—41no—
348C23×C32C22×D311yescharacteristic
349C23×C32C22×D311yescharacteristic
350C23×C32C22×D311yescharacteristic
351C22×C3⋊D3—41no—
352C22×C3⋊D3—41no—
353C22×C3⋊D3—41no—
354C22×C3⋊D3C22×D311yescharacteristic
355C22×C3⋊D3C22×D311yescharacteristic
356C22×C3⋊D3C22×D311yescharacteristic
357C22×C3×D3—21no—
358C22×C3×D3—21no—
359C22×C3×D3—31no—
360C22×C3×D3—31no—
361C22×C3×D3—31no—
362C22×C3×D3—31no—
363C22×C3×D3—31no—
364C22×C3×D3—31no—
365C22×C3×D3—61no—
366C22×C3×D3—61no—
367C22×C3×D3—61no—
368C22×C3×D3—121no—
369C22×C3×D3—121no—
370C22×C3×D3—121no—
371C22×C3×D3—121no—
372C22×C3×D3—121no—
373C22×C3×D3—121no—
374C22×C3×D3—122no—
375C22×C3×D3—122no—
376C22×C3×D3—122no—
377C22×C3×D3C22×D311yescharacteristic
378C22×C3×D3C22×D311yescharacteristic
379C22×C3×D3C22×D311yescharacteristic
380C22×C3×D3C22×D311yescharacteristic
381C32×D4—121no—
382C32×D4—121no—
383C2×C32×C4—31no—
384C2×C32×C4—31no—
385C2×C32×C4—31no—
386C2×C32×C4—31no—
387#638—41no—
388#638—121no—
389#638—121no—
390#638—121no—
391C2×C3⋊Dic3—31no—
392C2×C3⋊Dic3—31no—
393C2×C3⋊Dic3—31no—
394C2×C3⋊Dic3—31no—
395C2×C3⋊Dic3—31no—
396C2×C3⋊Dic3—31no—
397C2×C3⋊Dic3—61no—
398C2×C3⋊Dic3—61no—
399C2×C3⋊Dic3—61no—
400C2×C3⋊Dic3—61no—
401C2×C3⋊Dic3—61no—
402C2×C3⋊Dic3—61no—
403C2×C3⋊Dic3—121no—
404C2×C3⋊Dic3—121no—
405C2×C3⋊Dic3—121no—
406C2×C3⋊Dic3C22×D311yescharacteristic
407C2×C3⋊Dic3C22×D311yescharacteristic
408C2×C3⋊Dic3C22×D311yescharacteristic
409C3×#67—41no—
410C3×#67—41no—
411C3×#67—41no—
412C3×#67—41no—
413C3×#67—42no—
414C3×#67—42no—
415C3×#67—121no—
416C3×#67—121no—
417C3×#67—121no—
418C3×#67—121no—
419C3×#67—121no—
420C3×#67—121no—
421C3×#67—121no—
422C3×#67—122no—
423C2×C3×Dic3—21no—
424C2×C3×Dic3—21no—
425C2×C3×Dic3—21no—
426C2×C3×Dic3—21no—
427C2×C3×Dic3—31no—
428C2×C3×Dic3—31no—
429C2×C3×Dic3—31no—
430C2×C3×Dic3—31no—
431C2×C3×Dic3—31no—
432C2×C3×Dic3—31no—
433C2×C3×Dic3—61no—
434C2×C3×Dic3—61no—
435C2×C3×Dic3—61no—
436C2×C3×Dic3—121no—
437C2×C3×Dic3C22×D311yescharacteristic
438C2×C3×Dic3C22×D311yescharacteristic
439C2×C3×Dic3C22×D311yescharacteristic
440C2×C3×Dic3C22×D311yescharacteristic
441C2×C3×Dic3C22×D311yescharacteristic
442C2×C3×Dic3C22×D311yescharacteristic
443C2×C3×Dic3C22×D311yescharacteristic
444C2×C3×Dic3C22×D311yescharacteristic
445C3×D12—121no—
446C3×D12—121no—
447C3×D12—121no—
448C3×C4×D3—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#626—121no—
457#626—121no—
458#625—41no—
459#625—121no—
460#625—121no—
461#625—121no—
462#625—121no—
463#625—121no—
464#625—121no—
465#625—121no—
466#625—121no—
467#625—122no—
468#625—122no—
469#625—122no—
470#624—41no—
471D3×Dic3—41no—
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—
482C3×C3⋊D3—41no—
483C32×D3—41no—
484C32×D3—41no—
485C24×C3—91no—
486C23×D3—31no—
487C23×D3—31no—
488C23×D3—61no—
489C2×C3×D4—31no—
490C2×C3×D4—31no—
491C2×C3×D4—31no—
492C2×C3×D4—31no—
493C2×C3×D4—61no—
494C2×C3×D4—61no—
495C2×C3×D4—91no—
496C2×C3×D4—91no—
497C2×C3×D4—91no—
498C2×C3×D4—91no—
499C2×C3×D4—91no—
500C22×C3×C4—91no—
501C22×C3×C4—91no—
502C2×#67—31no—
503C2×#67—31no—
504C2×#67—31no—
505C2×#67—31no—
506C2×#67—31no—
507C2×#67—31no—
508C2×#67—31no—
509C2×#67—61no—
510C2×#67—91no—
511C2×#67—91no—
512C2×#67—91no—
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—181no—
524C2×#67—181no—
525C2×#67—181no—
526C2×#67D3211yescharacteristic
527C2×#67D3211yescharacteristic
528C22×Dic3—31no—
529C22×Dic3—91no—
530C22×Dic3—91no—
531C22×Dic3—181no—
532C2×D12—31no—
533C2×D12—31no—
534C2×D12—31no—
535C2×D12—91no—
536C2×D12—91no—
537C2×C4×D3—31no—
538C2×C4×D3—31no—
539C2×C4×D3—31no—
540C2×C4×D3—91no—
541C3×C4⋊C4—91no—
542C3×C4⋊C4—91no—
543C3×C22⋊C4—31no—
544C3×C22⋊C4—31no—
545C3×C22⋊C4—61no—
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—61no—
556#217—91no—
557#217—91no—
558#217—91no—
559#217—91no—
560#217—91no—
561#217—91no—
562#217—91no—
563#217—91no—
564#217—181no—
565#217—181no—
566#217—181no—
567#217—361no—
568#217D3211yescharacteristic
569(C2×D3)⋊C4—31no—
570(C2×D3)⋊C4—31no—
571(C2×D3)⋊C4—31no—
572(C2×D3)⋊C4—31no—
573(C2×D3)⋊C4—31no—
574(C2×D3)⋊C4—31no—
575(C2×D3)⋊C4—91no—
576(C2×D3)⋊C4—91no—
577(C2×D3)⋊C4—91no—
578(C2×D3)⋊C4—91no—
579(C2×D3)⋊C4—91no—
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—181no—
586(C2×D3)⋊C4—181no—
587(C2×D3)⋊C4—181no—
588C4⋊Dic3—31no—
589C4⋊Dic3—31no—
590C4⋊Dic3—91no—
591C4⋊Dic3—91no—
592C4⋊Dic3—91no—
593C4⋊Dic3—91no—
594C4⋊Dic3—181no—
595Dic3⋊C4—31no—
596Dic3⋊C4—31no—
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—81no—
642C22×C32—81no—
643C22×C32C23×D311yescharacteristic
644C22×C32C23×D311yescharacteristic
645C22×C32C23×D311yescharacteristic
646C2×C3⋊D3—21no—
647C2×C3⋊D3—21no—
648C2×C3⋊D3—21no—
649C2×C3⋊D3—21no—
650C2×C3⋊D3—21no—
651C2×C3⋊D3—21no—
652C2×C3⋊D3—21no—
653C2×C3⋊D3—21no—
654C2×C3⋊D3—21no—
655C2×C3⋊D3—44no—
656C2×C3×D3—22no—
657C2×C3×D3—21no—
658C2×C3×D3—21no—
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—41no—
670C2×C3×D3—41no—
671C2×C3×D3—41no—
672C2×C3×D3—41no—
673C2×C3×D3—41no—
674C2×C3×D3—62no—
675C2×C3×D3—62no—
676C2×C3×D3—61no—
677C2×C3×D3—61no—
678C2×C3×D3—61no—
679C2×C3×D3—61no—
680C2×C3×D3—61no—
681C2×C3×D3—61no—
682C2×C3×D3—61no—
683C2×C3×D3—61no—
684C2×C3×D3—61no—
685C2×C3×D3—61no—
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—121no—
695C2×C3×D3—121no—
696C2×C3×D3—121no—
697C2×C3×D3—121no—
698C2×C3×D3—121no—
699C2×C3×D3—121no—
700C2×C3×D3—121no—
701C2×C3×D3—128no—
702C2×C3×D3—124no—
703C2×C3×D3—124no—
704C32×C4—61no—
705C32×C4—61no—
706C32×C4—61no—
707C32×C4—61no—
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—21no—
732C3×Dic3—21no—
733C3×Dic3—41no—
734C3×Dic3—41no—
735C3×Dic3—41no—
736C3×Dic3—41no—
737C3×Dic3—62no—
738C3×Dic3—61no—
739C3×Dic3—61no—
740C3×Dic3—61no—
741C3×Dic3—61no—
742C3×Dic3—61no—
743C3×Dic3—61no—
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—91no—
754#121—271no—
755#121—271no—
756#121—271no—
757#121—271no—
758#120—91no—
759#120—271no—
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—41no—
770C23×C3—61no—
771C23×C3—61no—
772C23×C3—91no—
773C23×C3—91no—
774C23×C3—91no—
775C23×C3—361no—
776C23×C3—361no—
777C23×C3—361no—
778C23×C3C2×D3211yescharacteristic
779C23×C3C2×D3211yescharacteristic
780C23×C3C2×D3211yescharacteristic
781C22×D3—31no—
782C22×D3—31no—
783C22×D3—31no—
784C22×D3—31no—
785C22×D3—31no—
786C22×D3—31no—
787C22×D3—61no—
788C22×D3—61no—
789C22×D3—61no—
790C22×D3—121no—
791C22×D3—121no—
792C22×D3—121no—
793C22×D3—121no—
794C22×D3—121no—
795C22×D3—121no—
796C22×D3—122no—
797C22×D3—122no—
798C22×D3—122no—
799C22×D3C2×D3211yescharacteristic
800C22×D3C2×D3211yescharacteristic
801C3×D4—121no—
802C3×D4—121no—
803C3×D4—121no—
804C3×D4—121no—
805C3×D4—122no—
806C3×D4—122no—
807C3×D4—361no—
808C3×D4—361no—
809C3×D4—361no—
810C3×D4—361no—
811C3×D4—361no—
812C2×C3×C4—31no—
813C2×C3×C4—31no—
814C2×C3×C4—31no—
815C2×C3×C4—31no—
816C2×C3×C4—31no—
817C2×C3×C4—31no—
818C2×C3×C4—31no—
819C2×C3×C4—31no—
820C2×C3×C4—61no—
821C2×C3×C4—61no—
822C2×C3×C4—61no—
823C2×C3×C4—61no—
824C2×C3×C4—91no—
825C2×C3×C4—91no—
826C2×C3×C4—91no—
827C2×C3×C4—361no—
828C2×C3×C4—361no—
829#67—41no—
830#67—41no—
831#67—121no—
832#67—121no—
833#67—121no—
834#67—121no—
835#67—121no—
836#67—121no—
837#67—121no—
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—361no—
851#67—361no—
852#67—362no—
853#67—362no—
854#67—362no—
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—91no—
865C2×Dic3—91no—
866C2×Dic3—91no—
867C2×Dic3—91no—
868C2×Dic3—91no—
869C2×Dic3—91no—
870C2×Dic3—121no—
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—362no—
882C2×Dic3C2×D3211yescharacteristic
883C2×Dic3C2×D3211yescharacteristic
884C2×Dic3C2×D3211yescharacteristic
885C2×Dic3C2×D3211yescharacteristic
886D12—121no—
887D12—121no—
888D12—121no—
889D12—361no—
890D12—361no—
891C4×D3—121no—
892C4×D3—121no—
893C4×D3—121no—
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#100411yescharacteristic
917C2×C32#100411yescharacteristic
918C2×C32#100411yescharacteristic
919C2×C32#100411yescharacteristic
920C2×C32#100411yescharacteristic
921C2×C32#100411yescharacteristic
922C2×C32#100411yescharacteristic
923C2×C32#100911yescharacteristic
924C2×C32#100911yescharacteristic
925C3⋊D3—41no—
926C3⋊D3—41no—
927C3⋊D3—41no—
928C3×D3—42no—
929C3×D3—41no—
930C3×D3—41no—
931C3×D3—41no—
932C3×D3—41no—
933C3×D3—81no—
934C3×D3—122no—
935C3×D3—122no—
936C3×D3—121no—
937C3×D3—121no—
938C3×D3—121no—
939C3×D3—121no—
940C3×D3—121no—
941C3×D3—121no—
942C3×D3—241no—
943C24—91no—
944C2×D4—31no—
945C2×D4—31no—
946C2×D4—91no—
947C2×D4—91no—
948C2×D4—91no—
949C2×D4—91no—
950C2×D4—91no—
951C2×D4—271no—
952C2×D4—271no—
953C2×D4—271no—
954C2×D4—271no—
955C2×D4—271no—
956C22×C4—91no—
957C22×C4—91no—
958C22×C4—271no—
959C4⋊C4—91no—
960C4⋊C4—91no—
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—271no—
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—61no—
1003C22×C3—61no—
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—81no—
1015C22×C3—81no—
1016C22×C3—121no—
1017C22×C3—121no—
1018C22×C3—121no—
1019C22×C3—121no—
1020C22×C3—121no—
1021C22×C3—181no—
1022C22×C3—181no—
1023C22×C3—181no—
1024C22×C3—181no—
1025C22×C3—181no—
1026C22×C3—181no—
1027C22×C3—181no—
1028C22×C3—181no—
1029C22×C3—181no—
1030C22×C3—364no—
1031C22×C3C22×D3211yescharacteristic
1032C22×C3C22×D3211yescharacteristic
1033C22×C3C22×D3211yescharacteristic
1034C2×D3—21no—
1035C2×D3—21no—
1036C2×D3—21no—
1037C2×D3—21no—
1038C2×D3—21no—
1039C2×D3—21no—
1040C2×D3—62no—
1041C2×D3—62no—
1042C2×D3—61no—
1043C2×D3—61no—
1044C2×D3—61no—
1045C2×D3—61no—
1046C2×D3—61no—
1047C2×D3—61no—
1048C2×D3—61no—
1049C2×D3—61no—
1050C2×D3—61no—
1051C2×D3—61no—
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—121no—
1061C2×D3—121no—
1062C2×D3—121no—
1063C2×D3—121no—
1064C2×D3—121no—
1065C2×D3—121no—
1066C2×D3—121no—
1067C2×D3—128no—
1068C2×D3—124no—
1069C2×D3—124no—
1070C3×C4—61no—
1071C3×C4—61no—
1072C3×C4—61no—
1073C3×C4—61no—
1074C3×C4—61no—
1075C3×C4—61no—
1076C3×C4—61no—
1077C3×C4—61no—
1078C3×C4—121no—
1079C3×C4—121no—
1080C3×C4—121no—
1081C3×C4—121no—
1082C3×C4—181no—
1083C3×C4—181no—
1084C3×C4—181no—
1085Dic3—21no—
1086Dic3—21no—
1087Dic3—21no—
1088Dic3—21no—
1089Dic3—62no—
1090Dic3—61no—
1091Dic3—61no—
1092Dic3—61no—
1093Dic3—61no—
1094Dic3—61no—
1095Dic3—61no—
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#562011yescharacteristic, complemented
1118C32#562011yescharacteristic, complemented
1119C23—31no—
1120C23—31no—
1121C23—91no—
1122C23—91no—
1123C23—91no—
1124C23—361no—
1125C23—361no—
1126C23—361no—
1127C23D3311yescharacteristic
1128D4—121no—
1129D4—121no—
1130D4—361no—
1131D4—361no—
1132D4—361no—
1133D4—361no—
1134D4—361no—
1135D4—1081no—
1136D4—1081no—
1137D4—1081no—
1138D4—1081no—
1139D4—1081no—
1140C2×C4—31no—
1141C2×C4—31no—
1142C2×C4—31no—
1143C2×C4—31no—
1144C2×C4—91no—
1145C2×C4—91no—
1146C2×C4—91no—
1147C2×C4—271no—
1148C2×C4—271no—
1149C2×C4—361no—
1150C2×C4—361no—
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—121no—
1173C2×C3—121no—
1174C2×C3—121no—
1175C2×C3—121no—
1176C2×C3—241no—
1177C2×C3—361no—
1178C2×C3—361no—
1179C2×C3—361no—
1180C2×C3#6430711yescharacteristic
1181C2×C3#6431311yescharacteristic
1182C2×C3#6431311yescharacteristic
1183C2×C3#6431311yescharacteristic
1184C2×C3#6431411yescharacteristic
1185C2×C3#6431411yescharacteristic
1186C2×C3#6431411yescharacteristic
1187C2×C3#6433011yescharacteristic
1188C2×C3#6433011yescharacteristic
1189D3—41no—
1190D3—41no—
1191D3—122no—
1192D3—122no—
1193D3—121no—
1194D3—121no—
1195D3—121no—
1196D3—121no—
1197D3—121no—
1198D3—121no—
1199D3—241no—
1200C22—21no—
1201C22—21no—
1202C22—21no—
1203C22—61no—
1204C22—61no—
1205C22—61no—
1206C22—61no—
1207C22—61no—
1208C22—61no—
1209C22—181no—
1210C22—181no—
1211C22—181no—
1212C22—181no—
1213C22—181no—
1214C22—181no—
1215C22—181no—
1216C22—181no—
1217C22—181no—
1218C22—364no—
1219C22C2×D3311yescharacteristic
1220C4—61no—
1221C4—61no—
1222C4—61no—
1223C4—61no—
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#1059526411yescharacteristic, complemented
1236C2—41no—
1237C2—121no—
1238C2—121no—
1239C2—361no—
1240C2—361no—
1241C2—361no—
1242C2#1172441511yescharacteristic
1243C2#1172441611yescharacteristic
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. #11723727C2semidirect
2. #11723634C2semidirect
3. #11723615C2semidirect
4. #11723596C2semidirect
5. C3×#63981C2semidirect
6. C3×#63970C2semidirect
7. C3×#63958C2semidirect
8. #11723029C2semidirect
9. #11723025C2semidirect
10. #11722995C2semidirect
11. #11722990C2semidirect
12. #11722988C2semidirect
13. #11722960C2semidirect
14. #11722957C2semidirect
15. #11722954C2semidirect
27. C2×#6290C22semidirect
28. C2×D3×C3⋊Dic3C22semidirect
31. C2×C3×#626C22semidirect
32. C2×C3×#625C22semidirect
33. C2×C3×#624C22semidirect
34. C2×C3×D3×Dic3C22semidirect
40. #88807C22semidirect
41. #88807C22semidirect
42. #88806C22semidirect
43. Dic3⋊(C3⋊Dic3)C22semidirect
46. #88803C22semidirect
47. Dic3×C3⋊Dic3C22semidirect
48. C3×Dic3⋊Dic3C22semidirect
49. C3×Dic3⋊Dic3C22semidirect
52. C3×(C2×D3)⋊Dic3C22semidirect
53. C3×(C2×D3)⋊Dic3C22semidirect
64. #63981D3semidirect
78. #63970D3semidirect
82. #63958D3semidirect
176. C2×#626C2×D3semidirect
188. C2×#625C2×D3semidirect
189. C2×#624C2×D3semidirect
193. C2×D3×Dic3C2×D3semidirect
241. Dic3⋊Dic3C2×D3semidirect
242. Dic3⋊Dic3C2×D3semidirect
260. (C2×D3)⋊Dic3C2×D3semidirect
261. (C2×D3)⋊Dic3C2×D3semidirect
761. C33#560semidirect
1116. C32#5595semidirect
1117. C32#5620semidirect
1118. C32#5620semidirect
1233. C3#10594234semidirect
1234. C3#10595257semidirect
1235. C3#10595264semidirect

Maximal subgroups

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

subgroupindex
#117237272
#117236342
#117236152
#117235962
C3×#639812
C3×#639702
C3×#639582
#117230292
#117230252
#117229952
#117229902
#117229882
#117229602
#117229572
#117229542
#105952643
#105952573
#105942343