Finite Group Databasebeta

← #13172311

Subgroups — #13172311

Order 1728.

1380 conjugacy classes of subgroups.

The subgroup lattice has 1274 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723728C211yesmaximal, characteristic, complemented
2#11723643C211yesmaximal, characteristic, complemented
3#11723632C211yesmaximal, characteristic, complemented
4#11723624C211yesmaximal, characteristic, complemented
5C3×#63978C211yesmaximal, characteristic, complemented
6C3×#63966C211yesmaximal, characteristic, complemented
7C3×#63958C211yesmaximal, characteristic, complemented
8#11723028C211yesmaximal, characteristic, complemented
9#11723026C211yesmaximal, characteristic, complemented
10#11722997C211yesmaximal, characteristic, complemented
11#11722995C211yesmaximal, characteristic, complemented
12#11722962C211yesmaximal, characteristic, complemented
13#11722961C211yesmaximal, characteristic, complemented
14#11722950C211yesmaximal, characteristic, complemented
15#11722950C211yesmaximal, characteristic, complemented
16#10595264—31nomaximal
17#10595090—31nomaximal
18#10594308—31nomaximal
19C22×D3×C3⋊D3C2211yescharacteristic
20C2×#6312C2211yescharacteristic
21C2×C3×#638C2211yescharacteristic
22C2×C3×#638C2211yescharacteristic, complemented
23C2×C3×#638C2211yescharacteristic, complemented
24C2×C32×#67C2211yescharacteristic
25C22×C32×Dic3C2211yescharacteristic, complemented
26C2×#6295C2211yescharacteristic
27C2×#6295C2211yescharacteristic
28C2×#6295C2211yescharacteristic, complemented
29C2×#6292C2211yescharacteristic
30C2×#6292C2211yescharacteristic
31C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
32C2×C3×#626C2211yescharacteristic
33C2×C3×#626C2211yescharacteristic
34C2×C3×#624C2211yescharacteristic, complemented
35C32×#217C2211yescharacteristic, complemented
36#88813C2211yescharacteristic, complemented
37#88806C2211yescharacteristic, complemented
38Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
39#88804C2211yescharacteristic
40#88804C2211yescharacteristic
41#88804C2211yescharacteristic
42#88803C2211yescharacteristic
43#88803C2211yescharacteristic, complemented
44(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
45C3×Dic3⋊Dic3C2211yescharacteristic, complemented
46C3×Dic3⋊Dic3C2211yescharacteristic, complemented
47C3×Dic3⋊Dic3C2211yescharacteristic, complemented
48C3×Dic3⋊Dic3C2211yescharacteristic, complemented
49C3×#3722C2211yescharacteristic
50C3×#3722C2211yescharacteristic
51C3×#3722C2211yescharacteristic, complemented
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×(C2×D3)⋊Dic3C2211yescharacteristic
54#64146—31no—
55#64139—31no—
56#64093—31no—
57C3×#939—31no—
58C3×#938—31no—
59C3×#930—31no—
60C3×#929—31no—
61C3×#886—31no—
62C3×#884—31no—
63#63983—31no—
64#63983—31no—
65#63983—61no—
66#63981—31no—
67#63981—31no—
68#63979—31no—
69#63979—31no—
70#63979—31no—
71#63978—31no—
72#63978—31no—
73#63978—61no—
74#63978D311yescharacteristic, complemented
75#63971—31no—
76#63971—31no—
77#63971—61no—
78#63970—31no—
79#63966D311yescharacteristic, complemented
80#63958D311yescharacteristic, complemented
81#63956—31no—
82#63923—31no—
83#63923—31no—
84#63922—31no—
85#63922—31no—
86#63916—31no—
87#63910—31no—
88#63909—31no—
89#63906—31no—
90#63905—31no—
91#63891—31no—
92#63890—31no—
93#63886—31no—
94#63861—31no—
95#63858—31no—
96#63854—31no—
97#63853—31no—
98#63850—31no—
99#63848—31no—
100#63848—31no—
101#63848—31no—
102C23×C33C2311yescharacteristic
103C22×C3⋊(C3⋊D3)C2311yescharacteristic
104C22×C3×C3⋊D3C2311yescharacteristic
105C22×C3×C3⋊D3C2311yescharacteristic
106C22×C3×C3⋊D3C2311yescharacteristic
107C22×C32×D3C2311yescharacteristic
108C2×D3×C3⋊D3—41no—
109C2×D3×C3⋊D3—41no—
110C2×D3×C3⋊D3—41no—
111#6312—41no—
112C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
113C3×#638—41no—
114C3×#638—41no—
115C3×#638—41no—
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C2×C3×C3⋊Dic3C2311yescharacteristic
118C2×C3×C3⋊Dic3C2311yescharacteristic
119C32×#67—41no—
120C2×C32×Dic3—41no—
121C2×C32×Dic3C2311yescharacteristic
122C2×C32×Dic3C2311yescharacteristic
123C2×C32×Dic3C2311yescharacteristic
124C2×C32×Dic3C2311yescharacteristic
125C2×C32×Dic3C2311yescharacteristic
126#6295—41no—
127#6295—41no—
128#6295—41no—
129#6292—41no—
130#6292—41no—
131Dic3×C3⋊D3—41no—
132C3×#626—41no—
133C3×#626—41no—
134C3×#624—41no—
135#5666—91no—
136#5620—91no—
137#5620—91no—
138C23×C3⋊D3—31no—
139C22×D32—31no—
140C22×D32—31no—
141C22×D32—61no—
142C2×C32×D4—31no—
143C22×C32×C4—31no—
144C2×#638—31no—
145C2×#638—31no—
146C2×#638—31no—
147C2×#638—61no—
148C2×#638—61no—
149C2×#638—61no—
150C2×#638—121no—
151C2×#638C2×D311yescharacteristic
152C2×#638C2×D311yescharacteristic, complemented
153C2×#638C2×D311yescharacteristic, complemented
154C2×C4⋊(C3⋊D3)—31no—
155C2×C4⋊(C3⋊D3)—31no—
156C2×C4×C3⋊D3—31no—
157C2×C3×#67—21no—
158C2×C3×#67—31no—
159C2×C3×#67—31no—
160C2×C3×#67—31no—
161C2×C3×#67—31no—
162C2×C3×#67—31no—
163C2×C3×#67—31no—
164C2×C3×#67—31no—
165C2×C3×#67—31no—
166C2×C3×#67—61no—
167C2×C3×#67—61no—
168C2×C3×#67—61no—
169C2×C3×#67C2×D311yescharacteristic
170C2×C3×#67C2×D311yescharacteristic
171C22×C3×Dic3—21no—
172C22×C3×Dic3C2×D311yescharacteristic, complemented
173C22×C3×Dic3C2×D311yescharacteristic, complemented
174C2×C3×D12—31no—
175C2×C3×D12—31no—
176C2×C3×C4×D3—31no—
177C2×C3×C4×D3—31no—
178C2×#626—31no—
179C2×#626—31no—
180C2×#626—31no—
181C2×#626—31no—
182C2×#626—31no—
183C2×#626—31no—
184C2×#626—31no—
185C2×#626—31no—
186C2×#626—31no—
187C2×#626—31no—
188C2×#626—61no—
189C2×#626—61no—
190C2×#626C2×D311yescharacteristic
191C2×#626C2×D311yescharacteristic
192C2×#625—31no—
193C2×#625—31no—
194C2×#625—31no—
195C2×#624C2×D311yescharacteristic, complemented
196C2×D3×Dic3—31no—
197C2×D3×Dic3—31no—
198C2×D3×Dic3—61no—
199C32×C22⋊C4—31no—
200#3757—31no—
201#3752—31no—
202#3752—31no—
203#3752—31no—
204#3752—31no—
205#3752—31no—
206C4⋊(C3⋊Dic3)—31no—
207#3750—31no—
208C3×#217—21no—
209C3×#217—31no—
210C3×#217—31no—
211C3×#217C2×D311yescharacteristic, complemented
212C3×#217C2×D311yescharacteristic, complemented
213C3×(C2×D3)⋊C4—31no—
214C3×(C2×D3)⋊C4—31no—
215C3×(C2×D3)⋊C4—31no—
216C3×(C2×D3)⋊C4—31no—
217C3×(C2×D3)⋊C4—31no—
218C3×(C2×D3)⋊C4—31no—
219C3×(C2×D3)⋊C4—31no—
220C3×(C2×D3)⋊C4—31no—
221C3×C4⋊Dic3—31no—
222C3×C4⋊Dic3—31no—
223C3×C4⋊Dic3—31no—
224C3×C4⋊Dic3—31no—
225C3×Dic3⋊C4—31no—
226C3×Dic3⋊C4—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—61no—
235Dic3⋊Dic3C2×D311yescharacteristic, complemented
236Dic3⋊Dic3C2×D311yescharacteristic, complemented
237Dic3⋊Dic3C2×D311yescharacteristic, complemented
238Dic3⋊Dic3C2×D311yescharacteristic, complemented
239#3722—31no—
240#3722—31no—
241#3722—31no—
242#3722—31no—
243#3722—31no—
244#3722—31no—
245#3722—61no—
246#3722—61no—
247#3722—61no—
248#3722C2×D311yescharacteristic
249#3722C2×D311yescharacteristic
250#3722C2×D311yescharacteristic, complemented
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
261(C2×D3)⋊Dic3C2×D311yescharacteristic
262Dic32—31no—
263Dic32—31no—
264Dic32—31no—
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—21no—
279C2×C3×C3⋊D3—21no—
280C2×C3×C3⋊D3—21no—
281C2×C32×D3—21no—
282C2×C32×D3—21no—
283C2×C32×D3—21no—
284D3×C3⋊D3—44no—
285C3⋊(C3⋊Dic3)—21no—
286C3×C3⋊Dic3—21no—
287C3×C3⋊Dic3—21no—
288C3×C3⋊Dic3—21no—
289C32×Dic3—21no—
290C32×Dic3—21no—
291C32×Dic3—21no—
292C32×Dic3—21no—
293C32×Dic3—21no—
294C3×#123—91no—
295C3×#121—91no—
296C3×#121—91no—
297#940—91no—
298#940—91no—
299#940—91no—
300#939—31no—
301#939—91no—
302#939—91no—
303#939—91no—
304#938—31no—
305#938—91no—
306#937—91no—
307#937—91no—
308#937—91no—
309#937—91no—
310#937—91no—
311#937—181no—
312#930—31no—
313#930—91no—
314#930—91no—
315#930—91no—
316#930—181no—
317#929—31no—
318#929—91no—
319#898—91no—
320#898—91no—
321#898—91no—
322#898—91no—
323#895—91no—
324#895—91no—
325#894—91no—
326#894—91no—
327#886—31no—
328#886—91no—
329#884—31no—
330#884—91no—
331#884—91no—
332#884—91no—
333#884—181no—
334#883—91no—
335#883—91no—
336#882—91no—
337#882—91no—
338#882—91no—
339#882—91no—
340#879—91no—
341#879—91no—
342C23×C32—21no—
343C23×C32—21no—
344C23×C32—21no—
345C23×C32—31no—
346C23×C32—41no—
347C23×C32C22×D311yescharacteristic
348C23×C32C22×D311yescharacteristic
349C23×C32C22×D311yescharacteristic
350C22×C3⋊D3—31no—
351C22×C3⋊D3—31no—
352C22×C3⋊D3—31no—
353C22×C3⋊D3—61no—
354C22×C3⋊D3—61no—
355C22×C3⋊D3—61no—
356C22×C3⋊D3—121no—
357C22×C3⋊D3—121no—
358C22×C3⋊D3—121no—
359C22×C3⋊D3—121no—
360C22×C3⋊D3C22×D311yescharacteristic
361C22×C3⋊D3C22×D311yescharacteristic
362C22×C3⋊D3C22×D311yescharacteristic
363C22×C3×D3—21no—
364C22×C3×D3—31no—
365C22×C3×D3—31no—
366C22×C3×D3—31no—
367C22×C3×D3—31no—
368C22×C3×D3—31no—
369C22×C3×D3—31no—
370C22×C3×D3—61no—
371C22×C3×D3—61no—
372C22×C3×D3—61no—
373C22×C3×D3C22×D311yescharacteristic
374C22×C3×D3C22×D311yescharacteristic
375C2×D32—121no—
376C2×D32—121no—
377C2×D32—121no—
378C2×D32—121no—
379C2×D32—121no—
380C2×D32—121no—
381C2×D32—122no—
382C2×D32—122no—
383C2×D32—122no—
384C32×D4—121no—
385C2×C32×C4—31no—
386C2×C32×C4—31no—
387C2×C32×C4—31no—
388C2×C32×C4—31no—
389C2×C32×C4—31no—
390C2×C32×C4—121no—
391#638—41no—
392#638—41no—
393#638—41no—
394#638—121no—
395#638—121no—
396#638—121no—
397#638—122no—
398#638—122no—
399#638—122no—
400#638—124no—
401C2×C3⋊Dic3—31no—
402C2×C3⋊Dic3—31no—
403C2×C3⋊Dic3—31no—
404C2×C3⋊Dic3—61no—
405C2×C3⋊Dic3—61no—
406C2×C3⋊Dic3—61no—
407C2×C3⋊Dic3—121no—
408C2×C3⋊Dic3C22×D311yescharacteristic
409C2×C3⋊Dic3C22×D311yescharacteristic
410C2×C3⋊Dic3C22×D311yescharacteristic
411C4⋊(C3⋊D3)—121no—
412C4⋊(C3⋊D3)—121no—
413C4×C3⋊D3—121no—
414C3×#67—41no—
415C3×#67—41no—
416C3×#67—42no—
417C3×#67—121no—
418C3×#67—121no—
419C3×#67—121no—
420C3×#67—121no—
421C3×#67—121no—
422C3×#67—121no—
423C3×#67—121no—
424C3×#67—121no—
425C3×#67—122no—
426C3×#67—122no—
427C3×#67—122no—
428C2×C3×Dic3—21no—
429C2×C3×Dic3—21no—
430C2×C3×Dic3—21no—
431C2×C3×Dic3—21no—
432C2×C3×Dic3—21no—
433C2×C3×Dic3—31no—
434C2×C3×Dic3—31no—
435C2×C3×Dic3—31no—
436C2×C3×Dic3—31no—
437C2×C3×Dic3—31no—
438C2×C3×Dic3—31no—
439C2×C3×Dic3—41no—
440C2×C3×Dic3—41no—
441C2×C3×Dic3—42no—
442C2×C3×Dic3—61no—
443C2×C3×Dic3—61no—
444C2×C3×Dic3—61no—
445C2×C3×Dic3C22×D311yescharacteristic
446C2×C3×Dic3C22×D311yescharacteristic
447C2×C3×Dic3C22×D311yescharacteristic
448C2×C3×Dic3C22×D311yescharacteristic
449C2×C3×Dic3C22×D311yescharacteristic
450C2×C3×Dic3C22×D311yescharacteristic
451C2×C3×Dic3C22×D311yescharacteristic
452C2×C3×Dic3C22×D311yescharacteristic
453C2×C3×Dic3C22×D311yescharacteristic
454C2×C3×Dic3C22×D311yescharacteristic
455C3×D12—121no—
456C3×D12—121no—
457C3×C4×D3—121no—
458C3×C4×D3—121no—
459#626—41no—
460#626—41no—
461#626—121no—
462#626—121no—
463#626—121no—
464#626—121no—
465#626—122no—
466#626—122no—
467#626—121no—
468#626—121no—
469#626—121no—
470#626—121no—
471#626—121no—
472#626—121no—
473#625—121no—
474#625—121no—
475#625—121no—
476#624—41no—
477D3×Dic3—121no—
478D3×Dic3—121no—
479D3×Dic3—122no—
480#560—271noSylow
481C2×C33—41no—
482C2×C33H(5,𝔽2)11yescharacteristic
483C2×C33H(5,𝔽2)11yescharacteristic
484C2×C33H(5,𝔽2)11yescharacteristic
485C3⋊(C3⋊D3)—41no—
486C3×C3⋊D3—41no—
487C3×C3⋊D3—41no—
488C3×C3⋊D3—41no—
489C32×D3—41no—
490C23×D3—91no—
491C23×D3—91no—
492C23×D3—91no—
493C23×D3—181no—
494C2×C3×D4—31no—
495C2×C3×D4—31no—
496C2×C3×D4—61no—
497C2×C3×D4—91no—
498C2×C3×D4—91no—
499C2×C3×D4—91no—
500C2×C3×D4—91no—
501C2×C3×D4—91no—
502C22×C3×C4—31no—
503C22×C3×C4—31no—
504C22×C3×C4—61no—
505C22×C3×C4—91no—
506C2×#67—31no—
507C2×#67—31no—
508C2×#67—31no—
509C2×#67—31no—
510C2×#67—31no—
511C2×#67—31no—
512C2×#67—31no—
513C2×#67—31no—
514C2×#67—61no—
515C2×#67—61no—
516C2×#67—61no—
517C2×#67—91no—
518C2×#67—91no—
519C2×#67—91no—
520C2×#67—91no—
521C2×#67—91no—
522C2×#67—91no—
523C2×#67—91no—
524C2×#67—91no—
525C2×#67—91no—
526C2×#67—91no—
527C2×#67—91no—
528C2×#67—181no—
529C2×#67—181no—
530C2×#67—181no—
531C2×#67—361no—
532C2×#67D3211yescharacteristic
533C22×Dic3—91no—
534C22×Dic3D3211yescharacteristic, complemented
535C2×D12—31no—
536C2×D12—31no—
537C2×D12—91no—
538C2×D12—91no—
539C2×D12—91no—
540C2×D12—91no—
541C2×D12—91no—
542C2×D12—91no—
543C2×D12—91no—
544C2×D12—181no—
545C2×D12—181no—
546C2×C4×D3—31no—
547C2×C4×D3—31no—
548C2×C4×D3—91no—
549C2×C4×D3—91no—
550C2×C4×D3—181no—
551C3×C4⋊C4—91no—
552C3×C4⋊C4—91no—
553C3×C4⋊C4—91no—
554C3×C4⋊C4—91no—
555C3×C22⋊C4—31no—
556C3×C22⋊C4—31no—
557C3×C22⋊C4—61no—
558C3×C22⋊C4—91no—
559C3×C22⋊C4—91no—
560C3×C22⋊C4—91no—
561C3×C22⋊C4—91no—
562C3×C22⋊C4—91no—
563#217—31no—
564#217—31no—
565#217—91no—
566#217—91no—
567#217—91no—
568#217—91no—
569#217—181no—
570#217D3211yescharacteristic, complemented
571(C2×D3)⋊C4—31no—
572(C2×D3)⋊C4—31no—
573(C2×D3)⋊C4—31no—
574(C2×D3)⋊C4—31no—
575(C2×D3)⋊C4—31no—
576(C2×D3)⋊C4—31no—
577(C2×D3)⋊C4—31no—
578(C2×D3)⋊C4—31no—
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—91no—
586(C2×D3)⋊C4—91no—
587(C2×D3)⋊C4—91no—
588(C2×D3)⋊C4—91no—
589(C2×D3)⋊C4—91no—
590(C2×D3)⋊C4—91no—
591(C2×D3)⋊C4—91no—
592(C2×D3)⋊C4—91no—
593(C2×D3)⋊C4—181no—
594(C2×D3)⋊C4—181no—
595(C2×D3)⋊C4—181no—
596(C2×D3)⋊C4—181no—
597(C2×D3)⋊C4—181no—
598C4⋊Dic3—31no—
599C4⋊Dic3—31no—
600C4⋊Dic3—31no—
601C4⋊Dic3—31no—
602C4⋊Dic3—91no—
603C4⋊Dic3—91no—
604C4⋊Dic3—181no—
605Dic3⋊C4—31no—
606Dic3⋊C4—31no—
607Dic3⋊C4—31no—
608Dic3⋊C4—31no—
609Dic3⋊C4—91no—
610Dic3⋊C4—91no—
611Dic3⋊C4—91no—
612Dic3⋊C4—91no—
613Dic3⋊C4—181no—
614C4×Dic3—91no—
615C4×Dic3—91no—
616C4×Dic3—91no—
617C22×C32—21no—
618C22×C32—22no—
619C22×C32—21no—
620C22×C32—21no—
621C22×C32—21no—
622C22×C32—21no—
623C22×C32—21no—
624C22×C32—21no—
625C22×C32—21no—
626C22×C32—21no—
627C22×C32—21no—
628C22×C32—21no—
629C22×C32—21no—
630C22×C32—41no—
631C22×C32—41no—
632C22×C32—41no—
633C22×C32—42no—
634C22×C32—41no—
635C22×C32—41no—
636C22×C32—41no—
637C22×C32—41no—
638C22×C32—41no—
639C22×C32—41no—
640C22×C32—61no—
641C22×C32—61no—
642C22×C32—61no—
643C22×C32—81no—
644C22×C32—81no—
645C22×C32C23×D311yescharacteristic
646C22×C32C23×D311yescharacteristic
647C22×C32C23×D311yescharacteristic
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—21no—
656C2×C3⋊D3—21no—
657C2×C3⋊D3—61no—
658C2×C3⋊D3—62no—
659C2×C3⋊D3—61no—
660C2×C3⋊D3—61no—
661C2×C3⋊D3—61no—
662C2×C3⋊D3—61no—
663C2×C3⋊D3—61no—
664C2×C3⋊D3—61no—
665C2×C3⋊D3—61no—
666C2×C3⋊D3—61no—
667C2×C3⋊D3—121no—
668C2×C3⋊D3—121no—
669C2×C3⋊D3—122no—
670C2×C3⋊D3—121no—
671C2×C3⋊D3—121no—
672C2×C3⋊D3—121no—
673C2×C3⋊D3—121no—
674C2×C3⋊D3—121no—
675C2×C3⋊D3—121no—
676C2×C3⋊D3—124no—
677C2×C3⋊D3—241no—
678C2×C3⋊D3—241no—
679C2×C3×D3—22no—
680C2×C3×D3—21no—
681C2×C3×D3—21no—
682C2×C3×D3—21no—
683C2×C3×D3—21no—
684C2×C3×D3—21no—
685C2×C3×D3—21no—
686C2×C3×D3—41no—
687C2×C3×D3—41no—
688C2×C3×D3—62no—
689C2×C3×D3—62no—
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—61no—
699C2×C3×D3—61no—
700C2×C3×D3—61no—
701C2×C3×D3—61no—
702C2×C3×D3—61no—
703C2×C3×D3—61no—
704C2×C3×D3—61no—
705C2×C3×D3—61no—
706C2×C3×D3—61no—
707C2×C3×D3—61no—
708C2×C3×D3—121no—
709C2×C3×D3—121no—
710C2×C3×D3—121no—
711C2×C3×D3—121no—
712C2×C3×D3—121no—
713C2×C3×D3—121no—
714C2×C3×D3—121no—
715D32—128no—
716D32—124no—
717D32—124no—
718C32×C4—61no—
719C32×C4—61no—
720C32×C4—61no—
721C32×C4—61no—
722C32×C4—61no—
723C3⋊Dic3—21no—
724C3⋊Dic3—21no—
725C3⋊Dic3—21no—
726C3⋊Dic3—61no—
727C3⋊Dic3—62no—
728C3⋊Dic3—61no—
729C3⋊Dic3—61no—
730C3⋊Dic3—121no—
731C3⋊Dic3—121no—
732C3⋊Dic3—122no—
733C3×Dic3—22no—
734C3×Dic3—21no—
735C3×Dic3—21no—
736C3×Dic3—21no—
737C3×Dic3—21no—
738C3×Dic3—21no—
739C3×Dic3—21no—
740C3×Dic3—21no—
741C3×Dic3—21no—
742C3×Dic3—21no—
743C3×Dic3—21no—
744C3×Dic3—41no—
745C3×Dic3—41no—
746C3×Dic3—41no—
747C3×Dic3—41no—
748C3×Dic3—61no—
749C3×Dic3—61no—
750C3×Dic3—61no—
751C3×Dic3—61no—
752C3×Dic3—61no—
753C3×Dic3—61no—
754C3×Dic3—121no—
755C3×Dic3—121no—
756C3×Dic3—121no—
757#127—271no—
758#126—271no—
759#126—271no—
760#123—91no—
761#123—271no—
762#123—271no—
763#121—91no—
764#121—91no—
765#121—271no—
766#121—271no—
767#121—271no—
768#121—271no—
769#120—271no—
770#120—271no—
771#120—271no—
772C33#56011yescharacteristic, complemented, Sylow
773C23×C3—21no—
774C23×C3—21no—
775C23×C3—21no—
776C23×C3—31no—
777C23×C3—31no—
778C23×C3—41no—
779C23×C3—61no—
780C23×C3—91no—
781C23×C3—91no—
782C23×C3—91no—
783C23×C3C2×D3211yescharacteristic
784C23×C3C2×D3211yescharacteristic
785C23×C3C2×D3211yescharacteristic
786C22×D3—31no—
787C22×D3—31no—
788C22×D3—31no—
789C22×D3—31no—
790C22×D3—31no—
791C22×D3—31no—
792C22×D3—61no—
793C22×D3—61no—
794C22×D3—61no—
795C22×D3—91no—
796C22×D3—91no—
797C22×D3—91no—
798C22×D3—181no—
799C22×D3—181no—
800C22×D3—181no—
801C22×D3—361no—
802C22×D3—361no—
803C22×D3—361no—
804C22×D3—361no—
805C22×D3—361no—
806C22×D3—361no—
807C22×D3—361no—
808C22×D3—361no—
809C22×D3—361no—
810C22×D3—361no—
811C22×D3—362no—
812C22×D3—362no—
813C22×D3—362no—
814C22×D3C2×D3211yescharacteristic
815C3×D4—121no—
816C3×D4—121no—
817C3×D4—122no—
818C3×D4—361no—
819C3×D4—361no—
820C3×D4—361no—
821C3×D4—361no—
822C3×D4—361no—
823C2×C3×C4—31no—
824C2×C3×C4—31no—
825C2×C3×C4—31no—
826C2×C3×C4—31no—
827C2×C3×C4—31no—
828C2×C3×C4—31no—
829C2×C3×C4—31no—
830C2×C3×C4—31no—
831C2×C3×C4—31no—
832C2×C3×C4—31no—
833C2×C3×C4—61no—
834C2×C3×C4—61no—
835C2×C3×C4—61no—
836C2×C3×C4—61no—
837C2×C3×C4—61no—
838C2×C3×C4—91no—
839C2×C3×C4—91no—
840C2×C3×C4—91no—
841C2×C3×C4—121no—
842C2×C3×C4—121no—
843C2×C3×C4—122no—
844C2×C3×C4—361no—
845#67—41no—
846#67—121no—
847#67—121no—
848#67—121no—
849#67—121no—
850#67—121no—
851#67—121no—
852#67—121no—
853#67—121no—
854#67—122no—
855#67—122no—
856#67—122no—
857#67—361no—
858#67—361no—
859#67—361no—
860#67—361no—
861#67—361no—
862#67—361no—
863#67—361no—
864#67—361no—
865#67—361no—
866#67—361no—
867#67—361no—
868#67—362no—
869#67—362no—
870#67—362no—
871#67—364no—
872C2×Dic3—31no—
873C2×Dic3—31no—
874C2×Dic3—31no—
875C2×Dic3—31no—
876C2×Dic3—31no—
877C2×Dic3—31no—
878C2×Dic3—41no—
879C2×Dic3—61no—
880C2×Dic3—61no—
881C2×Dic3—61no—
882C2×Dic3—91no—
883C2×Dic3—91no—
884C2×Dic3—91no—
885C2×Dic3—181no—
886C2×Dic3—181no—
887C2×Dic3—181no—
888C2×Dic3—361no—
889C2×Dic3—361no—
890C2×Dic3C2×D3211yescharacteristic
891C2×Dic3C2×D3211yescharacteristic
892C2×Dic3C2×D3211yescharacteristic
893C2×Dic3C2×D3211yescharacteristic
894C2×Dic3C2×D3211yescharacteristic
895D12—121no—
896D12—121no—
897D12—361no—
898D12—361no—
899D12—361no—
900D12—361no—
901D12—362no—
902D12—362no—
903D12—361no—
904D12—361no—
905D12—361no—
906C4×D3—121no—
907C4×D3—121no—
908C4×D3—361no—
909C4×D3—361no—
910C4×D3—362no—
911C2×C32—21no—
912C2×C32—21no—
913C2×C32—21no—
914C2×C32—21no—
915C2×C32—21no—
916C2×C32—21no—
917C2×C32—21no—
918C2×C32—21no—
919C2×C32—21no—
920C2×C32—41no—
921C2×C32—41no—
922C2×C32—41no—
923C2×C32—41no—
924C2×C32—42no—
925C2×C32—41no—
926C2×C32—41no—
927C2×C32—81no—
928C2×C32—81no—
929C2×C32—82no—
930C2×C32—121no—
931C2×C32#100411yescharacteristic
932C2×C32#100411yescharacteristic
933C2×C32#100411yescharacteristic
934C2×C32#100411yescharacteristic
935C2×C32#100411yescharacteristic
936C2×C32#100911yescharacteristic
937C2×C32#100911yescharacteristic
938C2×C32#100911yescharacteristic
939C2×C32#100911yescharacteristic
940C3⋊D3—41no—
941C3⋊D3—41no—
942C3⋊D3—41no—
943C3⋊D3—121no—
944C3⋊D3—122no—
945C3⋊D3—121no—
946C3⋊D3—121no—
947C3⋊D3—241no—
948C3⋊D3—241no—
949C3⋊D3—242no—
950C3×D3—42no—
951C3×D3—41no—
952C3×D3—41no—
953C3×D3—122no—
954C3×D3—122no—
955C3×D3—121no—
956C3×D3—121no—
957C3×D3—121no—
958C3×D3—121no—
959C3×D3—121no—
960C3×D3—121no—
961C3×D3—241no—
962C24—271no—
963C2×D4—31no—
964C2×D4—91no—
965C2×D4—91no—
966C2×D4—91no—
967C2×D4—91no—
968C2×D4—91no—
969C2×D4—271no—
970C2×D4—271no—
971C2×D4—271no—
972C2×D4—271no—
973C2×D4—271no—
974C2×D4—271no—
975C22×C4—31no—
976C22×C4—91no—
977C22×C4—271no—
978C4⋊C4—91no—
979C4⋊C4—91no—
980C4⋊C4—91no—
981C4⋊C4—91no—
982C4⋊C4—271no—
983C4⋊C4—271no—
984C22⋊C4—31no—
985C22⋊C4—91no—
986C22⋊C4—91no—
987C22⋊C4—91no—
988C22⋊C4—91no—
989C22⋊C4—91no—
990C22⋊C4—271no—
991C22⋊C4—271no—
992C22⋊C4—271no—
993C22⋊C4—271no—
994C22⋊C4—271no—
995C22⋊C4—271no—
996C42—271no—
997C22×C3—22no—
998C22×C3—21no—
999C22×C3—21no—
1000C22×C3—21no—
1001C22×C3—21no—
1002C22×C3—21no—
1003C22×C3—21no—
1004C22×C3—21no—
1005C22×C3—21no—
1006C22×C3—21no—
1007C22×C3—21no—
1008C22×C3—21no—
1009C22×C3—21no—
1010C22×C3—41no—
1011C22×C3—41no—
1012C22×C3—41no—
1013C22×C3—41no—
1014C22×C3—41no—
1015C22×C3—41no—
1016C22×C3—41no—
1017C22×C3—41no—
1018C22×C3—42no—
1019C22×C3—41no—
1020C22×C3—62no—
1021C22×C3—61no—
1022C22×C3—61no—
1023C22×C3—61no—
1024C22×C3—61no—
1025C22×C3—61no—
1026C22×C3—61no—
1027C22×C3—81no—
1028C22×C3—81no—
1029C22×C3—121no—
1030C22×C3—121no—
1031C22×C3—181no—
1032C22×C3—181no—
1033C22×C3—181no—
1034C22×C3—181no—
1035C22×C3—181no—
1036C22×C3—181no—
1037C22×C3—181no—
1038C22×C3—181no—
1039C22×C3—181no—
1040C22×C3C22×D3211yescharacteristic
1041C22×C3C22×D3211yescharacteristic
1042C22×C3C22×D3211yescharacteristic
1043C2×D3—21no—
1044C2×D3—21no—
1045C2×D3—21no—
1046C2×D3—62no—
1047C2×D3—62no—
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—61no—
1061C2×D3—61no—
1062C2×D3—61no—
1063C2×D3—61no—
1064C2×D3—61no—
1065C2×D3—61no—
1066C2×D3—121no—
1067C2×D3—121no—
1068C2×D3—121no—
1069C2×D3—121no—
1070C2×D3—121no—
1071C2×D3—121no—
1072C2×D3—121no—
1073C2×D3—182no—
1074C2×D3—181no—
1075C2×D3—181no—
1076C2×D3—181no—
1077C2×D3—181no—
1078C2×D3—181no—
1079C2×D3—181no—
1080C2×D3—181no—
1081C2×D3—181no—
1082C2×D3—181no—
1083C2×D3—361no—
1084C2×D3—361no—
1085C2×D3—361no—
1086C2×D3—361no—
1087C2×D3—361no—
1088C2×D3—361no—
1089C2×D3—361no—
1090C2×D3—361no—
1091C2×D3—362no—
1092C2×D3—364no—
1093C2×D3—368no—
1094C2×D3—364no—
1095C2×D3—364no—
1096C2×D3—721no—
1097C2×D3—721no—
1098C3×C4—62no—
1099C3×C4—61no—
1100C3×C4—61no—
1101C3×C4—61no—
1102C3×C4—61no—
1103C3×C4—61no—
1104C3×C4—61no—
1105C3×C4—61no—
1106C3×C4—61no—
1107C3×C4—61no—
1108C3×C4—61no—
1109C3×C4—121no—
1110C3×C4—121no—
1111C3×C4—121no—
1112C3×C4—121no—
1113C3×C4—181no—
1114C3×C4—181no—
1115C3×C4—181no—
1116Dic3—21no—
1117Dic3—21no—
1118Dic3—21no—
1119Dic3—21no—
1120Dic3—21no—
1121Dic3—61no—
1122Dic3—61no—
1123Dic3—61no—
1124Dic3—61no—
1125Dic3—61no—
1126Dic3—61no—
1127Dic3—121no—
1128Dic3—121no—
1129Dic3—121no—
1130Dic3—182no—
1131Dic3—181no—
1132Dic3—181no—
1133Dic3—181no—
1134Dic3—361no—
1135Dic3—361no—
1136Dic3—362no—
1137C32—21no—
1138C32—21no—
1139C32—21no—
1140C32—41no—
1141C32#562011yescharacteristic, complemented
1142C32#562011yescharacteristic, complemented
1143C32#566611yescharacteristic, complemented
1144C23—31no—
1145C23—91no—
1146C23—91no—
1147C23—91no—
1148C23—271no—
1149C23—1081no—
1150C23—1081no—
1151C23—1081no—
1152C23D3311yescharacteristic
1153D4—121no—
1154D4—361no—
1155D4—361no—
1156D4—361no—
1157D4—361no—
1158D4—361no—
1159D4—1081no—
1160D4—1081no—
1161D4—1081no—
1162D4—1081no—
1163D4—1081no—
1164D4—1081no—
1165C2×C4—31no—
1166C2×C4—31no—
1167C2×C4—31no—
1168C2×C4—31no—
1169C2×C4—31no—
1170C2×C4—91no—
1171C2×C4—91no—
1172C2×C4—91no—
1173C2×C4—121no—
1174C2×C4—271no—
1175C2×C4—361no—
1176C2×C4—1081no—
1177C2×C3—21no—
1178C2×C3—21no—
1179C2×C3—21no—
1180C2×C3—21no—
1181C2×C3—21no—
1182C2×C3—21no—
1183C2×C3—21no—
1184C2×C3—21no—
1185C2×C3—21no—
1186C2×C3—42no—
1187C2×C3—41no—
1188C2×C3—41no—
1189C2×C3—41no—
1190C2×C3—41no—
1191C2×C3—41no—
1192C2×C3—41no—
1193C2×C3—81no—
1194C2×C3—81no—
1195C2×C3—82no—
1196C2×C3—122no—
1197C2×C3—121no—
1198C2×C3—121no—
1199C2×C3—361no—
1200C2×C3—361no—
1201C2×C3—361no—
1202C2×C3#6430711yescharacteristic
1203C2×C3#6430711yescharacteristic
1204C2×C3#6430811yescharacteristic
1205C2×C3#6431411yescharacteristic
1206C2×C3#6431411yescharacteristic
1207C2×C3#6431411yescharacteristic
1208C2×C3#6431411yescharacteristic
1209C2×C3#6433011yescharacteristic
1210C2×C3#6433011yescharacteristic
1211D3—41no—
1212D3—122no—
1213D3—122no—
1214D3—121no—
1215D3—121no—
1216D3—121no—
1217D3—121no—
1218D3—121no—
1219D3—121no—
1220D3—241no—
1221D3—362no—
1222D3—361no—
1223D3—361no—
1224D3—361no—
1225D3—721no—
1226D3—721no—
1227D3—722no—
1228C22—21no—
1229C22—21no—
1230C22—21no—
1231C22—61no—
1232C22—61no—
1233C22—61no—
1234C22—181no—
1235C22—181no—
1236C22—181no—
1237C22—181no—
1238C22—181no—
1239C22—181no—
1240C22—181no—
1241C22—181no—
1242C22—181no—
1243C22—541no—
1244C22—541no—
1245C22—541no—
1246C22—1084no—
1247C22C2×D3311yescharacteristic
1248C4—61no—
1249C4—61no—
1250C4—61no—
1251C4—61no—
1252C4—61no—
1253C4—181no—
1254C4—181no—
1255C4—181no—
1256C4—541no—
1257C3—21no—
1258C3—21no—
1259C3—21no—
1260C3—41no—
1261C3#1059430811yescharacteristic, complemented
1262C3#1059509011yescharacteristic, complemented
1263C3#1059526411yescharacteristic, complemented
1264C2—41no—
1265C2—121no—
1266C2—361no—
1267C2—361no—
1268C2—361no—
1269C2—1081no—
1270C2#1172441811yescharacteristic
1271C2#1172441811yescharacteristic
1272C2#1172442011yescharacteristic
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. #11723728C2semidirect
2. #11723643C2semidirect
3. #11723632C2semidirect
4. #11723624C2semidirect
5. C3×#63978C2semidirect
6. C3×#63966C2semidirect
7. C3×#63958C2semidirect
8. #11723028C2semidirect
9. #11723026C2semidirect
10. #11722997C2semidirect
11. #11722995C2semidirect
12. #11722962C2semidirect
13. #11722961C2semidirect
14. #11722950C2semidirect
15. #11722950C2semidirect
22. C2×C3×#638C22semidirect
23. C2×C3×#638C22semidirect
25. C22×C32×Dic3C22semidirect
28. C2×#6295C22semidirect
31. C2×Dic3×C3⋊D3C22semidirect
34. C2×C3×#624C22semidirect
35. C32×#217C22semidirect
36. #88813C22semidirect
37. #88806C22semidirect
38. Dic3⋊(C3⋊Dic3)C22semidirect
43. #88803C22semidirect
45. C3×Dic3⋊Dic3C22semidirect
46. C3×Dic3⋊Dic3C22semidirect
47. C3×Dic3⋊Dic3C22semidirect
48. C3×Dic3⋊Dic3C22semidirect
51. C3×#3722C22semidirect
74. #63978D3semidirect
79. #63966D3semidirect
80. #63958D3semidirect
152. C2×#638C2×D3semidirect
153. C2×#638C2×D3semidirect
172. C22×C3×Dic3C2×D3semidirect
173. C22×C3×Dic3C2×D3semidirect
195. C2×#624C2×D3semidirect
211. C3×#217C2×D3semidirect
212. C3×#217C2×D3semidirect
235. Dic3⋊Dic3C2×D3semidirect
236. Dic3⋊Dic3C2×D3semidirect
237. Dic3⋊Dic3C2×D3semidirect
238. Dic3⋊Dic3C2×D3semidirect
250. #3722C2×D3semidirect
534. C22×Dic3D32semidirect
570. #217D32semidirect
772. C33#560semidirect
1141. C32#5620semidirect
1142. C32#5620semidirect
1143. C32#5666semidirect
1261. C3#10594308semidirect
1262. C3#10595090semidirect
1263. C3#10595264semidirect

Maximal subgroups

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

subgroupindex
#117237282
#117236432
#117236322
#117236242
C3×#639782
C3×#639662
C3×#639582
#117230282
#117230262
#117229972
#117229952
#117229622
#117229612
#117229502
#105952643
#105950903
#105943083