Finite Group Databasebeta

← #13178680

Subgroups — #13178680

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
1C3×#64148C211yesmaximal, characteristic, complemented
2C3×#64147C211yesmaximal, characteristic, complemented
3C3×#64146C211yesmaximal, characteristic, complemented
4#11723728C211yesmaximal, characteristic, complemented
5#11723727C211yesmaximal, characteristic, complemented
6#11723727C211yesmaximal, characteristic, complemented
7#11723725C211yesmaximal, characteristic, complemented
8#11723725C211yesmaximal, characteristic, complemented
9#11723720C211yesmaximal, characteristic, complemented
10#11723717C211yesmaximal, characteristic, complemented
11#11723716C211yesmaximal, characteristic, complemented
12#11723695C211yesmaximal, characteristic, complemented
13#11723694C211yesmaximal, characteristic, complemented
14#11723690C211yesmaximal, characteristic, complemented
15#11723675C211yesmaximal, characteristic, complemented
16#10595264—31nomaximal
17#10595258—31nomaximal
18#10595257—31nomaximal
19C23×C3×C3⋊D3C2211yescharacteristic
20C2×C33×D4C2211yescharacteristic
21C2×C3×#638C2211yescharacteristic
22C2×C3×#638C2211yescharacteristic
23C2×C3×#638C2211yescharacteristic
24C2×C3×#638C2211yescharacteristic
25C2×C3×#638C2211yescharacteristic, complemented
26C2×C3×#638C2211yescharacteristic, complemented
27C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
28C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
29C2×#6295C2211yescharacteristic
30C2×#6295C2211yescharacteristic
31C2×#6295C2211yescharacteristic
32C2×#6295C2211yescharacteristic
33C2×#6295C2211yescharacteristic, complemented
34C2×#6294C2211yescharacteristic, complemented
35C3×#3757C2211yescharacteristic
36C3×#3757C2211yescharacteristic
37C3×#3757C2211yescharacteristic
38C3×#3757C2211yescharacteristic, complemented
39C3×#3752C2211yescharacteristic
40C3×#3752C2211yescharacteristic
41C3×#3752C2211yescharacteristic, complemented
42C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
43C3×#3750C2211yescharacteristic, complemented
44#88815C2211yescharacteristic, complemented
45#88815C2211yescharacteristic, complemented
46#88815C2211yescharacteristic, complemented
47#88815C2211yescharacteristic, complemented
48#88814C2211yescharacteristic
49#88814C2211yescharacteristic
50#88814C2211yescharacteristic
51#88814C2211yescharacteristic
52#88814C2211yescharacteristic, complemented
53#88813C2211yescharacteristic, complemented
54#64148D311yescharacteristic, complemented
55#64147D311yescharacteristic, complemented
56#64146D311yescharacteristic, complemented
57C3×#939—31no—
58C3×#939—31no—
59C3×#939—61no—
60C3×#938—31no—
61C3×#938—31no—
62C3×#938—61no—
63C3×#937—31no—
64C3×#937—31no—
65C3×#937—61no—
66#63981—31no—
67#63981—31no—
68#63980—31no—
69#63979—31no—
70#63979—31no—
71#63979—31no—
72#63978—31no—
73#63978—31no—
74#63977—31no—
75#63977—31no—
76#63976—31no—
77#63976—31no—
78#63971—31no—
79#63971—31no—
80#63970—31no—
81#63970—31no—
82#63966—31no—
83#63962—31no—
84#63961—31no—
85#63958—31no—
86#63958—31no—
87#63956—31no—
88#63956—31no—
89#63956—31no—
90#63912—31no—
91#63906—31no—
92#63906—31no—
93#63905—31no—
94#63891—31no—
95#63890—31no—
96#63861—31no—
97#63858—31no—
98#63854—31no—
99#63853—31no—
100#63850—31no—
101#63848—31no—
102C23×C33C2311yescharacteristic
103C23×C33C2311yescharacteristic
104C22×C3×C3⋊D3—41no—
105C22×C3×C3⋊D3—41no—
106C22×C3×C3⋊D3—41no—
107C22×C3×C3⋊D3C2311yescharacteristic
108C22×C3×C3⋊D3C2311yescharacteristic
109C22×C3×C3⋊D3C2311yescharacteristic
110C22×C3×C3⋊D3C2311yescharacteristic
111C33×D4—41no—
112C2×C33×C4C2311yescharacteristic
113C3×#638—41no—
114C3×#638—41no—
115C3×#638—41no—
116C3×#638—41no—
117C3×#638—41no—
118C3×#638—41no—
119C2×C3×C3⋊Dic3—41no—
120C2×C3×C3⋊Dic3C2311yescharacteristic
121C2×C3×C3⋊Dic3C2311yescharacteristic
122C2×C3×C3⋊Dic3C2311yescharacteristic
123C2×C3×C3⋊Dic3C2311yescharacteristic
124C2×C3×C3⋊Dic3C2311yescharacteristic
125C2×C3×C3⋊Dic3C2311yescharacteristic
126C2×C3×C3⋊Dic3C2311yescharacteristic
127C2×C3×C3⋊Dic3C2311yescharacteristic
128C3×C4×C3⋊D3—41no—
129#6295—41no—
130#6295—41no—
131#6295—41no—
132#6295—41no—
133#6295—41no—
134#6294—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—21no—
143C2×C32×D4—21no—
144C2×C32×D4—21no—
145C2×C32×D4—41no—
146C2×C32×D4C2×D311yescharacteristic
147C2×C32×D4C2×D311yescharacteristic
148C2×C32×D4C2×D311yescharacteristic
149C2×#638C2×D311yescharacteristic
150C2×#638C2×D311yescharacteristic
151C2×#638C2×D311yescharacteristic
152C2×#638C2×D311yescharacteristic
153C2×#638C2×D311yescharacteristic, complemented
154C2×#638C2×D311yescharacteristic, complemented
155C22×C3⋊Dic3C2×D311yescharacteristic, complemented
156C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
157C2×C3×#67—31no—
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—31no—
167C2×C3×#67—31no—
168C2×C3×#67—31no—
169C2×C3×#67—61no—
170C2×C3×#67—61no—
171C2×C3×#67—61no—
172C2×C3×#67—61no—
173C2×C3×#67—61no—
174C2×C3×#67—61no—
175C22×C3×Dic3—31no—
176C22×C3×Dic3—31no—
177C22×C3×Dic3—61no—
178C2×C3×C4×D3—31no—
179C2×C3×C4×D3—31no—
180C2×C3×C4×D3—61no—
181C2×#626—31no—
182C2×#626—31no—
183C2×#626—31no—
184C2×#626—31no—
185C2×#626—31no—
186C2×#626—31no—
187C2×#626—31no—
188C2×#626—31no—
189C2×#626—31no—
190C2×#626—31no—
191C2×#625—31no—
192C2×#625—31no—
193C2×#625—31no—
194C2×#625—31no—
195C2×#625—31no—
196C2×#624—31no—
197C2×D3×Dic3—31no—
198C2×D3×Dic3—31no—
199#3757C2×D311yescharacteristic
200#3757C2×D311yescharacteristic
201#3757C2×D311yescharacteristic
202#3757C2×D311yescharacteristic, complemented
203#3752C2×D311yescharacteristic
204#3752C2×D311yescharacteristic
205#3752C2×D311yescharacteristic, complemented
206C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
207#3750C2×D311yescharacteristic, complemented
208C3×#217—31no—
209C3×#217—31no—
210C3×#217—31no—
211C3×#217—31no—
212C3×#217—31no—
213C3×#217—31no—
214C3×#217—31no—
215C3×#217—31no—
216C3×#217—61no—
217C3×#217—61no—
218C3×#217—61no—
219C3×#217—61no—
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×(C2×D3)⋊C4—31no—
226C3×(C2×D3)⋊C4—61no—
227C3×(C2×D3)⋊C4—61no—
228C3×(C2×D3)⋊C4—61no—
229C3×C4⋊Dic3—31no—
230C3×C4⋊Dic3—31no—
231C3×C4⋊Dic3—61no—
232C3×Dic3⋊C4—31no—
233C3×Dic3⋊C4—31no—
234C3×Dic3⋊C4—61no—
235#3724—31no—
236#3724—31no—
237#3724—31no—
238#3724—31no—
239Dic3⋊Dic3—31no—
240Dic3⋊Dic3—31no—
241Dic3⋊Dic3—31no—
242Dic3⋊Dic3—31no—
243Dic3⋊Dic3—31no—
244Dic3⋊Dic3—31no—
245Dic3⋊Dic3—31no—
246Dic3⋊Dic3—31no—
247#3722—31no—
248#3722—31no—
249#3722—31no—
250#3722—31no—
251#3722—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—31no—
258(C2×D3)⋊Dic3—31no—
259(C2×D3)⋊Dic3—31no—
260(C2×D3)⋊Dic3—31no—
261(C2×D3)⋊Dic3—31no—
262Dic32—31no—
263Dic32—31no—
264Dic32—31no—
265C22×C33—21no—
266C22×C33—21no—
267C22×C33—21no—
268C22×C33—21no—
269C22×C33—21no—
270C22×C33—21no—
271C22×C33C2411yescharacteristic
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×C3×C3⋊D3—21no—
282C2×C3×C3⋊D3—21no—
283C2×C3×C3⋊D3—21no—
284C2×C3×C3⋊D3—44no—
285C33×C4—21no—
286C3×C3⋊Dic3—21no—
287C3×C3⋊Dic3—21no—
288C3×C3⋊Dic3—21no—
289C3×C3⋊Dic3—21no—
290C3×C3⋊Dic3—21no—
291C3×C3⋊Dic3—21no—
292C3×C3⋊Dic3—21no—
293C3×C3⋊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—31no—
304#939—61no—
305#939—91no—
306#939—91no—
307#939—91no—
308#939—91no—
309#938—31no—
310#938—31no—
311#938—61no—
312#938—91no—
313#938—91no—
314#937—31no—
315#937—31no—
316#937—61no—
317#937—91no—
318#937—91no—
319#935—91no—
320#930—91no—
321#930—91no—
322#929—91no—
323#929—91no—
324#898—91no—
325#898—91no—
326#894—91no—
327#894—91no—
328#886—91no—
329#886—91no—
330#884—91no—
331#884—91no—
332#884—91no—
333#884—91no—
334#883—91no—
335#883—91no—
336#882—91no—
337#882—91no—
338#879—91no—
339#879—91no—
340#879—91no—
341#879—91no—
342C23×C32—21no—
343C23×C32—21no—
344C23×C32—21no—
345C23×C32—21no—
346C23×C32—21no—
347C23×C32—21no—
348C23×C32—41no—
349C23×C32—41no—
350C23×C32C22×D311yescharacteristic
351C23×C32C22×D311yescharacteristic
352C23×C32C22×D311yescharacteristic
353C23×C32C22×D311yescharacteristic
354C23×C32C22×D311yescharacteristic
355C23×C32C22×D311yescharacteristic
356C22×C3⋊D3—41no—
357C22×C3⋊D3—41no—
358C22×C3⋊D3—41no—
359C22×C3⋊D3C22×D311yescharacteristic
360C22×C3⋊D3C22×D311yescharacteristic
361C22×C3⋊D3C22×D311yescharacteristic
362C22×C3⋊D3C22×D311yescharacteristic
363C22×C3×D3—31no—
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—31no—
371C22×C3×D3—61no—
372C22×C3×D3—61no—
373C22×C3×D3—61no—
374C22×C3×D3—61no—
375C22×C3×D3—121no—
376C22×C3×D3—121no—
377C22×C3×D3—121no—
378C22×C3×D3—121no—
379C22×C3×D3—121no—
380C22×C3×D3—121no—
381C22×C3×D3—122no—
382C22×C3×D3—122no—
383C22×C3×D3—122no—
384C32×D4—41no—
385C32×D4—41no—
386C32×D4—41no—
387C32×D4—42no—
388C32×D4—42no—
389C32×D4—42no—
390C32×D4—44no—
391C2×C32×C4—21no—
392C2×C32×C4—21no—
393C2×C32×C4—21no—
394C2×C32×C4—41no—
395C2×C32×C4C22×D311yescharacteristic
396C2×C32×C4C22×D311yescharacteristic
397C2×C32×C4C22×D311yescharacteristic
398#638—41no—
399#638—41no—
400#638—41no—
401#638—41no—
402#638—41no—
403#638—41no—
404C2×C3⋊Dic3—41no—
405C2×C3⋊Dic3C22×D311yescharacteristic
406C2×C3⋊Dic3C22×D311yescharacteristic
407C2×C3⋊Dic3C22×D311yescharacteristic
408C2×C3⋊Dic3C22×D311yescharacteristic
409C2×C3⋊Dic3C22×D311yescharacteristic
410C2×C3⋊Dic3C22×D311yescharacteristic
411C2×C3⋊Dic3C22×D311yescharacteristic
412C2×C3⋊Dic3C22×D311yescharacteristic
413C4×C3⋊D3—41no—
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—121no—
424C3×#67—121no—
425C3×#67—121no—
426C3×#67—122no—
427C3×#67—122no—
428C3×#67—122no—
429C3×#67—122no—
430C3×#67—122no—
431C3×#67—122no—
432C2×C3×Dic3—31no—
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—31no—
440C2×C3×Dic3—31no—
441C2×C3×Dic3—31no—
442C2×C3×Dic3—31no—
443C2×C3×Dic3—31no—
444C2×C3×Dic3—31no—
445C2×C3×Dic3—31no—
446C2×C3×Dic3—31no—
447C2×C3×Dic3—31no—
448C2×C3×Dic3—61no—
449C2×C3×Dic3—61no—
450C2×C3×Dic3—61no—
451C2×C3×Dic3—61no—
452C2×C3×Dic3—61no—
453C2×C3×Dic3—61no—
454C2×C3×Dic3—61no—
455C2×C3×Dic3—61no—
456C2×C3×Dic3—121no—
457C2×C3×Dic3—121no—
458C2×C3×Dic3—122no—
459C3×C4×D3—121no—
460C3×C4×D3—121no—
461C3×C4×D3—122no—
462#626—121no—
463#626—121no—
464#626—121no—
465#626—121no—
466#626—121no—
467#626—121no—
468#626—121no—
469#626—121no—
470#626—121no—
471#626—121no—
472#625—121no—
473#625—121no—
474#625—121no—
475#625—121no—
476#625—121no—
477#624—121no—
478D3×Dic3—121no—
479D3×Dic3—121no—
480#560—271noSylow
481C2×C33—41no—
482C2×C33—41no—
483C2×C33H(5,𝔽2)11yescharacteristic
484C2×C33H(5,𝔽2)11yescharacteristic
485C2×C33H(5,𝔽2)11yescharacteristic
486C3×C3⋊D3—41no—
487C3×C3⋊D3—41no—
488C3×C3⋊D3—41no—
489C3×C3⋊D3—41no—
490C24×C3—91no—
491C23×D3—31no—
492C23×D3—31no—
493C23×D3—61no—
494C2×C3×D4—21no—
495C2×C3×D4—21no—
496C2×C3×D4—21no—
497C2×C3×D4—41no—
498C2×C3×D4—91no—
499C2×C3×D4—91no—
500C2×C3×D4—91no—
501C2×C3×D4—91no—
502C2×C3×D4—91no—
503C2×C3×D4—91no—
504C2×C3×D4D3211yescharacteristic
505C2×C3×D4D3211yescharacteristic
506C2×C3×D4D3211yescharacteristic
507C22×C3×C4—91no—
508C22×C3×C4—91no—
509C2×#67—31no—
510C2×#67—31no—
511C2×#67—31no—
512C2×#67—31no—
513C2×#67—31no—
514C2×#67—31no—
515C2×#67—31no—
516C2×#67—31no—
517C2×#67—31no—
518C2×#67—31no—
519C2×#67—31no—
520C2×#67—31no—
521C2×#67—61no—
522C2×#67—61no—
523C2×#67—61no—
524C2×#67—61no—
525C2×#67—61no—
526C2×#67—61no—
527C2×#67—91no—
528C2×#67—91no—
529C2×#67—91no—
530C2×#67—91no—
531C2×#67—91no—
532C2×#67—91no—
533C2×#67—91no—
534C2×#67—91no—
535C2×#67—91no—
536C2×#67—91no—
537C22×Dic3—31no—
538C22×Dic3—31no—
539C22×Dic3—61no—
540C22×Dic3—91no—
541C2×D12—91no—
542C2×D12—91no—
543C2×D12—91no—
544C2×D12—91no—
545C2×D12—91no—
546C2×C4×D3—31no—
547C2×C4×D3—31no—
548C2×C4×D3—61no—
549C2×C4×D3—91no—
550C2×C4×D3—91no—
551C3×C4⋊C4—91no—
552C3×C4⋊C4—91no—
553C3×C22⋊C4—91no—
554C3×C22⋊C4—91no—
555C3×C22⋊C4—91no—
556C3×C22⋊C4—91no—
557C3×C22⋊C4—91no—
558C3×C22⋊C4—91no—
559C3×C22⋊C4—91no—
560#217—31no—
561#217—31no—
562#217—31no—
563#217—31no—
564#217—31no—
565#217—31no—
566#217—31no—
567#217—31no—
568#217—61no—
569#217—61no—
570#217—61no—
571#217—61no—
572#217—91no—
573#217—91no—
574#217—91no—
575#217—91no—
576#217—91no—
577(C2×D3)⋊C4—31no—
578(C2×D3)⋊C4—31no—
579(C2×D3)⋊C4—31no—
580(C2×D3)⋊C4—31no—
581(C2×D3)⋊C4—31no—
582(C2×D3)⋊C4—31no—
583(C2×D3)⋊C4—61no—
584(C2×D3)⋊C4—61no—
585(C2×D3)⋊C4—61no—
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—91no—
594(C2×D3)⋊C4—91no—
595(C2×D3)⋊C4—91no—
596C4⋊Dic3—31no—
597C4⋊Dic3—31no—
598C4⋊Dic3—61no—
599C4⋊Dic3—91no—
600C4⋊Dic3—91no—
601C4⋊Dic3—91no—
602C4⋊Dic3—91no—
603Dic3⋊C4—31no—
604Dic3⋊C4—31no—
605Dic3⋊C4—61no—
606Dic3⋊C4—91no—
607Dic3⋊C4—91no—
608Dic3⋊C4—91no—
609Dic3⋊C4—91no—
610Dic3⋊C4—91no—
611Dic3⋊C4—91no—
612Dic3⋊C4—91no—
613Dic3⋊C4—91no—
614C4×Dic3—91no—
615C4×Dic3—91no—
616C4×Dic3—91no—
617C22×C32—21no—
618C22×C32—21no—
619C22×C32—22no—
620C22×C32—22no—
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—21no—
631C22×C32—21no—
632C22×C32—21no—
633C22×C32—21no—
634C22×C32—21no—
635C22×C32—21no—
636C22×C32—21no—
637C22×C32—21no—
638C22×C32—21no—
639C22×C32—21no—
640C22×C32—41no—
641C22×C32—41no—
642C22×C32—41no—
643C22×C32—41no—
644C22×C32—41no—
645C22×C32—42no—
646C22×C32—42no—
647C22×C32—41no—
648C22×C32—41no—
649C22×C32—41no—
650C22×C32—41no—
651C22×C32—41no—
652C22×C32—41no—
653C22×C32—41no—
654C22×C32—41no—
655C22×C32—41no—
656C22×C32—41no—
657C22×C32—41no—
658C22×C32—41no—
659C22×C32—81no—
660C22×C32—81no—
661C22×C32—81no—
662C22×C32—81no—
663C22×C32C23×D311yescharacteristic
664C22×C32C23×D311yescharacteristic
665C22×C32C23×D311yescharacteristic
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—21no—
678C2×C3⋊D3—44no—
679C2×C3×D3—62no—
680C2×C3×D3—62no—
681C2×C3×D3—62no—
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—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—121no—
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—121no—
714C2×C3×D3—121no—
715C2×C3×D3—128no—
716C2×C3×D3—124no—
717C2×C3×D3—124no—
718C32×C4—21no—
719C32×C4—22no—
720C32×C4—21no—
721C32×C4—21no—
722C32×C4—41no—
723C32×C4—41no—
724C32×C4—42no—
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—62no—
734C3×Dic3—61no—
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—61no—
744C3×Dic3—61no—
745C3×Dic3—61no—
746C3×Dic3—61no—
747C3×Dic3—61no—
748C3×Dic3—61no—
749C3×Dic3—61no—
750C3×Dic3—121no—
751C3×Dic3—121no—
752C3×Dic3—121no—
753C3×Dic3—121no—
754C3×Dic3—121no—
755C3×Dic3—121no—
756C3×Dic3—121no—
757#127—271no—
758#126—271no—
759#126—271no—
760#123—271no—
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—91no—
770#120—271no—
771#120—271no—
772C33#56011yescharacteristic, complemented, Sylow
773C23×C3—21no—
774C23×C3—21no—
775C23×C3—21no—
776C23×C3—21no—
777C23×C3—21no—
778C23×C3—21no—
779C23×C3—41no—
780C23×C3—41no—
781C23×C3—91no—
782C23×C3—91no—
783C23×C3—91no—
784C23×C3—91no—
785C23×C3—361no—
786C23×C3—361no—
787C23×C3—361no—
788C23×C3C2×D3211yescharacteristic
789C23×C3C2×D3211yescharacteristic
790C23×C3C2×D3211yescharacteristic
791C23×C3C2×D3211yescharacteristic
792C23×C3C2×D3211yescharacteristic
793C23×C3C2×D3211yescharacteristic
794C22×D3—31no—
795C22×D3—31no—
796C22×D3—31no—
797C22×D3—31no—
798C22×D3—31no—
799C22×D3—31no—
800C22×D3—31no—
801C22×D3—31no—
802C22×D3—61no—
803C22×D3—61no—
804C22×D3—61no—
805C22×D3—61no—
806C22×D3—121no—
807C22×D3—121no—
808C22×D3—121no—
809C22×D3—121no—
810C22×D3—121no—
811C22×D3—121no—
812C22×D3—122no—
813C22×D3—122no—
814C22×D3—122no—
815C3×D4—41no—
816C3×D4—41no—
817C3×D4—41no—
818C3×D4—42no—
819C3×D4—42no—
820C3×D4—42no—
821C3×D4—44no—
822C3×D4—361no—
823C3×D4—361no—
824C3×D4—361no—
825C3×D4—361no—
826C3×D4—361no—
827C3×D4—361no—
828C2×C3×C4—21no—
829C2×C3×C4—21no—
830C2×C3×C4—21no—
831C2×C3×C4—41no—
832C2×C3×C4—91no—
833C2×C3×C4—91no—
834C2×C3×C4—91no—
835C2×C3×C4—91no—
836C2×C3×C4—91no—
837C2×C3×C4—91no—
838C2×C3×C4—91no—
839C2×C3×C4—91no—
840C2×C3×C4—361no—
841C2×C3×C4—361no—
842C2×C3×C4C2×D3211yescharacteristic
843C2×C3×C4C2×D3211yescharacteristic
844C2×C3×C4C2×D3211yescharacteristic
845#67—121no—
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—121no—
855#67—121no—
856#67—121no—
857#67—122no—
858#67—122no—
859#67—122no—
860#67—122no—
861#67—122no—
862#67—122no—
863#67—361no—
864#67—361no—
865#67—361no—
866#67—361no—
867#67—361no—
868#67—361no—
869#67—361no—
870#67—361no—
871#67—361no—
872#67—361no—
873C2×Dic3—31no—
874C2×Dic3—31no—
875C2×Dic3—31no—
876C2×Dic3—31no—
877C2×Dic3—31no—
878C2×Dic3—31no—
879C2×Dic3—31no—
880C2×Dic3—31no—
881C2×Dic3—31no—
882C2×Dic3—31no—
883C2×Dic3—31no—
884C2×Dic3—31no—
885C2×Dic3—31no—
886C2×Dic3—31no—
887C2×Dic3—31no—
888C2×Dic3—31no—
889C2×Dic3—61no—
890C2×Dic3—61no—
891C2×Dic3—61no—
892C2×Dic3—61no—
893C2×Dic3—61no—
894C2×Dic3—61no—
895C2×Dic3—61no—
896C2×Dic3—61no—
897C2×Dic3—121no—
898C2×Dic3—121no—
899C2×Dic3—122no—
900C2×Dic3—361no—
901D12—361no—
902D12—361no—
903D12—361no—
904D12—361no—
905D12—361no—
906C4×D3—121no—
907C4×D3—121no—
908C4×D3—122no—
909C4×D3—361no—
910C4×D3—361no—
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—41no—
925C2×C32—42no—
926C2×C32—42no—
927C2×C32—41no—
928C2×C32—41no—
929C2×C32—41no—
930C2×C32—41no—
931C2×C32—81no—
932C2×C32—81no—
933C2×C32—81no—
934C2×C32—81no—
935C2×C32—82no—
936C2×C32—82no—
937C2×C32#100411yescharacteristic
938C2×C32#100411yescharacteristic
939C2×C32#100411yescharacteristic
940C2×C32#100411yescharacteristic
941C2×C32#100411yescharacteristic
942C2×C32#100411yescharacteristic
943C2×C32#100411yescharacteristic
944C2×C32#100911yescharacteristic
945C2×C32#100911yescharacteristic
946C3⋊D3—41no—
947C3⋊D3—41no—
948C3⋊D3—41no—
949C3⋊D3—41no—
950C3×D3—122no—
951C3×D3—122no—
952C3×D3—122no—
953C3×D3—121no—
954C3×D3—121no—
955C3×D3—121no—
956C3×D3—121no—
957C3×D3—121no—
958C3×D3—121no—
959C3×D3—121no—
960C3×D3—121no—
961C3×D3—241no—
962C24—91no—
963C2×D4—91no—
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#111311yescharacteristic
975C22×C4—91no—
976C22×C4—91no—
977C22×C4—271no—
978C4⋊C4—91no—
979C4⋊C4—91no—
980C4⋊C4—271no—
981C4⋊C4—271no—
982C4⋊C4—271no—
983C4⋊C4—271no—
984C22⋊C4—91no—
985C22⋊C4—91no—
986C22⋊C4—91no—
987C22⋊C4—91no—
988C22⋊C4—91no—
989C22⋊C4—91no—
990C22⋊C4—91no—
991C22⋊C4—271no—
992C22⋊C4—271no—
993C22⋊C4—271no—
994C22⋊C4—271no—
995C22⋊C4—271no—
996C42—271no—
997C22×C3—22no—
998C22×C3—22no—
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—21no—
1011C22×C3—21no—
1012C22×C3—21no—
1013C22×C3—21no—
1014C22×C3—21no—
1015C22×C3—21no—
1016C22×C3—21no—
1017C22×C3—21no—
1018C22×C3—21no—
1019C22×C3—21no—
1020C22×C3—41no—
1021C22×C3—41no—
1022C22×C3—41no—
1023C22×C3—41no—
1024C22×C3—41no—
1025C22×C3—41no—
1026C22×C3—41no—
1027C22×C3—41no—
1028C22×C3—41no—
1029C22×C3—41no—
1030C22×C3—41no—
1031C22×C3—41no—
1032C22×C3—41no—
1033C22×C3—41no—
1034C22×C3—41no—
1035C22×C3—41no—
1036C22×C3—42no—
1037C22×C3—42no—
1038C22×C3—41no—
1039C22×C3—81no—
1040C22×C3—81no—
1041C22×C3—81no—
1042C22×C3—81no—
1043C22×C3—181no—
1044C22×C3—181no—
1045C22×C3—181no—
1046C22×C3—181no—
1047C22×C3—181no—
1048C22×C3—181no—
1049C22×C3—181no—
1050C22×C3—181no—
1051C22×C3—181no—
1052C22×C3—181no—
1053C22×C3—181no—
1054C22×C3—181no—
1055C22×C3—364no—
1056C22×C3C22×D3211yescharacteristic
1057C22×C3C22×D3211yescharacteristic
1058C22×C3C22×D3211yescharacteristic
1059C2×D3—62no—
1060C2×D3—62no—
1061C2×D3—62no—
1062C2×D3—61no—
1063C2×D3—61no—
1064C2×D3—61no—
1065C2×D3—61no—
1066C2×D3—61no—
1067C2×D3—61no—
1068C2×D3—61no—
1069C2×D3—61no—
1070C2×D3—61no—
1071C2×D3—61no—
1072C2×D3—61no—
1073C2×D3—61no—
1074C2×D3—61no—
1075C2×D3—61no—
1076C2×D3—61no—
1077C2×D3—61no—
1078C2×D3—61no—
1079C2×D3—61no—
1080C2×D3—61no—
1081C2×D3—61no—
1082C2×D3—61no—
1083C2×D3—61no—
1084C2×D3—61no—
1085C2×D3—61no—
1086C2×D3—121no—
1087C2×D3—121no—
1088C2×D3—121no—
1089C2×D3—121no—
1090C2×D3—121no—
1091C2×D3—121no—
1092C2×D3—121no—
1093C2×D3—121no—
1094C2×D3—121no—
1095C2×D3—128no—
1096C2×D3—124no—
1097C2×D3—124no—
1098C3×C4—22no—
1099C3×C4—21no—
1100C3×C4—21no—
1101C3×C4—21no—
1102C3×C4—41no—
1103C3×C4—41no—
1104C3×C4—42no—
1105C3×C4—181no—
1106C3×C4—181no—
1107C3×C4—181no—
1108C3×C4—181no—
1109C3×C4—181no—
1110C3×C4—181no—
1111C3×C4—181no—
1112C3×C4—181no—
1113Dic3—62no—
1114Dic3—61no—
1115Dic3—61no—
1116Dic3—61no—
1117Dic3—61no—
1118Dic3—61no—
1119Dic3—61no—
1120Dic3—61no—
1121Dic3—61no—
1122Dic3—61no—
1123Dic3—61no—
1124Dic3—61no—
1125Dic3—61no—
1126Dic3—61no—
1127Dic3—61no—
1128Dic3—61no—
1129Dic3—61no—
1130Dic3—121no—
1131Dic3—121no—
1132Dic3—121no—
1133Dic3—121no—
1134Dic3—121no—
1135Dic3—121no—
1136Dic3—121no—
1137C32—21no—
1138C32—21no—
1139C32—21no—
1140C32—41no—
1141C32#559511yescharacteristic, complemented
1142C32#562011yescharacteristic, complemented
1143C32#562011yescharacteristic, complemented
1144C23—91no—
1145C23—91no—
1146C23—91no—
1147C23—91no—
1148C23—361no—
1149C23—361no—
1150C23—361no—
1151C23C2×#111311yescharacteristic
1152C23C2×#111311yescharacteristic
1153D4—41no—
1154D4—361no—
1155D4—361no—
1156D4—361no—
1157D4—361no—
1158D4—361no—
1159D4—361no—
1160D4—1081no—
1161D4—1081no—
1162D4—1081no—
1163D4—1081no—
1164D4—1081no—
1165C2×C4—91no—
1166C2×C4—91no—
1167C2×C4—91no—
1168C2×C4—91no—
1169C2×C4—91no—
1170C2×C4—91no—
1171C2×C4—91no—
1172C2×C4—91no—
1173C2×C4—361no—
1174C2×C4—361no—
1175C2×C4—1081no—
1176C2×C4C2×#111311yescharacteristic
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—42no—
1188C2×C3—41no—
1189C2×C3—41no—
1190C2×C3—41no—
1191C2×C3—41no—
1192C2×C3—41no—
1193C2×C3—41no—
1194C2×C3—41no—
1195C2×C3—41no—
1196C2×C3—41no—
1197C2×C3—81no—
1198C2×C3—81no—
1199C2×C3—81no—
1200C2×C3—81no—
1201C2×C3—82no—
1202C2×C3—82no—
1203C2×C3—361no—
1204C2×C3—361no—
1205C2×C3—361no—
1206C2×C3—361no—
1207C2×C3#6431311yescharacteristic
1208C2×C3#6431311yescharacteristic
1209C2×C3#6431411yescharacteristic
1210C2×C3#6431411yescharacteristic
1211C2×C3#6431411yescharacteristic
1212C2×C3#6431411yescharacteristic
1213C2×C3#6433011yescharacteristic
1214C2×C3#6433011yescharacteristic
1215C2×C3#6433011yescharacteristic
1216D3—122no—
1217D3—122no—
1218D3—122no—
1219D3—121no—
1220D3—121no—
1221D3—121no—
1222D3—121no—
1223D3—121no—
1224D3—121no—
1225D3—121no—
1226D3—121no—
1227D3—241no—
1228C22—21no—
1229C22—21no—
1230C22—21no—
1231C22—21no—
1232C22—21no—
1233C22—21no—
1234C22—181no—
1235C22—181no—
1236C22—181no—
1237C22—181no—
1238C22—181no—
1239C22—181no—
1240C22—181no—
1241C22—181no—
1242C22—181no—
1243C22—181no—
1244C22—181no—
1245C22—181no—
1246C22—364no—
1247C22C22×#111311yescharacteristic
1248C4—21no—
1249C4—181no—
1250C4—181no—
1251C4—181no—
1252C4—181no—
1253C4—181no—
1254C4—181no—
1255C4—181no—
1256C4—181no—
1257C3—21no—
1258C3—21no—
1259C3—21no—
1260C3—41no—
1261C3#1059525711yescharacteristic, complemented
1262C3#1059525811yescharacteristic, complemented
1263C3#1059526411yescharacteristic, complemented
1264C2—41no—
1265C2—41no—
1266C2—361no—
1267C2—361no—
1268C2—361no—
1269C2—361no—
1270C2#1172462311yescharacteristic
1271C2#1172462311yescharacteristic
1272C2#1172463311yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC2×C33×D4C22
hypercenterC2×D4#1113
hypocenterC33#560
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C3×#64148C2semidirect
2. C3×#64147C2semidirect
3. C3×#64146C2semidirect
4. #11723728C2semidirect
5. #11723727C2semidirect
6. #11723727C2semidirect
7. #11723725C2semidirect
8. #11723725C2semidirect
9. #11723720C2semidirect
10. #11723717C2semidirect
11. #11723716C2semidirect
12. #11723695C2semidirect
13. #11723694C2semidirect
14. #11723690C2semidirect
15. #11723675C2semidirect
25. C2×C3×#638C22semidirect
26. C2×C3×#638C22semidirect
27. C22×C3×C3⋊Dic3C22semidirect
28. C2×C3×C4×C3⋊D3C22semidirect
33. C2×#6295C22semidirect
34. C2×#6294C22semidirect
38. C3×#3757C22semidirect
41. C3×#3752C22semidirect
42. C3×C4⋊(C3⋊Dic3)C22semidirect
43. C3×#3750C22semidirect
44. #88815C22semidirect
45. #88815C22semidirect
46. #88815C22semidirect
47. #88815C22semidirect
52. #88814C22semidirect
53. #88813C22semidirect
54. #64148D3semidirect
55. #64147D3semidirect
56. #64146D3semidirect
153. C2×#638C2×D3semidirect
154. C2×#638C2×D3semidirect
155. C22×C3⋊Dic3C2×D3semidirect
156. C2×C4×C3⋊D3C2×D3semidirect
202. #3757C2×D3semidirect
205. #3752C2×D3semidirect
206. C4⋊(C3⋊Dic3)C2×D3semidirect
207. #3750C2×D3semidirect
772. C33#560semidirect
1141. C32#5595semidirect
1142. C32#5620semidirect
1143. C32#5620semidirect
1261. C3#10595257semidirect
1262. C3#10595258semidirect
1263. C3#10595264semidirect

Maximal subgroups

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

subgroupindex
C3×#641482
C3×#641472
C3×#641462
#117237282
#117237272
#117237252
#117237202
#117237172
#117237162
#117236952
#117236942
#117236902
#117236752
#105952643
#105952583
#105952573