Finite Group Databasebeta

← #13168068

Subgroups — #13168068

Order 1728.

1298 conjugacy classes of subgroups.

The subgroup lattice has 1188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723676C211yesmaximal, characteristic, complemented
2#11723475C211yesmaximal, characteristic, complemented
3#11723461C211yesmaximal, characteristic, complemented
4#11723392C211yesmaximal, characteristic, complemented
5C3×#63922C211yesmaximal, characteristic, complemented
6C3×#63887C211yesmaximal, characteristic, complemented
7C3×#63863C211yesmaximal, characteristic, complemented
8#11723019C211yesmaximal, characteristic, complemented
9#11722996C211yesmaximal, characteristic, complemented
10#11722990C211yesmaximal, characteristic, complemented
11#11722963C211yesmaximal, characteristic, complemented
12#11722958C211yesmaximal, characteristic, complemented
13#11722948C211yesmaximal, characteristic, complemented
14#11722925C211yesmaximal, characteristic, complemented
15D3×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
16#10595435—31nomaximal
17#10595184—31nomaximal
18#10594173—31nomaximal
19C22×C3×D32C2211yescharacteristic
20C2×C32×D12C2211yescharacteristic
21C2×C32×Dic6C2211yescharacteristic, complemented
22C2×#6292C2211yescharacteristic
23C2×#6291C2211yescharacteristic
24C2×#6291C2211yescharacteristic
25C2×#6291C2211yescharacteristic, complemented
26C2×#6289C2211yescharacteristic, complemented
27C2×D3×C3⋊Dic3C2211yescharacteristic
28C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
29C2×C3×#626C2211yescharacteristic
30C2×C3×#625C2211yescharacteristic
31C2×C3×D3×Dic3C2211yescharacteristic
32#88859C2211yescharacteristic, complemented
33C3×#3752C2211yescharacteristic
34C3×#3750C2211yescharacteristic, complemented
35C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
36C32×(C2×D3)⋊C4C2211yescharacteristic
37#88815C2211yescharacteristic, complemented
38#88815C2211yescharacteristic, complemented
39#88814C2211yescharacteristic
40#88814C2211yescharacteristic
41#88807C2211yescharacteristic, complemented
42#88804C2211yescharacteristic, complemented
43#88803C2211yescharacteristic
44(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
45Dic3×C3⋊Dic3C2211yescharacteristic, complemented
46C3×Dic3⋊Dic3C2211yescharacteristic, complemented
47C3×Dic3⋊Dic3C2211yescharacteristic, complemented
48C3×(C2×D3)⋊Dic3C2211yescharacteristic
49C3×(C2×D3)⋊Dic3C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
53C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
54#64156—31no—
55#64148—31no—
56#64090—31no—
57C3×#947—31no—
58C3×#946—31no—
59C3×#937—31no—
60C3×#936—31no—
61C3×#882—31no—
62C3×#878—31no—
63#63978—31no—
64#63977—31no—
65#63977—31no—
66#63975—31no—
67#67⋊Dic3—31no—
68#67⋊Dic3—31no—
69#63971—31no—
70D3×#217—31no—
71#63962—31no—
72C2×(C2×D3)⋊Dic3—31no—
73#63958—31no—
74#63956—31no—
75#63923—31no—
76#63922D311yescharacteristic, complemented
77D3×(C2×D3)⋊C4—31no—
78#63916—31no—
79#63910—31no—
80#63907—31no—
81#63907—31no—
82#63907—61no—
83#63906—31no—
84#63902—31no—
85#63890—31no—
86#63887D311yescharacteristic, complemented
87#63886—31no—
88#63886—31no—
89#63886—61no—
90#63884—31no—
91#63880—31no—
92#63880—31no—
93#63880—61no—
94#63868—31no—
95#63863D311yescharacteristic, complemented
96#63862—31no—
97#63862—31no—
98#63859—31no—
99#63858—31no—
100#63854—31no—
101#63853—31no—
102C22×C3⋊(C3⋊D3)C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C32×D3C2311yescharacteristic
105C22×C32×D3C2311yescharacteristic
106C22×C32×D3C2311yescharacteristic
107C2×C3×D32—22no—
108C2×C3×D32—41no—
109C2×C3×D32—41no—
110C2×C33×C4C2311yescharacteristic
111C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C32×D12—41no—
121C32×Dic6—41no—
122#6292—41no—
123#6291—22no—
124#6291—41no—
125#6291—41no—
126#6289—41no—
127D3×C3⋊Dic3—41no—
128D3×C3⋊Dic3—41no—
129C3×#626—41no—
130C3×#625—22no—
131C3×D3×Dic3—41no—
132#5678—91no—
133#5644—91no—
134#5593—91no—
135C23×C3×D3—31no—
136C23×C3×D3—31no—
137C22×D32C2×D311yescharacteristic
138C2×C32×Q8—31no—
139C2×C32×D4—31no—
140C2×#638—31no—
141C2×#638—31no—
142C2×#638—31no—
143C22×C3⋊Dic3—31no—
144C22×C3⋊Dic3—31no—
145C2×C4⋊(C3⋊D3)—31no—
146C2×C4×C3⋊D3—31no—
147C2×C3×#67—31no—
148C2×C3×#67—31no—
149C2×C3×#67—31no—
150C22×C3×Dic3—31no—
151C2×C3×D12—21no—
152C2×C3×D12—31no—
153C2×C3×D12C2×D311yescharacteristic
154C2×C3×D12C2×D311yescharacteristic
155C2×C3×C4×D3—31no—
156C2×C3×Dic6—21no—
157C2×C3×Dic6C2×D311yescharacteristic, complemented
158C2×C3×Dic6C2×D311yescharacteristic, complemented
159C2×#626—31no—
160C2×#626—31no—
161C2×#626—31no—
162C2×#626—31no—
163C2×#626—31no—
164C2×#626—31no—
165C2×#626—31no—
166C2×#626—31no—
167C2×#626—61no—
168C2×#626—61no—
169C2×#626—61no—
170C2×#626—61no—
171C2×#626C2×D311yescharacteristic
172C2×#625C2×D311yescharacteristic
173C2×#624—31no—
174C2×#624—31no—
175C2×#624—61no—
176C2×D3×Dic3—31no—
177C2×D3×Dic3—31no—
178C2×D3×Dic3—31no—
179C2×D3×Dic3—31no—
180C2×D3×Dic3—61no—
181C2×D3×Dic3—61no—
182C2×D3×Dic3C2×D311yescharacteristic
183C32×C22⋊C4—31no—
184#3757—31no—
185#3752—31no—
186#3752—31no—
187#3752—31no—
188#3752—31no—
189#3752—31no—
190#3752—61no—
191#3752—61no—
192#3752—61no—
193#3752—121no—
194#3752C2×D311yescharacteristic
195#3750—31no—
196#3750C2×D311yescharacteristic, complemented
197C4×C3⋊Dic3—31no—
198C4×C3⋊Dic3C2×D311yescharacteristic, complemented
199C3×#217—31no—
200C3×#217—31no—
201C3×#217—31no—
202C3×#217—31no—
203C3×#217—31no—
204C3×#217—31no—
205C3×(C2×D3)⋊C4—21no—
206C3×(C2×D3)⋊C4—31no—
207C3×(C2×D3)⋊C4—31no—
208C3×(C2×D3)⋊C4—31no—
209C3×(C2×D3)⋊C4—31no—
210C3×(C2×D3)⋊C4—31no—
211C3×(C2×D3)⋊C4—31no—
212C3×(C2×D3)⋊C4—31no—
213C3×(C2×D3)⋊C4—31no—
214C3×(C2×D3)⋊C4—61no—
215C3×(C2×D3)⋊C4C2×D311yescharacteristic
216C3×(C2×D3)⋊C4C2×D311yescharacteristic
217C3×C4⋊Dic3—31no—
218C3×C4⋊Dic3—31no—
219C3×Dic3⋊C4—31no—
220C3×Dic3⋊C4—31no—
221C3×Dic3⋊C4—31no—
222C3×Dic3⋊C4—31no—
223C3×Dic3⋊C4—61no—
224C3×C4×Dic3—31no—
225C3×C4×Dic3—31no—
226C3×C4×Dic3—61no—
227#3724—31no—
228#3724—31no—
229Dic3⋊Dic3—31no—
230Dic3⋊Dic3—31no—
231Dic3⋊Dic3—31no—
232Dic3⋊Dic3—31no—
233Dic3⋊Dic3—31no—
234Dic3⋊Dic3—31no—
235Dic3⋊Dic3—61no—
236Dic3⋊Dic3C2×D311yescharacteristic, complemented
237Dic3⋊Dic3C2×D311yescharacteristic, complemented
238#3722—31no—
239#3722—31no—
240#3722—31no—
241#3722—31no—
242#3722—61no—
243(C2×D3)⋊Dic3—31no—
244(C2×D3)⋊Dic3—31no—
245(C2×D3)⋊Dic3—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—61no—
252(C2×D3)⋊Dic3—61no—
253(C2×D3)⋊Dic3C2×D311yescharacteristic
254(C2×D3)⋊Dic3C2×D311yescharacteristic
255(C2×D3)⋊Dic3C2×D311yescharacteristic
256(C2×D3)⋊Dic3C2×D311yescharacteristic
257(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
258(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
259Dic32—31no—
260Dic32—31no—
261Dic32—61no—
262C22×C33C2411yescharacteristic
263C2×C3⋊(C3⋊D3)—21no—
264C2×C3⋊(C3⋊D3)—21no—
265C2×C3⋊(C3⋊D3)—21no—
266C2×C3×C3⋊D3—21no—
267C2×C3×C3⋊D3—21no—
268C2×C3×C3⋊D3—21no—
269C2×C32×D3—21no—
270C2×C32×D3—21no—
271C2×C32×D3—21no—
272C2×C32×D3—21no—
273C2×C32×D3—21no—
274C2×C32×D3—21no—
275C2×C32×D3—21no—
276C2×C32×D3—21no—
277C2×C32×D3#4112yes—
278C3×D32—44no—
279C33×C4—21no—
280C3⋊(C3⋊Dic3)—21no—
281C3×C3⋊Dic3—21no—
282C3×C3⋊Dic3—21no—
283C3×C3⋊Dic3—21no—
284C3×C3⋊Dic3—21no—
285C3×C3⋊Dic3—21no—
286C32×Dic3—21no—
287C32×Dic3—21no—
288C32×Dic3—21no—
289C3×#124—91no—
290C3×C22⋊Q8—91no—
291C3×#120—91no—
292#953—91no—
293C2×#217—91no—
294#947—31no—
295#947—91no—
296#947—91no—
297#947—181no—
298#946—31no—
299#939—91no—
300#939—91no—
301#939—91no—
302#939—181no—
303#938—91no—
304#937—31no—
305#936—31no—
306#935—91no—
307D4×Dic3—91no—
308#930—91no—
309C2×(C2×D3)⋊C4—91no—
310#898—91no—
311#898—91no—
312#895—91no—
313#895—91no—
314#894—91no—
315#894—91no—
316#886—91no—
317#885—91no—
318#884—91no—
319#884—91no—
320#883—91no—
321#883—91no—
322#882—31no—
323#882—91no—
324#882—91no—
325#67⋊C4—91no—
326#67⋊C4—91no—
327#67⋊C4—91no—
328#67⋊C4—91no—
329#67⋊C4—181no—
330D3×C22⋊C4—91no—
331#879—91no—
332#879—91no—
333#879—91no—
334#878—31no—
335#876—91no—
336C4×D12—91no—
337C23×C32—31no—
338C23×C32—31no—
339C23×C32—31no—
340C22×C3⋊D3—31no—
341C22×C3⋊D3—31no—
342C22×C3⋊D3—31no—
343C22×C3⋊D3—61no—
344C22×C3⋊D3—61no—
345C22×C3⋊D3—61no—
346C22×C3⋊D3—121no—
347C22×C3⋊D3C22×D311yescharacteristic
348C22×C3×D3—21no—
349C22×C3×D3—21no—
350C22×C3×D3—21no—
351C22×C3×D3—31no—
352C22×C3×D3—31no—
353C22×C3×D3—61no—
354C22×C3×D3—62no—
355C22×C3×D3—62no—
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×D3C22×D311yescharacteristic
364C22×C3×D3C22×D311yescharacteristic
365C22×C3×D3C22×D311yescharacteristic
366C2×D32—22no—
367C2×D32—41no—
368C2×D32—41no—
369C32×Q8—121no—
370C32×D4—121no—
371C2×C32×C4—21no—
372C2×C32×C4—21no—
373C2×C32×C4—21no—
374C2×C32×C4—31no—
375C2×C32×C4—31no—
376C2×C32×C4—31no—
377C2×C32×C4—41no—
378C2×C32×C4C22×D311yescharacteristic
379C2×C32×C4C22×D311yescharacteristic
380C2×C32×C4C22×D311yescharacteristic
381#638—62no—
382#638—121no—
383#638—121no—
384C2×C3⋊Dic3—31no—
385C2×C3⋊Dic3—31no—
386C2×C3⋊Dic3—31no—
387C2×C3⋊Dic3—61no—
388C2×C3⋊Dic3—61no—
389C2×C3⋊Dic3—61no—
390C2×C3⋊Dic3—121no—
391C2×C3⋊Dic3—121no—
392C2×C3⋊Dic3—121no—
393C2×C3⋊Dic3C22×D311yescharacteristic
394C2×C3⋊Dic3C22×D311yescharacteristic
395C2×C3⋊Dic3C22×D311yescharacteristic
396C2×C3⋊Dic3C22×D311yescharacteristic
397C2×C3⋊Dic3C22×D311yescharacteristic
398C4⋊(C3⋊D3)—121no—
399C4×C3⋊D3—121no—
400C3×#67—62no—
401C3×#67—62no—
402C3×#67—121no—
403C2×C3×Dic3—21no—
404C2×C3×Dic3—21no—
405C2×C3×Dic3—21no—
406C2×C3×Dic3—31no—
407C2×C3×Dic3—31no—
408C2×C3×Dic3—31no—
409C2×C3×Dic3—31no—
410C2×C3×Dic3—31no—
411C2×C3×Dic3—31no—
412C2×C3×Dic3—31no—
413C2×C3×Dic3—31no—
414C2×C3×Dic3—31no—
415C2×C3×Dic3—31no—
416C2×C3×Dic3—61no—
417C2×C3×Dic3—61no—
418C2×C3×Dic3—61no—
419C2×C3×Dic3—61no—
420C2×C3×Dic3—61no—
421C2×C3×Dic3—121no—
422C2×C3×Dic3C22×D311yescharacteristic
423C2×C3×Dic3C22×D311yescharacteristic
424C2×C3×Dic3C22×D311yescharacteristic
425C2×C3×Dic3C22×D311yescharacteristic
426C2×C3×Dic3C22×D311yescharacteristic
427C2×C3×Dic3C22×D311yescharacteristic
428C3×D12—41no—
429C3×D12—41no—
430C3×D12—42no—
431C3×D12—121no—
432C3×C4×D3—121no—
433C3×Dic6—41no—
434C3×Dic6—41no—
435C3×Dic6—42no—
436#626—41no—
437#626—64no—
438#626—62no—
439#626—62no—
440#626—121no—
441#626—121no—
442#626—122no—
443#626—121no—
444#626—121no—
445#626—121no—
446#626—121no—
447#626—122no—
448#626—122no—
449#625—22no—
450#624—121no—
451#624—121no—
452#624—122no—
453D3×Dic3—41no—
454D3×Dic3—121no—
455D3×Dic3—121no—
456D3×Dic3—121no—
457D3×Dic3—121no—
458D3×Dic3—122no—
459D3×Dic3—122no—
460#538—271noSylow
461C2×C33C2×#4111yescharacteristic
462C2×C33H(5,𝔽2)11yescharacteristic
463C2×C33H(5,𝔽2)11yescharacteristic
464C3⋊(C3⋊D3)—41no—
465C3×C3⋊D3—41no—
466C32×D3—22no—
467C32×D3—41no—
468C32×D3—41no—
469C24×C3—91no—
470C23×D3—31no—
471C23×D3—31no—
472C2×C3×Q8—31no—
473C2×C3×Q8—31no—
474C2×C3×Q8—61no—
475C2×C3×D4—31no—
476C2×C3×D4—31no—
477C2×C3×D4—61no—
478C2×C3×D4—91no—
479C2×C3×D4—91no—
480C22×C3×C4—91no—
481C2×#67—31no—
482C2×#67—31no—
483C2×#67—31no—
484C2×#67—91no—
485C2×#67—91no—
486C2×#67—91no—
487C2×#67—91no—
488C2×#67—91no—
489C2×#67—91no—
490C2×#67—91no—
491C2×#67—181no—
492C2×#67—181no—
493C2×#67—181no—
494C22×Dic3—31no—
495C22×Dic3—91no—
496C22×Dic3—91no—
497C22×Dic3—91no—
498C22×Dic3—91no—
499C22×Dic3—181no—
500C22×Dic3—181no—
501C2×D12—31no—
502C2×D12—91no—
503C2×D12—91no—
504C2×D12—91no—
505C2×D12—91no—
506C2×D12—91no—
507C2×D12—181no—
508C2×D12D3211yescharacteristic
509C2×C4×D3—31no—
510C2×C4×D3—91no—
511C2×C4×D3—91no—
512C2×C4×D3—91no—
513C2×C4×D3—91no—
514C2×C4×D3—91no—
515C2×C4×D3—181no—
516C2×Dic6D3211yescharacteristic, complemented
517C3×C4⋊C4—91no—
518C3×C4⋊C4—91no—
519C3×C4⋊C4—91no—
520C3×C22⋊C4—31no—
521C3×C22⋊C4—31no—
522C3×C22⋊C4—61no—
523C3×C22⋊C4—91no—
524C3×C22⋊C4—91no—
525C3×C22⋊C4—91no—
526C3×C22⋊C4—91no—
527C3×C22⋊C4—91no—
528C3×C22⋊C4—91no—
529C3×C22⋊C4—91no—
530C3×C42—91no—
531#217—31no—
532#217—31no—
533#217—31no—
534#217—31no—
535#217—31no—
536#217—31no—
537#217—91no—
538#217—91no—
539#217—91no—
540#217—91no—
541#217—91no—
542#217—181no—
543(C2×D3)⋊C4—31no—
544(C2×D3)⋊C4—31no—
545(C2×D3)⋊C4—31no—
546(C2×D3)⋊C4—31no—
547(C2×D3)⋊C4—31no—
548(C2×D3)⋊C4—31no—
549(C2×D3)⋊C4—31no—
550(C2×D3)⋊C4—31no—
551(C2×D3)⋊C4—61no—
552(C2×D3)⋊C4—91no—
553(C2×D3)⋊C4—91no—
554(C2×D3)⋊C4—91no—
555(C2×D3)⋊C4—91no—
556(C2×D3)⋊C4—91no—
557(C2×D3)⋊C4—91no—
558(C2×D3)⋊C4—91no—
559(C2×D3)⋊C4—91no—
560(C2×D3)⋊C4—91no—
561(C2×D3)⋊C4—91no—
562(C2×D3)⋊C4—91no—
563(C2×D3)⋊C4—91no—
564(C2×D3)⋊C4—91no—
565(C2×D3)⋊C4—181no—
566(C2×D3)⋊C4—181no—
567(C2×D3)⋊C4—181no—
568(C2×D3)⋊C4—181no—
569(C2×D3)⋊C4—181no—
570(C2×D3)⋊C4—361no—
571(C2×D3)⋊C4D3211yescharacteristic
572C4⋊Dic3—31no—
573C4⋊Dic3—31no—
574C4⋊Dic3—91no—
575C4⋊Dic3—91no—
576C4⋊Dic3—91no—
577Dic3⋊C4—31no—
578Dic3⋊C4—31no—
579Dic3⋊C4—31no—
580Dic3⋊C4—31no—
581Dic3⋊C4—61no—
582Dic3⋊C4—91no—
583Dic3⋊C4—91no—
584Dic3⋊C4—91no—
585Dic3⋊C4—91no—
586Dic3⋊C4—91no—
587Dic3⋊C4—91no—
588Dic3⋊C4—181no—
589C4×Dic3—31no—
590C4×Dic3—31no—
591C4×Dic3—61no—
592C4×Dic3—91no—
593C4×Dic3—91no—
594C4×Dic3—91no—
595C4×Dic3—181no—
596C22×C32—21no—
597C22×C32—21no—
598C22×C32—21no—
599C22×C32—32no—
600C22×C32—41no—
601C22×C32—61no—
602C22×C32—61no—
603C22×C32—61no—
604C22×C32—61no—
605C22×C32—61no—
606C22×C32—61no—
607C22×C32—61no—
608C22×C32—61no—
609C22×C32C23×D311yescharacteristic
610C22×C32C23×D311yescharacteristic
611C22×C32C23×D311yescharacteristic
612C2×C3⋊D3—21no—
613C2×C3⋊D3—21no—
614C2×C3⋊D3—21no—
615C2×C3⋊D3—61no—
616C2×C3⋊D3—62no—
617C2×C3⋊D3—61no—
618C2×C3⋊D3—61no—
619C2×C3⋊D3—61no—
620C2×C3⋊D3—61no—
621C2×C3⋊D3—61no—
622C2×C3⋊D3—61no—
623C2×C3⋊D3—61no—
624C2×C3⋊D3—61no—
625C2×C3⋊D3—121no—
626C2×C3⋊D3—121no—
627C2×C3⋊D3—122no—
628C2×C3⋊D3—121no—
629C2×C3⋊D3—121no—
630C2×C3⋊D3—121no—
631C2×C3⋊D3—121no—
632C2×C3⋊D3—121no—
633C2×C3⋊D3—121no—
634C2×C3⋊D3—241no—
635C2×C3⋊D3—241no—
636C2×C3×D3—21no—
637C2×C3×D3—21no—
638C2×C3×D3—21no—
639C2×C3×D3—21no—
640C2×C3×D3—22no—
641C2×C3×D3—21no—
642C2×C3×D3—21no—
643C2×C3×D3—21no—
644C2×C3×D3—21no—
645C2×C3×D3—21no—
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—22no—
654C2×C3×D3—41no—
655C2×C3×D3—41no—
656C2×C3×D3—41no—
657C2×C3×D3—41no—
658C2×C3×D3—41no—
659C2×C3×D3—41no—
660C2×C3×D3—41no—
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—121no—
670C2×C3×D3—124no—
671C2×C3×D3—124no—
672C2×C3×D3#23712yes—
673C2×C3×D3#23912yes—
674D32—44no—
675C32×C4—21no—
676C32×C4—21no—
677C32×C4—21no—
678C32×C4—41no—
679C32×C4—41no—
680C32×C4—41no—
681C32×C4—61no—
682C32×C4—61no—
683C32×C4—61no—
684C32×C4—81no—
685C3⋊Dic3—21no—
686C3⋊Dic3—21no—
687C3⋊Dic3—21no—
688C3⋊Dic3—21no—
689C3⋊Dic3—21no—
690C3⋊Dic3—61no—
691C3⋊Dic3—61no—
692C3⋊Dic3—61no—
693C3⋊Dic3—121no—
694C3⋊Dic3—121no—
695C3⋊Dic3—121no—
696C3⋊Dic3—241no—
697C3×Dic3—22no—
698C3×Dic3—21no—
699C3×Dic3—21no—
700C3×Dic3—21no—
701C3×Dic3—21no—
702C3×Dic3—21no—
703C3×Dic3—21no—
704C3×Dic3—41no—
705C3×Dic3—41no—
706C3×Dic3—62no—
707C3×Dic3—62no—
708C3×Dic3—62no—
709C3×Dic3—61no—
710C3×Dic3—61no—
711C3×Dic3—61no—
712C3×Dic3—61no—
713C3×Dic3—61no—
714C3×Dic3—61no—
715C3×Dic3—61no—
716C3×Dic3—61no—
717C3×Dic3—61no—
718C3×Dic3—61no—
719C3×Dic3—121no—
720C3×Dic3—121no—
721#126—271no—
722#126—271no—
723#124—91no—
724#124—271no—
725#123—271no—
726#123—271no—
727C22⋊Q8—91no—
728#121—271no—
729#121—271no—
730#121—271no—
731#120—91no—
732#120—271no—
733C4×D4—271no—
734C4×D4—271no—
735C2×C22⋊C4—271no—
736C33#53811yescharacteristic, complemented, Sylow
737C23×C3—31no—
738C23×C3—31no—
739C23×C3—31no—
740C23×C3—31no—
741C23×C3—31no—
742C23×C3—31no—
743C23×C3—61no—
744C23×C3—61no—
745C23×C3—61no—
746C23×C3—91no—
747C23×C3—182no—
748C23×C3—361no—
749C23×C3—361no—
750C22×D3—31no—
751C22×D3—31no—
752C22×D3—61no—
753C22×D3—62no—
754C22×D3—62no—
755C22×D3—91no—
756C22×D3—91no—
757C22×D3—91no—
758C22×D3—121no—
759C22×D3—121no—
760C22×D3—121no—
761C22×D3—121no—
762C22×D3—181no—
763C22×D3—181no—
764C22×D3—181no—
765C22×D3—361no—
766C22×D3C2×D3211yescharacteristic
767C22×D3C2×D3211yescharacteristic
768C22×D3C2×D3211yescharacteristic
769C3×Q8—121no—
770C3×Q8—121no—
771C3×Q8—122no—
772C3×D4—121no—
773C3×D4—121no—
774C3×D4—122no—
775C3×D4—182no—
776C3×D4—361no—
777C2×C3×C4—21no—
778C2×C3×C4—21no—
779C2×C3×C4—21no—
780C2×C3×C4—31no—
781C2×C3×C4—31no—
782C2×C3×C4—31no—
783C2×C3×C4—31no—
784C2×C3×C4—31no—
785C2×C3×C4—31no—
786C2×C3×C4—41no—
787C2×C3×C4—61no—
788C2×C3×C4—61no—
789C2×C3×C4—61no—
790C2×C3×C4—91no—
791C2×C3×C4—91no—
792C2×C3×C4—91no—
793C2×C3×C4—91no—
794C2×C3×C4—91no—
795C2×C3×C4—361no—
796C2×C3×C4C2×D3211yescharacteristic
797C2×C3×C4C2×D3211yescharacteristic
798C2×C3×C4C2×D3211yescharacteristic
799#67—62no—
800#67—62no—
801#67—121no—
802#67—182no—
803#67—182no—
804#67—184no—
805#67—361no—
806#67—361no—
807#67—361no—
808#67—361no—
809#67—361no—
810#67—362no—
811#67—362no—
812C2×Dic3—31no—
813C2×Dic3—31no—
814C2×Dic3—31no—
815C2×Dic3—31no—
816C2×Dic3—31no—
817C2×Dic3—31no—
818C2×Dic3—31no—
819C2×Dic3—31no—
820C2×Dic3—31no—
821C2×Dic3—31no—
822C2×Dic3—61no—
823C2×Dic3—61no—
824C2×Dic3—61no—
825C2×Dic3—61no—
826C2×Dic3—61no—
827C2×Dic3—91no—
828C2×Dic3—91no—
829C2×Dic3—91no—
830C2×Dic3—121no—
831C2×Dic3—181no—
832C2×Dic3—181no—
833C2×Dic3—181no—
834C2×Dic3—361no—
835C2×Dic3—361no—
836C2×Dic3—361no—
837C2×Dic3—361no—
838C2×Dic3—361no—
839C2×Dic3—362no—
840C2×Dic3—362no—
841C2×Dic3C2×D3211yescharacteristic
842C2×Dic3C2×D3211yescharacteristic
843C2×Dic3C2×D3211yescharacteristic
844D12—41no—
845D12—121no—
846D12—182no—
847D12—361no—
848D12—361no—
849D12—362no—
850D12—361no—
851D12—361no—
852C4×D3—121no—
853C4×D3—361no—
854C4×D3—361no—
855C4×D3—361no—
856C4×D3—362no—
857C4×D3—361no—
858C4×D3—361no—
859Dic6—41no—
860C2×C32—21no—
861C2×C32—21no—
862C2×C32—21no—
863C2×C32—21no—
864C2×C32—21no—
865C2×C32—21no—
866C2×C32—21no—
867C2×C32—21no—
868C2×C32—21no—
869C2×C32—41no—
870C2×C32—41no—
871C2×C32—41no—
872C2×C32—62no—
873C2×C32—121no—
874C2×C32—121no—
875C2×C32C2×#23711yescharacteristic
876C2×C32#100411yescharacteristic
877C2×C32#100411yescharacteristic
878C2×C32#100411yescharacteristic
879C2×C32#100411yescharacteristic
880C2×C32C2×#23911yescharacteristic
881C2×C32D3×#4111yescharacteristic
882C2×C32#100911yescharacteristic
883C2×C32#100911yescharacteristic
884C3⋊D3—41no—
885C3⋊D3—121no—
886C3⋊D3—122no—
887C3⋊D3—121no—
888C3⋊D3—121no—
889C3⋊D3—241no—
890C3⋊D3—241no—
891C3⋊D3—242no—
892C3×D3—22no—
893C3×D3—22no—
894C3×D3—42no—
895C3×D3—42no—
896C3×D3—41no—
897C3×D3—41no—
898C3×D3—41no—
899C3×D3—41no—
900C3×D3—81no—
901C3×D3—121no—
902C3×D3—121no—
903C3×D3—241no—
904C24—91no—
905C2×Q8—31no—
906C2×D4—31no—
907C2×D4—91no—
908C2×D4—91no—
909C2×D4—271no—
910C2×D4—271no—
911C2×D4—271no—
912C2×D4—271no—
913C22×C4—91no—
914C22×C4—271no—
915C22×C4—271no—
916C22×C4—271no—
917C4⋊C4—91no—
918C4⋊C4—91no—
919C4⋊C4—91no—
920C4⋊C4—271no—
921C4⋊C4—271no—
922C4⋊C4—271no—
923C22⋊C4—31no—
924C22⋊C4—91no—
925C22⋊C4—91no—
926C22⋊C4—91no—
927C22⋊C4—91no—
928C22⋊C4—91no—
929C22⋊C4—91no—
930C22⋊C4—91no—
931C22⋊C4—271no—
932C22⋊C4—271no—
933C22⋊C4—271no—
934C22⋊C4—271no—
935C22⋊C4—271no—
936C22⋊C4—271no—
937C42—91no—
938C42—271no—
939C22×C3—21no—
940C22×C3—21no—
941C22×C3—21no—
942C22×C3—32no—
943C22×C3—32no—
944C22×C3—41no—
945C22×C3—62no—
946C22×C3—62no—
947C22×C3—61no—
948C22×C3—61no—
949C22×C3—61no—
950C22×C3—61no—
951C22×C3—61no—
952C22×C3—61no—
953C22×C3—61no—
954C22×C3—61no—
955C22×C3—61no—
956C22×C3—61no—
957C22×C3—61no—
958C22×C3—61no—
959C22×C3—61no—
960C22×C3—61no—
961C22×C3—61no—
962C22×C3—61no—
963C22×C3—121no—
964C22×C3—121no—
965C22×C3—121no—
966C22×C3—121no—
967C22×C3—121no—
968C22×C3—121no—
969C22×C3—121no—
970C22×C3—181no—
971C22×C3—181no—
972C22×C3—181no—
973C22×C3—364no—
974C22×C3C22×D3211yescharacteristic
975C22×C3C22×D3211yescharacteristic
976C22×C3C22×D3211yescharacteristic
977C2×D3—21no—
978C2×D3—21no—
979C2×D3—21no—
980C2×D3—21no—
981C2×D3—21no—
982C2×D3—21no—
983C2×D3—21no—
984C2×D3—21no—
985C2×D3—61no—
986C2×D3—61no—
987C2×D3—61no—
988C2×D3—61no—
989C2×D3—61no—
990C2×D3—61no—
991C2×D3—121no—
992C2×D3—121no—
993C2×D3—121no—
994C2×D3—124no—
995C2×D3—124no—
996C2×D3—182no—
997C2×D3—181no—
998C2×D3—181no—
999C2×D3—181no—
1000C2×D3—181no—
1001C2×D3—181no—
1002C2×D3—181no—
1003C2×D3—181no—
1004C2×D3—181no—
1005C2×D3—181no—
1006C2×D3—361no—
1007C2×D3—361no—
1008C2×D3—361no—
1009C2×D3—361no—
1010C2×D3—361no—
1011C2×D3—361no—
1012C2×D3—361no—
1013C2×D3—361no—
1014C2×D3—362no—
1015C2×D3—721no—
1016C2×D3—721no—
1017C2×D3#379612yes—
1018C3×C4—21no—
1019C3×C4—21no—
1020C3×C4—21no—
1021C3×C4—41no—
1022C3×C4—41no—
1023C3×C4—41no—
1024C3×C4—62no—
1025C3×C4—61no—
1026C3×C4—61no—
1027C3×C4—61no—
1028C3×C4—61no—
1029C3×C4—61no—
1030C3×C4—61no—
1031C3×C4—81no—
1032C3×C4—121no—
1033C3×C4—121no—
1034C3×C4—181no—
1035C3×C4—181no—
1036C3×C4—181no—
1037C3×C4—181no—
1038C3×C4—181no—
1039Dic3—21no—
1040Dic3—21no—
1041Dic3—21no—
1042Dic3—62no—
1043Dic3—62no—
1044Dic3—62no—
1045Dic3—61no—
1046Dic3—61no—
1047Dic3—61no—
1048Dic3—61no—
1049Dic3—61no—
1050Dic3—61no—
1051Dic3—61no—
1052Dic3—61no—
1053Dic3—61no—
1054Dic3—61no—
1055Dic3—121no—
1056Dic3—121no—
1057Dic3—181no—
1058Dic3—181no—
1059Dic3—181no—
1060Dic3—361no—
1061Dic3—361no—
1062Dic3—361no—
1063Dic3—721no—
1064C32—21no—
1065C32—21no—
1066C32—21no—
1067C32—41no—
1068C32#559311yescharacteristic, complemented
1069C32#564411yescharacteristic, complemented
1070C32#567811yescharacteristic, complemented
1071C23—31no—
1072C23—31no—
1073C23—31no—
1074C23—91no—
1075C23—182no—
1076C23—271no—
1077C23—361no—
1078C23—361no—
1079Q8—121no—
1080D4—121no—
1081D4—182no—
1082D4—361no—
1083D4—542no—
1084D4—1081no—
1085D4—1081no—
1086D4—1081no—
1087C2×C4—31no—
1088C2×C4—31no—
1089C2×C4—31no—
1090C2×C4—91no—
1091C2×C4—91no—
1092C2×C4—91no—
1093C2×C4—91no—
1094C2×C4—91no—
1095C2×C4—271no—
1096C2×C4—361no—
1097C2×C4—1081no—
1098C2×C4—1081no—
1099C2×C4—1081no—
1100C2×C4D3311yescharacteristic
1101C2×C3—21no—
1102C2×C3—21no—
1103C2×C3—21no—
1104C2×C3—21no—
1105C2×C3—21no—
1106C2×C3—21no—
1107C2×C3—21no—
1108C2×C3—21no—
1109C2×C3—21no—
1110C2×C3—41no—
1111C2×C3—41no—
1112C2×C3—41no—
1113C2×C3—62no—
1114C2×C3—62no—
1115C2×C3—122no—
1116C2×C3—122no—
1117C2×C3—121no—
1118C2×C3—121no—
1119C2×C3—121no—
1120C2×C3—121no—
1121C2×C3—241no—
1122C2×C3—361no—
1123C2×C3C2×#379611yescharacteristic
1124C2×C3D3×#23711yescharacteristic
1125C2×C3#6431311yescharacteristic
1126C2×C3#6431411yescharacteristic
1127C2×C3#6431411yescharacteristic
1128C2×C3D3×#23911yescharacteristic
1129C2×C3#6432011yescharacteristic
1130C2×C3#6433011yescharacteristic
1131C2×C3#6433011yescharacteristic
1132D3—22no—
1133D3—41no—
1134D3—41no—
1135D3—121no—
1136D3—121no—
1137D3—241no—
1138D3—362no—
1139D3—361no—
1140D3—361no—
1141D3—361no—
1142D3—721no—
1143D3—721no—
1144D3—722no—
1145C22—32no—
1146C22—61no—
1147C22—61no—
1148C22—61no—
1149C22—61no—
1150C22—61no—
1151C22—61no—
1152C22—61no—
1153C22—61no—
1154C22—181no—
1155C22—181no—
1156C22—181no—
1157C22—364no—
1158C22—541no—
1159C22—541no—
1160C22—541no—
1161C22C2×D3311yescharacteristic
1162C4—21no—
1163C4—61no—
1164C4—61no—
1165C4—61no—
1166C4—181no—
1167C4—181no—
1168C4—181no—
1169C4—181no—
1170C4—181no—
1171C4—541no—
1172C3—21no—
1173C3—21no—
1174C3—21no—
1175C3—41no—
1176C3#1059417311yescharacteristic, complemented
1177C3#1059518411yescharacteristic, complemented
1178C3#1059543511yescharacteristic, complemented
1179C2—62no—
1180C2—121no—
1181C2—121no—
1182C2—361no—
1183C2—1081no—
1184C2D3×#379611yescharacteristic
1185C2#1172438611yescharacteristic
1186C2#1172441411yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
hypercenterC2×C4D33
hypocenterC33#538
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. #11723676C2semidirect
2. #11723475C2semidirect
3. #11723461C2semidirect
4. #11723392C2semidirect
5. C3×#63922C2semidirect
6. C3×#63887C2semidirect
7. C3×#63863C2semidirect
8. #11723019C2semidirect
9. #11722996C2semidirect
10. #11722990C2semidirect
11. #11722963C2semidirect
12. #11722958C2semidirect
13. #11722948C2semidirect
14. #11722925C2semidirect
15. D3×(C2×D3)⋊Dic3C2semidirect
21. C2×C32×Dic6C22semidirect
25. C2×#6291C22semidirect
26. C2×#6289C22semidirect
28. C2×D3×C3⋊Dic3C22semidirect
32. #88859C22semidirect
34. C3×#3750C22semidirect
35. C3×C4×C3⋊Dic3C22semidirect
37. #88815C22semidirect
38. #88815C22semidirect
41. #88807C22semidirect
42. #88804C22semidirect
45. Dic3×C3⋊Dic3C22semidirect
46. C3×Dic3⋊Dic3C22semidirect
47. C3×Dic3⋊Dic3C22semidirect
52. C3×(C2×D3)⋊Dic3C22semidirect
53. C3×(C2×D3)⋊Dic3C22semidirect
76. #63922D3semidirect
86. #63887D3semidirect
95. #63863D3semidirect
157. C2×C3×Dic6C2×D3semidirect
158. C2×C3×Dic6C2×D3semidirect
196. #3750C2×D3semidirect
198. C4×C3⋊Dic3C2×D3semidirect
236. Dic3⋊Dic3C2×D3semidirect
237. Dic3⋊Dic3C2×D3semidirect
257. (C2×D3)⋊Dic3C2×D3semidirect
258. (C2×D3)⋊Dic3C2×D3semidirect
516. C2×Dic6D32semidirect
736. C33#538semidirect
1068. C32#5593semidirect
1069. C32#5644semidirect
1070. C32#5678semidirect
1176. C3#10594173semidirect
1177. C3#10595184semidirect
1178. C3#10595435semidirect

Maximal subgroups

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

subgroupindex
#117236762
#117234752
#117234612
#117233922
C3×#639222
C3×#638872
C3×#638632
#117230192
#117229962
#117229902
#117229632
#117229582
#117229482
#117229252
D3×(C2×D3)⋊Dic32
#105954353
#105951843
#105941733