Finite Group Databasebeta

← #13168053

Subgroups — #13168053

Order 1728.

1258 conjugacy classes of subgroups.

The subgroup lattice has 1162 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723672C211yesmaximal, characteristic, complemented
2#11723523C211yesmaximal, characteristic, complemented
3D12×C3⋊Dic3C211yesmaximal, characteristic, complemented
4#11723408C211yesmaximal, characteristic, complemented
5C3×#63922C211yesmaximal, characteristic, complemented
6C3×#63886C211yesmaximal, characteristic, complemented
7C3×#63862C211yesmaximal, characteristic, complemented
8#11723006C211yesmaximal, characteristic, complemented
9#11722990C211yesmaximal, characteristic, complemented
10#11722978C211yesmaximal, characteristic, complemented
11#11722962C211yesmaximal, characteristic, complemented
12#11722954C211yesmaximal, characteristic, complemented
13#11722947C211yesmaximal, characteristic, complemented
14#11722929C211yesmaximal, characteristic, complemented
15D3×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
16#10595267—31nomaximal
17#10594646—31nomaximal
18#10594127—31nomaximal
19C22×C3×D32C2211yescharacteristic
20C2×C32×D12C2211yescharacteristic
21C2×#6296C2211yescharacteristic, complemented
22C2×#6295C2211yescharacteristic
23C2×#6290C2211yescharacteristic
24C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
25C2×D3×C3⋊Dic3C2211yescharacteristic
26C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
27C2×C3×#626C2211yescharacteristic
28C2×C3×#626C2211yescharacteristic
29C2×C3×#626C2211yescharacteristic, complemented
30C2×C3×#625C2211yescharacteristic
31C2×C3×D3×Dic3C2211yescharacteristic
32C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic, complemented
33C3×#3752C2211yescharacteristic
34C3×#3752C2211yescharacteristic, complemented
35C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
36C32×(C2×D3)⋊C4C2211yescharacteristic
37C32×Dic3⋊C4C2211yescharacteristic, complemented
38#88814C2211yescharacteristic
39#88814C2211yescharacteristic, complemented
40#88807C2211yescharacteristic, complemented
41#88806C2211yescharacteristic, complemented
42#88803C2211yescharacteristic
43#88803C2211yescharacteristic
44(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
45(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
46(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
47Dic3×C3⋊Dic3C2211yescharacteristic, complemented
48C3×Dic3⋊Dic3C2211yescharacteristic, complemented
49C3×Dic3⋊Dic3C2211yescharacteristic, complemented
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
54D4×C3⋊Dic3—31no—
55#64107—31no—
56#64092—31no—
57C3×#939—31no—
58C3×#937—31no—
59C3×#898—31no—
60C3×#895—31no—
61C3×#882—31no—
62C3×#879—31no—
63#63980—31no—
64#63977—31no—
65#63976—31no—
66#67⋊Dic3—31no—
67#63971—31no—
68#63970—31no—
69D3×#217—31no—
70#63964—31no—
71#63962—31no—
72C2×(C2×D3)⋊Dic3—31no—
73#63959—31no—
74#63959—31no—
75#63922—31no—
76#63922D311yescharacteristic, complemented
77D3×(C2×D3)⋊C4—31no—
78#63916—31no—
79#63915—31no—
80#63915—31no—
81#63899—31no—
82#63898—31no—
83Dic3×D12—31no—
84Dic3×D12—31no—
85Dic3×D12—61no—
86#63891—31no—
87#63891—31no—
88#63891—61no—
89#63890—31no—
90#63886—31no—
91#63886D311yescharacteristic, complemented
92#63885—31no—
93#63884—31no—
94#63881—31no—
95#63862D311yescharacteristic, complemented
96#63861—31no—
97#63861—31no—
98#63861—61no—
99#63852—31no—
100#63852—31no—
101#63851—31no—
102C22×C3×C3⋊D3C2311yescharacteristic
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⋊Dic3)C2311yescharacteristic
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—22no—
121#6296—41no—
122#6295—41no—
123#6290—41no—
124Dic3×C3⋊D3—41no—
125D3×C3⋊Dic3—41no—
126D3×C3⋊Dic3—41no—
127C3×#626—22no—
128C3×#626—41no—
129C3×#626—41no—
130C3×#625—41no—
131C3×D3×Dic3—41no—
132#5704—91no—
133#5617—91no—
134#5593—91no—
135C23×C3×D3—31no—
136C23×C3×D3—31no—
137C22×D32C2×D311yescharacteristic
138C2×C32×D4—31no—
139C2×#638—31no—
140C22×C3⋊Dic3—31no—
141C22×C3⋊Dic3—31no—
142C2×C4×C3⋊D3—31no—
143C2×C3×#67—31no—
144C2×C3×#67—31no—
145C2×C3×#67—31no—
146C2×C3×#67—31no—
147C2×C3×#67—31no—
148C22×C3×Dic3—31no—
149C2×C3×D12—21no—
150C2×C3×D12—31no—
151C2×C3×D12—31no—
152C2×C3×D12—31no—
153C2×C3×D12C2×D311yescharacteristic
154C2×C3×D12C2×D311yescharacteristic
155C2×C3×C4×D3—31no—
156C2×#627—31no—
157C2×#627—31no—
158C2×#627—31no—
159C2×#626—31no—
160C2×#626—31no—
161C2×#626C2×D311yescharacteristic
162C2×#626C2×D311yescharacteristic
163C2×#626C2×D311yescharacteristic, complemented
164C2×#625—31no—
165C2×#625—31no—
166C2×#625—31no—
167C2×#625—61no—
168C2×#625C2×D311yescharacteristic
169C2×D3×Dic3—31no—
170C2×D3×Dic3—31no—
171C2×D3×Dic3—31no—
172C2×D3×Dic3—31no—
173C2×D3×Dic3—31no—
174C2×D3×Dic3—31no—
175C2×D3×Dic3—61no—
176C2×D3×Dic3—61no—
177C2×D3×Dic3—61no—
178C2×D3×Dic3C2×D311yescharacteristic
179C32×C4⋊C4—31no—
180C32×C22⋊C4—31no—
181#3757—31no—
182#3757—31no—
183#3757—31no—
184#3752—31no—
185#3752—31no—
186#3752C2×D311yescharacteristic
187#3752C2×D311yescharacteristic, complemented
188C4⋊(C3⋊Dic3)—31no—
189C4⋊(C3⋊Dic3)—31no—
190C4⋊(C3⋊Dic3)—31no—
191C4⋊(C3⋊Dic3)—61no—
192C4⋊(C3⋊Dic3)—61no—
193C4⋊(C3⋊Dic3)—61no—
194C4⋊(C3⋊Dic3)—121no—
195#3750—31no—
196#3750—31no—
197C4×C3⋊Dic3—31no—
198C4×C3⋊Dic3C2×D311yescharacteristic, complemented
199C3×#217—31no—
200C3×#217—31no—
201C3×#217—31no—
202C3×#217—31no—
203C3×(C2×D3)⋊C4—21no—
204C3×(C2×D3)⋊C4—31no—
205C3×(C2×D3)⋊C4—31no—
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—61no—
213C3×(C2×D3)⋊C4—61no—
214C3×(C2×D3)⋊C4C2×D311yescharacteristic
215C3×(C2×D3)⋊C4C2×D311yescharacteristic
216C3×C4⋊Dic3—31no—
217C3×C4⋊Dic3—31no—
218C3×Dic3⋊C4—21no—
219C3×Dic3⋊C4—31no—
220C3×Dic3⋊C4—31no—
221C3×Dic3⋊C4C2×D311yescharacteristic, complemented
222C3×Dic3⋊C4C2×D311yescharacteristic, complemented
223C3×C4×Dic3—31no—
224C3×C4×Dic3—31no—
225C3×C4×Dic3—61no—
226#3724—31no—
227#3724—31no—
228#3724—61no—
229Dic3⋊Dic3—31no—
230Dic3⋊Dic3—31no—
231Dic3⋊Dic3—61no—
232Dic3⋊Dic3C2×D311yescharacteristic, complemented
233Dic3⋊Dic3C2×D311yescharacteristic, complemented
234#3722—31no—
235#3722—31no—
236(C2×D3)⋊Dic3—31no—
237(C2×D3)⋊Dic3—31no—
238(C2×D3)⋊Dic3—31no—
239(C2×D3)⋊Dic3—31no—
240(C2×D3)⋊Dic3—31no—
241(C2×D3)⋊Dic3—31no—
242(C2×D3)⋊Dic3—31no—
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—61no—
251(C2×D3)⋊Dic3—61no—
252(C2×D3)⋊Dic3—61no—
253(C2×D3)⋊Dic3—61no—
254(C2×D3)⋊Dic3—61no—
255(C2×D3)⋊Dic3C2×D311yescharacteristic
256(C2×D3)⋊Dic3C2×D311yescharacteristic
257(C2×D3)⋊Dic3C2×D311yescharacteristic
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×#126—91no—
290C3×#121—91no—
291C3×#120—91no—
292#953—91no—
293C2×#217—91no—
294#939—31no—
295#939—91no—
296#939—91no—
297#939—91no—
298#938—91no—
299#937—31no—
300#937—91no—
301#936—91no—
302#935—91no—
303D4×Dic3—91no—
304D4×Dic3—91no—
305D4×Dic3—91no—
306D4×Dic3—181no—
307C2×(C2×D3)⋊C4—91no—
308#924—91no—
309#898—31no—
310#898—91no—
311#898—91no—
312#898—181no—
313#896—91no—
314#895—31no—
315#895—91no—
316#894—91no—
317#893—91no—
318#886—91no—
319#886—91no—
320#885—91no—
321#885—91no—
322#885—91no—
323#885—91no—
324#884—91no—
325#883—91no—
326#883—91no—
327#883—181no—
328#882—31no—
329#882—91no—
330#67⋊C4—91no—
331D3×C22⋊C4—91no—
332#879—31no—
333#879—91no—
334#878—91no—
335#875—91no—
336C4×D12—91no—
337C23×C32—31no—
338C23×C32—31no—
339C23×C32—31no—
340C22×C3⋊D3C22×D311yescharacteristic
341C22×C3⋊D3C22×D311yescharacteristic
342C22×C3×D3—21no—
343C22×C3×D3—21no—
344C22×C3×D3—21no—
345C22×C3×D3—31no—
346C22×C3×D3—31no—
347C22×C3×D3—31no—
348C22×C3×D3—31no—
349C22×C3×D3—61no—
350C22×C3×D3—61no—
351C22×C3×D3—62no—
352C22×C3×D3—62no—
353C22×C3×D3—121no—
354C22×C3×D3—121no—
355C22×C3×D3—121no—
356C22×C3×D3—121no—
357C22×C3×D3C22×D311yescharacteristic
358C22×C3×D3C22×D311yescharacteristic
359C22×C3×D3C22×D311yescharacteristic
360C22×C3×D3C22×D311yescharacteristic
361C22×C3×D3C22×D311yescharacteristic
362C22×C3×D3C22×D311yescharacteristic
363C2×D32—22no—
364C2×D32—41no—
365C2×D32—41no—
366C32×D4—62no—
367C2×C32×C4—21no—
368C2×C32×C4—21no—
369C2×C32×C4—21no—
370C2×C32×C4—31no—
371C2×C32×C4—31no—
372C2×C32×C4—31no—
373C2×C32×C4—41no—
374C2×C32×C4C22×D311yescharacteristic
375C2×C32×C4C22×D311yescharacteristic
376C2×C32×C4C22×D311yescharacteristic
377#638—121no—
378C2×C3⋊Dic3—31no—
379C2×C3⋊Dic3—31no—
380C2×C3⋊Dic3—31no—
381C2×C3⋊Dic3—31no—
382C2×C3⋊Dic3—31no—
383C2×C3⋊Dic3—31no—
384C2×C3⋊Dic3—61no—
385C2×C3⋊Dic3—61no—
386C2×C3⋊Dic3—61no—
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⋊Dic3—121no—
394C2×C3⋊Dic3C22×D311yescharacteristic
395C2×C3⋊Dic3C22×D311yescharacteristic
396C2×C3⋊Dic3C22×D311yescharacteristic
397C2×C3⋊Dic3C22×D311yescharacteristic
398C4×C3⋊D3—121no—
399C3×#67—62no—
400C3×#67—121no—
401C3×#67—121no—
402C3×#67—121no—
403C3×#67—121no—
404C2×C3×Dic3—21no—
405C2×C3×Dic3—21no—
406C2×C3×Dic3—21no—
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—61no—
416C2×C3×Dic3—61no—
417C2×C3×Dic3—61no—
418C2×C3×Dic3—61no—
419C2×C3×Dic3—121no—
420C2×C3×Dic3C22×D311yescharacteristic
421C2×C3×Dic3C22×D311yescharacteristic
422C2×C3×Dic3C22×D311yescharacteristic
423C2×C3×Dic3C22×D311yescharacteristic
424C2×C3×Dic3C22×D311yescharacteristic
425C2×C3×Dic3C22×D311yescharacteristic
426C3×D12—24no—
427C3×D12—22no—
428C3×D12—22no—
429C3×D12—62no—
430C3×D12—121no—
431C3×D12—121no—
432C3×C4×D3—121no—
433#627—121no—
434#627—121no—
435#627—121no—
436#626—22no—
437#626—41no—
438#626—41no—
439#626—121no—
440#626—121no—
441#625—41no—
442#625—121no—
443#625—121no—
444#625—121no—
445#625—122no—
446D3×Dic3—41no—
447D3×Dic3—121no—
448D3×Dic3—121no—
449D3×Dic3—122no—
450D3×Dic3—121no—
451D3×Dic3—121no—
452D3×Dic3—121no—
453D3×Dic3—121no—
454D3×Dic3—122no—
455D3×Dic3—122no—
456#538—271noSylow
457C2×C33C2×#4111yescharacteristic
458C2×C33H(5,𝔽2)11yescharacteristic
459C2×C33H(5,𝔽2)11yescharacteristic
460C3×C3⋊D3—41no—
461C3×C3⋊D3—41no—
462C32×D3—22no—
463C32×D3—41no—
464C32×D3—41no—
465C24×C3—91no—
466C23×D3—31no—
467C23×D3—31no—
468C2×C3×D4—31no—
469C2×C3×D4—31no—
470C2×C3×D4—61no—
471C2×C3×D4—91no—
472C2×C3×D4—91no—
473C2×C3×D4—91no—
474C2×C3×D4—91no—
475C22×C3×C4—91no—
476C2×#67—31no—
477C2×#67—31no—
478C2×#67—31no—
479C2×#67—31no—
480C2×#67—31no—
481C2×#67—91no—
482C2×#67—91no—
483C2×#67—91no—
484C2×#67—91no—
485C2×#67—91no—
486C2×#67—181no—
487C22×Dic3—31no—
488C22×Dic3—91no—
489C22×Dic3—91no—
490C22×Dic3—91no—
491C22×Dic3—91no—
492C22×Dic3—91no—
493C22×Dic3—181no—
494C22×Dic3—181no—
495C2×D12—31no—
496C2×D12—31no—
497C2×D12—31no—
498C2×D12—91no—
499C2×D12D3211yescharacteristic
500C2×C4×D3—31no—
501C2×C4×D3—91no—
502C2×C4×D3—91no—
503C2×C4×D3—91no—
504C2×C4×D3—91no—
505C2×C4×D3—181no—
506C2×Dic6—91no—
507C2×Dic6—91no—
508C2×Dic6—91no—
509C3×C4⋊C4—31no—
510C3×C4⋊C4—31no—
511C3×C4⋊C4—61no—
512C3×C4⋊C4—91no—
513C3×C4⋊C4—91no—
514C3×C22⋊C4—31no—
515C3×C22⋊C4—31no—
516C3×C22⋊C4—61no—
517C3×C22⋊C4—91no—
518C3×C22⋊C4—91no—
519C3×C22⋊C4—91no—
520C3×C22⋊C4—91no—
521C3×C22⋊C4—91no—
522C3×C22⋊C4—91no—
523C3×C42—91no—
524#217—31no—
525#217—31no—
526#217—31no—
527#217—31no—
528#217—91no—
529#217—91no—
530#217—91no—
531#217—91no—
532#217—91no—
533#217—91no—
534#217—91no—
535#217—91no—
536#217—91no—
537#217—91no—
538#217—181no—
539#217—181no—
540#217—181no—
541(C2×D3)⋊C4—31no—
542(C2×D3)⋊C4—31no—
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—61no—
550(C2×D3)⋊C4—61no—
551(C2×D3)⋊C4—91no—
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—181no—
563(C2×D3)⋊C4—181no—
564(C2×D3)⋊C4D3211yescharacteristic
565C4⋊Dic3—31no—
566C4⋊Dic3—31no—
567C4⋊Dic3—91no—
568C4⋊Dic3—91no—
569C4⋊Dic3—91no—
570C4⋊Dic3—91no—
571C4⋊Dic3—181no—
572C4⋊Dic3—181no—
573C4⋊Dic3—181no—
574C4⋊Dic3—361no—
575Dic3⋊C4—31no—
576Dic3⋊C4—31no—
577Dic3⋊C4—91no—
578Dic3⋊C4—91no—
579Dic3⋊C4—91no—
580Dic3⋊C4—91no—
581Dic3⋊C4—91no—
582Dic3⋊C4—181no—
583Dic3⋊C4—181no—
584Dic3⋊C4D3211yescharacteristic, complemented
585C4×Dic3—31no—
586C4×Dic3—31no—
587C4×Dic3—61no—
588C4×Dic3—91no—
589C4×Dic3—91no—
590C4×Dic3—91no—
591C4×Dic3—181no—
592C22×C32—21no—
593C22×C32—21no—
594C22×C32—21no—
595C22×C32—32no—
596C22×C32—41no—
597C22×C32—61no—
598C22×C32—61no—
599C22×C32—61no—
600C22×C32—61no—
601C22×C32—61no—
602C22×C32—61no—
603C22×C32—61no—
604C22×C32—61no—
605C22×C32C23×D311yescharacteristic
606C22×C32C23×D311yescharacteristic
607C22×C32C23×D311yescharacteristic
608C2×C3⋊D3—21no—
609C2×C3⋊D3—21no—
610C2×C3⋊D3—21no—
611C2×C3⋊D3—21no—
612C2×C3⋊D3—21no—
613C2×C3⋊D3—21no—
614C2×C3×D3—21no—
615C2×C3×D3—21no—
616C2×C3×D3—21no—
617C2×C3×D3—21no—
618C2×C3×D3—22no—
619C2×C3×D3—21no—
620C2×C3×D3—21no—
621C2×C3×D3—21no—
622C2×C3×D3—21no—
623C2×C3×D3—21no—
624C2×C3×D3—21no—
625C2×C3×D3—21no—
626C2×C3×D3—21no—
627C2×C3×D3—21no—
628C2×C3×D3—21no—
629C2×C3×D3—21no—
630C2×C3×D3—21no—
631C2×C3×D3—22no—
632C2×C3×D3—41no—
633C2×C3×D3—41no—
634C2×C3×D3—41no—
635C2×C3×D3—41no—
636C2×C3×D3—41no—
637C2×C3×D3—41no—
638C2×C3×D3—41no—
639C2×C3×D3—62no—
640C2×C3×D3—61no—
641C2×C3×D3—61no—
642C2×C3×D3—61no—
643C2×C3×D3—61no—
644C2×C3×D3—61no—
645C2×C3×D3—61no—
646C2×C3×D3—61no—
647C2×C3×D3—61no—
648C2×C3×D3—61no—
649C2×C3×D3—61no—
650C2×C3×D3—61no—
651C2×C3×D3—61no—
652C2×C3×D3—121no—
653C2×C3×D3—121no—
654C2×C3×D3—121no—
655C2×C3×D3—121no—
656C2×C3×D3—121no—
657C2×C3×D3—124no—
658C2×C3×D3—124no—
659C2×C3×D3#23712yes—
660C2×C3×D3#23712yes—
661D32—44no—
662C32×C4—21no—
663C32×C4—22no—
664C32×C4—21no—
665C32×C4—21no—
666C32×C4—41no—
667C32×C4—41no—
668C32×C4—42no—
669C32×C4—61no—
670C32×C4—61no—
671C32×C4—61no—
672C3⋊Dic3—21no—
673C3⋊Dic3—21no—
674C3⋊Dic3—21no—
675C3⋊Dic3—21no—
676C3⋊Dic3—61no—
677C3⋊Dic3—61no—
678C3⋊Dic3—61no—
679C3⋊Dic3—61no—
680C3⋊Dic3—61no—
681C3⋊Dic3—61no—
682C3⋊Dic3—121no—
683C3⋊Dic3—121no—
684C3⋊Dic3—121no—
685C3⋊Dic3—121no—
686C3⋊Dic3—121no—
687C3⋊Dic3—121no—
688C3⋊Dic3—241no—
689C3⋊Dic3—241no—
690C3×Dic3—21no—
691C3×Dic3—21no—
692C3×Dic3—21no—
693C3×Dic3—21no—
694C3×Dic3—21no—
695C3×Dic3—21no—
696C3×Dic3—41no—
697C3×Dic3—41no—
698C3×Dic3—41no—
699C3×Dic3—62no—
700C3×Dic3—61no—
701C3×Dic3—61no—
702C3×Dic3—61no—
703C3×Dic3—61no—
704C3×Dic3—61no—
705C3×Dic3—61no—
706C3×Dic3—61no—
707C3×Dic3—61no—
708C3×Dic3—121no—
709C3×Dic3—121no—
710C3×Dic3—121no—
711#126—91no—
712#126—271no—
713#124—271no—
714#124—271no—
715#123—271no—
716#123—271no—
717C22⋊Q8—271no—
718#121—91no—
719#121—271no—
720#121—271no—
721#120—91no—
722#120—271no—
723C4×D4—271no—
724C4×D4—271no—
725C2×C22⋊C4—271no—
726C33#53811yescharacteristic, complemented, Sylow
727C23×C3—31no—
728C23×C3—31no—
729C23×C3—31no—
730C23×C3—31no—
731C23×C3—31no—
732C23×C3—31no—
733C23×C3—61no—
734C23×C3—61no—
735C23×C3—61no—
736C23×C3—91no—
737C23×C3—91no—
738C23×C3—182no—
739C23×C3—361no—
740C23×C3—361no—
741C22×D3—31no—
742C22×D3—31no—
743C22×D3—31no—
744C22×D3—31no—
745C22×D3—61no—
746C22×D3—61no—
747C22×D3—62no—
748C22×D3—62no—
749C22×D3—121no—
750C22×D3—121no—
751C22×D3—121no—
752C22×D3—121no—
753C22×D3C2×D3211yescharacteristic
754C22×D3C2×D3211yescharacteristic
755C22×D3C2×D3211yescharacteristic
756C3×D4—62no—
757C3×D4—62no—
758C3×D4—64no—
759C3×D4—182no—
760C3×D4—361no—
761C3×D4—361no—
762C3×D4—361no—
763C2×C3×C4—21no—
764C2×C3×C4—21no—
765C2×C3×C4—21no—
766C2×C3×C4—31no—
767C2×C3×C4—31no—
768C2×C3×C4—31no—
769C2×C3×C4—31no—
770C2×C3×C4—31no—
771C2×C3×C4—31no—
772C2×C3×C4—41no—
773C2×C3×C4—61no—
774C2×C3×C4—61no—
775C2×C3×C4—61no—
776C2×C3×C4—91no—
777C2×C3×C4—91no—
778C2×C3×C4—91no—
779C2×C3×C4—91no—
780C2×C3×C4—361no—
781C2×C3×C4C2×D3211yescharacteristic
782C2×C3×C4C2×D3211yescharacteristic
783C2×C3×C4C2×D3211yescharacteristic
784#67—62no—
785#67—121no—
786#67—121no—
787#67—121no—
788#67—121no—
789#67—361no—
790#67—361no—
791#67—361no—
792#67—361no—
793#67—361no—
794#67—362no—
795C2×Dic3—31no—
796C2×Dic3—31no—
797C2×Dic3—31no—
798C2×Dic3—31no—
799C2×Dic3—31no—
800C2×Dic3—31no—
801C2×Dic3—31no—
802C2×Dic3—31no—
803C2×Dic3—61no—
804C2×Dic3—61no—
805C2×Dic3—61no—
806C2×Dic3—61no—
807C2×Dic3—91no—
808C2×Dic3—91no—
809C2×Dic3—91no—
810C2×Dic3—91no—
811C2×Dic3—91no—
812C2×Dic3—91no—
813C2×Dic3—121no—
814C2×Dic3—181no—
815C2×Dic3—181no—
816C2×Dic3—181no—
817C2×Dic3—181no—
818C2×Dic3—181no—
819C2×Dic3—181no—
820C2×Dic3—361no—
821C2×Dic3—361no—
822C2×Dic3—361no—
823C2×Dic3—361no—
824C2×Dic3—361no—
825C2×Dic3—361no—
826C2×Dic3—361no—
827C2×Dic3—362no—
828C2×Dic3—362no—
829C2×Dic3C2×D3211yescharacteristic
830C2×Dic3C2×D3211yescharacteristic
831C2×Dic3C2×D3211yescharacteristic
832D12—22no—
833D12—62no—
834D12—121no—
835D12—121no—
836D12—361no—
837C4×D3—121no—
838C4×D3—361no—
839C4×D3—361no—
840C4×D3—361no—
841C4×D3—361no—
842C4×D3—362no—
843Dic6—361no—
844Dic6—361no—
845Dic6—361no—
846C2×C32—21no—
847C2×C32—21no—
848C2×C32—21no—
849C2×C32—21no—
850C2×C32—21no—
851C2×C32—21no—
852C2×C32—21no—
853C2×C32—21no—
854C2×C32—21no—
855C2×C32—41no—
856C2×C32—41no—
857C2×C32—41no—
858C2×C32—62no—
859C2×C32—121no—
860C2×C32—121no—
861C2×C32C2×#23711yescharacteristic
862C2×C32C2×#23711yescharacteristic
863C2×C32#100411yescharacteristic
864C2×C32#100411yescharacteristic
865C2×C32#100411yescharacteristic
866C2×C32D3×#4111yescharacteristic
867C2×C32#100911yescharacteristic
868C2×C32#100911yescharacteristic
869C2×C32#100911yescharacteristic
870C3⋊D3—41no—
871C3⋊D3—41no—
872C3×D3—22no—
873C3×D3—22no—
874C3×D3—42no—
875C3×D3—42no—
876C3×D3—41no—
877C3×D3—41no—
878C3×D3—41no—
879C3×D3—41no—
880C3×D3—81no—
881C3×D3—122no—
882C3×D3—121no—
883C3×D3—121no—
884C3×D3—121no—
885C3×D3—121no—
886C3×D3—241no—
887C24—91no—
888C2×Q8—271no—
889C2×D4—31no—
890C2×D4—91no—
891C2×D4—91no—
892C2×D4—91no—
893C2×D4—91no—
894C2×D4—271no—
895C2×D4—271no—
896C22×C4—91no—
897C22×C4—271no—
898C22×C4—271no—
899C22×C4—271no—
900C4⋊C4—31no—
901C4⋊C4—91no—
902C4⋊C4—91no—
903C4⋊C4—271no—
904C4⋊C4—271no—
905C4⋊C4—271no—
906C22⋊C4—31no—
907C22⋊C4—91no—
908C22⋊C4—91no—
909C22⋊C4—91no—
910C22⋊C4—91no—
911C22⋊C4—91no—
912C22⋊C4—91no—
913C22⋊C4—271no—
914C22⋊C4—271no—
915C22⋊C4—271no—
916C22⋊C4—271no—
917C22⋊C4—271no—
918C22⋊C4—271no—
919C22⋊C4—271no—
920C42—91no—
921C42—271no—
922C22×C3—21no—
923C22×C3—21no—
924C22×C3—21no—
925C22×C3—32no—
926C22×C3—32no—
927C22×C3—41no—
928C22×C3—62no—
929C22×C3—62no—
930C22×C3—61no—
931C22×C3—61no—
932C22×C3—61no—
933C22×C3—61no—
934C22×C3—61no—
935C22×C3—61no—
936C22×C3—61no—
937C22×C3—61no—
938C22×C3—61no—
939C22×C3—61no—
940C22×C3—61no—
941C22×C3—61no—
942C22×C3—61no—
943C22×C3—61no—
944C22×C3—61no—
945C22×C3—61no—
946C22×C3—121no—
947C22×C3—121no—
948C22×C3—121no—
949C22×C3—121no—
950C22×C3—121no—
951C22×C3—121no—
952C22×C3—121no—
953C22×C3—181no—
954C22×C3—181no—
955C22×C3—181no—
956C22×C3—181no—
957C22×C3—181no—
958C22×C3—181no—
959C22×C3—364no—
960C22×C3C22×D3211yescharacteristic
961C22×C3C22×D3211yescharacteristic
962C22×C3C22×D3211yescharacteristic
963C2×D3—21no—
964C2×D3—21no—
965C2×D3—21no—
966C2×D3—21no—
967C2×D3—21no—
968C2×D3—21no—
969C2×D3—21no—
970C2×D3—21no—
971C2×D3—62no—
972C2×D3—61no—
973C2×D3—61no—
974C2×D3—61no—
975C2×D3—61no—
976C2×D3—61no—
977C2×D3—61no—
978C2×D3—61no—
979C2×D3—61no—
980C2×D3—61no—
981C2×D3—61no—
982C2×D3—61no—
983C2×D3—61no—
984C2×D3—121no—
985C2×D3—121no—
986C2×D3—121no—
987C2×D3—121no—
988C2×D3—121no—
989C2×D3—124no—
990C2×D3—124no—
991C2×D3#380512yes—
992C3×C4—22no—
993C3×C4—21no—
994C3×C4—21no—
995C3×C4—21no—
996C3×C4—41no—
997C3×C4—41no—
998C3×C4—42no—
999C3×C4—61no—
1000C3×C4—61no—
1001C3×C4—61no—
1002C3×C4—61no—
1003C3×C4—61no—
1004C3×C4—61no—
1005C3×C4—121no—
1006C3×C4—121no—
1007C3×C4—121no—
1008C3×C4—181no—
1009C3×C4—181no—
1010C3×C4—181no—
1011C3×C4—181no—
1012Dic3—21no—
1013Dic3—21no—
1014Dic3—21no—
1015Dic3—62no—
1016Dic3—61no—
1017Dic3—61no—
1018Dic3—61no—
1019Dic3—61no—
1020Dic3—61no—
1021Dic3—61no—
1022Dic3—61no—
1023Dic3—61no—
1024Dic3—121no—
1025Dic3—121no—
1026Dic3—121no—
1027Dic3—181no—
1028Dic3—181no—
1029Dic3—181no—
1030Dic3—181no—
1031Dic3—181no—
1032Dic3—181no—
1033Dic3—361no—
1034Dic3—361no—
1035Dic3—361no—
1036Dic3—361no—
1037Dic3—361no—
1038Dic3—361no—
1039Dic3—721no—
1040Dic3—721no—
1041C32—21no—
1042C32—21no—
1043C32—21no—
1044C32—41no—
1045C32#559311yescharacteristic, complemented
1046C32#561711yescharacteristic, complemented
1047C32#570411yescharacteristic, complemented
1048C23—31no—
1049C23—31no—
1050C23—31no—
1051C23—91no—
1052C23—91no—
1053C23—182no—
1054C23—361no—
1055C23—361no—
1056Q8—1081no—
1057D4—62no—
1058D4—182no—
1059D4—361no—
1060D4—361no—
1061D4—361no—
1062D4—1081no—
1063D4—1081no—
1064C2×C4—31no—
1065C2×C4—31no—
1066C2×C4—31no—
1067C2×C4—91no—
1068C2×C4—91no—
1069C2×C4—91no—
1070C2×C4—91no—
1071C2×C4—271no—
1072C2×C4—271no—
1073C2×C4—361no—
1074C2×C4—1081no—
1075C2×C4—1081no—
1076C2×C4—1081no—
1077C2×C4D3311yescharacteristic
1078C2×C3—21no—
1079C2×C3—21no—
1080C2×C3—21no—
1081C2×C3—21no—
1082C2×C3—21no—
1083C2×C3—21no—
1084C2×C3—21no—
1085C2×C3—21no—
1086C2×C3—21no—
1087C2×C3—41no—
1088C2×C3—41no—
1089C2×C3—41no—
1090C2×C3—62no—
1091C2×C3—62no—
1092C2×C3—122no—
1093C2×C3—122no—
1094C2×C3—121no—
1095C2×C3—121no—
1096C2×C3—121no—
1097C2×C3—121no—
1098C2×C3—241no—
1099C2×C3—361no—
1100C2×C3—361no—
1101C2×C3#6430711yescharacteristic
1102C2×C3#6430711yescharacteristic
1103C2×C3D3×#23711yescharacteristic
1104C2×C3D3×#23711yescharacteristic
1105C2×C3#6431311yescharacteristic
1106C2×C3#6431411yescharacteristic
1107C2×C3#6431411yescharacteristic
1108C2×C3#6432011yescharacteristic
1109C2×C3C2×#380511yescharacteristic
1110D3—22no—
1111D3—41no—
1112D3—41no—
1113D3—122no—
1114D3—121no—
1115D3—121no—
1116D3—121no—
1117D3—121no—
1118D3—241no—
1119C22—32no—
1120C22—61no—
1121C22—61no—
1122C22—61no—
1123C22—61no—
1124C22—61no—
1125C22—61no—
1126C22—61no—
1127C22—61no—
1128C22—181no—
1129C22—181no—
1130C22—181no—
1131C22—181no—
1132C22—181no—
1133C22—181no—
1134C22—364no—
1135C22C2×D3311yescharacteristic
1136C4—21no—
1137C4—61no—
1138C4—61no—
1139C4—61no—
1140C4—181no—
1141C4—181no—
1142C4—181no—
1143C4—181no—
1144C4—541no—
1145C4—541no—
1146C3—21no—
1147C3—21no—
1148C3—21no—
1149C3—41no—
1150C3#1059412711yescharacteristic, complemented
1151C3#1059464611yescharacteristic, complemented
1152C3#1059526711yescharacteristic, complemented
1153C2—62no—
1154C2—121no—
1155C2—121no—
1156C2—361no—
1157C2—361no—
1158C2#1172438011yescharacteristic
1159C2#1172438611yescharacteristic
1160C2D3×#380511yescharacteristic
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. #11723672C2semidirect
2. #11723523C2semidirect
3. D12×C3⋊Dic3C2semidirect
4. #11723408C2semidirect
5. C3×#63922C2semidirect
6. C3×#63886C2semidirect
7. C3×#63862C2semidirect
8. #11723006C2semidirect
9. #11722990C2semidirect
10. #11722978C2semidirect
11. #11722962C2semidirect
12. #11722954C2semidirect
13. #11722947C2semidirect
14. #11722929C2semidirect
15. D3×(C2×D3)⋊Dic3C2semidirect
21. C2×#6296C22semidirect
24. C2×Dic3×C3⋊D3C22semidirect
26. C2×D3×C3⋊Dic3C22semidirect
29. C2×C3×#626C22semidirect
32. C4⋊(C3⋊(C3⋊Dic3))C22semidirect
34. C3×#3752C22semidirect
35. C3×C4×C3⋊Dic3C22semidirect
37. C32×Dic3⋊C4C22semidirect
39. #88814C22semidirect
40. #88807C22semidirect
41. #88806C22semidirect
46. (C2×D3)⋊(C3⋊Dic3)C22semidirect
47. Dic3×C3⋊Dic3C22semidirect
48. C3×Dic3⋊Dic3C22semidirect
49. C3×Dic3⋊Dic3C22semidirect
53. C3×(C2×D3)⋊Dic3C22semidirect
76. #63922D3semidirect
91. #63886D3semidirect
95. #63862D3semidirect
163. C2×#626C2×D3semidirect
187. #3752C2×D3semidirect
198. C4×C3⋊Dic3C2×D3semidirect
221. C3×Dic3⋊C4C2×D3semidirect
222. C3×Dic3⋊C4C2×D3semidirect
232. Dic3⋊Dic3C2×D3semidirect
233. Dic3⋊Dic3C2×D3semidirect
258. (C2×D3)⋊Dic3C2×D3semidirect
584. Dic3⋊C4D32semidirect
726. C33#538semidirect
1045. C32#5593semidirect
1046. C32#5617semidirect
1047. C32#5704semidirect
1150. C3#10594127semidirect
1151. C3#10594646semidirect
1152. C3#10595267semidirect

Maximal subgroups

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

subgroupindex
#117236722
#117235232
D12×C3⋊Dic32
#117234082
C3×#639222
C3×#638862
C3×#638622
#117230062
#117229902
#117229782
#117229622
#117229542
#117229472
#117229292
D3×(C2×D3)⋊Dic32
#105952673
#105946463
#105941273