Finite Group Databasebeta

← #13169184

Subgroups — #13169184

Order 1728.

1306 conjugacy classes of subgroups.

The subgroup lattice has 1136 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723677C211yesmaximal, characteristic, complemented
2#11723541C211yesmaximal, characteristic
3#11723489C211yesmaximal, characteristic, complemented
4#11723469C211yesmaximal, characteristic, complemented
5C3×#63897C211yesmaximal, characteristic, complemented
6C3×#63896C211yesmaximal, characteristic, complemented
7C3×#63878C211yesmaximal, characteristic, complemented
8#11723025C211yesmaximal, characteristic, complemented
9#11723023C211yesmaximal, characteristic, complemented
10#11723000C211yesmaximal, characteristic, complemented
11#11722988C211yesmaximal, characteristic, complemented
12#11722933C211yesmaximal, characteristic, complemented
13#11722930C211yesmaximal, characteristic, complemented
14#11722906C211yesmaximal, characteristic, complemented
15D3×#3722C211yesmaximal, characteristic, complemented
16#10594653—31nomaximal
17#10594644—31nomaximal
18#10594166—31nomaximal
19C22×D3×C3⋊D3C2211yescharacteristic
20C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
21C2×C3×#634C2211yescharacteristic, complemented
22C2×#6292C2211yescharacteristic
23C2×#6290C2211yescharacteristic
24C2×#6289C2211yescharacteristic
25C2×#6289C2211yescharacteristic
26C2×C3×#624C2211yescharacteristic, complemented
27C2×C3×D3×Dic3C2211yescharacteristic
28C2×C3×D3×Dic3C2211yescharacteristic
29#88859C2211yescharacteristic
30C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
31C32×(C2×D3)⋊C4C2211yescharacteristic
32C32×Dic3⋊C4C2211yescharacteristic, complemented
33C32×Dic3⋊C4C2211yescharacteristic, complemented
34#88814C2211yescharacteristic
35#88814C2211yescharacteristic
36#88814C2211yescharacteristic, complemented
37#88814C2211yescharacteristic, complemented
38#88807C2211yescharacteristic, complemented
39#88806C2211yescharacteristic, complemented
40Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
41#88804C2211yescharacteristic
42#88804C2211yescharacteristic
43#88803C2211yescharacteristic
44Dic3×C3⋊Dic3C2211yescharacteristic, complemented
45C3×#3724C2211yescharacteristic, complemented
46C3×Dic3⋊Dic3C2211yescharacteristic, complemented
47C3×Dic3⋊Dic3C2211yescharacteristic, complemented
48C3×#3722C2211yescharacteristic
49C3×#3722C2211yescharacteristic
50C3×#3722C2211yescharacteristic, complemented
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×Dic32C2211yescharacteristic, complemented
54#64105—31no—
55#64101—31no—
56#64091—31no—
57C3×#896—31no—
58C3×#894—31no—
59C3×#894—31no—
60C3×#892—31no—
61C3×#878—31no—
62C3×#877—31no—
63#63974—31no—
64#63966—31no—
65C2×#3722—31no—
66#63952—31no—
67#63922—31no—
68#63922—31no—
69#63922—61no—
70#63921—31no—
71#63921—31no—
72D3×(C2×D3)⋊C4—31no—
73D3×(C2×D3)⋊C4—31no—
74#63905—31no—
75#63904—31no—
76C4×#626—31no—
77C4×#625—31no—
78#63897—31no—
79#63897D311yescharacteristic, complemented
80#63896D311yescharacteristic, complemented
81#63894—31no—
82#63891—31no—
83#63888—31no—
84#63888—31no—
85#63888—61no—
86#63879—31no—
87#63878D311yescharacteristic, complemented
88#63868—31no—
89#63864—31no—
90#63863—31no—
91#63862—31no—
92#63861—31no—
93#63860—31no—
94#63859—31no—
95#63858—31no—
96#63854—31no—
97#63853—31no—
98#63848—31no—
99#63836—31no—
100#63836—31no—
101#63836—61no—
102C22×C3⋊(C3⋊D3)C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C3×C3⋊D3C2311yescharacteristic
105C22×C32×D3C2311yescharacteristic
106C2×D3×C3⋊D3—22no—
107C2×D3×C3⋊D3—22no—
108C2×D3×C3⋊D3—41no—
109C2×C33×C4C2311yescharacteristic
110C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C3×C4⋊(C3⋊D3)—41no—
116C3×#634—41no—
117C2×C32×Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122#6292—22no—
123#6290—22no—
124#6289—22no—
125#6289—41no—
126C3×#624—41no—
127C3×D3×Dic3—22no—
128C3×D3×Dic3—41no—
129#5659—91no—
130#5637—91no—
131#5527—91no—
132C23×C3⋊D3—31no—
133C22×D32—31no—
134C22×D32—31no—
135C22×D32—61no—
136C2×#638—31no—
137C2×C4⋊(C3⋊D3)—31no—
138C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
139C2×C4×C3⋊D3—31no—
140C2×C4×C3⋊D3—31no—
141C2×#634C2×D311yescharacteristic, complemented
142C22×C3×Dic3—31no—
143C22×C3×Dic3—31no—
144C2×C3×D12—31no—
145C2×C3×D12—31no—
146C2×C3×D12—61no—
147C2×C3×C4×D3—31no—
148C2×C3×C4×D3—31no—
149C2×C3×C4×D3—31no—
150C2×C3×C4×D3—31no—
151C2×C3×Dic6—31no—
152C2×C3×Dic6—31no—
153C2×C3×Dic6—61no—
154C2×#626—31no—
155C2×#626—31no—
156C2×#626—61no—
157C2×#625—31no—
158C2×#625—31no—
159C2×#625—61no—
160C2×#624—31no—
161C2×#624—31no—
162C2×#624—31no—
163C2×#624—31no—
164C2×#624—61no—
165C2×#624—61no—
166C2×#624C2×D311yescharacteristic, complemented
167C2×D3×Dic3C2×D311yescharacteristic
168C2×D3×Dic3C2×D311yescharacteristic
169C32×C4⋊C4—31no—
170C32×C4⋊C4—31no—
171C32×C22⋊C4—31no—
172#3752—31no—
173#3752—31no—
174#3752—31no—
175#3752—31no—
176#3752—31no—
177#3752—31no—
178#3752—61no—
179#3752—61no—
180#3752—61no—
181#3752—121no—
182C4⋊(C3⋊Dic3)—31no—
183#3750—31no—
184#3750—31no—
185C4×C3⋊Dic3—31no—
186C4×C3⋊Dic3C2×D311yescharacteristic, complemented
187C3×#217—31no—
188C3×#217—31no—
189C3×(C2×D3)⋊C4—21no—
190C3×(C2×D3)⋊C4—31no—
191C3×(C2×D3)⋊C4—31no—
192C3×(C2×D3)⋊C4—31no—
193C3×(C2×D3)⋊C4—31no—
194C3×(C2×D3)⋊C4—31no—
195C3×(C2×D3)⋊C4—31no—
196C3×(C2×D3)⋊C4—31no—
197C3×(C2×D3)⋊C4—31no—
198C3×(C2×D3)⋊C4C2×D311yescharacteristic
199C3×(C2×D3)⋊C4C2×D311yescharacteristic
200C3×C4⋊Dic3—31no—
201C3×C4⋊Dic3—31no—
202C3×Dic3⋊C4—21no—
203C3×Dic3⋊C4—21no—
204C3×Dic3⋊C4—31no—
205C3×Dic3⋊C4—31no—
206C3×Dic3⋊C4—31no—
207C3×Dic3⋊C4—31no—
208C3×Dic3⋊C4C2×D311yescharacteristic, complemented
209C3×Dic3⋊C4C2×D311yescharacteristic, complemented
210C3×Dic3⋊C4C2×D311yescharacteristic, complemented
211C3×Dic3⋊C4C2×D311yescharacteristic, complemented
212C3×C4×Dic3—31no—
213C3×C4×Dic3—31no—
214C3×C4×Dic3—31no—
215C3×C4×Dic3—31no—
216C3×C4×Dic3—61no—
217#3724—31no—
218#3724—31no—
219#3724—61no—
220#3724C2×D311yescharacteristic, complemented
221Dic3⋊Dic3—31no—
222Dic3⋊Dic3—31no—
223Dic3⋊Dic3—31no—
224Dic3⋊Dic3—31no—
225Dic3⋊Dic3—61no—
226Dic3⋊Dic3—61no—
227Dic3⋊Dic3C2×D311yescharacteristic, complemented
228Dic3⋊Dic3C2×D311yescharacteristic, complemented
229#3722—31no—
230#3722—31no—
231#3722—31no—
232#3722—31no—
233#3722—31no—
234#3722—31no—
235#3722—31no—
236#3722—31no—
237#3722—61no—
238#3722—61no—
239#3722C2×D311yescharacteristic
240#3722C2×D311yescharacteristic
241#3722C2×D311yescharacteristic, complemented
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—31no—
251(C2×D3)⋊Dic3—31no—
252(C2×D3)⋊Dic3—61no—
253(C2×D3)⋊Dic3C2×D311yescharacteristic
254(C2×D3)⋊Dic3C2×D311yescharacteristic
255Dic32—31no—
256Dic32—31no—
257Dic32—61no—
258Dic32C2×D311yescharacteristic, complemented
259C22×C33C2411yescharacteristic
260C2×C3⋊(C3⋊D3)—21no—
261C2×C3⋊(C3⋊D3)—21no—
262C2×C3⋊(C3⋊D3)#4112yes—
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#4112yes—
272D3×C3⋊D3—44no—
273C33×C4—21no—
274C3⋊(C3⋊Dic3)—21no—
275C3×C3⋊Dic3—21no—
276C3×C3⋊Dic3—21no—
277C3×C3⋊Dic3—21no—
278C3×C3⋊Dic3—21no—
279C32×Dic3—21no—
280C32×Dic3—21no—
281C32×Dic3—21no—
282C32×Dic3—21no—
283C32×Dic3—21no—
284C3×#123—91no—
285C3×C22⋊Q8—91no—
286C3×#117—91no—
287#947—91no—
288#946—91no—
289#937—91no—
290#936—91no—
291#929—91no—
292C4×#67—91no—
293C4×#67—91no—
294C4×#67—91no—
295C2×(C2×D3)⋊C4—91no—
296C2×(C2×D3)⋊C4—91no—
297#898—91no—
298#898—91no—
299#898—91no—
300#896—31no—
301#896—91no—
302#896—91no—
303#896—181no—
304#894—31no—
305#894—31no—
306#894—91no—
307#894—91no—
308#893—91no—
309#892—31no—
310#892—91no—
311#892—91no—
312#892—181no—
313#886—91no—
314#883—91no—
315#883—91no—
316#882—91no—
317#882—91no—
318#882—181no—
319#67⋊C4—91no—
320D3×C22⋊C4—91no—
321D3×C22⋊C4—91no—
322D3×C22⋊C4—91no—
323D3×C22⋊C4—91no—
324#879—91no—
325#879—91no—
326#878—31no—
327#877—31no—
328#876—91no—
329#875—91no—
330C4×D12—91no—
331#872—91no—
332C23×C32—31no—
333C22×C3⋊D3—31no—
334C22×C3⋊D3—31no—
335C22×C3⋊D3—31no—
336C22×C3⋊D3—61no—
337C22×C3⋊D3—61no—
338C22×C3⋊D3—61no—
339C22×C3⋊D3—62no—
340C22×C3⋊D3—62no—
341C22×C3⋊D3—121no—
342C22×C3⋊D3—121no—
343C22×C3⋊D3C22×D311yescharacteristic
344C22×C3⋊D3C22×D311yescharacteristic
345C22×C3×D3—21no—
346C22×C3×D3—31no—
347C22×C3×D3—31no—
348C22×C3×D3—31no—
349C22×C3×D3—31no—
350C22×C3×D3—61no—
351C22×C3×D3—61no—
352C22×C3×D3C22×D311yescharacteristic
353C22×C3×D3C22×D311yescharacteristic
354C2×D32—62no—
355C2×D32—62no—
356C2×D32—62no—
357C2×D32—62no—
358C2×D32—122no—
359C2×D32—122no—
360C2×D32—121no—
361C2×D32—121no—
362C2×D32—122no—
363C2×C32×C4—21no—
364C2×C32×C4—21no—
365C2×C32×C4—21no—
366C2×C32×C4—31no—
367C2×C32×C4—31no—
368C2×C32×C4—31no—
369C2×C32×C4—31no—
370C2×C32×C4—31no—
371C2×C32×C4—41no—
372C2×C32×C4C22×D311yescharacteristic
373C2×C32×C4C22×D311yescharacteristic
374C2×C32×C4C22×D311yescharacteristic
375#638—62no—
376C2×C3⋊Dic3—31no—
377C2×C3⋊Dic3—31no—
378C2×C3⋊Dic3—31no—
379C2×C3⋊Dic3—61no—
380C2×C3⋊Dic3—61no—
381C2×C3⋊Dic3—61no—
382C2×C3⋊Dic3—121no—
383C2×C3⋊Dic3C22×D311yescharacteristic
384C2×C3⋊Dic3C22×D311yescharacteristic
385C2×C3⋊Dic3C22×D311yescharacteristic
386C2×C3⋊Dic3C22×D311yescharacteristic
387C4⋊(C3⋊D3)—41no—
388C4⋊(C3⋊D3)—62no—
389C4×C3⋊D3—62no—
390C4×C3⋊D3—121no—
391#634—41no—
392C2×C3×Dic3—21no—
393C2×C3×Dic3—21no—
394C2×C3×Dic3—21no—
395C2×C3×Dic3—21no—
396C2×C3×Dic3—21no—
397C2×C3×Dic3—31no—
398C2×C3×Dic3—31no—
399C2×C3×Dic3—31no—
400C2×C3×Dic3—31no—
401C2×C3×Dic3—31no—
402C2×C3×Dic3—31no—
403C2×C3×Dic3—31no—
404C2×C3×Dic3—31no—
405C2×C3×Dic3—61no—
406C2×C3×Dic3—61no—
407C2×C3×Dic3—61no—
408C2×C3×Dic3—61no—
409C2×C3×Dic3—62no—
410C2×C3×Dic3—121no—
411C2×C3×Dic3C22×D311yescharacteristic
412C2×C3×Dic3C22×D311yescharacteristic
413C2×C3×Dic3C22×D311yescharacteristic
414C2×C3×Dic3C22×D311yescharacteristic
415C2×C3×Dic3C22×D311yescharacteristic
416C2×C3×Dic3C22×D311yescharacteristic
417C2×C3×Dic3C22×D311yescharacteristic
418C2×C3×Dic3C22×D311yescharacteristic
419C2×C3×Dic3C22×D311yescharacteristic
420C2×C3×Dic3C22×D311yescharacteristic
421C3×D12—121no—
422C3×D12—121no—
423C3×D12—122no—
424C3×C4×D3—62no—
425C3×C4×D3—121no—
426C3×C4×D3—121no—
427C3×C4×D3—121no—
428C3×Dic6—121no—
429C3×Dic6—121no—
430C3×Dic6—122no—
431#626—62no—
432#626—62no—
433#626—122no—
434#625—62no—
435#625—62no—
436#625—122no—
437#624—41no—
438#624—62no—
439#624—62no—
440#624—64no—
441#624—121no—
442#624—121no—
443#624—122no—
444D3×Dic3—22no—
445D3×Dic3—41no—
446#551—271noSylow
447C2×C33C2×#4111yescharacteristic
448C2×C33C2×#4111yescharacteristic
449C2×C33H(5,𝔽2)11yescharacteristic
450C3⋊(C3⋊D3)—22no—
451C3×C3⋊D3—41no—
452C3×C3⋊D3—41no—
453C32×D3—22no—
454C23×D3—91no—
455C23×D3—91no—
456C23×D3—91no—
457C23×D3—181no—
458C2×C3×Q8—91no—
459C2×C3×D4—91no—
460C22×C3×C4—91no—
461C22×C3×C4—91no—
462C22×C3×C4—91no—
463C2×#67—91no—
464C2×#67—91no—
465C2×#67—91no—
466C2×#67—91no—
467C2×#67—181no—
468C22×Dic3—31no—
469C22×Dic3—31no—
470C2×D12—31no—
471C2×D12—31no—
472C2×D12—61no—
473C2×D12—91no—
474C2×D12—91no—
475C2×D12—181no—
476C2×C4×D3—31no—
477C2×C4×D3—31no—
478C2×C4×D3—31no—
479C2×C4×D3—31no—
480C2×C4×D3—91no—
481C2×C4×D3—91no—
482C2×C4×D3—91no—
483C2×C4×D3—91no—
484C2×C4×D3—91no—
485C2×C4×D3—91no—
486C2×C4×D3—181no—
487C2×C4×D3—181no—
488C2×Dic6—31no—
489C2×Dic6—31no—
490C2×Dic6—61no—
491C3×C4⋊C4—31no—
492C3×C4⋊C4—31no—
493C3×C4⋊C4—31no—
494C3×C4⋊C4—31no—
495C3×C4⋊C4—61no—
496C3×C4⋊C4—61no—
497C3×C4⋊C4—91no—
498C3×C4⋊C4—91no—
499C3×C4⋊C4—91no—
500C3×C22⋊C4—31no—
501C3×C22⋊C4—31no—
502C3×C22⋊C4—61no—
503C3×C22⋊C4—91no—
504C3×C22⋊C4—91no—
505C3×C22⋊C4—91no—
506C3×C22⋊C4—91no—
507C3×C22⋊C4—91no—
508C3×C42—91no—
509C3×C42—91no—
510#217—31no—
511#217—31no—
512#217—91no—
513#217—91no—
514#217—91no—
515#217—91no—
516#217—91no—
517(C2×D3)⋊C4—31no—
518(C2×D3)⋊C4—31no—
519(C2×D3)⋊C4—31no—
520(C2×D3)⋊C4—31no—
521(C2×D3)⋊C4—31no—
522(C2×D3)⋊C4—31no—
523(C2×D3)⋊C4—31no—
524(C2×D3)⋊C4—31no—
525(C2×D3)⋊C4—91no—
526(C2×D3)⋊C4—91no—
527(C2×D3)⋊C4—91no—
528(C2×D3)⋊C4—91no—
529(C2×D3)⋊C4—91no—
530(C2×D3)⋊C4—91no—
531(C2×D3)⋊C4—91no—
532(C2×D3)⋊C4—91no—
533(C2×D3)⋊C4—91no—
534(C2×D3)⋊C4—91no—
535(C2×D3)⋊C4—91no—
536(C2×D3)⋊C4—91no—
537(C2×D3)⋊C4—91no—
538(C2×D3)⋊C4—91no—
539(C2×D3)⋊C4—91no—
540(C2×D3)⋊C4—91no—
541(C2×D3)⋊C4—91no—
542(C2×D3)⋊C4—91no—
543(C2×D3)⋊C4—91no—
544(C2×D3)⋊C4—181no—
545(C2×D3)⋊C4—181no—
546(C2×D3)⋊C4—181no—
547(C2×D3)⋊C4—181no—
548(C2×D3)⋊C4—181no—
549(C2×D3)⋊C4—181no—
550(C2×D3)⋊C4—361no—
551(C2×D3)⋊C4D3211yescharacteristic
552C4⋊Dic3—31no—
553C4⋊Dic3—31no—
554C4⋊Dic3—91no—
555C4⋊Dic3—91no—
556C4⋊Dic3—91no—
557C4⋊Dic3—181no—
558Dic3⋊C4—31no—
559Dic3⋊C4—31no—
560Dic3⋊C4—31no—
561Dic3⋊C4—31no—
562Dic3⋊C4—91no—
563Dic3⋊C4—91no—
564Dic3⋊C4—91no—
565Dic3⋊C4—91no—
566Dic3⋊C4—91no—
567Dic3⋊C4—91no—
568Dic3⋊C4—181no—
569Dic3⋊C4—181no—
570Dic3⋊C4D3211yescharacteristic, complemented
571Dic3⋊C4D3211yescharacteristic, complemented
572C4×Dic3—31no—
573C4×Dic3—31no—
574C4×Dic3—31no—
575C4×Dic3—31no—
576C4×Dic3—61no—
577C4×Dic3—91no—
578C4×Dic3—91no—
579C4×Dic3—91no—
580C4×Dic3—181no—
581C22×C32—21no—
582C22×C32—21no—
583C22×C32—21no—
584C22×C32—32no—
585C22×C32—41no—
586C22×C32—61no—
587C22×C32—61no—
588C22×C32C23×D311yescharacteristic
589C22×C32C23×D311yescharacteristic
590C22×C32C23×D311yescharacteristic
591C2×C3⋊D3—21no—
592C2×C3⋊D3—21no—
593C2×C3⋊D3—21no—
594C2×C3⋊D3—21no—
595C2×C3⋊D3—21no—
596C2×C3⋊D3—21no—
597C2×C3⋊D3—32no—
598C2×C3⋊D3—32no—
599C2×C3⋊D3—32no—
600C2×C3⋊D3—62no—
601C2×C3⋊D3—62no—
602C2×C3⋊D3—62no—
603C2×C3⋊D3—61no—
604C2×C3⋊D3—61no—
605C2×C3⋊D3—61no—
606C2×C3⋊D3—61no—
607C2×C3⋊D3—61no—
608C2×C3⋊D3—61no—
609C2×C3⋊D3—122no—
610C2×C3⋊D3—121no—
611C2×C3⋊D3—121no—
612C2×C3⋊D3—121no—
613C2×C3⋊D3—121no—
614C2×C3⋊D3—121no—
615C2×C3⋊D3—121no—
616C2×C3⋊D3—124no—
617C2×C3⋊D3—241no—
618C2×C3⋊D3—241no—
619C2×C3×D3—21no—
620C2×C3×D3—21no—
621C2×C3×D3—21no—
622C2×C3×D3—21no—
623C2×C3×D3—22no—
624C2×C3×D3—41no—
625C2×C3×D3—41no—
626C2×C3×D3—62no—
627C2×C3×D3—61no—
628C2×C3×D3—61no—
629C2×C3×D3—61no—
630C2×C3×D3—61no—
631C2×C3×D3—61no—
632C2×C3×D3—61no—
633C2×C3×D3—61no—
634C2×C3×D3—61no—
635C2×C3×D3—61no—
636C2×C3×D3—61no—
637C2×C3×D3—61no—
638C2×C3×D3—61no—
639C2×C3×D3—121no—
640C2×C3×D3—121no—
641C2×C3×D3—121no—
642C2×C3×D3—121no—
643C2×C3×D3—121no—
644C2×C3×D3#23512yes—
645C2×C3×D3#23912yes—
646D32—124no—
647D32—124no—
648D32—128no—
649C32×C4—21no—
650C32×C4—21no—
651C32×C4—21no—
652C32×C4—41no—
653C32×C4—41no—
654C32×C4—41no—
655C32×C4—61no—
656C32×C4—61no—
657C32×C4—61no—
658C32×C4—61no—
659C32×C4—61no—
660C32×C4—81no—
661C3⋊Dic3—21no—
662C3⋊Dic3—21no—
663C3⋊Dic3—21no—
664C3⋊Dic3—21no—
665C3⋊Dic3—61no—
666C3⋊Dic3—61no—
667C3⋊Dic3—61no—
668C3⋊Dic3—121no—
669C3⋊Dic3—121no—
670C3⋊Dic3—121no—
671C3⋊Dic3—241no—
672C3×Dic3—22no—
673C3×Dic3—21no—
674C3×Dic3—21no—
675C3×Dic3—21no—
676C3×Dic3—21no—
677C3×Dic3—21no—
678C3×Dic3—21no—
679C3×Dic3—21no—
680C3×Dic3—21no—
681C3×Dic3—21no—
682C3×Dic3—21no—
683C3×Dic3—41no—
684C3×Dic3—41no—
685C3×Dic3—41no—
686C3×Dic3—41no—
687C3×Dic3—62no—
688C3×Dic3—62no—
689C3×Dic3—61no—
690C3×Dic3—61no—
691C3×Dic3—61no—
692C3×Dic3—61no—
693C3×Dic3—61no—
694C3×Dic3—61no—
695C3×Dic3—61no—
696C3×Dic3—61no—
697C3×Dic3—121no—
698C3×Dic3—121no—
699#126—271no—
700#126—271no—
701#124—271no—
702#123—91no—
703#123—271no—
704#123—271no—
705C22⋊Q8—91no—
706C22⋊Q8—271no—
707#120—271no—
708C4×D4—271no—
709C4×D4—271no—
710#117—91no—
711#117—271no—
712C2×C22⋊C4—271no—
713C2×C22⋊C4—271no—
714C33#55111yescharacteristic, complemented, Sylow
715C23×C3—31no—
716C23×C3—31no—
717C23×C3—61no—
718C23×C3—91no—
719C23×C3—91no—
720C22×D3—31no—
721C22×D3—31no—
722C22×D3—31no—
723C22×D3—31no—
724C22×D3—61no—
725C22×D3—61no—
726C22×D3—91no—
727C22×D3—91no—
728C22×D3—91no—
729C22×D3—181no—
730C22×D3—181no—
731C22×D3—181no—
732C22×D3—182no—
733C22×D3—182no—
734C22×D3—182no—
735C22×D3—182no—
736C22×D3—182no—
737C22×D3—182no—
738C22×D3—361no—
739C22×D3—362no—
740C22×D3—362no—
741C22×D3—361no—
742C22×D3—361no—
743C22×D3—361no—
744C22×D3—362no—
745C22×D3C2×D3211yescharacteristic
746C3×Q8—361no—
747C3×D4—361no—
748C2×C3×C4—21no—
749C2×C3×C4—21no—
750C2×C3×C4—21no—
751C2×C3×C4—31no—
752C2×C3×C4—31no—
753C2×C3×C4—31no—
754C2×C3×C4—31no—
755C2×C3×C4—31no—
756C2×C3×C4—31no—
757C2×C3×C4—31no—
758C2×C3×C4—31no—
759C2×C3×C4—31no—
760C2×C3×C4—31no—
761C2×C3×C4—41no—
762C2×C3×C4—61no—
763C2×C3×C4—61no—
764C2×C3×C4—61no—
765C2×C3×C4—61no—
766C2×C3×C4—61no—
767C2×C3×C4—91no—
768C2×C3×C4—91no—
769C2×C3×C4—91no—
770C2×C3×C4—91no—
771C2×C3×C4—182no—
772C2×C3×C4—361no—
773C2×C3×C4—361no—
774C2×C3×C4C2×D3211yescharacteristic
775C2×C3×C4C2×D3211yescharacteristic
776C2×C3×C4C2×D3211yescharacteristic
777#67—182no—
778#67—182no—
779#67—182no—
780#67—182no—
781#67—362no—
782C2×Dic3—31no—
783C2×Dic3—31no—
784C2×Dic3—31no—
785C2×Dic3—31no—
786C2×Dic3—31no—
787C2×Dic3—31no—
788C2×Dic3—31no—
789C2×Dic3—31no—
790C2×Dic3—61no—
791C2×Dic3—61no—
792C2×Dic3—61no—
793C2×Dic3—61no—
794C2×Dic3—62no—
795C2×Dic3—91no—
796C2×Dic3—91no—
797C2×Dic3—91no—
798C2×Dic3—121no—
799C2×Dic3—181no—
800C2×Dic3—181no—
801C2×Dic3—181no—
802C2×Dic3—361no—
803C2×Dic3C2×D3211yescharacteristic
804C2×Dic3C2×D3211yescharacteristic
805C2×Dic3C2×D3211yescharacteristic
806C2×Dic3C2×D3211yescharacteristic
807C2×Dic3C2×D3211yescharacteristic
808D12—121no—
809D12—121no—
810D12—122no—
811D12—182no—
812D12—182no—
813D12—362no—
814C4×D3—62no—
815C4×D3—121no—
816C4×D3—121no—
817C4×D3—121no—
818C4×D3—182no—
819C4×D3—182no—
820C4×D3—182no—
821C4×D3—184no—
822C4×D3—361no—
823C4×D3—361no—
824C4×D3—361no—
825C4×D3—362no—
826Dic6—121no—
827Dic6—121no—
828Dic6—122no—
829C2×C32—21no—
830C2×C32—21no—
831C2×C32—21no—
832C2×C32—21no—
833C2×C32—21no—
834C2×C32—21no—
835C2×C32—21no—
836C2×C32—21no—
837C2×C32—21no—
838C2×C32—41no—
839C2×C32—41no—
840C2×C32—41no—
841C2×C32—62no—
842C2×C32C2×#23511yescharacteristic
843C2×C32#100411yescharacteristic
844C2×C32#100411yescharacteristic
845C2×C32C2×#23911yescharacteristic
846C2×C32D3×#4111yescharacteristic
847C2×C32D3×#4111yescharacteristic
848C2×C32D3×#4111yescharacteristic
849C2×C32D3×#4111yescharacteristic
850C2×C32#100911yescharacteristic
851C3⋊D3—41no—
852C3⋊D3—41no—
853C3⋊D3—62no—
854C3⋊D3—62no—
855C3⋊D3—62no—
856C3⋊D3—122no—
857C3⋊D3—122no—
858C3⋊D3—122no—
859C3⋊D3—242no—
860C3×D3—22no—
861C3×D3—22no—
862C3×D3—42no—
863C3×D3—122no—
864C3×D3—121no—
865C3×D3—121no—
866C3×D3—121no—
867C3×D3—121no—
868C3×D3—241no—
869C24—271no—
870C2×Q8—91no—
871C2×D4—91no—
872C2×D4—271no—
873C2×D4—271no—
874C22×C4—91no—
875C22×C4—91no—
876C22×C4—91no—
877C22×C4—271no—
878C22×C4—271no—
879C4⋊C4—31no—
880C4⋊C4—31no—
881C4⋊C4—91no—
882C4⋊C4—91no—
883C4⋊C4—91no—
884C4⋊C4—271no—
885C4⋊C4—271no—
886C4⋊C4—271no—
887C22⋊C4—31no—
888C22⋊C4—91no—
889C22⋊C4—91no—
890C22⋊C4—91no—
891C22⋊C4—91no—
892C22⋊C4—91no—
893C22⋊C4—271no—
894C22⋊C4—271no—
895C22⋊C4—271no—
896C22⋊C4—271no—
897C22⋊C4—271no—
898C22⋊C4—271no—
899C22⋊C4—271no—
900C22⋊C4—271no—
901C42—91no—
902C42—91no—
903C42—271no—
904C22×C3—21no—
905C22×C3—21no—
906C22×C3—21no—
907C22×C3—32no—
908C22×C3—32no—
909C22×C3—41no—
910C22×C3—62no—
911C22×C3—61no—
912C22×C3—61no—
913C22×C3—61no—
914C22×C3—61no—
915C22×C3—121no—
916C22×C3—121no—
917C22×C3—181no—
918C22×C3—181no—
919C22×C3—181no—
920C22×C3—181no—
921C22×C3—181no—
922C22×C3—181no—
923C22×C3C22×D3211yescharacteristic
924C22×C3C22×D3211yescharacteristic
925C22×C3C22×D3211yescharacteristic
926C2×D3—21no—
927C2×D3—21no—
928C2×D3—62no—
929C2×D3—61no—
930C2×D3—61no—
931C2×D3—61no—
932C2×D3—61no—
933C2×D3—61no—
934C2×D3—61no—
935C2×D3—61no—
936C2×D3—61no—
937C2×D3—61no—
938C2×D3—61no—
939C2×D3—61no—
940C2×D3—61no—
941C2×D3—92no—
942C2×D3—92no—
943C2×D3—92no—
944C2×D3—121no—
945C2×D3—121no—
946C2×D3—121no—
947C2×D3—121no—
948C2×D3—121no—
949C2×D3—182no—
950C2×D3—182no—
951C2×D3—182no—
952C2×D3—181no—
953C2×D3—181no—
954C2×D3—181no—
955C2×D3—181no—
956C2×D3—181no—
957C2×D3—181no—
958C2×D3—362no—
959C2×D3—361no—
960C2×D3—361no—
961C2×D3—361no—
962C2×D3—361no—
963C2×D3—361no—
964C2×D3—361no—
965C2×D3—364no—
966C2×D3—364no—
967C2×D3—364no—
968C2×D3—368no—
969C2×D3—721no—
970C2×D3—721no—
971C2×D3#379912yes—
972C3×C4—21no—
973C3×C4—21no—
974C3×C4—21no—
975C3×C4—41no—
976C3×C4—41no—
977C3×C4—41no—
978C3×C4—62no—
979C3×C4—61no—
980C3×C4—61no—
981C3×C4—61no—
982C3×C4—61no—
983C3×C4—61no—
984C3×C4—61no—
985C3×C4—61no—
986C3×C4—61no—
987C3×C4—61no—
988C3×C4—61no—
989C3×C4—81no—
990C3×C4—121no—
991C3×C4—121no—
992C3×C4—121no—
993C3×C4—121no—
994C3×C4—181no—
995C3×C4—181no—
996C3×C4—181no—
997C3×C4—181no—
998Dic3—21no—
999Dic3—21no—
1000Dic3—21no—
1001Dic3—21no—
1002Dic3—21no—
1003Dic3—62no—
1004Dic3—62no—
1005Dic3—61no—
1006Dic3—61no—
1007Dic3—61no—
1008Dic3—61no—
1009Dic3—61no—
1010Dic3—61no—
1011Dic3—61no—
1012Dic3—61no—
1013Dic3—121no—
1014Dic3—121no—
1015Dic3—181no—
1016Dic3—181no—
1017Dic3—181no—
1018Dic3—361no—
1019Dic3—361no—
1020Dic3—361no—
1021Dic3—721no—
1022C32—21no—
1023C32—21no—
1024C32—21no—
1025C32—41no—
1026C32#552711yescharacteristic, complemented
1027C32#563711yescharacteristic, complemented
1028C32#565911yescharacteristic, complemented
1029C23—31no—
1030C23—91no—
1031C23—91no—
1032C23—271no—
1033C23—542no—
1034C23—542no—
1035C23—1081no—
1036Q8—361no—
1037D4—361no—
1038D4—542no—
1039D4—542no—
1040C2×C4—31no—
1041C2×C4—31no—
1042C2×C4—31no—
1043C2×C4—31no—
1044C2×C4—31no—
1045C2×C4—91no—
1046C2×C4—91no—
1047C2×C4—91no—
1048C2×C4—91no—
1049C2×C4—182no—
1050C2×C4—271no—
1051C2×C4—361no—
1052C2×C4—361no—
1053C2×C4—542no—
1054C2×C4—1081no—
1055C2×C4D3311yescharacteristic
1056C2×C3—21no—
1057C2×C3—21no—
1058C2×C3—21no—
1059C2×C3—21no—
1060C2×C3—21no—
1061C2×C3—21no—
1062C2×C3—21no—
1063C2×C3—21no—
1064C2×C3—21no—
1065C2×C3—41no—
1066C2×C3—41no—
1067C2×C3—41no—
1068C2×C3—62no—
1069C2×C3—62no—
1070C2×C3—122no—
1071C2×C3—361no—
1072C2×C3—361no—
1073C2×C3C2×#379911yescharacteristic
1074C2×C3D3×#23511yescharacteristic
1075C2×C3#6430611yescharacteristic
1076C2×C3#6431211yescharacteristic
1077C2×C3#6431311yescharacteristic
1078C2×C3#6431411yescharacteristic
1079C2×C3#6431411yescharacteristic
1080C2×C3D3×#23911yescharacteristic
1081C2×C3#6431911yescharacteristic
1082D3—22no—
1083D3—122no—
1084D3—121no—
1085D3—121no—
1086D3—121no—
1087D3—121no—
1088D3—182no—
1089D3—182no—
1090D3—182no—
1091D3—241no—
1092D3—362no—
1093D3—362no—
1094D3—362no—
1095D3—722no—
1096C22—32no—
1097C22—61no—
1098C22—61no—
1099C22—181no—
1100C22—181no—
1101C22—181no—
1102C22—181no—
1103C22—181no—
1104C22—181no—
1105C22—272no—
1106C22—541no—
1107C22—541no—
1108C22—1084no—
1109C22C2×D3311yescharacteristic
1110C4—21no—
1111C4—61no—
1112C4—61no—
1113C4—61no—
1114C4—61no—
1115C4—61no—
1116C4—181no—
1117C4—181no—
1118C4—181no—
1119C4—181no—
1120C4—541no—
1121C3—21no—
1122C3—21no—
1123C3—21no—
1124C3—41no—
1125C3#1059416611yescharacteristic, complemented
1126C3#1059464411yescharacteristic, complemented
1127C3#1059465311yescharacteristic, complemented
1128C2—62no—
1129C2—361no—
1130C2—361no—
1131C2—542no—
1132C2#1172437611yescharacteristic
1133C2D3×#379911yescharacteristic
1134C2#1172441611yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radical#11723541C2
hypercenterC2×C4D33
hypocenterC33#551
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. #11723677C2semidirect
3. #11723489C2semidirect
4. #11723469C2semidirect
5. C3×#63897C2semidirect
6. C3×#63896C2semidirect
7. C3×#63878C2semidirect
8. #11723025C2semidirect
9. #11723023C2semidirect
10. #11723000C2semidirect
11. #11722988C2semidirect
12. #11722933C2semidirect
13. #11722930C2semidirect
14. #11722906C2semidirect
15. D3×#3722C2semidirect
21. C2×C3×#634C22semidirect
26. C2×C3×#624C22semidirect
30. C3×C4×C3⋊Dic3C22semidirect
32. C32×Dic3⋊C4C22semidirect
33. C32×Dic3⋊C4C22semidirect
36. #88814C22semidirect
37. #88814C22semidirect
38. #88807C22semidirect
39. #88806C22semidirect
40. Dic3⋊(C3⋊Dic3)C22semidirect
44. Dic3×C3⋊Dic3C22semidirect
45. C3×#3724C22semidirect
46. C3×Dic3⋊Dic3C22semidirect
47. C3×Dic3⋊Dic3C22semidirect
50. C3×#3722C22semidirect
53. C3×Dic32C22semidirect
79. #63897D3semidirect
80. #63896D3semidirect
87. #63878D3semidirect
141. C2×#634C2×D3semidirect
166. C2×#624C2×D3semidirect
186. C4×C3⋊Dic3C2×D3semidirect
208. C3×Dic3⋊C4C2×D3semidirect
209. C3×Dic3⋊C4C2×D3semidirect
210. C3×Dic3⋊C4C2×D3semidirect
211. C3×Dic3⋊C4C2×D3semidirect
220. #3724C2×D3semidirect
227. Dic3⋊Dic3C2×D3semidirect
228. Dic3⋊Dic3C2×D3semidirect
241. #3722C2×D3semidirect
258. Dic32C2×D3semidirect
570. Dic3⋊C4D32semidirect
571. Dic3⋊C4D32semidirect
714. C33#551semidirect
1026. C32#5527semidirect
1027. C32#5637semidirect
1028. C32#5659semidirect
1125. C3#10594166semidirect
1126. C3#10594644semidirect
1127. C3#10594653semidirect

Maximal subgroups

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

subgroupindex
#117236772
#117235412
#117234892
#117234692
C3×#638972
C3×#638962
C3×#638782
#117230252
#117230232
#117230002
#117229882
#117229332
#117229302
#117229062
D3×#37222
#105946533
#105946443
#105941663