Finite Group Databasebeta

← #13171918

Subgroups — #13171918

Order 1728.

1218 conjugacy classes of subgroups.

The subgroup lattice has 1120 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723725C211yesmaximal, characteristic, complemented
2#11723631C211yesmaximal, characteristic, complemented
3#11723605C211yesmaximal, characteristic, complemented
4#11723596C211yesmaximal, characteristic, complemented
5C3×Dic3×#67C211yesmaximal, characteristic, complemented
6C3×#63958C211yesmaximal, characteristic, complemented
7C3×#63952C211yesmaximal, characteristic, complemented
8#11723020C211yesmaximal, characteristic, complemented
9#11723011C211yesmaximal, characteristic, complemented
10#11722986C211yesmaximal, characteristic, complemented
11#11722957C211yesmaximal, characteristic, complemented
12#11722936C211yesmaximal, characteristic, complemented
13#11722934C211yesmaximal, characteristic, complemented
14#11722915C211yesmaximal, characteristic, complemented
15#11722911C211yesmaximal, characteristic, complemented
16#10595122—31nomaximal
17#10594943—31nomaximal
18#10594198—31nomaximal
19C2×C3×#638C2211yescharacteristic
20C2×C3×#638C2211yescharacteristic
21C2×C32×#67C2211yescharacteristic
22C22×C32×Dic3C2211yescharacteristic
23C2×#6295C2211yescharacteristic
24C2×#6294C2211yescharacteristic
25C2×#6290C2211yescharacteristic
26C2×Dic3×C3⋊D3C2211yescharacteristic
27C2×C3×#626C2211yescharacteristic
28C2×C3×#624C2211yescharacteristic
29C2×C3×#624C2211yescharacteristic
30C2×C3×D3×Dic3C2211yescharacteristic
31#88864C2211yescharacteristic
32C3×#3757C2211yescharacteristic
33C32×#217C2211yescharacteristic
34#88815C2211yescharacteristic
35#88814C2211yescharacteristic
36#88807C2211yescharacteristic
37#88806C2211yescharacteristic
38#88806C2211yescharacteristic
39#88806C2211yescharacteristic
40Dic3⋊(C3⋊Dic3)C2211yescharacteristic
41Dic3⋊(C3⋊Dic3)C2211yescharacteristic
42#88803C2211yescharacteristic
43#88803C2211yescharacteristic
44(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
45Dic3×C3⋊Dic3C2211yescharacteristic
46C3×#3724C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×#3722C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×Dic32C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64147—31no—
55#64138—31no—
56#64088—31no—
57C3×#938—31no—
58C3×D4×Dic3—31no—
59C3×C4×#67—31no—
60C3×C4×#67—31no—
61C3×#884—31no—
62C3×#67⋊C4—31no—
63Dic3×#67D311yescharacteristic, complemented
64#63971—31no—
65#63970—31no—
66#63970—31no—
67#63970—31no—
68#63970—61no—
69#63961—31no—
70#63961—31no—
71#63961—31no—
72#63961—61no—
73#63958—31no—
74#63958—31no—
75#63958D311yescharacteristic, complemented
76#63956—31no—
77#63956—31no—
78#63956—31no—
79#63956—61no—
80#63952—31no—
81#63952D311yescharacteristic, complemented
82#63908—31no—
83#63906—31no—
84C4×#626—31no—
85#63902—31no—
86#63900—31no—
87#63884—31no—
88#63880—31no—
89#63879—31no—
90#63879—31no—
91D3×Dic3⋊C4—31no—
92D3×Dic3⋊C4—31no—
93#63869—31no—
94#63867—31no—
95#63859—31no—
96#63859—31no—
97#63855—31no—
98#63850—31no—
99#63845—31no—
100#63841—31no—
101#63836—31no—
102C23×C33C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C3×C3⋊D3C2311yescharacteristic
105C22×C32×D3C2311yescharacteristic
106C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
107C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
108C3×#638—22no—
109C3×#638—41no—
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C32×#67—22no—
115C2×C32×Dic3—41no—
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121#6295—22no—
122#6294—41no—
123#6290—22no—
124Dic3×C3⋊D3—22no—
125C3×#626—41no—
126C3×#624—22no—
127C3×#624—41no—
128C3×D3×Dic3—41no—
129#5614—91no—
130#5558—91no—
131#5540—91no—
132C2×C32×D4—31no—
133C22×C32×C4—31no—
134C2×#638—31no—
135C2×#638C2×D311yescharacteristic
136C2×#638C2×D311yescharacteristic
137C2×C4×C3⋊D3—31no—
138C2×C3×#67—21no—
139C2×C3×#67—31no—
140C2×C3×#67—31no—
141C2×C3×#67—31no—
142C2×C3×#67—31no—
143C2×C3×#67—31no—
144C2×C3×#67—61no—
145C2×C3×#67—61no—
146C2×C3×#67C2×D311yescharacteristic
147C2×C3×#67C2×D311yescharacteristic
148C22×C3×Dic3—21no—
149C22×C3×Dic3—31no—
150C22×C3×Dic3C2×D311yescharacteristic
151C22×C3×Dic3C2×D311yescharacteristic
152C2×C3×D12—31no—
153C2×C3×C4×D3—31no—
154C2×C3×C4×D3—31no—
155C2×C3×C4×D3—31no—
156C2×C3×C4×D3—31no—
157C2×C3×C4×D3—31no—
158C2×#626—31no—
159C2×#626—31no—
160C2×#626C2×D311yescharacteristic
161C2×#625—31no—
162C2×#625—31no—
163C2×#625—31no—
164C2×#625—61no—
165C2×#624—31no—
166C2×#624C2×D311yescharacteristic
167C2×#624C2×D311yescharacteristic
168C2×D3×Dic3—31no—
169C2×D3×Dic3—31no—
170C2×D3×Dic3—31no—
171C2×D3×Dic3—31no—
172C2×D3×Dic3—61no—
173C2×D3×Dic3C2×D311yescharacteristic
174C32×C22⋊C4—31no—
175#3757—31no—
176#3757—31no—
177#3757—31no—
178#3757—31no—
179#3757—61no—
180#3757—61no—
181#3757—61no—
182#3757—121no—
183#3757C2×D311yescharacteristic
184#3752—31no—
185#3752—31no—
186C4⋊(C3⋊Dic3)—31no—
187C4⋊(C3⋊Dic3)—31no—
188#3750—31no—
189#3750—31no—
190#3750—31no—
191#3750—31no—
192C4×C3⋊Dic3—31no—
193C3×#217—21no—
194C3×#217—31no—
195C3×#217—31no—
196C3×#217—31no—
197C3×#217—31no—
198C3×#217—61no—
199C3×#217C2×D311yescharacteristic
200C3×#217C2×D311yescharacteristic
201C3×(C2×D3)⋊C4—31no—
202C3×(C2×D3)⋊C4—31no—
203C3×(C2×D3)⋊C4—31no—
204C3×(C2×D3)⋊C4—31no—
205C3×C4⋊Dic3—31no—
206C3×C4⋊Dic3—31no—
207C3×Dic3⋊C4—31no—
208C3×Dic3⋊C4—31no—
209C3×Dic3⋊C4—31no—
210C3×Dic3⋊C4—31no—
211C3×C4×Dic3—31no—
212C3×C4×Dic3—31no—
213C3×C4×Dic3—31no—
214C3×C4×Dic3—31no—
215#3724—31no—
216#3724—31no—
217#3724—31no—
218#3724—31no—
219#3724—31no—
220#3724—31no—
221#3724—31no—
222#3724—61no—
223#3724—61no—
224#3724—61no—
225#3724C2×D311yescharacteristic
226Dic3⋊Dic3—31no—
227Dic3⋊Dic3—31no—
228Dic3⋊Dic3—31no—
229Dic3⋊Dic3—31no—
230Dic3⋊Dic3—31no—
231Dic3⋊Dic3—31no—
232Dic3⋊Dic3—31no—
233Dic3⋊Dic3—31no—
234Dic3⋊Dic3—61no—
235Dic3⋊Dic3—61no—
236Dic3⋊Dic3—61no—
237Dic3⋊Dic3C2×D311yescharacteristic
238Dic3⋊Dic3C2×D311yescharacteristic
239#3722—31no—
240#3722C2×D311yescharacteristic
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—61no—
250(C2×D3)⋊Dic3—61no—
251(C2×D3)⋊Dic3—61no—
252(C2×D3)⋊Dic3C2×D311yescharacteristic
253(C2×D3)⋊Dic3C2×D311yescharacteristic
254Dic32—31no—
255Dic32—31no—
256Dic32—61no—
257Dic32C2×D311yescharacteristic
258Dic32C2×D311yescharacteristic
259C22×C33—21no—
260C22×C33—21no—
261C22×C33—21no—
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#4112yes—
269C2×C32×D3—21no—
270C2×C32×D3—21no—
271C2×C32×D3—21no—
272C3⋊(C3⋊Dic3)—21no—
273C3⋊(C3⋊Dic3)—21no—
274C3×C3⋊Dic3—21no—
275C3×C3⋊Dic3—21no—
276C3×C3⋊Dic3—21no—
277C3×C3⋊Dic3—21no—
278C32×Dic3—21no—
279C32×Dic3—21no—
280C32×Dic3—21no—
281C32×Dic3—21no—
282C32×Dic3#4112yes—
283C3×#121—91no—
284C3×C4×D4—91no—
285C3×C4×D4—91no—
286#939—91no—
287#939—91no—
288#938—31no—
289#938—91no—
290#938—91no—
291#938—91no—
292#938—91no—
293#938—181no—
294#935—91no—
295#935—91no—
296D4×Dic3—31no—
297#930—91no—
298#929—91no—
299#929—91no—
300#929—91no—
301#929—181no—
302C4×#67—31no—
303C4×#67—31no—
304C4×#67—91no—
305C4×#67—91no—
306#926—91no—
307C2×Dic3⋊C4—91no—
308#894—91no—
309#892—91no—
310D3×C4⋊C4—91no—
311D3×C4⋊C4—91no—
312#890—91no—
313#889—91no—
314#884—31no—
315#884—91no—
316#884—91no—
317#67⋊C4—31no—
318#67⋊C4—91no—
319#67⋊C4—91no—
320#67⋊C4—91no—
321#879—91no—
322#879—91no—
323#879—91no—
324#879—91no—
325#879—91no—
326#879—181no—
327#876—91no—
328C4×D12—91no—
329#872—91no—
330#870—91no—
331C23×C32—21no—
332C23×C32—21no—
333C23×C32—21no—
334C23×C32—31no—
335C23×C32—41no—
336C23×C32C22×D311yescharacteristic
337C23×C32C22×D311yescharacteristic
338C23×C32C22×D311yescharacteristic
339C22×C3⋊D3C22×D311yescharacteristic
340C22×C3⋊D3C22×D311yescharacteristic
341C22×C3×D3—21no—
342C22×C3×D3—31no—
343C22×C3×D3—31no—
344C22×C3×D3—31no—
345C22×C3×D3—31no—
346C22×C3×D3—61no—
347C22×C3×D3—61no—
348C22×C3×D3C22×D311yescharacteristic
349C22×C3×D3C22×D311yescharacteristic
350C32×D4—62no—
351C2×C32×C4—31no—
352C2×C32×C4—31no—
353C2×C32×C4—31no—
354C2×C32×C4—31no—
355C2×C32×C4—31no—
356C2×C32×C4—121no—
357#638—22no—
358#638—41no—
359#638—62no—
360C2×C3⋊Dic3—31no—
361C2×C3⋊Dic3—31no—
362C2×C3⋊Dic3—31no—
363C2×C3⋊Dic3—31no—
364C2×C3⋊Dic3—31no—
365C2×C3⋊Dic3—31no—
366C2×C3⋊Dic3—61no—
367C2×C3⋊Dic3—61no—
368C2×C3⋊Dic3—61no—
369C2×C3⋊Dic3—61no—
370C2×C3⋊Dic3—61no—
371C2×C3⋊Dic3—61no—
372C2×C3⋊Dic3—121no—
373C2×C3⋊Dic3—121no—
374C2×C3⋊Dic3C22×D311yescharacteristic
375C2×C3⋊Dic3C22×D311yescharacteristic
376C2×C3⋊Dic3C22×D311yescharacteristic
377C2×C3⋊Dic3C22×D311yescharacteristic
378C4×C3⋊D3—62no—
379C3×#67—22no—
380C3×#67—22no—
381C3×#67—42no—
382C3×#67—62no—
383C3×#67—62no—
384C3×#67—122no—
385C3×#67—121no—
386C3×#67—121no—
387C3×#67—121no—
388C3×#67—122no—
389C2×C3×Dic3—21no—
390C2×C3×Dic3—21no—
391C2×C3×Dic3—21no—
392C2×C3×Dic3—21no—
393C2×C3×Dic3—21no—
394C2×C3×Dic3—31no—
395C2×C3×Dic3—31no—
396C2×C3×Dic3—31no—
397C2×C3×Dic3—31no—
398C2×C3×Dic3—31no—
399C2×C3×Dic3—31no—
400C2×C3×Dic3—31no—
401C2×C3×Dic3—31no—
402C2×C3×Dic3—41no—
403C2×C3×Dic3—41no—
404C2×C3×Dic3—42no—
405C2×C3×Dic3—61no—
406C2×C3×Dic3—61no—
407C2×C3×Dic3—61no—
408C2×C3×Dic3—61no—
409C2×C3×Dic3—121no—
410C2×C3×Dic3C22×D311yescharacteristic
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
420C3×D12—121no—
421C3×C4×D3—62no—
422C3×C4×D3—62no—
423C3×C4×D3—121no—
424C3×C4×D3—121no—
425C3×C4×D3—121no—
426#626—41no—
427#626—62no—
428#626—62no—
429#625—62no—
430#625—62no—
431#625—62no—
432#625—122no—
433#624—22no—
434#624—41no—
435#624—121no—
436D3×Dic3—41no—
437D3×Dic3—62no—
438D3×Dic3—62no—
439D3×Dic3—122no—
440D3×Dic3—121no—
441D3×Dic3—121no—
442#553—271noSylow
443C2×C33—41no—
444C2×C33C2×#4111yescharacteristic
445C2×C33C2×#4111yescharacteristic
446C2×C33H(5,𝔽2)11yescharacteristic
447C3×C3⋊D3—22no—
448C3×C3⋊D3—41no—
449C32×D3—41no—
450C2×C3×D4—31no—
451C2×C3×D4—31no—
452C2×C3×D4—61no—
453C2×C3×D4—91no—
454C2×C3×D4—91no—
455C2×C3×D4—91no—
456C22×C3×C4—31no—
457C22×C3×C4—31no—
458C22×C3×C4—61no—
459C22×C3×C4—91no—
460C22×C3×C4—91no—
461C22×C3×C4—91no—
462C2×#67—31no—
463C2×#67—31no—
464C2×#67—31no—
465C2×#67—31no—
466C2×#67—31no—
467C2×#67—61no—
468C2×#67—61no—
469C2×#67—91no—
470C2×#67—91no—
471C2×#67—91no—
472C2×#67—91no—
473C2×#67—91no—
474C2×#67—181no—
475C2×#67D3211yescharacteristic
476C22×Dic3—31no—
477C22×Dic3—91no—
478C22×Dic3—91no—
479C22×Dic3D3211yescharacteristic
480C2×D12—31no—
481C2×D12—91no—
482C2×C4×D3—31no—
483C2×C4×D3—31no—
484C2×C4×D3—31no—
485C2×C4×D3—31no—
486C2×C4×D3—31no—
487C2×C4×D3—91no—
488C2×C4×D3—91no—
489C2×C4×D3—91no—
490C2×C4×D3—91no—
491C2×C4×D3—181no—
492C3×C4⋊C4—91no—
493C3×C4⋊C4—91no—
494C3×C4⋊C4—91no—
495C3×C22⋊C4—31no—
496C3×C22⋊C4—31no—
497C3×C22⋊C4—61no—
498C3×C22⋊C4—91no—
499C3×C22⋊C4—91no—
500C3×C22⋊C4—91no—
501C3×C22⋊C4—91no—
502C3×C42—91no—
503C3×C42—91no—
504#217—31no—
505#217—31no—
506#217—31no—
507#217—31no—
508#217—61no—
509#217—91no—
510#217—91no—
511#217—91no—
512#217—91no—
513#217—91no—
514#217—91no—
515#217—91no—
516#217—91no—
517#217—181no—
518#217—181no—
519#217—181no—
520#217—181no—
521#217—361no—
522#217D3211yescharacteristic
523(C2×D3)⋊C4—31no—
524(C2×D3)⋊C4—31no—
525(C2×D3)⋊C4—31no—
526(C2×D3)⋊C4—31no—
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—181no—
535(C2×D3)⋊C4—181no—
536C4⋊Dic3—31no—
537C4⋊Dic3—31no—
538C4⋊Dic3—91no—
539C4⋊Dic3—91no—
540C4⋊Dic3—91no—
541C4⋊Dic3—91no—
542C4⋊Dic3—91no—
543C4⋊Dic3—91no—
544C4⋊Dic3—181no—
545C4⋊Dic3—181no—
546Dic3⋊C4—31no—
547Dic3⋊C4—31no—
548Dic3⋊C4—31no—
549Dic3⋊C4—31no—
550Dic3⋊C4—91no—
551Dic3⋊C4—91no—
552Dic3⋊C4—91no—
553Dic3⋊C4—91no—
554Dic3⋊C4—91no—
555Dic3⋊C4—91no—
556Dic3⋊C4—91no—
557Dic3⋊C4—91no—
558Dic3⋊C4—91no—
559Dic3⋊C4—91no—
560Dic3⋊C4—91no—
561Dic3⋊C4—91no—
562Dic3⋊C4—91no—
563Dic3⋊C4—91no—
564Dic3⋊C4—91no—
565Dic3⋊C4—181no—
566Dic3⋊C4—181no—
567Dic3⋊C4—181no—
568Dic3⋊C4—181no—
569C4×Dic3—31no—
570C4×Dic3—31no—
571C4×Dic3—31no—
572C4×Dic3—31no—
573C4×Dic3—91no—
574C4×Dic3—91no—
575C4×Dic3—91no—
576C4×Dic3—181no—
577C22×C32—21no—
578C22×C32—22no—
579C22×C32—21no—
580C22×C32—21no—
581C22×C32—21no—
582C22×C32—21no—
583C22×C32—21no—
584C22×C32—21no—
585C22×C32—21no—
586C22×C32—21no—
587C22×C32—21no—
588C22×C32—21no—
589C22×C32—21no—
590C22×C32—41no—
591C22×C32—41no—
592C22×C32—41no—
593C22×C32—42no—
594C22×C32—41no—
595C22×C32—41no—
596C22×C32—41no—
597C22×C32—41no—
598C22×C32—41no—
599C22×C32—41no—
600C22×C32—61no—
601C22×C32—61no—
602C22×C32—61no—
603C22×C32—81no—
604C22×C32—81no—
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#23512yes—
614C2×C3×D3—21no—
615C2×C3×D3—21no—
616C2×C3×D3—21no—
617C2×C3×D3—21no—
618C2×C3×D3—21no—
619C2×C3×D3—21no—
620C2×C3×D3—32no—
621C2×C3×D3—32no—
622C2×C3×D3—41no—
623C2×C3×D3—41no—
624C2×C3×D3—41no—
625C2×C3×D3—62no—
626C2×C3×D3—61no—
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—121no—
637C2×C3×D3—121no—
638C2×C3×D3—121no—
639C2×C3×D3—121no—
640C2×C3×D3—121no—
641C32×C4—32no—
642C32×C4—61no—
643C32×C4—61no—
644C32×C4—61no—
645C32×C4—61no—
646C3⋊Dic3—21no—
647C3⋊Dic3—21no—
648C3⋊Dic3—21no—
649C3⋊Dic3—21no—
650C3⋊Dic3—61no—
651C3⋊Dic3—61no—
652C3⋊Dic3—61no—
653C3⋊Dic3—61no—
654C3⋊Dic3—61no—
655C3⋊Dic3—61no—
656C3⋊Dic3—121no—
657C3⋊Dic3—121no—
658C3⋊Dic3—121no—
659C3⋊Dic3—121no—
660C3⋊Dic3—121no—
661C3⋊Dic3—121no—
662C3⋊Dic3—241no—
663C3⋊Dic3—241no—
664C3×Dic3—21no—
665C3×Dic3—21no—
666C3×Dic3—21no—
667C3×Dic3—21no—
668C3×Dic3—21no—
669C3×Dic3—21no—
670C3×Dic3—21no—
671C3×Dic3—21no—
672C3×Dic3—22no—
673C3×Dic3—41no—
674C3×Dic3—41no—
675C3×Dic3—41no—
676C3×Dic3—41no—
677C3×Dic3—61no—
678C3×Dic3—61no—
679C3×Dic3—61no—
680C3×Dic3—61no—
681C3×Dic3—61no—
682C3×Dic3—61no—
683C3×Dic3—61no—
684C3×Dic3—61no—
685C3×Dic3—121no—
686C3×Dic3—121no—
687C3×Dic3—121no—
688C3×Dic3—121no—
689C3×Dic3#23512yes—
690C3×Dic3#23712yes—
691#126—271no—
692#126—271no—
693#125—271no—
694#123—271no—
695#123—271no—
696#121—91no—
697#121—271no—
698#121—271no—
699#121—271no—
700C4×D4—91no—
701C4×D4—91no—
702C4×D4—271no—
703C4×D4—271no—
704#117—271no—
705C2×C4⋊C4—271no—
706C33#55311yescharacteristic, complemented, Sylow
707C23×C3—21no—
708C23×C3—21no—
709C23×C3—21no—
710C23×C3—31no—
711C23×C3—31no—
712C23×C3—41no—
713C23×C3—61no—
714C23×C3—91no—
715C23×C3—91no—
716C23×C3C2×D3211yescharacteristic
717C23×C3C2×D3211yescharacteristic
718C23×C3C2×D3211yescharacteristic
719C22×D3—31no—
720C22×D3—31no—
721C22×D3—31no—
722C22×D3—31no—
723C22×D3—61no—
724C22×D3—61no—
725C22×D3C2×D3211yescharacteristic
726C3×D4—62no—
727C3×D4—62no—
728C3×D4—122no—
729C3×D4—182no—
730C3×D4—361no—
731C3×D4—361no—
732C2×C3×C4—31no—
733C2×C3×C4—31no—
734C2×C3×C4—31no—
735C2×C3×C4—31no—
736C2×C3×C4—31no—
737C2×C3×C4—31no—
738C2×C3×C4—31no—
739C2×C3×C4—31no—
740C2×C3×C4—31no—
741C2×C3×C4—31no—
742C2×C3×C4—61no—
743C2×C3×C4—61no—
744C2×C3×C4—61no—
745C2×C3×C4—61no—
746C2×C3×C4—61no—
747C2×C3×C4—91no—
748C2×C3×C4—91no—
749C2×C3×C4—91no—
750C2×C3×C4—91no—
751C2×C3×C4—121no—
752C2×C3×C4—121no—
753C2×C3×C4—122no—
754C2×C3×C4—182no—
755C2×C3×C4—361no—
756C2×C3×C4—361no—
757#67—22no—
758#67—62no—
759#67—62no—
760#67—122no—
761#67—121no—
762#67—121no—
763#67—121no—
764#67—122no—
765#67—182no—
766#67—182no—
767#67—182no—
768#67—182no—
769#67—182no—
770#67—362no—
771C2×Dic3—31no—
772C2×Dic3—31no—
773C2×Dic3—31no—
774C2×Dic3—31no—
775C2×Dic3—31no—
776C2×Dic3—31no—
777C2×Dic3—31no—
778C2×Dic3—31no—
779C2×Dic3—41no—
780C2×Dic3—61no—
781C2×Dic3—61no—
782C2×Dic3—61no—
783C2×Dic3—61no—
784C2×Dic3—91no—
785C2×Dic3—91no—
786C2×Dic3—91no—
787C2×Dic3—91no—
788C2×Dic3—91no—
789C2×Dic3—91no—
790C2×Dic3—121no—
791C2×Dic3—181no—
792C2×Dic3—181no—
793C2×Dic3—181no—
794C2×Dic3—181no—
795C2×Dic3—181no—
796C2×Dic3—181no—
797C2×Dic3—182no—
798C2×Dic3—361no—
799C2×Dic3—361no—
800C2×Dic3—361no—
801C2×Dic3C2×D3211yescharacteristic
802C2×Dic3C2×D3211yescharacteristic
803C2×Dic3C2×D3211yescharacteristic
804C2×Dic3C2×D3211yescharacteristic
805C2×Dic3C2×D3211yescharacteristic
806D12—121no—
807D12—182no—
808C4×D3—62no—
809C4×D3—62no—
810C4×D3—121no—
811C4×D3—121no—
812C4×D3—121no—
813C4×D3—182no—
814C4×D3—182no—
815C4×D3—362no—
816C4×D3—361no—
817C4×D3—361no—
818C2×C32—21no—
819C2×C32—21no—
820C2×C32—21no—
821C2×C32—21no—
822C2×C32—21no—
823C2×C32—21no—
824C2×C32—21no—
825C2×C32—21no—
826C2×C32—21no—
827C2×C32—41no—
828C2×C32—41no—
829C2×C32—41no—
830C2×C32—41no—
831C2×C32—42no—
832C2×C32—41no—
833C2×C32—41no—
834C2×C32—81no—
835C2×C32—81no—
836C2×C32—82no—
837C2×C32—121no—
838C2×C32C2×#23511yescharacteristic
839C2×C32C2×#23511yescharacteristic
840C2×C32C2×#23711yescharacteristic
841C2×C32#100411yescharacteristic
842C2×C32#100411yescharacteristic
843C2×C32#100411yescharacteristic
844C2×C32D3×#4111yescharacteristic
845C2×C32D3×#4111yescharacteristic
846C2×C32D3×#4111yescharacteristic
847C3⋊D3—22no—
848C3⋊D3—41no—
849C3×D3—41no—
850C3×D3—41no—
851C3×D3—62no—
852C3×D3—62no—
853C3×D3—81no—
854C3×D3—122no—
855C3×D3—121no—
856C3×D3—121no—
857C3×D3—241no—
858C2×D4—31no—
859C2×D4—91no—
860C2×D4—91no—
861C2×D4—91no—
862C2×D4—271no—
863C2×D4—271no—
864C22×C4—31no—
865C22×C4—91no—
866C22×C4—91no—
867C22×C4—91no—
868C22×C4—271no—
869C22×C4—271no—
870C4⋊C4—91no—
871C4⋊C4—91no—
872C4⋊C4—91no—
873C4⋊C4—271no—
874C4⋊C4—271no—
875C4⋊C4—271no—
876C4⋊C4—271no—
877C4⋊C4—271no—
878C4⋊C4—271no—
879C4⋊C4—271no—
880C22⋊C4—31no—
881C22⋊C4—91no—
882C22⋊C4—91no—
883C22⋊C4—91no—
884C22⋊C4—91no—
885C22⋊C4—271no—
886C22⋊C4—271no—
887C22⋊C4—271no—
888C22⋊C4—271no—
889C22⋊C4—271no—
890C42—91no—
891C42—91no—
892C42—271no—
893C22×C3—22no—
894C22×C3—21no—
895C22×C3—21no—
896C22×C3—21no—
897C22×C3—21no—
898C22×C3—21no—
899C22×C3—21no—
900C22×C3—21no—
901C22×C3—21no—
902C22×C3—21no—
903C22×C3—21no—
904C22×C3—21no—
905C22×C3—21no—
906C22×C3—41no—
907C22×C3—41no—
908C22×C3—41no—
909C22×C3—41no—
910C22×C3—41no—
911C22×C3—41no—
912C22×C3—41no—
913C22×C3—41no—
914C22×C3—42no—
915C22×C3—41no—
916C22×C3—61no—
917C22×C3—61no—
918C22×C3—61no—
919C22×C3—61no—
920C22×C3—61no—
921C22×C3—61no—
922C22×C3—81no—
923C22×C3—81no—
924C22×C3—92no—
925C22×C3—121no—
926C22×C3—121no—
927C22×C3—121no—
928C22×C3—181no—
929C22×C3—181no—
930C22×C3—181no—
931C22×C3—181no—
932C22×C3—181no—
933C22×C3C22×D3211yescharacteristic
934C22×C3C22×D3211yescharacteristic
935C22×C3C22×D3211yescharacteristic
936C2×D3—21no—
937C2×D3—21no—
938C2×D3—21no—
939C2×D3—32no—
940C2×D3—32no—
941C2×D3—62no—
942C2×D3—61no—
943C2×D3—61no—
944C2×D3—61no—
945C2×D3—61no—
946C2×D3—61no—
947C2×D3—61no—
948C2×D3—61no—
949C2×D3—61no—
950C2×D3—61no—
951C2×D3—61no—
952C2×D3—121no—
953C2×D3—121no—
954C2×D3—121no—
955C2×D3—121no—
956C2×D3—121no—
957C3×C4—32no—
958C3×C4—32no—
959C3×C4—62no—
960C3×C4—61no—
961C3×C4—61no—
962C3×C4—61no—
963C3×C4—61no—
964C3×C4—61no—
965C3×C4—61no—
966C3×C4—61no—
967C3×C4—61no—
968C3×C4—121no—
969C3×C4—121no—
970C3×C4—121no—
971C3×C4—121no—
972C3×C4—181no—
973C3×C4—181no—
974C3×C4—181no—
975C3×C4—181no—
976Dic3—21no—
977Dic3—21no—
978Dic3—21no—
979Dic3—21no—
980Dic3—61no—
981Dic3—61no—
982Dic3—61no—
983Dic3—61no—
984Dic3—61no—
985Dic3—61no—
986Dic3—61no—
987Dic3—61no—
988Dic3—121no—
989Dic3—121no—
990Dic3—121no—
991Dic3—121no—
992Dic3—181no—
993Dic3—181no—
994Dic3—181no—
995Dic3—181no—
996Dic3—181no—
997Dic3—181no—
998Dic3—361no—
999Dic3—361no—
1000Dic3—361no—
1001Dic3—361no—
1002Dic3—361no—
1003Dic3—361no—
1004Dic3—721no—
1005Dic3—721no—
1006Dic3#380412yes—
1007C32—21no—
1008C32—21no—
1009C32—21no—
1010C32—41no—
1011C32#554011yescharacteristic, complemented
1012C32#555811yescharacteristic, complemented
1013C32#561411yescharacteristic, complemented
1014C23—31no—
1015C23—91no—
1016C23—91no—
1017C23D3311yescharacteristic
1018D4—62no—
1019D4—182no—
1020D4—361no—
1021D4—361no—
1022D4—542no—
1023D4—542no—
1024C2×C4—31no—
1025C2×C4—31no—
1026C2×C4—31no—
1027C2×C4—31no—
1028C2×C4—31no—
1029C2×C4—91no—
1030C2×C4—91no—
1031C2×C4—91no—
1032C2×C4—91no—
1033C2×C4—121no—
1034C2×C4—182no—
1035C2×C4—271no—
1036C2×C4—271no—
1037C2×C4—361no—
1038C2×C4—361no—
1039C2×C4—542no—
1040C2×C4—1081no—
1041C2×C3—21no—
1042C2×C3—21no—
1043C2×C3—21no—
1044C2×C3—21no—
1045C2×C3—21no—
1046C2×C3—21no—
1047C2×C3—21no—
1048C2×C3—21no—
1049C2×C3—21no—
1050C2×C3—42no—
1051C2×C3—41no—
1052C2×C3—41no—
1053C2×C3—41no—
1054C2×C3—41no—
1055C2×C3—41no—
1056C2×C3—41no—
1057C2×C3—81no—
1058C2×C3—81no—
1059C2×C3—82no—
1060C2×C3—121no—
1061C2×C3—121no—
1062C2×C3—182no—
1063C2×C3—241no—
1064C2×C3—361no—
1065C2×C3D3×#23511yescharacteristic
1066C2×C3D3×#23511yescharacteristic
1067C2×C3D3×#23511yescharacteristic
1068C2×C3D3×#23711yescharacteristic
1069C2×C3#6431211yescharacteristic
1070C2×C3#6431311yescharacteristic
1071C2×C3#6431311yescharacteristic
1072C2×C3C2×#380411yescharacteristic
1073C2×C3#6433011yescharacteristic
1074D3—41no—
1075D3—62no—
1076D3—62no—
1077D3—122no—
1078D3—121no—
1079D3—121no—
1080D3—241no—
1081C22—21no—
1082C22—21no—
1083C22—21no—
1084C22—61no—
1085C22—61no—
1086C22—61no—
1087C22—92no—
1088C22—181no—
1089C22—181no—
1090C22—181no—
1091C22—181no—
1092C22—181no—
1093C22C2×D3311yescharacteristic
1094C4—32no—
1095C4—61no—
1096C4—61no—
1097C4—61no—
1098C4—61no—
1099C4—181no—
1100C4—181no—
1101C4—181no—
1102C4—181no—
1103C4—541no—
1104C4—541no—
1105C3—21no—
1106C3—21no—
1107C3—21no—
1108C3—41no—
1109C3#1059419811yescharacteristic, complemented
1110C3#1059494311yescharacteristic, complemented
1111C3#1059512211yescharacteristic, complemented
1112C2—41no—
1113C2—121no—
1114C2—182no—
1115C2—361no—
1116C2D3×#380411yescharacteristic
1117C2#1172441011yescharacteristic
1118C2#1172441511yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
hypercenterC23D33
hypocenterC33#553
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. #11723725C2semidirect
2. #11723631C2semidirect
3. #11723605C2semidirect
4. #11723596C2semidirect
5. C3×Dic3×#67C2semidirect
6. C3×#63958C2semidirect
7. C3×#63952C2semidirect
8. #11723020C2semidirect
9. #11723011C2semidirect
10. #11722986C2semidirect
11. #11722957C2semidirect
12. #11722936C2semidirect
13. #11722934C2semidirect
14. #11722915C2semidirect
15. #11722911C2semidirect
63. Dic3×#67D3semidirect
75. #63958D3semidirect
81. #63952D3semidirect
706. C33#553semidirect
1011. C32#5540semidirect
1012. C32#5558semidirect
1013. C32#5614semidirect
1109. C3#10594198semidirect
1110. C3#10594943semidirect
1111. C3#10595122semidirect

Maximal subgroups

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

subgroupindex
#117237252
#117236312
#117236052
#117235962
C3×Dic3×#672
C3×#639582
C3×#639522
#117230202
#117230112
#117229862
#117229572
#117229362
#117229342
#117229152
#117229112
#105951223
#105949433
#105941983