Finite Group Databasebeta

← #13168524

Subgroups — #13168524

Order 1728.

1260 conjugacy classes of subgroups.

The subgroup lattice has 1180 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723694C211yesmaximal, characteristic, complemented
2#11723512C211yesmaximal, characteristic, complemented
3#11723493C211yesmaximal, characteristic, complemented
4#11723475C211yesmaximal, characteristic, complemented
5C3×#63916C211yesmaximal, characteristic, complemented
6C3×#63886C211yesmaximal, characteristic, complemented
7C3×#63846C211yesmaximal, characteristic, complemented
8#11723030C211yesmaximal, characteristic, complemented
9#11722996C211yesmaximal, characteristic, complemented
10#11722990C211yesmaximal, characteristic, complemented
11#11722963C211yesmaximal, characteristic, complemented
12#11722962C211yesmaximal, characteristic, complemented
13#11722959C211yesmaximal, characteristic, complemented
14#11722929C211yesmaximal, characteristic, complemented
15#11722913C211yesmaximal, characteristic, complemented
16#10595250—31nomaximal
17#10594563—31nomaximal
18#10594501—31nomaximal
19C2×C3×C4×C3⋊D3C2211yescharacteristic
20C2×C32×D12C2211yescharacteristic
21C2×#6295C2211yescharacteristic
22C2×#6292C2211yescharacteristic
23C2×#6292C2211yescharacteristic
24C2×#6291C2211yescharacteristic
25C2×#6291C2211yescharacteristic
26C2×#6289C2211yescharacteristic
27C2×Dic3×C3⋊D3C2211yescharacteristic
28C2×D3×C3⋊Dic3C2211yescharacteristic
29C2×C3×#626C2211yescharacteristic
30C2×C3×#626C2211yescharacteristic
31C2×C3×#626C2211yescharacteristic
32C2×C3×#626C2211yescharacteristic
33C2×C3×D3×Dic3C2211yescharacteristic
34#88859C2211yescharacteristic
35C3×#3752C2211yescharacteristic
36C3×#3750C2211yescharacteristic
37C32×C4⋊Dic3C2211yescharacteristic
38C32×Dic3⋊C4C2211yescharacteristic
39#88815C2211yescharacteristic
40#88814C2211yescharacteristic
41#88814C2211yescharacteristic
42#88807C2211yescharacteristic
43#88804C2211yescharacteristic
44#88803C2211yescharacteristic
45(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
46Dic3×C3⋊Dic3C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×Dic3⋊Dic3C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64148—31no—
55#64103—31no—
56#64102—31no—
57C3×#939—31no—
58C3×#938—31no—
59C3×#895—31no—
60C3×#895—31no—
61C3×#890—31no—
62C3×#889—31no—
63#63979—31no—
64#63978—31no—
65#63975—31no—
66#67⋊Dic3—31no—
67#63970—31no—
68#63962—31no—
69#63958—31no—
70#63955—31no—
71#63916—31no—
72#63916—31no—
73#63916D311yescharacteristic, complemented
74#63911—31no—
75#63911—31no—
76#63910—31no—
77#63909—31no—
78#63905—31no—
79#63904—31no—
80#63904—31no—
81#63904—61no—
82#63898—31no—
83#63890—31no—
84#63890—31no—
85#63890—31no—
86#63890—61no—
87#63886—31no—
88#63886—31no—
89#63886—31no—
90#63886—31no—
91#63886—61no—
92#63886D311yescharacteristic, complemented
93#63884—31no—
94#63881—31no—
95#63877—31no—
96#63855—31no—
97#63854—31no—
98#63853—31no—
99#63853—31no—
100#63850—31no—
101#63846D311yescharacteristic, complemented
102C22×C3⋊(C3⋊D3)C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C3×C3⋊D3C2311yescharacteristic
105C22×C32×D3C2311yescharacteristic
106C22×C32×D3C2311yescharacteristic
107C2×C33×C4C2311yescharacteristic
108C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C3×C4×C3⋊D3—41no—
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118C32×D12—41no—
119#6295—41no—
120#6292—22no—
121#6292—41no—
122#6291—41no—
123#6291—41no—
124#6289—41no—
125Dic3×C3⋊D3—41no—
126D3×C3⋊Dic3—41no—
127C3×#626—22no—
128C3×#626—41no—
129C3×#626—41no—
130C3×#626—41no—
131C3×D3×Dic3—22no—
132#5697—91no—
133#5619—91no—
134#5615—91no—
135C2×C32×D4—31no—
136C2×#638—31no—
137C2×#638—31no—
138C22×C3⋊Dic3—31no—
139C2×C4⋊(C3⋊D3)—31no—
140C2×C4⋊(C3⋊D3)—31no—
141C2×C4×C3⋊D3—31no—
142C2×C4×C3⋊D3—31no—
143C2×C4×C3⋊D3C2×D311yescharacteristic
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×D12—31no—
154C2×C3×D12C2×D311yescharacteristic
155C2×C3×D12C2×D311yescharacteristic
156C2×C3×C4×D3—31no—
157C2×C3×C4×D3—31no—
158C2×C3×C4×D3—31no—
159C2×C3×C4×D3—61no—
160C2×#626—31no—
161C2×#626—31no—
162C2×#626—31no—
163C2×#626—31no—
164C2×#626—31no—
165C2×#626—31no—
166C2×#626—31no—
167C2×#626—31no—
168C2×#626—31no—
169C2×#626—31no—
170C2×#626—61no—
171C2×#626—61no—
172C2×#626—61no—
173C2×#626—61no—
174C2×#626C2×D311yescharacteristic
175C2×#626C2×D311yescharacteristic
176C2×#626C2×D311yescharacteristic
177C2×#626C2×D311yescharacteristic
178C2×#625—31no—
179C2×#624—31no—
180C2×#624—31no—
181C2×#624—61no—
182C2×D3×Dic3—31no—
183C2×D3×Dic3—31no—
184C2×D3×Dic3—31no—
185C2×D3×Dic3—31no—
186C2×D3×Dic3—61no—
187C2×D3×Dic3—61no—
188C2×D3×Dic3C2×D311yescharacteristic
189C32×C4⋊C4—31no—
190C32×C4⋊C4—31no—
191#3757—31no—
192#3752—31no—
193#3752—31no—
194#3752—31no—
195#3752—31no—
196#3752—31no—
197#3752—61no—
198#3752—61no—
199#3752—61no—
200#3752—121no—
201#3752C2×D311yescharacteristic
202#3750—31no—
203#3750C2×D311yescharacteristic
204C4×C3⋊Dic3—31no—
205C3×#217—31no—
206C3×#217—31no—
207C3×#217—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—61no—
214C3×C4⋊Dic3—21no—
215C3×C4⋊Dic3—31no—
216C3×C4⋊Dic3—31no—
217C3×C4⋊Dic3—31no—
218C3×C4⋊Dic3C2×D311yescharacteristic
219C3×C4⋊Dic3C2×D311yescharacteristic
220C3×Dic3⋊C4—21no—
221C3×Dic3⋊C4—31no—
222C3×Dic3⋊C4—31no—
223C3×Dic3⋊C4—31no—
224C3×Dic3⋊C4—31no—
225C3×Dic3⋊C4—31no—
226C3×Dic3⋊C4—61no—
227C3×Dic3⋊C4C2×D311yescharacteristic
228C3×Dic3⋊C4C2×D311yescharacteristic
229C3×C4×Dic3—31no—
230C3×C4×Dic3—31no—
231#3724—31no—
232Dic3⋊Dic3—31no—
233Dic3⋊Dic3—31no—
234Dic3⋊Dic3—31no—
235Dic3⋊Dic3—31no—
236Dic3⋊Dic3—61no—
237Dic3⋊Dic3C2×D311yescharacteristic
238Dic3⋊Dic3C2×D311yescharacteristic
239Dic3⋊Dic3C2×D311yescharacteristic
240#3722—31no—
241#3722—31no—
242#3722—31no—
243#3722—31no—
244#3722—61no—
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—31no—
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
258Dic32—31no—
259Dic32—31no—
260Dic32—61no—
261Dic32C2×D311yescharacteristic
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×C3×C3⋊D3—21no—
270C2×C3×C3⋊D3—21no—
271C2×C3×C3⋊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—21no—
278C33×C4—21no—
279C3⋊(C3⋊Dic3)—21no—
280C3×C3⋊Dic3—21no—
281C3×C3⋊Dic3—21no—
282C3×C3⋊Dic3—21no—
283C3×C3⋊Dic3—21no—
284C32×Dic3—21no—
285C32×Dic3—21no—
286C32×Dic3—21no—
287C32×Dic3#4112yes—
288C3×#125—91no—
289C3×#121—91no—
290C3×#121—91no—
291#940—91no—
292#940—91no—
293#939—31no—
294#939—91no—
295#939—91no—
296#939—91no—
297#939—91no—
298#939—181no—
299#938—31no—
300#938—91no—
301#938—91no—
302#935—91no—
303D4×Dic3—91no—
304#930—91no—
305#929—91no—
306C4×#67—91no—
307#926—91no—
308#895—31no—
309#895—31no—
310#895—91no—
311#895—91no—
312#895—91no—
313#895—91no—
314#894—91no—
315#894—91no—
316#894—91no—
317#894—91no—
318#894—91no—
319#894—181no—
320#893—91no—
321#893—91no—
322#893—91no—
323#893—181no—
324#890—31no—
325#889—31no—
326#886—91no—
327#886—91no—
328#884—91no—
329#883—91no—
330#883—91no—
331#883—91no—
332#67⋊C4—91no—
333#877—91no—
334#874—91no—
335#872—91no—
336C23×C32—31no—
337C23×C32—31no—
338C22×C3⋊D3—31no—
339C22×C3⋊D3—31no—
340C22×C3⋊D3—31no—
341C22×C3⋊D3—61no—
342C22×C3⋊D3—61no—
343C22×C3⋊D3—61no—
344C22×C3⋊D3—121no—
345C22×C3⋊D3C22×D311yescharacteristic
346C22×C3⋊D3C22×D311yescharacteristic
347C22×C3×D3—21no—
348C22×C3×D3—21no—
349C22×C3×D3—31no—
350C22×C3×D3—31no—
351C22×C3×D3—31no—
352C22×C3×D3—31no—
353C22×C3×D3—61no—
354C22×C3×D3—61no—
355C22×C3×D3C22×D311yescharacteristic
356C22×C3×D3C22×D311yescharacteristic
357C22×C3×D3C22×D311yescharacteristic
358C22×C3×D3C22×D311yescharacteristic
359C32×D4—121no—
360C2×C32×C4—21no—
361C2×C32×C4—21no—
362C2×C32×C4—21no—
363C2×C32×C4—31no—
364C2×C32×C4—31no—
365C2×C32×C4—31no—
366C2×C32×C4—31no—
367C2×C32×C4—41no—
368C2×C32×C4C22×D311yescharacteristic
369C2×C32×C4C22×D311yescharacteristic
370C2×C32×C4C22×D311yescharacteristic
371#638—121no—
372#638—121no—
373C2×C3⋊Dic3—31no—
374C2×C3⋊Dic3—31no—
375C2×C3⋊Dic3—31no—
376C2×C3⋊Dic3—61no—
377C2×C3⋊Dic3—61no—
378C2×C3⋊Dic3—61no—
379C2×C3⋊Dic3—121no—
380C2×C3⋊Dic3—121no—
381C2×C3⋊Dic3C22×D311yescharacteristic
382C2×C3⋊Dic3C22×D311yescharacteristic
383C2×C3⋊Dic3C22×D311yescharacteristic
384C2×C3⋊Dic3C22×D311yescharacteristic
385C4⋊(C3⋊D3)—62no—
386C4⋊(C3⋊D3)—121no—
387C4×C3⋊D3—41no—
388C4×C3⋊D3—121no—
389C4×C3⋊D3—121no—
390C3×#67—62no—
391C3×#67—121no—
392C3×#67—121no—
393C3×#67—121no—
394C2×C3×Dic3—21no—
395C2×C3×Dic3—21no—
396C2×C3×Dic3—21no—
397C2×C3×Dic3—21no—
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—31no—
406C2×C3×Dic3—61no—
407C2×C3×Dic3—61no—
408C2×C3×Dic3—61no—
409C2×C3×Dic3—61no—
410C2×C3×Dic3—62no—
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
419C3×D12—41no—
420C3×D12—41no—
421C3×D12—42no—
422C3×D12—62no—
423C3×D12—121no—
424C3×D12—121no—
425C3×D12—121no—
426C3×C4×D3—62no—
427C3×C4×D3—121no—
428C3×C4×D3—121no—
429C3×C4×D3—122no—
430#626—22no—
431#626—41no—
432#626—41no—
433#626—41no—
434#626—64no—
435#626—62no—
436#626—62no—
437#626—121no—
438#626—121no—
439#626—122no—
440#626—121no—
441#626—121no—
442#626—121no—
443#626—121no—
444#626—122no—
445#626—121no—
446#626—121no—
447#626—122no—
448#625—121no—
449#624—121no—
450#624—121no—
451#624—122no—
452D3×Dic3—22no—
453D3×Dic3—121no—
454D3×Dic3—121no—
455D3×Dic3—122no—
456D3×Dic3—121no—
457D3×Dic3—121no—
458D3×Dic3—122no—
459#540—271noSylow
460C2×C33C2×#4111yescharacteristic
461C2×C33H(5,𝔽2)11yescharacteristic
462C2×C33H(5,𝔽2)11yescharacteristic
463C3⋊(C3⋊D3)—41no—
464C3×C3⋊D3—41no—
465C3×C3⋊D3—41no—
466C32×D3—41no—
467C32×D3—41no—
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—
476C22×C3×C4—91no—
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—91no—
487C2×#67—91no—
488C2×#67—91no—
489C2×#67—181no—
490C2×#67—181no—
491C22×Dic3—31no—
492C22×Dic3—91no—
493C22×Dic3—91no—
494C22×Dic3—91no—
495C22×Dic3—181no—
496C2×D12—31no—
497C2×D12—31no—
498C2×D12—31no—
499C2×D12—31no—
500C2×D12—91no—
501C2×D12—91no—
502C2×D12—91no—
503C2×D12—91no—
504C2×D12—91no—
505C2×D12—91no—
506C2×D12—91no—
507C2×D12—181no—
508C2×D12—181no—
509C2×D12D3211yescharacteristic
510C2×C4×D3—31no—
511C2×C4×D3—31no—
512C2×C4×D3—31no—
513C2×C4×D3—61no—
514C2×C4×D3—91no—
515C2×C4×D3—91no—
516C2×C4×D3—91no—
517C2×C4×D3—91no—
518C2×C4×D3—91no—
519C2×C4×D3—91no—
520C2×C4×D3—181no—
521C2×C4×D3—181no—
522C3×C4⋊C4—31no—
523C3×C4⋊C4—31no—
524C3×C4⋊C4—31no—
525C3×C4⋊C4—31no—
526C3×C4⋊C4—61no—
527C3×C4⋊C4—61no—
528C3×C4⋊C4—91no—
529C3×C4⋊C4—91no—
530C3×C4⋊C4—91no—
531C3×C4⋊C4—91no—
532C3×C22⋊C4—91no—
533C3×C22⋊C4—91no—
534C3×C22⋊C4—91no—
535C3×C22⋊C4—91no—
536C3×C42—91no—
537#217—31no—
538#217—31no—
539#217—31no—
540#217—91no—
541#217—91no—
542#217—91no—
543#217—91no—
544#217—91no—
545#217—181no—
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—
571C4⋊Dic3—31no—
572C4⋊Dic3—31no—
573C4⋊Dic3—31no—
574C4⋊Dic3—91no—
575C4⋊Dic3—91no—
576C4⋊Dic3D3211yescharacteristic
577Dic3⋊C4—31no—
578Dic3⋊C4—31no—
579Dic3⋊C4—31no—
580Dic3⋊C4—31no—
581Dic3⋊C4—31no—
582Dic3⋊C4—61no—
583Dic3⋊C4—91no—
584Dic3⋊C4—91no—
585Dic3⋊C4—91no—
586Dic3⋊C4—91no—
587Dic3⋊C4—181no—
588Dic3⋊C4D3211yescharacteristic
589C4×Dic3—31no—
590C4×Dic3—31no—
591C4×Dic3—91no—
592C4×Dic3—91no—
593C4×Dic3—91no—
594C4×Dic3—181no—
595C22×C32—21no—
596C22×C32—21no—
597C22×C32—21no—
598C22×C32—41no—
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—61no—
615C2×C3⋊D3—62no—
616C2×C3⋊D3—61no—
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—121no—
625C2×C3⋊D3—121no—
626C2×C3⋊D3—122no—
627C2×C3⋊D3—121no—
628C2×C3⋊D3—121no—
629C2×C3⋊D3—121no—
630C2×C3⋊D3—121no—
631C2×C3⋊D3—121no—
632C2×C3⋊D3—121no—
633C2×C3⋊D3—241no—
634C2×C3⋊D3—241no—
635C2×C3×D3—22no—
636C2×C3×D3—21no—
637C2×C3×D3—21no—
638C2×C3×D3—21no—
639C2×C3×D3—21no—
640C2×C3×D3—21no—
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—41no—
649C2×C3×D3—41no—
650C2×C3×D3—41no—
651C2×C3×D3—41no—
652C2×C3×D3—41no—
653C2×C3×D3—62no—
654C2×C3×D3—62no—
655C2×C3×D3—61no—
656C2×C3×D3—61no—
657C2×C3×D3—61no—
658C2×C3×D3—61no—
659C2×C3×D3—61no—
660C2×C3×D3—61no—
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—121no—
671C32×C4—21no—
672C32×C4—21no—
673C32×C4—21no—
674C32×C4—32no—
675C32×C4—41no—
676C32×C4—41no—
677C32×C4—41no—
678C32×C4—61no—
679C32×C4—61no—
680C32×C4—61no—
681C32×C4—81no—
682C3⋊Dic3—21no—
683C3⋊Dic3—21no—
684C3⋊Dic3—21no—
685C3⋊Dic3—21no—
686C3⋊Dic3—61no—
687C3⋊Dic3—61no—
688C3⋊Dic3—61no—
689C3⋊Dic3—121no—
690C3⋊Dic3—121no—
691C3⋊Dic3—121no—
692C3⋊Dic3—241no—
693C3×Dic3—21no—
694C3×Dic3—21no—
695C3×Dic3—21no—
696C3×Dic3—21no—
697C3×Dic3—21no—
698C3×Dic3—21no—
699C3×Dic3—22no—
700C3×Dic3—41no—
701C3×Dic3—41no—
702C3×Dic3—41no—
703C3×Dic3—62no—
704C3×Dic3—62no—
705C3×Dic3—61no—
706C3×Dic3—61no—
707C3×Dic3—61no—
708C3×Dic3—61no—
709C3×Dic3—61no—
710C3×Dic3—61no—
711C3×Dic3—61no—
712C3×Dic3—61no—
713C3×Dic3—121no—
714C3×Dic3—121no—
715C3×Dic3#23712yes—
716C3×Dic3#23912yes—
717#127—271no—
718#125—91no—
719#123—271no—
720#123—271no—
721#123—271no—
722#123—271no—
723#121—91no—
724#121—91no—
725#121—271no—
726#121—271no—
727#121—271no—
728#121—271no—
729C4×D4—271no—
730C4×D4—271no—
731#117—271no—
732C33#54011yescharacteristic, complemented, Sylow
733C23×C3—31no—
734C23×C3—31no—
735C23×C3—31no—
736C23×C3—31no—
737C23×C3—61no—
738C23×C3—61no—
739C23×C3—91no—
740C23×C3—91no—
741C22×D3—31no—
742C22×D3—31no—
743C22×D3—31no—
744C22×D3—31no—
745C22×D3—61no—
746C22×D3—61no—
747C22×D3—91no—
748C22×D3—91no—
749C22×D3—91no—
750C22×D3—181no—
751C22×D3—181no—
752C22×D3—181no—
753C22×D3—361no—
754C22×D3C2×D3211yescharacteristic
755C22×D3C2×D3211yescharacteristic
756C3×D4—121no—
757C3×D4—121no—
758C3×D4—122no—
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—31no—
773C2×C3×C4—31no—
774C2×C3×C4—41no—
775C2×C3×C4—61no—
776C2×C3×C4—61no—
777C2×C3×C4—61no—
778C2×C3×C4—61no—
779C2×C3×C4—91no—
780C2×C3×C4—91no—
781C2×C3×C4—91no—
782C2×C3×C4—91no—
783C2×C3×C4—182no—
784C2×C3×C4—361no—
785C2×C3×C4C2×D3211yescharacteristic
786C2×C3×C4C2×D3211yescharacteristic
787C2×C3×C4C2×D3211yescharacteristic
788#67—62no—
789#67—121no—
790#67—121no—
791#67—121no—
792#67—182no—
793#67—361no—
794#67—361no—
795#67—361no—
796#67—361no—
797#67—361no—
798#67—361no—
799#67—361no—
800#67—362no—
801#67—362no—
802C2×Dic3—31no—
803C2×Dic3—31no—
804C2×Dic3—31no—
805C2×Dic3—31no—
806C2×Dic3—31no—
807C2×Dic3—31no—
808C2×Dic3—31no—
809C2×Dic3—31no—
810C2×Dic3—61no—
811C2×Dic3—61no—
812C2×Dic3—61no—
813C2×Dic3—61no—
814C2×Dic3—62no—
815C2×Dic3—91no—
816C2×Dic3—91no—
817C2×Dic3—91no—
818C2×Dic3—181no—
819C2×Dic3—181no—
820C2×Dic3—181no—
821C2×Dic3—361no—
822C2×Dic3—361no—
823C2×Dic3—361no—
824C2×Dic3—361no—
825C2×Dic3—362no—
826C2×Dic3C2×D3211yescharacteristic
827C2×Dic3C2×D3211yescharacteristic
828C2×Dic3C2×D3211yescharacteristic
829C2×Dic3C2×D3211yescharacteristic
830D12—41no—
831D12—62no—
832D12—121no—
833D12—121no—
834D12—121no—
835D12—182no—
836D12—182no—
837D12—184no—
838D12—361no—
839D12—361no—
840D12—362no—
841D12—361no—
842D12—361no—
843D12—361no—
844C4×D3—62no—
845C4×D3—121no—
846C4×D3—121no—
847C4×D3—122no—
848C4×D3—361no—
849C4×D3—361no—
850C4×D3—361no—
851C4×D3—362no—
852C4×D3—361no—
853C4×D3—361no—
854C4×D3—361no—
855C4×D3—362no—
856C2×C32—21no—
857C2×C32—21no—
858C2×C32—21no—
859C2×C32—21no—
860C2×C32—21no—
861C2×C32—21no—
862C2×C32—21no—
863C2×C32—21no—
864C2×C32—21no—
865C2×C32—41no—
866C2×C32—41no—
867C2×C32—41no—
868C2×C32—121no—
869C2×C32—121no—
870C2×C32C2×#23711yescharacteristic
871C2×C32#100411yescharacteristic
872C2×C32#100411yescharacteristic
873C2×C32#100411yescharacteristic
874C2×C32C2×#23911yescharacteristic
875C2×C32D3×#4111yescharacteristic
876C2×C32#100911yescharacteristic
877C2×C32#100911yescharacteristic
878C2×C32#100911yescharacteristic
879C3⋊D3—41no—
880C3⋊D3—41no—
881C3⋊D3—121no—
882C3⋊D3—122no—
883C3⋊D3—121no—
884C3⋊D3—121no—
885C3⋊D3—241no—
886C3⋊D3—241no—
887C3⋊D3—242no—
888C3×D3—42no—
889C3×D3—41no—
890C3×D3—41no—
891C3×D3—41no—
892C3×D3—41no—
893C3×D3—81no—
894C3×D3—122no—
895C3×D3—122no—
896C3×D3—121no—
897C3×D3—121no—
898C3×D3—121no—
899C3×D3—121no—
900C2×D4—31no—
901C2×D4—91no—
902C2×D4—91no—
903C2×D4—91no—
904C2×D4—91no—
905C2×D4—271no—
906C2×D4—271no—
907C2×D4—271no—
908C2×D4—271no—
909C2×D4—271no—
910C22×C4—91no—
911C22×C4—91no—
912C22×C4—271no—
913C22×C4—271no—
914C22×C4—271no—
915C4⋊C4—31no—
916C4⋊C4—31no—
917C4⋊C4—91no—
918C4⋊C4—91no—
919C4⋊C4—91no—
920C4⋊C4—91no—
921C4⋊C4—271no—
922C4⋊C4—271no—
923C22⋊C4—91no—
924C22⋊C4—91no—
925C22⋊C4—91no—
926C22⋊C4—91no—
927C22⋊C4—271no—
928C22⋊C4—271no—
929C22⋊C4—271no—
930C22⋊C4—271no—
931C22⋊C4—271no—
932C22⋊C4—271no—
933C42—91no—
934C42—271no—
935C22×C3—21no—
936C22×C3—21no—
937C22×C3—21no—
938C22×C3—41no—
939C22×C3—62no—
940C22×C3—61no—
941C22×C3—61no—
942C22×C3—61no—
943C22×C3—61no—
944C22×C3—61no—
945C22×C3—61no—
946C22×C3—61no—
947C22×C3—61no—
948C22×C3—61no—
949C22×C3—61no—
950C22×C3—61no—
951C22×C3—61no—
952C22×C3—121no—
953C22×C3—121no—
954C22×C3—121no—
955C22×C3—121no—
956C22×C3—121no—
957C22×C3—181no—
958C22×C3—181no—
959C22×C3—181no—
960C22×C3—181no—
961C22×C3—181no—
962C22×C3—181no—
963C22×C3C22×D3211yescharacteristic
964C22×C3C22×D3211yescharacteristic
965C22×C3C22×D3211yescharacteristic
966C2×D3—21no—
967C2×D3—21no—
968C2×D3—21no—
969C2×D3—21no—
970C2×D3—21no—
971C2×D3—21no—
972C2×D3—62no—
973C2×D3—62no—
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—61no—
985C2×D3—61no—
986C2×D3—121no—
987C2×D3—121no—
988C2×D3—121no—
989C2×D3—121no—
990C2×D3—182no—
991C2×D3—181no—
992C2×D3—181no—
993C2×D3—181no—
994C2×D3—181no—
995C2×D3—181no—
996C2×D3—181no—
997C2×D3—181no—
998C2×D3—181no—
999C2×D3—181no—
1000C2×D3—361no—
1001C2×D3—361no—
1002C2×D3—361no—
1003C2×D3—361no—
1004C2×D3—361no—
1005C2×D3—361no—
1006C2×D3—361no—
1007C2×D3—361no—
1008C2×D3—362no—
1009C2×D3—721no—
1010C2×D3—721no—
1011C3×C4—21no—
1012C3×C4—21no—
1013C3×C4—21no—
1014C3×C4—32no—
1015C3×C4—32no—
1016C3×C4—41no—
1017C3×C4—41no—
1018C3×C4—41no—
1019C3×C4—62no—
1020C3×C4—61no—
1021C3×C4—61no—
1022C3×C4—61no—
1023C3×C4—61no—
1024C3×C4—61no—
1025C3×C4—61no—
1026C3×C4—81no—
1027C3×C4—121no—
1028C3×C4—121no—
1029C3×C4—121no—
1030C3×C4—181no—
1031C3×C4—181no—
1032C3×C4—181no—
1033C3×C4—181no—
1034Dic3—21no—
1035Dic3—21no—
1036Dic3—21no—
1037Dic3—62no—
1038Dic3—62no—
1039Dic3—61no—
1040Dic3—61no—
1041Dic3—61no—
1042Dic3—61no—
1043Dic3—61no—
1044Dic3—61no—
1045Dic3—61no—
1046Dic3—61no—
1047Dic3—121no—
1048Dic3—121no—
1049Dic3—181no—
1050Dic3—181no—
1051Dic3—181no—
1052Dic3—361no—
1053Dic3—361no—
1054Dic3—361no—
1055Dic3—721no—
1056Dic3#379612yes—
1057C32—21no—
1058C32—21no—
1059C32—21no—
1060C32—41no—
1061C32#561511yescharacteristic, complemented
1062C32#561911yescharacteristic, complemented
1063C32#569711yescharacteristic, complemented
1064C23—31no—
1065C23—31no—
1066C23—91no—
1067C23—91no—
1068C23—271no—
1069D4—121no—
1070D4—182no—
1071D4—361no—
1072D4—361no—
1073D4—361no—
1074D4—542no—
1075D4—1081no—
1076D4—1081no—
1077D4—1081no—
1078D4—1081no—
1079C2×C4—31no—
1080C2×C4—31no—
1081C2×C4—31no—
1082C2×C4—31no—
1083C2×C4—91no—
1084C2×C4—91no—
1085C2×C4—91no—
1086C2×C4—91no—
1087C2×C4—182no—
1088C2×C4—271no—
1089C2×C4—361no—
1090C2×C4—1081no—
1091C2×C4—1081no—
1092C2×C4—1081no—
1093C2×C4D3311yescharacteristic
1094C2×C3—21no—
1095C2×C3—21no—
1096C2×C3—21no—
1097C2×C3—21no—
1098C2×C3—21no—
1099C2×C3—21no—
1100C2×C3—21no—
1101C2×C3—21no—
1102C2×C3—21no—
1103C2×C3—41no—
1104C2×C3—41no—
1105C2×C3—41no—
1106C2×C3—122no—
1107C2×C3—121no—
1108C2×C3—121no—
1109C2×C3—121no—
1110C2×C3—121no—
1111C2×C3—241no—
1112C2×C3—361no—
1113C2×C3—361no—
1114C2×C3C2×#379611yescharacteristic
1115C2×C3#6430711yescharacteristic
1116C2×C3D3×#23711yescharacteristic
1117C2×C3#6431411yescharacteristic
1118C2×C3#6431411yescharacteristic
1119C2×C3#6431411yescharacteristic
1120C2×C3D3×#23911yescharacteristic
1121C2×C3#6432011yescharacteristic
1122C2×C3#6433011yescharacteristic
1123D3—41no—
1124D3—41no—
1125D3—122no—
1126D3—122no—
1127D3—121no—
1128D3—121no—
1129D3—121no—
1130D3—121no—
1131D3—362no—
1132D3—361no—
1133D3—361no—
1134D3—361no—
1135D3—721no—
1136D3—721no—
1137D3—722no—
1138C22—61no—
1139C22—61no—
1140C22—61no—
1141C22—61no—
1142C22—61no—
1143C22—61no—
1144C22—181no—
1145C22—181no—
1146C22—181no—
1147C22—181no—
1148C22—181no—
1149C22—181no—
1150C22—541no—
1151C22—541no—
1152C22—541no—
1153C22C2×D3311yescharacteristic
1154C4—21no—
1155C4—32no—
1156C4—61no—
1157C4—61no—
1158C4—61no—
1159C4—181no—
1160C4—181no—
1161C4—181no—
1162C4—181no—
1163C4—541no—
1164C3—21no—
1165C3—21no—
1166C3—21no—
1167C3—41no—
1168C3#1059450111yescharacteristic, complemented
1169C3#1059456311yescharacteristic, complemented
1170C3#1059525011yescharacteristic, complemented
1171C2—121no—
1172C2—121no—
1173C2—361no—
1174C2—361no—
1175C2—1081no—
1176C2D3×#379611yescharacteristic
1177C2#1172438611yescharacteristic
1178C2#1172441811yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
hypercenterC2×C4D33
hypocenterC33#540
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. #11723694C2semidirect
2. #11723512C2semidirect
3. #11723493C2semidirect
4. #11723475C2semidirect
5. C3×#63916C2semidirect
6. C3×#63886C2semidirect
7. C3×#63846C2semidirect
8. #11723030C2semidirect
9. #11722996C2semidirect
10. #11722990C2semidirect
11. #11722963C2semidirect
12. #11722962C2semidirect
13. #11722959C2semidirect
14. #11722929C2semidirect
15. #11722913C2semidirect
73. #63916D3semidirect
92. #63886D3semidirect
101. #63846D3semidirect
732. C33#540semidirect
1061. C32#5615semidirect
1062. C32#5619semidirect
1063. C32#5697semidirect
1168. C3#10594501semidirect
1169. C3#10594563semidirect
1170. C3#10595250semidirect

Maximal subgroups

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

subgroupindex
#117236942
#117235122
#117234932
#117234752
C3×#639162
C3×#638862
C3×#638462
#117230302
#117229962
#117229902
#117229632
#117229622
#117229592
#117229292
#117229132
#105952503
#105945633
#105945013