Finite Group Databasebeta

← #13168518

Subgroups — #13168518

Order 1728.

1280 conjugacy classes of subgroups.

The subgroup lattice has 1182 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723690C211yesmaximal, characteristic, complemented
2#11723531C211yesmaximal, characteristic, complemented
3#11723472C211yesmaximal, characteristic, complemented
4#11723421C211yesmaximal, characteristic, complemented
5C3×#63886C211yesmaximal, characteristic, complemented
6C3×#63886C211yesmaximal, characteristic, complemented
7C3×#63845C211yesmaximal, characteristic, complemented
8#11723030C211yesmaximal, characteristic, complemented
9#11722991C211yesmaximal, characteristic, complemented
10#11722987C211yesmaximal, characteristic, complemented
11#11722966C211yesmaximal, characteristic, complemented
12#11722962C211yesmaximal, characteristic, complemented
13#11722959C211yesmaximal, characteristic, complemented
14#11722927C211yesmaximal, characteristic, complemented
15#11722913C211yesmaximal, characteristic, complemented
16#10595197—31nomaximal
17#10594563—31nomaximal
18#10594501—31nomaximal
19C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
20C2×C32×D12C2211yescharacteristic
21C2×#6295C2211yescharacteristic
22C2×#6294C2211yescharacteristic
23C2×#6292C2211yescharacteristic
24C2×#6292C2211yescharacteristic
25C2×#6291C2211yescharacteristic
26C2×#6291C2211yescharacteristic
27C2×Dic3×C3⋊D3C2211yescharacteristic
28C2×C3×#626C2211yescharacteristic
29C2×C3×#626C2211yescharacteristic
30C2×C3×#626C2211yescharacteristic
31C2×C3×#626C2211yescharacteristic
32C2×C3×D3×Dic3C2211yescharacteristic
33C2×C3×D3×Dic3C2211yescharacteristic
34C3×#3752C2211yescharacteristic
35C3×#3752C2211yescharacteristic
36C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
37C32×Dic3⋊C4C2211yescharacteristic
38C32×Dic3⋊C4C2211yescharacteristic
39#88815C2211yescharacteristic
40#88814C2211yescharacteristic
41#88807C2211yescharacteristic
42#88804C2211yescharacteristic
43#88804C2211yescharacteristic
44#88803C2211yescharacteristic
45(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
46(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
47Dic3×C3⋊Dic3C2211yescharacteristic
48C3×#3724C2211yescharacteristic
49C3×Dic3⋊Dic3C2211yescharacteristic
50C3×Dic3⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64147—31no—
55#64103—31no—
56#64102—31no—
57C3×#939—31no—
58C3×#939—31no—
59C3×#895—31no—
60C3×#895—31no—
61C3×#890—31no—
62C3×#889—31no—
63#63979—31no—
64#63978—31no—
65Dic3×#67—31no—
66#63971—31no—
67#63970—31no—
68#63969—31no—
69#63966—31no—
70#63955—31no—
71#63916—31no—
72#63916—31no—
73#63916—31no—
74#63916—61no—
75#63911—31no—
76#63911—31no—
77#63910—31no—
78#63909—31no—
79#63904—31no—
80#63898—31no—
81#63891—31no—
82#63890—31no—
83#63890—31no—
84#63886—31no—
85#63886—31no—
86#63886—31no—
87#63886D311yescharacteristic, complemented
88#63886D311yescharacteristic, complemented
89#63884—31no—
90#63881—31no—
91#63881—31no—
92#63881—61no—
93#63877—31no—
94#63855—31no—
95#63854—31no—
96#63853—31no—
97#63853—31no—
98#63853—31no—
99#63853—61no—
100#63850—31no—
101#63845D311yescharacteristic, 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
109C4×C3⋊(C3⋊D3)—41no—
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118C32×D12—41no—
119#6295—41no—
120#6294—41no—
121#6292—22no—
122#6292—41no—
123#6291—41no—
124#6291—41no—
125Dic3×C3⋊D3—41no—
126C3×#626—22no—
127C3×#626—41no—
128C3×#626—41no—
129C3×#626—41no—
130C3×D3×Dic3—22no—
131C3×D3×Dic3—41no—
132#5697—91no—
133#5619—91no—
134#5615—91no—
135C2×C32×D4—31no—
136C2×#638—31no—
137C2×#638—31no—
138C2×C4⋊(C3⋊D3)—31no—
139C2×C4⋊(C3⋊D3)—31no—
140C2×C4×C3⋊D3—31no—
141C2×C4×C3⋊D3—31no—
142C2×C4×C3⋊D3—31no—
143C2×C4×C3⋊D3—31no—
144C2×C4×C3⋊D3—61no—
145C2×C4×C3⋊D3—61no—
146C2×C4×C3⋊D3—61no—
147C2×C4×C3⋊D3—121no—
148C2×C3×#67—31no—
149C2×C3×#67—31no—
150C2×C3×#67—31no—
151C2×C3×#67—31no—
152C22×C3×Dic3—31no—
153C22×C3×Dic3—31no—
154C2×C3×D12—21no—
155C2×C3×D12—31no—
156C2×C3×D12—31no—
157C2×C3×D12—31no—
158C2×C3×D12—31no—
159C2×C3×D12C2×D311yescharacteristic
160C2×C3×D12C2×D311yescharacteristic
161C2×C3×C4×D3—31no—
162C2×C3×C4×D3—31no—
163C2×#626—31no—
164C2×#626—31no—
165C2×#626—31no—
166C2×#626—31no—
167C2×#626—31no—
168C2×#626—31no—
169C2×#626—31no—
170C2×#626—31no—
171C2×#626—31no—
172C2×#626—31no—
173C2×#626—61no—
174C2×#626—61no—
175C2×#626—61no—
176C2×#626—61no—
177C2×#626C2×D311yescharacteristic
178C2×#626C2×D311yescharacteristic
179C2×#626C2×D311yescharacteristic
180C2×#626C2×D311yescharacteristic
181C2×#625—31no—
182C2×#624—31no—
183C2×D3×Dic3—31no—
184C2×D3×Dic3—31no—
185C2×D3×Dic3—31no—
186C2×D3×Dic3—31no—
187C2×D3×Dic3—61no—
188C2×D3×Dic3C2×D311yescharacteristic
189C2×D3×Dic3C2×D311yescharacteristic
190C32×C4⋊C4—31no—
191C32×C4⋊C4—31no—
192#3757—31no—
193#3757—31no—
194#3752—31no—
195#3752—31no—
196#3752—31no—
197#3752C2×D311yescharacteristic
198#3752C2×D311yescharacteristic
199C4⋊(C3⋊Dic3)C2×D311yescharacteristic
200#3750—31no—
201C4×C3⋊Dic3—31no—
202C3×#217—31no—
203C3×#217—31no—
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—61no—
211C3×(C2×D3)⋊C4—61no—
212C3×C4⋊Dic3—31no—
213C3×C4⋊Dic3—31no—
214C3×C4⋊Dic3—31no—
215C3×C4⋊Dic3—31no—
216C3×C4⋊Dic3—61no—
217C3×Dic3⋊C4—21no—
218C3×Dic3⋊C4—21no—
219C3×Dic3⋊C4—31no—
220C3×Dic3⋊C4—31no—
221C3×Dic3⋊C4—31no—
222C3×Dic3⋊C4—31no—
223C3×Dic3⋊C4C2×D311yescharacteristic
224C3×Dic3⋊C4C2×D311yescharacteristic
225C3×Dic3⋊C4C2×D311yescharacteristic
226C3×Dic3⋊C4C2×D311yescharacteristic
227C3×C4×Dic3—31no—
228C3×C4×Dic3—31no—
229#3724—31no—
230#3724C2×D311yescharacteristic
231Dic3⋊Dic3—31no—
232Dic3⋊Dic3—31no—
233Dic3⋊Dic3—31no—
234Dic3⋊Dic3—31no—
235Dic3⋊Dic3—61no—
236Dic3⋊Dic3C2×D311yescharacteristic
237Dic3⋊Dic3C2×D311yescharacteristic
238#3722—31no—
239#3722—31no—
240#3722—31no—
241#3722—31no—
242#3722—31no—
243#3722—61no—
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)⋊Dic3—61no—
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—31no—
295#939—91no—
296#939—91no—
297#939—91no—
298#938—91no—
299#938—91no—
300#938—91no—
301#938—181no—
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⋊Dic3C22×D311yescharacteristic
381C2×C3⋊Dic3C22×D311yescharacteristic
382C2×C3⋊Dic3C22×D311yescharacteristic
383C2×C3⋊Dic3C22×D311yescharacteristic
384C4⋊(C3⋊D3)—62no—
385C4⋊(C3⋊D3)—121no—
386C4×C3⋊D3—121no—
387C4×C3⋊D3—121no—
388C4×C3⋊D3—121no—
389C4×C3⋊D3—122no—
390C4×C3⋊D3—121no—
391C4×C3⋊D3—122no—
392C4×C3⋊D3—122no—
393C4×C3⋊D3—124no—
394C3×#67—62no—
395C3×#67—121no—
396C3×#67—121no—
397C3×#67—121no—
398C2×C3×Dic3—21no—
399C2×C3×Dic3—21no—
400C2×C3×Dic3—21no—
401C2×C3×Dic3—21no—
402C2×C3×Dic3—31no—
403C2×C3×Dic3—31no—
404C2×C3×Dic3—31no—
405C2×C3×Dic3—31no—
406C2×C3×Dic3—31no—
407C2×C3×Dic3—31no—
408C2×C3×Dic3—31no—
409C2×C3×Dic3—31no—
410C2×C3×Dic3—61no—
411C2×C3×Dic3—61no—
412C2×C3×Dic3—61no—
413C2×C3×Dic3—61no—
414C2×C3×Dic3—62no—
415C2×C3×Dic3—121no—
416C2×C3×Dic3C22×D311yescharacteristic
417C2×C3×Dic3C22×D311yescharacteristic
418C2×C3×Dic3C22×D311yescharacteristic
419C2×C3×Dic3C22×D311yescharacteristic
420C2×C3×Dic3C22×D311yescharacteristic
421C2×C3×Dic3C22×D311yescharacteristic
422C2×C3×Dic3C22×D311yescharacteristic
423C2×C3×Dic3C22×D311yescharacteristic
424C3×D12—41no—
425C3×D12—41no—
426C3×D12—42no—
427C3×D12—62no—
428C3×D12—121no—
429C3×D12—121no—
430C3×D12—121no—
431C3×C4×D3—62no—
432C3×C4×D3—121no—
433#626—22no—
434#626—41no—
435#626—41no—
436#626—41no—
437#626—64no—
438#626—62no—
439#626—62no—
440#626—121no—
441#626—121no—
442#626—122no—
443#626—121no—
444#626—121no—
445#626—121no—
446#626—121no—
447#626—121no—
448#626—121no—
449#626—122no—
450#626—122no—
451#625—121no—
452#624—121no—
453D3×Dic3—22no—
454D3×Dic3—41no—
455D3×Dic3—121no—
456D3×Dic3—121no—
457D3×Dic3—122no—
458D3×Dic3—121no—
459D3×Dic3—121no—
460#540—271noSylow
461C2×C33C2×#4111yescharacteristic
462C2×C33H(5,𝔽2)11yescharacteristic
463C2×C33H(5,𝔽2)11yescharacteristic
464C3⋊(C3⋊D3)—41no—
465C3×C3⋊D3—41no—
466C3×C3⋊D3—41no—
467C32×D3—41no—
468C32×D3—41no—
469C2×C3×D4—31no—
470C2×C3×D4—31no—
471C2×C3×D4—61no—
472C2×C3×D4—91no—
473C2×C3×D4—91no—
474C2×C3×D4—91no—
475C2×C3×D4—91no—
476C22×C3×C4—91no—
477C22×C3×C4—91no—
478C2×#67—31no—
479C2×#67—31no—
480C2×#67—31no—
481C2×#67—31no—
482C2×#67—91no—
483C2×#67—91no—
484C2×#67—91no—
485C2×#67—91no—
486C2×#67—91no—
487C2×#67—91no—
488C2×#67—91no—
489C2×#67—91no—
490C2×#67—181no—
491C2×#67—181no—
492C22×Dic3—31no—
493C22×Dic3—31no—
494C22×Dic3—91no—
495C22×Dic3—91no—
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—91no—
513C2×C4×D3—91no—
514C2×C4×D3—91no—
515C2×C4×D3—91no—
516C2×C4×D3—91no—
517C2×C4×D3—91no—
518C2×C4×D3—91no—
519C2×C4×D3—181no—
520C2×C4×D3—181no—
521C2×C4×D3—181no—
522C2×C4×D3—181no—
523C2×C4×D3—361no—
524C3×C4⋊C4—31no—
525C3×C4⋊C4—31no—
526C3×C4⋊C4—31no—
527C3×C4⋊C4—31no—
528C3×C4⋊C4—61no—
529C3×C4⋊C4—61no—
530C3×C4⋊C4—91no—
531C3×C4⋊C4—91no—
532C3×C4⋊C4—91no—
533C3×C4⋊C4—91no—
534C3×C22⋊C4—91no—
535C3×C22⋊C4—91no—
536C3×C22⋊C4—91no—
537C3×C22⋊C4—91no—
538C3×C42—91no—
539#217—31no—
540#217—31no—
541#217—91no—
542#217—91no—
543#217—91no—
544#217—91no—
545#217—91no—
546#217—91no—
547#217—181no—
548#217—181no—
549(C2×D3)⋊C4—31no—
550(C2×D3)⋊C4—31no—
551(C2×D3)⋊C4—31no—
552(C2×D3)⋊C4—31no—
553(C2×D3)⋊C4—31no—
554(C2×D3)⋊C4—31no—
555(C2×D3)⋊C4—61no—
556(C2×D3)⋊C4—61no—
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—91no—
566(C2×D3)⋊C4—91no—
567(C2×D3)⋊C4—91no—
568(C2×D3)⋊C4—91no—
569(C2×D3)⋊C4—181no—
570(C2×D3)⋊C4—181no—
571(C2×D3)⋊C4—181no—
572C4⋊Dic3—31no—
573C4⋊Dic3—31no—
574C4⋊Dic3—31no—
575C4⋊Dic3—31no—
576C4⋊Dic3—61no—
577C4⋊Dic3—91no—
578C4⋊Dic3—91no—
579Dic3⋊C4—31no—
580Dic3⋊C4—31no—
581Dic3⋊C4—31no—
582Dic3⋊C4—31no—
583Dic3⋊C4—91no—
584Dic3⋊C4—91no—
585Dic3⋊C4—91no—
586Dic3⋊C4—91no—
587Dic3⋊C4—181no—
588Dic3⋊C4D3211yescharacteristic
589Dic3⋊C4D3211yescharacteristic
590C4×Dic3—31no—
591C4×Dic3—31no—
592C4×Dic3—91no—
593C4×Dic3—91no—
594C4×Dic3—91no—
595C4×Dic3—181no—
596C22×C32—21no—
597C22×C32—21no—
598C22×C32—21no—
599C22×C32—41no—
600C22×C32—61no—
601C22×C32—61no—
602C22×C32—61no—
603C22×C32—61no—
604C22×C32—61no—
605C22×C32—61no—
606C22×C32C23×D311yescharacteristic
607C22×C32C23×D311yescharacteristic
608C22×C32C23×D311yescharacteristic
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—61no—
616C2×C3⋊D3—61no—
617C2×C3⋊D3—61no—
618C2×C3⋊D3—62no—
619C2×C3⋊D3—62no—
620C2×C3⋊D3—62no—
621C2×C3⋊D3—61no—
622C2×C3⋊D3—61no—
623C2×C3⋊D3—61no—
624C2×C3⋊D3—61no—
625C2×C3⋊D3—61no—
626C2×C3⋊D3—61no—
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—122no—
634C2×C3⋊D3—122no—
635C2×C3⋊D3—122no—
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—41no—
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—
671C2×C3×D3—121no—
672C32×C4—21no—
673C32×C4—22no—
674C32×C4—21no—
675C32×C4—21no—
676C32×C4—32no—
677C32×C4—41no—
678C32×C4—41no—
679C32×C4—42no—
680C32×C4—61no—
681C32×C4—61no—
682C32×C4—61no—
683C3⋊Dic3—21no—
684C3⋊Dic3—21no—
685C3⋊Dic3—21no—
686C3⋊Dic3—21no—
687C3⋊Dic3—61no—
688C3⋊Dic3—62no—
689C3⋊Dic3—61no—
690C3⋊Dic3—61no—
691C3⋊Dic3—121no—
692C3⋊Dic3—121no—
693C3⋊Dic3—122no—
694C3×Dic3—21no—
695C3×Dic3—21no—
696C3×Dic3—21no—
697C3×Dic3—21no—
698C3×Dic3—21no—
699C3×Dic3—21no—
700C3×Dic3—22no—
701C3×Dic3—41no—
702C3×Dic3—41no—
703C3×Dic3—41no—
704C3×Dic3—61no—
705C3×Dic3—61no—
706C3×Dic3—61no—
707C3×Dic3—61no—
708C3×Dic3—61no—
709C3×Dic3—61no—
710C3×Dic3—61no—
711C3×Dic3—61no—
712C3×Dic3—121no—
713C3×Dic3—121no—
714C3×Dic3—121no—
715C3×Dic3—121no—
716C3×Dic3#23712yes—
717C3×Dic3#23912yes—
718#127—271no—
719#125—91no—
720#123—271no—
721#123—271no—
722#123—271no—
723#123—271no—
724#121—91no—
725#121—91no—
726#121—271no—
727#121—271no—
728#121—271no—
729#121—271no—
730C4×D4—271no—
731C4×D4—271no—
732#117—271no—
733C33#54011yescharacteristic, complemented, Sylow
734C23×C3—31no—
735C23×C3—31no—
736C23×C3—31no—
737C23×C3—31no—
738C23×C3—61no—
739C23×C3—61no—
740C23×C3—91no—
741C23×C3—91no—
742C22×D3—31no—
743C22×D3—31no—
744C22×D3—31no—
745C22×D3—31no—
746C22×D3—61no—
747C22×D3—61no—
748C22×D3—91no—
749C22×D3—91no—
750C22×D3—91no—
751C22×D3—181no—
752C22×D3—181no—
753C22×D3—181no—
754C22×D3—361no—
755C22×D3C2×D3211yescharacteristic
756C22×D3C2×D3211yescharacteristic
757C3×D4—121no—
758C3×D4—121no—
759C3×D4—122no—
760C3×D4—182no—
761C3×D4—361no—
762C3×D4—361no—
763C3×D4—361no—
764C2×C3×C4—21no—
765C2×C3×C4—21no—
766C2×C3×C4—21no—
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—31no—
775C2×C3×C4—41no—
776C2×C3×C4—61no—
777C2×C3×C4—61no—
778C2×C3×C4—61no—
779C2×C3×C4—61no—
780C2×C3×C4—91no—
781C2×C3×C4—91no—
782C2×C3×C4—91no—
783C2×C3×C4—91no—
784C2×C3×C4—182no—
785C2×C3×C4—361no—
786C2×C3×C4C2×D3211yescharacteristic
787C2×C3×C4C2×D3211yescharacteristic
788C2×C3×C4C2×D3211yescharacteristic
789#67—62no—
790#67—121no—
791#67—121no—
792#67—121no—
793#67—182no—
794#67—361no—
795#67—361no—
796#67—361no—
797#67—361no—
798#67—361no—
799#67—361no—
800#67—361no—
801#67—362no—
802#67—362no—
803C2×Dic3—31no—
804C2×Dic3—31no—
805C2×Dic3—31no—
806C2×Dic3—31no—
807C2×Dic3—31no—
808C2×Dic3—31no—
809C2×Dic3—31no—
810C2×Dic3—31no—
811C2×Dic3—61no—
812C2×Dic3—61no—
813C2×Dic3—61no—
814C2×Dic3—61no—
815C2×Dic3—62no—
816C2×Dic3—91no—
817C2×Dic3—91no—
818C2×Dic3—91no—
819C2×Dic3—121no—
820C2×Dic3—181no—
821C2×Dic3—181no—
822C2×Dic3—181no—
823C2×Dic3—361no—
824C2×Dic3—361no—
825C2×Dic3—361no—
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—361no—
847C4×D3—361no—
848C4×D3—361no—
849C4×D3—361no—
850C4×D3—361no—
851C4×D3—362no—
852C4×D3—361no—
853C4×D3—361no—
854C4×D3—362no—
855C4×D3—362no—
856C4×D3—362no—
857C4×D3—364no—
858C2×C32—21no—
859C2×C32—21no—
860C2×C32—21no—
861C2×C32—21no—
862C2×C32—21no—
863C2×C32—21no—
864C2×C32—21no—
865C2×C32—21no—
866C2×C32—21no—
867C2×C32—41no—
868C2×C32—41no—
869C2×C32—41no—
870C2×C32—121no—
871C2×C32—121no—
872C2×C32C2×#23711yescharacteristic
873C2×C32#100411yescharacteristic
874C2×C32#100411yescharacteristic
875C2×C32#100411yescharacteristic
876C2×C32C2×#23911yescharacteristic
877C2×C32D3×#4111yescharacteristic
878C2×C32#100911yescharacteristic
879C2×C32#100911yescharacteristic
880C2×C32#100911yescharacteristic
881C3⋊D3—41no—
882C3⋊D3—41no—
883C3⋊D3—122no—
884C3⋊D3—122no—
885C3⋊D3—122no—
886C3⋊D3—124no—
887C3⋊D3—121no—
888C3⋊D3—121no—
889C3⋊D3—121no—
890C3×D3—41no—
891C3×D3—41no—
892C3×D3—41no—
893C3×D3—41no—
894C3×D3—81no—
895C3×D3—81no—
896C3×D3—122no—
897C3×D3—121no—
898C3×D3—121no—
899C3×D3—121no—
900C3×D3—121no—
901C3×D3—241no—
902C2×D4—31no—
903C2×D4—91no—
904C2×D4—91no—
905C2×D4—91no—
906C2×D4—91no—
907C2×D4—271no—
908C2×D4—271no—
909C2×D4—271no—
910C2×D4—271no—
911C2×D4—271no—
912C22×C4—91no—
913C22×C4—91no—
914C22×C4—271no—
915C22×C4—271no—
916C22×C4—271no—
917C4⋊C4—31no—
918C4⋊C4—31no—
919C4⋊C4—91no—
920C4⋊C4—91no—
921C4⋊C4—91no—
922C4⋊C4—91no—
923C4⋊C4—271no—
924C4⋊C4—271no—
925C22⋊C4—91no—
926C22⋊C4—91no—
927C22⋊C4—91no—
928C22⋊C4—91no—
929C22⋊C4—271no—
930C22⋊C4—271no—
931C22⋊C4—271no—
932C22⋊C4—271no—
933C22⋊C4—271no—
934C22⋊C4—271no—
935C42—91no—
936C42—271no—
937C22×C3—21no—
938C22×C3—21no—
939C22×C3—21no—
940C22×C3—41no—
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—61no—
953C22×C3—121no—
954C22×C3—121no—
955C22×C3—121no—
956C22×C3—121no—
957C22×C3—121no—
958C22×C3—121no—
959C22×C3—181no—
960C22×C3—181no—
961C22×C3—181no—
962C22×C3—181no—
963C22×C3—181no—
964C22×C3—181no—
965C22×C3C22×D3211yescharacteristic
966C22×C3C22×D3211yescharacteristic
967C22×C3C22×D3211yescharacteristic
968C2×D3—21no—
969C2×D3—21no—
970C2×D3—21no—
971C2×D3—21no—
972C2×D3—21no—
973C2×D3—21no—
974C2×D3—62no—
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—61no—
987C2×D3—121no—
988C2×D3—121no—
989C2×D3—121no—
990C2×D3—121no—
991C2×D3—121no—
992C2×D3—182no—
993C2×D3—182no—
994C2×D3—182no—
995C2×D3—181no—
996C2×D3—181no—
997C2×D3—181no—
998C2×D3—181no—
999C2×D3—181no—
1000C2×D3—181no—
1001C2×D3—181no—
1002C2×D3—181no—
1003C2×D3—181no—
1004C2×D3—361no—
1005C2×D3—361no—
1006C2×D3—361no—
1007C2×D3—361no—
1008C2×D3—361no—
1009C2×D3—361no—
1010C2×D3—362no—
1011C2×D3—362no—
1012C2×D3—362no—
1013C3×C4—22no—
1014C3×C4—21no—
1015C3×C4—21no—
1016C3×C4—21no—
1017C3×C4—32no—
1018C3×C4—32no—
1019C3×C4—41no—
1020C3×C4—41no—
1021C3×C4—42no—
1022C3×C4—62no—
1023C3×C4—61no—
1024C3×C4—61no—
1025C3×C4—61no—
1026C3×C4—61no—
1027C3×C4—61no—
1028C3×C4—61no—
1029C3×C4—121no—
1030C3×C4—121no—
1031C3×C4—121no—
1032C3×C4—181no—
1033C3×C4—181no—
1034C3×C4—181no—
1035C3×C4—181no—
1036Dic3—21no—
1037Dic3—21no—
1038Dic3—21no—
1039Dic3—61no—
1040Dic3—61no—
1041Dic3—61no—
1042Dic3—61no—
1043Dic3—61no—
1044Dic3—61no—
1045Dic3—61no—
1046Dic3—61no—
1047Dic3—121no—
1048Dic3—121no—
1049Dic3—121no—
1050Dic3—121no—
1051Dic3—182no—
1052Dic3—181no—
1053Dic3—181no—
1054Dic3—181no—
1055Dic3—361no—
1056Dic3—361no—
1057Dic3—362no—
1058Dic3#379612yes—
1059C32—21no—
1060C32—21no—
1061C32—21no—
1062C32—41no—
1063C32#561511yescharacteristic, complemented
1064C32#561911yescharacteristic, complemented
1065C32#569711yescharacteristic, complemented
1066C23—31no—
1067C23—31no—
1068C23—91no—
1069C23—91no—
1070C23—271no—
1071D4—121no—
1072D4—182no—
1073D4—361no—
1074D4—361no—
1075D4—361no—
1076D4—542no—
1077D4—1081no—
1078D4—1081no—
1079D4—1081no—
1080D4—1081no—
1081C2×C4—31no—
1082C2×C4—31no—
1083C2×C4—31no—
1084C2×C4—31no—
1085C2×C4—91no—
1086C2×C4—91no—
1087C2×C4—91no—
1088C2×C4—91no—
1089C2×C4—182no—
1090C2×C4—271no—
1091C2×C4—361no—
1092C2×C4—1081no—
1093C2×C4—1081no—
1094C2×C4—1081no—
1095C2×C4D3311yescharacteristic
1096C2×C3—21no—
1097C2×C3—21no—
1098C2×C3—21no—
1099C2×C3—21no—
1100C2×C3—21no—
1101C2×C3—21no—
1102C2×C3—21no—
1103C2×C3—21no—
1104C2×C3—21no—
1105C2×C3—41no—
1106C2×C3—41no—
1107C2×C3—41no—
1108C2×C3—121no—
1109C2×C3—121no—
1110C2×C3—121no—
1111C2×C3—121no—
1112C2×C3—241no—
1113C2×C3—241no—
1114C2×C3—361no—
1115C2×C3—361no—
1116C2×C3C2×#379611yescharacteristic
1117C2×C3#6430711yescharacteristic
1118C2×C3D3×#23711yescharacteristic
1119C2×C3#6431411yescharacteristic
1120C2×C3#6431411yescharacteristic
1121C2×C3#6431411yescharacteristic
1122C2×C3D3×#23911yescharacteristic
1123C2×C3#6432011yescharacteristic
1124C2×C3#6433011yescharacteristic
1125D3—41no—
1126D3—41no—
1127D3—122no—
1128D3—121no—
1129D3—121no—
1130D3—121no—
1131D3—121no—
1132D3—241no—
1133D3—362no—
1134D3—362no—
1135D3—362no—
1136D3—364no—
1137D3—361no—
1138D3—361no—
1139D3—361no—
1140C22—61no—
1141C22—61no—
1142C22—61no—
1143C22—61no—
1144C22—61no—
1145C22—61no—
1146C22—181no—
1147C22—181no—
1148C22—181no—
1149C22—181no—
1150C22—181no—
1151C22—181no—
1152C22—541no—
1153C22—541no—
1154C22—541no—
1155C22C2×D3311yescharacteristic
1156C4—21no—
1157C4—32no—
1158C4—61no—
1159C4—61no—
1160C4—61no—
1161C4—181no—
1162C4—181no—
1163C4—181no—
1164C4—181no—
1165C4—541no—
1166C3—21no—
1167C3—21no—
1168C3—21no—
1169C3—41no—
1170C3#1059450111yescharacteristic, complemented
1171C3#1059456311yescharacteristic, complemented
1172C3#1059519711yescharacteristic, complemented
1173C2—121no—
1174C2—121no—
1175C2—361no—
1176C2—361no—
1177C2—1081no—
1178C2D3×#379611yescharacteristic
1179C2#1172438511yescharacteristic
1180C2#1172441911yescharacteristic
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. #11723690C2semidirect
2. #11723531C2semidirect
3. #11723472C2semidirect
4. #11723421C2semidirect
5. C3×#63886C2semidirect
6. C3×#63886C2semidirect
7. C3×#63845C2semidirect
8. #11723030C2semidirect
9. #11722991C2semidirect
10. #11722987C2semidirect
11. #11722966C2semidirect
12. #11722962C2semidirect
13. #11722959C2semidirect
14. #11722927C2semidirect
15. #11722913C2semidirect
87. #63886D3semidirect
88. #63886D3semidirect
101. #63845D3semidirect
733. C33#540semidirect
1063. C32#5615semidirect
1064. C32#5619semidirect
1065. C32#5697semidirect
1170. C3#10594501semidirect
1171. C3#10594563semidirect
1172. C3#10595197semidirect

Maximal subgroups

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

subgroupindex
#117236902
#117235312
#117234722
#117234212
C3×#638862
C3×#638452
#117230302
#117229912
#117229872
#117229662
#117229622
#117229592
#117229272
#117229132
#105951973
#105945633
#105945013