Finite Group Databasebeta

← #13167980

Subgroups — #13167980

Order 1728.

1234 conjugacy classes of subgroups.

The subgroup lattice has 998 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723669C211yesmaximal, characteristic, complemented
2#11723503C211yesmaximal, characteristic
3#11723470C211yesmaximal, characteristic
4#11723470C211yesmaximal, characteristic
5C3×#63847C211yesmaximal, characteristic, complemented
6C3×#63846C211yesmaximal, characteristic, complemented
7C3×#63845C211yesmaximal, characteristic, complemented
8#11723017C211yesmaximal, characteristic, complemented
9#11723014C211yesmaximal, characteristic, complemented
10#11723012C211yesmaximal, characteristic, complemented
11#11723011C211yesmaximal, characteristic, complemented
12#11722912C211yesmaximal, characteristic
13#11722912C211yesmaximal, characteristic
14#11722912C211yesmaximal, characteristic
15#11722900C211yesmaximal, characteristic
16#10594482—31nomaximal
17#10594399—31nomaximal
18#10594399—31nomaximal
19C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
20C2×#6289C2211yescharacteristic
21C2×#6289C2211yescharacteristic
22C2×#6289C2211yescharacteristic
23C2×#6289C2211yescharacteristic
24C2×#6289C2211yescharacteristic
25C2×#6289C2211yescharacteristic
26C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
27C3×#3750C2211yescharacteristic
28C3×#3750C2211yescharacteristic
29C32×C4⋊Dic3C2211yescharacteristic
30C32×Dic3⋊C4C2211yescharacteristic
31C32×Dic3⋊C4C2211yescharacteristic
32#88815C2211yescharacteristic
33#88815C2211yescharacteristic
34#88815C2211yescharacteristic
35#88813C2211yescharacteristic
36#88807C2211yescharacteristic
37#88807C2211yescharacteristic
38#88806C2211yescharacteristic
39#88806C2211yescharacteristic
40Dic3⋊(C3⋊Dic3)C2211yescharacteristic
41Dic3⋊(C3⋊Dic3)C2211yescharacteristic
42C3×#3724C2211yescharacteristic
43C3×#3724C2211yescharacteristic
44C3×#3724C2211yescharacteristic
45C3×Dic3⋊Dic3C2211yescharacteristic
46C3×Dic3⋊Dic3C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×Dic3⋊Dic3C2211yescharacteristic
50C3×Dic3⋊Dic3C2211yescharacteristic
51C3×Dic32C2211yescharacteristic
52C3×Dic32C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54C4⋊C4×C3⋊D3—31no—
55C4⋊C4×C3⋊D3—31no—
56C4⋊C4×C3⋊D3—31no—
57C3×#890—31no—
58C3×#890—31no—
59C3×#889—31no—
60C3×#889—31no—
61C3×#889—31no—
62C3×#889—31no—
63#63900—31no—
64#63900—31no—
65#63900—31no—
66#63900—31no—
67#63900—31no—
68#63900—61no—
69#63883—31no—
70#63883—31no—
71#63883—31no—
72#63883—31no—
73#63883—31no—
74#63883—31no—
75#63883—31no—
76#63883—31no—
77#63883—31no—
78#63883—31no—
79#63883—61no—
80#63883—61no—
81C4×#624—31no—
82C4×#624—31no—
83C4×#624—31no—
84#63869—31no—
85#63869—31no—
86#63867—31no—
87#63867—31no—
88#63867—31no—
89#63867—31no—
90#63847—31no—
91#63847—31no—
92#63847—31no—
93#63847D311yescharacteristic, complemented
94#63846—31no—
95#63846—31no—
96#63846—31no—
97#63846D311yescharacteristic, complemented
98#63845—31no—
99#63845—31no—
100#63845—31no—
101#63845D311yescharacteristic, complemented
102C22×C3⋊(C3⋊D3)C2311yescharacteristic
103C2×C33×C4C2311yescharacteristic
104C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
105C4×C3⋊(C3⋊D3)—22no—
106C2×C3×C3⋊Dic3C2311yescharacteristic
107C2×C3×C3⋊Dic3C2311yescharacteristic
108C2×C3×C3⋊Dic3C2311yescharacteristic
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C32×Dic3C2311yescharacteristic
113C2×C32×Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118#6289—22no—
119#6289—22no—
120#6289—22no—
121#6289—22no—
122#6289—22no—
123#6289Q814yes—
124D3×#125—91no—
125D3×#125—91no—
126D3×#125—91no—
127C2×C4×C3⋊D3—31no—
128C2×C4×C3⋊D3—31no—
129C2×C4×C3⋊D3—31no—
130C2×C4×C3⋊D3—31no—
131C2×C4×C3⋊D3—31no—
132C2×C4×C3⋊D3—31no—
133C2×C4×C3⋊D3—31no—
134C2×C4×C3⋊D3—31no—
135C2×C4×C3⋊D3—31no—
136C2×C4×C3⋊D3—61no—
137C2×C4×C3⋊D3—61no—
138C2×C4×C3⋊D3—61no—
139C2×C4×C3⋊D3—121no—
140C2×#624—31no—
141C2×#624—31no—
142C2×#624—31no—
143C2×#624—31no—
144C2×#624—31no—
145C2×#624—31no—
146C2×#624—31no—
147C2×#624—31no—
148C2×#624—31no—
149C2×#624—31no—
150C2×#624—31no—
151C2×#624—31no—
152C2×#624—61no—
153C2×#624—61no—
154C2×#624—61no—
155C2×#624—61no—
156C2×#624—61no—
157C2×#624—61no—
158C32×C4⋊C4—31no—
159C32×C4⋊C4—31no—
160C32×C4⋊C4—31no—
161C4⋊(C3⋊Dic3)—31no—
162C4⋊(C3⋊Dic3)—31no—
163C4⋊(C3⋊Dic3)C2×D311yescharacteristic
164#3750—31no—
165#3750—31no—
166#3750—31no—
167#3750—31no—
168#3750C2×D311yescharacteristic
169#3750C2×D311yescharacteristic
170C3×C4⋊Dic3—21no—
171C3×C4⋊Dic3—31no—
172C3×C4⋊Dic3—31no—
173C3×C4⋊Dic3—31no—
174C3×C4⋊Dic3—31no—
175C3×C4⋊Dic3—31no—
176C3×C4⋊Dic3—31no—
177C3×C4⋊Dic3—31no—
178C3×C4⋊Dic3—31no—
179C3×C4⋊Dic3—61no—
180C3×C4⋊Dic3C2×D311yescharacteristic
181C3×C4⋊Dic3C2×D311yescharacteristic
182C3×Dic3⋊C4—21no—
183C3×Dic3⋊C4—21no—
184C3×Dic3⋊C4—31no—
185C3×Dic3⋊C4—31no—
186C3×Dic3⋊C4—31no—
187C3×Dic3⋊C4—31no—
188C3×Dic3⋊C4—31no—
189C3×Dic3⋊C4—31no—
190C3×Dic3⋊C4—31no—
191C3×Dic3⋊C4—31no—
192C3×Dic3⋊C4—31no—
193C3×Dic3⋊C4—31no—
194C3×Dic3⋊C4—31no—
195C3×Dic3⋊C4—31no—
196C3×Dic3⋊C4—31no—
197C3×Dic3⋊C4—31no—
198C3×Dic3⋊C4—31no—
199C3×Dic3⋊C4—31no—
200C3×Dic3⋊C4—61no—
201C3×Dic3⋊C4—61no—
202C3×Dic3⋊C4C2×D311yescharacteristic
203C3×Dic3⋊C4C2×D311yescharacteristic
204C3×Dic3⋊C4C2×D311yescharacteristic
205C3×Dic3⋊C4C2×D311yescharacteristic
206C3×C4×Dic3—31no—
207C3×C4×Dic3—31no—
208C3×C4×Dic3—31no—
209C3×C4×Dic3—31no—
210C3×C4×Dic3—31no—
211C3×C4×Dic3—31no—
212#3724—31no—
213#3724—31no—
214#3724—31no—
215#3724—31no—
216#3724—31no—
217#3724—31no—
218#3724—31no—
219#3724—61no—
220#3724—61no—
221#3724C2×D311yescharacteristic
222#3724C2×D311yescharacteristic
223#3724C2×D311yescharacteristic
224Dic3⋊Dic3—31no—
225Dic3⋊Dic3—31no—
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—31no—
235Dic3⋊Dic3—31no—
236Dic3⋊Dic3—31no—
237Dic3⋊Dic3—31no—
238Dic3⋊Dic3—61no—
239Dic3⋊Dic3—61no—
240Dic3⋊Dic3—61no—
241Dic3⋊Dic3—61no—
242Dic3⋊Dic3C2×D311yescharacteristic
243Dic3⋊Dic3C2×D311yescharacteristic
244Dic3⋊Dic3C2×D311yescharacteristic
245Dic3⋊Dic3C2×D311yescharacteristic
246Dic3⋊Dic3C2×D311yescharacteristic
247Dic3⋊Dic3C2×D311yescharacteristic
248Dic32—31no—
249Dic32—31no—
250Dic32—31no—
251Dic32C2×D311yescharacteristic
252Dic32C2×D311yescharacteristic
253Dic32C2×D311yescharacteristic
254C22×C33C2411yescharacteristic
255C2×C3⋊(C3⋊D3)C2×Q812yes—
256C2×C3⋊(C3⋊D3)#4112yes—
257C2×C3⋊(C3⋊D3)#4112yes—
258C33×C4—21no—
259C3⋊(C3⋊Dic3)—21no—
260C3×C3⋊Dic3—21no—
261C3×C3⋊Dic3—21no—
262C3×C3⋊Dic3—21no—
263C3×C3⋊Dic3—21no—
264C3×C3⋊Dic3—21no—
265C3×C3⋊Dic3C2×Q812yes—
266C32×Dic3—21no—
267C32×Dic3—21no—
268C32×Dic3—21no—
269C32×Dic3—21no—
270C32×Dic3—21no—
271C32×Dic3C2×Q812yes—
272C3×#125—91no—
273C3×#125—91no—
274C3×#125—91no—
275D3×C4⋊C4—91no—
276D3×C4⋊C4—91no—
277D3×C4⋊C4—91no—
278D3×C4⋊C4—91no—
279D3×C4⋊C4—91no—
280D3×C4⋊C4—91no—
281D3×C4⋊C4—91no—
282D3×C4⋊C4—91no—
283D3×C4⋊C4—91no—
284D3×C4⋊C4—91no—
285D3×C4⋊C4—91no—
286D3×C4⋊C4—91no—
287D3×C4⋊C4—91no—
288D3×C4⋊C4—91no—
289D3×C4⋊C4—91no—
290D3×C4⋊C4—91no—
291D3×C4⋊C4—91no—
292D3×C4⋊C4—91no—
293D3×C4⋊C4—181no—
294D3×C4⋊C4—181no—
295D3×C4⋊C4—181no—
296#890—31no—
297#890—31no—
298#890—91no—
299#890—91no—
300#890—91no—
301#890—91no—
302#889—31no—
303#889—31no—
304#889—31no—
305#889—31no—
306#889—91no—
307#889—91no—
308#889—91no—
309#889—91no—
310#889—91no—
311#889—91no—
312#889—91no—
313#889—91no—
314C42×D3—91no—
315C42×D3—91no—
316C42×D3—91no—
317#870—91no—
318#870—91no—
319#870—91no—
320C22×C3⋊D3—31no—
321C22×C3⋊D3—31no—
322C22×C3⋊D3—31no—
323C22×C3⋊D3—61no—
324C22×C3⋊D3—61no—
325C22×C3⋊D3—61no—
326C22×C3⋊D3—121no—
327C2×C32×C4—21no—
328C2×C32×C4—21no—
329C2×C32×C4—21no—
330C2×C32×C4—31no—
331C2×C32×C4—31no—
332C2×C32×C4—31no—
333C2×C32×C4—31no—
334C2×C32×C4—31no—
335C2×C32×C4—31no—
336C2×C32×C4—41no—
337C2×C32×C4C22×D311yescharacteristic
338C2×C32×C4C22×D311yescharacteristic
339C2×C32×C4C22×D311yescharacteristic
340C2×C3⋊Dic3—31no—
341C2×C3⋊Dic3—31no—
342C2×C3⋊Dic3—31no—
343C2×C3⋊Dic3—61no—
344C2×C3⋊Dic3—61no—
345C2×C3⋊Dic3—61no—
346C2×C3⋊Dic3—121no—
347C2×C3⋊Dic3C22×D311yescharacteristic
348C2×C3⋊Dic3C22×D311yescharacteristic
349C2×C3⋊Dic3C22×D311yescharacteristic
350C2×C3⋊Dic3C22×D311yescharacteristic
351C2×C3⋊Dic3C22×D311yescharacteristic
352C2×C3⋊Dic3C22×D311yescharacteristic
353C4×C3⋊D3—34no—
354C4×C3⋊D3—62no—
355C4×C3⋊D3—62no—
356C4×C3⋊D3—62no—
357C4×C3⋊D3—62no—
358C4×C3⋊D3—62no—
359C4×C3⋊D3—62no—
360C4×C3⋊D3—62no—
361C4×C3⋊D3—62no—
362C4×C3⋊D3—64no—
363C4×C3⋊D3—122no—
364C4×C3⋊D3—122no—
365C4×C3⋊D3—124no—
366C2×C3×Dic3—21no—
367C2×C3×Dic3—21no—
368C2×C3×Dic3—21no—
369C2×C3×Dic3—21no—
370C2×C3×Dic3—21no—
371C2×C3×Dic3—21no—
372C2×C3×Dic3—31no—
373C2×C3×Dic3—31no—
374C2×C3×Dic3—31no—
375C2×C3×Dic3—31no—
376C2×C3×Dic3—31no—
377C2×C3×Dic3—31no—
378C2×C3×Dic3—31no—
379C2×C3×Dic3—31no—
380C2×C3×Dic3—31no—
381C2×C3×Dic3—31no—
382C2×C3×Dic3—31no—
383C2×C3×Dic3—31no—
384C2×C3×Dic3—61no—
385C2×C3×Dic3—61no—
386C2×C3×Dic3—61no—
387C2×C3×Dic3—61no—
388C2×C3×Dic3—61no—
389C2×C3×Dic3—61no—
390C2×C3×Dic3C22×D311yescharacteristic
391C2×C3×Dic3C22×D311yescharacteristic
392C2×C3×Dic3C22×D311yescharacteristic
393C2×C3×Dic3C22×D311yescharacteristic
394C2×C3×Dic3C22×D311yescharacteristic
395C2×C3×Dic3C22×D311yescharacteristic
396C2×C3×Dic3C22×D311yescharacteristic
397C2×C3×Dic3C22×D311yescharacteristic
398C2×C3×Dic3C22×D311yescharacteristic
399C2×C3×Dic3C22×D311yescharacteristic
400C2×C3×Dic3C22×D311yescharacteristic
401C2×C3×Dic3C22×D311yescharacteristic
402#624—34no—
403#624—34no—
404#624—64no—
405#624—62no—
406#624—62no—
407#624—62no—
408#624—62no—
409#624—62no—
410#624—62no—
411#624—62no—
412#624—62no—
413#624—62no—
414#624—62no—
415#624—64no—
416#624—122no—
417#624—122no—
418#624—122no—
419#624—122no—
420C2×#125—271noSylow
421C2×C33C22×Q811yescharacteristic
422C2×C33C2×#4111yescharacteristic
423C2×C33C2×#4111yescharacteristic
424C3⋊(C3⋊D3)#12514yescomplemented
425C2×C4×D3—91no—
426C2×C4×D3—91no—
427C2×C4×D3—91no—
428C2×C4×D3—91no—
429C2×C4×D3—91no—
430C2×C4×D3—91no—
431C2×C4×D3—91no—
432C2×C4×D3—91no—
433C2×C4×D3—91no—
434C2×C4×D3—91no—
435C2×C4×D3—91no—
436C2×C4×D3—91no—
437C2×C4×D3—91no—
438C2×C4×D3—91no—
439C2×C4×D3—91no—
440C2×C4×D3—91no—
441C2×C4×D3—91no—
442C2×C4×D3—91no—
443C2×C4×D3—91no—
444C2×C4×D3—91no—
445C2×C4×D3—91no—
446C2×C4×D3—181no—
447C2×C4×D3—181no—
448C2×C4×D3—181no—
449C2×C4×D3—181no—
450C2×C4×D3—181no—
451C2×C4×D3—181no—
452C2×C4×D3—181no—
453C2×C4×D3—181no—
454C2×C4×D3—181no—
455C2×C4×D3—361no—
456C3×C4⋊C4—31no—
457C3×C4⋊C4—31no—
458C3×C4⋊C4—31no—
459C3×C4⋊C4—31no—
460C3×C4⋊C4—31no—
461C3×C4⋊C4—31no—
462C3×C4⋊C4—61no—
463C3×C4⋊C4—61no—
464C3×C4⋊C4—61no—
465C3×C4⋊C4—91no—
466C3×C4⋊C4—91no—
467C3×C4⋊C4—91no—
468C3×C4⋊C4—91no—
469C3×C4⋊C4—91no—
470C3×C4⋊C4—91no—
471C3×C4⋊C4—91no—
472C3×C4⋊C4—91no—
473C3×C4⋊C4—91no—
474C3×C4⋊C4—91no—
475C3×C4⋊C4—91no—
476C3×C4⋊C4—91no—
477C3×C42—91no—
478C3×C42—91no—
479C3×C42—91no—
480C4⋊Dic3—31no—
481C4⋊Dic3—31no—
482C4⋊Dic3—31no—
483C4⋊Dic3—31no—
484C4⋊Dic3—31no—
485C4⋊Dic3—31no—
486C4⋊Dic3—31no—
487C4⋊Dic3—31no—
488C4⋊Dic3—61no—
489C4⋊Dic3—91no—
490C4⋊Dic3—91no—
491C4⋊Dic3—91no—
492C4⋊Dic3—91no—
493C4⋊Dic3—91no—
494C4⋊Dic3—91no—
495C4⋊Dic3—91no—
496C4⋊Dic3—91no—
497C4⋊Dic3—91no—
498C4⋊Dic3—181no—
499C4⋊Dic3—181no—
500C4⋊Dic3D3211yescharacteristic
501Dic3⋊C4—31no—
502Dic3⋊C4—31no—
503Dic3⋊C4—31no—
504Dic3⋊C4—31no—
505Dic3⋊C4—31no—
506Dic3⋊C4—31no—
507Dic3⋊C4—31no—
508Dic3⋊C4—31no—
509Dic3⋊C4—31no—
510Dic3⋊C4—31no—
511Dic3⋊C4—31no—
512Dic3⋊C4—31no—
513Dic3⋊C4—31no—
514Dic3⋊C4—31no—
515Dic3⋊C4—31no—
516Dic3⋊C4—31no—
517Dic3⋊C4—61no—
518Dic3⋊C4—61no—
519Dic3⋊C4—91no—
520Dic3⋊C4—91no—
521Dic3⋊C4—91no—
522Dic3⋊C4—91no—
523Dic3⋊C4—91no—
524Dic3⋊C4—91no—
525Dic3⋊C4—91no—
526Dic3⋊C4—91no—
527Dic3⋊C4—91no—
528Dic3⋊C4—91no—
529Dic3⋊C4—91no—
530Dic3⋊C4—91no—
531Dic3⋊C4—91no—
532Dic3⋊C4—91no—
533Dic3⋊C4—91no—
534Dic3⋊C4—91no—
535Dic3⋊C4—91no—
536Dic3⋊C4—91no—
537Dic3⋊C4—181no—
538Dic3⋊C4—181no—
539Dic3⋊C4—181no—
540Dic3⋊C4—181no—
541Dic3⋊C4D3211yescharacteristic
542Dic3⋊C4D3211yescharacteristic
543C4×Dic3—31no—
544C4×Dic3—31no—
545C4×Dic3—31no—
546C4×Dic3—31no—
547C4×Dic3—31no—
548C4×Dic3—31no—
549C4×Dic3—91no—
550C4×Dic3—91no—
551C4×Dic3—91no—
552C22×C32—21no—
553C22×C32—21no—
554C22×C32—21no—
555C22×C32—41no—
556C22×C32C23×D311yescharacteristic
557C22×C32C23×D311yescharacteristic
558C22×C32C23×D311yescharacteristic
559C2×C3⋊D3—32no—
560C2×C3⋊D3—32no—
561C2×C3⋊D3—32no—
562C2×C3⋊D3—32no—
563C2×C3⋊D3—32no—
564C2×C3⋊D3—32no—
565C2×C3⋊D3—32no—
566C2×C3⋊D3—32no—
567C2×C3⋊D3—32no—
568C2×C3⋊D3—62no—
569C2×C3⋊D3—62no—
570C2×C3⋊D3—62no—
571C2×C3⋊D3—62no—
572C2×C3⋊D3—62no—
573C2×C3⋊D3—62no—
574C2×C3⋊D3—62no—
575C2×C3⋊D3—62no—
576C2×C3⋊D3—62no—
577C2×C3⋊D3—122no—
578C2×C3⋊D3—122no—
579C2×C3⋊D3—122no—
580C32×C4—21no—
581C32×C4—22no—
582C32×C4—21no—
583C32×C4—21no—
584C32×C4—32no—
585C32×C4—41no—
586C32×C4—41no—
587C32×C4—42no—
588C32×C4—61no—
589C32×C4—61no—
590C32×C4—61no—
591C32×C4—61no—
592C32×C4—61no—
593C3⋊Dic3—21no—
594C3⋊Dic3—21no—
595C3⋊Dic3—21no—
596C3⋊Dic3—21no—
597C3⋊Dic3—21no—
598C3⋊Dic3—61no—
599C3⋊Dic3—62no—
600C3⋊Dic3—61no—
601C3⋊Dic3—61no—
602C3⋊Dic3—121no—
603C3⋊Dic3—121no—
604C3⋊Dic3—122no—
605C3⋊Dic3D3×Q812yes—
606C3×Dic3—22no—
607C3×Dic3—21no—
608C3×Dic3—21no—
609C3×Dic3—21no—
610C3×Dic3—21no—
611C3×Dic3—21no—
612C3×Dic3—21no—
613C3×Dic3—21no—
614C3×Dic3—21no—
615C3×Dic3—21no—
616C3×Dic3—21no—
617C3×Dic3—22no—
618C3×Dic3—32no—
619C3×Dic3—32no—
620C3×Dic3—41no—
621C3×Dic3—41no—
622C3×Dic3—41no—
623C3×Dic3—41no—
624C3×Dic3—62no—
625C3×Dic3—62no—
626C3×Dic3—61no—
627C3×Dic3—61no—
628C3×Dic3—61no—
629C3×Dic3—61no—
630C3×Dic3—61no—
631C3×Dic3—61no—
632C3×Dic3—61no—
633C3×Dic3—61no—
634C3×Dic3—61no—
635C3×Dic3—61no—
636C3×Dic3—121no—
637C3×Dic3—121no—
638C3×Dic3—121no—
639C3×Dic3—121no—
640C3×Dic3D3×Q812yes—
641C3×Dic3D3×Q812yes—
642#125—91no—
643#125—91no—
644#125—91no—
645#125—271no—
646#125—271no—
647#125—271no—
648#125—271no—
649#125—271no—
650C2×C4⋊C4—271no—
651C2×C4⋊C4—271no—
652C2×C4⋊C4—271no—
653C2×C4⋊C4—271no—
654C2×C4⋊C4—271no—
655C2×C4⋊C4—271no—
656C2×C42—271no—
657C33C2×#12511yescharacteristic, complemented, Sylow
658C22×D3—91no—
659C22×D3—91no—
660C22×D3—91no—
661C22×D3—181no—
662C22×D3—181no—
663C22×D3—181no—
664C22×D3—361no—
665C2×C3×C4—21no—
666C2×C3×C4—21no—
667C2×C3×C4—21no—
668C2×C3×C4—31no—
669C2×C3×C4—31no—
670C2×C3×C4—31no—
671C2×C3×C4—31no—
672C2×C3×C4—31no—
673C2×C3×C4—31no—
674C2×C3×C4—31no—
675C2×C3×C4—31no—
676C2×C3×C4—31no—
677C2×C3×C4—31no—
678C2×C3×C4—31no—
679C2×C3×C4—31no—
680C2×C3×C4—41no—
681C2×C3×C4—61no—
682C2×C3×C4—61no—
683C2×C3×C4—61no—
684C2×C3×C4—61no—
685C2×C3×C4—61no—
686C2×C3×C4—61no—
687C2×C3×C4—91no—
688C2×C3×C4—91no—
689C2×C3×C4—91no—
690C2×C3×C4—91no—
691C2×C3×C4—91no—
692C2×C3×C4—91no—
693C2×C3×C4C2×D3211yescharacteristic
694C2×C3×C4C2×D3211yescharacteristic
695C2×C3×C4C2×D3211yescharacteristic
696C2×Dic3—31no—
697C2×Dic3—31no—
698C2×Dic3—31no—
699C2×Dic3—31no—
700C2×Dic3—31no—
701C2×Dic3—31no—
702C2×Dic3—31no—
703C2×Dic3—31no—
704C2×Dic3—31no—
705C2×Dic3—31no—
706C2×Dic3—31no—
707C2×Dic3—31no—
708C2×Dic3—61no—
709C2×Dic3—61no—
710C2×Dic3—61no—
711C2×Dic3—61no—
712C2×Dic3—61no—
713C2×Dic3—61no—
714C2×Dic3—91no—
715C2×Dic3—91no—
716C2×Dic3—91no—
717C2×Dic3—181no—
718C2×Dic3—181no—
719C2×Dic3—181no—
720C2×Dic3—361no—
721C2×Dic3C2×D3211yescharacteristic
722C2×Dic3C2×D3211yescharacteristic
723C2×Dic3C2×D3211yescharacteristic
724C2×Dic3C2×D3211yescharacteristic
725C2×Dic3C2×D3211yescharacteristic
726C2×Dic3C2×D3211yescharacteristic
727C4×D3—94no—
728C4×D3—94no—
729C4×D3—94no—
730C4×D3—184no—
731C4×D3—182no—
732C4×D3—182no—
733C4×D3—182no—
734C4×D3—182no—
735C4×D3—182no—
736C4×D3—182no—
737C4×D3—182no—
738C4×D3—182no—
739C4×D3—182no—
740C4×D3—182no—
741C4×D3—182no—
742C4×D3—182no—
743C4×D3—182no—
744C4×D3—182no—
745C4×D3—182no—
746C4×D3—184no—
747C4×D3—182no—
748C4×D3—182no—
749C4×D3—182no—
750C4×D3—184no—
751C4×D3—362no—
752C4×D3—362no—
753C4×D3—362no—
754C4×D3—362no—
755C4×D3—362no—
756C4×D3—362no—
757C4×D3—364no—
758C2×C32—21no—
759C2×C32—21no—
760C2×C32—21no—
761C2×C32—21no—
762C2×C32—21no—
763C2×C32—21no—
764C2×C32—21no—
765C2×C32—21no—
766C2×C32—21no—
767C2×C32—41no—
768C2×C32—41no—
769C2×C32—41no—
770C2×C32C2×D3×Q811yescharacteristic
771C2×C32C2×D3×Q811yescharacteristic
772C2×C32C2×D3×Q811yescharacteristic
773C2×C32D3×#4111yescharacteristic
774C2×C32D3×#4111yescharacteristic
775C2×C32D3×#4111yescharacteristic
776C2×C32D3×#4111yescharacteristic
777C2×C32D3×#4111yescharacteristic
778C2×C32D3×#4111yescharacteristic
779C3⋊D3—34no—
780C3⋊D3—34no—
781C3⋊D3—34no—
782C3⋊D3—64no—
783C3⋊D3—64no—
784C3⋊D3—64no—
785C3⋊D3—124no—
786C22×C4—271no—
787C22×C4—271no—
788C22×C4—271no—
789C22×C4—271no—
790C22×C4—271no—
791C22×C4—271no—
792C22×C4—271no—
793C4⋊C4—31no—
794C4⋊C4—31no—
795C4⋊C4—31no—
796C4⋊C4—91no—
797C4⋊C4—91no—
798C4⋊C4—91no—
799C4⋊C4—91no—
800C4⋊C4—91no—
801C4⋊C4—91no—
802C4⋊C4—91no—
803C4⋊C4—91no—
804C4⋊C4—91no—
805C4⋊C4—91no—
806C4⋊C4—91no—
807C4⋊C4—91no—
808C4⋊C4—271no—
809C4⋊C4—271no—
810C4⋊C4—271no—
811C4⋊C4—271no—
812C4⋊C4—271no—
813C4⋊C4—271no—
814C4⋊C4—271no—
815C4⋊C4—271no—
816C4⋊C4—271no—
817C42—91no—
818C42—91no—
819C42—91no—
820C42—271no—
821C22×C3—21no—
822C22×C3—21no—
823C22×C3—21no—
824C22×C3—41no—
825C22×C3C22×D3211yescharacteristic
826C22×C3C22×D3211yescharacteristic
827C22×C3C22×D3211yescharacteristic
828C2×D3—92no—
829C2×D3—92no—
830C2×D3—92no—
831C2×D3—92no—
832C2×D3—92no—
833C2×D3—92no—
834C2×D3—92no—
835C2×D3—92no—
836C2×D3—92no—
837C2×D3—182no—
838C2×D3—182no—
839C2×D3—182no—
840C2×D3—182no—
841C2×D3—182no—
842C2×D3—182no—
843C2×D3—182no—
844C2×D3—182no—
845C2×D3—182no—
846C2×D3—362no—
847C2×D3—362no—
848C2×D3—362no—
849C3×C4—22no—
850C3×C4—21no—
851C3×C4—21no—
852C3×C4—21no—
853C3×C4—32no—
854C3×C4—32no—
855C3×C4—41no—
856C3×C4—41no—
857C3×C4—42no—
858C3×C4—62no—
859C3×C4—62no—
860C3×C4—61no—
861C3×C4—61no—
862C3×C4—61no—
863C3×C4—61no—
864C3×C4—61no—
865C3×C4—61no—
866C3×C4—61no—
867C3×C4—61no—
868C3×C4—61no—
869C3×C4—61no—
870C3×C4—92no—
871C3×C4—121no—
872C3×C4—121no—
873C3×C4—121no—
874C3×C4—121no—
875C3×C4—181no—
876C3×C4—181no—
877C3×C4—181no—
878C3×C4—181no—
879C3×C4—181no—
880Dic3—21no—
881Dic3—21no—
882Dic3—21no—
883Dic3—21no—
884Dic3—21no—
885Dic3—32no—
886Dic3—32no—
887Dic3—62no—
888Dic3—62no—
889Dic3—61no—
890Dic3—61no—
891Dic3—61no—
892Dic3—61no—
893Dic3—61no—
894Dic3—61no—
895Dic3—61no—
896Dic3—61no—
897Dic3—61no—
898Dic3—61no—
899Dic3—121no—
900Dic3—121no—
901Dic3—121no—
902Dic3—121no—
903Dic3—182no—
904Dic3—181no—
905Dic3—181no—
906Dic3—181no—
907Dic3—361no—
908Dic3—361no—
909Dic3—362no—
910Dic3#379712yes—
911C32—21no—
912C32—21no—
913C32—21no—
914C32—41no—
915C32D3×#12511yescharacteristic, complemented
916C32D3×#12511yescharacteristic, complemented
917C32D3×#12511yescharacteristic, complemented
918C23—271no—
919C2×C4—31no—
920C2×C4—31no—
921C2×C4—31no—
922C2×C4—31no—
923C2×C4—31no—
924C2×C4—31no—
925C2×C4—91no—
926C2×C4—91no—
927C2×C4—91no—
928C2×C4—91no—
929C2×C4—91no—
930C2×C4—91no—
931C2×C4—274no—
932C2×C4—271no—
933C2×C4—542no—
934C2×C4—542no—
935C2×C4—542no—
936C2×C4—542no—
937C2×C4—542no—
938C2×C4—542no—
939C2×C4D3311yescharacteristic
940C2×C3—21no—
941C2×C3—21no—
942C2×C3—21no—
943C2×C3—21no—
944C2×C3—21no—
945C2×C3—21no—
946C2×C3—21no—
947C2×C3—21no—
948C2×C3—21no—
949C2×C3—41no—
950C2×C3—41no—
951C2×C3—41no—
952C2×C3C2×#379711yescharacteristic
953C2×C3#6430611yescharacteristic
954C2×C3#6430611yescharacteristic
955C2×C3#6431211yescharacteristic
956C2×C3#6431211yescharacteristic
957C2×C3#6431211yescharacteristic
958C2×C3D32×Q811yescharacteristic
959C2×C3D32×Q811yescharacteristic
960C2×C3#6431911yescharacteristic
961D3—94no—
962D3—94no—
963D3—94no—
964D3—184no—
965D3—184no—
966D3—184no—
967D3—364no—
968C22—272no—
969C22—272no—
970C22—272no—
971C22C2×D3311yescharacteristic
972C4—21no—
973C4—32no—
974C4—61no—
975C4—61no—
976C4—61no—
977C4—61no—
978C4—61no—
979C4—92no—
980C4—181no—
981C4—181no—
982C4—181no—
983C4—181no—
984C4—181no—
985C4—541no—
986C3—21no—
987C3—21no—
988C3—21no—
989C3—41no—
990C3#1059439911yescharacteristic, complemented
991C3#1059439911yescharacteristic, complemented
992C3#1059448211yescharacteristic, complemented
993C2—274no—
994C2D3×#379711yescharacteristic
995C2#1172437611yescharacteristic
996C2#1172441111yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC22×C3⋊(C3⋊D3)C23
hypercenterC2×C4D33
hypocenterC33C2×#125
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. #11723669C2semidirect
5. C3×#63847C2semidirect
6. C3×#63846C2semidirect
7. C3×#63845C2semidirect
8. #11723017C2semidirect
9. #11723014C2semidirect
10. #11723012C2semidirect
11. #11723011C2semidirect
93. #63847D3semidirect
97. #63846D3semidirect
101. #63845D3semidirect
424. C3⋊(C3⋊D3)#125semidirect
657. C33C2×#125semidirect
915. C32D3×#125semidirect
916. C32D3×#125semidirect
917. C32D3×#125semidirect
990. C3#10594399semidirect
991. C3#10594399semidirect
992. C3#10594482semidirect

Maximal subgroups

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

subgroupindex
#117236692
#117235032
#117234702
C3×#638472
C3×#638462
C3×#638452
#117230172
#117230142
#117230122
#117230112
#117229122
#117229002
#105944823
#105943993