Finite Group Databasebeta

← #13178129

Subgroups — #13178129

Order 1728.

1112 conjugacy classes of subgroups.

The subgroup lattice has 1042 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64085C211yesmaximal, characteristic, complemented
2C3×C4×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
3C3×#64079C211yesmaximal, characteristic, complemented
4#11723694C211yesmaximal, characteristic, complemented
5#11723692C211yesmaximal, characteristic, complemented
6#11723692C211yesmaximal, characteristic, complemented
7#11723690C211yesmaximal, characteristic, complemented
8#11723690C211yesmaximal, characteristic, complemented
9#11723687C211yesmaximal, characteristic
10#11723686C211yesmaximal, characteristic, complemented
11#11723684C211yesmaximal, characteristic, complemented
12#11723682C211yesmaximal, characteristic, complemented
13#11723675C211yesmaximal, characteristic, complemented
14#11723671C211yesmaximal, characteristic, complemented
15#11723669C211yesmaximal, characteristic, complemented
16#10593946—31nomaximal
17#10593914—31nomaximal
18#10593913—31nomaximal
19C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
20C2×C3×C4×C3⋊D3C2211yescharacteristic
21C2×C3×C4×C3⋊D3C2211yescharacteristic
22C2×#6296C2211yescharacteristic
23C2×#6295C2211yescharacteristic
24C2×#6295C2211yescharacteristic
25C2×#6294C2211yescharacteristic
26C2×#6294C2211yescharacteristic
27C2×#6294C2211yescharacteristic
28C33×C42C2211yescharacteristic
29C3×#3752C2211yescharacteristic
30C3×#3752C2211yescharacteristic
31C3×#3752C2211yescharacteristic
32C3×#3752C2211yescharacteristic
33C3×#3752C2211yescharacteristic
34C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
35C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
36C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
37C3×#3750C2211yescharacteristic
38C3×#3750C2211yescharacteristic
39C3×#3750C2211yescharacteristic
40C3×#3750C2211yescharacteristic
41C3×#3750C2211yescharacteristic
42C3×#3750C2211yescharacteristic
43C3×#3750C2211yescharacteristic
44#88815C2211yescharacteristic
45#88815C2211yescharacteristic
46#88815C2211yescharacteristic
47#88815C2211yescharacteristic
48#88814C2211yescharacteristic
49#88814C2211yescharacteristic
50#88814C2211yescharacteristic
51#88814C2211yescharacteristic
52#88814C2211yescharacteristic
53#88813C2211yescharacteristic
54#64085D311yescharacteristic, complemented
55C4×C4⋊(C3⋊D3)D311yescharacteristic, complemented
56#64079D311yescharacteristic, complemented
57C3×#876—31no—
58C3×#876—31no—
59C3×#876—61no—
60C3×C4×D12—31no—
61C3×C4×D12—31no—
62C3×C4×D12—61no—
63C3×#870—31no—
64C3×#870—31no—
65C3×#870—61no—
66#63910—31no—
67#63905—31no—
68#63904—31no—
69#63899—31no—
70#63899—31no—
71#63897—31no—
72#63895—31no—
73#63895—31no—
74#63893—31no—
75#63893—31no—
76#63891—31no—
77#63891—31no—
78#63890—31no—
79#63890—31no—
80#63886—31no—
81#63885—31no—
82#63884—31no—
83#63884—31no—
84#63883—31no—
85#63881—31no—
86#63879—31no—
87D3×Dic3⋊C4—31no—
88D3×Dic3⋊C4—31no—
89#63865—31no—
90#63861—31no—
91#63858—31no—
92#63854—31no—
93#63854—31no—
94#63853—31no—
95#63851—31no—
96#63851—31no—
97#63850—31no—
98#63848—31no—
99#63847—31no—
100#63846—31no—
101#63845—31no—
102C22×C3×C3⋊D3C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C3×C3⋊D3C2311yescharacteristic
105C2×C33×C4C2311yescharacteristic
106C2×C33×C4C2311yescharacteristic
107C2×C33×C4C2311yescharacteristic
108C2×C3×C3⋊Dic3C2311yescharacteristic
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C3×C4⋊(C3⋊D3)—22no—
118C3×C4×C3⋊D3—41no—
119C3×C4×C3⋊D3—41no—
120#6296—41no—
121#6295—22no—
122#6295—41no—
123#6294—22no—
124#6294—41no—
125#6294—41no—
126#5707—91no—
127#5692—91no—
128#5564—91no—
129C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
130C2×C4×C3⋊D3C2×D311yescharacteristic
131C2×C4×C3⋊D3C2×D311yescharacteristic
132C2×C3×D12—31no—
133C2×C3×D12—31no—
134C2×C3×D12—61no—
135C2×C3×C4×D3—31no—
136C2×C3×C4×D3—31no—
137C2×C3×C4×D3—31no—
138C2×C3×C4×D3—31no—
139C2×C3×C4×D3—61no—
140C2×C3×C4×D3—61no—
141C2×#627—31no—
142C2×#627—31no—
143C2×#627—31no—
144C2×#626—31no—
145C2×#626—31no—
146C2×#626—31no—
147C2×#626—31no—
148C2×#625—31no—
149C2×#625—31no—
150C2×#624—31no—
151C2×#624—31no—
152C2×#624—31no—
153C2×D3×Dic3—31no—
154C2×D3×Dic3—31no—
155C2×D3×Dic3—31no—
156C2×D3×Dic3—31no—
157C2×D3×Dic3—31no—
158C2×D3×Dic3—31no—
159C32×C42—21no—
160C32×C42—21no—
161C32×C42—21no—
162C32×C42—41no—
163C32×C42C2×D311yescharacteristic
164C32×C42C2×D311yescharacteristic
165C32×C42C2×D311yescharacteristic
166#3752C2×D311yescharacteristic
167#3752C2×D311yescharacteristic
168#3752C2×D311yescharacteristic
169#3752C2×D311yescharacteristic
170#3752C2×D311yescharacteristic
171C4⋊(C3⋊Dic3)C2×D311yescharacteristic
172C4⋊(C3⋊Dic3)C2×D311yescharacteristic
173C4⋊(C3⋊Dic3)C2×D311yescharacteristic
174#3750C2×D311yescharacteristic
175#3750C2×D311yescharacteristic
176#3750C2×D311yescharacteristic
177#3750C2×D311yescharacteristic
178#3750C2×D311yescharacteristic
179#3750C2×D311yescharacteristic
180#3750C2×D311yescharacteristic
181C3×(C2×D3)⋊C4—31no—
182C3×(C2×D3)⋊C4—31no—
183C3×(C2×D3)⋊C4—31no—
184C3×(C2×D3)⋊C4—31no—
185C3×(C2×D3)⋊C4—31no—
186C3×(C2×D3)⋊C4—31no—
187C3×(C2×D3)⋊C4—31no—
188C3×(C2×D3)⋊C4—31no—
189C3×(C2×D3)⋊C4—31no—
190C3×(C2×D3)⋊C4—31no—
191C3×(C2×D3)⋊C4—61no—
192C3×(C2×D3)⋊C4—61no—
193C3×(C2×D3)⋊C4—61no—
194C3×(C2×D3)⋊C4—61no—
195C3×(C2×D3)⋊C4—61no—
196C3×C4⋊Dic3—31no—
197C3×C4⋊Dic3—31no—
198C3×C4⋊Dic3—31no—
199C3×C4⋊Dic3—31no—
200C3×C4⋊Dic3—31no—
201C3×C4⋊Dic3—31no—
202C3×C4⋊Dic3—61no—
203C3×C4⋊Dic3—61no—
204C3×C4⋊Dic3—61no—
205C3×Dic3⋊C4—31no—
206C3×Dic3⋊C4—31no—
207C3×Dic3⋊C4—31no—
208C3×Dic3⋊C4—31no—
209C3×Dic3⋊C4—31no—
210C3×Dic3⋊C4—31no—
211C3×Dic3⋊C4—31no—
212C3×Dic3⋊C4—31no—
213C3×Dic3⋊C4—31no—
214C3×Dic3⋊C4—31no—
215C3×Dic3⋊C4—31no—
216C3×Dic3⋊C4—31no—
217C3×Dic3⋊C4—31no—
218C3×Dic3⋊C4—31no—
219C3×Dic3⋊C4—61no—
220C3×Dic3⋊C4—61no—
221C3×Dic3⋊C4—61no—
222C3×Dic3⋊C4—61no—
223C3×Dic3⋊C4—61no—
224C3×Dic3⋊C4—61no—
225C3×Dic3⋊C4—61no—
226#3724—31no—
227#3724—31no—
228#3724—31no—
229#3724—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—
238#3722—31no—
239#3722—31no—
240#3722—31no—
241#3722—31no—
242#3722—31no—
243(C2×D3)⋊Dic3—31no—
244(C2×D3)⋊Dic3—31no—
245(C2×D3)⋊Dic3—31no—
246(C2×D3)⋊Dic3—31no—
247(C2×D3)⋊Dic3—31no—
248(C2×D3)⋊Dic3—31no—
249(C2×D3)⋊Dic3—31no—
250(C2×D3)⋊Dic3—31no—
251(C2×D3)⋊Dic3—31no—
252(C2×D3)⋊Dic3—31no—
253Dic32—31no—
254Dic32—31no—
255Dic32—31no—
256C22×C33C2411yescharacteristic
257C2×C3×C3⋊D3—21no—
258C2×C3×C3⋊D3—21no—
259C2×C3×C3⋊D3—21no—
260C2×C3×C3⋊D3—21no—
261C2×C3×C3⋊D3—21no—
262C2×C3×C3⋊D3—21no—
263C2×C3×C3⋊D3—21no—
264C2×C3×C3⋊D3—21no—
265C2×C3×C3⋊D3#4112yes—
266C33×C4—21no—
267C33×C4—21no—
268C33×C4—21no—
269C3×C3⋊Dic3—21no—
270C3×C3⋊Dic3—21no—
271C3×C3⋊Dic3—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—
278C3×#126—91no—
279C3×#125—91no—
280C3×C4×D4—91no—
281#939—91no—
282#935—91no—
283#929—91no—
284C4×#67—91no—
285#924—91no—
286C2×Dic3⋊C4—91no—
287#898—91no—
288#898—91no—
289#897—91no—
290#897—91no—
291#896—91no—
292#896—91no—
293#896—91no—
294#896—91no—
295#895—91no—
296#894—91no—
297#894—91no—
298#894—91no—
299#894—91no—
300#894—91no—
301#893—91no—
302D3×C4⋊C4—91no—
303D3×C4⋊C4—91no—
304#890—91no—
305#889—91no—
306#889—91no—
307#886—91no—
308#886—91no—
309#884—91no—
310#883—91no—
311#883—91no—
312#883—91no—
313#67⋊C4—91no—
314#879—91no—
315#878—91no—
316#878—91no—
317#876—31no—
318#876—31no—
319#876—61no—
320C4×D12—31no—
321C4×D12—31no—
322C4×D12—61no—
323#870—31no—
324#870—31no—
325#870—61no—
326C22×C3⋊D3C22×D311yescharacteristic
327C22×C3⋊D3C22×D311yescharacteristic
328C22×C3⋊D3C22×D311yescharacteristic
329C22×C3×D3—31no—
330C22×C3×D3—31no—
331C22×C3×D3—31no—
332C22×C3×D3—31no—
333C22×C3×D3—31no—
334C22×C3×D3—31no—
335C22×C3×D3—61no—
336C22×C3×D3—61no—
337C22×C3×D3—61no—
338C2×C32×C4—21no—
339C2×C32×C4—21no—
340C2×C32×C4—21no—
341C2×C32×C4—21no—
342C2×C32×C4—21no—
343C2×C32×C4—21no—
344C2×C32×C4—21no—
345C2×C32×C4—21no—
346C2×C32×C4—21no—
347C2×C32×C4—41no—
348C2×C32×C4—41no—
349C2×C32×C4—41no—
350C2×C32×C4C22×D311yescharacteristic
351C2×C32×C4C22×D311yescharacteristic
352C2×C32×C4C22×D311yescharacteristic
353C2×C32×C4C22×D311yescharacteristic
354C2×C32×C4C22×D311yescharacteristic
355C2×C32×C4C22×D311yescharacteristic
356C2×C32×C4C22×D311yescharacteristic
357C2×C32×C4C22×D311yescharacteristic
358C2×C32×C4C22×D311yescharacteristic
359C2×C3⋊Dic3C22×D311yescharacteristic
360C2×C3⋊Dic3C22×D311yescharacteristic
361C2×C3⋊Dic3C22×D311yescharacteristic
362C2×C3⋊Dic3C22×D311yescharacteristic
363C2×C3⋊Dic3C22×D311yescharacteristic
364C2×C3⋊Dic3C22×D311yescharacteristic
365C2×C3⋊Dic3C22×D311yescharacteristic
366C2×C3⋊Dic3C22×D311yescharacteristic
367C2×C3⋊Dic3C22×D311yescharacteristic
368C4⋊(C3⋊D3)—22no—
369C4×C3⋊D3—41no—
370C4×C3⋊D3—41no—
371C2×C3×Dic3—31no—
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—31no—
385C2×C3×Dic3—31no—
386C2×C3×Dic3—31no—
387C2×C3×Dic3—31no—
388C2×C3×Dic3—31no—
389C2×C3×Dic3—61no—
390C2×C3×Dic3—61no—
391C2×C3×Dic3—61no—
392C2×C3×Dic3—61no—
393C2×C3×Dic3—61no—
394C2×C3×Dic3—61no—
395C2×C3×Dic3—61no—
396C2×C3×Dic3—61no—
397C2×C3×Dic3—61no—
398C3×D12—62no—
399C3×D12—62no—
400C3×D12—64no—
401C3×C4×D3—121no—
402C3×C4×D3—121no—
403C3×C4×D3—121no—
404C3×C4×D3—121no—
405C3×C4×D3—122no—
406C3×C4×D3—122no—
407#627—121no—
408#627—121no—
409#627—121no—
410#626—62no—
411#626—62no—
412#626—121no—
413#626—121no—
414#625—62no—
415#625—121no—
416#624—62no—
417#624—121no—
418#624—121no—
419D3×Dic3—62no—
420D3×Dic3—62no—
421D3×Dic3—121no—
422D3×Dic3—121no—
423D3×Dic3—121no—
424D3×Dic3—121no—
425#539—271noSylow
426C2×C33C2×#4111yescharacteristic
427C2×C33H(5,𝔽2)11yescharacteristic
428C2×C332−1+411yescharacteristic
429C3×C3⋊D3—22no—
430C3×C3⋊D3—41no—
431C3×C3⋊D3—41no—
432C2×C3×D4—91no—
433C22×C3×C4—91no—
434C22×C3×C4—91no—
435C2×#67—91no—
436C2×#67—91no—
437C2×#67—91no—
438C2×#67—91no—
439C22×Dic3—91no—
440C22×Dic3—91no—
441C22×Dic3—91no—
442C2×D12—31no—
443C2×D12—31no—
444C2×D12—61no—
445C2×D12—91no—
446C2×D12—91no—
447C2×C4×D3—31no—
448C2×C4×D3—31no—
449C2×C4×D3—31no—
450C2×C4×D3—31no—
451C2×C4×D3—61no—
452C2×C4×D3—61no—
453C2×C4×D3—91no—
454C2×C4×D3—91no—
455C2×C4×D3—91no—
456C2×C4×D3—91no—
457C2×C4×D3—91no—
458C2×C4×D3—91no—
459C2×Dic6—91no—
460C2×Dic6—91no—
461C2×Dic6—91no—
462C3×C4⋊C4—91no—
463C3×C4⋊C4—91no—
464C3×C4⋊C4—91no—
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×C22⋊C4—91no—
473C3×C22⋊C4—91no—
474C3×C22⋊C4—91no—
475C3×C22⋊C4—91no—
476C3×C22⋊C4—91no—
477C3×C42—21no—
478C3×C42—21no—
479C3×C42—21no—
480C3×C42—41no—
481C3×C42D3211yescharacteristic
482C3×C42D3211yescharacteristic
483C3×C42D3211yescharacteristic
484#217—91no—
485#217—91no—
486#217—91no—
487#217—91no—
488#217—91no—
489(C2×D3)⋊C4—31no—
490(C2×D3)⋊C4—31no—
491(C2×D3)⋊C4—31no—
492(C2×D3)⋊C4—31no—
493(C2×D3)⋊C4—31no—
494(C2×D3)⋊C4—31no—
495(C2×D3)⋊C4—31no—
496(C2×D3)⋊C4—31no—
497(C2×D3)⋊C4—31no—
498(C2×D3)⋊C4—31no—
499(C2×D3)⋊C4—61no—
500(C2×D3)⋊C4—61no—
501(C2×D3)⋊C4—61no—
502(C2×D3)⋊C4—61no—
503(C2×D3)⋊C4—61no—
504(C2×D3)⋊C4—91no—
505(C2×D3)⋊C4—91no—
506(C2×D3)⋊C4—91no—
507(C2×D3)⋊C4—91no—
508(C2×D3)⋊C4—91no—
509(C2×D3)⋊C4—91no—
510(C2×D3)⋊C4—91no—
511(C2×D3)⋊C4—91no—
512(C2×D3)⋊C4—91no—
513(C2×D3)⋊C4—91no—
514C4⋊Dic3—31no—
515C4⋊Dic3—31no—
516C4⋊Dic3—31no—
517C4⋊Dic3—31no—
518C4⋊Dic3—31no—
519C4⋊Dic3—31no—
520C4⋊Dic3—61no—
521C4⋊Dic3—61no—
522C4⋊Dic3—61no—
523C4⋊Dic3—91no—
524C4⋊Dic3—91no—
525C4⋊Dic3—91no—
526C4⋊Dic3—91no—
527Dic3⋊C4—31no—
528Dic3⋊C4—31no—
529Dic3⋊C4—31no—
530Dic3⋊C4—31no—
531Dic3⋊C4—31no—
532Dic3⋊C4—31no—
533Dic3⋊C4—31no—
534Dic3⋊C4—31no—
535Dic3⋊C4—31no—
536Dic3⋊C4—31no—
537Dic3⋊C4—31no—
538Dic3⋊C4—31no—
539Dic3⋊C4—31no—
540Dic3⋊C4—31no—
541Dic3⋊C4—61no—
542Dic3⋊C4—61no—
543Dic3⋊C4—61no—
544Dic3⋊C4—61no—
545Dic3⋊C4—61no—
546Dic3⋊C4—61no—
547Dic3⋊C4—61no—
548Dic3⋊C4—91no—
549Dic3⋊C4—91no—
550Dic3⋊C4—91no—
551Dic3⋊C4—91no—
552Dic3⋊C4—91no—
553Dic3⋊C4—91no—
554Dic3⋊C4—91no—
555Dic3⋊C4—91no—
556C4×Dic3—91no—
557C4×Dic3—91no—
558C4×Dic3—91no—
559C22×C32—21no—
560C22×C32—21no—
561C22×C32—21no—
562C22×C32—41no—
563C22×C32C23×D311yescharacteristic
564C22×C32C23×D311yescharacteristic
565C22×C32C23×D311yescharacteristic
566C2×C3⋊D3—21no—
567C2×C3⋊D3—21no—
568C2×C3⋊D3—21no—
569C2×C3⋊D3—21no—
570C2×C3⋊D3—21no—
571C2×C3⋊D3—21no—
572C2×C3⋊D3—21no—
573C2×C3⋊D3—21no—
574C2×C3⋊D3#23512yes—
575C2×C3×D3—32no—
576C2×C3×D3—32no—
577C2×C3×D3—62no—
578C2×C3×D3—61no—
579C2×C3×D3—61no—
580C2×C3×D3—61no—
581C2×C3×D3—61no—
582C2×C3×D3—62no—
583C2×C3×D3—61no—
584C2×C3×D3—61no—
585C2×C3×D3—61no—
586C2×C3×D3—61no—
587C2×C3×D3—61no—
588C2×C3×D3—61no—
589C2×C3×D3—61no—
590C2×C3×D3—61no—
591C2×C3×D3—61no—
592C2×C3×D3—61no—
593C2×C3×D3—61no—
594C2×C3×D3—61no—
595C2×C3×D3—121no—
596C2×C3×D3—121no—
597C2×C3×D3—121no—
598C2×C3×D3—121no—
599C2×C3×D3—121no—
600C2×C3×D3—121no—
601C2×C3×D3—121no—
602C32×C4—21no—
603C32×C4—21no—
604C32×C4—21no—
605C32×C4—22no—
606C32×C4—22no—
607C32×C4—22no—
608C32×C4—21no—
609C32×C4—21no—
610C32×C4—21no—
611C32×C4—21no—
612C32×C4—21no—
613C32×C4—21no—
614C32×C4—41no—
615C32×C4—41no—
616C32×C4—41no—
617C32×C4—41no—
618C32×C4—41no—
619C32×C4—41no—
620C32×C4—42no—
621C32×C4—42no—
622C32×C4—42no—
623C3⋊Dic3—21no—
624C3⋊Dic3—21no—
625C3⋊Dic3—21no—
626C3⋊Dic3—21no—
627C3⋊Dic3—21no—
628C3⋊Dic3—21no—
629C3⋊Dic3—21no—
630C3⋊Dic3—21no—
631C3⋊Dic3—21no—
632C3×Dic3—61no—
633C3×Dic3—61no—
634C3×Dic3—61no—
635C3×Dic3—61no—
636C3×Dic3—61no—
637C3×Dic3—61no—
638C3×Dic3—61no—
639C3×Dic3—61no—
640C3×Dic3—61no—
641C3×Dic3—61no—
642C3×Dic3—61no—
643C3×Dic3—61no—
644C3×Dic3—61no—
645C3×Dic3—61no—
646C3×Dic3—61no—
647C3×Dic3—61no—
648C3×Dic3—61no—
649C3×Dic3—61no—
650C3×Dic3—121no—
651C3×Dic3—121no—
652C3×Dic3—121no—
653C3×Dic3—121no—
654C3×Dic3—121no—
655C3×Dic3—121no—
656C3×Dic3—121no—
657C3×Dic3—121no—
658C3×Dic3—121no—
659#126—91no—
660#126—271no—
661#125—91no—
662#125—271no—
663#123—271no—
664#123—271no—
665#123—271no—
666#123—271no—
667C22⋊Q8—271no—
668C22⋊Q8—271no—
669C22⋊Q8—271no—
670#121—271no—
671C4×D4—91no—
672C4×D4—271no—
673C2×C4⋊C4—271no—
674C33#53911yescharacteristic, complemented, Sylow
675C23×C3—91no—
676C23×C3—91no—
677C23×C3—91no—
678C22×D3—31no—
679C22×D3—31no—
680C22×D3—31no—
681C22×D3—31no—
682C22×D3—31no—
683C22×D3—31no—
684C22×D3—61no—
685C22×D3—61no—
686C22×D3—61no—
687C3×D4—182no—
688C2×C3×C4—21no—
689C2×C3×C4—21no—
690C2×C3×C4—21no—
691C2×C3×C4—21no—
692C2×C3×C4—21no—
693C2×C3×C4—21no—
694C2×C3×C4—21no—
695C2×C3×C4—21no—
696C2×C3×C4—21no—
697C2×C3×C4—41no—
698C2×C3×C4—41no—
699C2×C3×C4—41no—
700C2×C3×C4—91no—
701C2×C3×C4—91no—
702C2×C3×C4—91no—
703C2×C3×C4—91no—
704C2×C3×C4—91no—
705C2×C3×C4—91no—
706C2×C3×C4—91no—
707C2×C3×C4—91no—
708C2×C3×C4—91no—
709C2×C3×C4—361no—
710C2×C3×C4—361no—
711C2×C3×C4C2×D3211yescharacteristic
712C2×C3×C4C2×D3211yescharacteristic
713C2×C3×C4C2×D3211yescharacteristic
714C2×C3×C4C2×D3211yescharacteristic
715C2×C3×C4C2×D3211yescharacteristic
716C2×C3×C4C2×D3211yescharacteristic
717C2×C3×C4C2×D3211yescharacteristic
718C2×C3×C4C2×D3211yescharacteristic
719C2×C3×C4C2×D3211yescharacteristic
720#67—182no—
721#67—182no—
722#67—361no—
723#67—361no—
724C2×Dic3—31no—
725C2×Dic3—31no—
726C2×Dic3—31no—
727C2×Dic3—31no—
728C2×Dic3—31no—
729C2×Dic3—31no—
730C2×Dic3—31no—
731C2×Dic3—31no—
732C2×Dic3—31no—
733C2×Dic3—31no—
734C2×Dic3—31no—
735C2×Dic3—31no—
736C2×Dic3—31no—
737C2×Dic3—31no—
738C2×Dic3—31no—
739C2×Dic3—31no—
740C2×Dic3—31no—
741C2×Dic3—31no—
742C2×Dic3—61no—
743C2×Dic3—61no—
744C2×Dic3—61no—
745C2×Dic3—61no—
746C2×Dic3—61no—
747C2×Dic3—61no—
748C2×Dic3—61no—
749C2×Dic3—61no—
750C2×Dic3—61no—
751C2×Dic3—182no—
752C2×Dic3—361no—
753C2×Dic3—361no—
754D12—62no—
755D12—62no—
756D12—64no—
757D12—182no—
758D12—361no—
759C4×D3—121no—
760C4×D3—121no—
761C4×D3—121no—
762C4×D3—121no—
763C4×D3—122no—
764C4×D3—122no—
765C4×D3—182no—
766C4×D3—182no—
767C4×D3—361no—
768C4×D3—361no—
769C4×D3—361no—
770C4×D3—361no—
771Dic6—361no—
772Dic6—361no—
773Dic6—361no—
774C2×C32—21no—
775C2×C32—21no—
776C2×C32—21no—
777C2×C32—21no—
778C2×C32—21no—
779C2×C32—21no—
780C2×C32—21no—
781C2×C32—21no—
782C2×C32—21no—
783C2×C32—41no—
784C2×C32—41no—
785C2×C32—41no—
786C2×C32C2×#23511yescharacteristic
787C2×C32#100411yescharacteristic
788C2×C32#100711yescharacteristic
789C2×C32D3×#4111yescharacteristic
790C2×C32D3×#4111yescharacteristic
791C2×C32#100911yescharacteristic
792C2×C32#100911yescharacteristic
793C2×C32#101011yescharacteristic
794C2×C32#101011yescharacteristic
795C3⋊D3—22no—
796C3⋊D3—41no—
797C3⋊D3—41no—
798C3×D3—62no—
799C3×D3—62no—
800C3×D3—122no—
801C3×D3—122no—
802C3×D3—121no—
803C3×D3—121no—
804C3×D3—121no—
805C3×D3—121no—
806C3×D3—241no—
807C2×Q8—271no—
808C2×D4—91no—
809C2×D4—271no—
810C2×D4—271no—
811C22×C4—91no—
812C22×C4—91no—
813C22×C4—271no—
814C22×C4—271no—
815C22×C4—271no—
816C4⋊C4—91no—
817C4⋊C4—91no—
818C4⋊C4—91no—
819C4⋊C4—91no—
820C4⋊C4—91no—
821C4⋊C4—91no—
822C4⋊C4—91no—
823C4⋊C4—91no—
824C4⋊C4—91no—
825C4⋊C4—91no—
826C4⋊C4—271no—
827C4⋊C4—271no—
828C4⋊C4—271no—
829C4⋊C4—271no—
830C22⋊C4—91no—
831C22⋊C4—91no—
832C22⋊C4—91no—
833C22⋊C4—91no—
834C22⋊C4—91no—
835C22⋊C4—271no—
836C22⋊C4—271no—
837C22⋊C4—271no—
838C22⋊C4—271no—
839C22⋊C4—271no—
840C42—271no—
841C42#111311yescharacteristic
842C22×C3—21no—
843C22×C3—21no—
844C22×C3—21no—
845C22×C3—41no—
846C22×C3—92no—
847C22×C3—181no—
848C22×C3—181no—
849C22×C3—181no—
850C22×C3—181no—
851C22×C3—181no—
852C22×C3—181no—
853C22×C3—181no—
854C22×C3—181no—
855C22×C3C22×D3211yescharacteristic
856C22×C3C22×D3211yescharacteristic
857C22×C3C22×D3211yescharacteristic
858C2×D3—32no—
859C2×D3—32no—
860C2×D3—62no—
861C2×D3—61no—
862C2×D3—61no—
863C2×D3—61no—
864C2×D3—61no—
865C2×D3—62no—
866C2×D3—61no—
867C2×D3—61no—
868C2×D3—61no—
869C2×D3—61no—
870C2×D3—61no—
871C2×D3—61no—
872C2×D3—61no—
873C2×D3—61no—
874C2×D3—61no—
875C2×D3—61no—
876C2×D3—61no—
877C2×D3—61no—
878C2×D3—121no—
879C2×D3—121no—
880C2×D3—121no—
881C2×D3—121no—
882C2×D3—121no—
883C2×D3—121no—
884C2×D3—121no—
885C3×C4—22no—
886C3×C4—22no—
887C3×C4—22no—
888C3×C4—21no—
889C3×C4—21no—
890C3×C4—21no—
891C3×C4—21no—
892C3×C4—21no—
893C3×C4—21no—
894C3×C4—21no—
895C3×C4—21no—
896C3×C4—21no—
897C3×C4—41no—
898C3×C4—41no—
899C3×C4—41no—
900C3×C4—41no—
901C3×C4—41no—
902C3×C4—41no—
903C3×C4—42no—
904C3×C4—42no—
905C3×C4—42no—
906C3×C4—181no—
907C3×C4—181no—
908C3×C4—181no—
909C3×C4—181no—
910C3×C4—181no—
911C3×C4—181no—
912C3×C4—181no—
913C3×C4—181no—
914C3×C4—181no—
915Dic3—61no—
916Dic3—61no—
917Dic3—61no—
918Dic3—61no—
919Dic3—61no—
920Dic3—61no—
921Dic3—61no—
922Dic3—61no—
923Dic3—61no—
924Dic3—61no—
925Dic3—61no—
926Dic3—61no—
927Dic3—61no—
928Dic3—61no—
929Dic3—61no—
930Dic3—61no—
931Dic3—61no—
932Dic3—61no—
933Dic3—121no—
934Dic3—121no—
935Dic3—121no—
936Dic3—121no—
937Dic3—121no—
938Dic3—121no—
939Dic3—121no—
940Dic3—121no—
941Dic3—121no—
942C32—21no—
943C32—21no—
944C32—21no—
945C32—41no—
946C32#556411yescharacteristic, complemented
947C32#569211yescharacteristic, complemented
948C32#570711yescharacteristic, complemented
949C23—91no—
950C23—91no—
951C23—91no—
952Q8—1081no—
953D4—182no—
954D4—542no—
955D4—1081no—
956C2×C4—91no—
957C2×C4—91no—
958C2×C4—91no—
959C2×C4—91no—
960C2×C4—91no—
961C2×C4—91no—
962C2×C4—91no—
963C2×C4—91no—
964C2×C4—91no—
965C2×C4—361no—
966C2×C4—361no—
967C2×C4—542no—
968C2×C4—1081no—
969C2×C4—1081no—
970C2×C4C2×#111311yescharacteristic
971C2×C4C2×#111311yescharacteristic
972C2×C4C2×#111311yescharacteristic
973C2×C3—21no—
974C2×C3—21no—
975C2×C3—21no—
976C2×C3—21no—
977C2×C3—21no—
978C2×C3—21no—
979C2×C3—21no—
980C2×C3—21no—
981C2×C3—21no—
982C2×C3—41no—
983C2×C3—41no—
984C2×C3—41no—
985C2×C3—182no—
986C2×C3—361no—
987C2×C3—361no—
988C2×C3#6429711yescharacteristic
989C2×C3#6429711yescharacteristic
990C2×C3#6429811yescharacteristic
991C2×C3D3×#23511yescharacteristic
992C2×C3D3×#23511yescharacteristic
993C2×C3#6430611yescharacteristic
994C2×C3#6430711yescharacteristic
995C2×C3#6430711yescharacteristic
996C2×C3#6430811yescharacteristic
997D3—62no—
998D3—62no—
999D3—122no—
1000D3—122no—
1001D3—121no—
1002D3—121no—
1003D3—121no—
1004D3—121no—
1005D3—241no—
1006C22—92no—
1007C22—181no—
1008C22—181no—
1009C22—181no—
1010C22—181no—
1011C22—181no—
1012C22—181no—
1013C22—181no—
1014C22—181no—
1015C22C22×#111311yescharacteristic
1016C4—21no—
1017C4—21no—
1018C4—21no—
1019C4—181no—
1020C4—181no—
1021C4—181no—
1022C4—181no—
1023C4—181no—
1024C4—181no—
1025C4—181no—
1026C4—181no—
1027C4—181no—
1028C3—21no—
1029C3—21no—
1030C3—21no—
1031C3—41no—
1032C3#1059391311yescharacteristic, complemented
1033C3#1059391411yescharacteristic, complemented
1034C3#1059394611yescharacteristic, complemented
1035C2—182no—
1036C2—361no—
1037C2—361no—
1038C2#1172461411yescharacteristic
1039C2#1172461811yescharacteristic
1040C2#1172461911yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC33×C42C22
prime radical#11723687C2
hypercenterC42#1113
hypocenterC33#539
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
1. C3×#64085C2semidirect
2. C3×C4×C4⋊(C3⋊D3)C2semidirect
3. C3×#64079C2semidirect
4. #11723694C2semidirect
5. #11723692C2semidirect
6. #11723692C2semidirect
7. #11723690C2semidirect
8. #11723690C2semidirect
10. #11723686C2semidirect
11. #11723684C2semidirect
12. #11723682C2semidirect
13. #11723675C2semidirect
14. #11723671C2semidirect
15. #11723669C2semidirect
54. #64085D3semidirect
55. C4×C4⋊(C3⋊D3)D3semidirect
56. #64079D3semidirect
674. C33#539semidirect
946. C32#5564semidirect
947. C32#5692semidirect
948. C32#5707semidirect
1032. C3#10593913semidirect
1033. C3#10593914semidirect
1034. C3#10593946semidirect

Maximal subgroups

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

subgroupindex
C3×#640852
C3×C4×C4⋊(C3⋊D3)2
C3×#640792
#117236942
#117236922
#117236902
#117236872
#117236862
#117236842
#117236822
#117236752
#117236712
#117236692
#105939463
#105939143
#105939133