Finite Group Databasebeta

← #13169265

Subgroups — #13169265

Order 1728.

1106 conjugacy classes of subgroups.

The subgroup lattice has 1044 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723687C211yesmaximal, characteristic
2#11723502C211yesmaximal, characteristic, complemented
3#11723488C211yesmaximal, characteristic, complemented
4#11723444C211yesmaximal, characteristic, complemented
5C3×#63894C211yesmaximal, characteristic, complemented
6C3×#63868C211yesmaximal, characteristic, complemented
7C3×#63846C211yesmaximal, characteristic, complemented
8#11723023C211yesmaximal, characteristic, complemented
9#11722997C211yesmaximal, characteristic, complemented
10#11722997C211yesmaximal, characteristic, complemented
11#11722995C211yesmaximal, characteristic, complemented
12#11722984C211yesmaximal, characteristic, complemented
13#11722972C211yesmaximal, characteristic, complemented
14#11722934C211yesmaximal, characteristic, complemented
15#11722911C211yesmaximal, characteristic, complemented
16#10594481—31nomaximal
17#10594407—31nomaximal
18#10593914—31nomaximal
19C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
20C2×#6295C2211yescharacteristic
21C2×#6295C2211yescharacteristic
22C2×#6294C2211yescharacteristic
23C2×#6293C2211yescharacteristic
24C2×Dic3×C3⋊D3C2211yescharacteristic
25C2×Dic3×C3⋊D3C2211yescharacteristic
26C2×C3×#624C2211yescharacteristic
27C2×C3×#624C2211yescharacteristic
28#88857C2211yescharacteristic
29C3×#3752C2211yescharacteristic
30C3×#3750C2211yescharacteristic
31C32×C4⋊Dic3C2211yescharacteristic
32C32×Dic3⋊C4C2211yescharacteristic
33C32×C4×Dic3C2211yescharacteristic
34#88814C2211yescharacteristic
35#88807C2211yescharacteristic
36#88806C2211yescharacteristic
37#88806C2211yescharacteristic
38Dic3⋊(C3⋊Dic3)C2211yescharacteristic
39Dic3⋊(C3⋊Dic3)C2211yescharacteristic
40#88803C2211yescharacteristic
41#88803C2211yescharacteristic
42#88803C2211yescharacteristic
43#88803C2211yescharacteristic
44C3×#3724C2211yescharacteristic
45C3×Dic3⋊Dic3C2211yescharacteristic
46C3×Dic3⋊Dic3C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×#3722C2211yescharacteristic
50C3×#3722C2211yescharacteristic
51C3×#3722C2211yescharacteristic
52C3×#3722C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64105—31no—
55#64103—31no—
56#64079—31no—
57C3×#898—31no—
58C3×#893—31no—
59C3×#890—31no—
60C3×#889—31no—
61C3×#876—31no—
62C3×C4×D12—31no—
63#63910—31no—
64#63905—31no—
65C4×#626—31no—
66#63900—31no—
67#63899—31no—
68#63899—31no—
69#63899—61no—
70#63896—31no—
71#63895—31no—
72#63895—31no—
73#63894D311yescharacteristic, complemented
74#63893—31no—
75#63891—31no—
76#63891—31no—
77#63890—31no—
78#63890—31no—
79#63886—31no—
80#63885—31no—
81#63884—31no—
82#63884—31no—
83#63884—61no—
84#63880—31no—
85#63879—31no—
86D3×Dic3⋊C4—31no—
87D3×Dic3⋊C4—31no—
88#63868—31no—
89#63868D311yescharacteristic, complemented
90#63867—31no—
91#63867—31no—
92#63867—61no—
93#63861—31no—
94#63859—31no—
95#63857—31no—
96#63854—31no—
97#63853—31no—
98#63853—31no—
99#63851—31no—
100#63850—31no—
101#63846D311yescharacteristic, complemented
102C22×C3×C3⋊D3C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C3×C3⋊D3C2311yescharacteristic
105C2×C33×C4C2311yescharacteristic
106C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
107C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
108C2×C3×C3⋊Dic3C2311yescharacteristic
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C3×C4⋊(C3⋊D3)—22no—
112C2×C32×Dic3C2311yescharacteristic
113C2×C32×Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118#6295—22no—
119#6295—41no—
120#6294—41no—
121#6293—41no—
122Dic3×C3⋊D3—22no—
123Dic3×C3⋊D3—41no—
124C3×#624—41no—
125C3×#624—41no—
126#5707—91no—
127#5692—91no—
128#5564—91no—
129C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
130C2×C4×C3⋊D3—31no—
131C2×C4×C3⋊D3—31no—
132C2×#634—31no—
133C2×C3×D12—31no—
134C2×C3×D12—31no—
135C2×C3×D12—61no—
136C2×C3×C4×D3—31no—
137C2×C3×C4×D3—31no—
138C2×C3×C4×D3—31no—
139C2×C3×C4×D3—31no—
140C2×#627—31no—
141C2×#627—31no—
142C2×#627—61no—
143C2×#626—31no—
144C2×#626—31no—
145C2×#626—31no—
146C2×#626—31no—
147C2×#625—31no—
148C2×#625—31no—
149C2×#624—31no—
150C2×#624C2×D311yescharacteristic
151C2×#624C2×D311yescharacteristic
152C2×D3×Dic3—31no—
153C2×D3×Dic3—31no—
154C2×D3×Dic3—31no—
155C2×D3×Dic3—31no—
156C2×D3×Dic3—31no—
157C2×D3×Dic3—31no—
158C2×D3×Dic3—61no—
159C2×D3×Dic3—61no—
160C32×C4⋊C4—31no—
161C32×C4⋊C4—31no—
162C32×C42—31no—
163#3752—31no—
164#3752—31no—
165#3752—31no—
166#3752—31no—
167#3752C2×D311yescharacteristic
168C4⋊(C3⋊Dic3)—31no—
169C4⋊(C3⋊Dic3)—31no—
170#3750—31no—
171#3750—31no—
172#3750—31no—
173#3750—31no—
174#3750—31no—
175#3750—31no—
176#3750—61no—
177#3750—61no—
178#3750—61no—
179#3750—121no—
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×C4⋊Dic3—21no—
193C3×C4⋊Dic3—31no—
194C3×C4⋊Dic3—31no—
195C3×C4⋊Dic3—31no—
196C3×C4⋊Dic3—31no—
197C3×C4⋊Dic3C2×D311yescharacteristic
198C3×C4⋊Dic3C2×D311yescharacteristic
199C3×Dic3⋊C4—21no—
200C3×Dic3⋊C4—31no—
201C3×Dic3⋊C4—31no—
202C3×Dic3⋊C4—31no—
203C3×Dic3⋊C4—31no—
204C3×Dic3⋊C4—31no—
205C3×Dic3⋊C4—31no—
206C3×Dic3⋊C4—31no—
207C3×Dic3⋊C4—31no—
208C3×Dic3⋊C4—61no—
209C3×Dic3⋊C4C2×D311yescharacteristic
210C3×Dic3⋊C4C2×D311yescharacteristic
211C3×C4×Dic3—21no—
212C3×C4×Dic3—31no—
213C3×C4×Dic3—31no—
214C3×C4×Dic3C2×D311yescharacteristic
215C3×C4×Dic3C2×D311yescharacteristic
216#3724—31no—
217#3724—31no—
218#3724—31no—
219#3724—31no—
220#3724—61no—
221#3724—61no—
222#3724C2×D311yescharacteristic
223Dic3⋊Dic3—31no—
224Dic3⋊Dic3—31no—
225Dic3⋊Dic3—31no—
226Dic3⋊Dic3—31no—
227Dic3⋊Dic3—31no—
228Dic3⋊Dic3—31no—
229Dic3⋊Dic3—61no—
230Dic3⋊Dic3—61no—
231Dic3⋊Dic3—61no—
232Dic3⋊Dic3C2×D311yescharacteristic
233Dic3⋊Dic3C2×D311yescharacteristic
234Dic3⋊Dic3C2×D311yescharacteristic
235Dic3⋊Dic3C2×D311yescharacteristic
236#3722—31no—
237#3722C2×D311yescharacteristic
238#3722C2×D311yescharacteristic
239#3722C2×D311yescharacteristic
240#3722C2×D311yescharacteristic
241(C2×D3)⋊Dic3—31no—
242(C2×D3)⋊Dic3—31no—
243(C2×D3)⋊Dic3—31no—
244(C2×D3)⋊Dic3—31no—
245(C2×D3)⋊Dic3—31no—
246(C2×D3)⋊Dic3—31no—
247(C2×D3)⋊Dic3—31no—
248(C2×D3)⋊Dic3—31no—
249(C2×D3)⋊Dic3—31no—
250(C2×D3)⋊Dic3—31no—
251(C2×D3)⋊Dic3—61no—
252(C2×D3)⋊Dic3—61no—
253(C2×D3)⋊Dic3—61no—
254(C2×D3)⋊Dic3—61no—
255Dic32C2×D311yescharacteristic
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—
267C3⋊(C3⋊Dic3)—21no—
268C3⋊(C3⋊Dic3)—21no—
269C3×C3⋊Dic3—21no—
270C3×C3⋊Dic3—21no—
271C3×C3⋊Dic3—21no—
272C32×Dic3—21no—
273C32×Dic3—21no—
274C32×Dic3—21no—
275C32×Dic3—21no—
276C32×Dic3—21no—
277C32×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—31no—
288#898—91no—
289#897—91no—
290#897—91no—
291#896—91no—
292#896—91no—
293#896—91no—
294#896—91no—
295#896—181no—
296#895—91no—
297#894—91no—
298#894—91no—
299#894—91no—
300#894—91no—
301#894—91no—
302#894—181no—
303#893—31no—
304D3×C4⋊C4—91no—
305D3×C4⋊C4—91no—
306#890—31no—
307#889—31no—
308#889—91no—
309#886—91no—
310#886—91no—
311#884—91no—
312#883—91no—
313#883—91no—
314#883—91no—
315#67⋊C4—91no—
316#879—91no—
317#878—91no—
318#878—91no—
319#876—31no—
320#876—91no—
321C4×D12—31no—
322C4×D12—91no—
323#870—91no—
324#870—91no—
325#870—181no—
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—31no—
342C2×C32×C4—31no—
343C2×C32×C4—31no—
344C2×C32×C4—31no—
345C2×C32×C4—31no—
346C2×C32×C4—31no—
347C2×C32×C4—41no—
348C2×C32×C4C22×D311yescharacteristic
349C2×C32×C4C22×D311yescharacteristic
350C2×C32×C4C22×D311yescharacteristic
351C2×C3⋊Dic3—31no—
352C2×C3⋊Dic3—31no—
353C2×C3⋊Dic3—31no—
354C2×C3⋊Dic3—31no—
355C2×C3⋊Dic3—31no—
356C2×C3⋊Dic3—31no—
357C2×C3⋊Dic3—61no—
358C2×C3⋊Dic3—61no—
359C2×C3⋊Dic3—61no—
360C2×C3⋊Dic3—61no—
361C2×C3⋊Dic3—61no—
362C2×C3⋊Dic3—61no—
363C2×C3⋊Dic3—121no—
364C2×C3⋊Dic3—121no—
365C2×C3⋊Dic3C22×D311yescharacteristic
366C2×C3⋊Dic3C22×D311yescharacteristic
367C2×C3⋊Dic3C22×D311yescharacteristic
368C4⋊(C3⋊D3)—22no—
369C4×C3⋊D3—62no—
370C4×C3⋊D3—121no—
371#634—121no—
372C2×C3×Dic3—21no—
373C2×C3×Dic3—21no—
374C2×C3×Dic3—21no—
375C2×C3×Dic3—21no—
376C2×C3×Dic3—21no—
377C2×C3×Dic3—21no—
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×Dic3C22×D311yescharacteristic
388C2×C3×Dic3C22×D311yescharacteristic
389C2×C3×Dic3C22×D311yescharacteristic
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
399C3×D12—62no—
400C3×D12—62no—
401C3×D12—122no—
402C3×C4×D3—121no—
403C3×C4×D3—121no—
404C3×C4×D3—121no—
405C3×C4×D3—121no—
406#627—121no—
407#627—121no—
408#627—122no—
409#626—62no—
410#626—62no—
411#626—121no—
412#626—121no—
413#625—62no—
414#625—121no—
415#624—41no—
416#624—41no—
417#624—121no—
418D3×Dic3—62no—
419D3×Dic3—62no—
420D3×Dic3—122no—
421D3×Dic3—121no—
422D3×Dic3—121no—
423D3×Dic3—122no—
424D3×Dic3—121no—
425D3×Dic3—121no—
426#539—271noSylow
427C2×C33C2×#4111yescharacteristic
428C2×C33H(5,𝔽2)11yescharacteristic
429C2×C332−1+411yescharacteristic
430C3×C3⋊D3—22no—
431C3×C3⋊D3—41no—
432C3×C3⋊D3—41no—
433C2×C3×D4—91no—
434C22×C3×C4—91no—
435C22×C3×C4—91no—
436C2×#67—91no—
437C2×#67—91no—
438C2×#67—91no—
439C2×#67—91no—
440C22×Dic3—91no—
441C22×Dic3—91no—
442C22×Dic3—91no—
443C2×D12—31no—
444C2×D12—31no—
445C2×D12—61no—
446C2×D12—91no—
447C2×D12—91no—
448C2×C4×D3—31no—
449C2×C4×D3—31no—
450C2×C4×D3—31no—
451C2×C4×D3—31no—
452C2×C4×D3—91no—
453C2×C4×D3—91no—
454C2×C4×D3—91no—
455C2×C4×D3—91no—
456C2×C4×D3—91no—
457C2×C4×D3—91no—
458C2×C4×D3—181no—
459C2×C4×D3—181no—
460C2×Dic6—91no—
461C2×Dic6—91no—
462C2×Dic6—91no—
463C2×Dic6—181no—
464C3×C4⋊C4—31no—
465C3×C4⋊C4—31no—
466C3×C4⋊C4—31no—
467C3×C4⋊C4—31no—
468C3×C4⋊C4—61no—
469C3×C4⋊C4—61no—
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×C22⋊C4—91no—
477C3×C22⋊C4—91no—
478C3×C22⋊C4—91no—
479C3×C22⋊C4—91no—
480C3×C22⋊C4—91no—
481C3×C42—31no—
482C3×C42—31no—
483C3×C42—61no—
484C3×C42—91no—
485#217—91no—
486#217—91no—
487#217—91no—
488#217—91no—
489#217—91no—
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—31no—
500(C2×D3)⋊C4—61no—
501(C2×D3)⋊C4—91no—
502(C2×D3)⋊C4—91no—
503(C2×D3)⋊C4—91no—
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—181no—
512(C2×D3)⋊C4—181no—
513(C2×D3)⋊C4—181no—
514(C2×D3)⋊C4—181no—
515C4⋊Dic3—31no—
516C4⋊Dic3—31no—
517C4⋊Dic3—31no—
518C4⋊Dic3—31no—
519C4⋊Dic3—91no—
520C4⋊Dic3—91no—
521C4⋊Dic3—91no—
522C4⋊Dic3—91no—
523C4⋊Dic3—91no—
524C4⋊Dic3—181no—
525C4⋊Dic3—181no—
526C4⋊Dic3D3211yescharacteristic
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—61no—
536Dic3⋊C4—91no—
537Dic3⋊C4—91no—
538Dic3⋊C4—91no—
539Dic3⋊C4—91no—
540Dic3⋊C4—91no—
541Dic3⋊C4—91no—
542Dic3⋊C4—91no—
543Dic3⋊C4—91no—
544Dic3⋊C4—91no—
545Dic3⋊C4—91no—
546Dic3⋊C4—91no—
547Dic3⋊C4—91no—
548Dic3⋊C4—91no—
549Dic3⋊C4—181no—
550Dic3⋊C4—181no—
551Dic3⋊C4—181no—
552Dic3⋊C4—181no—
553Dic3⋊C4—181no—
554Dic3⋊C4—181no—
555Dic3⋊C4—361no—
556Dic3⋊C4D3211yescharacteristic
557C4×Dic3—31no—
558C4×Dic3—31no—
559C4×Dic3D3211yescharacteristic
560C22×C32—21no—
561C22×C32—21no—
562C22×C32—21no—
563C22×C32—41no—
564C22×C32C23×D311yescharacteristic
565C22×C32C23×D311yescharacteristic
566C22×C32C23×D311yescharacteristic
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—21no—
575C2×C3⋊D3#23512yes—
576C2×C3×D3—32no—
577C2×C3×D3—32no—
578C2×C3×D3—62no—
579C2×C3×D3—61no—
580C2×C3×D3—61no—
581C2×C3×D3—61no—
582C2×C3×D3—61no—
583C2×C3×D3—62no—
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—61no—
596C2×C3×D3—121no—
597C2×C3×D3—121no—
598C2×C3×D3—121no—
599C2×C3×D3—121no—
600C2×C3×D3—121no—
601C2×C3×D3—121no—
602C2×C3×D3—121no—
603C32×C4—21no—
604C32×C4—21no—
605C32×C4—21no—
606C32×C4—41no—
607C32×C4—41no—
608C32×C4—41no—
609C32×C4—61no—
610C32×C4—61no—
611C32×C4—61no—
612C32×C4—61no—
613C32×C4—61no—
614C32×C4—61no—
615C32×C4—81no—
616C3⋊Dic3—21no—
617C3⋊Dic3—21no—
618C3⋊Dic3—21no—
619C3⋊Dic3—61no—
620C3⋊Dic3—62no—
621C3⋊Dic3—61no—
622C3⋊Dic3—61no—
623C3⋊Dic3—61no—
624C3⋊Dic3—61no—
625C3⋊Dic3—61no—
626C3⋊Dic3—121no—
627C3⋊Dic3—121no—
628C3⋊Dic3—122no—
629C3⋊Dic3—121no—
630C3⋊Dic3—121no—
631C3⋊Dic3—121no—
632C3⋊Dic3—241no—
633C3×Dic3—22no—
634C3×Dic3—21no—
635C3×Dic3—21no—
636C3×Dic3—21no—
637C3×Dic3—21no—
638C3×Dic3—21no—
639C3×Dic3—21no—
640C3×Dic3—21no—
641C3×Dic3—21no—
642C3×Dic3—21no—
643C3×Dic3—21no—
644C3×Dic3—21no—
645C3×Dic3—21no—
646C3×Dic3—41no—
647C3×Dic3—41no—
648C3×Dic3—41no—
649C3×Dic3—41no—
650C3×Dic3—41no—
651C3×Dic3—61no—
652C3×Dic3—61no—
653C3×Dic3—61no—
654C3×Dic3—61no—
655C3×Dic3—61no—
656C3×Dic3—61no—
657C3×Dic3—121no—
658C3×Dic3—121no—
659C3×Dic3—121no—
660#126—91no—
661#126—271no—
662#125—91no—
663#125—271no—
664#123—271no—
665#123—271no—
666#123—271no—
667#123—271no—
668C22⋊Q8—271no—
669C22⋊Q8—271no—
670C22⋊Q8—271no—
671#121—271no—
672C4×D4—91no—
673C4×D4—271no—
674C2×C4⋊C4—271no—
675C33#53911yescharacteristic, complemented, Sylow
676C23×C3—91no—
677C23×C3—91no—
678C23×C3—91no—
679C22×D3—31no—
680C22×D3—31no—
681C22×D3—31no—
682C22×D3—31no—
683C22×D3—31no—
684C22×D3—31no—
685C22×D3—61no—
686C22×D3—61no—
687C22×D3—61no—
688C3×D4—182no—
689C2×C3×C4—21no—
690C2×C3×C4—21no—
691C2×C3×C4—21no—
692C2×C3×C4—31no—
693C2×C3×C4—31no—
694C2×C3×C4—31no—
695C2×C3×C4—31no—
696C2×C3×C4—31no—
697C2×C3×C4—31no—
698C2×C3×C4—31no—
699C2×C3×C4—31no—
700C2×C3×C4—31no—
701C2×C3×C4—31no—
702C2×C3×C4—31no—
703C2×C3×C4—31no—
704C2×C3×C4—41no—
705C2×C3×C4—61no—
706C2×C3×C4—61no—
707C2×C3×C4—61no—
708C2×C3×C4—61no—
709C2×C3×C4—61no—
710C2×C3×C4—61no—
711C2×C3×C4—91no—
712C2×C3×C4—91no—
713C2×C3×C4—91no—
714C2×C3×C4—361no—
715C2×C3×C4—361no—
716C2×C3×C4C2×D3211yescharacteristic
717C2×C3×C4C2×D3211yescharacteristic
718C2×C3×C4C2×D3211yescharacteristic
719#67—182no—
720#67—182no—
721#67—361no—
722#67—361no—
723C2×Dic3—31no—
724C2×Dic3—31no—
725C2×Dic3—31no—
726C2×Dic3—31no—
727C2×Dic3—31no—
728C2×Dic3—31no—
729C2×Dic3—61no—
730C2×Dic3—61no—
731C2×Dic3—61no—
732C2×Dic3—91no—
733C2×Dic3—91no—
734C2×Dic3—91no—
735C2×Dic3—91no—
736C2×Dic3—91no—
737C2×Dic3—91no—
738C2×Dic3—181no—
739C2×Dic3—181no—
740C2×Dic3—181no—
741C2×Dic3—181no—
742C2×Dic3—181no—
743C2×Dic3—181no—
744C2×Dic3—182no—
745C2×Dic3—361no—
746C2×Dic3—361no—
747C2×Dic3—361no—
748C2×Dic3—361no—
749C2×Dic3C2×D3211yescharacteristic
750C2×Dic3C2×D3211yescharacteristic
751C2×Dic3C2×D3211yescharacteristic
752C2×Dic3C2×D3211yescharacteristic
753C2×Dic3C2×D3211yescharacteristic
754C2×Dic3C2×D3211yescharacteristic
755D12—62no—
756D12—62no—
757D12—122no—
758D12—182no—
759D12—361no—
760C4×D3—121no—
761C4×D3—121no—
762C4×D3—121no—
763C4×D3—121no—
764C4×D3—182no—
765C4×D3—182no—
766C4×D3—362no—
767C4×D3—361no—
768C4×D3—361no—
769C4×D3—361no—
770C4×D3—361no—
771C4×D3—362no—
772Dic6—361no—
773Dic6—361no—
774Dic6—361no—
775Dic6—362no—
776C2×C32—21no—
777C2×C32—21no—
778C2×C32—21no—
779C2×C32—21no—
780C2×C32—21no—
781C2×C32—21no—
782C2×C32—21no—
783C2×C32—21no—
784C2×C32—21no—
785C2×C32—41no—
786C2×C32—41no—
787C2×C32—41no—
788C2×C32C2×#23511yescharacteristic
789C2×C32#100411yescharacteristic
790C2×C32#100711yescharacteristic
791C2×C32D3×#4111yescharacteristic
792C2×C32D3×#4111yescharacteristic
793C2×C32#100911yescharacteristic
794C2×C32#100911yescharacteristic
795C2×C32#101011yescharacteristic
796C2×C32#101011yescharacteristic
797C3⋊D3—22no—
798C3⋊D3—41no—
799C3⋊D3—41no—
800C3×D3—62no—
801C3×D3—62no—
802C3×D3—122no—
803C3×D3—122no—
804C3×D3—121no—
805C3×D3—121no—
806C3×D3—121no—
807C3×D3—121no—
808C3×D3—241no—
809C2×Q8—271no—
810C2×D4—91no—
811C2×D4—271no—
812C2×D4—271no—
813C22×C4—91no—
814C22×C4—91no—
815C22×C4—271no—
816C22×C4—271no—
817C22×C4—271no—
818C4⋊C4—31no—
819C4⋊C4—31no—
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—
830C4⋊C4—271no—
831C4⋊C4—271no—
832C22⋊C4—91no—
833C22⋊C4—91no—
834C22⋊C4—91no—
835C22⋊C4—91no—
836C22⋊C4—91no—
837C22⋊C4—271no—
838C22⋊C4—271no—
839C22⋊C4—271no—
840C22⋊C4—271no—
841C22⋊C4—271no—
842C42—31no—
843C42—91no—
844C22×C3—21no—
845C22×C3—21no—
846C22×C3—21no—
847C22×C3—41no—
848C22×C3—92no—
849C22×C3—181no—
850C22×C3—181no—
851C22×C3—181no—
852C22×C3—181no—
853C22×C3—181no—
854C22×C3—181no—
855C22×C3—181no—
856C22×C3—181no—
857C22×C3C22×D3211yescharacteristic
858C22×C3C22×D3211yescharacteristic
859C22×C3C22×D3211yescharacteristic
860C2×D3—32no—
861C2×D3—32no—
862C2×D3—62no—
863C2×D3—61no—
864C2×D3—61no—
865C2×D3—61no—
866C2×D3—61no—
867C2×D3—62no—
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—61no—
879C2×D3—61no—
880C2×D3—121no—
881C2×D3—121no—
882C2×D3—121no—
883C2×D3—121no—
884C2×D3—121no—
885C2×D3—121no—
886C2×D3—121no—
887C3×C4—21no—
888C3×C4—21no—
889C3×C4—21no—
890C3×C4—41no—
891C3×C4—41no—
892C3×C4—41no—
893C3×C4—62no—
894C3×C4—61no—
895C3×C4—61no—
896C3×C4—61no—
897C3×C4—61no—
898C3×C4—61no—
899C3×C4—61no—
900C3×C4—61no—
901C3×C4—61no—
902C3×C4—61no—
903C3×C4—61no—
904C3×C4—61no—
905C3×C4—61no—
906C3×C4—81no—
907C3×C4—121no—
908C3×C4—121no—
909C3×C4—121no—
910C3×C4—121no—
911C3×C4—121no—
912C3×C4—181no—
913C3×C4—181no—
914C3×C4—181no—
915Dic3—21no—
916Dic3—21no—
917Dic3—21no—
918Dic3—21no—
919Dic3—21no—
920Dic3—21no—
921Dic3—61no—
922Dic3—61no—
923Dic3—61no—
924Dic3—61no—
925Dic3—61no—
926Dic3—61no—
927Dic3—121no—
928Dic3—121no—
929Dic3—121no—
930Dic3—182no—
931Dic3—181no—
932Dic3—181no—
933Dic3—181no—
934Dic3—181no—
935Dic3—181no—
936Dic3—181no—
937Dic3—361no—
938Dic3—361no—
939Dic3—361no—
940Dic3—361no—
941Dic3—361no—
942Dic3—362no—
943Dic3—721no—
944C32—21no—
945C32—21no—
946C32—21no—
947C32—41no—
948C32#556411yescharacteristic, complemented
949C32#569211yescharacteristic, complemented
950C32#570711yescharacteristic, complemented
951C23—91no—
952C23—91no—
953C23—91no—
954Q8—1081no—
955D4—182no—
956D4—542no—
957D4—1081no—
958C2×C4—31no—
959C2×C4—31no—
960C2×C4—31no—
961C2×C4—31no—
962C2×C4—31no—
963C2×C4—31no—
964C2×C4—91no—
965C2×C4—91no—
966C2×C4—91no—
967C2×C4—271no—
968C2×C4—271no—
969C2×C4—361no—
970C2×C4—361no—
971C2×C4—542no—
972C2×C4—1081no—
973C2×C4—1081no—
974C2×C4D3311yescharacteristic
975C2×C3—21no—
976C2×C3—21no—
977C2×C3—21no—
978C2×C3—21no—
979C2×C3—21no—
980C2×C3—21no—
981C2×C3—21no—
982C2×C3—21no—
983C2×C3—21no—
984C2×C3—41no—
985C2×C3—41no—
986C2×C3—41no—
987C2×C3—182no—
988C2×C3—361no—
989C2×C3—361no—
990C2×C3#6429711yescharacteristic
991C2×C3#6429811yescharacteristic
992C2×C3D3×#23511yescharacteristic
993C2×C3D3×#23511yescharacteristic
994C2×C3#6430711yescharacteristic
995C2×C3#6431211yescharacteristic
996C2×C3#6431411yescharacteristic
997C2×C3#6431511yescharacteristic
998C2×C3#6432011yescharacteristic
999D3—62no—
1000D3—62no—
1001D3—122no—
1002D3—122no—
1003D3—121no—
1004D3—121no—
1005D3—121no—
1006D3—121no—
1007D3—241no—
1008C22—92no—
1009C22—181no—
1010C22—181no—
1011C22—181no—
1012C22—181no—
1013C22—181no—
1014C22—181no—
1015C22—181no—
1016C22—181no—
1017C22C2×D3311yescharacteristic
1018C4—21no—
1019C4—61no—
1020C4—61no—
1021C4—61no—
1022C4—61no—
1023C4—61no—
1024C4—61no—
1025C4—181no—
1026C4—181no—
1027C4—181no—
1028C4—541no—
1029C4—541no—
1030C3—21no—
1031C3—21no—
1032C3—21no—
1033C3—41no—
1034C3#1059391411yescharacteristic, complemented
1035C3#1059440711yescharacteristic, complemented
1036C3#1059448111yescharacteristic, complemented
1037C2—182no—
1038C2—361no—
1039C2—361no—
1040C2#1172438511yescharacteristic
1041C2#1172439611yescharacteristic
1042C2#1172441011yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radical#11723687C2
hypercenterC2×C4D33
hypocenterC33#539
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. #11723502C2semidirect
3. #11723488C2semidirect
4. #11723444C2semidirect
5. C3×#63894C2semidirect
6. C3×#63868C2semidirect
7. C3×#63846C2semidirect
8. #11723023C2semidirect
9. #11722997C2semidirect
10. #11722997C2semidirect
11. #11722995C2semidirect
12. #11722984C2semidirect
13. #11722972C2semidirect
14. #11722934C2semidirect
15. #11722911C2semidirect
73. #63894D3semidirect
89. #63868D3semidirect
101. #63846D3semidirect
675. C33#539semidirect
948. C32#5564semidirect
949. C32#5692semidirect
950. C32#5707semidirect
1034. C3#10593914semidirect
1035. C3#10594407semidirect
1036. C3#10594481semidirect

Maximal subgroups

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

subgroupindex
#117236872
#117235022
#117234882
#117234442
C3×#638942
C3×#638682
C3×#638462
#117230232
#117229972
#117229952
#117229842
#117229722
#117229342
#117229112
#105944813
#105944073
#105939143