Finite Group Databasebeta

← D3×#4959 #11808152

Subgroups — D3×#4959 #11808152

Order 1152.

2623 conjugacy classes of subgroups.

The subgroup lattice has 1258 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×#67C211yesmaximal, characteristic
2C2×C3×D3×C22⋊C4C211yesmaximal, characteristic, complemented
3C2×D3×#217C211yesmaximal, characteristic, complemented
4C2×D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
5C2×D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
6C2×D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
7#10592658C211yesmaximal, characteristic, complemented
8C3×#4959C211yesmaximal, characteristic, complemented
9#10591712C211yesmaximal, characteristic, complemented
10#10591708C211yesmaximal, characteristic, complemented
11#10591390C211yesmaximal, characteristic, complemented
12#10591388C211yesmaximal, characteristic, complemented
13D3×C3⋊#95C211yesmaximal, characteristic, complemented
14#10591292C211yesmaximal, characteristic, complemented
15#10591291C211yesmaximal, characteristic, complemented
16C2×#4959—31nomaximal
17D3×#394—31nomaximal
18C24×C3×D3C2211yescharacteristic
19C23×D32C2211yescharacteristic
20C22×#638C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C22×C3×C4×D3C2211yescharacteristic
24C2×D3×#67—24no—
25C2×D3×#67—24no—
26C2×D3×#67—24no—
27C22×#626C2211yescharacteristic
28C22×#625C2211yescharacteristic
29C22×D3×Dic3C2211yescharacteristic
30C22×D3×Dic3C2211yescharacteristic
31C22×D3×Dic3C2211yescharacteristic
32C2×C32×C22⋊C4C2211yescharacteristic, complemented
33C2×#3757C2211yescharacteristic, complemented
34C2×#3752C2211yescharacteristic, complemented
35C2×#3752C2211yescharacteristic, complemented
36C2×#3750C2211yescharacteristic, complemented
37C2×C3×#217C2211yescharacteristic, complemented
38C2×C3×#217C2211yescharacteristic, complemented
39C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
40C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
41C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
42C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
43C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
44C3×D3×C22⋊C4—24no—
45D3×#217—24no—
46C2×#3724C2211yescharacteristic, complemented
47C2×Dic3⋊Dic3C2211yescharacteristic, complemented
48C2×#3722C2211yescharacteristic, complemented
49C2×#3722C2211yescharacteristic, complemented
50C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
51C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
52C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
53C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
54D3×(C2×D3)⋊C4—24no—
55D3×(C2×D3)⋊C4—24no—
56D3×Dic3⋊C4—24no—
57#63658C2211yescharacteristic, complemented
58C3×C3⋊#95C2211yescharacteristic, complemented
59#63579C2211yescharacteristic, complemented
60#63579C2211yescharacteristic, complemented
61C23×#67—31no—
62C22×D3×D4—31no—
63C22×C3×C22⋊C4—31no—
64C22×#217—31no—
65C22×(C2×D3)⋊C4—31no—
66C22×(C2×D3)⋊C4—31no—
67C22×Dic3⋊C4—31no—
68C2×D3×C4⋊C4—31no—
69C2×D3×C22⋊C4—31no—
70C2×D3×C22⋊C4—31no—
71C2×D3×C22⋊C4—31no—
72C2×D3×C22⋊C4D311yescharacteristic, complemented
73C3×#394—31no—
74#5222—31no—
75C2×C3⋊#95—31no—
76#4991—31no—
77#4961—31no—
78#4961—31no—
79#4959—31no—
80#4959—31no—
81#4959—31no—
82#4959—31no—
83#4959—31no—
84#4959—31no—
85#4959—31no—
86#4959—31no—
87#4959—31no—
88#4959—61no—
89#4959D311yescharacteristic, direct product factor
90#4672—31no—
91D3×#95—31no—
92C24×C32C2311yescharacteristic
93C23×C3⋊D3C2311yescharacteristic
94C23×C3×D3—22no—
95C23×C3×D3—22no—
96C23×C3×D3—22no—
97C23×C3×D3—22no—
98C23×C3×D3—22no—
99C23×C3×D3—22no—
100C23×C3×D3D414yes—
101C23×C3×D3C2311yescharacteristic
102C23×C3×D3C2311yescharacteristic
103C23×C3×D3C2311yescharacteristic
104C22×D32—22no—
105C22×D32—22no—
106C22×D32—22no—
107C22×D32—22no—
108C22×D32—22no—
109C22×D32—22no—
110C22×D32D414yes—
111C22×C32×C4C2311yescharacteristic
112C22×C32×C4C2311yescharacteristic
113C2×#638—22no—
114C2×#638—22no—
115C2×#638—22no—
116C22×C3⋊Dic3C2311yescharacteristic
117C22×C3⋊Dic3C2311yescharacteristic
118C22×C3⋊Dic3C2311yescharacteristic
119C2×C3×#67—22no—
120C2×C3×#67—22no—
121C2×C3×#67—22no—
122C22×C3×Dic3C2311yescharacteristic
123C22×C3×Dic3C2311yescharacteristic
124C22×C3×Dic3C2311yescharacteristic
125C22×C3×Dic3C2311yescharacteristic
126C22×C3×Dic3C2311yescharacteristic
127C2×C3×C4×D3—22no—
128C2×C3×C4×D3—22no—
129C2×C3×C4×D3—22no—
130C2×C3×C4×D3—22no—
131C2×C3×C4×D3—22no—
132C2×C3×C4×D3—22no—
133D3×#67—232no—
134C2×#626—22no—
135C2×#626—22no—
136C2×#626—22no—
137C2×#625—22no—
138C2×#625—22no—
139C2×#625—22no—
140C2×D3×Dic3—22no—
141C2×D3×Dic3—22no—
142C2×D3×Dic3—22no—
143C2×D3×Dic3—22no—
144C2×D3×Dic3—22no—
145C2×D3×Dic3—22no—
146C2×D3×Dic3—22no—
147C2×D3×Dic3D414yes—
148C2×D3×Dic3D414yescomplemented
149C32×C22⋊C4—22no—
150#3757—22no—
151#3752—22no—
152#3752—22no—
153#3750—22no—
154C3×#217—22no—
155C3×#217—22no—
156C3×(C2×D3)⋊C4—22no—
157C3×(C2×D3)⋊C4—22no—
158C3×(C2×D3)⋊C4—22no—
159C3×(C2×D3)⋊C4—22no—
160C3×Dic3⋊C4—22no—
161#3724—22no—
162Dic3⋊Dic3—22no—
163#3722—22no—
164#3722—22no—
165(C2×D3)⋊Dic3—22no—
166(C2×D3)⋊Dic3—22no—
167(C2×D3)⋊Dic3—22no—
168(C2×D3)⋊Dic3—22no—
169C2×#394—91noSylow
170C25×C3—31no—
171C24×D3—31no—
172C24×D3—31no—
173C24×D3C2×D311yescharacteristic
174C22×C3×D4—31no—
175C23×C3×C4—31no—
176C23×C3×C4—31no—
177C22×#67—31no—
178C22×#67—31no—
179C22×#67—31no—
180C22×#67—31no—
181C22×#67—31no—
182C22×#67—61no—
183C22×#67—64no—
184C22×#67—64no—
185C22×#67—64no—
186C22×#67C2×D311yescharacteristic
187C23×Dic3—31no—
188C23×Dic3—31no—
189C23×Dic3—31no—
190C2×D3×D4—64no—
191C2×D3×D4—64no—
192C2×D3×D4—64no—
193C22×D12—31no—
194C22×C4×D3—31no—
195C22×C4×D3—31no—
196C22×C4×D3—31no—
197C22×C4×D3C2×D311yescharacteristic
198C22×C4×D3C2×D311yescharacteristic
199C2×C3×C4⋊C4—31no—
200C2×C3×C22⋊C4—21no—
201C2×C3×C22⋊C4—31no—
202C2×C3×C22⋊C4—31no—
203C2×C3×C22⋊C4—31no—
204C2×C3×C22⋊C4—31no—
205C2×C3×C22⋊C4—31no—
206C2×C3×C22⋊C4—31no—
207C2×C3×C22⋊C4—64no—
208C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
209C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
210C2×#217—31no—
211C2×#217—31no—
212C2×#217—31no—
213C2×#217—31no—
214C2×#217—31no—
215C2×#217—31no—
216C2×#217—61no—
217C2×#217—64no—
218C2×#217C2×D311yescharacteristic, complemented
219C2×#217C2×D311yescharacteristic, complemented
220C2×(C2×D3)⋊C4—31no—
221C2×(C2×D3)⋊C4—31no—
222C2×(C2×D3)⋊C4—31no—
223C2×(C2×D3)⋊C4—31no—
224C2×(C2×D3)⋊C4—31no—
225C2×(C2×D3)⋊C4—31no—
226C2×(C2×D3)⋊C4—31no—
227C2×(C2×D3)⋊C4—31no—
228C2×(C2×D3)⋊C4—31no—
229C2×(C2×D3)⋊C4—31no—
230C2×(C2×D3)⋊C4—31no—
231C2×(C2×D3)⋊C4—31no—
232C2×(C2×D3)⋊C4—61no—
233C2×(C2×D3)⋊C4—61no—
234C2×(C2×D3)⋊C4—64no—
235C2×(C2×D3)⋊C4—64no—
236C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
237C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
238C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
239C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
240C2×C4⋊Dic3—31no—
241C2×Dic3⋊C4—31no—
242C2×Dic3⋊C4—31no—
243C2×Dic3⋊C4—31no—
244C2×Dic3⋊C4—31no—
245C2×Dic3⋊C4—31no—
246C2×Dic3⋊C4—61no—
247C2×Dic3⋊C4—64no—
248C2×Dic3⋊C4C2×D311yescharacteristic, complemented
249D3×C4⋊C4—64no—
250D3×C22⋊C4—24no—
251D3×C22⋊C4—64no—
252D3×C22⋊C4—64no—
253D3×C22⋊C4—64no—
254C3×#95—31no—
255C3⋊#95—31no—
256C3⋊#95—31no—
257C3⋊#95—31no—
258C3⋊#95—31no—
259C3⋊#95—31no—
260C3⋊#95—31no—
261C3⋊#95—61no—
262C3⋊#95C2×D311yescharacteristic, complemented
263C23×C32—21no—
264C23×C32—21no—
265C23×C32—21no—
266C23×C32—21no—
267C23×C32—21no—
268C23×C32—21no—
269C23×C32C2×D412yes—
270C23×C32C2411yescharacteristic
271C22×C3⋊D3—21no—
272C22×C3⋊D3—21no—
273C22×C3⋊D3—21no—
274C22×C3⋊D3—21no—
275C22×C3⋊D3—21no—
276C22×C3⋊D3—21no—
277C22×C3⋊D3C2×D412yes—
278C22×C3×D3—21no—
279C22×C3×D3—21no—
280C22×C3×D3—21no—
281C22×C3×D3—21no—
282C22×C3×D3—21no—
283C22×C3×D3—21no—
284C22×C3×D3—21no—
285C22×C3×D3—21no—
286C22×C3×D3—21no—
287C22×C3×D3—21no—
288C22×C3×D3—21no—
289C22×C3×D3—21no—
290C22×C3×D3—28no—
291C22×C3×D3—28no—
292C22×C3×D3—28no—
293C22×C3×D3—44no—
294C22×C3×D3—44no—
295C22×C3×D3—44no—
296C22×C3×D3—44no—
297C22×C3×D3C2×D412yes—
298C22×C3×D3C2×D412yes—
299C22×C3×D3C2×D412yes—
300C22×C3×D3C2×D412yes—
301C22×C3×D3C2×D412yes—
302C22×C3×D3C2×D412yes—
303C22×C3×D3#4112yes—
304C22×C3×D3#4112yes—
305C22×C3×D3#4112yes—
306C2×D32—28no—
307C2×D32—28no—
308C2×D32—28no—
309C2×D32—44no—
310C2×D32—44no—
311C2×D32—44no—
312C2×D32—44no—
313C2×C32×C4—21no—
314C2×C32×C4—21no—
315C2×C32×C4—21no—
316C2×C32×C4—21no—
317C2×C32×C4—21no—
318C2×C32×C4—21no—
319#638—28no—
320C2×C3⋊Dic3—21no—
321C2×C3⋊Dic3—21no—
322C2×C3⋊Dic3—21no—
323C2×C3⋊Dic3—21no—
324C2×C3⋊Dic3—21no—
325C2×C3⋊Dic3—21no—
326C2×C3⋊Dic3—21no—
327C2×C3⋊Dic3C2×D412yes—
328C2×C3⋊Dic3C2×D412yescomplemented
329C3×#67—28no—
330C2×C3×Dic3—21no—
331C2×C3×Dic3—21no—
332C2×C3×Dic3—21no—
333C2×C3×Dic3—21no—
334C2×C3×Dic3—21no—
335C2×C3×Dic3—21no—
336C2×C3×Dic3—21no—
337C2×C3×Dic3—21no—
338C2×C3×Dic3—21no—
339C2×C3×Dic3—21no—
340C2×C3×Dic3—21no—
341C2×C3×Dic3—21no—
342C2×C3×Dic3—21no—
343C2×C3×Dic3C2×D412yes—
344C2×C3×Dic3C2×D412yescomplemented
345C3×C4×D3—44no—
346C3×C4×D3—44no—
347#626—28no—
348#625—28no—
349D3×Dic3—28no—
350D3×Dic3—28no—
351D3×Dic3—44no—
352C23×D4—91no—
353C22×C4⋊C4—91no—
354C22×C22⋊C4—31no—
355C22×C22⋊C4—91no—
356C22×C22⋊C4—91no—
357C22×C22⋊C4—91no—
358#394—31no—
359#394—91no—
360#394—91no—
361#394—91no—
362#394—91no—
363#394—91no—
364#394—91no—
365#394—91no—
366C2×#95—91no—
367C24×C3—21no—
368C24×C3—31no—
369C24×C3—34no—
370C24×C3—31no—
371C24×C3—31no—
372C24×C3—62no—
373C24×C3—62no—
374C24×C3—62no—
375C24×C3—62no—
376C24×C3—62no—
377C24×C3—62no—
378C24×C3C22×D311yescharacteristic
379C24×C3C22×D311yescharacteristic
380C23×D3—22no—
381C23×D3—22no—
382C23×D3—22no—
383C23×D3—22no—
384C23×D3—22no—
385C23×D3—22no—
386C23×D3—31no—
387C23×D3—31no—
388C23×D3—34no—
389C23×D3—34no—
390C23×D3—61no—
391C23×D3—62no—
392C23×D3—62no—
393C23×D3—62no—
394C23×D3—62no—
395C23×D3—62no—
396C23×D3—62no—
397C23×D3—62no—
398C23×D3—62no—
399C23×D3—62no—
400C23×D3—62no—
401C23×D3—62no—
402C23×D3—62no—
403C23×D3#6714yes—
404C23×D3C22×D311yescharacteristic
405C23×D3C22×D311yescharacteristic
406C23×D3C22×D311yescharacteristic
407C2×C3×D4—62no—
408C2×C3×D4—62no—
409C2×C3×D4—62no—
410C22×C3×C4—21no—
411C22×C3×C4—21no—
412C22×C3×C4—31no—
413C22×C3×C4—31no—
414C22×C3×C4—31no—
415C22×C3×C4—31no—
416C22×C3×C4—31no—
417C22×C3×C4—62no—
418C22×C3×C4—62no—
419C22×C3×C4—62no—
420C22×C3×C4—62no—
421C22×C3×C4—62no—
422C22×C3×C4—62no—
423C22×C3×C4C22×D311yescharacteristic
424C22×C3×C4C22×D311yescharacteristic
425C22×C3×C4C22×D311yescharacteristic
426C22×C3×C4C22×D311yescharacteristic
427C2×#67—22no—
428C2×#67—22no—
429C2×#67—22no—
430C2×#67—62no—
431C2×#67—62no—
432C2×#67—62no—
433C2×#67—62no—
434C2×#67—62no—
435C2×#67—62no—
436C2×#67—632no—
437C2×#67—62no—
438C2×#67—62no—
439C2×#67—62no—
440C2×#67—62no—
441C2×#67—62no—
442C2×#67—62no—
443C2×#67—62no—
444C2×#67—62no—
445C2×#67—62no—
446C2×#67—122no—
447C2×#67—122no—
448C2×#67—122no—
449C22×Dic3—31no—
450C22×Dic3—31no—
451C22×Dic3—31no—
452C22×Dic3—31no—
453C22×Dic3—34no—
454C22×Dic3—34no—
455C22×Dic3—31no—
456C22×Dic3—31no—
457C22×Dic3—61no—
458C22×Dic3—61no—
459C22×Dic3—61no—
460C22×Dic3—62no—
461C22×Dic3—62no—
462C22×Dic3—62no—
463C22×Dic3—62no—
464C22×Dic3—62no—
465C22×Dic3—62no—
466C22×Dic3—62no—
467C22×Dic3C22×D311yescharacteristic
468C22×Dic3C22×D311yescharacteristic
469C22×Dic3C22×D311yescharacteristic
470C22×Dic3C22×D311yescharacteristic
471C22×Dic3C22×D311yescharacteristic
472D3×D4—632no—
473C2×D12—62no—
474C2×D12—62no—
475C2×D12—62no—
476C2×C4×D3—22no—
477C2×C4×D3—22no—
478C2×C4×D3—22no—
479C2×C4×D3—22no—
480C2×C4×D3—22no—
481C2×C4×D3—22no—
482C2×C4×D3—34no—
483C2×C4×D3—34no—
484C2×C4×D3—62no—
485C2×C4×D3—62no—
486C2×C4×D3—62no—
487C2×C4×D3—62no—
488C2×C4×D3—62no—
489C2×C4×D3—62no—
490C2×C4×D3—62no—
491C3×C4⋊C4—62no—
492C3×C22⋊C4—22no—
493C3×C22⋊C4—22no—
494C3×C22⋊C4—42no—
495C3×C22⋊C4—62no—
496C3×C22⋊C4—62no—
497C3×C22⋊C4—62no—
498C3×C22⋊C4—62no—
499C3×C22⋊C4—62no—
500C3×C22⋊C4—62no—
501#217—22no—
502#217—22no—
503#217—62no—
504#217—62no—
505#217—62no—
506#217—62no—
507#217—62no—
508#217—62no—
509#217—122no—
510(C2×D3)⋊C4—22no—
511(C2×D3)⋊C4—22no—
512(C2×D3)⋊C4—22no—
513(C2×D3)⋊C4—22no—
514(C2×D3)⋊C4—62no—
515(C2×D3)⋊C4—62no—
516(C2×D3)⋊C4—62no—
517(C2×D3)⋊C4—62no—
518(C2×D3)⋊C4—62no—
519(C2×D3)⋊C4—62no—
520(C2×D3)⋊C4—62no—
521(C2×D3)⋊C4—62no—
522(C2×D3)⋊C4—62no—
523(C2×D3)⋊C4—62no—
524(C2×D3)⋊C4—62no—
525(C2×D3)⋊C4—62no—
526(C2×D3)⋊C4—122no—
527(C2×D3)⋊C4—122no—
528C4⋊Dic3—62no—
529Dic3⋊C4—22no—
530Dic3⋊C4—62no—
531Dic3⋊C4—62no—
532Dic3⋊C4—62no—
533Dic3⋊C4—62no—
534Dic3⋊C4—62no—
535Dic3⋊C4—122no—
536C22×C32—22no—
537C22×C32—22no—
538C22×C32—22no—
539C22×C32—41no—
540C22×C32—41no—
541C22×C32—41no—
542C22×C32—41no—
543C22×C32C22×D411yescharacteristic
544C22×C32C22×D411yescharacteristic
545C22×C32C22×D411yescharacteristic
546C22×C32C22×D411yescharacteristic
547C22×C32C2×#4111yescharacteristic
548C22×C32C2×#4111yescharacteristic
549C22×C32C2×#4111yescharacteristic
550C2×C3⋊D3—22no—
551C2×C3⋊D3—22no—
552C2×C3⋊D3—22no—
553C2×C3⋊D3—41no—
554C2×C3⋊D3—41no—
555C2×C3⋊D3—41no—
556C2×C3⋊D3—41no—
557C2×C3×D3—22no—
558C2×C3×D3—22no—
559C2×C3×D3—22no—
560C2×C3×D3—22no—
561C2×C3×D3—22no—
562C2×C3×D3—22no—
563C2×C3×D3—41no—
564C2×C3×D3—41no—
565C2×C3×D3—41no—
566C2×C3×D3—41no—
567C2×C3×D3—41no—
568C2×C3×D3—41no—
569C2×C3×D3—41no—
570C2×C3×D3—41no—
571C2×C3×D3—416no—
572C2×C3×D3#12014yes—
573C2×C3×D3#12114yes—
574C2×C3×D3#12114yes—
575C2×C3×D3#12114yes—
576C2×C3×D3#12314yes—
577C2×C3×D3#12314yes—
578C2×C3×D3#12414yes—
579D32—416no—
580C32×C4—41no—
581C32×C4—41no—
582C3⋊Dic3—22no—
583C3⋊Dic3—22no—
584C3⋊Dic3—41no—
585C3×Dic3—22no—
586C3×Dic3—22no—
587C3×Dic3—41no—
588C3×Dic3—41no—
589C3×Dic3—41no—
590C25—31no—
591C25—91no—
592C22×D4—31no—
593C22×D4—91no—
594C22×D4—91no—
595C22×D4—91no—
596C22×D4—184no—
597C22×D4—184no—
598C22×D4—184no—
599C23×C4—31no—
600C23×C4—31no—
601C23×C4—91no—
602C23×C4—91no—
603C23×C4—91no—
604C2×C4⋊C4—31no—
605C2×C4⋊C4—91no—
606C2×C4⋊C4—91no—
607C2×C4⋊C4—91no—
608C2×C4⋊C4—184no—
609C2×C22⋊C4—31no—
610C2×C22⋊C4—31no—
611C2×C22⋊C4—31no—
612C2×C22⋊C4—31no—
613C2×C22⋊C4—31no—
614C2×C22⋊C4—31no—
615C2×C22⋊C4—64no—
616C2×C22⋊C4—91no—
617C2×C22⋊C4—91no—
618C2×C22⋊C4—91no—
619C2×C22⋊C4—91no—
620C2×C22⋊C4—91no—
621C2×C22⋊C4—91no—
622C2×C22⋊C4—91no—
623C2×C22⋊C4—91no—
624C2×C22⋊C4—91no—
625C2×C22⋊C4—184no—
626C2×C22⋊C4—184no—
627C2×C22⋊C4—184no—
628C2×C22⋊C4D3211yescharacteristic, complemented
629#95—31no—
630#95—91no—
631#95—91no—
632#95—91no—
633C23×C3—21no—
634C23×C3—21no—
635C23×C3—21no—
636C23×C3—21no—
637C23×C3—21no—
638C23×C3—21no—
639C23×C3—21no—
640C23×C3—21no—
641C23×C3—21no—
642C23×C3—21no—
643C23×C3—21no—
644C23×C3—21no—
645C23×C3—21no—
646C23×C3—22no—
647C23×C3—32no—
648C23×C3—32no—
649C23×C3—32no—
650C23×C3—32no—
651C23×C3—32no—
652C23×C3—32no—
653C23×C3—32no—
654C23×C3—32no—
655C23×C3—32no—
656C23×C3—41no—
657C23×C3—41no—
658C23×C3—41no—
659C23×C3—41no—
660C23×C3—41no—
661C23×C3—41no—
662C23×C3—68no—
663C23×C3—68no—
664C23×C3—68no—
665C23×C3—61no—
666C23×C3—61no—
667C23×C3—61no—
668C23×C3—61no—
669C23×C3—61no—
670C23×C3—61no—
671C23×C3—61no—
672C23×C3—61no—
673C23×C3—61no—
674C23×C3—61no—
675C23×C3—61no—
676C23×C3—61no—
677C23×C3—124no—
678C23×C3—124no—
679C23×C3—124no—
680C23×C3—124no—
681C23×C3D3×D412yes—
682C23×C3C2×#6712yes—
683C23×C3C23×D311yescharacteristic
684C23×C3C23×D311yescharacteristic
685C22×D3—21no—
686C22×D3—21no—
687C22×D3—21no—
688C22×D3—21no—
689C22×D3—21no—
690C22×D3—21no—
691C22×D3—21no—
692C22×D3—21no—
693C22×D3—21no—
694C22×D3—21no—
695C22×D3—21no—
696C22×D3—21no—
697C22×D3—28no—
698C22×D3—28no—
699C22×D3—28no—
700C22×D3—32no—
701C22×D3—32no—
702C22×D3—44no—
703C22×D3—44no—
704C22×D3—44no—
705C22×D3—44no—
706C22×D3—62no—
707C22×D3—68no—
708C22×D3—68no—
709C22×D3—68no—
710C22×D3—61no—
711C22×D3—61no—
712C22×D3—61no—
713C22×D3—61no—
714C22×D3—61no—
715C22×D3—61no—
716C22×D3—61no—
717C22×D3—61no—
718C22×D3—61no—
719C22×D3—61no—
720C22×D3—61no—
721C22×D3—61no—
722C22×D3—68no—
723C22×D3—68no—
724C22×D3—68no—
725C22×D3—121no—
726C22×D3—121no—
727C22×D3—121no—
728C22×D3—121no—
729C22×D3—121no—
730C22×D3—121no—
731C22×D3—124no—
732C22×D3—124no—
733C22×D3—124no—
734C22×D3—124no—
735C22×D3—124no—
736C22×D3—124no—
737C22×D3—124no—
738C22×D3—124no—
739C22×D3#23512yes—
740C22×D3#23512yes—
741C22×D3D3×D412yes—
742C22×D3D3×D412yes—
743C22×D3D3×D412yes—
744C22×D3D3×D412yes—
745C22×D3#23712yes—
746C22×D3C2×#6712yes—
747C22×D3C2×#6712yes—
748C3×D4—68no—
749C2×C3×C4—21no—
750C2×C3×C4—21no—
751C2×C3×C4—21no—
752C2×C3×C4—21no—
753C2×C3×C4—21no—
754C2×C3×C4—21no—
755C2×C3×C4—21no—
756C2×C3×C4—21no—
757C2×C3×C4—21no—
758C2×C3×C4—21no—
759C2×C3×C4—21no—
760C2×C3×C4—21no—
761C2×C3×C4—32no—
762C2×C3×C4—32no—
763C2×C3×C4—41no—
764C2×C3×C4—41no—
765C2×C3×C4—41no—
766C2×C3×C4—41no—
767C2×C3×C4—41no—
768C2×C3×C4—41no—
769C2×C3×C4—61no—
770C2×C3×C4—61no—
771C2×C3×C4—61no—
772C2×C3×C4—61no—
773C2×C3×C4—61no—
774C2×C3×C4—61no—
775C2×C3×C4—61no—
776C2×C3×C4—61no—
777C2×C3×C4—61no—
778C2×C3×C4—61no—
779C2×C3×C4—61no—
780C2×C3×C4—61no—
781C2×C3×C4—61no—
782C2×C3×C4—124no—
783C2×C3×C4—124no—
784#67—28no—
785#67—68no—
786#67—68no—
787#67—68no—
788#67—68no—
789#67—68no—
790#67—128no—
791C2×Dic3—21no—
792C2×Dic3—21no—
793C2×Dic3—21no—
794C2×Dic3—21no—
795C2×Dic3—21no—
796C2×Dic3—21no—
797C2×Dic3—21no—
798C2×Dic3—21no—
799C2×Dic3—21no—
800C2×Dic3—21no—
801C2×Dic3—21no—
802C2×Dic3—21no—
803C2×Dic3—21no—
804C2×Dic3—32no—
805C2×Dic3—32no—
806C2×Dic3—32no—
807C2×Dic3—32no—
808C2×Dic3—62no—
809C2×Dic3—62no—
810C2×Dic3—68no—
811C2×Dic3—68no—
812C2×Dic3—61no—
813C2×Dic3—61no—
814C2×Dic3—61no—
815C2×Dic3—61no—
816C2×Dic3—61no—
817C2×Dic3—61no—
818C2×Dic3—61no—
819C2×Dic3—61no—
820C2×Dic3—61no—
821C2×Dic3—61no—
822C2×Dic3—61no—
823C2×Dic3—61no—
824C2×Dic3—61no—
825C2×Dic3—61no—
826C2×Dic3—121no—
827C2×Dic3—121no—
828C2×Dic3—121no—
829C2×Dic3—121no—
830C2×Dic3—121no—
831C2×Dic3—121no—
832C2×Dic3—121no—
833C2×Dic3—124no—
834C2×Dic3D3×D412yes—
835C2×Dic3D3×D412yescomplemented
836D12—68no—
837C4×D3—44no—
838C4×D3—44no—
839C4×D3—68no—
840C4×D3—68no—
841C4×D3—124no—
842C2×C32—42no—
843C2×C32C2×#12011yescharacteristic
844C2×C32C2×#12111yescharacteristic
845C2×C32C2×#12111yescharacteristic
846C2×C32C2×#12111yescharacteristic
847C2×C32C2×#12311yescharacteristic
848C2×C32C2×#12311yescharacteristic
849C2×C32C2×#12411yescharacteristic
850C3⋊D3—42no—
851C3×D3—42no—
852C3×D3—42no—
853C3×D3#39418yescomplemented
854C24—31no—
855C24—31no—
856C24—31no—
857C24—34no—
858C24—62no—
859C24—62no—
860C24—62no—
861C24—62no—
862C24—62no—
863C24—62no—
864C24—94no—
865C24—91no—
866C24—182no—
867C24—182no—
868C24—182no—
869C24—182no—
870C24—182no—
871C24—182no—
872C24C2×D3211yescharacteristic
873C2×D4—62no—
874C2×D4—62no—
875C2×D4—62no—
876C2×D4—182no—
877C2×D4—182no—
878C2×D4—182no—
879C2×D4—182no—
880C2×D4—182no—
881C2×D4—1832no—
882C2×D4—182no—
883C2×D4—182no—
884C2×D4—182no—
885C2×D4—182no—
886C22×C4—31no—
887C22×C4—31no—
888C22×C4—31no—
889C22×C4—31no—
890C22×C4—31no—
891C22×C4—62no—
892C22×C4—62no—
893C22×C4—62no—
894C22×C4—62no—
895C22×C4—62no—
896C22×C4—62no—
897C22×C4—94no—
898C22×C4—94no—
899C22×C4—91no—
900C22×C4—91no—
901C22×C4—91no—
902C22×C4—182no—
903C22×C4—182no—
904C22×C4—182no—
905C22×C4—182no—
906C22×C4—182no—
907C22×C4—182no—
908C22×C4—182no—
909C22×C4C2×D3211yescharacteristic
910C22×C4C2×D3211yescharacteristic
911C4⋊C4—62no—
912C4⋊C4—182no—
913C4⋊C4—182no—
914C4⋊C4—182no—
915C22⋊C4—22no—
916C22⋊C4—62no—
917C22⋊C4—62no—
918C22⋊C4—62no—
919C22⋊C4—62no—
920C22⋊C4—62no—
921C22⋊C4—62no—
922C22⋊C4—182no—
923C22⋊C4—182no—
924C22⋊C4—182no—
925C22⋊C4—182no—
926C22⋊C4—182no—
927C22⋊C4—182no—
928C22⋊C4—182no—
929C22⋊C4—182no—
930C22⋊C4—182no—
931C22×C3—22no—
932C22×C3—22no—
933C22×C3—22no—
934C22×C3—22no—
935C22×C3—22no—
936C22×C3—22no—
937C22×C3—21no—
938C22×C3—21no—
939C22×C3—21no—
940C22×C3—21no—
941C22×C3—21no—
942C22×C3—21no—
943C22×C3—21no—
944C22×C3—34no—
945C22×C3—34no—
946C22×C3—34no—
947C22×C3—34no—
948C22×C3—34no—
949C22×C3—34no—
950C22×C3—34no—
951C22×C3—42no—
952C22×C3—42no—
953C22×C3—42no—
954C22×C3—41no—
955C22×C3—41no—
956C22×C3—41no—
957C22×C3—41no—
958C22×C3—41no—
959C22×C3—41no—
960C22×C3—41no—
961C22×C3—41no—
962C22×C3—62no—
963C22×C3—62no—
964C22×C3—62no—
965C22×C3—62no—
966C22×C3—62no—
967C22×C3—62no—
968C22×C3—81no—
969C22×C3—81no—
970C22×C3—81no—
971C22×C3—81no—
972C22×C3—1216no—
973C22×C3—121no—
974C22×C3—121no—
975C22×C3—121no—
976C22×C3—121no—
977C22×C3—121no—
978C22×C3—121no—
979C22×C3—121no—
980C22×C3—121no—
981C22×C3C2×#23511yescharacteristic
982C22×C3C2×#23511yescharacteristic
983C22×C3C2×D3×D411yescharacteristic
984C22×C3C2×D3×D411yescharacteristic
985C22×C3C2×D3×D411yescharacteristic
986C22×C3C2×D3×D411yescharacteristic
987C22×C3C2×D3×D411yescharacteristic
988C22×C3C2×D3×D411yescharacteristic
989C22×C3C2×D3×D411yescharacteristic
990C22×C3C2×#23711yescharacteristic
991C22×C3D3×#4111yescharacteristic
992C22×C3D3×#4111yescharacteristic
993C22×C3D3×#4111yescharacteristic
994C22×C3C22×#6711yescharacteristic
995C2×D3—22no—
996C2×D3—22no—
997C2×D3—22no—
998C2×D3—22no—
999C2×D3—22no—
1000C2×D3—22no—
1001C2×D3—41no—
1002C2×D3—41no—
1003C2×D3—41no—
1004C2×D3—41no—
1005C2×D3—41no—
1006C2×D3—41no—
1007C2×D3—41no—
1008C2×D3—41no—
1009C2×D3—416no—
1010C2×D3—62no—
1011C2×D3—62no—
1012C2×D3—62no—
1013C2×D3—62no—
1014C2×D3—62no—
1015C2×D3—62no—
1016C2×D3—122no—
1017C2×D3—122no—
1018C2×D3—122no—
1019C2×D3—1216no—
1020C2×D3—121no—
1021C2×D3—121no—
1022C2×D3—121no—
1023C2×D3—121no—
1024C2×D3—121no—
1025C2×D3—121no—
1026C2×D3—121no—
1027C2×D3—121no—
1028C2×D3—1216no—
1029C2×D3—241no—
1030C2×D3—241no—
1031C2×D3—241no—
1032C2×D3—241no—
1033C2×D3#88314yes—
1034C2×D3#88414yes—
1035C2×D3#88414yes—
1036C2×D3#88514yes—
1037C2×D3#92914yes—
1038C2×D3#93714yes—
1039C2×D3#93914yes—
1040C3×C4—41no—
1041C3×C4—41no—
1042C3×C4—41no—
1043C3×C4—41no—
1044C3×C4—62no—
1045C3×C4—62no—
1046C3×C4—81no—
1047C3×C4—81no—
1048C3×C4—121no—
1049C3×C4—121no—
1050C3×C4—121no—
1051Dic3—22no—
1052Dic3—22no—
1053Dic3—41no—
1054Dic3—41no—
1055Dic3—41no—
1056Dic3—62no—
1057Dic3—62no—
1058Dic3—62no—
1059Dic3—62no—
1060Dic3—122no—
1061Dic3—122no—
1062Dic3—121no—
1063Dic3—121no—
1064Dic3—241no—
1065C32C2×#39411yescharacteristic, complemented, Sylow
1066C23—21no—
1067C23—21no—
1068C23—21no—
1069C23—21no—
1070C23—21no—
1071C23—21no—
1072C23—32no—
1073C23—32no—
1074C23—32no—
1075C23—32no—
1076C23—32no—
1077C23—32no—
1078C23—32no—
1079C23—32no—
1080C23—32no—
1081C23—68no—
1082C23—68no—
1083C23—68no—
1084C23—61no—
1085C23—61no—
1086C23—61no—
1087C23—61no—
1088C23—61no—
1089C23—61no—
1090C23—61no—
1091C23—61no—
1092C23—61no—
1093C23—61no—
1094C23—61no—
1095C23—61no—
1096C23—92no—
1097C23—124no—
1098C23—124no—
1099C23—124no—
1100C23—124no—
1101C23—188no—
1102C23—188no—
1103C23—188no—
1104C23—181no—
1105C23—181no—
1106C23—181no—
1107C23—181no—
1108C23—181no—
1109C23—181no—
1110C23—364no—
1111C23—364no—
1112C23—364no—
1113C23—364no—
1114C23D3×#6712yes—
1115C23C22×D3211yescharacteristic
1116D4—68no—
1117D4—188no—
1118D4—188no—
1119D4—188no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—32no—
1127C2×C4—32no—
1128C2×C4—61no—
1129C2×C4—61no—
1130C2×C4—61no—
1131C2×C4—61no—
1132C2×C4—61no—
1133C2×C4—61no—
1134C2×C4—61no—
1135C2×C4—61no—
1136C2×C4—61no—
1137C2×C4—61no—
1138C2×C4—61no—
1139C2×C4—61no—
1140C2×C4—61no—
1141C2×C4—92no—
1142C2×C4—92no—
1143C2×C4—124no—
1144C2×C4—124no—
1145C2×C4—188no—
1146C2×C4—188no—
1147C2×C4—181no—
1148C2×C4—181no—
1149C2×C4—181no—
1150C2×C4—181no—
1151C2×C4—181no—
1152C2×C4—181no—
1153C2×C4—181no—
1154C2×C4—364no—
1155C2×C3—21no—
1156C2×C3—21no—
1157C2×C3—21no—
1158C2×C3—21no—
1159C2×C3—21no—
1160C2×C3—21no—
1161C2×C3—21no—
1162C2×C3—38no—
1163C2×C3—42no—
1164C2×C3—42no—
1165C2×C3—82no—
1166C2×C3—122no—
1167C2×C3—122no—
1168C2×C3C2×#88311yescharacteristic
1169C2×C3C2×#88411yescharacteristic
1170C2×C3C2×#88411yescharacteristic
1171C2×C3C2×#88511yescharacteristic
1172C2×C3D3×#12011yescharacteristic
1173C2×C3D3×#12111yescharacteristic
1174C2×C3D3×#12111yescharacteristic
1175C2×C3D3×#12111yescharacteristic
1176C2×C3D3×#12311yescharacteristic
1177C2×C3D3×#12311yescharacteristic
1178C2×C3D3×#12411yescharacteristic
1179C2×C3C2×#92911yescharacteristic
1180C2×C3C2×#93711yescharacteristic
1181C2×C3C2×#93911yescharacteristic
1182D3—42no—
1183D3—42no—
1184D3—122no—
1185D3—122no—
1186D3—242no—
1187D3#495918yesdirect product factor
1188C22—22no—
1189C22—22no—
1190C22—22no—
1191C22—34no—
1192C22—34no—
1193C22—34no—
1194C22—34no—
1195C22—34no—
1196C22—34no—
1197C22—34no—
1198C22—41no—
1199C22—41no—
1200C22—41no—
1201C22—41no—
1202C22—62no—
1203C22—62no—
1204C22—62no—
1205C22—62no—
1206C22—62no—
1207C22—62no—
1208C22—1216no—
1209C22—121no—
1210C22—121no—
1211C22—121no—
1212C22—121no—
1213C22—121no—
1214C22—121no—
1215C22—121no—
1216C22—121no—
1217C22—182no—
1218C22—182no—
1219C22—182no—
1220C22—3616no—
1221C22—361no—
1222C22—361no—
1223C22—361no—
1224C22—361no—
1225C22D3×#23511yescharacteristic
1226C22D3×#23511yescharacteristic
1227C22D32×D411yescharacteristic
1228C22D32×D411yescharacteristic
1229C22D32×D411yescharacteristic
1230C22D3×#23711yescharacteristic
1231C22C2×D3×#6711yescharacteristic
1232C4—41no—
1233C4—41no—
1234C4—62no—
1235C4—62no—
1236C4—121no—
1237C4—121no—
1238C4—121no—
1239C4—182no—
1240C4—182no—
1241C4—361no—
1242C3—21no—
1243C3D3×#39411yescharacteristic, complemented
1244C3C2×#495911yescharacteristic, complemented
1245C2—38no—
1246C2—42no—
1247C2—122no—
1248C2—122no—
1249C2—362no—
1250C2D3×#88311yescharacteristic
1251C2D3×#88411yescharacteristic
1252C2D3×#88411yescharacteristic
1253C2D3×#88511yescharacteristic
1254C2D3×#92911yescharacteristic
1255C2D3×#93711yescharacteristic
1256C2D3×#93911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C22⋊C4C22
prime radicalC22×D3×#67C2
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#394
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×D3×C22⋊C4C2semidirect
3. C2×D3×#217C2semidirect
4. C2×D3×(C2×D3)⋊C4C2semidirect
5. C2×D3×(C2×D3)⋊C4C2semidirect
6. C2×D3×Dic3⋊C4C2semidirect
7. #10592658C2semidirect
8. C3×#4959C2semidirect
9. #10591712C2semidirect
10. #10591708C2semidirect
11. #10591390C2semidirect
12. #10591388C2semidirect
13. D3×C3⋊#95C2semidirect
14. #10591292C2semidirect
15. #10591291C2semidirect
32. C2×C32×C22⋊C4C22semidirect
33. C2×#3757C22semidirect
34. C2×#3752C22semidirect
35. C2×#3752C22semidirect
36. C2×#3750C22semidirect
37. C2×C3×#217C22semidirect
38. C2×C3×#217C22semidirect
39. C2×C3×(C2×D3)⋊C4C22semidirect
40. C2×C3×(C2×D3)⋊C4C22semidirect
41. C2×C3×(C2×D3)⋊C4C22semidirect
42. C2×C3×(C2×D3)⋊C4C22semidirect
43. C2×C3×Dic3⋊C4C22semidirect
46. C2×#3724C22semidirect
47. C2×Dic3⋊Dic3C22semidirect
48. C2×#3722C22semidirect
49. C2×#3722C22semidirect
50. C2×(C2×D3)⋊Dic3C22semidirect
51. C2×(C2×D3)⋊Dic3C22semidirect
52. C2×(C2×D3)⋊Dic3C22semidirect
53. C2×(C2×D3)⋊Dic3C22semidirect
57. #63658C22semidirect
58. C3×C3⋊#95C22semidirect
59. #63579C22semidirect
60. #63579C22semidirect
72. C2×D3×C22⋊C4D3semidirect
89. #4959D3direct (N × H)
148. C2×D3×Dic3D4semidirect
208. C2×C3×C22⋊C4C2×D3semidirect
209. C2×C3×C22⋊C4C2×D3semidirect
218. C2×#217C2×D3semidirect
219. C2×#217C2×D3semidirect
236. C2×(C2×D3)⋊C4C2×D3semidirect
237. C2×(C2×D3)⋊C4C2×D3semidirect
238. C2×(C2×D3)⋊C4C2×D3semidirect
239. C2×(C2×D3)⋊C4C2×D3semidirect
248. C2×Dic3⋊C4C2×D3semidirect
262. C3⋊#95C2×D3semidirect
328. C2×C3⋊Dic3C2×D4semidirect
344. C2×C3×Dic3C2×D4semidirect
628. C2×C22⋊C4D32semidirect
835. C2×Dic3D3×D4semidirect
853. C3×D3#394semidirect
1065. C32C2×#394semidirect
1187. D3#4959direct (N × H)
1243. C3D3×#394semidirect
1244. C3C2×#4959semidirect

Maximal subgroups

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

subgroupindex
C22×D3×#672
C2×C3×D3×C22⋊C42
C2×D3×#2172
C2×D3×(C2×D3)⋊C42
C2×D3×Dic3⋊C42
#105926582
C3×#49592
#105917122
#105917082
#105913902
#105913882
D3×C3⋊#952
#105912922
#105912912
C2×#49593
D3×#3943