Finite Group Databasebeta

← #10726421

Subgroups — #10726421

Order 768.

2746 conjugacy classes of subgroups.

The subgroup lattice has 1212 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C42×D3C211yesmaximal, characteristic, complemented
2C2×#4940C211yesmaximal, characteristic, complemented
3C2×#4665C211yesmaximal, characteristic
4C2×#4665C211yesmaximal, characteristic
5C2×#4665C211yesmaximal, characteristic
6C2×#4668C211yesmaximal, characteristic, complemented
7C2×#4670C211yesmaximal, characteristic, complemented
8C3×#1434C211yesmaximal, characteristic, complemented
9(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
10(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
11#69408C211yesmaximal, characteristic, complemented
12#69408C211yesmaximal, characteristic, complemented
13#69407C211yesmaximal, characteristic, complemented
14#69405C211yesmaximal, characteristic, complemented
15#69402C211yesmaximal, characteristic, complemented
16#14696—31nomaximal, Sylow
17C23×D12C2211yescharacteristic
18C23×C4×D3C2211yescharacteristic
19C23×C4×D3C2211yescharacteristic
20C23×C4×D3C2211yescharacteristic
21C22×C3×C42C2211yescharacteristic
22C22×(C2×D3)⋊C4C2211yescharacteristic
23C22×(C2×D3)⋊C4C2211yescharacteristic
24C22×(C2×D3)⋊C4C2211yescharacteristic
25C22×(C2×D3)⋊C4C2211yescharacteristic
26C22×(C2×D3)⋊C4C2211yescharacteristic
27C22×(C2×D3)⋊C4C2211yescharacteristic
28C22×(C2×D3)⋊C4C2211yescharacteristic
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×(C2×D3)⋊C4C2211yescharacteristic
31C22×C4⋊Dic3C2211yescharacteristic
32C22×Dic3⋊C4C2211yescharacteristic
33C22×C4×Dic3C2211yescharacteristic
34C22×C4×Dic3C2211yescharacteristic
35C22×C4×Dic3C2211yescharacteristic
36C2×C42×D3—24no—
37C2×C42×D3—24no—
38C2×C42×D3—24no—
39C2×C3×#95C2211yescharacteristic
40C2×C3×#95C2211yescharacteristic
41C2×C3×#95C2211yescharacteristic
42C2×C3×#95C2211yescharacteristic
43C2×C3×#95C2211yescharacteristic
44C2×C3×#95C2211yescharacteristic
45C2×C3⋊#95C2211yescharacteristic
46C2×C3⋊#95C2211yescharacteristic
47C2×C3⋊#95C2211yescharacteristic
48C2×C3⋊#95C2211yescharacteristic
49C2×C3⋊#95C2211yescharacteristic
50C2×C3⋊#95C2211yescharacteristic
51C2×C3⋊#95C2211yescharacteristic
52C2×C3⋊#95C2211yescharacteristic
53C2×C3⋊#95C2211yescharacteristic
54C2×C3⋊#95C2211yescharacteristic
55#4940—24no—
56#4670—24no—
57#4668—24no—
58#4665—24no—
59#4665—24no—
60#4665C418yescomplemented
61C23×C42—31no—
62C2×#388—31no—
63C2×#388—31no—
64C2×#386—31no—
65C2×#386—31no—
66C2×#386—31no—
67C2×#385—31no—
68#1437—31no—
69#1437—31no—
70#1436—31no—
71#1436—31no—
72#1434—31no—
73#1434D311yescharacteristic, complemented
74C22⋊#95—31no—
75C22⋊#95—31no—
76C24×D3C2311yescharacteristic
77C24×D3C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C23×Dic3C2311yescharacteristic
86C23×Dic3C2311yescharacteristic
87C23×Dic3C2311yescharacteristic
88C23×Dic3C2311yescharacteristic
89C23×Dic3C2311yescharacteristic
90C23×Dic3C2311yescharacteristic
91C22×D12—22no—
92C22×D12—22no—
93C22×D12—22no—
94C22×D12—22no—
95C22×D12—22no—
96C22×D12—22no—
97C22×D12C2×C414yes—
98C22×C4×D3—22no—
99C22×C4×D3—22no—
100C22×C4×D3—22no—
101C22×C4×D3—22no—
102C22×C4×D3—22no—
103C22×C4×D3—22no—
104C22×C4×D3—22no—
105C22×C4×D3—22no—
106C22×C4×D3—22no—
107C22×C4×D3—22no—
108C22×C4×D3—22no—
109C22×C4×D3—22no—
110C22×C4×D3—22no—
111C22×C4×D3—22no—
112C22×C4×D3—22no—
113C22×C4×D3—22no—
114C22×C4×D3—22no—
115C22×C4×D3—22no—
116C22×C4×D3C2×C414yes—
117C22×C4×D3D414yes—
118C22×C4×D3D414yes—
119C2×C3×C42—22no—
120C2×C3×C42—22no—
121C2×C3×C42D414yescomplemented
122C2×(C2×D3)⋊C4—22no—
123C2×(C2×D3)⋊C4—22no—
124C2×(C2×D3)⋊C4—22no—
125C2×(C2×D3)⋊C4—22no—
126C2×(C2×D3)⋊C4—22no—
127C2×(C2×D3)⋊C4—22no—
128C2×(C2×D3)⋊C4—22no—
129C2×(C2×D3)⋊C4—22no—
130C2×(C2×D3)⋊C4—22no—
131C2×(C2×D3)⋊C4—22no—
132C2×(C2×D3)⋊C4—22no—
133C2×(C2×D3)⋊C4—22no—
134C2×(C2×D3)⋊C4—22no—
135C2×(C2×D3)⋊C4—22no—
136C2×(C2×D3)⋊C4—22no—
137C2×(C2×D3)⋊C4—22no—
138C2×(C2×D3)⋊C4—22no—
139C2×(C2×D3)⋊C4—22no—
140C2×(C2×D3)⋊C4—22no—
141C2×(C2×D3)⋊C4—22no—
142C2×(C2×D3)⋊C4—22no—
143C2×(C2×D3)⋊C4—22no—
144C2×(C2×D3)⋊C4—22no—
145C2×(C2×D3)⋊C4—22no—
146C2×(C2×D3)⋊C4C2×C414yes—
147C2×(C2×D3)⋊C4C2×C414yescomplemented
148C2×(C2×D3)⋊C4C2×C414yescomplemented
149C2×C4⋊Dic3—22no—
150C2×C4⋊Dic3—22no—
151C2×C4⋊Dic3—22no—
152C2×Dic3⋊C4—22no—
153C2×Dic3⋊C4—22no—
154C2×Dic3⋊C4—22no—
155C2×C4×Dic3—22no—
156C2×C4×Dic3—22no—
157C2×C4×Dic3—22no—
158C2×C4×Dic3—22no—
159C2×C4×Dic3—22no—
160C2×C4×Dic3—22no—
161C2×C4×Dic3—22no—
162C2×C4×Dic3—22no—
163C2×C4×Dic3D414yescomplemented
164C42×D3—232no—
165C3×#95—22no—
166C3×#95—22no—
167C3×#95—22no—
168C3×#95—22no—
169C3×#95—22no—
170C3×#95C2×C414yescomplemented
171C3⋊#95—22no—
172C3⋊#95—22no—
173C3⋊#95—22no—
174C3⋊#95—22no—
175C3⋊#95—22no—
176C3⋊#95—22no—
177C3⋊#95—22no—
178C3⋊#95—22no—
179C3⋊#95—22no—
180C3⋊#95C2×C414yescomplemented
181C23×D4—31no—
182C24×C4—31no—
183C24×C4—31no—
184C24×C4—31no—
185C22×C4⋊C4—31no—
186C22×C4⋊C4—31no—
187C22×C22⋊C4—31no—
188C22×C22⋊C4—31no—
189C22×C22⋊C4—31no—
190C22×C22⋊C4—31no—
191C22×C22⋊C4—31no—
192C22×C22⋊C4—31no—
193C22×C22⋊C4—31no—
194C22×C22⋊C4—31no—
195C22×C22⋊C4—31no—
196C22×C42—31no—
197C22×C42—31no—
198C22×C42—31no—
199C22×C42—64no—
200C22×C42—64no—
201C22×C42—64no—
202C22×C42C2×D311yescharacteristic
203#388—64no—
204#388—64no—
205#386—38no—
206#386—64no—
207#386—64no—
208#385—64no—
209C2×#95—31no—
210C2×#95—31no—
211C2×#95—31no—
212C2×#95—31no—
213C2×#95—31no—
214C2×#95—31no—
215C2×#95—31no—
216C2×#95—31no—
217C2×#95—31no—
218C2×#95—31no—
219C2×#95C2×D311yescharacteristic
220C2×#95C2×D311yescharacteristic
221C2×#95C2×D311yescharacteristic
222C2×#95C2×D311yescharacteristic
223C2×#95C2×D311yescharacteristic
224C2×#95C2×D311yescharacteristic
225C24×C3C2411yescharacteristic
226C23×D3—21no—
227C23×D3—21no—
228C23×D3—21no—
229C23×D3—21no—
230C23×D3—21no—
231C23×D3—21no—
232C23×D3—21no—
233C23×D3—21no—
234C23×D3—21no—
235C23×D3—21no—
236C23×D3—21no—
237C23×D3—21no—
238C23×D3—21no—
239C23×D3—21no—
240C23×D3—21no—
241C23×D3—21no—
242C23×D3—21no—
243C23×D3—21no—
244C23×D3—21no—
245C23×D3—21no—
246C23×D3—21no—
247C23×D3—21no—
248C23×D3C22×C412yes—
249C23×D3C22×C412yes—
250C23×D3C2×D412yes—
251C23×D3C2×D412yes—
252C23×D3#4112yes—
253C23×D3#4112yes—
254C23×D3#4112yes—
255C23×D3#4112yes—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—21no—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—21no—
273C22×C3×C4—21no—
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—21no—
280C22×C3×C4—21no—
281C22×C3×C4—21no—
282C22×C3×C4—21no—
283C22×C3×C4—21no—
284C22×C3×C4—21no—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4C22×C412yes—
295C22×C3×C4C22×C412yes—
296C22×C3×C4C22×C412yes—
297C22×C3×C4C2×D412yes—
298C22×C3×C4C2×D412yes—
299C22×C3×C4C2×D412yes—
300C22×C3×C4C2×D412yes—
301C22×C3×C4C2×D412yes—
302C22×C3×C4C2×D412yes—
303C22×C3×C4#4112yes—
304C22×C3×C4#4112yes—
305C22×Dic3—21no—
306C22×Dic3—21no—
307C22×Dic3—21no—
308C22×Dic3—21no—
309C22×Dic3—21no—
310C22×Dic3—21no—
311C22×Dic3—21no—
312C22×Dic3—21no—
313C22×Dic3—21no—
314C22×Dic3—21no—
315C22×Dic3—21no—
316C22×Dic3—21no—
317C22×Dic3—21no—
318C22×Dic3—21no—
319C22×Dic3—21no—
320C22×Dic3—21no—
321C22×Dic3—21no—
322C22×Dic3—21no—
323C22×Dic3—21no—
324C22×Dic3—21no—
325C22×Dic3—21no—
326C22×Dic3—21no—
327C22×Dic3—21no—
328C22×Dic3—21no—
329C22×Dic3—21no—
330C22×Dic3—21no—
331C22×Dic3—21no—
332C22×Dic3—21no—
333C22×Dic3—21no—
334C22×Dic3—21no—
335C22×Dic3—21no—
336C22×Dic3—21no—
337C22×Dic3C22×C412yes—
338C22×Dic3C22×C412yes—
339C22×Dic3C2×D412yes—
340C22×Dic3C2×D412yes—
341C22×Dic3C2×D412yes—
342C22×Dic3C2×D412yes—
343C22×Dic3#4112yes—
344C22×Dic3#4112yes—
345C22×Dic3#4112yes—
346C22×Dic3#4112yes—
347C2×D12—28no—
348C2×D12—28no—
349C2×D12—28no—
350C2×D12—44no—
351C2×D12—44no—
352C2×D12—44no—
353C2×D12—44no—
354C2×C4×D3—28no—
355C2×C4×D3—28no—
356C2×C4×D3—28no—
357C2×C4×D3—28no—
358C2×C4×D3—28no—
359C2×C4×D3—28no—
360C2×C4×D3—28no—
361C2×C4×D3—28no—
362C2×C4×D3—28no—
363C2×C4×D3—28no—
364C2×C4×D3—28no—
365C2×C4×D3—28no—
366C2×C4×D3—28no—
367C2×C4×D3—28no—
368C2×C4×D3—28no—
369C2×C4×D3—28no—
370C2×C4×D3—28no—
371C2×C4×D3—28no—
372C2×C4×D3—28no—
373C2×C4×D3—28no—
374C2×C4×D3—28no—
375C3×C42—28no—
376(C2×D3)⋊C4—28no—
377(C2×D3)⋊C4—28no—
378(C2×D3)⋊C4—28no—
379(C2×D3)⋊C4—44no—
380(C2×D3)⋊C4—44no—
381(C2×D3)⋊C4—44no—
382(C2×D3)⋊C4—44no—
383(C2×D3)⋊C4—44no—
384(C2×D3)⋊C4—44no—
385C4⋊Dic3—44no—
386Dic3⋊C4—44no—
387C4×Dic3—28no—
388C4×Dic3—28no—
389C4×Dic3—28no—
390C25—31no—
391C25—31no—
392C22×D4—34no—
393C22×D4—62no—
394C22×D4—62no—
395C22×D4—62no—
396C22×D4—62no—
397C22×D4—62no—
398C22×D4—62no—
399C23×C4—31no—
400C23×C4—31no—
401C23×C4—31no—
402C23×C4—31no—
403C23×C4—34no—
404C23×C4—34no—
405C23×C4—34no—
406C23×C4—31no—
407C23×C4—31no—
408C23×C4—62no—
409C23×C4—62no—
410C23×C4—62no—
411C23×C4—62no—
412C23×C4—62no—
413C23×C4—62no—
414C23×C4—62no—
415C23×C4—62no—
416C23×C4—62no—
417C23×C4—62no—
418C23×C4—62no—
419C23×C4—62no—
420C23×C4—62no—
421C23×C4—62no—
422C23×C4—62no—
423C23×C4—62no—
424C23×C4—62no—
425C23×C4—62no—
426C23×C4C22×D311yescharacteristic
427C23×C4C22×D311yescharacteristic
428C23×C4C22×D311yescharacteristic
429C23×C4C22×D311yescharacteristic
430C23×C4C22×D311yescharacteristic
431C23×C4C22×D311yescharacteristic
432C23×C4C22×D311yescharacteristic
433C2×C4⋊C4—62no—
434C2×C4⋊C4—62no—
435C2×C4⋊C4—62no—
436C2×C4⋊C4—62no—
437C2×C4⋊C4—62no—
438C2×C4⋊C4—62no—
439C2×C22⋊C4—34no—
440C2×C22⋊C4—34no—
441C2×C22⋊C4—34no—
442C2×C22⋊C4—62no—
443C2×C22⋊C4—62no—
444C2×C22⋊C4—62no—
445C2×C22⋊C4—62no—
446C2×C22⋊C4—62no—
447C2×C22⋊C4—62no—
448C2×C22⋊C4—62no—
449C2×C22⋊C4—62no—
450C2×C22⋊C4—62no—
451C2×C22⋊C4—62no—
452C2×C22⋊C4—62no—
453C2×C22⋊C4—62no—
454C2×C22⋊C4—62no—
455C2×C22⋊C4—62no—
456C2×C22⋊C4—62no—
457C2×C22⋊C4—62no—
458C2×C22⋊C4—62no—
459C2×C22⋊C4—62no—
460C2×C22⋊C4—62no—
461C2×C22⋊C4—62no—
462C2×C22⋊C4—62no—
463C2×C22⋊C4—62no—
464C2×C22⋊C4—62no—
465C2×C22⋊C4—62no—
466C2×C42—22no—
467C2×C42—22no—
468C2×C42—34no—
469C2×C42—632no—
470C2×C42—62no—
471C2×C42—62no—
472C2×C42—62no—
473C2×C42—62no—
474C2×C42—62no—
475C2×C42—62no—
476C2×C42—62no—
477C2×C42—62no—
478C2×C42D1214yescomplemented
479#95—22no—
480#95—22no—
481#95—22no—
482#95—22no—
483#95—22no—
484#95—34no—
485#95—62no—
486#95—62no—
487#95—62no—
488#95—62no—
489#95—62no—
490#95—62no—
491#95—62no—
492#95—62no—
493#95—62no—
494#95C4×D314yescomplemented
495C23×C3C23×C411yescharacteristic
496C23×C3C22×D411yescharacteristic
497C23×C3C22×D411yescharacteristic
498C23×C3C22×D411yescharacteristic
499C23×C3C22×D411yescharacteristic
500C23×C3C2×#4111yescharacteristic
501C23×C3C2×#4111yescharacteristic
502C23×C3C2×#4111yescharacteristic
503C23×C3C2×#4111yescharacteristic
504C23×C3C2×#4111yescharacteristic
505C23×C3C2×#4111yescharacteristic
506C23×C3C2×#4111yescharacteristic
507C23×C3C2×#4111yescharacteristic
508C23×C3C2×#4111yescharacteristic
509C23×C3C2×#4111yescharacteristic
510C22×D3—22no—
511C22×D3—22no—
512C22×D3—22no—
513C22×D3—22no—
514C22×D3—22no—
515C22×D3—22no—
516C22×D3—22no—
517C22×D3—22no—
518C22×D3—22no—
519C22×D3—22no—
520C22×D3—22no—
521C22×D3—22no—
522C22×D3—22no—
523C22×D3—22no—
524C22×D3—22no—
525C22×D3—22no—
526C22×D3—22no—
527C22×D3—22no—
528C22×D3—22no—
529C22×D3—22no—
530C22×D3—22no—
531C22×D3—22no—
532C22×D3—22no—
533C22×D3—22no—
534C22×D3—22no—
535C22×D3—22no—
536C22×D3—22no—
537C22×D3—22no—
538C22×D3—22no—
539C22×D3—22no—
540C22×D3—22no—
541C22×D3—22no—
542C22×D3—22no—
543C22×D3—22no—
544C22×D3—22no—
545C22×D3—41no—
546C22×D3—41no—
547C22×D3—41no—
548C22×D3—41no—
549C22×D3—41no—
550C22×D3—41no—
551C22×D3—41no—
552C22×D3—41no—
553C22×D3—41no—
554C22×D3—41no—
555C22×D3—41no—
556C22×D3—41no—
557C22×D3—41no—
558C22×D3—41no—
559C22×D3—41no—
560C22×D3—41no—
561C22×D3—41no—
562C22×D3—41no—
563C22×D3—41no—
564C22×D3—41no—
565C22×D3—41no—
566C22×D3—41no—
567C22×D3—41no—
568C22×D3—41no—
569C22×D3—41no—
570C22×D3—41no—
571C22×D3—41no—
572C22×D3—41no—
573C22×D3#11714yes—
574C22×D3C4×D414yes—
575C22×D3C4×D414yes—
576C22×D3#12114yes—
577C22×D3#12314yes—
578C22×D3#12414yes—
579C22×D3#12614yes—
580C2×C3×C4—22no—
581C2×C3×C4—22no—
582C2×C3×C4—22no—
583C2×C3×C4—22no—
584C2×C3×C4—22no—
585C2×C3×C4—22no—
586C2×C3×C4—22no—
587C2×C3×C4—22no—
588C2×C3×C4—22no—
589C2×C3×C4—22no—
590C2×C3×C4—22no—
591C2×C3×C4—22no—
592C2×C3×C4—22no—
593C2×C3×C4—22no—
594C2×C3×C4—22no—
595C2×C3×C4—22no—
596C2×C3×C4—22no—
597C2×C3×C4—22no—
598C2×C3×C4—22no—
599C2×C3×C4—22no—
600C2×C3×C4—22no—
601C2×C3×C4—22no—
602C2×C3×C4—22no—
603C2×C3×C4—22no—
604C2×C3×C4—41no—
605C2×C3×C4—41no—
606C2×C3×C4—41no—
607C2×C3×C4—41no—
608C2×C3×C4—41no—
609C2×C3×C4—41no—
610C2×C3×C4—41no—
611C2×C3×C4—41no—
612C2×C3×C4—41no—
613C2×C3×C4—41no—
614C2×C3×C4—41no—
615C2×C3×C4—41no—
616C2×C3×C4—41no—
617C2×C3×C4—41no—
618C2×C3×C4—41no—
619C2×C3×C4—41no—
620C2×C3×C4—41no—
621C2×C3×C4—41no—
622C2×C3×C4—41no—
623C2×C3×C4—41no—
624C2×C3×C4—41no—
625C2×C3×C4—41no—
626C2×C3×C4C4×D414yes—
627C2×C3×C4#12014yes—
628C2×C3×C4#12114yes—
629C2×Dic3—22no—
630C2×Dic3—22no—
631C2×Dic3—22no—
632C2×Dic3—22no—
633C2×Dic3—22no—
634C2×Dic3—22no—
635C2×Dic3—22no—
636C2×Dic3—22no—
637C2×Dic3—22no—
638C2×Dic3—22no—
639C2×Dic3—22no—
640C2×Dic3—22no—
641C2×Dic3—22no—
642C2×Dic3—22no—
643C2×Dic3—22no—
644C2×Dic3—22no—
645C2×Dic3—22no—
646C2×Dic3—22no—
647C2×Dic3—22no—
648C2×Dic3—22no—
649C2×Dic3—22no—
650C2×Dic3—41no—
651C2×Dic3—41no—
652C2×Dic3—41no—
653C2×Dic3—41no—
654C2×Dic3—41no—
655C2×Dic3—41no—
656C2×Dic3—41no—
657C2×Dic3—41no—
658C2×Dic3—41no—
659C2×Dic3—41no—
660C2×Dic3—41no—
661C2×Dic3—41no—
662C2×Dic3—41no—
663C2×Dic3—41no—
664C2×Dic3—41no—
665C2×Dic3—41no—
666C2×Dic3—41no—
667C2×Dic3—41no—
668C2×Dic3C4×D414yes—
669C2×Dic3#12114yes—
670C2×Dic3#12314yes—
671D12—416no—
672C4×D3—232no—
673C4×D3—232no—
674C4×D3—232no—
675C24—32no—
676C24—32no—
677C24—32no—
678C24—32no—
679C24—32no—
680C24—32no—
681C24—32no—
682C24—32no—
683C24—61no—
684C24—61no—
685C24—61no—
686C24—61no—
687C24—61no—
688C24—61no—
689C24—61no—
690C24—61no—
691C24—61no—
692C24—61no—
693C24—61no—
694C24—61no—
695C24—61no—
696C24—61no—
697C24—61no—
698C24—61no—
699C24—61no—
700C24—61no—
701C24—61no—
702C24—61no—
703C24—61no—
704C24—61no—
705C24C23×D311yescharacteristic
706C2×D4—68no—
707C2×D4—68no—
708C2×D4—68no—
709C2×D4—124no—
710C2×D4—124no—
711C2×D4—124no—
712C2×D4—124no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—32no—
752C22×C4—32no—
753C22×C4—32no—
754C22×C4—32no—
755C22×C4—32no—
756C22×C4—32no—
757C22×C4—32no—
758C22×C4—32no—
759C22×C4—32no—
760C22×C4—32no—
761C22×C4—68no—
762C22×C4—68no—
763C22×C4—68no—
764C22×C4—68no—
765C22×C4—68no—
766C22×C4—68no—
767C22×C4—68no—
768C22×C4—68no—
769C22×C4—68no—
770C22×C4—68no—
771C22×C4—68no—
772C22×C4—68no—
773C22×C4—68no—
774C22×C4—68no—
775C22×C4—68no—
776C22×C4—68no—
777C22×C4—68no—
778C22×C4—68no—
779C22×C4—61no—
780C22×C4—61no—
781C22×C4—61no—
782C22×C4—61no—
783C22×C4—61no—
784C22×C4—61no—
785C22×C4—61no—
786C22×C4—61no—
787C22×C4—61no—
788C22×C4—61no—
789C22×C4—61no—
790C22×C4—61no—
791C22×C4—68no—
792C22×C4—68no—
793C22×C4—68no—
794C22×C4—61no—
795C22×C4—61no—
796C22×C4—61no—
797C22×C4—61no—
798C22×C4—61no—
799C22×C4—61no—
800C22×C4—61no—
801C22×C4—61no—
802C22×C4—61no—
803C22×C4—61no—
804C22×C4—61no—
805C22×C4—61no—
806C22×C4—61no—
807C22×C4—61no—
808C22×C4—61no—
809C22×C4—61no—
810C22×C4—61no—
811C22×C4—61no—
812C22×C4—61no—
813C22×C4—61no—
814C22×C4C2×C4×D312yes—
815C22×C4C2×C4×D312yes—
816C22×C4C2×C4×D312yes—
817C22×C4C2×D1212yes—
818C22×C4C2×D1212yes—
819C22×C4C2×D1212yes—
820C22×C4#23512yes—
821C22×C4D3×D412yes—
822C22×C4D3×D412yes—
823C22×C4D3×D412yes—
824C22×C4#23912yes—
825C4⋊C4—124no—
826C4⋊C4—124no—
827C22⋊C4—68no—
828C22⋊C4—68no—
829C22⋊C4—68no—
830C22⋊C4—124no—
831C22⋊C4—124no—
832C22⋊C4—124no—
833C22⋊C4—124no—
834C22⋊C4—124no—
835C22⋊C4—124no—
836C42—28no—
837C42—68no—
838C42—68no—
839C42—68no—
840C22×C3C2×#11711yescharacteristic
841C22×C3C2×C4×D411yescharacteristic
842C22×C3C2×C4×D411yescharacteristic
843C22×C3C2×C4×D411yescharacteristic
844C22×C3C2×C4×D411yescharacteristic
845C22×C3C4×#4111yescharacteristic
846C22×C3C4×#4111yescharacteristic
847C22×C3C2×#12011yescharacteristic
848C22×C3C2×#12111yescharacteristic
849C22×C3C2×#12111yescharacteristic
850C22×C3C2×#12111yescharacteristic
851C22×C3C2×#12311yescharacteristic
852C22×C3C2×#12311yescharacteristic
853C22×C3#52511yescharacteristic
854C22×C3#52511yescharacteristic
855C22×C3#52511yescharacteristic
856C22×C3#52511yescharacteristic
857C22×C3#52511yescharacteristic
858C22×C3#52511yescharacteristic
859C22×C3#52511yescharacteristic
860C22×C3#52511yescharacteristic
861C22×C3#52511yescharacteristic
862C22×C3#52511yescharacteristic
863C22×C3C2×#12411yescharacteristic
864C22×C3C2×#12611yescharacteristic
865C22×C3#52911yescharacteristic
866C22×C3#52911yescharacteristic
867C22×C3#52911yescharacteristic
868C22×C3#52911yescharacteristic
869C22×C3#52911yescharacteristic
870C22×C3#52911yescharacteristic
871C22×C3#52911yescharacteristic
872C22×C3#52911yescharacteristic
873C22×C3#53211yescharacteristic
874C22×C3#53211yescharacteristic
875C2×D3—24no—
876C2×D3—24no—
877C2×D3—24no—
878C2×D3—24no—
879C2×D3—24no—
880C2×D3—24no—
881C2×D3—24no—
882C2×D3—24no—
883C2×D3—24no—
884C2×D3—24no—
885C2×D3—24no—
886C2×D3—24no—
887C2×D3—24no—
888C2×D3—24no—
889C2×D3—42no—
890C2×D3—42no—
891C2×D3—42no—
892C2×D3—42no—
893C2×D3—42no—
894C2×D3—42no—
895C2×D3—42no—
896C2×D3—81no—
897C2×D3—81no—
898C2×D3—81no—
899C2×D3—81no—
900C2×D3—81no—
901C2×D3—81no—
902C2×D3—81no—
903C2×D3—81no—
904C2×D3#38818yescomplemented
905C3×C4—24no—
906C3×C4—24no—
907C3×C4—24no—
908C3×C4—42no—
909C3×C4—42no—
910C3×C4—81no—
911C3×C4—81no—
912Dic3—24no—
913Dic3—24no—
914Dic3—24no—
915Dic3—42no—
916Dic3—81no—
917Dic3—81no—
918C23—34no—
919C23—34no—
920C23—34no—
921C23—34no—
922C23—34no—
923C23—34no—
924C23—34no—
925C23—62no—
926C23—62no—
927C23—62no—
928C23—62no—
929C23—62no—
930C23—62no—
931C23—62no—
932C23—62no—
933C23—62no—
934C23—62no—
935C23—62no—
936C23—62no—
937C23—62no—
938C23—62no—
939C23—62no—
940C23—62no—
941C23—62no—
942C23—62no—
943C23—62no—
944C23—62no—
945C23—62no—
946C23—62no—
947C23—62no—
948C23—62no—
949C23—62no—
950C23—62no—
951C23—62no—
952C23—62no—
953C23—62no—
954C23—62no—
955C23—62no—
956C23—62no—
957C23—62no—
958C23—62no—
959C23—62no—
960C23—121no—
961C23—121no—
962C23—121no—
963C23—121no—
964C23—121no—
965C23—121no—
966C23—121no—
967C23—121no—
968C23—121no—
969C23—121no—
970C23—121no—
971C23—121no—
972C23—121no—
973C23—121no—
974C23—121no—
975C23—121no—
976C23—121no—
977C23—121no—
978C23—121no—
979C23—121no—
980C23—121no—
981C23—121no—
982C23—121no—
983C23—121no—
984C23—121no—
985C23—121no—
986C23—121no—
987C23—121no—
988C23C22×C4×D311yescharacteristic
989C23C22×D1211yescharacteristic
990C23C2×#23511yescharacteristic
991C23C2×D3×D411yescharacteristic
992C23C2×D3×D411yescharacteristic
993C23C2×D3×D411yescharacteristic
994C23C2×#23911yescharacteristic
995C23D3×#4111yescharacteristic
996C23D3×#4111yescharacteristic
997C23D3×#4111yescharacteristic
998C23D3×#4111yescharacteristic
999C23D3×#4111yescharacteristic
1000C23D3×#4111yescharacteristic
1001C23D3×#4111yescharacteristic
1002C23D3×#4111yescharacteristic
1003D4—1216no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—34no—
1029C2×C4—34no—
1030C2×C4—34no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—632no—
1054C2×C4—632no—
1055C2×C4—632no—
1056C2×C4—62no—
1057C2×C4—62no—
1058C2×C4—62no—
1059C2×C4—62no—
1060C2×C4—62no—
1061C2×C4—62no—
1062C2×C4—62no—
1063C2×C4—62no—
1064C2×C4—62no—
1065C2×C4—62no—
1066C2×C4—62no—
1067C2×C4—62no—
1068C2×C4—62no—
1069C2×C4—62no—
1070C2×C4—62no—
1071C2×C4—62no—
1072C2×C4—62no—
1073C2×C4—62no—
1074C2×C4—62no—
1075C2×C4—62no—
1076C2×C4—62no—
1077C2×C4—121no—
1078C2×C4—121no—
1079C2×C4—121no—
1080C2×C4—121no—
1081C2×C4—121no—
1082C2×C4—121no—
1083C2×C4—121no—
1084C2×C4—121no—
1085C2×C4—121no—
1086C2×C4—121no—
1087C2×C4—121no—
1088C2×C4—121no—
1089C2×C4—121no—
1090C2×C4—121no—
1091C2×C4—121no—
1092C2×C4—121no—
1093C2×C4—121no—
1094C2×C4—121no—
1095C2×C4C4×D1214yes—
1096C2×C4#88214yes—
1097C2×C4#89514yes—
1098C2×C3C2×#38811yescharacteristic
1099C2×C3#229011yescharacteristic
1100C2×C3#229011yescharacteristic
1101C2×C3C4×#12011yescharacteristic
1102C2×C3C4×#12111yescharacteristic
1103C2×C3C4×#12111yescharacteristic
1104C2×C3C4×#12311yescharacteristic
1105C2×C3#284711yescharacteristic
1106C2×C3#284911yescharacteristic
1107C2×C3#285011yescharacteristic
1108C2×C3#285011yescharacteristic
1109C2×C3#285211yescharacteristic
1110C2×C3#285211yescharacteristic
1111C2×C3#285311yescharacteristic
1112C2×C3#285411yescharacteristic
1113D3—28no—
1114D3—82no—
1115C22—38no—
1116C22—64no—
1117C22—64no—
1118C22—64no—
1119C22—64no—
1120C22—64no—
1121C22—64no—
1122C22—64no—
1123C22—64no—
1124C22—64no—
1125C22—64no—
1126C22—64no—
1127C22—64no—
1128C22—64no—
1129C22—64no—
1130C22—122no—
1131C22—122no—
1132C22—122no—
1133C22—122no—
1134C22—122no—
1135C22—122no—
1136C22—122no—
1137C22—241no—
1138C22—241no—
1139C22—241no—
1140C22—241no—
1141C22—241no—
1142C22—241no—
1143C22—241no—
1144C22—241no—
1145C22C2×C4×D1211yescharacteristic
1146C22C2×#88211yescharacteristic
1147C22C2×#89511yescharacteristic
1148C22D3×#11711yescharacteristic
1149C22#552211yescharacteristic
1150C22#552411yescharacteristic
1151C22#552411yescharacteristic
1152C22#552411yescharacteristic
1153C22#552411yescharacteristic
1154C22#552811yescharacteristic
1155C22#552811yescharacteristic
1156C22C4×D3×D411yescharacteristic
1157C22C4×D3×D411yescharacteristic
1158C22C4×D3×D411yescharacteristic
1159C22#554711yescharacteristic
1160C22#554711yescharacteristic
1161C22#554811yescharacteristic
1162C22C4×#23911yescharacteristic
1163C22#558011yescharacteristic
1164C22D3×#12111yescharacteristic
1165C22D3×#12111yescharacteristic
1166C22#562711yescharacteristic
1167C22#562711yescharacteristic
1168C22D3×#12311yescharacteristic
1169C22D3×#12311yescharacteristic
1170C22#565611yescharacteristic
1171C22#565611yescharacteristic
1172C22#566811yescharacteristic
1173C22D3×#12411yescharacteristic
1174C22#569111yescharacteristic
1175C22#569111yescharacteristic
1176C22D3×#12611yescharacteristic
1177C22#570611yescharacteristic
1178C22#570611yescharacteristic
1179C22#570611yescharacteristic
1180C4—24no—
1181C4—24no—
1182C4—24no—
1183C4—42no—
1184C4—42no—
1185C4—64no—
1186C4—64no—
1187C4—64no—
1188C4—81no—
1189C4—81no—
1190C4—122no—
1191C4—241no—
1192C4—241no—
1193C3#1469611yescharacteristic, complemented, Sylow
1194C2—68no—
1195C2—242no—
1196C2#7341411yescharacteristic
1197C2C4×#88211yescharacteristic
1198C2C4×#89511yescharacteristic
1199C2#7404811yescharacteristic
1200C2#7414611yescharacteristic
1201C2#7425611yescharacteristic
1202C2#7431711yescharacteristic
1203C2#7493711yescharacteristic
1204C2#7494011yescharacteristic
1205C2#7544611yescharacteristic
1206C2#7544711yescharacteristic
1207C2#7545211yescharacteristic
1208C2D3×#38811yescharacteristic
1209C2#7595711yescharacteristic
1210C2#7596011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC3×#1434C2
socle, cosocleC24×C3C24
prime radicalC23×D12C22
hypercenter#1434D3
hypocenterC3#14696
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
1. C22×C42×D3C2semidirect
2. C2×#4940C2semidirect
6. C2×#4668C2semidirect
7. C2×#4670C2semidirect
8. C3×#1434C2semidirect
9. (C2×D3)⋊#95C2semidirect
10. (C2×D3)⋊#95C2semidirect
11. #69408C2semidirect
12. #69408C2semidirect
13. #69407C2semidirect
14. #69405C2semidirect
15. #69402C2semidirect
60. #4665C4semidirect
73. #1434D3semidirect
121. C2×C3×C42D4semidirect
147. C2×(C2×D3)⋊C4C2×C4semidirect
148. C2×(C2×D3)⋊C4C2×C4semidirect
163. C2×C4×Dic3D4semidirect
170. C3×#95C2×C4semidirect
180. C3⋊#95C2×C4semidirect
478. C2×C42D12semidirect
494. #95C4×D3semidirect
904. C2×D3#388semidirect
1193. C3#14696semidirect

Maximal subgroups

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

subgroupindex
C22×C42×D32
C2×#49402
C2×#46652
C2×#46682
C2×#46702
C3×#14342
(C2×D3)⋊#952
#694082
#694072
#694052
#694022
#146963