Finite Group Databasebeta

← #10732509

Subgroups — #10732509

Order 768.

2878 conjugacy classes of subgroups.

The subgroup lattice has 1382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#896C211yesmaximal, characteristic, complemented
2C22×#884C211yesmaximal, characteristic
3C22×#885C211yesmaximal, characteristic, complemented
4C2×#4957C211yesmaximal, characteristic, complemented
5C2×#4646C211yesmaximal, characteristic, complemented
6C2×#4666C211yesmaximal, characteristic, complemented
7C3×#1439C211yesmaximal, characteristic, complemented
8#71570C211yesmaximal, characteristic, complemented
9#71550C211yesmaximal, characteristic, complemented
10#71550C211yesmaximal, characteristic, complemented
11#71547C211yesmaximal, characteristic, complemented
12#69428C211yesmaximal, characteristic, complemented
13#69426C211yesmaximal, characteristic, complemented
14#69426C211yesmaximal, characteristic, complemented
15Dic3⋊#95C211yesmaximal, characteristic, complemented
16#15215—31nomaximal, Sylow
17C23×#67C2211yescharacteristic
18C23×#67C2211yescharacteristic
19C23×D12C2211yescharacteristic
20C23×C4×D3C2211yescharacteristic
21C23×Dic6C2211yescharacteristic
22C22×C3×C4⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×C3×C22⋊C4C2211yescharacteristic
26C22×#217C2211yescharacteristic
27C22×#217C2211yescharacteristic
28C22×(C2×D3)⋊C4C2211yescharacteristic
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×(C2×D3)⋊C4C2211yescharacteristic
31C22×(C2×D3)⋊C4C2211yescharacteristic
32C22×(C2×D3)⋊C4C2211yescharacteristic
33C22×(C2×D3)⋊C4C2211yescharacteristic
34C22×(C2×D3)⋊C4C2211yescharacteristic
35C22×(C2×D3)⋊C4C2211yescharacteristic
36C22×(C2×D3)⋊C4C2211yescharacteristic
37C22×Dic3⋊C4C2211yescharacteristic
38C22×Dic3⋊C4C2211yescharacteristic
39C22×Dic3⋊C4C2211yescharacteristic
40C22×C4×Dic3C2211yescharacteristic
41C22×C4×Dic3C2211yescharacteristic
42C2×#896—24no—
43C2×#896—24no—
44C2×#896—24no—
45C2×#885—24no—
46C2×#885—24no—
47C2×#885—24no—
48C2×#884—24no—
49C2×#884—24no—
50C2×#884—24no—
51C2×C3×#95C2211yescharacteristic
52C2×C3×#95C2211yescharacteristic
53C2×C3×#95C2211yescharacteristic
54C2×C3⋊#95C2211yescharacteristic
55C2×C3⋊#95C2211yescharacteristic
56C2×C3⋊#95C2211yescharacteristic
57C2×C3⋊#95C2211yescharacteristic
58C2×C3⋊#95C2211yescharacteristic
59C2×C3⋊#95C2211yescharacteristic
60C2×C3⋊#95C2211yescharacteristic
61#4957—24no—
62#4666—24no—
63#4646—24no—
64C22×#124—31no—
65C22×C22⋊Q8—31no—
66C22×#121—31no—
67C2×#391—31no—
68C2×#390—31no—
69C2×C4×C22⋊C4—31no—
70#1439—31no—
71#1439—31no—
72#1439—31no—
73#1439D311yescharacteristic, complemented
74#1438—31no—
75#1438—31no—
76#1438—31no—
77#1438—31no—
78C4⋊#95—31no—
79C25×C3C2311yescharacteristic
80C24×D3C2311yescharacteristic
81C24×D3C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C23×C3×C4C2311yescharacteristic
87C23×C3×C4C2311yescharacteristic
88C22×#67—22no—
89C22×#67—22no—
90C22×#67—22no—
91C22×#67—22no—
92C22×#67—22no—
93C22×#67—22no—
94C22×#67—22no—
95C22×#67—22no—
96C22×#67—22no—
97C22×#67—22no—
98C22×#67—22no—
99C22×#67—41no—
100C22×#67—41no—
101C22×#67D414yes—
102C23×Dic3C2311yescharacteristic
103C23×Dic3C2311yescharacteristic
104C23×Dic3C2311yescharacteristic
105C23×Dic3C2311yescharacteristic
106C23×Dic3C2311yescharacteristic
107C23×Dic3C2311yescharacteristic
108C22×D12—22no—
109C22×D12—22no—
110C22×D12—22no—
111C22×D12—22no—
112C22×D12—22no—
113C22×D12—41no—
114C22×D12—41no—
115C22×C4×D3—22no—
116C22×C4×D3—22no—
117C22×C4×D3—22no—
118C22×C4×D3—22no—
119C22×C4×D3—22no—
120C22×C4×D3—22no—
121C22×C4×D3D414yes—
122C22×Dic6—22no—
123C22×Dic6—22no—
124C22×Dic6—22no—
125C22×Dic6—22no—
126C22×Dic6—22no—
127C22×Dic6—22no—
128C22×Dic6D414yescomplemented
129C2×C3×C4⋊C4—22no—
130C2×C3×C4⋊C4—22no—
131C2×C3×C4⋊C4—22no—
132C2×C3×C22⋊C4—22no—
133C2×C3×C22⋊C4—22no—
134C2×C3×C22⋊C4—22no—
135C2×C3×C22⋊C4—22no—
136C2×C3×C22⋊C4—22no—
137C2×C3×C22⋊C4—22no—
138C2×C3×C22⋊C4—22no—
139C2×C3×C22⋊C4—22no—
140C2×C3×C22⋊C4—41no—
141C2×#217—22no—
142C2×#217—22no—
143C2×#217—22no—
144C2×#217—22no—
145C2×#217—22no—
146C2×#217—41no—
147C2×(C2×D3)⋊C4—22no—
148C2×(C2×D3)⋊C4—22no—
149C2×(C2×D3)⋊C4—22no—
150C2×(C2×D3)⋊C4—22no—
151C2×(C2×D3)⋊C4—22no—
152C2×(C2×D3)⋊C4—22no—
153C2×(C2×D3)⋊C4—22no—
154C2×(C2×D3)⋊C4—22no—
155C2×(C2×D3)⋊C4—22no—
156C2×(C2×D3)⋊C4—22no—
157C2×(C2×D3)⋊C4—22no—
158C2×(C2×D3)⋊C4—22no—
159C2×(C2×D3)⋊C4—22no—
160C2×(C2×D3)⋊C4—22no—
161C2×(C2×D3)⋊C4—22no—
162C2×(C2×D3)⋊C4—22no—
163C2×(C2×D3)⋊C4—22no—
164C2×(C2×D3)⋊C4—22no—
165C2×(C2×D3)⋊C4—22no—
166C2×(C2×D3)⋊C4—22no—
167C2×(C2×D3)⋊C4—22no—
168C2×(C2×D3)⋊C4—22no—
169C2×(C2×D3)⋊C4—22no—
170C2×(C2×D3)⋊C4—22no—
171C2×(C2×D3)⋊C4—22no—
172C2×(C2×D3)⋊C4—41no—
173C2×(C2×D3)⋊C4—41no—
174C2×Dic3⋊C4—22no—
175C2×Dic3⋊C4—22no—
176C2×Dic3⋊C4—22no—
177C2×Dic3⋊C4—22no—
178C2×Dic3⋊C4—22no—
179C2×Dic3⋊C4—22no—
180C2×Dic3⋊C4—22no—
181C2×Dic3⋊C4D414yes—
182C2×Dic3⋊C4D414yescomplemented
183C2×C4×Dic3—22no—
184C2×C4×Dic3—22no—
185C2×C4×Dic3—22no—
186C2×C4×Dic3—22no—
187C2×C4×Dic3—22no—
188C2×C4×Dic3D414yescomplemented
189#896—232no—
190#885—232no—
191#884—232no—
192C3×#95—22no—
193C3×#95—22no—
194C3×#95—41no—
195C3⋊#95—22no—
196C3⋊#95—22no—
197C3⋊#95—22no—
198C3⋊#95—22no—
199C3⋊#95—41no—
200C3⋊#95—41no—
201C3⋊#95—41no—
202C23×Q8—31no—
203C23×D4—31no—
204C23×D4—31no—
205C23×D4—31no—
206C24×C4—31no—
207C2×#124—64no—
208C2×#124—64no—
209C2×#124—64no—
210C2×C22⋊Q8—64no—
211C2×C22⋊Q8—64no—
212C2×C22⋊Q8—64no—
213C2×#121—64no—
214C2×#121—64no—
215C2×#121—64no—
216C22×C4⋊C4—31no—
217C22×C4⋊C4—31no—
218C22×C4⋊C4—31no—
219C22×C4⋊C4C2×D311yescharacteristic
220C22×C22⋊C4—31no—
221C22×C22⋊C4—31no—
222C22×C22⋊C4—31no—
223C22×C22⋊C4—31no—
224C22×C22⋊C4—31no—
225C22×C22⋊C4—31no—
226C22×C22⋊C4—31no—
227C22×C22⋊C4—31no—
228C22×C22⋊C4—31no—
229C22×C22⋊C4—31no—
230C22×C22⋊C4—31no—
231C22×C22⋊C4C2×D311yescharacteristic
232C22×C22⋊C4C2×D311yescharacteristic
233C22×C22⋊C4C2×D311yescharacteristic
234C22×C42—31no—
235C22×C42—31no—
236#391—64no—
237#390—64no—
238C4×C22⋊C4—64no—
239C2×#95—31no—
240C2×#95—31no—
241C2×#95—31no—
242C2×#95—31no—
243C2×#95—31no—
244C2×#95—31no—
245C2×#95—31no—
246C2×#95C2×D311yescharacteristic
247C2×#95C2×D311yescharacteristic
248C2×#95C2×D311yescharacteristic
249C24×C3—21no—
250C24×C3—21no—
251C24×C3—21no—
252C24×C3—21no—
253C24×C3—21no—
254C24×C3—21no—
255C24×C3—21no—
256C24×C3—21no—
257C24×C3—21no—
258C24×C3—21no—
259C24×C3—21no—
260C24×C3—21no—
261C24×C3—21no—
262C24×C3—21no—
263C24×C3C2×D412yes—
264C24×C3C2411yescharacteristic
265C23×D3—21no—
266C23×D3—21no—
267C23×D3—21no—
268C23×D3—21no—
269C23×D3—21no—
270C23×D3—21no—
271C23×D3—21no—
272C23×D3—21no—
273C23×D3—21no—
274C23×D3—21no—
275C23×D3—21no—
276C23×D3—21no—
277C23×D3—21no—
278C23×D3—21no—
279C23×D3—21no—
280C23×D3—21no—
281C23×D3—21no—
282C23×D3—21no—
283C23×D3—21no—
284C23×D3—21no—
285C23×D3—21no—
286C23×D3—21no—
287C23×D3—21no—
288C23×D3—21no—
289C23×D3—21no—
290C23×D3—21no—
291C23×D3C2×D412yes—
292C23×D3C2×D412yes—
293C23×D3#4112yes—
294C23×D3#4112yes—
295C22×C3×C4—21no—
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4—21no—
299C22×C3×C4—21no—
300C22×C3×C4—21no—
301C22×C3×C4—21no—
302C22×C3×C4—21no—
303C22×C3×C4—21no—
304C22×C3×C4—21no—
305C22×C3×C4—21no—
306C22×C3×C4—21no—
307C22×C3×C4—21no—
308C22×C3×C4—21no—
309C22×C3×C4—21no—
310C22×C3×C4—21no—
311C22×C3×C4—21no—
312C22×C3×C4—21no—
313C22×C3×C4—21no—
314C22×C3×C4—21no—
315C22×C3×C4—21no—
316C22×C3×C4—21no—
317C22×C3×C4—21no—
318C22×C3×C4—21no—
319C22×C3×C4—21no—
320C22×C3×C4—21no—
321C22×C3×C4—21no—
322C22×C3×C4—21no—
323C22×C3×C4—21no—
324C22×C3×C4—21no—
325C22×C3×C4—21no—
326C22×C3×C4—21no—
327C22×C3×C4—21no—
328C22×C3×C4—21no—
329C22×C3×C4—21no—
330C22×C3×C4—21no—
331C22×C3×C4C2×D412yes—
332C22×C3×C4C2×D412yes—
333C22×C3×C4C2×D412yes—
334C22×C3×C4C2×D412yes—
335C22×C3×C4C2×D412yes—
336C22×C3×C4#4112yes—
337C2×#67—28no—
338C2×#67—28no—
339C2×#67—28no—
340C2×#67—28no—
341C2×#67—44no—
342C2×#67—44no—
343C2×#67—44no—
344C2×#67—44no—
345C2×#67—44no—
346C2×#67—44no—
347C2×#67—44no—
348C2×#67—44no—
349C2×#67—44no—
350C2×#67—44no—
351C22×Dic3—21no—
352C22×Dic3—21no—
353C22×Dic3—21no—
354C22×Dic3—21no—
355C22×Dic3—21no—
356C22×Dic3—21no—
357C22×Dic3—21no—
358C22×Dic3—21no—
359C22×Dic3—21no—
360C22×Dic3—21no—
361C22×Dic3—21no—
362C22×Dic3—21no—
363C22×Dic3—21no—
364C22×Dic3—21no—
365C22×Dic3—21no—
366C22×Dic3—21no—
367C22×Dic3—21no—
368C22×Dic3—21no—
369C22×Dic3—21no—
370C22×Dic3—21no—
371C22×Dic3—21no—
372C22×Dic3—21no—
373C22×Dic3—21no—
374C22×Dic3—21no—
375C22×Dic3—21no—
376C22×Dic3—21no—
377C22×Dic3—21no—
378C22×Dic3—21no—
379C22×Dic3—21no—
380C22×Dic3—21no—
381C22×Dic3C2×D412yes—
382C22×Dic3C2×D412yes—
383C22×Dic3C2×D412yes—
384C22×Dic3C2×D412yes—
385C22×Dic3C2×D412yes—
386C22×Dic3C2×D412yes—
387C22×Dic3C2×D412yes—
388C22×Dic3C2×D412yes—
389C22×Dic3C2×D412yes—
390C22×Dic3C2×D412yes—
391C22×Dic3#4112yes—
392C22×Dic3#4112yes—
393C2×D12—28no—
394C2×D12—44no—
395C2×D12—44no—
396C2×D12—44no—
397C2×D12—44no—
398C2×D12—44no—
399C2×D12—44no—
400C2×C4×D3—28no—
401C2×C4×D3—28no—
402C2×C4×D3—28no—
403C2×C4×D3—44no—
404C2×C4×D3—44no—
405C2×C4×D3—44no—
406C2×C4×D3—44no—
407C2×Dic6—28no—
408C2×Dic6—28no—
409C2×Dic6—28no—
410C2×Dic6—44no—
411C2×Dic6—44no—
412C2×Dic6—44no—
413C2×Dic6—44no—
414C3×C4⋊C4—28no—
415C3×C22⋊C4—28no—
416C3×C22⋊C4—28no—
417C3×C22⋊C4—44no—
418#217—28no—
419#217—44no—
420(C2×D3)⋊C4—28no—
421(C2×D3)⋊C4—28no—
422(C2×D3)⋊C4—28no—
423(C2×D3)⋊C4—28no—
424(C2×D3)⋊C4—28no—
425(C2×D3)⋊C4—28no—
426(C2×D3)⋊C4—28no—
427(C2×D3)⋊C4—44no—
428(C2×D3)⋊C4—44no—
429Dic3⋊C4—28no—
430Dic3⋊C4—28no—
431Dic3⋊C4—28no—
432C4×Dic3—28no—
433C4×Dic3—44no—
434C25—31no—
435C25—31no—
436C25C22×D311yescharacteristic
437C22×Q8—34no—
438C22×Q8—62no—
439C22×Q8—62no—
440C22×Q8—62no—
441C22×Q8—62no—
442C22×Q8—62no—
443C22×Q8—62no—
444C22×D4—34no—
445C22×D4—62no—
446C22×D4—62no—
447C22×D4—62no—
448C22×D4—62no—
449C22×D4—62no—
450C22×D4—62no—
451C22×D4—62no—
452C22×D4—62no—
453C22×D4—62no—
454C22×D4—62no—
455C22×D4—62no—
456C22×D4—62no—
457C22×D4—62no—
458C22×D4—62no—
459C22×D4—62no—
460C22×D4—62no—
461C22×D4—121no—
462C22×D4—121no—
463C22×D4—121no—
464C22×D4—121no—
465C23×C4—31no—
466C23×C4—31no—
467C23×C4—31no—
468C23×C4—31no—
469C23×C4—31no—
470C23×C4—31no—
471C23×C4—34no—
472C23×C4—62no—
473C23×C4—62no—
474C23×C4—62no—
475C23×C4—62no—
476C23×C4—62no—
477C23×C4—62no—
478C23×C4C22×D311yescharacteristic
479C23×C4C22×D311yescharacteristic
480C23×C4C22×D311yescharacteristic
481C23×C4C22×D311yescharacteristic
482C23×C4C22×D311yescharacteristic
483C23×C4C22×D311yescharacteristic
484#124—632no—
485C22⋊Q8—632no—
486#121—632no—
487C2×C4⋊C4—22no—
488C2×C4⋊C4—22no—
489C2×C4⋊C4—22no—
490C2×C4⋊C4—34no—
491C2×C4⋊C4—34no—
492C2×C4⋊C4—62no—
493C2×C4⋊C4—62no—
494C2×C4⋊C4—62no—
495C2×C4⋊C4—62no—
496C2×C4⋊C4—62no—
497C2×C4⋊C4—62no—
498C2×C4⋊C4—62no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—41no—
508C2×C22⋊C4—62no—
509C2×C22⋊C4—62no—
510C2×C22⋊C4—62no—
511C2×C22⋊C4—62no—
512C2×C22⋊C4—62no—
513C2×C22⋊C4—62no—
514C2×C22⋊C4—62no—
515C2×C22⋊C4—62no—
516C2×C22⋊C4—62no—
517C2×C22⋊C4—62no—
518C2×C22⋊C4—62no—
519C2×C22⋊C4—62no—
520C2×C22⋊C4—62no—
521C2×C22⋊C4—62no—
522C2×C22⋊C4—62no—
523C2×C22⋊C4—62no—
524C2×C22⋊C4—62no—
525C2×C22⋊C4—62no—
526C2×C22⋊C4—62no—
527C2×C22⋊C4—62no—
528C2×C22⋊C4—62no—
529C2×C22⋊C4—62no—
530C2×C22⋊C4—62no—
531C2×C22⋊C4—62no—
532C2×C22⋊C4—62no—
533C2×C22⋊C4—62no—
534C2×C22⋊C4—62no—
535C2×C22⋊C4—62no—
536C2×C22⋊C4—62no—
537C2×C22⋊C4—62no—
538C2×C22⋊C4—121no—
539C2×C22⋊C4—121no—
540C2×C22⋊C4—121no—
541C2×C42—34no—
542C2×C42—62no—
543C2×C42—62no—
544C2×C42—62no—
545C2×C42—62no—
546C2×C42—62no—
547#95—22no—
548#95—22no—
549#95—41no—
550#95—62no—
551#95—62no—
552#95—62no—
553#95—62no—
554#95—121no—
555#95—121no—
556#95—121no—
557C23×C3—22no—
558C23×C3—22no—
559C23×C3—22no—
560C23×C3—22no—
561C23×C3—22no—
562C23×C3—22no—
563C23×C3—22no—
564C23×C3—41no—
565C23×C3—41no—
566C23×C3—41no—
567C23×C3—41no—
568C23×C3—41no—
569C23×C3—41no—
570C23×C3—41no—
571C23×C3—41no—
572C23×C3—41no—
573C23×C3—41no—
574C23×C3—41no—
575C23×C3—41no—
576C23×C3—41no—
577C23×C3—41no—
578C23×C3—41no—
579C23×C3—41no—
580C23×C3—41no—
581C23×C3—41no—
582C23×C3—41no—
583C23×C3—41no—
584C23×C3—41no—
585C23×C3—41no—
586C23×C3—41no—
587C23×C3—41no—
588C23×C3—41no—
589C23×C3—41no—
590C23×C3—41no—
591C23×C3—41no—
592C23×C3C22×D411yescharacteristic
593C23×C3C22×D411yescharacteristic
594C23×C3C22×D411yescharacteristic
595C23×C3C22×D411yescharacteristic
596C23×C3C22×D411yescharacteristic
597C23×C3C22×D411yescharacteristic
598C23×C3C2×#4111yescharacteristic
599C23×C3C2×#4111yescharacteristic
600C23×C3C2×#4111yescharacteristic
601C23×C3C2×#4111yescharacteristic
602C23×C3C2×#4111yescharacteristic
603C23×C3H(5,𝔽2)11yescharacteristic
604C23×C3H(5,𝔽2)11yescharacteristic
605C23×C32−1+411yescharacteristic
606C23×C32−1+411yescharacteristic
607C22×D3—22no—
608C22×D3—22no—
609C22×D3—22no—
610C22×D3—22no—
611C22×D3—22no—
612C22×D3—22no—
613C22×D3—22no—
614C22×D3—22no—
615C22×D3—22no—
616C22×D3—22no—
617C22×D3—22no—
618C22×D3—22no—
619C22×D3—22no—
620C22×D3—22no—
621C22×D3—22no—
622C22×D3—22no—
623C22×D3—22no—
624C22×D3—22no—
625C22×D3—22no—
626C22×D3—22no—
627C22×D3—22no—
628C22×D3—22no—
629C22×D3—22no—
630C22×D3—22no—
631C22×D3—22no—
632C22×D3—41no—
633C22×D3—41no—
634C22×D3—41no—
635C22×D3—41no—
636C22×D3—41no—
637C22×D3—41no—
638C22×D3—41no—
639C22×D3—41no—
640C22×D3—41no—
641C22×D3—41no—
642C22×D3—41no—
643C22×D3—41no—
644C22×D3—41no—
645C22×D3—41no—
646C22×D3—41no—
647C22×D3—41no—
648C22×D3—41no—
649C22×D3—41no—
650C22×D3—41no—
651C22×D3—41no—
652C22×D3—41no—
653C22×D3—41no—
654C22×D3—41no—
655C22×D3—41no—
656C22×D3—41no—
657C22×D3—41no—
658C22×D3—41no—
659C22×D3—41no—
660C22×D3—41no—
661C22×D3—41no—
662C22×D3—41no—
663C22×D3—41no—
664C22×D3—41no—
665C22×D3—41no—
666C22×D3—41no—
667C22×D3—41no—
668C22×D3—41no—
669C22×D3—41no—
670C22×D3—41no—
671C22×D3—41no—
672C22×D3—41no—
673C22×D3—41no—
674C22×D3—41no—
675C22×D3—41no—
676C22×D3#12414yescomplemented
677C2×C3×C4—22no—
678C2×C3×C4—22no—
679C2×C3×C4—22no—
680C2×C3×C4—22no—
681C2×C3×C4—22no—
682C2×C3×C4—22no—
683C2×C3×C4—22no—
684C2×C3×C4—22no—
685C2×C3×C4—22no—
686C2×C3×C4—22no—
687C2×C3×C4—22no—
688C2×C3×C4—22no—
689C2×C3×C4—22no—
690C2×C3×C4—22no—
691C2×C3×C4—22no—
692C2×C3×C4—22no—
693C2×C3×C4—22no—
694C2×C3×C4—22no—
695C2×C3×C4—41no—
696C2×C3×C4—41no—
697C2×C3×C4—41no—
698C2×C3×C4—41no—
699C2×C3×C4—41no—
700C2×C3×C4—41no—
701C2×C3×C4—41no—
702C2×C3×C4—41no—
703C2×C3×C4—41no—
704C2×C3×C4—41no—
705C2×C3×C4—41no—
706C2×C3×C4—41no—
707C2×C3×C4—41no—
708C2×C3×C4—41no—
709C2×C3×C4—41no—
710C2×C3×C4—41no—
711C2×C3×C4—41no—
712C2×C3×C4—41no—
713C2×C3×C4—41no—
714C2×C3×C4—41no—
715C2×C3×C4—41no—
716C2×C3×C4—41no—
717C2×C3×C4—41no—
718C2×C3×C4—41no—
719#67—416no—
720#67—416no—
721C2×Dic3—22no—
722C2×Dic3—22no—
723C2×Dic3—22no—
724C2×Dic3—22no—
725C2×Dic3—22no—
726C2×Dic3—22no—
727C2×Dic3—22no—
728C2×Dic3—22no—
729C2×Dic3—22no—
730C2×Dic3—22no—
731C2×Dic3—22no—
732C2×Dic3—22no—
733C2×Dic3—22no—
734C2×Dic3—22no—
735C2×Dic3—22no—
736C2×Dic3—41no—
737C2×Dic3—41no—
738C2×Dic3—41no—
739C2×Dic3—41no—
740C2×Dic3—41no—
741C2×Dic3—41no—
742C2×Dic3—41no—
743C2×Dic3—41no—
744C2×Dic3—41no—
745C2×Dic3—41no—
746C2×Dic3—41no—
747C2×Dic3—41no—
748C2×Dic3—41no—
749C2×Dic3—41no—
750C2×Dic3—41no—
751C2×Dic3—41no—
752C2×Dic3—41no—
753C2×Dic3—41no—
754C2×Dic3—41no—
755C2×Dic3—41no—
756C2×Dic3#12014yes—
757C2×Dic3#12014yes—
758C2×Dic3#12014yes—
759C2×Dic3#12114yes—
760C2×Dic3#12114yes—
761C2×Dic3#12114yes—
762C2×Dic3#12714yes—
763D12—416no—
764C4×D3—416no—
765Dic6—416no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24—21no—
776C24—21no—
777C24—21no—
778C24—21no—
779C24—21no—
780C24—32no—
781C24—32no—
782C24—32no—
783C24—32no—
784C24—61no—
785C24—61no—
786C24—61no—
787C24—61no—
788C24—61no—
789C24—61no—
790C24—61no—
791C24—61no—
792C24—61no—
793C24—61no—
794C24—61no—
795C24—61no—
796C24—61no—
797C24—61no—
798C24—61no—
799C24—61no—
800C24—61no—
801C24—61no—
802C24—61no—
803C24—61no—
804C24—61no—
805C24—61no—
806C24—61no—
807C24—61no—
808C24—61no—
809C24—61no—
810C24D3×D412yes—
811C24C23×D311yescharacteristic
812C2×Q8—68no—
813C2×Q8—68no—
814C2×Q8—68no—
815C2×Q8—124no—
816C2×Q8—124no—
817C2×Q8—124no—
818C2×Q8—124no—
819C2×D4—68no—
820C2×D4—68no—
821C2×D4—68no—
822C2×D4—68no—
823C2×D4—68no—
824C2×D4—124no—
825C2×D4—124no—
826C2×D4—124no—
827C2×D4—124no—
828C2×D4—124no—
829C2×D4—124no—
830C2×D4—124no—
831C2×D4—124no—
832C2×D4—124no—
833C2×D4—124no—
834C2×D4—124no—
835C2×D4—124no—
836C2×D4—124no—
837C2×D4—124no—
838C2×D4—124no—
839C2×D4—124no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—32no—
877C22×C4—32no—
878C22×C4—32no—
879C22×C4—32no—
880C22×C4—32no—
881C22×C4—32no—
882C22×C4—32no—
883C22×C4—32no—
884C22×C4—32no—
885C22×C4—32no—
886C22×C4—32no—
887C22×C4—32no—
888C22×C4—68no—
889C22×C4—68no—
890C22×C4—68no—
891C22×C4—61no—
892C22×C4—61no—
893C22×C4—61no—
894C22×C4—61no—
895C22×C4—61no—
896C22×C4—61no—
897C22×C4—61no—
898C22×C4—61no—
899C22×C4—61no—
900C22×C4—61no—
901C22×C4—61no—
902C22×C4—61no—
903C22×C4—61no—
904C22×C4—61no—
905C22×C4—61no—
906C22×C4—61no—
907C22×C4—61no—
908C22×C4—61no—
909C22×C4—61no—
910C22×C4—61no—
911C22×C4—61no—
912C22×C4—61no—
913C22×C4—61no—
914C22×C4—61no—
915C22×C4—61no—
916C22×C4—61no—
917C22×C4—61no—
918C22×C4—61no—
919C22×C4—61no—
920C22×C4—61no—
921C22×C4—124no—
922C22×C4—124no—
923C22×C4—124no—
924C22×C4—124no—
925C22×C4#23512yes—
926C22×C4D3×D412yes—
927C22×C4D3×D412yes—
928C22×C4D3×D412yes—
929C22×C4D3×D412yes—
930C22×C4D3×D412yes—
931C4⋊C4—28no—
932C4⋊C4—68no—
933C4⋊C4—68no—
934C4⋊C4—68no—
935C22⋊C4—28no—
936C22⋊C4—28no—
937C22⋊C4—44no—
938C22⋊C4—68no—
939C22⋊C4—68no—
940C22⋊C4—68no—
941C22⋊C4—68no—
942C22⋊C4—68no—
943C22⋊C4—68no—
944C22⋊C4—68no—
945C22⋊C4—68no—
946C22⋊C4—124no—
947C22⋊C4—124no—
948C22⋊C4—124no—
949C42—68no—
950C42—124no—
951C22×C3—42no—
952C22×C3—42no—
953C22×C3—42no—
954C22×C3—42no—
955C22×C3—42no—
956C22×C3—42no—
957C22×C3—42no—
958C22×C3—81no—
959C22×C3—81no—
960C22×C3—81no—
961C22×C3—81no—
962C22×C3—81no—
963C22×C3—81no—
964C22×C3—81no—
965C22×C3—81no—
966C22×C3C2×#12011yescharacteristic
967C22×C3C2×#12011yescharacteristic
968C22×C3C2×#12011yescharacteristic
969C22×C3C2×#12111yescharacteristic
970C22×C3C2×#12111yescharacteristic
971C22×C3C2×#12111yescharacteristic
972C22×C3#52511yescharacteristic
973C22×C3#52511yescharacteristic
974C22×C3C2×#12411yescharacteristic
975C22×C3#52911yescharacteristic
976C22×C3#52911yescharacteristic
977C22×C3C2×#12711yescharacteristic
978C22×C3#53211yescharacteristic
979C22×C3#53511yescharacteristic
980C22×C3#53611yescharacteristic
981C22×C3#53711yescharacteristic
982C22×C3#53711yescharacteristic
983C22×C3#54211yescharacteristic
984C22×C3#54211yescharacteristic
985C22×C3#54611yescharacteristic
986C22×C3#54611yescharacteristic
987C22×C3#54611yescharacteristic
988C22×C3#54611yescharacteristic
989C22×C3#54611yescharacteristic
990C22×C3#54611yescharacteristic
991C22×C3#54711yescharacteristic
992C22×C3#54711yescharacteristic
993C22×C3#54811yescharacteristic
994C22×C3#54811yescharacteristic
995C22×C3#54811yescharacteristic
996C22×C3#54811yescharacteristic
997C22×C3#54811yescharacteristic
998C22×C3#54811yescharacteristic
999C22×C3#55011yescharacteristic
1000C22×C3#55011yescharacteristic
1001C2×D3—24no—
1002C2×D3—24no—
1003C2×D3—24no—
1004C2×D3—42no—
1005C2×D3—42no—
1006C2×D3—42no—
1007C2×D3—42no—
1008C2×D3—42no—
1009C2×D3—42no—
1010C2×D3—42no—
1011C2×D3—42no—
1012C2×D3—42no—
1013C2×D3—42no—
1014C2×D3—42no—
1015C2×D3—42no—
1016C2×D3—42no—
1017C2×D3—42no—
1018C2×D3—42no—
1019C2×D3—42no—
1020C2×D3—42no—
1021C2×D3—42no—
1022C2×D3—42no—
1023C2×D3—81no—
1024C2×D3—81no—
1025C2×D3—81no—
1026C2×D3—81no—
1027C2×D3—81no—
1028C2×D3—81no—
1029C2×D3—81no—
1030C2×D3—81no—
1031C3×C4—42no—
1032C3×C4—42no—
1033C3×C4—42no—
1034C3×C4—42no—
1035C3×C4—42no—
1036C3×C4—42no—
1037Dic3—42no—
1038Dic3—42no—
1039Dic3—42no—
1040Dic3—42no—
1041Dic3—42no—
1042Dic3#39218yes—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—34no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—62no—
1080C23—62no—
1081C23—62no—
1082C23—62no—
1083C23—62no—
1084C23—62no—
1085C23—62no—
1086C23—62no—
1087C23—62no—
1088C23—62no—
1089C23—62no—
1090C23—62no—
1091C23—62no—
1092C23—62no—
1093C23—62no—
1094C23—62no—
1095C23—62no—
1096C23—62no—
1097C23—62no—
1098C23—62no—
1099C23—62no—
1100C23—62no—
1101C23—62no—
1102C23—62no—
1103C23—62no—
1104C23—121no—
1105C23—121no—
1106C23—121no—
1107C23—121no—
1108C23—121no—
1109C23—121no—
1110C23—121no—
1111C23—121no—
1112C23—121no—
1113C23—121no—
1114C23—121no—
1115C23—121no—
1116C23—121no—
1117C23—121no—
1118C23—121no—
1119C23—121no—
1120C23—121no—
1121C23—121no—
1122C23—121no—
1123C23—121no—
1124C23—121no—
1125C23—121no—
1126C23—121no—
1127C23—121no—
1128C23—121no—
1129C23—121no—
1130C23—121no—
1131C23—121no—
1132C23—121no—
1133C23—121no—
1134C23—121no—
1135C23—121no—
1136C23—121no—
1137C23—121no—
1138C23—121no—
1139C23—121no—
1140C23—121no—
1141C23—121no—
1142C23—121no—
1143C23—121no—
1144C23—121no—
1145C23—121no—
1146C23—121no—
1147C23—121no—
1148C23C2×#23511yescharacteristic
1149C23C2×D3×D411yescharacteristic
1150C23C2×D3×D411yescharacteristic
1151C23C2×D3×D411yescharacteristic
1152C23C2×D3×D411yescharacteristic
1153C23C2×D3×D411yescharacteristic
1154C23C2×D3×D411yescharacteristic
1155C23#100411yescharacteristic
1156C23#100711yescharacteristic
1157C23D3×#4111yescharacteristic
1158C23D3×#4111yescharacteristic
1159C23D3×#4111yescharacteristic
1160C23D3×#4111yescharacteristic
1161C23#100911yescharacteristic
1162C23#101011yescharacteristic
1163Q8—1216no—
1164D4—1216no—
1165D4—1216no—
1166D4—1216no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—34no—
1186C2×C4—34no—
1187C2×C4—34no—
1188C2×C4—34no—
1189C2×C4—34no—
1190C2×C4—34no—
1191C2×C4—34no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—62no—
1217C2×C4—62no—
1218C2×C4—62no—
1219C2×C4—62no—
1220C2×C4—62no—
1221C2×C4—62no—
1222C2×C4—62no—
1223C2×C4—62no—
1224C2×C4—62no—
1225C2×C4—62no—
1226C2×C4—62no—
1227C2×C4—62no—
1228C2×C4—62no—
1229C2×C4—62no—
1230C2×C4—62no—
1231C2×C4—1216no—
1232C2×C4—121no—
1233C2×C4—121no—
1234C2×C4—121no—
1235C2×C4—121no—
1236C2×C4—121no—
1237C2×C4—121no—
1238C2×C4—121no—
1239C2×C4—121no—
1240C2×C4—121no—
1241C2×C4—121no—
1242C2×C4—121no—
1243C2×C4—121no—
1244C2×C4—121no—
1245C2×C4—121no—
1246C2×C4—121no—
1247C2×C4—121no—
1248C2×C4—121no—
1249C2×C4—121no—
1250C2×C4—121no—
1251C2×C4—121no—
1252C2×C3—82no—
1253C2×C3C2×#39211yescharacteristic
1254C2×C3#240711yescharacteristic
1255C2×C3#240711yescharacteristic
1256C2×C3#242611yescharacteristic
1257C2×C3#242611yescharacteristic
1258C2×C3#242711yescharacteristic
1259C2×C3#242711yescharacteristic
1260C2×C3#243111yescharacteristic
1261C2×C3#243211yescharacteristic
1262C2×C3#243511yescharacteristic
1263C2×C3#243611yescharacteristic
1264C2×C3#254011yescharacteristic
1265C2×C3#254011yescharacteristic
1266C2×C3#262011yescharacteristic
1267C2×C3#285011yescharacteristic
1268D3—44no—
1269D3—82no—
1270C22—42no—
1271C22—42no—
1272C22—42no—
1273C22—42no—
1274C22—42no—
1275C22—42no—
1276C22—42no—
1277C22—64no—
1278C22—64no—
1279C22—64no—
1280C22—81no—
1281C22—81no—
1282C22—81no—
1283C22—81no—
1284C22—81no—
1285C22—81no—
1286C22—81no—
1287C22—81no—
1288C22—122no—
1289C22—122no—
1290C22—122no—
1291C22—122no—
1292C22—122no—
1293C22—122no—
1294C22—122no—
1295C22—122no—
1296C22—122no—
1297C22—122no—
1298C22—122no—
1299C22—122no—
1300C22—122no—
1301C22—122no—
1302C22—122no—
1303C22—122no—
1304C22—122no—
1305C22—122no—
1306C22—122no—
1307C22—241no—
1308C22—241no—
1309C22—241no—
1310C22—241no—
1311C22—241no—
1312C22—241no—
1313C22—241no—
1314C22—241no—
1315C22#549011yescharacteristic
1316C22#550711yescharacteristic
1317C22#552811yescharacteristic
1318C22#554711yescharacteristic
1319C22#554811yescharacteristic
1320C22#555211yescharacteristic
1321C22#555311yescharacteristic
1322C22D3×#12011yescharacteristic
1323C22D3×#12011yescharacteristic
1324C22D3×#12011yescharacteristic
1325C22#559711yescharacteristic
1326C22#559911yescharacteristic
1327C22D3×#12111yescharacteristic
1328C22D3×#12111yescharacteristic
1329C22D3×#12111yescharacteristic
1330C22#560711yescharacteristic
1331C22#561011yescharacteristic
1332C22#561011yescharacteristic
1333C22#562811yescharacteristic
1334C22#562911yescharacteristic
1335C22#563311yescharacteristic
1336C22#563311yescharacteristic
1337C22#563311yescharacteristic
1338C22#564011yescharacteristic
1339C22#565411yescharacteristic
1340C22#565411yescharacteristic
1341C22#565411yescharacteristic
1342C22#565511yescharacteristic
1343C22#565611yescharacteristic
1344C22D3×#12411yescharacteristic
1345C22#567711yescharacteristic
1346C22#567711yescharacteristic
1347C22#570611yescharacteristic
1348C22#571011yescharacteristic
1349C22D3×#12711yescharacteristic
1350C4—38no—
1351C4—42no—
1352C4—42no—
1353C4—42no—
1354C4—42no—
1355C4—42no—
1356C4—42no—
1357C4—122no—
1358C4—122no—
1359C4—122no—
1360C4—122no—
1361C4—122no—
1362C3#1521511yescharacteristic, complemented, Sylow
1363C2—82no—
1364C2—124no—
1365C2—242no—
1366C2#7389511yescharacteristic
1367C2#7440411yescharacteristic
1368C2#7441111yescharacteristic
1369C2#7470011yescharacteristic
1370C2#7549911yescharacteristic
1371C2#7595711yescharacteristic
1372C2#7634711yescharacteristic
1373C2D3×#39211yescharacteristic
1374C2#7678111yescharacteristic
1375C2#7689411yescharacteristic
1376C2#7690511yescharacteristic
1377C2#7728611yescharacteristic
1378C2#7733111yescharacteristic
1379C2#7746611yescharacteristic
1380C2#7803611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1439C2
prime radicalC22×#884C2
hypercenter#1439D3
hypocenterC3#15215
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
1. C22×#896C2semidirect
3. C22×#885C2semidirect
4. C2×#4957C2semidirect
5. C2×#4646C2semidirect
6. C2×#4666C2semidirect
7. C3×#1439C2semidirect
8. #71570C2semidirect
9. #71550C2semidirect
10. #71550C2semidirect
11. #71547C2semidirect
12. #69428C2semidirect
13. #69426C2semidirect
14. #69426C2semidirect
15. Dic3⋊#95C2semidirect
73. #1439D3semidirect
128. C22×Dic6D4semidirect
182. C2×Dic3⋊C4D4semidirect
188. C2×C4×Dic3D4semidirect
676. C22×D3#124semidirect
1362. C3#15215semidirect

Maximal subgroups

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

subgroupindex
C22×#8962
C22×#8842
C22×#8852
C2×#49572
C2×#46462
C2×#46662
C3×#14392
#715702
#715502
#715472
#694282
#694262
Dic3⋊#952
#152153