Finite Group Databasebeta

← #10724545

Subgroups — #10724545

Order 768.

2282 conjugacy classes of subgroups.

The subgroup lattice has 1332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#386C211yesmaximal, characteristic, complemented
2C2×#5223C211yesmaximal, characteristic
3C2×#5221C211yesmaximal, characteristic, complemented
4C2×#5213C211yesmaximal, characteristic, complemented
5C2×#4957C211yesmaximal, characteristic, complemented
6C2×#4945C211yesmaximal, characteristic, complemented
7C2×#4669C211yesmaximal, characteristic, complemented
8#72127C211yesmaximal, characteristic, complemented
9#71550C211yesmaximal, characteristic, complemented
10#71550C211yesmaximal, characteristic, complemented
11#71547C211yesmaximal, characteristic, complemented
12#71547C211yesmaximal, characteristic, complemented
13#69427C211yesmaximal, characteristic, complemented
14#69407C211yesmaximal, characteristic, complemented
15#69406C211yesmaximal, characteristic, complemented
16#14521—31nomaximal, Sylow
17C23×C3×D4C2211yescharacteristic
18C24×C3×C4C2211yescharacteristic
19C23×#67C2211yescharacteristic
20C23×#67C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×#217C2211yescharacteristic
25C22×#217C2211yescharacteristic
26C22×#217C2211yescharacteristic
27C22×#217C2211yescharacteristic
28C22×#217C2211yescharacteristic
29C22×#217C2211yescharacteristic
30C22×(C2×D3)⋊C4C2211yescharacteristic
31C22×(C2×D3)⋊C4C2211yescharacteristic
32C22×(C2×D3)⋊C4C2211yescharacteristic
33C22×(C2×D3)⋊C4C2211yescharacteristic
34C22×(C2×D3)⋊C4C2211yescharacteristic
35C22×C4⋊Dic3C2211yescharacteristic
36C22×Dic3⋊C4C2211yescharacteristic
37C22×Dic3⋊C4C2211yescharacteristic
38C22×C4×Dic3C2211yescharacteristic
39C22×C4×Dic3C2211yescharacteristic
40C3×#386—24no—
41C2×C3×#95C2211yescharacteristic
42C2×C3×#95C2211yescharacteristic
43#5223C418yescomplemented
44#5221—24no—
45#5213—24no—
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
55C2×C3⋊#95C2211yescharacteristic
56#4957—24no—
57#4945—24no—
58#4669—24no—
59C2×#392—31no—
60C2×#390—31no—
61C2×#390—31no—
62C2×#388—31no—
63C2×#388—31no—
64C2×#386—31no—
65C2×#386D311yescharacteristic, complemented
66#1439—31no—
67#1439—31no—
68#1439—31no—
69#1438—31no—
70#1438—31no—
71#1436—31no—
72#1436—31no—
73C22⋊#95—31no—
74C25×C3C2311yescharacteristic
75C25×C3C2311yescharacteristic
76C24×D3C2311yescharacteristic
77C22×C3×D4—22no—
78C22×C3×D4—22no—
79C22×C3×D4—22no—
80C22×C3×D4—22no—
81C22×C3×D4—41no—
82C22×C3×D4—41no—
83C22×C3×D4C2×C414yes—
84C23×C3×C4—22no—
85C23×C3×C4—22no—
86C23×C3×C4—22no—
87C23×C3×C4—41no—
88C23×C3×C4—41no—
89C23×C3×C4—41no—
90C23×C3×C4—41no—
91C23×C3×C4C2311yescharacteristic
92C23×C3×C4C2311yescharacteristic
93C23×C3×C4C2311yescharacteristic
94C23×C3×C4C2311yescharacteristic
95C23×C3×C4C2311yescharacteristic
96C22×#67—22no—
97C22×#67—22no—
98C22×#67—22no—
99C22×#67—22no—
100C22×#67—41no—
101C22×#67—41no—
102C22×#67—41no—
103C22×#67—41no—
104C22×#67—41no—
105C22×#67—41no—
106C22×#67—41no—
107C22×#67—41no—
108C22×#67C2×C414yes—
109C22×#67C2×C414yescomplemented
110C23×Dic3C2311yescharacteristic
111C23×Dic3C2311yescharacteristic
112C23×Dic3C2311yescharacteristic
113C23×Dic3C2311yescharacteristic
114C23×Dic3C2311yescharacteristic
115C23×Dic3C2311yescharacteristic
116C23×Dic3C2311yescharacteristic
117C2×C3×C22⋊C4—22no—
118C2×C3×C22⋊C4—22no—
119C2×C3×C22⋊C4—22no—
120C2×C3×C22⋊C4—22no—
121C2×C3×C22⋊C4—22no—
122C2×C3×C22⋊C4—41no—
123C2×C3×C22⋊C4—41no—
124C2×C3×C22⋊C4—41no—
125C2×C3×C22⋊C4—41no—
126C2×#217—22no—
127C2×#217—22no—
128C2×#217—22no—
129C2×#217—22no—
130C2×#217—22no—
131C2×#217—22no—
132C2×#217—22no—
133C2×#217—41no—
134C2×#217—41no—
135C2×#217—41no—
136C2×#217—41no—
137C2×#217—41no—
138C2×#217—41no—
139C2×#217—41no—
140C2×#217—41no—
141C2×#217C2×C414yes—
142C2×#217C2×C414yescomplemented
143C2×#217D414yescomplemented
144C2×(C2×D3)⋊C4—22no—
145C2×(C2×D3)⋊C4—22no—
146C2×(C2×D3)⋊C4—22no—
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—41no—
153C2×(C2×D3)⋊C4—41no—
154C2×(C2×D3)⋊C4—41no—
155C2×(C2×D3)⋊C4—41no—
156C2×(C2×D3)⋊C4—41no—
157C2×(C2×D3)⋊C4—41no—
158C2×(C2×D3)⋊C4C2×C414yescomplemented
159C2×C4⋊Dic3—22no—
160C2×C4⋊Dic3—22no—
161C2×C4⋊Dic3—41no—
162C2×Dic3⋊C4—22no—
163C2×Dic3⋊C4—22no—
164C2×Dic3⋊C4—22no—
165C2×Dic3⋊C4—22no—
166C2×Dic3⋊C4—41no—
167C2×Dic3⋊C4—41no—
168C2×C4×Dic3—22no—
169C2×C4×Dic3—22no—
170C2×C4×Dic3—22no—
171C2×C4×Dic3—22no—
172C2×C4×Dic3—41no—
173C2×C4×Dic3—41no—
174C3×#95—22no—
175C3×#95D414yescomplemented
176C3⋊#95—22no—
177C3⋊#95—22no—
178C3⋊#95—22no—
179C3⋊#95—41no—
180C3⋊#95—41no—
181C3⋊#95—41no—
182C3⋊#95—41no—
183C3⋊#95—41no—
184C3⋊#95C2×C414yescomplemented
185C3⋊#95D414yescomplemented
186C23×D4—31no—
187C23×D4—31no—
188C23×D4C2×D311yescharacteristic
189C24×C4C2×D311yescharacteristic
190C22×C4⋊C4—31no—
191C22×C4⋊C4—31no—
192C22×C4⋊C4—31no—
193C22×C22⋊C4—31no—
194C22×C22⋊C4—31no—
195C22×C22⋊C4—31no—
196C22×C22⋊C4—31no—
197C22×C22⋊C4—31no—
198C22×C22⋊C4—31no—
199C22×C22⋊C4—31no—
200C22×C22⋊C4—31no—
201C22×C22⋊C4—31no—
202C22×C22⋊C4—31no—
203C22×C22⋊C4—31no—
204C22×C22⋊C4C2×D311yescharacteristic
205C22×C22⋊C4C2×D311yescharacteristic
206C22×C22⋊C4C2×D311yescharacteristic
207C22×C42—31no—
208C22×C42—31no—
209#392—38no—
210#390—64no—
211#390—64no—
212#388—64no—
213#388—64no—
214#386—24no—
215#386—64no—
216C2×#95—31no—
217C2×#95—31no—
218C2×#95—31no—
219C2×#95—31no—
220C2×#95—31no—
221C2×#95—31no—
222C2×#95—31no—
223C2×#95—31no—
224C2×#95—31no—
225C2×#95—31no—
226C2×#95C2×D311yescharacteristic
227C2×#95C2×D311yescharacteristic
228C24×C3—21no—
229C24×C3—21no—
230C24×C3—21no—
231C24×C3—21no—
232C24×C3—21no—
233C24×C3—21no—
234C24×C3—21no—
235C24×C3—21no—
236C24×C3—21no—
237C24×C3—21no—
238C24×C3—21no—
239C24×C3—21no—
240C24×C3—21no—
241C24×C3—21no—
242C24×C3—21no—
243C24×C3—21no—
244C24×C3—21no—
245C24×C3—21no—
246C24×C3—21no—
247C24×C3—21no—
248C24×C3—21no—
249C24×C3—21no—
250C24×C3—21no—
251C24×C3—21no—
252C24×C3—21no—
253C24×C3—21no—
254C24×C3C22×C412yes—
255C24×C3C22×C412yes—
256C24×C3C2×D412yes—
257C24×C3#4112yes—
258C24×C3C2411yescharacteristic
259C23×D3—21no—
260C23×D3—21no—
261C23×D3—21no—
262C23×D3—21no—
263C23×D3—21no—
264C23×D3—21no—
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×D3C22×C412yes—
274C2×C3×D4—28no—
275C2×C3×D4—28no—
276C2×C3×D4—44no—
277C2×C3×D4—44no—
278C2×C3×D4—44no—
279C2×C3×D4—44no—
280C2×C3×D4—44no—
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×C4—21no—
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—44no—
311C22×C3×C4—44no—
312C22×C3×C4—44no—
313C22×C3×C4—44no—
314C22×C3×C4—44no—
315C22×C3×C4—44no—
316C22×C3×C4—44no—
317C22×C3×C4C22×C412yes—
318C22×C3×C4C2×D412yes—
319C22×C3×C4C2×D412yes—
320C22×C3×C4C2×D412yes—
321C22×C3×C4C2×D412yes—
322C22×C3×C4#4112yes—
323C2×#67—28no—
324C2×#67—28no—
325C2×#67—44no—
326C2×#67—44no—
327C2×#67—44no—
328C2×#67—44no—
329C2×#67—44no—
330C2×#67—44no—
331C2×#67—44no—
332C2×#67—44no—
333C2×#67—44no—
334C2×#67—44no—
335C2×#67—44no—
336C2×#67—44no—
337C22×Dic3—21no—
338C22×Dic3—21no—
339C22×Dic3—21no—
340C22×Dic3—21no—
341C22×Dic3—21no—
342C22×Dic3—21no—
343C22×Dic3—21no—
344C22×Dic3—21no—
345C22×Dic3—21no—
346C22×Dic3—21no—
347C22×Dic3—21no—
348C22×Dic3—21no—
349C22×Dic3—21no—
350C22×Dic3—21no—
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×Dic3C22×C412yes—
379C22×Dic3C22×C412yes—
380C22×Dic3C22×C412yes—
381C22×Dic3C2×D412yes—
382C22×Dic3C2×D412yes—
383C22×Dic3C2×D412yes—
384C22×Dic3C2×D412yes—
385C22×Dic3#4112yes—
386C3×C22⋊C4—44no—
387C3×C22⋊C4—44no—
388C3×C22⋊C4—44no—
389#217—28no—
390#217—44no—
391#217—44no—
392#217—44no—
393#217—44no—
394#217—44no—
395(C2×D3)⋊C4—28no—
396(C2×D3)⋊C4—44no—
397(C2×D3)⋊C4—44no—
398(C2×D3)⋊C4—44no—
399(C2×D3)⋊C4—44no—
400C4⋊Dic3—44no—
401Dic3⋊C4—44no—
402Dic3⋊C4—44no—
403C4×Dic3—44no—
404C4×Dic3—44no—
405C25—31no—
406C25C22×D311yescharacteristic
407C25C22×D311yescharacteristic
408C22×D4—22no—
409C22×D4—22no—
410C22×D4—22no—
411C22×D4—22no—
412C22×D4—34no—
413C22×D4—34no—
414C22×D4—41no—
415C22×D4—41no—
416C22×D4—62no—
417C22×D4—62no—
418C22×D4—62no—
419C22×D4—62no—
420C22×D4—121no—
421C22×D4—121no—
422C22×D4—121no—
423C22×D4—121no—
424C22×D4—121no—
425C22×D4—121no—
426C22×D4—121no—
427C22×D4—121no—
428C22×D4C4×D314yes—
429C23×C4—22no—
430C23×C4—22no—
431C23×C4—22no—
432C23×C4—31no—
433C23×C4—31no—
434C23×C4—31no—
435C23×C4—31no—
436C23×C4—31no—
437C23×C4—31no—
438C23×C4—31no—
439C23×C4—41no—
440C23×C4—41no—
441C23×C4—41no—
442C23×C4—41no—
443C23×C4C22×D311yescharacteristic
444C23×C4C22×D311yescharacteristic
445C23×C4C22×D311yescharacteristic
446C23×C4C22×D311yescharacteristic
447C23×C4C22×D311yescharacteristic
448C2×C4⋊C4—62no—
449C2×C4⋊C4—62no—
450C2×C4⋊C4—62no—
451C2×C4⋊C4—62no—
452C2×C4⋊C4—62no—
453C2×C4⋊C4—62no—
454C2×C4⋊C4—121no—
455C2×C4⋊C4—121no—
456C2×C4⋊C4—121no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4—22no—
462C2×C22⋊C4—34no—
463C2×C22⋊C4—34no—
464C2×C22⋊C4—34no—
465C2×C22⋊C4—34no—
466C2×C22⋊C4—41no—
467C2×C22⋊C4—41no—
468C2×C22⋊C4—41no—
469C2×C22⋊C4—41no—
470C2×C22⋊C4—62no—
471C2×C22⋊C4—62no—
472C2×C22⋊C4—62no—
473C2×C22⋊C4—62no—
474C2×C22⋊C4—62no—
475C2×C22⋊C4—62no—
476C2×C22⋊C4—62no—
477C2×C22⋊C4—62no—
478C2×C22⋊C4—62no—
479C2×C22⋊C4—62no—
480C2×C22⋊C4—62no—
481C2×C22⋊C4—62no—
482C2×C22⋊C4—62no—
483C2×C22⋊C4—62no—
484C2×C22⋊C4—62no—
485C2×C22⋊C4—121no—
486C2×C22⋊C4—121no—
487C2×C22⋊C4—121no—
488C2×C22⋊C4—121no—
489C2×C22⋊C4—121no—
490C2×C22⋊C4—121no—
491C2×C22⋊C4—121no—
492C2×C22⋊C4—121no—
493C2×C22⋊C4—121no—
494C2×C22⋊C4—121no—
495C2×C22⋊C4—121no—
496C2×C22⋊C4—121no—
497C2×C22⋊C4—121no—
498C2×C22⋊C4—121no—
499C2×C42—62no—
500C2×C42—62no—
501C2×C42—62no—
502C2×C42—62no—
503C2×C42—121no—
504C2×C42—121no—
505#95—22no—
506#95—34no—
507#95—34no—
508#95—62no—
509#95—62no—
510#95—62no—
511#95—121no—
512#95—121no—
513#95—121no—
514#95—121no—
515#95—121no—
516#95#6714yescomplemented
517C23×C3—22no—
518C23×C3—22no—
519C23×C3—22no—
520C23×C3—22no—
521C23×C3—22no—
522C23×C3—22no—
523C23×C3—22no—
524C23×C3—22no—
525C23×C3—22no—
526C23×C3—22no—
527C23×C3—22no—
528C23×C3—22no—
529C23×C3—22no—
530C23×C3—22no—
531C23×C3—22no—
532C23×C3—22no—
533C23×C3—22no—
534C23×C3—22no—
535C23×C3—22no—
536C23×C3—22no—
537C23×C3—22no—
538C23×C3—22no—
539C23×C3—22no—
540C23×C3—22no—
541C23×C3—22no—
542C23×C3—41no—
543C23×C3—41no—
544C23×C3—41no—
545C23×C3—41no—
546C23×C3—41no—
547C23×C3—41no—
548C23×C3—41no—
549C23×C3—41no—
550C23×C3—41no—
551C23×C3—41no—
552C23×C3—41no—
553C23×C3—41no—
554C23×C3—41no—
555C23×C3—41no—
556C23×C3—41no—
557C23×C3—41no—
558C23×C3—41no—
559C23×C3—41no—
560C23×C3—41no—
561C23×C3—41no—
562C23×C3—41no—
563C23×C3—41no—
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×C3C4×D414yes—
587C23×C3C23×C411yescharacteristic
588C23×C3C22×D411yescharacteristic
589C23×C3C22×D411yescharacteristic
590C23×C3C22×D411yescharacteristic
591C23×C3C2×#4111yescharacteristic
592C23×C3C2×#4111yescharacteristic
593C23×C3C2×#4111yescharacteristic
594C23×C3H(5,𝔽2)11yescharacteristic
595C23×C3H(5,𝔽2)11yescharacteristic
596C23×C3H(5,𝔽2)11yescharacteristic
597C23×C3H(5,𝔽2)11yescharacteristic
598C23×C3H(5,𝔽2)11yescharacteristic
599C23×C3H(5,𝔽2)11yescharacteristic
600C23×C3H(5,𝔽2)11yescharacteristic
601C23×C32−1+411yescharacteristic
602C22×D3—22no—
603C22×D3—22no—
604C22×D3—22no—
605C22×D3—22no—
606C22×D3—22no—
607C22×D3—22no—
608C22×D3—22no—
609C22×D3—41no—
610C22×D3—41no—
611C22×D3—41no—
612C22×D3—41no—
613C22×D3—41no—
614C22×D3—41no—
615C22×D3—41no—
616C22×D3—41no—
617C22×D3—41no—
618C22×D3—41no—
619C22×D3—41no—
620C22×D3—41no—
621C22×D3—41no—
622C22×D3—41no—
623C22×D3—41no—
624C22×D3—41no—
625C22×D3—41no—
626C22×D3—41no—
627C22×D3—41no—
628C22×D3—41no—
629C22×D3—41no—
630C22×D3—41no—
631C22×D3—41no—
632C22×D3—41no—
633C22×D3—41no—
634C22×D3—41no—
635C22×D3—41no—
636C22×D3—41no—
637C3×D4—416no—
638C2×C3×C4—22no—
639C2×C3×C4—22no—
640C2×C3×C4—22no—
641C2×C3×C4—22no—
642C2×C3×C4—22no—
643C2×C3×C4—22no—
644C2×C3×C4—22no—
645C2×C3×C4—22no—
646C2×C3×C4—22no—
647C2×C3×C4—22no—
648C2×C3×C4—22no—
649C2×C3×C4—22no—
650C2×C3×C4—22no—
651C2×C3×C4—22no—
652C2×C3×C4—22no—
653C2×C3×C4—416no—
654C2×C3×C4—41no—
655C2×C3×C4—41no—
656C2×C3×C4—41no—
657C2×C3×C4—41no—
658C2×C3×C4—41no—
659C2×C3×C4—41no—
660C2×C3×C4—41no—
661C2×C3×C4—41no—
662C2×C3×C4—41no—
663C2×C3×C4—41no—
664C2×C3×C4—41no—
665C2×C3×C4—41no—
666C2×C3×C4—41no—
667C2×C3×C4—41no—
668C2×C3×C4—41no—
669C2×C3×C4—41no—
670C2×C3×C4—41no—
671C2×C3×C4—41no—
672C2×C3×C4—41no—
673C2×C3×C4C4×D414yes—
674#67—416no—
675#67—416no—
676C2×Dic3—22no—
677C2×Dic3—22no—
678C2×Dic3—22no—
679C2×Dic3—22no—
680C2×Dic3—22no—
681C2×Dic3—22no—
682C2×Dic3—22no—
683C2×Dic3—22no—
684C2×Dic3—22no—
685C2×Dic3—22no—
686C2×Dic3—22no—
687C2×Dic3—22no—
688C2×Dic3—22no—
689C2×Dic3—22no—
690C2×Dic3—22no—
691C2×Dic3—22no—
692C2×Dic3—22no—
693C2×Dic3—22no—
694C2×Dic3—22no—
695C2×Dic3—22no—
696C2×Dic3—22no—
697C2×Dic3—41no—
698C2×Dic3—41no—
699C2×Dic3—41no—
700C2×Dic3—41no—
701C2×Dic3—41no—
702C2×Dic3—41no—
703C2×Dic3—41no—
704C2×Dic3—41no—
705C2×Dic3—41no—
706C2×Dic3—41no—
707C2×Dic3—41no—
708C2×Dic3—41no—
709C2×Dic3—41no—
710C2×Dic3—41no—
711C2×Dic3—41no—
712C2×Dic3—41no—
713C2×Dic3—41no—
714C2×Dic3—41no—
715C2×Dic3—41no—
716C2×Dic3—41no—
717C2×Dic3—41no—
718C2×Dic3—41no—
719C2×Dic3—41no—
720C2×Dic3—41no—
721C2×Dic3—41no—
722C2×Dic3—41no—
723C2×Dic3—41no—
724C2×Dic3C4×D414yes—
725C24—21no—
726C24—21no—
727C24—21no—
728C24—21no—
729C24—21no—
730C24—21no—
731C24—21no—
732C24—21no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—21no—
743C24—21no—
744C24—21no—
745C24—21no—
746C24—21no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—32no—
752C24—61no—
753C24—61no—
754C24—61no—
755C24—61no—
756C24—61no—
757C24—61no—
758C24—61no—
759C24—61no—
760C24—61no—
761C24—61no—
762C24—61no—
763C24—61no—
764C24—61no—
765C24—61no—
766C24C2×C4×D312yes—
767C24C2×C4×D312yes—
768C24D3×D412yes—
769C24#23712yes—
770C24C23×D311yescharacteristic
771C2×D4—28no—
772C2×D4—28no—
773C2×D4—44no—
774C2×D4—44no—
775C2×D4—44no—
776C2×D4—44no—
777C2×D4—44no—
778C2×D4—68no—
779C2×D4—68no—
780C2×D4—124no—
781C2×D4—124no—
782C2×D4—124no—
783C2×D4—124no—
784C2×D4—124no—
785C2×D4—124no—
786C2×D4—124no—
787C2×D4—124no—
788C2×D4—124no—
789C2×D4—124no—
790C2×D4—124no—
791C2×D4—124no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—32no—
822C22×C4—32no—
823C22×C4—32no—
824C22×C4—32no—
825C22×C4—32no—
826C22×C4—32no—
827C22×C4—32no—
828C22×C4—32no—
829C22×C4—44no—
830C22×C4—44no—
831C22×C4—44no—
832C22×C4—44no—
833C22×C4—44no—
834C22×C4—44no—
835C22×C4—44no—
836C22×C4—61no—
837C22×C4—61no—
838C22×C4—61no—
839C22×C4—61no—
840C22×C4—61no—
841C22×C4—61no—
842C22×C4—61no—
843C22×C4—61no—
844C22×C4—61no—
845C22×C4—61no—
846C22×C4—61no—
847C22×C4—61no—
848C22×C4—61no—
849C22×C4—61no—
850C22×C4—61no—
851C22×C4—61no—
852C22×C4—61no—
853C22×C4—61no—
854C22×C4—61no—
855C22×C4—61no—
856C22×C4—61no—
857C22×C4—61no—
858C22×C4—61no—
859C22×C4—61no—
860C22×C4—61no—
861C22×C4—61no—
862C22×C4—61no—
863C22×C4—61no—
864C22×C4—61no—
865C22×C4—61no—
866C22×C4—61no—
867C22×C4—61no—
868C22×C4—61no—
869C22×C4—61no—
870C22×C4—61no—
871C22×C4—61no—
872C22×C4—61no—
873C22×C4—61no—
874C22×C4—61no—
875C22×C4—61no—
876C22×C4—61no—
877C22×C4C2×C4×D312yes—
878C22×C4#23512yes—
879C22×C4D3×D412yes—
880C22×C4C2×#6712yes—
881C22×C4C2×#6712yes—
882C22×C4C2×#6712yes—
883C4⋊C4—124no—
884C4⋊C4—124no—
885C4⋊C4—124no—
886C22⋊C4—44no—
887C22⋊C4—44no—
888C22⋊C4—44no—
889C22⋊C4—68no—
890C22⋊C4—68no—
891C22⋊C4—124no—
892C22⋊C4—124no—
893C22⋊C4—124no—
894C22⋊C4—124no—
895C22⋊C4—124no—
896C22⋊C4—124no—
897C22⋊C4—124no—
898C22⋊C4—124no—
899C22⋊C4—124no—
900C42—124no—
901C42—124no—
902C22×C3—24no—
903C22×C3—24no—
904C22×C3—24no—
905C22×C3—42no—
906C22×C3—42no—
907C22×C3—42no—
908C22×C3—42no—
909C22×C3—42no—
910C22×C3—42no—
911C22×C3—42no—
912C22×C3—42no—
913C22×C3—42no—
914C22×C3—42no—
915C22×C3—42no—
916C22×C3—42no—
917C22×C3—42no—
918C22×C3—42no—
919C22×C3—42no—
920C22×C3—42no—
921C22×C3—42no—
922C22×C3—42no—
923C22×C3—42no—
924C22×C3—81no—
925C22×C3—81no—
926C22×C3—81no—
927C22×C3—81no—
928C22×C3—81no—
929C22×C3—81no—
930C22×C3—81no—
931C22×C3—81no—
932C22×C3C2×C4×D411yescharacteristic
933C22×C3C2×C4×D411yescharacteristic
934C22×C3C2×C4×D411yescharacteristic
935C22×C3#51811yescharacteristic
936C22×C3#51811yescharacteristic
937C22×C3#51811yescharacteristic
938C22×C3#52011yescharacteristic
939C22×C3#53411yescharacteristic
940C22×C3#53511yescharacteristic
941C22×C3#53511yescharacteristic
942C22×C3#53711yescharacteristic
943C22×C3#53711yescharacteristic
944C22×C3#53711yescharacteristic
945C22×C3#53811yescharacteristic
946C22×C3#53911yescharacteristic
947C22×C3#54011yescharacteristic
948C22×C3#54011yescharacteristic
949C22×C3#54211yescharacteristic
950C22×C3#54211yescharacteristic
951C22×C3D4211yescharacteristic
952C22×C3D4211yescharacteristic
953C22×C3D4211yescharacteristic
954C22×C3#54611yescharacteristic
955C22×C3#54611yescharacteristic
956C22×C3#54611yescharacteristic
957C22×C3#54611yescharacteristic
958C22×C3#55011yescharacteristic
959C22×C3#55011yescharacteristic
960C22×C3#55111yescharacteristic
961C22×C3#55111yescharacteristic
962C22×C3#55911yescharacteristic
963C22×C3#56011yescharacteristic
964C22×C3#56011yescharacteristic
965C22×C3#56011yescharacteristic
966C22×C3H(3,𝔽4)11yescharacteristic
967C2×D3—42no—
968C2×D3—42no—
969C2×D3—42no—
970C2×D3—42no—
971C2×D3—42no—
972C2×D3—42no—
973C2×D3—42no—
974C2×D3—81no—
975C2×D3—81no—
976C2×D3—81no—
977C2×D3—81no—
978C2×D3—81no—
979C2×D3—81no—
980C2×D3—81no—
981C2×D3—81no—
982C3×C4—24no—
983C3×C4—42no—
984C3×C4—42no—
985C3×C4—42no—
986C3×C4—81no—
987Dic3—24no—
988Dic3—42no—
989Dic3—42no—
990Dic3—42no—
991Dic3—42no—
992Dic3—42no—
993Dic3—81no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
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—62no—
1064C23—62no—
1065C23—62no—
1066C23—62no—
1067C23—62no—
1068C23—62no—
1069C23—62no—
1070C23—121no—
1071C23—121no—
1072C23—121no—
1073C23—121no—
1074C23—121no—
1075C23—121no—
1076C23—121no—
1077C23—121no—
1078C23—121no—
1079C23—121no—
1080C23—121no—
1081C23—121no—
1082C23—121no—
1083C23—121no—
1084C23—121no—
1085C23—121no—
1086C23—121no—
1087C23—121no—
1088C23—121no—
1089C23—121no—
1090C23—121no—
1091C23—121no—
1092C23—121no—
1093C23—121no—
1094C23—121no—
1095C23—121no—
1096C23—121no—
1097C23—121no—
1098C23#67⋊C414yes—
1099C23C22×C4×D311yescharacteristic
1100C23C2×#23511yescharacteristic
1101C23C2×D3×D411yescharacteristic
1102C23C2×D3×D411yescharacteristic
1103C23C2×#23711yescharacteristic
1104C23#100411yescharacteristic
1105C23#100411yescharacteristic
1106C23#100411yescharacteristic
1107C23#100411yescharacteristic
1108C23#100411yescharacteristic
1109C23D3×#4111yescharacteristic
1110C23#100911yescharacteristic
1111C23#100911yescharacteristic
1112C23#101011yescharacteristic
1113C23C22×#6711yescharacteristic
1114D4—416no—
1115D4—1216no—
1116D4—1216no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—34no—
1133C2×C4—416no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—62no—
1154C2×C4—62no—
1155C2×C4—62no—
1156C2×C4—62no—
1157C2×C4—62no—
1158C2×C4—62no—
1159C2×C4—62no—
1160C2×C4—62no—
1161C2×C4—62no—
1162C2×C4—62no—
1163C2×C4—62no—
1164C2×C4—62no—
1165C2×C4—62no—
1166C2×C4—62no—
1167C2×C4—62no—
1168C2×C4—62no—
1169C2×C4—62no—
1170C2×C4—62no—
1171C2×C4—62no—
1172C2×C4—62no—
1173C2×C4—62no—
1174C2×C4—121no—
1175C2×C4—121no—
1176C2×C4—121no—
1177C2×C4—121no—
1178C2×C4—121no—
1179C2×C4—121no—
1180C2×C4—121no—
1181C2×C4—121no—
1182C2×C4—121no—
1183C2×C4—121no—
1184C2×C4—121no—
1185C2×C4—121no—
1186C2×C4—121no—
1187C2×C4—121no—
1188C2×C4—121no—
1189C2×C4—121no—
1190C2×C4—121no—
1191C2×C4—121no—
1192C2×C4—121no—
1193C2×C4—121no—
1194C2×C4—121no—
1195C2×C4—121no—
1196C2×C4—121no—
1197C2×C4—121no—
1198C2×C4—121no—
1199C2×C4—121no—
1200C2×C4—121no—
1201C2×C4C4×#6714yes—
1202C2×C3—44no—
1203C2×C3—82no—
1204C2×C3#232411yescharacteristic
1205C2×C3#232411yescharacteristic
1206C2×C3#232511yescharacteristic
1207C2×C3#235811yescharacteristic
1208C2×C3#235811yescharacteristic
1209C2×C3#236611yescharacteristic
1210C2×C3#237511yescharacteristic
1211C2×C3#267011yescharacteristic
1212C2×C3#267311yescharacteristic
1213C2×C3#267311yescharacteristic
1214C2×C3#267511yescharacteristic
1215C2×C3#270511yescharacteristic
1216C2×C3#270511yescharacteristic
1217C2×C3#271211yescharacteristic
1218C2×C3#275211yescharacteristic
1219D3—82no—
1220C22—24no—
1221C22—24no—
1222C22—24no—
1223C22—42no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—42no—
1235C22—42no—
1236C22—42no—
1237C22—42no—
1238C22—42no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22—122no—
1251C22—122no—
1252C22—122no—
1253C22—122no—
1254C22—122no—
1255C22—122no—
1256C22—122no—
1257C22—241no—
1258C22—241no—
1259C22—241no—
1260C22—241no—
1261C22—241no—
1262C22—241no—
1263C22—241no—
1264C22—241no—
1265C22C2×#67⋊C411yescharacteristic
1266C22#548611yescharacteristic
1267C22#549011yescharacteristic
1268C22#549511yescharacteristic
1269C22C4×D3×D411yescharacteristic
1270C22#554511yescharacteristic
1271C22#554511yescharacteristic
1272C22#554611yescharacteristic
1273C22#555311yescharacteristic
1274C22#555911yescharacteristic
1275C22#556111yescharacteristic
1276C22#556211yescharacteristic
1277C22#559111yescharacteristic
1278C22#559211yescharacteristic
1279C22#559311yescharacteristic
1280C22#559411yescharacteristic
1281C22#559711yescharacteristic
1282C22#560511yescharacteristic
1283C22#560811yescharacteristic
1284C22#560911yescharacteristic
1285C22#561011yescharacteristic
1286C22#561511yescharacteristic
1287C22#562011yescharacteristic
1288C22#562011yescharacteristic
1289C22#565811yescharacteristic
1290C22#566211yescharacteristic
1291C22#566511yescharacteristic
1292C22#566611yescharacteristic
1293C22C2×C4×#6711yescharacteristic
1294C22D4×#6711yescharacteristic
1295C22D4×#6711yescharacteristic
1296C22#580511yescharacteristic
1297C22#580611yescharacteristic
1298C22#583311yescharacteristic
1299C22#583411yescharacteristic
1300C4—24no—
1301C4—42no—
1302C4—42no—
1303C4—42no—
1304C4—64no—
1305C4—81no—
1306C4—122no—
1307C4—122no—
1308C4—122no—
1309C4—122no—
1310C4—122no—
1311C4—241no—
1312C3#1452111yescharacteristic, complemented, Sylow
1313C2—44no—
1314C2—82no—
1315C2—242no—
1316C2#7466511yescharacteristic
1317C2#7466611yescharacteristic
1318C2#7481611yescharacteristic
1319C2#7482211yescharacteristic
1320C2#7484511yescharacteristic
1321C2#7487911yescharacteristic
1322C2#7488211yescharacteristic
1323C2#7491511yescharacteristic
1324C2#8209911yescharacteristic
1325C2#8234311yescharacteristic
1326C2#8239611yescharacteristic
1327C2#8259511yescharacteristic
1328C2#8271711yescharacteristic
1329C2#8271811yescharacteristic
1330C2#8288011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC2×C3×#386C2
socle, cosocleC24×C3C24
prime radicalC2×#5223C2
hypercenterC2×#386D3
hypocenterC3#14521
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. C2×C3×#386C2semidirect
3. C2×#5221C2semidirect
4. C2×#5213C2semidirect
5. C2×#4957C2semidirect
6. C2×#4945C2semidirect
7. C2×#4669C2semidirect
8. #72127C2semidirect
9. #71550C2semidirect
10. #71550C2semidirect
11. #71547C2semidirect
12. #71547C2semidirect
13. #69427C2semidirect
14. #69407C2semidirect
15. #69406C2semidirect
43. #5223C4semidirect
65. C2×#386D3semidirect
109. C22×#67C2×C4semidirect
142. C2×#217C2×C4semidirect
143. C2×#217D4semidirect
158. C2×(C2×D3)⋊C4C2×C4semidirect
175. C3×#95D4semidirect
184. C3⋊#95C2×C4semidirect
185. C3⋊#95D4semidirect
516. #95#67semidirect
1312. C3#14521semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#3862
C2×#52232
C2×#52212
C2×#52132
C2×#49572
C2×#49452
C2×#46692
#721272
#715502
#715472
#694272
#694072
#694062
#145213