Finite Group Databasebeta

← #10742717

Subgroups — #10742717

Order 768.

2678 conjugacy classes of subgroups.

The subgroup lattice has 1364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#883C211yesmaximal, characteristic, complemented
2C22×#884C211yesmaximal, characteristic
3C2×#4989C211yesmaximal, characteristic, complemented
4C2×#4989C211yesmaximal, characteristic, complemented
5C2×#4665C211yesmaximal, characteristic, complemented
6C2×#4668C211yesmaximal, characteristic, complemented
7C3×#1439C211yesmaximal, characteristic, complemented
8#71550C211yesmaximal, characteristic, complemented
9#71550C211yesmaximal, characteristic, complemented
10#71550C211yesmaximal, characteristic, complemented
11#71547C211yesmaximal, characteristic, complemented
12#69429C211yesmaximal, characteristic, complemented
13#69426C211yesmaximal, characteristic, complemented
14#69411C211yesmaximal, characteristic, complemented
15#69409C211yesmaximal, characteristic, complemented
16#15950—31nomaximal, Sylow
17C23×#67C2211yescharacteristic
18C23×#67C2211yescharacteristic
19C23×D12C2211yescharacteristic
20C23×C4×D3C2211yescharacteristic
21C23×C4×D3C2211yescharacteristic
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×C4⋊Dic3C2211yescharacteristic
37C22×Dic3⋊C4C2211yescharacteristic
38C22×Dic3⋊C4C2211yescharacteristic
39C22×Dic3⋊C4C2211yescharacteristic
40C2×#884—24no—
41C2×#884—24no—
42C2×#884—24no—
43C2×#883—24no—
44C2×#883—24no—
45C2×#883—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
56C2×C3⋊#95C2211yescharacteristic
57C2×C3⋊#95C2211yescharacteristic
58#4989—24no—
59#4989—24no—
60#4668—24no—
61#4665—24no—
62C22×#123—31no—
63C22×#121—31no—
64C2×#386—31no—
65C2×#385—31no—
66C2×#385—31no—
67C2×#385—31no—
68#1441—31no—
69#1441—31no—
70#1440—31no—
71#1439—31no—
72#1439D311yescharacteristic, complemented
73#1438—31no—
74#1438—31no—
75#1438—31no—
76#1438—31no—
77C25×C3C2311yescharacteristic
78C24×D3C2311yescharacteristic
79C24×D3C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C22×#67—22no—
87C22×#67—22no—
88C22×#67—22no—
89C22×#67—22no—
90C22×#67—22no—
91C22×#67—22no—
92C22×#67—22no—
93C22×#67—22no—
94C22×#67—22no—
95C22×#67—41no—
96C22×#67—41no—
97C22×#67—41no—
98C22×#67—41no—
99C22×#67D414yes—
100C23×Dic3C2311yescharacteristic
101C23×Dic3C2311yescharacteristic
102C23×Dic3C2311yescharacteristic
103C23×Dic3C2311yescharacteristic
104C23×Dic3C2311yescharacteristic
105C23×Dic3C2311yescharacteristic
106C22×D12—22no—
107C22×D12—22no—
108C22×D12—22no—
109C22×D12—22no—
110C22×D12—41no—
111C22×D12—41no—
112C22×D12D414yes—
113C22×C4×D3—22no—
114C22×C4×D3—22no—
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×D3—22no—
122C22×C4×D3—22no—
123C22×C4×D3—41no—
124C22×C4×D3—41no—
125C22×C4×D3—41no—
126C22×C4×D3—41no—
127C2×C3×C4⋊C4—22no—
128C2×C3×C4⋊C4—22no—
129C2×C3×C4⋊C4—41no—
130C2×C3×C22⋊C4—22no—
131C2×C3×C22⋊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—41no—
138C2×C3×C22⋊C4—41no—
139C2×#217—22no—
140C2×#217—22no—
141C2×#217—22no—
142C2×#217—22no—
143C2×#217—41no—
144C2×#217—41no—
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—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—41no—
165C2×(C2×D3)⋊C4—41no—
166C2×(C2×D3)⋊C4—41no—
167C2×(C2×D3)⋊C4—41no—
168C2×(C2×D3)⋊C4D414yes—
169C2×C4⋊Dic3—22no—
170C2×C4⋊Dic3—22no—
171C2×C4⋊Dic3D414yescomplemented
172C2×Dic3⋊C4—22no—
173C2×Dic3⋊C4—22no—
174C2×Dic3⋊C4—22no—
175C2×Dic3⋊C4—22no—
176C2×Dic3⋊C4—22no—
177C2×Dic3⋊C4—22no—
178C2×Dic3⋊C4—22no—
179C2×Dic3⋊C4—41no—
180C2×Dic3⋊C4D414yescomplemented
181#884—232no—
182#883—232no—
183C3×#95—22no—
184C3×#95—22no—
185C3×#95—41no—
186C3⋊#95—22no—
187C3⋊#95—22no—
188C3⋊#95—22no—
189C3⋊#95—22no—
190C3⋊#95—22no—
191C3⋊#95—22no—
192C3⋊#95—41no—
193C3⋊#95—41no—
194C3⋊#95—41no—
195C23×D4—31no—
196C23×D4—31no—
197C23×D4—31no—
198C24×C4—31no—
199C24×C4—31no—
200C2×#123—64no—
201C2×#123—64no—
202C2×#123—64no—
203C2×#121—64no—
204C2×#121—64no—
205C2×#121—64no—
206C22×C4⋊C4—31no—
207C22×C4⋊C4—31no—
208C22×C4⋊C4—31no—
209C22×C4⋊C4—31no—
210C22×C4⋊C4C2×D311yescharacteristic
211C22×C22⋊C4—31no—
212C22×C22⋊C4—31no—
213C22×C22⋊C4—31no—
214C22×C22⋊C4—31no—
215C22×C22⋊C4—31no—
216C22×C22⋊C4—31no—
217C22×C22⋊C4—31no—
218C22×C22⋊C4—31no—
219C22×C22⋊C4—31no—
220C22×C22⋊C4—31no—
221C22×C22⋊C4C2×D311yescharacteristic
222C22×C22⋊C4C2×D311yescharacteristic
223C22×C22⋊C4C2×D311yescharacteristic
224#386—64no—
225#385—64no—
226#385—64no—
227#385—64no—
228C2×#95—31no—
229C2×#95—31no—
230C2×#95—31no—
231C2×#95—31no—
232C2×#95—31no—
233C2×#95—31no—
234C2×#95—31no—
235C2×#95—31no—
236C2×#95—31no—
237C2×#95C2×D311yescharacteristic
238C2×#95C2×D311yescharacteristic
239C2×#95C2×D311yescharacteristic
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×C3C2×D412yes—
255C24×C3C2411yescharacteristic
256C23×D3—21no—
257C23×D3—21no—
258C23×D3—21no—
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×D3—21no—
274C23×D3—21no—
275C23×D3—21no—
276C23×D3—21no—
277C23×D3—21no—
278C23×D3—21no—
279C23×D3—21no—
280C23×D3C2×D412yes—
281C23×D3C2×D412yes—
282C23×D3C2×D412yes—
283C23×D3C2×D412yes—
284C23×D3#4112yes—
285C23×D3#4112yes—
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—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×C4C2×D412yes—
324C22×C3×C4C2×D412yes—
325C22×C3×C4C2×D412yes—
326C22×C3×C4C2×D412yes—
327C22×C3×C4#4112yes—
328C2×#67—28no—
329C2×#67—28no—
330C2×#67—28no—
331C2×#67—44no—
332C2×#67—44no—
333C2×#67—44no—
334C2×#67—44no—
335C2×#67—44no—
336C2×#67—44no—
337C2×#67—44no—
338C2×#67—44no—
339C2×#67—44no—
340C2×#67—44no—
341C2×#67—44no—
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×Dic3C2×D412yes—
378C22×Dic3C2×D412yes—
379C22×Dic3C2×D412yes—
380C22×Dic3C2×D412yes—
381C22×Dic3C2×D412yes—
382C22×Dic3C2×D412yes—
383C22×Dic3#4112yes—
384C2×D12—28no—
385C2×D12—28no—
386C2×D12—44no—
387C2×D12—44no—
388C2×D12—44no—
389C2×D12—44no—
390C2×D12—44no—
391C2×C4×D3—28no—
392C2×C4×D3—28no—
393C2×C4×D3—44no—
394C2×C4×D3—44no—
395C2×C4×D3—44no—
396C2×C4×D3—44no—
397C2×C4×D3—44no—
398C2×C4×D3—44no—
399C2×C4×D3—44no—
400C2×C4×D3—44no—
401C2×C4×D3—44no—
402C2×C4×D3—44no—
403C2×C4×D3—44no—
404C2×C4×D3—44no—
405C3×C4⋊C4—44no—
406C3×C22⋊C4—28no—
407C3×C22⋊C4—28no—
408C3×C22⋊C4—44no—
409#217—28no—
410#217—44no—
411(C2×D3)⋊C4—28no—
412(C2×D3)⋊C4—28no—
413(C2×D3)⋊C4—28no—
414(C2×D3)⋊C4—28no—
415(C2×D3)⋊C4—28no—
416(C2×D3)⋊C4—44no—
417(C2×D3)⋊C4—44no—
418(C2×D3)⋊C4—44no—
419C4⋊Dic3—28no—
420Dic3⋊C4—28no—
421Dic3⋊C4—28no—
422Dic3⋊C4—44no—
423C25—31no—
424C25—31no—
425C25C22×D311yescharacteristic
426C22×D4—34no—
427C22×D4—34no—
428C22×D4—62no—
429C22×D4—62no—
430C22×D4—62no—
431C22×D4—62no—
432C22×D4—62no—
433C22×D4—62no—
434C22×D4—62no—
435C22×D4—62no—
436C22×D4—62no—
437C22×D4—62no—
438C22×D4—62no—
439C22×D4—62no—
440C22×D4—62no—
441C22×D4—121no—
442C22×D4—121no—
443C22×D4—121no—
444C22×D4—121no—
445C22×D4—121no—
446C22×D4—121no—
447C23×C4—31no—
448C23×C4—31no—
449C23×C4—31no—
450C23×C4—31no—
451C23×C4—31no—
452C23×C4—31no—
453C23×C4—62no—
454C23×C4—62no—
455C23×C4—62no—
456C23×C4—62no—
457C23×C4—62no—
458C23×C4—62no—
459C23×C4—62no—
460C23×C4—62no—
461C23×C4—62no—
462C23×C4—62no—
463C23×C4—121no—
464C23×C4—121no—
465C23×C4—121no—
466C23×C4—121no—
467C23×C4C22×D311yescharacteristic
468C23×C4C22×D311yescharacteristic
469C23×C4C22×D311yescharacteristic
470C23×C4C22×D311yescharacteristic
471C23×C4C22×D311yescharacteristic
472C23×C4C22×D311yescharacteristic
473#123—632no—
474#121—632no—
475C2×C4⋊C4—22no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—34no—
478C2×C4⋊C4—34no—
479C2×C4⋊C4—41no—
480C2×C4⋊C4—62no—
481C2×C4⋊C4—62no—
482C2×C4⋊C4—62no—
483C2×C4⋊C4—62no—
484C2×C4⋊C4—62no—
485C2×C4⋊C4—62no—
486C2×C4⋊C4—62no—
487C2×C4⋊C4—62no—
488C2×C4⋊C4—62no—
489C2×C4⋊C4—121no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—22no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—34no—
498C2×C22⋊C4—41no—
499C2×C22⋊C4—41no—
500C2×C22⋊C4—62no—
501C2×C22⋊C4—62no—
502C2×C22⋊C4—62no—
503C2×C22⋊C4—62no—
504C2×C22⋊C4—62no—
505C2×C22⋊C4—62no—
506C2×C22⋊C4—62no—
507C2×C22⋊C4—62no—
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—121no—
524C2×C22⋊C4—121no—
525C2×C22⋊C4—121no—
526C2×C22⋊C4—121no—
527C2×C22⋊C4—121no—
528C2×C22⋊C4—121no—
529#95—22no—
530#95—22no—
531#95—41no—
532#95—62no—
533#95—62no—
534#95—62no—
535#95—62no—
536#95—62no—
537#95—62no—
538#95—121no—
539#95—121no—
540#95—121no—
541C23×C3—22no—
542C23×C3—22no—
543C23×C3—22no—
544C23×C3—22no—
545C23×C3—22no—
546C23×C3—22no—
547C23×C3—22no—
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×C3C22×D411yescharacteristic
577C23×C3C22×D411yescharacteristic
578C23×C3C22×D411yescharacteristic
579C23×C3C22×D411yescharacteristic
580C23×C3C22×D411yescharacteristic
581C23×C3C2×#4111yescharacteristic
582C23×C3C2×#4111yescharacteristic
583C23×C3C2×#4111yescharacteristic
584C23×C3C2×#4111yescharacteristic
585C23×C3H(5,𝔽2)11yescharacteristic
586C23×C3H(5,𝔽2)11yescharacteristic
587C23×C3H(5,𝔽2)11yescharacteristic
588C23×C3H(5,𝔽2)11yescharacteristic
589C23×C32−1+411yescharacteristic
590C23×C32−1+411yescharacteristic
591C22×D3—22no—
592C22×D3—22no—
593C22×D3—22no—
594C22×D3—22no—
595C22×D3—22no—
596C22×D3—22no—
597C22×D3—22no—
598C22×D3—22no—
599C22×D3—22no—
600C22×D3—22no—
601C22×D3—22no—
602C22×D3—22no—
603C22×D3—22no—
604C22×D3—22no—
605C22×D3—22no—
606C22×D3—22no—
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—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—
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#12014yes—
660C22×D3#12314yescomplemented
661C2×C3×C4—22no—
662C2×C3×C4—22no—
663C2×C3×C4—22no—
664C2×C3×C4—22no—
665C2×C3×C4—22no—
666C2×C3×C4—22no—
667C2×C3×C4—22no—
668C2×C3×C4—22no—
669C2×C3×C4—22no—
670C2×C3×C4—22no—
671C2×C3×C4—22no—
672C2×C3×C4—22no—
673C2×C3×C4—22no—
674C2×C3×C4—22no—
675C2×C3×C4—22no—
676C2×C3×C4—41no—
677C2×C3×C4—41no—
678C2×C3×C4—41no—
679C2×C3×C4—41no—
680C2×C3×C4—41no—
681C2×C3×C4—41no—
682C2×C3×C4—41no—
683C2×C3×C4—41no—
684C2×C3×C4—41no—
685C2×C3×C4—41no—
686C2×C3×C4—41no—
687C2×C3×C4—41no—
688C2×C3×C4—41no—
689C2×C3×C4—41no—
690C2×C3×C4—41no—
691C2×C3×C4—41no—
692C2×C3×C4—41no—
693C2×C3×C4—41no—
694C2×C3×C4—41no—
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—
703#67—416no—
704#67—416no—
705C2×Dic3—22no—
706C2×Dic3—22no—
707C2×Dic3—22no—
708C2×Dic3—22no—
709C2×Dic3—22no—
710C2×Dic3—22no—
711C2×Dic3—22no—
712C2×Dic3—22no—
713C2×Dic3—22no—
714C2×Dic3—22no—
715C2×Dic3—22no—
716C2×Dic3—22no—
717C2×Dic3—22no—
718C2×Dic3—22no—
719C2×Dic3—22no—
720C2×Dic3—22no—
721C2×Dic3—22no—
722C2×Dic3—22no—
723C2×Dic3—41no—
724C2×Dic3—41no—
725C2×Dic3—41no—
726C2×Dic3—41no—
727C2×Dic3—41no—
728C2×Dic3—41no—
729C2×Dic3—41no—
730C2×Dic3—41no—
731C2×Dic3—41no—
732C2×Dic3—41no—
733C2×Dic3—41no—
734C2×Dic3—41no—
735C2×Dic3—41no—
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#12014yes—
747D12—416no—
748C4×D3—416no—
749C4×D3—416no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—32no—
765C24—32no—
766C24—32no—
767C24—32no—
768C24—32no—
769C24—32no—
770C24—61no—
771C24—61no—
772C24—61no—
773C24—61no—
774C24—61no—
775C24—61no—
776C24—61no—
777C24—61no—
778C24—61no—
779C24—61no—
780C24—61no—
781C24—61no—
782C24—61no—
783C24—61no—
784C24—61no—
785C24—61no—
786C24—61no—
787C24—61no—
788C24—61no—
789C24—61no—
790C24—61no—
791C24—61no—
792C24—61no—
793C24—61no—
794C24D3×D412yes—
795C24C23×D311yescharacteristic
796C2×D4—68no—
797C2×D4—68no—
798C2×D4—68no—
799C2×D4—68no—
800C2×D4—68no—
801C2×D4—124no—
802C2×D4—124no—
803C2×D4—124no—
804C2×D4—124no—
805C2×D4—124no—
806C2×D4—124no—
807C2×D4—124no—
808C2×D4—124no—
809C2×D4—124no—
810C2×D4—124no—
811C2×D4—124no—
812C2×D4—124no—
813C2×D4—124no—
814C2×D4—124no—
815C2×D4—124no—
816C2×D4—124no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
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—32no—
855C22×C4—32no—
856C22×C4—32no—
857C22×C4—32no—
858C22×C4—32no—
859C22×C4—32no—
860C22×C4—32no—
861C22×C4—68no—
862C22×C4—68no—
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×C4—61no—
878C22×C4—61no—
879C22×C4—61no—
880C22×C4—61no—
881C22×C4—61no—
882C22×C4—61no—
883C22×C4—61no—
884C22×C4—61no—
885C22×C4—61no—
886C22×C4—61no—
887C22×C4—61no—
888C22×C4—61no—
889C22×C4—61no—
890C22×C4—61no—
891C22×C4—61no—
892C22×C4—61no—
893C22×C4—61no—
894C22×C4—61no—
895C22×C4—61no—
896C22×C4—61no—
897C22×C4—61no—
898C22×C4—124no—
899C22×C4—124no—
900C22×C4—124no—
901C22×C4—124no—
902C22×C4—124no—
903C22×C4—124no—
904C22×C4—124no—
905C22×C4—124no—
906C22×C4—124no—
907C22×C4—124no—
908C22×C4—124no—
909C22×C4—124no—
910C22×C4#23512yes—
911C22×C4D3×D412yes—
912C22×C4D3×D412yes—
913C22×C4D3×D412yes—
914C22×C4D3×D412yes—
915C4⋊C4—44no—
916C4⋊C4—68no—
917C4⋊C4—68no—
918C4⋊C4—68no—
919C4⋊C4—124no—
920C22⋊C4—28no—
921C22⋊C4—28no—
922C22⋊C4—44no—
923C22⋊C4—68no—
924C22⋊C4—68no—
925C22⋊C4—68no—
926C22⋊C4—68no—
927C22⋊C4—68no—
928C22⋊C4—68no—
929C22⋊C4—124no—
930C22⋊C4—124no—
931C22⋊C4—124no—
932C22⋊C4—124no—
933C22×C3—42no—
934C22×C3—42no—
935C22×C3—42no—
936C22×C3—42no—
937C22×C3—42no—
938C22×C3—42no—
939C22×C3—42no—
940C22×C3—81no—
941C22×C3—81no—
942C22×C3—81no—
943C22×C3—81no—
944C22×C3—81no—
945C22×C3—81no—
946C22×C3—81no—
947C22×C3—81no—
948C22×C3C2×#12011yescharacteristic
949C22×C3C2×#12011yescharacteristic
950C22×C3C2×#12311yescharacteristic
951C22×C3#52511yescharacteristic
952C22×C3#52511yescharacteristic
953C22×C3#52511yescharacteristic
954C22×C3#53411yescharacteristic
955C22×C3#53411yescharacteristic
956C22×C3#53611yescharacteristic
957C22×C3#53711yescharacteristic
958C22×C3#53711yescharacteristic
959C22×C3#53811yescharacteristic
960C22×C3#53811yescharacteristic
961C22×C3#53911yescharacteristic
962C22×C3#53911yescharacteristic
963C22×C3D4211yescharacteristic
964C22×C3D4211yescharacteristic
965C22×C3D4211yescharacteristic
966C22×C3D4211yescharacteristic
967C22×C3#54611yescharacteristic
968C22×C3#54611yescharacteristic
969C22×C3#54611yescharacteristic
970C22×C3#54611yescharacteristic
971C22×C3#54711yescharacteristic
972C22×C3#54711yescharacteristic
973C22×C3#54711yescharacteristic
974C22×C3#54711yescharacteristic
975C22×C3#54811yescharacteristic
976C22×C3#54811yescharacteristic
977C22×C3#55011yescharacteristic
978C22×C3#55011yescharacteristic
979C22×C3#55311yescharacteristic
980C22×C3#55311yescharacteristic
981C22×C3#56211yescharacteristic
982C22×C3#56211yescharacteristic
983C2×D3—24no—
984C2×D3—24no—
985C2×D3—24no—
986C2×D3—24no—
987C2×D3—24no—
988C2×D3—24no—
989C2×D3—42no—
990C2×D3—42no—
991C2×D3—42no—
992C2×D3—42no—
993C2×D3—42no—
994C2×D3—42no—
995C2×D3—42no—
996C2×D3—42no—
997C2×D3—42no—
998C2×D3—42no—
999C2×D3—42no—
1000C2×D3—42no—
1001C2×D3—42no—
1002C2×D3—42no—
1003C2×D3—42no—
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—
1013C3×C4—42no—
1014C3×C4—42no—
1015C3×C4—42no—
1016C3×C4—42no—
1017C3×C4—42no—
1018C3×C4—81no—
1019Dic3—24no—
1020Dic3—42no—
1021Dic3—42no—
1022Dic3—42no—
1023Dic3—42no—
1024Dic3—81no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—34no—
1033C23—34no—
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—62no—
1063C23—62no—
1064C23—62no—
1065C23—62no—
1066C23—62no—
1067C23—62no—
1068C23—62no—
1069C23—62no—
1070C23—62no—
1071C23—62no—
1072C23—62no—
1073C23—62no—
1074C23—62no—
1075C23—62no—
1076C23—62no—
1077C23—62no—
1078C23—62no—
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—121no—
1099C23—121no—
1100C23—121no—
1101C23—121no—
1102C23—121no—
1103C23—121no—
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—
1130C23C2×#23511yescharacteristic
1131C23C2×D3×D411yescharacteristic
1132C23C2×D3×D411yescharacteristic
1133C23C2×D3×D411yescharacteristic
1134C23C2×D3×D411yescharacteristic
1135C23C2×D3×D411yescharacteristic
1136C23#100411yescharacteristic
1137C23#100411yescharacteristic
1138C23#100711yescharacteristic
1139C23D3×#4111yescharacteristic
1140C23D3×#4111yescharacteristic
1141C23D3×#4111yescharacteristic
1142C23#100911yescharacteristic
1143C23#100911yescharacteristic
1144C23#101011yescharacteristic
1145D4—1216no—
1146D4—1216no—
1147D4—1216no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—34no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—62no—
1192C2×C4—62no—
1193C2×C4—62no—
1194C2×C4—62no—
1195C2×C4—62no—
1196C2×C4—62no—
1197C2×C4—62no—
1198C2×C4—62no—
1199C2×C4—62no—
1200C2×C4—62no—
1201C2×C4—62no—
1202C2×C4—62no—
1203C2×C4—62no—
1204C2×C4—62no—
1205C2×C4—62no—
1206C2×C4—62no—
1207C2×C4—62no—
1208C2×C4—62no—
1209C2×C4—1216no—
1210C2×C4—1216no—
1211C2×C4—121no—
1212C2×C4—121no—
1213C2×C4—121no—
1214C2×C4—121no—
1215C2×C4—121no—
1216C2×C4—121no—
1217C2×C4—121no—
1218C2×C4—121no—
1219C2×C4—121no—
1220C2×C4—121no—
1221C2×C4—121no—
1222C2×C4—121no—
1223C2×C4—121no—
1224C2×C4—121no—
1225C2×C4—121no—
1226C2×C4—121no—
1227C2×C4—121no—
1228C2×C4—121no—
1229C2×C4—121no—
1230C2×C4—121no—
1231C2×C4—121no—
1232C2×C4—121no—
1233C2×C4—121no—
1234C2×C3—82no—
1235C2×C3#240311yescharacteristic
1236C2×C3#240511yescharacteristic
1237C2×C3#240611yescharacteristic
1238C2×C3#240711yescharacteristic
1239C2×C3#240711yescharacteristic
1240C2×C3#244311yescharacteristic
1241C2×C3#244311yescharacteristic
1242C2×C3#245611yescharacteristic
1243C2×C3#245611yescharacteristic
1244C2×C3#268111yescharacteristic
1245C2×C3#268111yescharacteristic
1246C2×C3#268211yescharacteristic
1247C2×C3#268211yescharacteristic
1248C2×C3#270811yescharacteristic
1249C2×C3#270811yescharacteristic
1250D3—44no—
1251D3—44no—
1252C22—42no—
1253C22—42no—
1254C22—42no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—64no—
1260C22—64no—
1261C22—64no—
1262C22—64no—
1263C22—64no—
1264C22—64no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22—81no—
1269C22—81no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22—122no—
1274C22—122no—
1275C22—122no—
1276C22—122no—
1277C22—122no—
1278C22—122no—
1279C22—122no—
1280C22—122no—
1281C22—122no—
1282C22—122no—
1283C22—122no—
1284C22—122no—
1285C22—122no—
1286C22—122no—
1287C22—122no—
1288C22—122no—
1289C22—122no—
1290C22—122no—
1291C22—122no—
1292C22—122no—
1293C22—122no—
1294C22—122no—
1295C22—122no—
1296C22—122no—
1297C22#549411yescharacteristic
1298C22#550711yescharacteristic
1299C22#553011yescharacteristic
1300C22#554711yescharacteristic
1301C22#554711yescharacteristic
1302C22#555111yescharacteristic
1303C22#555311yescharacteristic
1304C22D3×#12011yescharacteristic
1305C22D3×#12011yescharacteristic
1306C22#559011yescharacteristic
1307C22#559711yescharacteristic
1308C22#559911yescharacteristic
1309C22#560511yescharacteristic
1310C22#560511yescharacteristic
1311C22#560911yescharacteristic
1312C22#560911yescharacteristic
1313C22#561011yescharacteristic
1314C22#561211yescharacteristic
1315C22#562811yescharacteristic
1316C22#562911yescharacteristic
1317C22#563111yescharacteristic
1318C22#563311yescharacteristic
1319C22#563811yescharacteristic
1320C22#564711yescharacteristic
1321C22D3×#12311yescharacteristic
1322C22#565411yescharacteristic
1323C22#565511yescharacteristic
1324C22#565611yescharacteristic
1325C22#566111yescharacteristic
1326C22#567611yescharacteristic
1327C22#567711yescharacteristic
1328C22#568411yescharacteristic
1329C22#570411yescharacteristic
1330C22#570711yescharacteristic
1331C22#571711yescharacteristic
1332C4—42no—
1333C4—42no—
1334C4—42no—
1335C4—42no—
1336C4—42no—
1337C4—64no—
1338C4—81no—
1339C4—122no—
1340C4—122no—
1341C4—122no—
1342C4—122no—
1343C4—241no—
1344C3#1595011yescharacteristic, complemented, Sylow
1345C2—82no—
1346C2—124no—
1347C2—124no—
1348C2#7404211yescharacteristic
1349C2#7440411yescharacteristic
1350C2#7460011yescharacteristic
1351C2#7489911yescharacteristic
1352C2#7550411yescharacteristic
1353C2#7584811yescharacteristic
1354C2#7646611yescharacteristic
1355C2#7675311yescharacteristic
1356C2#7687511yescharacteristic
1357C2#7689411yescharacteristic
1358C2#7710611yescharacteristic
1359C2#7743111yescharacteristic
1360C2#7743211yescharacteristic
1361C2#7770011yescharacteristic
1362C2#7810311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1439C2
prime radicalC22×#884C2
hypercenter#1439D3
hypocenterC3#15950
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
1. C22×#883C2semidirect
3. C2×#4989C2semidirect
4. C2×#4989C2semidirect
5. C2×#4665C2semidirect
6. C2×#4668C2semidirect
7. C3×#1439C2semidirect
8. #71550C2semidirect
9. #71550C2semidirect
10. #71550C2semidirect
11. #71547C2semidirect
12. #69429C2semidirect
13. #69426C2semidirect
14. #69411C2semidirect
15. #69409C2semidirect
72. #1439D3semidirect
171. C2×C4⋊Dic3D4semidirect
180. C2×Dic3⋊C4D4semidirect
660. C22×D3#123semidirect
1344. C3#15950semidirect

Maximal subgroups

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

subgroupindex
C22×#8832
C22×#8842
C2×#49892
C2×#46652
C2×#46682
C3×#14392
#715502
#715472
#694292
#694262
#694112
#694092
#159503