Finite Group Databasebeta

← #10718644

Subgroups — #10718644

Order 768.

3166 conjugacy classes of subgroups.

The subgroup lattice has 1398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#895C211yesmaximal, characteristic
2C22×C4×D12C211yesmaximal, characteristic, complemented
3C2×#4665C211yesmaximal, characteristic, complemented
4C2×#4665C211yesmaximal, characteristic, complemented
5C2×#4665C211yesmaximal, characteristic, complemented
6C2×#4665C211yesmaximal, characteristic, complemented
7C2×D3×#95C211yesmaximal, characteristic, complemented
8C3×#1436C211yesmaximal, characteristic, complemented
9#71565C211yesmaximal, characteristic, complemented
10#71537C211yesmaximal, characteristic, complemented
11#69429C211yesmaximal, characteristic, complemented
12#69427C211yesmaximal, characteristic, complemented
13#69426C211yesmaximal, characteristic, complemented
14(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
15(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
16#14023—31nomaximal, Sylow
17C23×D12C2211yescharacteristic
18C23×D12C2211yescharacteristic
19C23×D12C2211yescharacteristic
20C23×C4×D3C2211yescharacteristic
21C23×C4×D3C2211yescharacteristic
22C23×C4×D3C2211yescharacteristic
23C23×C4×D3C2211yescharacteristic
24C22×C3×C4⋊C4C2211yescharacteristic
25C22×C3×C42C2211yescharacteristic
26C22×(C2×D3)⋊C4C2211yescharacteristic
27C22×(C2×D3)⋊C4C2211yescharacteristic
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×C4⋊Dic3C2211yescharacteristic
38C2×#895—24no—
39C2×#895—24no—
40C2×#895C418yescomplemented
41C2×C4×D12—24no—
42C2×C4×D12—24no—
43C2×C4×D12—24no—
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
55C2×C3⋊#95C2211yescharacteristic
56C2×C3⋊#95C2211yescharacteristic
57C2×C3⋊#95C2211yescharacteristic
58#4665—24no—
59#4665—24no—
60#4665—24no—
61#4665—24no—
62D3×#95—24no—
63C22×#121—31no—
64C22×C4×D4—31no—
65C2×#386—31no—
66C2×#386—31no—
67C2×#386—31no—
68C2×#386—31no—
69C22×#95—31no—
70#1441—31no—
71#1440—31no—
72#1439—31no—
73#1438—31no—
74#1437—31no—
75#1436D311yescharacteristic, complemented
76C22⋊#95—31no—
77C22⋊#95—31no—
78C24×D3C2311yescharacteristic
79C24×D3C2311yescharacteristic
80C24×D3C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C23×C3×C4C2311yescharacteristic
87C23×C3×C4C2311yescharacteristic
88C23×Dic3C2311yescharacteristic
89C23×Dic3C2311yescharacteristic
90C23×Dic3C2311yescharacteristic
91C23×Dic3C2311yescharacteristic
92C23×Dic3C2311yescharacteristic
93C22×D12—22no—
94C22×D12—22no—
95C22×D12—22no—
96C22×D12—22no—
97C22×D12—22no—
98C22×D12—22no—
99C22×D12—22no—
100C22×D12—22no—
101C22×D12—22no—
102C22×D12—22no—
103C22×D12—22no—
104C22×D12—22no—
105C22×D12—22no—
106C22×D12—22no—
107C22×D12—41no—
108C22×D12—41no—
109C22×D12C2×C414yes—
110C22×D12C2×C414yescomplemented
111C22×D12C2×C414yescomplemented
112C22×D12D414yes—
113C22×D12D414yes—
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—22no—
124C22×C4×D3—22no—
125C22×C4×D3—22no—
126C22×C4×D3—22no—
127C22×C4×D3—22no—
128C22×C4×D3—22no—
129C22×C4×D3—22no—
130C22×C4×D3—22no—
131C22×C4×D3—22no—
132C22×C4×D3—41no—
133C22×C4×D3—41no—
134C22×C4×D3—41no—
135C22×C4×D3—41no—
136C22×C4×D3—41no—
137C22×C4×D3—41no—
138C22×C4×D3—41no—
139C22×C4×D3—41no—
140C22×C4×D3C2×C414yescomplemented
141C22×C4×D3D414yescomplemented
142C2×C3×C4⋊C4—22no—
143C2×C3×C4⋊C4—22no—
144C2×C3×C4⋊C4C2×C414yescomplemented
145C2×C3×C42—22no—
146C2×C3×C42—22no—
147C2×C3×C42—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×(C2×D3)⋊C4—41no—
175C2×(C2×D3)⋊C4—41no—
176C2×(C2×D3)⋊C4—41no—
177C2×(C2×D3)⋊C4—41no—
178C2×(C2×D3)⋊C4C2×C414yescomplemented
179C2×(C2×D3)⋊C4C2×C414yescomplemented
180C2×(C2×D3)⋊C4D414yescomplemented
181C2×C4⋊Dic3—22no—
182C2×C4⋊Dic3—22no—
183C2×C4⋊Dic3—22no—
184#895—232no—
185C4×D12—232no—
186C3×#95—22no—
187C3×#95—22no—
188C3×#95—22no—
189C3×#95—22no—
190C3×#95D414yescomplemented
191C3⋊#95—22no—
192C3⋊#95—22no—
193C3⋊#95—22no—
194C3⋊#95—22no—
195C3⋊#95—22no—
196C3⋊#95—22no—
197C3⋊#95—22no—
198C3⋊#95—41no—
199C3⋊#95—41no—
200C23×D4—31no—
201C23×D4—31no—
202C23×D4—31no—
203C24×C4—31no—
204C24×C4—31no—
205C24×C4—31no—
206C24×C4—31no—
207C2×#121—38no—
208C2×#121—64no—
209C2×#121—64no—
210C2×C4×D4—64no—
211C2×C4×D4—64no—
212C2×C4×D4—64no—
213C22×C4⋊C4—31no—
214C22×C4⋊C4C2×D311yescharacteristic
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⋊C4—31no—
222C22×C22⋊C4—31no—
223C22×C22⋊C4—31no—
224C22×C22⋊C4—31no—
225C22×C22⋊C4—31no—
226C22×C42C2×D311yescharacteristic
227#386—64no—
228#386—64no—
229#386—64no—
230#386—64no—
231C2×#95—31no—
232C2×#95—31no—
233C2×#95—31no—
234C2×#95—31no—
235C2×#95—31no—
236C2×#95—31no—
237C2×#95—31no—
238C2×#95—31no—
239C2×#95—31no—
240C2×#95—64no—
241C2×#95C2×D311yescharacteristic
242C2×#95C2×D311yescharacteristic
243C2×#95C2×D311yescharacteristic
244C2×#95C2×D311yescharacteristic
245C2×#95C2×D311yescharacteristic
246C24×C3C2411yescharacteristic
247C23×D3—21no—
248C23×D3—21no—
249C23×D3—21no—
250C23×D3—21no—
251C23×D3—21no—
252C23×D3—21no—
253C23×D3—21no—
254C23×D3—21no—
255C23×D3—21no—
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×D3—21no—
281C23×D3C22×C412yes—
282C23×D3C22×C412yes—
283C23×D3C22×C412yes—
284C23×D3C2×D412yes—
285C23×D3C2×D412yes—
286C23×D3C2×D412yes—
287C23×D3C2×D412yes—
288C23×D3C2×D412yes—
289C23×D3C2×D412yes—
290C23×D3#4112yes—
291C23×D3#4112yes—
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×C4—21no—
324C22×C3×C4—21no—
325C22×C3×C4—21no—
326C22×C3×C4—21no—
327C22×C3×C4—21no—
328C22×C3×C4—21no—
329C22×C3×C4C22×C412yes—
330C22×C3×C4C22×C412yes—
331C22×C3×C4C22×C412yes—
332C22×C3×C4C2×D412yes—
333C22×C3×C4C2×D412yes—
334C22×C3×C4C2×D412yes—
335C22×C3×C4C2×D412yes—
336C22×C3×C4C2×D412yes—
337C22×C3×C4C2×D412yes—
338C22×C3×C4C2×D412yes—
339C22×C3×C4#4112yes—
340C22×C3×C4#4112yes—
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×Dic3C22×C412yes—
373C22×Dic3C2×D412yes—
374C22×Dic3C2×D412yes—
375C22×Dic3#4112yes—
376C2×D12—28no—
377C2×D12—28no—
378C2×D12—28no—
379C2×D12—28no—
380C2×D12—28no—
381C2×D12—28no—
382C2×D12—28no—
383C2×D12—28no—
384C2×D12—28no—
385C2×D12—28no—
386C2×D12—28no—
387C2×D12—44no—
388C2×D12—44no—
389C2×D12—44no—
390C2×D12—44no—
391C2×D12—44no—
392C2×D12—44no—
393C2×D12—44no—
394C2×D12—44no—
395C2×D12—44no—
396C2×D12C22⋊C4116yescomplemented
397C2×C4×D3—28no—
398C2×C4×D3—28no—
399C2×C4×D3—28no—
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×C4×D3—44no—
408C2×C4×D3—44no—
409C2×C4×D3—44no—
410C2×C4×D3—44no—
411C2×C4×D3—44no—
412C2×C4×D3—44no—
413C2×C4×D3—44no—
414C2×C4×D3—44no—
415C2×C4×D3—44no—
416C2×C4×D3—44no—
417C2×C4×D3—44no—
418C2×C4×D3—44no—
419C2×C4×D3—44no—
420C2×C4×D3—44no—
421C2×C4×D3—44no—
422C2×C4×D3—44no—
423C2×C4×D3—44no—
424C2×C4×D3—44no—
425C3×C4⋊C4—28no—
426C3×C42—28no—
427(C2×D3)⋊C4—28no—
428(C2×D3)⋊C4—28no—
429(C2×D3)⋊C4—28no—
430(C2×D3)⋊C4—28no—
431(C2×D3)⋊C4—44no—
432(C2×D3)⋊C4—44no—
433(C2×D3)⋊C4—44no—
434(C2×D3)⋊C4—44no—
435(C2×D3)⋊C4—44no—
436(C2×D3)⋊C4—44no—
437(C2×D3)⋊C4—44no—
438C4⋊Dic3—28no—
439C25—31no—
440C25—31no—
441C25—31no—
442C22×D4—34no—
443C22×D4—34no—
444C22×D4—34no—
445C22×D4—34no—
446C22×D4—34no—
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—
463C23×C4—31no—
464C23×C4—31no—
465C23×C4—31no—
466C23×C4—31no—
467C23×C4—34no—
468C23×C4—34no—
469C23×C4—31no—
470C23×C4—62no—
471C23×C4—62no—
472C23×C4—62no—
473C23×C4—62no—
474C23×C4—62no—
475C23×C4—62no—
476C23×C4—62no—
477C23×C4—62no—
478C23×C4—62no—
479C23×C4—62no—
480C23×C4—62no—
481C23×C4—62no—
482C23×C4—62no—
483C23×C4—62no—
484C23×C4—62no—
485C23×C4—62no—
486C23×C4—62no—
487C23×C4—62no—
488C23×C4—121no—
489C23×C4—121no—
490C23×C4—121no—
491C23×C4—121no—
492C23×C4—121no—
493C23×C4—121no—
494C23×C4—121no—
495C23×C4—121no—
496C23×C4C22×D311yescharacteristic
497C23×C4C22×D311yescharacteristic
498C23×C4C22×D311yescharacteristic
499C23×C4C22×D311yescharacteristic
500C23×C4C22×D311yescharacteristic
501C23×C4C22×D311yescharacteristic
502C23×C4C22×D311yescharacteristic
503#121—632no—
504C4×D4—632no—
505C2×C4⋊C4—22no—
506C2×C4⋊C4—22no—
507C2×C4⋊C4—62no—
508C2×C4⋊C4—62no—
509C2×C4⋊C4—62no—
510C2×C4⋊C4C4×D314yescomplemented
511C2×C22⋊C4—34no—
512C2×C22⋊C4—34no—
513C2×C22⋊C4—34no—
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×C22⋊C4—121no—
542C2×C22⋊C4—121no—
543C2×C22⋊C4—121no—
544C2×C42—22no—
545C2×C42—22no—
546C2×C42—22no—
547#95—22no—
548#95—22no—
549#95—22no—
550#95—22no—
551#95—62no—
552#95—62no—
553#95—62no—
554#95—62no—
555#95—62no—
556#95—62no—
557#95—62no—
558#95—121no—
559#95—121no—
560#95D1214yescomplemented
561C23×C3C23×C411yescharacteristic
562C23×C3C22×D411yescharacteristic
563C23×C3C22×D411yescharacteristic
564C23×C3C22×D411yescharacteristic
565C23×C3C22×D411yescharacteristic
566C23×C3C22×D411yescharacteristic
567C23×C3C2×#4111yescharacteristic
568C23×C3C2×#4111yescharacteristic
569C23×C3C2×#4111yescharacteristic
570C23×C3C2×#4111yescharacteristic
571C23×C3C2×#4111yescharacteristic
572C23×C3H(5,𝔽2)11yescharacteristic
573C23×C3H(5,𝔽2)11yescharacteristic
574C23×C3H(5,𝔽2)11yescharacteristic
575C23×C32−1+411yescharacteristic
576C22×D3—22no—
577C22×D3—22no—
578C22×D3—22no—
579C22×D3—22no—
580C22×D3—22no—
581C22×D3—22no—
582C22×D3—22no—
583C22×D3—22no—
584C22×D3—22no—
585C22×D3—22no—
586C22×D3—22no—
587C22×D3—22no—
588C22×D3—22no—
589C22×D3—22no—
590C22×D3—22no—
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—22no—
628C22×D3—22no—
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—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×D3C2×C22⋊C414yes—
674C22×D3C2×C22⋊C414yes—
675C22×D3C4×D414yes—
676C22×D3C4×D414yes—
677C22×D3#12014yes—
678C22×D3#12114yes—
679C22×D3#12114yes—
680C22×D3#12314yes—
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—22no—
696C2×C3×C4—22no—
697C2×C3×C4—22no—
698C2×C3×C4—22no—
699C2×C3×C4—22no—
700C2×C3×C4—22no—
701C2×C3×C4—22no—
702C2×C3×C4—22no—
703C2×C3×C4—22no—
704C2×C3×C4—22no—
705C2×C3×C4—22no—
706C2×C3×C4—22no—
707C2×C3×C4—22no—
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—
719C2×C3×C4—41no—
720C2×C3×C4—41no—
721C2×C3×C4—41no—
722C2×C3×C4—41no—
723C2×C3×C4—41no—
724C2×C3×C4—41no—
725C2×C3×C4—41no—
726C2×C3×C4—41no—
727C2×C3×C4C2×C22⋊C414yes—
728C2×C3×C4C4×D414yescomplemented
729C2×C3×C4#12114yescomplemented
730C2×Dic3—22no—
731C2×Dic3—22no—
732C2×Dic3—22no—
733C2×Dic3—22no—
734C2×Dic3—22no—
735C2×Dic3—22no—
736C2×Dic3—22no—
737C2×Dic3—22no—
738C2×Dic3—22no—
739C2×Dic3—22no—
740C2×Dic3—22no—
741C2×Dic3—22no—
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—41no—
757C2×Dic3—41no—
758C2×Dic3—41no—
759C2×Dic3—41no—
760C2×Dic3—41no—
761C2×Dic3—41no—
762C2×Dic3—41no—
763C2×Dic3—41no—
764C2×Dic3—41no—
765D12—232no—
766D12—416no—
767D12—416no—
768C4×D3—416no—
769C4×D3—416no—
770C4×D3—416no—
771C4×D3—416no—
772C24—32no—
773C24—32no—
774C24—32no—
775C24—32no—
776C24—32no—
777C24—32no—
778C24—32no—
779C24—32no—
780C24—32no—
781C24—32no—
782C24—32no—
783C24—61no—
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—
810C24—61no—
811C24—61no—
812C24—61no—
813C24—61no—
814C24—61no—
815C24—61no—
816C24—61no—
817C24C23×D311yescharacteristic
818C2×D4—316no—
819C2×D4—68no—
820C2×D4—68no—
821C2×D4—68no—
822C2×D4—68no—
823C2×D4—68no—
824C2×D4—68no—
825C2×D4—68no—
826C2×D4—68no—
827C2×D4—68no—
828C2×D4—68no—
829C2×D4—68no—
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—
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—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—68no—
881C22×C4—68no—
882C22×C4—68no—
883C22×C4—68no—
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—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—68no—
909C22×C4—68no—
910C22×C4—61no—
911C22×C4—61no—
912C22×C4—61no—
913C22×C4—61no—
914C22×C4—61no—
915C22×C4—61no—
916C22×C4—61no—
917C22×C4—124no—
918C22×C4—124no—
919C22×C4—124no—
920C22×C4—124no—
921C22×C4—124no—
922C22×C4—124no—
923C22×C4—124no—
924C22×C4—124no—
925C22×C4—124no—
926C22×C4—124no—
927C22×C4—124no—
928C22×C4—124no—
929C22×C4—124no—
930C22×C4—124no—
931C22×C4—124no—
932C22×C4—124no—
933C22×C4—124no—
934C22×C4—124no—
935C22×C4—124no—
936C22×C4—124no—
937C22×C4—124no—
938C22×C4—124no—
939C22×C4C2×C4×D312yes—
940C22×C4C2×C4×D312yes—
941C22×C4C2×C4×D312yes—
942C22×C4C2×D1212yes—
943C22×C4C2×D1212yes—
944C22×C4C2×D1212yes—
945C22×C4#23512yes—
946C22×C4D3×D412yes—
947C22×C4D3×D412yes—
948C22×C4D3×D412yes—
949C22×C4D3×D412yes—
950C22×C4#23912yes—
951C4⋊C4—28no—
952C4⋊C4—68no—
953C22⋊C4—68no—
954C22⋊C4—68no—
955C22⋊C4—68no—
956C22⋊C4—68no—
957C22⋊C4—124no—
958C22⋊C4—124no—
959C22⋊C4—124no—
960C22⋊C4—124no—
961C22⋊C4—124no—
962C22⋊C4—124no—
963C22⋊C4—124no—
964C42—28no—
965C22×C3C22×C22⋊C411yescharacteristic
966C22×C3C2×C4×D411yescharacteristic
967C22×C3C2×C4×D411yescharacteristic
968C22×C3C2×C4×D411yescharacteristic
969C22×C3C4×#4111yescharacteristic
970C22×C3#51811yescharacteristic
971C22×C3#52011yescharacteristic
972C22×C3C2×#12011yescharacteristic
973C22×C3C2×#12111yescharacteristic
974C22×C3C2×#12111yescharacteristic
975C22×C3C2×#12111yescharacteristic
976C22×C3C2×#12311yescharacteristic
977C22×C3#52511yescharacteristic
978C22×C3#52911yescharacteristic
979C22×C3#53211yescharacteristic
980C22×C3#53411yescharacteristic
981C22×C3#53711yescharacteristic
982C22×C3#53811yescharacteristic
983C22×C3#53911yescharacteristic
984C22×C3D4211yescharacteristic
985C22×C3D4211yescharacteristic
986C22×C3D4211yescharacteristic
987C22×C3#54611yescharacteristic
988C22×C3#54611yescharacteristic
989C22×C3#54611yescharacteristic
990C22×C3#54611yescharacteristic
991C22×C3#54611yescharacteristic
992C22×C3#54611yescharacteristic
993C22×C3#54711yescharacteristic
994C22×C3#54711yescharacteristic
995C22×C3#54711yescharacteristic
996C22×C3#54811yescharacteristic
997C22×C3#55311yescharacteristic
998C22×C3#55311yescharacteristic
999C22×C3#55311yescharacteristic
1000C2×D3—24no—
1001C2×D3—24no—
1002C2×D3—24no—
1003C2×D3—24no—
1004C2×D3—24no—
1005C2×D3—24no—
1006C2×D3—24no—
1007C2×D3—24no—
1008C2×D3—24no—
1009C2×D3—24no—
1010C2×D3—24no—
1011C2×D3—24no—
1012C2×D3—24no—
1013C2×D3—24no—
1014C2×D3—24no—
1015C2×D3—24no—
1016C2×D3—24no—
1017C2×D3—42no—
1018C2×D3—42no—
1019C2×D3—42no—
1020C2×D3—42no—
1021C2×D3—42no—
1022C2×D3—42no—
1023C2×D3—42no—
1024C2×D3—42no—
1025C2×D3—42no—
1026C2×D3—42no—
1027C2×D3—42no—
1028C2×D3—42no—
1029C2×D3—42no—
1030C2×D3—42no—
1031C2×D3—42no—
1032C2×D3—42no—
1033C2×D3—42no—
1034C2×D3—42no—
1035C2×D3—42no—
1036C2×D3—81no—
1037C2×D3—81no—
1038C2×D3—81no—
1039C2×D3—81no—
1040C2×D3—81no—
1041C2×D3—81no—
1042C2×D3—81no—
1043C2×D3—81no—
1044C2×D3#38618yescomplemented
1045C3×C4—24no—
1046C3×C4—24no—
1047C3×C4—24no—
1048C3×C4—42no—
1049C3×C4—42no—
1050C3×C4—42no—
1051C3×C4—81no—
1052Dic3—42no—
1053Dic3—42no—
1054Dic3—42no—
1055Dic3—42no—
1056Dic3—81no—
1057C23—34no—
1058C23—34no—
1059C23—34no—
1060C23—34no—
1061C23—34no—
1062C23—34no—
1063C23—34no—
1064C23—34no—
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—62no—
1099C23—62no—
1100C23—62no—
1101C23—62no—
1102C23—62no—
1103C23—62no—
1104C23—62no—
1105C23—62no—
1106C23—62no—
1107C23—62no—
1108C23—62no—
1109C23—62no—
1110C23—62no—
1111C23—62no—
1112C23—62no—
1113C23—62no—
1114C23—62no—
1115C23—62no—
1116C23—62no—
1117C23—62no—
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—
1148C23—121no—
1149C23—121no—
1150C23—121no—
1151C23—121no—
1152C23—121no—
1153C23—121no—
1154C23—121no—
1155C23—121no—
1156C23—121no—
1157C23—121no—
1158C23—121no—
1159C23—121no—
1160C23—121no—
1161C23—121no—
1162C23C22×C4×D311yescharacteristic
1163C23C22×D1211yescharacteristic
1164C23C2×#23511yescharacteristic
1165C23C2×D3×D411yescharacteristic
1166C23C2×D3×D411yescharacteristic
1167C23C2×D3×D411yescharacteristic
1168C23C2×D3×D411yescharacteristic
1169C23C2×#23911yescharacteristic
1170C23#100711yescharacteristic
1171C23D3×#4111yescharacteristic
1172C23D3×#4111yescharacteristic
1173C23D3×#4111yescharacteristic
1174C23#100911yescharacteristic
1175C23#100911yescharacteristic
1176C23#100911yescharacteristic
1177D4—632no—
1178D4—1216no—
1179D4—1216no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—22no—
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—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—62no—
1227C2×C4—62no—
1228C2×C4—62no—
1229C2×C4—62no—
1230C2×C4—62no—
1231C2×C4—62no—
1232C2×C4—62no—
1233C2×C4—62no—
1234C2×C4—62no—
1235C2×C4—62no—
1236C2×C4—62no—
1237C2×C4—62no—
1238C2×C4—1216no—
1239C2×C4—1216no—
1240C2×C4—1216no—
1241C2×C4—1216no—
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×C4—121no—
1253C2×C4—121no—
1254C2×C4—121no—
1255C2×C4—121no—
1256C2×C4—121no—
1257C2×C4—121no—
1258C2×C4—121no—
1259C2×C4—121no—
1260C2×C4—121no—
1261C2×C4—121no—
1262C2×C4—121no—
1263C2×C4—121no—
1264C2×C4—121no—
1265C2×C4C4×D1214yescomplemented
1266C2×C4D3×C22⋊C414yes—
1267C2×C4#89514yescomplemented
1268C2×C3C2×#38611yescharacteristic
1269C2×C3C4×#12111yescharacteristic
1270C2×C3#232511yescharacteristic
1271C2×C3D4×C22⋊C411yescharacteristic
1272C2×C3#233911yescharacteristic
1273C2×C3#236111yescharacteristic
1274C2×C3#236411yescharacteristic
1275C2×C3#241011yescharacteristic
1276C2×C3#241611yescharacteristic
1277C2×C3#242411yescharacteristic
1278C2×C3#242511yescharacteristic
1279C2×C3#243011yescharacteristic
1280C2×C3#244311yescharacteristic
1281C2×C3#244411yescharacteristic
1282C2×C3#254311yescharacteristic
1283D3—28no—
1284D3—44no—
1285D3—82no—
1286C22—38no—
1287C22—64no—
1288C22—64no—
1289C22—64no—
1290C22—64no—
1291C22—64no—
1292C22—64no—
1293C22—64no—
1294C22—64no—
1295C22—64no—
1296C22—64no—
1297C22—64no—
1298C22—64no—
1299C22—64no—
1300C22—64no—
1301C22—64no—
1302C22—64no—
1303C22—64no—
1304C22—122no—
1305C22—122no—
1306C22—122no—
1307C22—122no—
1308C22—122no—
1309C22—122no—
1310C22—122no—
1311C22—122no—
1312C22—122no—
1313C22—122no—
1314C22—122no—
1315C22—122no—
1316C22—122no—
1317C22—122no—
1318C22—122no—
1319C22—122no—
1320C22—122no—
1321C22—122no—
1322C22—122no—
1323C22—241no—
1324C22—241no—
1325C22—241no—
1326C22—241no—
1327C22—241no—
1328C22—241no—
1329C22—241no—
1330C22—241no—
1331C22C2×C4×D1211yescharacteristic
1332C22C2×D3×C22⋊C411yescharacteristic
1333C22C2×#89511yescharacteristic
1334C22#550711yescharacteristic
1335C22#552111yescharacteristic
1336C22#552411yescharacteristic
1337C22#553011yescharacteristic
1338C22C4×D3×D411yescharacteristic
1339C22C4×D3×D411yescharacteristic
1340C22#554811yescharacteristic
1341C22D4×D1211yescharacteristic
1342C22D4×D1211yescharacteristic
1343C22D4×D1211yescharacteristic
1344C22#555011yescharacteristic
1345C22#555011yescharacteristic
1346C22C4×#23911yescharacteristic
1347C22#557411yescharacteristic
1348C22#557611yescharacteristic
1349C22#558011yescharacteristic
1350C22D3×#12011yescharacteristic
1351C22D3×#12111yescharacteristic
1352C22D3×#12111yescharacteristic
1353C22#562911yescharacteristic
1354C22#563011yescharacteristic
1355C22#563011yescharacteristic
1356C22#563111yescharacteristic
1357C22D3×#12311yescharacteristic
1358C22#565311yescharacteristic
1359C22#565411yescharacteristic
1360C22#567611yescharacteristic
1361C22#569211yescharacteristic
1362C22#569511yescharacteristic
1363C22#570411yescharacteristic
1364C22#570911yescharacteristic
1365C22#572611yescharacteristic
1366C4—24no—
1367C4—24no—
1368C4—24no—
1369C4—42no—
1370C4—42no—
1371C4—42no—
1372C4—81no—
1373C4—122no—
1374C4—122no—
1375C4—122no—
1376C4—122no—
1377C4—241no—
1378C3#1402311yescharacteristic, complemented, Sylow
1379C2—68no—
1380C2—124no—
1381C2—242no—
1382C2C22⋊C4×D1211yescharacteristic
1383C2C4×#89511yescharacteristic
1384C2#7377411yescharacteristic
1385C2#7460111yescharacteristic
1386C2#7460611yescharacteristic
1387C2D3×#38611yescharacteristic
1388C2#7529811yescharacteristic
1389C2#7530911yescharacteristic
1390C2#7531911yescharacteristic
1391C2#7532011yescharacteristic
1392C2#7584611yescharacteristic
1393C2#7588211yescharacteristic
1394C2#7621111yescharacteristic
1395C2#7621711yescharacteristic
1396C2#7661311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC3×#1436C2
socle, cosocleC24×C3C24
prime radicalC22×#895C2
hypercenter#1436D3
hypocenterC3#14023
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
2. C22×C4×D12C2semidirect
3. C2×#4665C2semidirect
4. C2×#4665C2semidirect
5. C2×#4665C2semidirect
6. C2×#4665C2semidirect
7. C2×D3×#95C2semidirect
8. C3×#1436C2semidirect
9. #71565C2semidirect
10. #71537C2semidirect
11. #69429C2semidirect
12. #69427C2semidirect
13. #69426C2semidirect
14. (C2×D3)⋊#95C2semidirect
15. (C2×D3)⋊#95C2semidirect
40. C2×#895C4semidirect
75. #1436D3semidirect
110. C22×D12C2×C4semidirect
111. C22×D12C2×C4semidirect
140. C22×C4×D3C2×C4semidirect
141. C22×C4×D3D4semidirect
144. C2×C3×C4⋊C4C2×C4semidirect
178. C2×(C2×D3)⋊C4C2×C4semidirect
179. C2×(C2×D3)⋊C4C2×C4semidirect
180. C2×(C2×D3)⋊C4D4semidirect
190. C3×#95D4semidirect
396. C2×D12C22⋊C4semidirect
510. C2×C4⋊C4C4×D3semidirect
560. #95D12semidirect
728. C2×C3×C4C4×D4semidirect
729. C2×C3×C4#121semidirect
1044. C2×D3#386semidirect
1265. C2×C4C4×D12semidirect
1267. C2×C4#895semidirect
1378. C3#14023semidirect

Maximal subgroups

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

subgroupindex
C22×#8952
C22×C4×D122
C2×#46652
C2×D3×#952
C3×#14362
#715652
#715372
#694292
#694272
#694262
(C2×D3)⋊#952
#140233