Finite Group Databasebeta

← #10718309

Subgroups — #10718309

Order 768.

2474 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#883C211yesmaximal, characteristic
2C2×#4956C211yesmaximal, characteristic
3C2×#4956C211yesmaximal, characteristic
4C2×C4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
5C2×#4668C211yesmaximal, characteristic, complemented
6C2×#4664C211yesmaximal, characteristic, complemented
7C2×D3×#95C211yesmaximal, characteristic, complemented
8C3×#1437C211yesmaximal, characteristic, complemented
9#71547C211yesmaximal, characteristic, complemented
10#71546C211yesmaximal, characteristic, complemented
11#71545C211yesmaximal, characteristic, complemented
12#71535C211yesmaximal, characteristic, complemented
13#69423C211yesmaximal, characteristic, complemented
14#69421C211yesmaximal, characteristic, complemented
15Dic3⋊#95C211yesmaximal, characteristic, complemented
16#13996—31nomaximal, Sylow
17C23×#67C2211yescharacteristic
18C23×C4×D3C2211yescharacteristic
19C23×C4×D3C2211yescharacteristic
20C23×C4×D3C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C42C2211yescharacteristic
25C22×#217C2211yescharacteristic
26C22×#217C2211yescharacteristic
27C22×#217C2211yescharacteristic
28C22×(C2×D3)⋊C4C2211yescharacteristic
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×(C2×D3)⋊C4C2211yescharacteristic
31C22×C4⋊Dic3C2211yescharacteristic
32C22×C4⋊Dic3C2211yescharacteristic
33C22×Dic3⋊C4C2211yescharacteristic
34C22×Dic3⋊C4C2211yescharacteristic
35C22×C4×Dic3C2211yescharacteristic
36C2×#883—24no—
37C2×#883—24no—
38C2×#883C418yescomplemented
39C2×C3×#95C2211yescharacteristic
40C2×C3×#95C2211yescharacteristic
41C2×C3×#95C2211yescharacteristic
42C2×C3⋊#95C2211yescharacteristic
43C2×C3⋊#95C2211yescharacteristic
44C2×C3⋊#95C2211yescharacteristic
45C2×C3⋊#95C2211yescharacteristic
46C2×C3⋊#95C2211yescharacteristic
47C2×C3⋊#95C2211yescharacteristic
48C2×C3⋊#95C2211yescharacteristic
49C2×C3⋊#95C2211yescharacteristic
50C2×C3⋊#95C2211yescharacteristic
51C2×C3⋊#95C2211yescharacteristic
52C2×C3⋊#95C2211yescharacteristic
53C2×C3⋊#95C2211yescharacteristic
54C2×C3⋊#95C2211yescharacteristic
55#4956—24no—
56#4956—24no—
57C4×(C2×D3)⋊C4—24no—
58#4668—24no—
59#4664—24no—
60D3×#95—24no—
61C22×#123—31no—
62C2×#386—31no—
63C2×#386—31no—
64C2×#385—31no—
65C2×#381—31no—
66C2×C4×C22⋊C4—31no—
67C22×#95—31no—
68#1445—31no—
69#1445—31no—
70#1439—31no—
71#1439—31no—
72#1437—31no—
73#1437D311yescharacteristic, complemented
74C4⋊#95—31no—
75C4⋊#95—31no—
76C25×C3C2311yescharacteristic
77C24×D3C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C22×#67—22no—
85C22×#67—22no—
86C22×#67—22no—
87C22×#67—22no—
88C22×#67—22no—
89C22×#67—22no—
90C22×#67C2×C414yes—
91C23×Dic3C2311yescharacteristic
92C23×Dic3C2311yescharacteristic
93C23×Dic3C2311yescharacteristic
94C23×Dic3C2311yescharacteristic
95C23×Dic3C2311yescharacteristic
96C23×Dic3C2311yescharacteristic
97C23×Dic3C2311yescharacteristic
98C22×C4×D3—22no—
99C22×C4×D3—22no—
100C22×C4×D3—22no—
101C22×C4×D3—22no—
102C22×C4×D3—22no—
103C22×C4×D3—22no—
104C22×C4×D3—22no—
105C22×C4×D3—22no—
106C22×C4×D3—22no—
107C22×C4×D3—22no—
108C22×C4×D3—22no—
109C22×C4×D3—22no—
110C22×C4×D3—22no—
111C22×C4×D3—22no—
112C22×C4×D3—22no—
113C22×C4×D3—41no—
114C22×C4×D3—41no—
115C22×C4×D3—41no—
116C22×C4×D3—41no—
117C22×C4×D3C2×C414yes—
118C22×C4×D3D414yes—
119C2×C3×C22⋊C4—22no—
120C2×C3×C22⋊C4—22no—
121C2×C3×C22⋊C4—22no—
122C2×C3×C22⋊C4—22no—
123C2×C3×C22⋊C4—22no—
124C2×C3×C22⋊C4—22no—
125C2×C3×C22⋊C4—22no—
126C2×C3×C22⋊C4—41no—
127C2×C3×C22⋊C4C2×C414yescomplemented
128C2×C3×C42—22no—
129C2×C3×C42—22no—
130C2×C3×C42—41no—
131C2×#217—22no—
132C2×#217—22no—
133C2×#217—22no—
134C2×#217—22no—
135C2×#217—22no—
136C2×#217—41no—
137C2×#217—41no—
138C2×#217—41no—
139C2×#217C2×C414yescomplemented
140C2×(C2×D3)⋊C4—22no—
141C2×(C2×D3)⋊C4—22no—
142C2×(C2×D3)⋊C4—22no—
143C2×(C2×D3)⋊C4—22no—
144C2×(C2×D3)⋊C4—22no—
145C2×(C2×D3)⋊C4C2×C414yes—
146C2×(C2×D3)⋊C4D414yes—
147C2×(C2×D3)⋊C4D414yes—
148C2×(C2×D3)⋊C4D414yes—
149C2×C4⋊Dic3—22no—
150C2×C4⋊Dic3—22no—
151C2×C4⋊Dic3—22no—
152C2×C4⋊Dic3—22no—
153C2×C4⋊Dic3—41no—
154C2×C4⋊Dic3C2×C414yescomplemented
155C2×Dic3⋊C4—22no—
156C2×Dic3⋊C4—22no—
157C2×Dic3⋊C4—22no—
158C2×Dic3⋊C4—22no—
159C2×Dic3⋊C4—41no—
160C2×Dic3⋊C4C2×C414yescomplemented
161C2×C4×Dic3—22no—
162C2×C4×Dic3—22no—
163C2×C4×Dic3—41no—
164#883—232no—
165C3×#95—22no—
166C3×#95—22no—
167C3×#95—22no—
168C3⋊#95—22no—
169C3⋊#95—22no—
170C3⋊#95—22no—
171C3⋊#95—22no—
172C3⋊#95—22no—
173C3⋊#95—22no—
174C3⋊#95—22no—
175C3⋊#95—22no—
176C3⋊#95—22no—
177C3⋊#95—22no—
178C3⋊#95—22no—
179C3⋊#95—22no—
180C3⋊#95—22no—
181C23×D4—31no—
182C24×C4—31no—
183C24×C4—31no—
184C24×C4—31no—
185C2×#123—38no—
186C2×#123—64no—
187C2×#123—64no—
188C22×C4⋊C4—31no—
189C22×C4⋊C4—31no—
190C22×C4⋊C4—31no—
191C22×C4⋊C4—31no—
192C22×C22⋊C4—31no—
193C22×C22⋊C4—31no—
194C22×C22⋊C4—31no—
195C22×C22⋊C4—31no—
196C22×C22⋊C4—31no—
197C22×C22⋊C4—31no—
198C22×C22⋊C4C2×D311yescharacteristic
199C22×C22⋊C4C2×D311yescharacteristic
200C22×C22⋊C4C2×D311yescharacteristic
201C22×C42—31no—
202C22×C42C2×D311yescharacteristic
203#386—64no—
204#386—64no—
205#385—64no—
206#381—64no—
207C4×C22⋊C4—64no—
208C2×#95—31no—
209C2×#95—31no—
210C2×#95—31no—
211C2×#95—31no—
212C2×#95—31no—
213C2×#95—31no—
214C2×#95—31no—
215C2×#95—31no—
216C2×#95—31no—
217C2×#95—31no—
218C2×#95—31no—
219C2×#95—31no—
220C2×#95—31no—
221C2×#95—64no—
222C2×#95C2×D311yescharacteristic
223C2×#95C2×D311yescharacteristic
224C2×#95C2×D311yescharacteristic
225C24×C3—21no—
226C24×C3—21no—
227C24×C3—21no—
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×C3C22×C412yes—
240C24×C3C2411yescharacteristic
241C23×D3—21no—
242C23×D3—21no—
243C23×D3—21no—
244C23×D3—21no—
245C23×D3—21no—
246C23×D3—21no—
247C23×D3—21no—
248C23×D3—21no—
249C23×D3C22×C412yes—
250C23×D3C2×D412yes—
251C23×D3C2×D412yes—
252C23×D3C2×D412yes—
253C23×D3C2×D412yes—
254C23×D3#4112yes—
255C23×D3#4112yes—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—21no—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—21no—
273C22×C3×C4—21no—
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—21no—
280C22×C3×C4—21no—
281C22×C3×C4—21no—
282C22×C3×C4—21no—
283C22×C3×C4—21no—
284C22×C3×C4—21no—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4C22×C412yes—
290C22×C3×C4C22×C412yes—
291C22×C3×C4C2×D412yes—
292C22×C3×C4C2×D412yes—
293C22×C3×C4C2×D412yes—
294C22×C3×C4C2×D412yes—
295C22×C3×C4#4112yes—
296C22×C3×C4#4112yes—
297C22×C3×C4#4112yes—
298C2×#67—28no—
299C2×#67—28no—
300C2×#67—28no—
301C2×#67—44no—
302C2×#67—44no—
303C2×#67—44no—
304C2×#67—44no—
305C22×Dic3—21no—
306C22×Dic3—21no—
307C22×Dic3—21no—
308C22×Dic3—21no—
309C22×Dic3—21no—
310C22×Dic3—21no—
311C22×Dic3—21no—
312C22×Dic3—21no—
313C22×Dic3—21no—
314C22×Dic3—21no—
315C22×Dic3—21no—
316C22×Dic3—21no—
317C22×Dic3—21no—
318C22×Dic3—21no—
319C22×Dic3—21no—
320C22×Dic3—21no—
321C22×Dic3—21no—
322C22×Dic3—21no—
323C22×Dic3—21no—
324C22×Dic3—21no—
325C22×Dic3—21no—
326C22×Dic3—21no—
327C22×Dic3—21no—
328C22×Dic3—21no—
329C22×Dic3—21no—
330C22×Dic3—21no—
331C22×Dic3—21no—
332C22×Dic3—21no—
333C22×Dic3—21no—
334C22×Dic3—21no—
335C22×Dic3—21no—
336C22×Dic3—21no—
337C22×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×Dic3C22×C412yes—
347C22×Dic3C22×C412yes—
348C22×Dic3C22×C412yes—
349C22×Dic3C2×D412yes—
350C22×Dic3C2×D412yes—
351C22×Dic3C2×D412yes—
352C22×Dic3C2×D412yes—
353C22×Dic3#4112yes—
354C2×C4×D3—28no—
355C2×C4×D3—28no—
356C2×C4×D3—28no—
357C2×C4×D3—28no—
358C2×C4×D3—28no—
359C2×C4×D3—28no—
360C2×C4×D3—44no—
361C2×C4×D3—44no—
362C2×C4×D3—44no—
363C2×C4×D3—44no—
364C2×C4×D3—44no—
365C2×C4×D3—44no—
366C2×C4×D3—44no—
367C2×C4×D3—44no—
368C2×C4×D3—44no—
369C2×C4×D3—44no—
370C2×C4×D3—44no—
371C2×C4×D3—44no—
372C2×C4×D3—44no—
373C2×C4×D3—44no—
374C2×C4×D3—44no—
375C3×C22⋊C4—28no—
376C3×C22⋊C4—44no—
377C3×C22⋊C4—44no—
378C3×C42—44no—
379#217—28no—
380#217—44no—
381#217—44no—
382(C2×D3)⋊C4—28no—
383(C2×D3)⋊C4—44no—
384(C2×D3)⋊C4C22⋊C4116yescomplemented
385C4⋊Dic3—28no—
386C4⋊Dic3—44no—
387Dic3⋊C4—28no—
388Dic3⋊C4—44no—
389C4×Dic3—44no—
390C25—31no—
391C25C22×D311yescharacteristic
392C22×D4—34no—
393C22×D4—62no—
394C22×D4—62no—
395C22×D4—62no—
396C22×D4—62no—
397C22×D4—62no—
398C22×D4—62no—
399C23×C4—31no—
400C23×C4—31no—
401C23×C4—31no—
402C23×C4—31no—
403C23×C4—31no—
404C23×C4—31no—
405C23×C4—34no—
406C23×C4—34no—
407C23×C4—31no—
408C23×C4—62no—
409C23×C4—62no—
410C23×C4—62no—
411C23×C4—62no—
412C23×C4—62no—
413C23×C4—62no—
414C23×C4—62no—
415C23×C4—62no—
416C23×C4—62no—
417C23×C4—62no—
418C23×C4—62no—
419C23×C4—62no—
420C23×C4—62no—
421C23×C4—62no—
422C23×C4—62no—
423C23×C4—121no—
424C23×C4—121no—
425C23×C4—121no—
426C23×C4—121no—
427C23×C4C22×D311yescharacteristic
428C23×C4C22×D311yescharacteristic
429C23×C4C22×D311yescharacteristic
430C23×C4C22×D311yescharacteristic
431C23×C4C22×D311yescharacteristic
432C23×C4C22×D311yescharacteristic
433#123—632no—
434C2×C4⋊C4—34no—
435C2×C4⋊C4—34no—
436C2×C4⋊C4—62no—
437C2×C4⋊C4—62no—
438C2×C4⋊C4—62no—
439C2×C4⋊C4—62no—
440C2×C4⋊C4—62no—
441C2×C4⋊C4—62no—
442C2×C4⋊C4—62no—
443C2×C4⋊C4—62no—
444C2×C4⋊C4—121no—
445C2×C4⋊C4—121no—
446C2×C22⋊C4—22no—
447C2×C22⋊C4—22no—
448C2×C22⋊C4—22no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—22no—
452C2×C22⋊C4—22no—
453C2×C22⋊C4—34no—
454C2×C22⋊C4—34no—
455C2×C22⋊C4—34no—
456C2×C22⋊C4—34no—
457C2×C22⋊C4—34no—
458C2×C22⋊C4—41no—
459C2×C22⋊C4—62no—
460C2×C22⋊C4—62no—
461C2×C22⋊C4—62no—
462C2×C22⋊C4—62no—
463C2×C22⋊C4—62no—
464C2×C22⋊C4—62no—
465C2×C22⋊C4—62no—
466C2×C22⋊C4—62no—
467C2×C22⋊C4—62no—
468C2×C22⋊C4—62no—
469C2×C22⋊C4—121no—
470C2×C22⋊C4—121no—
471C2×C22⋊C4—121no—
472C2×C22⋊C4C4×D314yescomplemented
473C2×C42—22no—
474C2×C42—22no—
475C2×C42—41no—
476C2×C42—62no—
477C2×C42—62no—
478C2×C42—121no—
479#95—22no—
480#95—22no—
481#95—22no—
482#95—62no—
483#95—62no—
484#95—62no—
485#95—62no—
486#95—62no—
487#95—62no—
488#95—62no—
489#95—62no—
490#95—62no—
491#95—62no—
492#95—62no—
493#95—62no—
494#95—62no—
495C23×C3—22no—
496C23×C3—22no—
497C23×C3—22no—
498C23×C3—22no—
499C23×C3—22no—
500C23×C3—22no—
501C23×C3—22no—
502C23×C3—41no—
503C23×C3—41no—
504C23×C3—41no—
505C23×C3—41no—
506C23×C3—41no—
507C23×C3—41no—
508C23×C3—41no—
509C23×C3—41no—
510C23×C3—41no—
511C23×C3—41no—
512C23×C3—41no—
513C23×C3—41no—
514C23×C3—41no—
515C23×C3—41no—
516C23×C3—41no—
517C23×C3—41no—
518C23×C3—41no—
519C23×C3—41no—
520C23×C3—41no—
521C23×C3—41no—
522C23×C3—41no—
523C23×C3—41no—
524C23×C3—41no—
525C23×C3—41no—
526C23×C3—41no—
527C23×C3—41no—
528C23×C3—41no—
529C23×C3—41no—
530C23×C3C23×C411yescharacteristic
531C23×C3C22×D411yescharacteristic
532C23×C3C22×D411yescharacteristic
533C23×C3C22×D411yescharacteristic
534C23×C3C22×D411yescharacteristic
535C23×C3C2×#4111yescharacteristic
536C23×C3C2×#4111yescharacteristic
537C23×C3C2×#4111yescharacteristic
538C23×C3C2×#4111yescharacteristic
539C23×C3C2×#4111yescharacteristic
540C23×C3C2×#4111yescharacteristic
541C23×C3H(5,𝔽2)11yescharacteristic
542C23×C3H(5,𝔽2)11yescharacteristic
543C23×C32−1+411yescharacteristic
544C23×C32−1+411yescharacteristic
545C22×D3—22no—
546C22×D3—22no—
547C22×D3—22no—
548C22×D3—22no—
549C22×D3—22no—
550C22×D3—22no—
551C22×D3—22no—
552C22×D3—22no—
553C22×D3—22no—
554C22×D3—22no—
555C22×D3—22no—
556C22×D3—22no—
557C22×D3—22no—
558C22×D3—22no—
559C22×D3—22no—
560C22×D3—22no—
561C22×D3—22no—
562C22×D3—22no—
563C22×D3—22no—
564C22×D3—22no—
565C22×D3—22no—
566C22×D3—22no—
567C22×D3—22no—
568C22×D3—22no—
569C22×D3—22no—
570C22×D3—22no—
571C22×D3—22no—
572C22×D3—22no—
573C22×D3C2×C22⋊C414yes—
574C22×D3C4×D414yes—
575C22×D3C4×D414yes—
576C22×D3#12114yes—
577C22×D3#12114yes—
578C22×D3#12414yes—
579C22×D3#12714yes—
580C2×C3×C4—22no—
581C2×C3×C4—22no—
582C2×C3×C4—22no—
583C2×C3×C4—22no—
584C2×C3×C4—22no—
585C2×C3×C4—22no—
586C2×C3×C4—22no—
587C2×C3×C4—22no—
588C2×C3×C4—22no—
589C2×C3×C4—22no—
590C2×C3×C4—22no—
591C2×C3×C4—22no—
592C2×C3×C4—22no—
593C2×C3×C4—22no—
594C2×C3×C4—22no—
595C2×C3×C4—22no—
596C2×C3×C4—22no—
597C2×C3×C4—22no—
598C2×C3×C4—22no—
599C2×C3×C4—22no—
600C2×C3×C4—22no—
601C2×C3×C4—41no—
602C2×C3×C4—41no—
603C2×C3×C4—41no—
604C2×C3×C4—41no—
605C2×C3×C4—41no—
606C2×C3×C4—41no—
607C2×C3×C4—41no—
608C2×C3×C4—41no—
609C2×C3×C4—41no—
610C2×C3×C4—41no—
611C2×C3×C4—41no—
612C2×C3×C4—41no—
613C2×C3×C4—41no—
614C2×C3×C4—41no—
615C2×C3×C4—41no—
616C2×C3×C4—41no—
617C2×C3×C4—41no—
618C2×C3×C4—41no—
619C2×C3×C4—41no—
620C2×C3×C4C2×C22⋊C414yes—
621C2×C3×C4#12314yescomplemented
622#67—416no—
623C2×Dic3—22no—
624C2×Dic3—22no—
625C2×Dic3—22no—
626C2×Dic3—22no—
627C2×Dic3—22no—
628C2×Dic3—22no—
629C2×Dic3—22no—
630C2×Dic3—22no—
631C2×Dic3—22no—
632C2×Dic3—22no—
633C2×Dic3—22no—
634C2×Dic3—22no—
635C2×Dic3—22no—
636C2×Dic3—22no—
637C2×Dic3—22no—
638C2×Dic3—22no—
639C2×Dic3—22no—
640C2×Dic3—22no—
641C2×Dic3—22no—
642C2×Dic3—22no—
643C2×Dic3—22no—
644C2×Dic3—41no—
645C2×Dic3—41no—
646C2×Dic3—41no—
647C2×Dic3—41no—
648C2×Dic3—41no—
649C2×Dic3—41no—
650C2×Dic3—41no—
651C2×Dic3—41no—
652C2×Dic3—41no—
653C2×Dic3—41no—
654C2×Dic3—41no—
655C2×Dic3—41no—
656C2×Dic3—41no—
657C2×Dic3—41no—
658C2×Dic3—41no—
659C2×Dic3—41no—
660C2×Dic3—41no—
661C2×Dic3—41no—
662C2×Dic3—41no—
663C2×Dic3—41no—
664C2×Dic3—41no—
665C2×Dic3—41no—
666C2×Dic3—41no—
667C2×Dic3—41no—
668C2×Dic3—41no—
669C2×Dic3—41no—
670C2×Dic3—41no—
671C2×Dic3C2×C22⋊C414yes—
672C4×D3—416no—
673C4×D3—416no—
674C4×D3—416no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—21no—
681C24—21no—
682C24—21no—
683C24—21no—
684C24—21no—
685C24—21no—
686C24—21no—
687C24—21no—
688C24—21no—
689C24—32no—
690C24—32no—
691C24—32no—
692C24—32no—
693C24—32no—
694C24—32no—
695C24—32no—
696C24—61no—
697C24—61no—
698C24—61no—
699C24—61no—
700C24—61no—
701C24—61no—
702C24—61no—
703C24—61no—
704C24C2×C4×D312yes—
705C24C23×D311yescharacteristic
706C2×D4—68no—
707C2×D4—68no—
708C2×D4—68no—
709C2×D4—124no—
710C2×D4—124no—
711C2×D4—124no—
712C2×D4—124no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—32no—
747C22×C4—32no—
748C22×C4—32no—
749C22×C4—32no—
750C22×C4—32no—
751C22×C4—32no—
752C22×C4—32no—
753C22×C4—32no—
754C22×C4—68no—
755C22×C4—68no—
756C22×C4—68no—
757C22×C4—68no—
758C22×C4—68no—
759C22×C4—61no—
760C22×C4—61no—
761C22×C4—61no—
762C22×C4—61no—
763C22×C4—61no—
764C22×C4—61no—
765C22×C4—61no—
766C22×C4—61no—
767C22×C4—61no—
768C22×C4—61no—
769C22×C4—61no—
770C22×C4—61no—
771C22×C4—61no—
772C22×C4—61no—
773C22×C4—61no—
774C22×C4—61no—
775C22×C4—61no—
776C22×C4—61no—
777C22×C4—61no—
778C22×C4—61no—
779C22×C4—61no—
780C22×C4—61no—
781C22×C4—61no—
782C22×C4—61no—
783C22×C4—61no—
784C22×C4—61no—
785C22×C4—61no—
786C22×C4—61no—
787C22×C4—61no—
788C22×C4—61no—
789C22×C4—61no—
790C22×C4—61no—
791C22×C4—61no—
792C22×C4—61no—
793C22×C4—68no—
794C22×C4—61no—
795C22×C4—61no—
796C22×C4—61no—
797C22×C4—61no—
798C22×C4—61no—
799C22×C4—61no—
800C22×C4—61no—
801C22×C4—124no—
802C22×C4—124no—
803C22×C4—124no—
804C22×C4—124no—
805C22×C4—124no—
806C22×C4—124no—
807C22×C4—124no—
808C22×C4—124no—
809C22×C4—124no—
810C22×C4—124no—
811C22×C4—124no—
812C22×C4—124no—
813C22×C4—124no—
814C22×C4—124no—
815C22×C4—124no—
816C22×C4C2×C4×D312yes—
817C22×C4C2×C4×D312yes—
818C22×C4#23512yes—
819C22×C4#23512yes—
820C22×C4D3×D412yes—
821C22×C4D3×D412yes—
822C22×C4D3×D412yes—
823C22×C4D3×D412yes—
824C22×C4#23712yes—
825C4⋊C4—68no—
826C4⋊C4—68no—
827C4⋊C4—124no—
828C4⋊C4—124no—
829C22⋊C4—28no—
830C22⋊C4—316no—
831C22⋊C4—44no—
832C22⋊C4—44no—
833C22⋊C4—68no—
834C22⋊C4—68no—
835C22⋊C4—124no—
836C22⋊C4—124no—
837C22⋊C4—124no—
838C42—44no—
839C42—124no—
840C22×C3—42no—
841C22×C3—42no—
842C22×C3—42no—
843C22×C3—42no—
844C22×C3—42no—
845C22×C3—42no—
846C22×C3—42no—
847C22×C3—81no—
848C22×C3—81no—
849C22×C3—81no—
850C22×C3—81no—
851C22×C3—81no—
852C22×C3—81no—
853C22×C3—81no—
854C22×C3—81no—
855C22×C3C22×C22⋊C411yescharacteristic
856C22×C3C2×C4×D411yescharacteristic
857C22×C3C2×C4×D411yescharacteristic
858C22×C3C4×#4111yescharacteristic
859C22×C3C4×#4111yescharacteristic
860C22×C3#52011yescharacteristic
861C22×C3#52011yescharacteristic
862C22×C3C2×#12111yescharacteristic
863C22×C3C2×#12111yescharacteristic
864C22×C3C2×#12311yescharacteristic
865C22×C3#52511yescharacteristic
866C22×C3C2×#12411yescharacteristic
867C22×C3#52911yescharacteristic
868C22×C3#52911yescharacteristic
869C22×C3C2×#12711yescharacteristic
870C22×C3#53411yescharacteristic
871C22×C3#53611yescharacteristic
872C22×C3#53911yescharacteristic
873C22×C3#53911yescharacteristic
874C22×C3#54611yescharacteristic
875C22×C3#54611yescharacteristic
876C22×C3#54611yescharacteristic
877C22×C3#54611yescharacteristic
878C22×C3#54611yescharacteristic
879C22×C3#54611yescharacteristic
880C22×C3#54711yescharacteristic
881C22×C3#54711yescharacteristic
882C22×C3#54711yescharacteristic
883C22×C3#54711yescharacteristic
884C22×C3#54711yescharacteristic
885C22×C3#54711yescharacteristic
886C22×C3#55111yescharacteristic
887C22×C3#55111yescharacteristic
888C22×C3#55211yescharacteristic
889C22×C3#55211yescharacteristic
890C2×D3—24no—
891C2×D3—24no—
892C2×D3—24no—
893C2×D3—24no—
894C2×D3—24no—
895C2×D3—24no—
896C2×D3—24no—
897C2×D3—24no—
898C2×D3—24no—
899C2×D3—24no—
900C2×D3—24no—
901C2×D3—24no—
902C2×D3—24no—
903C2×D3—24no—
904C2×D3#39018yes—
905C3×C4—24no—
906C3×C4—24no—
907C3×C4—42no—
908C3×C4—42no—
909C3×C4—42no—
910C3×C4—81no—
911Dic3—24no—
912Dic3—42no—
913Dic3—42no—
914Dic3—42no—
915Dic3—42no—
916Dic3—42no—
917Dic3—81no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—34no—
926C23—34no—
927C23—34no—
928C23—34no—
929C23—34no—
930C23—34no—
931C23—34no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—62no—
961C23—62no—
962C23—62no—
963C23—62no—
964C23—62no—
965C23—62no—
966C23—62no—
967C23—62no—
968C23—62no—
969C23—62no—
970C23—62no—
971C23—62no—
972C23—62no—
973C23—62no—
974C23—62no—
975C23—62no—
976C23—62no—
977C23—62no—
978C23—62no—
979C23—62no—
980C23—62no—
981C23—62no—
982C23—62no—
983C23—62no—
984C23—62no—
985C23—62no—
986C23—62no—
987C23—62no—
988C23C22×C4×D311yescharacteristic
989C23C2×#23511yescharacteristic
990C23C2×#23511yescharacteristic
991C23C2×D3×D411yescharacteristic
992C23C2×D3×D411yescharacteristic
993C23C2×D3×D411yescharacteristic
994C23C2×D3×D411yescharacteristic
995C23C2×#23711yescharacteristic
996C23#100411yescharacteristic
997C23D3×#4111yescharacteristic
998C23D3×#4111yescharacteristic
999C23D3×#4111yescharacteristic
1000C23#100911yescharacteristic
1001C23#101011yescharacteristic
1002C23#101011yescharacteristic
1003D4—1216no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—34no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—62no—
1046C2×C4—62no—
1047C2×C4—62no—
1048C2×C4—62no—
1049C2×C4—62no—
1050C2×C4—62no—
1051C2×C4—62no—
1052C2×C4—62no—
1053C2×C4—62no—
1054C2×C4—62no—
1055C2×C4—62no—
1056C2×C4—62no—
1057C2×C4—62no—
1058C2×C4—62no—
1059C2×C4—62no—
1060C2×C4—62no—
1061C2×C4—62no—
1062C2×C4—62no—
1063C2×C4—62no—
1064C2×C4—62no—
1065C2×C4—62no—
1066C2×C4—1216no—
1067C2×C4—1216no—
1068C2×C4—1216no—
1069C2×C4—121no—
1070C2×C4—121no—
1071C2×C4—121no—
1072C2×C4—121no—
1073C2×C4—121no—
1074C2×C4—121no—
1075C2×C4—121no—
1076C2×C4—121no—
1077C2×C4—121no—
1078C2×C4—121no—
1079C2×C4—121no—
1080C2×C4—121no—
1081C2×C4—121no—
1082C2×C4—121no—
1083C2×C4—121no—
1084C2×C4—121no—
1085C2×C4—121no—
1086C2×C4—121no—
1087C2×C4—121no—
1088C2×C4—121no—
1089C2×C4—121no—
1090C2×C4—121no—
1091C2×C4—121no—
1092C2×C4—121no—
1093C2×C4—121no—
1094C2×C4—121no—
1095C2×C4—121no—
1096C2×C4D3×C22⋊C414yes—
1097C2×C4#88314yescomplemented
1098C2×C3—82no—
1099C2×C3C2×#39011yescharacteristic
1100C2×C3C4×#12311yescharacteristic
1101C2×C3#232211yescharacteristic
1102C2×C3#233911yescharacteristic
1103C2×C3#233911yescharacteristic
1104C2×C3#235911yescharacteristic
1105C2×C3#235911yescharacteristic
1106C2×C3#241211yescharacteristic
1107C2×C3#241311yescharacteristic
1108C2×C3#242511yescharacteristic
1109C2×C3#242511yescharacteristic
1110C2×C3#248811yescharacteristic
1111C2×C3#248811yescharacteristic
1112C2×C3#250111yescharacteristic
1113C2×C3#253911yescharacteristic
1114D3—28no—
1115C22—38no—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22—42no—
1121C22—42no—
1122C22—42no—
1123C22—64no—
1124C22—64no—
1125C22—64no—
1126C22—64no—
1127C22—64no—
1128C22—64no—
1129C22—64no—
1130C22—64no—
1131C22—64no—
1132C22—64no—
1133C22—64no—
1134C22—64no—
1135C22—64no—
1136C22—64no—
1137C22—81no—
1138C22—81no—
1139C22—81no—
1140C22—81no—
1141C22—81no—
1142C22—81no—
1143C22—81no—
1144C22—81no—
1145C22C4×#23511yescharacteristic
1146C22C2×D3×C22⋊C411yescharacteristic
1147C22C2×#88311yescharacteristic
1148C22#549011yescharacteristic
1149C22#552311yescharacteristic
1150C22#552811yescharacteristic
1151C22#552911yescharacteristic
1152C22C4×#23711yescharacteristic
1153C22C4×D3×D411yescharacteristic
1154C22C4×D3×D411yescharacteristic
1155C22#554611yescharacteristic
1156C22#554711yescharacteristic
1157C22#555011yescharacteristic
1158C22#555011yescharacteristic
1159C22#555111yescharacteristic
1160C22#555111yescharacteristic
1161C22#555111yescharacteristic
1162C22#555611yescharacteristic
1163C22#555711yescharacteristic
1164C22#559111yescharacteristic
1165C22D3×#12111yescharacteristic
1166C22D3×#12111yescharacteristic
1167C22#560511yescharacteristic
1168C22#561011yescharacteristic
1169C22#561111yescharacteristic
1170C22#561111yescharacteristic
1171C22#565511yescharacteristic
1172C22#565811yescharacteristic
1173C22#566011yescharacteristic
1174C22D3×#12411yescharacteristic
1175C22#567511yescharacteristic
1176C22#567611yescharacteristic
1177C22#570711yescharacteristic
1178C22#570811yescharacteristic
1179C22D3×#12711yescharacteristic
1180C4—24no—
1181C4—24no—
1182C4—42no—
1183C4—42no—
1184C4—42no—
1185C4—64no—
1186C4—81no—
1187C4—122no—
1188C4—122no—
1189C4—122no—
1190C4—122no—
1191C4—122no—
1192C4—241no—
1193C3#1399611yescharacteristic, complemented, Sylow
1194C2—68no—
1195C2—82no—
1196C2C4×#88311yescharacteristic
1197C2#7357311yescharacteristic
1198C2#7357811yescharacteristic
1199C2#7467211yescharacteristic
1200C2#7489011yescharacteristic
1201C2#7489511yescharacteristic
1202C2#7582811yescharacteristic
1203C2#7583811yescharacteristic
1204C2#7584311yescharacteristic
1205C2#7584711yescharacteristic
1206C2#7586711yescharacteristic
1207C2#7586811yescharacteristic
1208C2#7633511yescharacteristic
1209C2D3×#39011yescharacteristic
1210C2#7645411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC3×#1437C2
socle, cosocleC24×C3C24
prime radicalC23×#67C22
hypercenter#1437D3
hypocenterC3#13996
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
4. C2×C4×(C2×D3)⋊C4C2semidirect
5. C2×#4668C2semidirect
6. C2×#4664C2semidirect
7. C2×D3×#95C2semidirect
8. C3×#1437C2semidirect
9. #71547C2semidirect
10. #71546C2semidirect
11. #71545C2semidirect
12. #71535C2semidirect
13. #69423C2semidirect
14. #69421C2semidirect
15. Dic3⋊#95C2semidirect
38. C2×#883C4semidirect
73. #1437D3semidirect
127. C2×C3×C22⋊C4C2×C4semidirect
139. C2×#217C2×C4semidirect
154. C2×C4⋊Dic3C2×C4semidirect
160. C2×Dic3⋊C4C2×C4semidirect
384. (C2×D3)⋊C4C22⋊C4semidirect
472. C2×C22⋊C4C4×D3semidirect
621. C2×C3×C4#123semidirect
1097. C2×C4#883semidirect
1193. C3#13996semidirect

Maximal subgroups

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

subgroupindex
C22×#8832
C2×#49562
C2×C4×(C2×D3)⋊C42
C2×#46682
C2×#46642
C2×D3×#952
C3×#14372
#715472
#715462
#715452
#715352
#694232
#694212
Dic3⋊#952
#139963