Finite Group Databasebeta

← #10733152

Subgroups — #10733152

Order 768.

2142 conjugacy classes of subgroups.

The subgroup lattice has 1200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#878C211yesmaximal, characteristic, complemented
2C2×#4994C211yesmaximal, characteristic, complemented
3C2×#4973C211yesmaximal, characteristic, complemented
4C2×#4957C211yesmaximal, characteristic
5C2×#4958C211yesmaximal, characteristic
6C2×#4673C211yesmaximal, characteristic, complemented
7C3×#1439C211yesmaximal, characteristic, complemented
8#71550C211yesmaximal, characteristic
9#71546C211yesmaximal, characteristic, complemented
10#71544C211yesmaximal, characteristic, complemented
11#69428C211yesmaximal, characteristic, complemented
12#69427C211yesmaximal, characteristic, complemented
13#69420C211yesmaximal, characteristic, complemented
14#69410C211yesmaximal, characteristic, complemented
15#69405C211yesmaximal, characteristic, complemented
16#15280—31nomaximal, Sylow
17C23×#67C2211yescharacteristic
18C24×Dic3C2211yescharacteristic
19C23×Dic6C2211yescharacteristic
20C22×C3×C4⋊C4C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×#217C2211yescharacteristic
25C22×#217C2211yescharacteristic
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×C4⋊Dic3C2211yescharacteristic
33C22×C4⋊Dic3C2211yescharacteristic
34C22×Dic3⋊C4C2211yescharacteristic
35C22×Dic3⋊C4C2211yescharacteristic
36C22×Dic3⋊C4C2211yescharacteristic
37C22×C4×Dic3C2211yescharacteristic
38C2×#878—24no—
39C2×#878—24no—
40C2×#878—24no—
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#4994—24no—
56#4973—24no—
57#4958—24no—
58#4957—24no—
59#4673—24no—
60C22×C22⋊Q8—31no—
61C2×#396—31no—
62C2×#393—31no—
63C2×#391—31no—
64C2×#390—31no—
65C2×#386—31no—
66#1444—31no—
67#1441—31no—
68#1439—31no—
69#1439—31no—
70#1439—31no—
71#1439D311yescharacteristic, complemented
72#1438—31no—
73#1436—31no—
74C22⋊#95—31no—
75C25×C3C2311yescharacteristic
76C24×D3C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C22×#67—22no—
84C22×#67—22no—
85C22×#67—22no—
86C22×#67—22no—
87C22×#67—41no—
88C22×#67—41no—
89C22×#67Q814yescomplemented
90C23×Dic3—22no—
91C23×Dic3—22no—
92C23×Dic3—22no—
93C23×Dic3—22no—
94C23×Dic3—22no—
95C23×Dic3—41no—
96C23×Dic3—41no—
97C23×Dic3C2311yescharacteristic
98C23×Dic3C2311yescharacteristic
99C23×Dic3C2311yescharacteristic
100C23×Dic3C2311yescharacteristic
101C23×Dic3C2311yescharacteristic
102C23×Dic3C2311yescharacteristic
103C23×Dic3C2311yescharacteristic
104C22×Dic6—22no—
105C22×Dic6—22no—
106C22×Dic6—22no—
107C22×Dic6—22no—
108C22×Dic6—41no—
109C22×Dic6—41no—
110C22×Dic6D414yescomplemented
111C2×C3×C4⋊C4—22no—
112C2×C3×C4⋊C4—22no—
113C2×C3×C4⋊C4—41no—
114C2×C3×C22⋊C4—22no—
115C2×C3×C22⋊C4—22no—
116C2×C3×C22⋊C4—22no—
117C2×C3×C22⋊C4—22no—
118C2×C3×C22⋊C4—22no—
119C2×C3×C22⋊C4—41no—
120C2×C3×C22⋊C4—41no—
121C2×C3×C22⋊C4—41no—
122C2×C3×C22⋊C4D414yes—
123C2×#217—22no—
124C2×#217—22no—
125C2×#217—22no—
126C2×#217—22no—
127C2×#217—22no—
128C2×#217—41no—
129C2×(C2×D3)⋊C4—22no—
130C2×(C2×D3)⋊C4—22no—
131C2×(C2×D3)⋊C4—22no—
132C2×(C2×D3)⋊C4—22no—
133C2×(C2×D3)⋊C4—22no—
134C2×(C2×D3)⋊C4—22no—
135C2×(C2×D3)⋊C4—22no—
136C2×(C2×D3)⋊C4—22no—
137C2×(C2×D3)⋊C4—22no—
138C2×(C2×D3)⋊C4—22no—
139C2×(C2×D3)⋊C4—22no—
140C2×(C2×D3)⋊C4—22no—
141C2×(C2×D3)⋊C4—41no—
142C2×(C2×D3)⋊C4—41no—
143C2×(C2×D3)⋊C4—41no—
144C2×(C2×D3)⋊C4—41no—
145C2×(C2×D3)⋊C4—41no—
146C2×(C2×D3)⋊C4—41no—
147C2×C4⋊Dic3—22no—
148C2×C4⋊Dic3—22no—
149C2×C4⋊Dic3—22no—
150C2×C4⋊Dic3—22no—
151C2×C4⋊Dic3—41no—
152C2×C4⋊Dic3—41no—
153C2×Dic3⋊C4—22no—
154C2×Dic3⋊C4—22no—
155C2×Dic3⋊C4—22no—
156C2×Dic3⋊C4—22no—
157C2×Dic3⋊C4—22no—
158C2×Dic3⋊C4—22no—
159C2×Dic3⋊C4—22no—
160C2×Dic3⋊C4—41no—
161C2×Dic3⋊C4D414yescomplemented
162C2×C4×Dic3—22no—
163C2×C4×Dic3—22no—
164C2×C4×Dic3—41no—
165#878—232no—
166C3×#95—22no—
167C3×#95—41no—
168C3×#95—41no—
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—41no—
179C3⋊#95D414yes—
180C23×Q8—31no—
181C23×D4—31no—
182C24×C4—31no—
183C2×C22⋊Q8—64no—
184C2×C22⋊Q8—64no—
185C2×C22⋊Q8—64no—
186C22×C4⋊C4—31no—
187C22×C4⋊C4—31no—
188C22×C4⋊C4—31no—
189C22×C4⋊C4—31no—
190C22×C4⋊C4—31no—
191C22×C4⋊C4C2×D311yescharacteristic
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⋊C4—31no—
199C22×C22⋊C4—31no—
200C22×C22⋊C4C2×D311yescharacteristic
201C22×C22⋊C4C2×D311yescharacteristic
202C22×C22⋊C4C2×D311yescharacteristic
203C22×C42—31no—
204#396—64no—
205#393—64no—
206#391—64no—
207#390—64no—
208#386—64no—
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×#95C2×D311yescharacteristic
221C2×#95C2×D311yescharacteristic
222C2×#95C2×D311yescharacteristic
223C24×C3—21no—
224C24×C3—21no—
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×C3C2×D412yes—
236C24×C3C2×Q812yes—
237C24×C3#4112yes—
238C24×C3C2411yescharacteristic
239C23×D3—21no—
240C23×D3—21no—
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×D3—21no—
250C23×D3—21no—
251C23×D3—21no—
252C23×D3—21no—
253C23×D3C2×Q812yes—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
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×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4C2×D412yes—
292C22×C3×C4C2×D412yes—
293C22×C3×C4C2×D412yes—
294C22×C3×C4C2×D412yes—
295C22×C3×C4C2×D412yes—
296C2×#67—28no—
297C2×#67—28no—
298C2×#67—44no—
299C2×#67—44no—
300C2×#67—44no—
301C2×#67—44no—
302C2×#67—44no—
303C22×Dic3—21no—
304C22×Dic3—21no—
305C22×Dic3—21no—
306C22×Dic3—21no—
307C22×Dic3—21no—
308C22×Dic3—21no—
309C22×Dic3—21no—
310C22×Dic3—21no—
311C22×Dic3—28no—
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—44no—
344C22×Dic3—44no—
345C22×Dic3—44no—
346C22×Dic3—44no—
347C22×Dic3—44no—
348C22×Dic3—44no—
349C22×Dic3C2×D412yes—
350C22×Dic3C2×D412yes—
351C22×Dic3C2×D412yes—
352C22×Dic3C2×D412yes—
353C22×Dic3C2×D412yes—
354C22×Dic3C2×D412yes—
355C22×Dic3C2×Q812yes—
356C22×Dic3#4112yes—
357C22×Dic3#4112yes—
358C22×Dic3#4112yes—
359C2×Dic6—28no—
360C2×Dic6—28no—
361C2×Dic6—44no—
362C2×Dic6—44no—
363C2×Dic6—44no—
364C2×Dic6—44no—
365C2×Dic6—44no—
366C3×C4⋊C4—44no—
367C3×C22⋊C4—28no—
368C3×C22⋊C4—44no—
369C3×C22⋊C4—44no—
370#217—28no—
371#217—44no—
372(C2×D3)⋊C4—44no—
373(C2×D3)⋊C4—44no—
374(C2×D3)⋊C4—44no—
375(C2×D3)⋊C4—44no—
376(C2×D3)⋊C4—44no—
377(C2×D3)⋊C4—44no—
378C4⋊Dic3—28no—
379C4⋊Dic3—44no—
380Dic3⋊C4—28no—
381Dic3⋊C4—28no—
382Dic3⋊C4—44no—
383C4×Dic3—44no—
384C25—31no—
385C25C22×D311yescharacteristic
386C22×Q8—34no—
387C22×Q8—62no—
388C22×Q8—62no—
389C22×Q8—62no—
390C22×Q8—62no—
391C22×Q8—121no—
392C22×Q8—121no—
393C22×D4—34no—
394C22×D4—62no—
395C22×D4—62no—
396C22×D4—62no—
397C22×D4—62no—
398C22×D4—121no—
399C22×D4—121no—
400C23×C4—31no—
401C23×C4—31no—
402C23×C4—31no—
403C23×C4—31no—
404C23×C4—31no—
405C23×C4—31no—
406C23×C4—31no—
407C23×C4—62no—
408C23×C4—62no—
409C23×C4—62no—
410C23×C4—62no—
411C23×C4—62no—
412C23×C4—121no—
413C23×C4—121no—
414C23×C4C22×D311yescharacteristic
415C23×C4C22×D311yescharacteristic
416C23×C4C22×D311yescharacteristic
417C23×C4C22×D311yescharacteristic
418C23×C4C22×D311yescharacteristic
419C23×C4C22×D311yescharacteristic
420C22⋊Q8—632no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—34no—
424C2×C4⋊C4—41no—
425C2×C4⋊C4—62no—
426C2×C4⋊C4—62no—
427C2×C4⋊C4—62no—
428C2×C4⋊C4—62no—
429C2×C4⋊C4—62no—
430C2×C4⋊C4—62no—
431C2×C4⋊C4—62no—
432C2×C4⋊C4—62no—
433C2×C4⋊C4—62no—
434C2×C4⋊C4—62no—
435C2×C4⋊C4—62no—
436C2×C4⋊C4—121no—
437C2×C4⋊C4—121no—
438C2×C4⋊C4—121no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—22no—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—22no—
444C2×C22⋊C4—41no—
445C2×C22⋊C4—41no—
446C2×C22⋊C4—41no—
447C2×C22⋊C4—62no—
448C2×C22⋊C4—62no—
449C2×C22⋊C4—62no—
450C2×C22⋊C4—62no—
451C2×C22⋊C4—62no—
452C2×C22⋊C4—62no—
453C2×C22⋊C4—62no—
454C2×C22⋊C4—62no—
455C2×C22⋊C4—62no—
456C2×C22⋊C4—62no—
457C2×C22⋊C4—62no—
458C2×C22⋊C4—62no—
459C2×C22⋊C4—62no—
460C2×C22⋊C4—62no—
461C2×C22⋊C4—62no—
462C2×C22⋊C4—62no—
463C2×C22⋊C4—62no—
464C2×C22⋊C4—121no—
465C2×C22⋊C4—121no—
466C2×C22⋊C4—121no—
467C2×C22⋊C4—121no—
468C2×C22⋊C4—121no—
469C2×C22⋊C4—121no—
470C2×C22⋊C4—121no—
471C2×C22⋊C4D1214yes—
472C2×C42—62no—
473C2×C42—62no—
474C2×C42—121no—
475#95—22no—
476#95—34no—
477#95—41no—
478#95—41no—
479#95—62no—
480#95—62no—
481#95—62no—
482#95—62no—
483#95—62no—
484#95—62no—
485#95—62no—
486#95—62no—
487#95—62no—
488#95—121no—
489C23×C3—22no—
490C23×C3—22no—
491C23×C3—22no—
492C23×C3—22no—
493C23×C3—22no—
494C23×C3—22no—
495C23×C3—22no—
496C23×C3—22no—
497C23×C3—22no—
498C23×C3—22no—
499C23×C3—22no—
500C23×C3—22no—
501C23×C3—22no—
502C23×C3—22no—
503C23×C3—22no—
504C23×C3—22no—
505C23×C3—22no—
506C23×C3—22no—
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×C3C22⋊Q814yes—
524C23×C3C22×D411yescharacteristic
525C23×C3C22×D411yescharacteristic
526C23×C3C22×D411yescharacteristic
527C23×C3C22×D411yescharacteristic
528C23×C3C22×Q811yescharacteristic
529C23×C3C2×#4111yescharacteristic
530C23×C3C2×#4111yescharacteristic
531C23×C3C2×#4111yescharacteristic
532C23×C3C2×#4111yescharacteristic
533C23×C3H(5,𝔽2)11yescharacteristic
534C23×C3H(5,𝔽2)11yescharacteristic
535C23×C3H(5,𝔽2)11yescharacteristic
536C23×C3H(5,𝔽2)11yescharacteristic
537C23×C32−1+411yescharacteristic
538C23×C32−1+411yescharacteristic
539C22×D3—22no—
540C22×D3—22no—
541C22×D3—22no—
542C22×D3—22no—
543C22×D3—22no—
544C22×D3—22no—
545C22×D3—22no—
546C22×D3—41no—
547C22×D3—41no—
548C22×D3—41no—
549C22×D3—41no—
550C22×D3—41no—
551C22×D3—41no—
552C22×D3—41no—
553C22×D3—41no—
554C22×D3—41no—
555C22×D3—41no—
556C22×D3—41no—
557C22×D3—41no—
558C22×D3—41no—
559C22×D3—41no—
560C22×D3—41no—
561C22×D3—41no—
562C22×D3—41no—
563C22×D3—41no—
564C22×D3—41no—
565C22×D3—41no—
566C22×D3—41no—
567C22×D3—41no—
568C22×D3—41no—
569C22×D3—41no—
570C22×D3—41no—
571C22×D3—41no—
572C22×D3—41no—
573C22×D3—41no—
574C2×C3×C4—22no—
575C2×C3×C4—22no—
576C2×C3×C4—22no—
577C2×C3×C4—22no—
578C2×C3×C4—22no—
579C2×C3×C4—22no—
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—41no—
587C2×C3×C4—41no—
588C2×C3×C4—41no—
589C2×C3×C4—41no—
590C2×C3×C4—41no—
591C2×C3×C4—41no—
592C2×C3×C4—41no—
593C2×C3×C4—41no—
594C2×C3×C4—41no—
595C2×C3×C4—41no—
596C2×C3×C4—41no—
597C2×C3×C4—41no—
598C2×C3×C4—41no—
599C2×C3×C4—41no—
600C2×C3×C4—41no—
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#12014yes—
616#67—416no—
617C2×Dic3—22no—
618C2×Dic3—22no—
619C2×Dic3—22no—
620C2×Dic3—22no—
621C2×Dic3—22no—
622C2×Dic3—22no—
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—416no—
642C2×Dic3—41no—
643C2×Dic3—41no—
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#12114yes—
666C2×Dic3C22⋊Q814yescomplemented
667Dic6—416no—
668C24—21no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24—21no—
674C24—21no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—32no—
681C24—61no—
682C24—61no—
683C24—61no—
684C24—61no—
685C24—61no—
686C24—61no—
687C24—61no—
688C24—61no—
689C24—61no—
690C24—61no—
691C24—61no—
692C24—61no—
693C24—61no—
694C24—61no—
695C24C2×D1212yes—
696C24#23712yes—
697C24D3×Q812yes—
698C24C23×D311yescharacteristic
699C2×Q8—68no—
700C2×Q8—68no—
701C2×Q8—124no—
702C2×Q8—124no—
703C2×Q8—124no—
704C2×Q8—124no—
705C2×Q8—124no—
706C2×D4—68no—
707C2×D4—68no—
708C2×D4—124no—
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—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—32no—
751C22×C4—32no—
752C22×C4—32no—
753C22×C4—32no—
754C22×C4—32no—
755C22×C4—32no—
756C22×C4—32no—
757C22×C4—32no—
758C22×C4—32no—
759C22×C4—32no—
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—68no—
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—61no—
794C22×C4—61no—
795C22×C4—61no—
796C22×C4—61no—
797C22×C4—61no—
798C22×C4—61no—
799C22×C4—61no—
800C22×C4—124no—
801C22×C4—124no—
802C22×C4—124no—
803C22×C4—124no—
804C22×C4—124no—
805C22×C4—124no—
806C22×C4C2×D1212yes—
807C22×C4C2×D1212yes—
808C22×C4D3×D412yes—
809C22×C4D3×D412yes—
810C22×C4D3×D412yes—
811C4⋊C4—44no—
812C4⋊C4—68no—
813C4⋊C4—68no—
814C4⋊C4—68no—
815C4⋊C4—124no—
816C4⋊C4—124no—
817C22⋊C4—28no—
818C22⋊C4—44no—
819C22⋊C4—44no—
820C22⋊C4—68no—
821C22⋊C4—124no—
822C22⋊C4—124no—
823C22⋊C4—124no—
824C22⋊C4—124no—
825C22⋊C4—124no—
826C22⋊C4—124no—
827C22⋊C4—124no—
828C42—124no—
829C22×C3—24no—
830C22×C3—24no—
831C22×C3—24no—
832C22×C3—42no—
833C22×C3—42no—
834C22×C3—42no—
835C22×C3—42no—
836C22×C3—42no—
837C22×C3—42no—
838C22×C3—42no—
839C22×C3—42no—
840C22×C3—42no—
841C22×C3—42no—
842C22×C3—42no—
843C22×C3—42no—
844C22×C3C2×#12011yescharacteristic
845C22×C3C2×#12111yescharacteristic
846C22×C3C2×C22⋊Q811yescharacteristic
847C22×C3C2×C22⋊Q811yescharacteristic
848C22×C3#52911yescharacteristic
849C22×C3#53211yescharacteristic
850C22×C3#53411yescharacteristic
851C22×C3#53511yescharacteristic
852C22×C3#53611yescharacteristic
853C22×C3#53711yescharacteristic
854C22×C3#53811yescharacteristic
855C22×C3#53911yescharacteristic
856C22×C3#54211yescharacteristic
857C22×C3#54211yescharacteristic
858C22×C3#54311yescharacteristic
859C22×C3D4211yescharacteristic
860C22×C3D4211yescharacteristic
861C22×C3#54611yescharacteristic
862C22×C3#54611yescharacteristic
863C22×C3#54611yescharacteristic
864C22×C3#54611yescharacteristic
865C22×C3#54611yescharacteristic
866C22×C3#54811yescharacteristic
867C22×C3#54811yescharacteristic
868C22×C3#54811yescharacteristic
869C22×C3D4×Q811yescharacteristic
870C22×C3D4×Q811yescharacteristic
871C22×C3#55011yescharacteristic
872C22×C3#55011yescharacteristic
873C22×C3#55111yescharacteristic
874C22×C3#55411yescharacteristic
875C22×C3#55411yescharacteristic
876C22×C3#55611yescharacteristic
877C22×C3#56211yescharacteristic
878C22×C3#56211yescharacteristic
879C2×D3—42no—
880C2×D3—42no—
881C2×D3—42no—
882C2×D3—42no—
883C2×D3—42no—
884C2×D3—42no—
885C2×D3—42no—
886C2×D3—81no—
887C2×D3—81no—
888C2×D3—81no—
889C2×D3—81no—
890C2×D3—81no—
891C2×D3—81no—
892C2×D3—81no—
893C2×D3—81no—
894C3×C4—24no—
895C3×C4—42no—
896C3×C4—42no—
897C3×C4—81no—
898C3×C4—81no—
899C3×C4—81no—
900Dic3—24no—
901Dic3—24no—
902Dic3—42no—
903Dic3—42no—
904Dic3—42no—
905Dic3—42no—
906Dic3—81no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—62no—
942C23—62no—
943C23—62no—
944C23—62no—
945C23—62no—
946C23—62no—
947C23—62no—
948C23—121no—
949C23—121no—
950C23—121no—
951C23—121no—
952C23—121no—
953C23—121no—
954C23—121no—
955C23—121no—
956C23—121no—
957C23—121no—
958C23—121no—
959C23—121no—
960C23—121no—
961C23—121no—
962C23—121no—
963C23—121no—
964C23—121no—
965C23—121no—
966C23—121no—
967C23—121no—
968C23—121no—
969C23—121no—
970C23—121no—
971C23—121no—
972C23—121no—
973C23—121no—
974C23—121no—
975C23—121no—
976C23#89714yes—
977C23C22×D1211yescharacteristic
978C23C2×D3×D411yescharacteristic
979C23C2×D3×D411yescharacteristic
980C23C2×D3×D411yescharacteristic
981C23C2×#23711yescharacteristic
982C23#100411yescharacteristic
983C23#100411yescharacteristic
984C23#100411yescharacteristic
985C23C2×D3×Q811yescharacteristic
986C23D3×#4111yescharacteristic
987C23D3×#4111yescharacteristic
988C23D3×#4111yescharacteristic
989C23#100911yescharacteristic
990C23#101011yescharacteristic
991C23#101011yescharacteristic
992Q8—1216no—
993D4—1216no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—34no—
1007C2×C4—34no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
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—62no—
1038C2×C4—62no—
1039C2×C4—62no—
1040C2×C4—62no—
1041C2×C4—62no—
1042C2×C4—62no—
1043C2×C4—62no—
1044C2×C4—62no—
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—1216no—
1062C2×C4—121no—
1063C2×C4—121no—
1064C2×C4—121no—
1065C2×C4—121no—
1066C2×C4—121no—
1067C2×C4—121no—
1068C2×C4—121no—
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#88214yes—
1086C2×C3—44no—
1087C2×C3#240911yescharacteristic
1088C2×C3#241011yescharacteristic
1089C2×C3#242611yescharacteristic
1090C2×C3#243111yescharacteristic
1091C2×C3#243711yescharacteristic
1092C2×C3#245011yescharacteristic
1093C2×C3#245211yescharacteristic
1094C2×C3#253811yescharacteristic
1095C2×C3#256011yescharacteristic
1096C2×C3#267611yescharacteristic
1097C2×C3#268111yescharacteristic
1098C2×C3#269211yescharacteristic
1099C2×C3#270011yescharacteristic
1100C2×C3#273011yescharacteristic
1101C2×C3#273211yescharacteristic
1102D3—82no—
1103C22—24no—
1104C22—24no—
1105C22—24no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22—122no—
1119C22—122no—
1120C22—122no—
1121C22—122no—
1122C22—122no—
1123C22—122no—
1124C22—122no—
1125C22—241no—
1126C22—241no—
1127C22—241no—
1128C22—241no—
1129C22—241no—
1130C22—241no—
1131C22—241no—
1132C22—241no—
1133C22C2×#88211yescharacteristic
1134C22C2×#89711yescharacteristic
1135C22#552611yescharacteristic
1136C22D4×D1211yescharacteristic
1137C22#555411yescharacteristic
1138C22#555411yescharacteristic
1139C22#555411yescharacteristic
1140C22#559011yescharacteristic
1141C22#559111yescharacteristic
1142C22#559311yescharacteristic
1143C22#559711yescharacteristic
1144C22#559811yescharacteristic
1145C22#559811yescharacteristic
1146C22#559911yescharacteristic
1147C22#559911yescharacteristic
1148C22D3×#12111yescharacteristic
1149C22#560511yescharacteristic
1150C22#562111yescharacteristic
1151C22D3×C22⋊Q811yescharacteristic
1152C22#563211yescharacteristic
1153C22#563211yescharacteristic
1154C22#563411yescharacteristic
1155C22#563611yescharacteristic
1156C22#563611yescharacteristic
1157C22#564911yescharacteristic
1158C22#565411yescharacteristic
1159C22#565811yescharacteristic
1160C22#566211yescharacteristic
1161C22#566711yescharacteristic
1162C22#566811yescharacteristic
1163C22#566911yescharacteristic
1164C22#567711yescharacteristic
1165C22#570211yescharacteristic
1166C22#570711yescharacteristic
1167C22#571511yescharacteristic
1168C4—24no—
1169C4—42no—
1170C4—42no—
1171C4—64no—
1172C4—64no—
1173C4—81no—
1174C4—81no—
1175C4—81no—
1176C4—122no—
1177C4—122no—
1178C4—122no—
1179C4—122no—
1180C4—241no—
1181C3#1528011yescharacteristic, complemented, Sylow
1182C2—44no—
1183C2—242no—
1184C2#7401711yescharacteristic
1185C2#7441311yescharacteristic
1186C2#7442411yescharacteristic
1187C2#7488811yescharacteristic
1188C2#7566911yescharacteristic
1189C2#7567911yescharacteristic
1190C2#7631311yescharacteristic
1191C2#7671411yescharacteristic
1192C2#7678311yescharacteristic
1193C2#7690111yescharacteristic
1194C2#7704511yescharacteristic
1195C2#7731411yescharacteristic
1196C2#7737211yescharacteristic
1197C2#7751811yescharacteristic
1198C2#7806211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1439C2
prime radicalC23×#67C22
hypercenter#1439D3
hypocenterC3#15280
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
1. C22×#878C2semidirect
2. C2×#4994C2semidirect
3. C2×#4973C2semidirect
6. C2×#4673C2semidirect
7. C3×#1439C2semidirect
9. #71546C2semidirect
10. #71544C2semidirect
11. #69428C2semidirect
12. #69427C2semidirect
13. #69420C2semidirect
14. #69410C2semidirect
15. #69405C2semidirect
71. #1439D3semidirect
89. C22×#67Q8semidirect
110. C22×Dic6D4semidirect
161. C2×Dic3⋊C4D4semidirect
666. C2×Dic3C22⋊Q8semidirect
1181. C3#15280semidirect

Maximal subgroups

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

subgroupindex
C22×#8782
C2×#49942
C2×#49732
C2×#49572
C2×#49582
C2×#46732
C3×#14392
#715502
#715462
#715442
#694282
#694272
#694202
#694102
#694052
#152803