Finite Group Databasebeta

← #10746865

Subgroups — #10746865

Order 768.

2246 conjugacy classes of subgroups.

The subgroup lattice has 1206 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#886C211yesmaximal, characteristic
2C22×#878C211yesmaximal, characteristic, complemented
3C2×#4959C211yesmaximal, characteristic
4C2×#4961C211yesmaximal, characteristic
5C2×#4673C211yesmaximal, characteristic, complemented
6C2×#4656C211yesmaximal, characteristic, complemented
7C3×#1440C211yesmaximal, characteristic, complemented
8#71549C211yesmaximal, characteristic, complemented
9#71544C211yesmaximal, characteristic, complemented
10#69428C211yesmaximal, characteristic, complemented
11#69428C211yesmaximal, characteristic, complemented
12#69427C211yesmaximal, characteristic, complemented
13#69420C211yesmaximal, characteristic, complemented
14#69419C211yesmaximal, characteristic, complemented
15#69411C211yesmaximal, characteristic, complemented
16#16251—31nomaximal, Sylow
17C23×#67C2211yescharacteristic
18C24×Dic3C2211yescharacteristic
19C23×Dic6C2211yescharacteristic
20C22×C3×C22⋊C4C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×#217C2211yescharacteristic
24C22×#217C2211yescharacteristic
25C22×(C2×D3)⋊C4C2211yescharacteristic
26C22×(C2×D3)⋊C4C2211yescharacteristic
27C22×(C2×D3)⋊C4C2211yescharacteristic
28C22×(C2×D3)⋊C4C2211yescharacteristic
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×(C2×D3)⋊C4C2211yescharacteristic
31C22×C4⋊Dic3C2211yescharacteristic
32C22×C4⋊Dic3C2211yescharacteristic
33C22×C4⋊Dic3C2211yescharacteristic
34C22×C4⋊Dic3C2211yescharacteristic
35C22×Dic3⋊C4C2211yescharacteristic
36C22×Dic3⋊C4C2211yescharacteristic
37C22×Dic3⋊C4C2211yescharacteristic
38C2×#886—24no—
39C2×#886—24no—
40C2×#886—24no—
41C2×#878—24no—
42C2×#878—24no—
43C2×#878—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#4961—24no—
59#4959—24no—
60#4673—24no—
61#4656—24no—
62C22×#123—31no—
63C22×C22⋊Q8—31no—
64C2×#395—31no—
65C2×#394—31no—
66C2×#394—31no—
67C2×#393—31no—
68#1444—31no—
69#1444—31no—
70#1441—31no—
71#1440—31no—
72#1440D311yescharacteristic, complemented
73#1439—31no—
74#1439—31no—
75#1439—31no—
76C22⋊#95—31no—
77C25×C3C2311yescharacteristic
78C24×D3C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C22×#67—22no—
86C22×#67—22no—
87C22×#67—22no—
88C22×#67—22no—
89C22×#67—22no—
90C22×#67—41no—
91C22×#67—41no—
92C23×Dic3—22no—
93C23×Dic3—22no—
94C23×Dic3—22no—
95C23×Dic3—22no—
96C23×Dic3—41no—
97C23×Dic3—41no—
98C23×Dic3D414yes—
99C23×Dic3C2311yescharacteristic
100C23×Dic3C2311yescharacteristic
101C23×Dic3C2311yescharacteristic
102C23×Dic3C2311yescharacteristic
103C23×Dic3C2311yescharacteristic
104C23×Dic3C2311yescharacteristic
105C23×Dic3C2311yescharacteristic
106C22×Dic6—22no—
107C22×Dic6—22no—
108C22×Dic6—22no—
109C22×Dic6—22no—
110C22×Dic6—22no—
111C22×Dic6—41no—
112C22×Dic6—41no—
113C2×C3×C22⋊C4—22no—
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—22no—
120C2×C3×C22⋊C4—41no—
121C2×C3×C22⋊C4D414yes—
122C2×#217—22no—
123C2×#217—22no—
124C2×#217—22no—
125C2×#217—22no—
126C2×#217—41no—
127C2×#217D414yes—
128C2×(C2×D3)⋊C4—22no—
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)⋊C4D414yes—
146C2×C4⋊Dic3—22no—
147C2×C4⋊Dic3—22no—
148C2×C4⋊Dic3—22no—
149C2×C4⋊Dic3—22no—
150C2×C4⋊Dic3—22no—
151C2×C4⋊Dic3—22no—
152C2×C4⋊Dic3—22no—
153C2×C4⋊Dic3—22no—
154C2×C4⋊Dic3—22no—
155C2×C4⋊Dic3—22no—
156C2×C4⋊Dic3—41no—
157C2×C4⋊Dic3D414yes—
158C2×Dic3⋊C4—22no—
159C2×Dic3⋊C4—22no—
160C2×Dic3⋊C4—22no—
161C2×Dic3⋊C4—22no—
162C2×Dic3⋊C4—22no—
163C2×Dic3⋊C4—22no—
164C2×Dic3⋊C4—22no—
165C2×Dic3⋊C4—22no—
166C2×Dic3⋊C4—41no—
167#886—232no—
168#878—232no—
169C3×#95—22no—
170C3×#95—22no—
171C3×#95—22no—
172C3×#95—41no—
173C3⋊#95—22no—
174C3⋊#95—22no—
175C3⋊#95—22no—
176C3⋊#95—22no—
177C3⋊#95—22no—
178C3⋊#95—22no—
179C3⋊#95—22no—
180C3⋊#95—41no—
181C3⋊#95—41no—
182C3⋊#95—41no—
183C23×Q8—31no—
184C23×D4—31no—
185C24×C4—31no—
186C2×#123—64no—
187C2×#123—64no—
188C2×#123—64no—
189C2×C22⋊Q8—64no—
190C2×C22⋊Q8—64no—
191C2×C22⋊Q8—64no—
192C22×C4⋊C4—31no—
193C22×C4⋊C4—31no—
194C22×C4⋊C4—31no—
195C22×C4⋊C4—31no—
196C22×C4⋊C4—31no—
197C22×C4⋊C4—31no—
198C22×C4⋊C4—31no—
199C22×C22⋊C4—31no—
200C22×C22⋊C4—31no—
201C22×C22⋊C4—31no—
202C22×C22⋊C4—31no—
203C22×C22⋊C4—31no—
204C22×C22⋊C4—31no—
205C22×C22⋊C4—31no—
206C22×C22⋊C4—31no—
207C22×C22⋊C4C2×D311yescharacteristic
208C22×C22⋊C4C2×D311yescharacteristic
209C22×C22⋊C4C2×D311yescharacteristic
210#395—64no—
211#394—64no—
212#394—64no—
213#393—64no—
214C2×#95—31no—
215C2×#95—31no—
216C2×#95—31no—
217C2×#95—31no—
218C2×#95—31no—
219C2×#95—31no—
220C2×#95—31no—
221C2×#95—31no—
222C2×#95—31no—
223C2×#95—31no—
224C2×#95C2×D311yescharacteristic
225C2×#95C2×D311yescharacteristic
226C2×#95C2×D311yescharacteristic
227C2×#95C2×D311yescharacteristic
228C24×C3—21no—
229C24×C3—21no—
230C24×C3—21no—
231C24×C3—21no—
232C24×C3—21no—
233C24×C3—21no—
234C24×C3—21no—
235C24×C3—21no—
236C24×C3—21no—
237C24×C3—21no—
238C24×C3—21no—
239C24×C3—21no—
240C24×C3C2×D412yes—
241C24×C3C2×D412yes—
242C24×C3C2×D412yes—
243C24×C3C2411yescharacteristic
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×D3—21no—
254C23×D3—21no—
255C23×D3—21no—
256C23×D3—21no—
257C23×D3—21no—
258C23×D3C2×D412yes—
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×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4C2×D412yes—
297C22×C3×C4C2×D412yes—
298C22×C3×C4C2×D412yes—
299C22×C3×C4C2×D412yes—
300C22×C3×C4#4112yes—
301C2×#67—28no—
302C2×#67—44no—
303C2×#67—44no—
304C2×#67—44no—
305C2×#67—44no—
306C2×#67—44no—
307C2×#67—44no—
308C22×Dic3—21no—
309C22×Dic3—21no—
310C22×Dic3—21no—
311C22×Dic3—21no—
312C22×Dic3—28no—
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—28no—
344C22×Dic3—21no—
345C22×Dic3—21no—
346C22×Dic3—21no—
347C22×Dic3—21no—
348C22×Dic3—21no—
349C22×Dic3—21no—
350C22×Dic3—21no—
351C22×Dic3—44no—
352C22×Dic3—44no—
353C22×Dic3—44no—
354C22×Dic3—44no—
355C22×Dic3—44no—
356C22×Dic3C2×D412yes—
357C22×Dic3C2×D412yes—
358C22×Dic3C2×D412yes—
359C22×Dic3C2×D412yes—
360C22×Dic3C2×D412yes—
361C22×Dic3C2×D412yes—
362C22×Dic3C2×D412yes—
363C22×Dic3#4112yes—
364C2×Dic6—28no—
365C2×Dic6—44no—
366C2×Dic6—44no—
367C2×Dic6—44no—
368C2×Dic6—44no—
369C2×Dic6—44no—
370C2×Dic6—44no—
371C3×C22⋊C4—28no—
372C3×C22⋊C4—28no—
373C3×C22⋊C4—44no—
374#217—28no—
375#217—44no—
376(C2×D3)⋊C4—28no—
377(C2×D3)⋊C4—28no—
378(C2×D3)⋊C4—44no—
379(C2×D3)⋊C4—44no—
380(C2×D3)⋊C4—44no—
381(C2×D3)⋊C4—44no—
382C4⋊Dic3—28no—
383C4⋊Dic3—28no—
384C4⋊Dic3—28no—
385C4⋊Dic3—44no—
386Dic3⋊C4—28no—
387Dic3⋊C4—28no—
388Dic3⋊C4—44no—
389C25—31no—
390C25C22×D311yescharacteristic
391C22×Q8—62no—
392C22×Q8—62no—
393C22×Q8—62no—
394C22×Q8—62no—
395C22×Q8—62no—
396C22×Q8—121no—
397C22×Q8—121no—
398C22×D4—62no—
399C22×D4—62no—
400C22×D4—62no—
401C22×D4—62no—
402C22×D4—62no—
403C22×D4—121no—
404C22×D4—121no—
405C23×C4—31no—
406C23×C4—31no—
407C23×C4—31no—
408C23×C4—31no—
409C23×C4—31no—
410C23×C4—31no—
411C23×C4—34no—
412C23×C4—31no—
413C23×C4—62no—
414C23×C4—62no—
415C23×C4—62no—
416C23×C4—62no—
417C23×C4—121no—
418C23×C4—121no—
419C23×C4C22×D311yescharacteristic
420C23×C4C22×D311yescharacteristic
421C23×C4C22×D311yescharacteristic
422C23×C4C22×D311yescharacteristic
423C23×C4C22×D311yescharacteristic
424C23×C4C22×D311yescharacteristic
425#123—632no—
426C22⋊Q8—632no—
427C2×C4⋊C4—34no—
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—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—62no—
445C2×C4⋊C4—62no—
446C2×C4⋊C4—121no—
447C2×C4⋊C4—121no—
448C2×C22⋊C4—22no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—22no—
452C2×C22⋊C4—22no—
453C2×C22⋊C4—22no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—34no—
456C2×C22⋊C4—34no—
457C2×C22⋊C4—41no—
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—62no—
465C2×C22⋊C4—62no—
466C2×C22⋊C4—62no—
467C2×C22⋊C4—62no—
468C2×C22⋊C4—62no—
469C2×C22⋊C4—62no—
470C2×C22⋊C4—62no—
471C2×C22⋊C4—62no—
472C2×C22⋊C4—62no—
473C2×C22⋊C4—62no—
474C2×C22⋊C4—62no—
475C2×C22⋊C4—121no—
476C2×C22⋊C4—121no—
477C2×C22⋊C4—121no—
478C2×C22⋊C4—121no—
479C2×C22⋊C4—121no—
480C2×C22⋊C4D1214yes—
481#95—22no—
482#95—22no—
483#95—22no—
484#95—41no—
485#95—62no—
486#95—62no—
487#95—62no—
488#95—62no—
489#95—62no—
490#95—62no—
491#95—62no—
492#95—121no—
493#95—121no—
494#95—121no—
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—22no—
508C23×C3—22no—
509C23×C3—22no—
510C23×C3—22no—
511C23×C3—22no—
512C23×C3—22no—
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#12014yes—
530C23×C3C22×D411yescharacteristic
531C23×C3C22×D411yescharacteristic
532C23×C3C22×D411yescharacteristic
533C23×C3C22×D411yescharacteristic
534C23×C3C22×D411yescharacteristic
535C23×C3C2×#4111yescharacteristic
536C23×C3C2×#4111yescharacteristic
537C23×C3H(5,𝔽2)11yescharacteristic
538C23×C3H(5,𝔽2)11yescharacteristic
539C23×C3H(5,𝔽2)11yescharacteristic
540C23×C32−1+411yescharacteristic
541C23×C32−1+411yescharacteristic
542C23×C32−1+411yescharacteristic
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—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—
574C22×D3—41no—
575C22×D3—41no—
576C22×D3—41no—
577C22×D3—41no—
578C22×D3—41no—
579C22×D3—41no—
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—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—41no—
616C2×C3×C4—41no—
617C2×C3×C4—41no—
618C2×C3×C4—41no—
619C2×C3×C4—41no—
620C2×C3×C4—41no—
621C2×C3×C4—41no—
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—416no—
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×Dic3—41no—
672C2×Dic3#12014yes—
673Dic6—416no—
674C24—21no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—21no—
681C24—21no—
682C24—21no—
683C24—21no—
684C24—21no—
685C24—21no—
686C24—32no—
687C24—61no—
688C24—61no—
689C24—61no—
690C24—61no—
691C24—61no—
692C24—61no—
693C24—61no—
694C24—61no—
695C24—61no—
696C24—61no—
697C24—61no—
698C24—61no—
699C24—61no—
700C24—61no—
701C24C2×D1212yes—
702C24D3×D412yes—
703C24D3×D412yes—
704C24C23×D311yescharacteristic
705C2×Q8—68no—
706C2×Q8—124no—
707C2×Q8—124no—
708C2×Q8—124no—
709C2×Q8—124no—
710C2×Q8—124no—
711C2×Q8—124no—
712C2×D4—68no—
713C2×D4—124no—
714C2×D4—124no—
715C2×D4—124no—
716C2×D4—124no—
717C2×D4—124no—
718C2×D4—124no—
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—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—32no—
757C22×C4—32no—
758C22×C4—32no—
759C22×C4—32no—
760C22×C4—32no—
761C22×C4—32no—
762C22×C4—32no—
763C22×C4—32no—
764C22×C4—68no—
765C22×C4—61no—
766C22×C4—61no—
767C22×C4—61no—
768C22×C4—61no—
769C22×C4—68no—
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—61no—
801C22×C4—61no—
802C22×C4—61no—
803C22×C4—61no—
804C22×C4—61no—
805C22×C4—61no—
806C22×C4—61no—
807C22×C4—124no—
808C22×C4—124no—
809C22×C4—124no—
810C22×C4—124no—
811C22×C4—124no—
812C22×C4C2×D1212yes—
813C22×C4C2×D1212yes—
814C22×C4D3×D412yes—
815C22×C4D3×D412yes—
816C22×C4#23712yes—
817C4⋊C4—68no—
818C4⋊C4—68no—
819C4⋊C4—68no—
820C4⋊C4—68no—
821C4⋊C4—68no—
822C4⋊C4—124no—
823C4⋊C4—124no—
824C22⋊C4—28no—
825C22⋊C4—28no—
826C22⋊C4—44no—
827C22⋊C4—68no—
828C22⋊C4—68no—
829C22⋊C4—68no—
830C22⋊C4—124no—
831C22⋊C4—124no—
832C22⋊C4—124no—
833C22⋊C4—124no—
834C22⋊C4—124no—
835C22×C3—24no—
836C22×C3—24no—
837C22×C3—24no—
838C22×C3—42no—
839C22×C3—42no—
840C22×C3—42no—
841C22×C3—42no—
842C22×C3—42no—
843C22×C3—42no—
844C22×C3—42no—
845C22×C3—42no—
846C22×C3—42no—
847C22×C3—42no—
848C22×C3—42no—
849C22×C3—42no—
850C22×C3C2×#12011yescharacteristic
851C22×C3C2×#12011yescharacteristic
852C22×C3#53211yescharacteristic
853C22×C3#53411yescharacteristic
854C22×C3#53611yescharacteristic
855C22×C3#53611yescharacteristic
856C22×C3#53611yescharacteristic
857C22×C3#53611yescharacteristic
858C22×C3#53611yescharacteristic
859C22×C3#53611yescharacteristic
860C22×C3#53611yescharacteristic
861C22×C3#53611yescharacteristic
862C22×C3#53711yescharacteristic
863C22×C3#53711yescharacteristic
864C22×C3#53711yescharacteristic
865C22×C3#53911yescharacteristic
866C22×C3#53911yescharacteristic
867C22×C3#54211yescharacteristic
868C22×C3#54211yescharacteristic
869C22×C3D4211yescharacteristic
870C22×C3D4211yescharacteristic
871C22×C3D4211yescharacteristic
872C22×C3D4211yescharacteristic
873C22×C3#54611yescharacteristic
874C22×C3#54611yescharacteristic
875C22×C3#54711yescharacteristic
876C22×C3#54711yescharacteristic
877C22×C3#54711yescharacteristic
878C22×C3#54711yescharacteristic
879C22×C3#54811yescharacteristic
880C22×C3#54811yescharacteristic
881C22×C3#56211yescharacteristic
882C22×C3#56211yescharacteristic
883C22×C3#56311yescharacteristic
884C22×C3#56311yescharacteristic
885C2×D3—42no—
886C2×D3—42no—
887C2×D3—42no—
888C2×D3—42no—
889C2×D3—42no—
890C2×D3—42no—
891C2×D3—42no—
892C2×D3—81no—
893C2×D3—81no—
894C2×D3—81no—
895C2×D3—81no—
896C2×D3—81no—
897C2×D3—81no—
898C2×D3—81no—
899C2×D3—81no—
900C3×C4—42no—
901C3×C4—42no—
902C3×C4—42no—
903C3×C4—42no—
904C3×C4—42no—
905C3×C4—81no—
906Dic3—24no—
907Dic3—42no—
908Dic3—42no—
909Dic3—42no—
910Dic3—42no—
911Dic3—42no—
912Dic3—81no—
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—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—41no—
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—62no—
948C23—62no—
949C23—62no—
950C23—62no—
951C23—62no—
952C23—62no—
953C23—62no—
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—121no—
977C23—121no—
978C23—121no—
979C23—121no—
980C23—121no—
981C23—121no—
982C23#88214yes—
983C23C22×D1211yescharacteristic
984C23C2×D3×D411yescharacteristic
985C23C2×D3×D411yescharacteristic
986C23C2×D3×D411yescharacteristic
987C23C2×D3×D411yescharacteristic
988C23C2×#23711yescharacteristic
989C23#100411yescharacteristic
990C23D3×#4111yescharacteristic
991C23#100911yescharacteristic
992C23#100911yescharacteristic
993C23#101011yescharacteristic
994C23#101011yescharacteristic
995C23#101011yescharacteristic
996C23#101011yescharacteristic
997C23#101011yescharacteristic
998Q8—1216no—
999D4—1216no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
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—34no—
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—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
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—62no—
1062C2×C4—62no—
1063C2×C4—62no—
1064C2×C4—1216no—
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—121no—
1086C2×C4—121no—
1087C2×C4—121no—
1088C2×C4—121no—
1089C2×C4—121no—
1090C2×C4—121no—
1091C2×C4—121no—
1092C2×C3—44no—
1093C2×C3#240311yescharacteristic
1094C2×C3#243011yescharacteristic
1095C2×C3#243211yescharacteristic
1096C2×C3#261411yescharacteristic
1097C2×C3#261611yescharacteristic
1098C2×C3#266311yescharacteristic
1099C2×C3#267211yescharacteristic
1100C2×C3#267211yescharacteristic
1101C2×C3#267411yescharacteristic
1102C2×C3#267411yescharacteristic
1103C2×C3#268011yescharacteristic
1104C2×C3#268011yescharacteristic
1105C2×C3#268111yescharacteristic
1106C2×C3#268111yescharacteristic
1107C2×C3#281411yescharacteristic
1108D3—82no—
1109C22—24no—
1110C22—24no—
1111C22—24no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22—42no—
1121C22—42no—
1122C22—42no—
1123C22—42no—
1124C22—122no—
1125C22—122no—
1126C22—122no—
1127C22—122no—
1128C22—122no—
1129C22—122no—
1130C22—122no—
1131C22—241no—
1132C22—241no—
1133C22—241no—
1134C22—241no—
1135C22—241no—
1136C22—241no—
1137C22—241no—
1138C22—241no—
1139C22C2×#88211yescharacteristic
1140C22#552611yescharacteristic
1141C22#552611yescharacteristic
1142C22D4×D1211yescharacteristic
1143C22D4×D1211yescharacteristic
1144C22#555411yescharacteristic
1145C22#555511yescharacteristic
1146C22D3×#12011yescharacteristic
1147C22#559111yescharacteristic
1148C22#559611yescharacteristic
1149C22#559711yescharacteristic
1150C22#559711yescharacteristic
1151C22#559811yescharacteristic
1152C22#560811yescharacteristic
1153C22#560911yescharacteristic
1154C22#560911yescharacteristic
1155C22#561111yescharacteristic
1156C22#564811yescharacteristic
1157C22#564811yescharacteristic
1158C22#564811yescharacteristic
1159C22#564811yescharacteristic
1160C22#564811yescharacteristic
1161C22#565311yescharacteristic
1162C22#565511yescharacteristic
1163C22#565511yescharacteristic
1164C22#566511yescharacteristic
1165C22#566711yescharacteristic
1166C22#567511yescharacteristic
1167C22#567711yescharacteristic
1168C22#568211yescharacteristic
1169C22#568411yescharacteristic
1170C22#570711yescharacteristic
1171C22#571011yescharacteristic
1172C22#571211yescharacteristic
1173C22#571211yescharacteristic
1174C4—42no—
1175C4—42no—
1176C4—42no—
1177C4—42no—
1178C4—42no—
1179C4—64no—
1180C4—81no—
1181C4—122no—
1182C4—122no—
1183C4—122no—
1184C4—122no—
1185C4—122no—
1186C4—241no—
1187C3#1625111yescharacteristic, complemented, Sylow
1188C2—44no—
1189C2—242no—
1190C2#7413511yescharacteristic
1191C2#7469911yescharacteristic
1192C2#7488411yescharacteristic
1193C2#7566511yescharacteristic
1194C2#7566611yescharacteristic
1195C2#7566811yescharacteristic
1196C2#7566911yescharacteristic
1197C2#7690411yescharacteristic
1198C2#7697011yescharacteristic
1199C2#7700111yescharacteristic
1200C2#7700611yescharacteristic
1201C2#7756511yescharacteristic
1202C2#7756711yescharacteristic
1203C2#7756811yescharacteristic
1204C2#7772711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1440C2
prime radicalC23×#67C22
hypercenter#1440D3
hypocenterC3#16251
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1440

Complements

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

NH ≅ G/Ntype
2. C22×#878C2semidirect
5. C2×#4673C2semidirect
6. C2×#4656C2semidirect
7. C3×#1440C2semidirect
8. #71549C2semidirect
9. #71544C2semidirect
10. #69428C2semidirect
11. #69428C2semidirect
12. #69427C2semidirect
13. #69420C2semidirect
14. #69419C2semidirect
15. #69411C2semidirect
72. #1440D3semidirect
1187. C3#16251semidirect

Maximal subgroups

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

subgroupindex
C22×#8862
C22×#8782
C2×#49592
C2×#49612
C2×#46732
C2×#46562
C3×#14402
#715492
#715442
#694282
#694272
#694202
#694192
#694112
#162513