Finite Group Databasebeta

← #10733689

Subgroups — #10733689

Order 768.

2306 conjugacy classes of subgroups.

The subgroup lattice has 1336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#875C211yesmaximal, characteristic, complemented
2C2×#4959C211yesmaximal, characteristic, complemented
3C2×#4960C211yesmaximal, characteristic
4C2×#4947C211yesmaximal, characteristic, complemented
5C2×#4957C211yesmaximal, characteristic, complemented
6C2×#4646C211yesmaximal, characteristic, complemented
7C3×#1437C211yesmaximal, characteristic, complemented
8#71550C211yesmaximal, characteristic, complemented
9#71550C211yesmaximal, characteristic, complemented
10#71536C211yesmaximal, characteristic, complemented
11#69429C211yesmaximal, characteristic, complemented
12#69428C211yesmaximal, characteristic, complemented
13#69428C211yesmaximal, characteristic, complemented
14#69426C211yesmaximal, characteristic, complemented
15#69408C211yesmaximal, characteristic, complemented
16#15317—31nomaximal, Sylow
17C23×#67C2211yescharacteristic
18C23×#67C2211yescharacteristic
19C23×D12C2211yescharacteristic
20C23×Dic6C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C42C2211yescharacteristic
25C22×#217C2211yescharacteristic
26C22×#217C2211yescharacteristic
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×Dic3⋊C4C2211yescharacteristic
38C22×Dic3⋊C4C2211yescharacteristic
39C22×C4×Dic3C2211yescharacteristic
40C2×#875—24no—
41C2×#875—24no—
42C2×#875—24no—
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#4960—24no—
56#4959—24no—
57#4957—24no—
58#4947—24no—
59#4646—24no—
60C22×#124—31no—
61C2×#394—31no—
62C2×#393—31no—
63C2×#392—31no—
64C2×#391—31no—
65C2×#390—31no—
66#1440—31no—
67#1439—31no—
68#1439—31no—
69#1438—31no—
70#1438—31no—
71#1438—31no—
72#1437—31no—
73#1437D311yescharacteristic, complemented
74#1436—31no—
75C25×C3C2311yescharacteristic
76C24×D3C2311yescharacteristic
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×#67—22no—
91C22×#67—22no—
92C22×#67—41no—
93C22×#67—41no—
94C22×#67—41no—
95C22×#67—41no—
96C22×#67—41no—
97C22×#67—41no—
98C23×Dic3C2311yescharacteristic
99C23×Dic3C2311yescharacteristic
100C23×Dic3C2311yescharacteristic
101C23×Dic3C2311yescharacteristic
102C23×Dic3C2311yescharacteristic
103C23×Dic3C2311yescharacteristic
104C22×D12—22no—
105C22×D12—22no—
106C22×D12—22no—
107C22×D12—22no—
108C22×D12—22no—
109C22×D12—41no—
110C22×D12—41no—
111C22×Dic6—22no—
112C22×Dic6—22no—
113C22×Dic6—22no—
114C22×Dic6—22no—
115C22×Dic6—41no—
116C22×Dic6—41no—
117C22×Dic6D414yescomplemented
118C2×C3×C22⋊C4—22no—
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—41no—
126C2×C3×C22⋊C4—41no—
127C2×C3×C42—22no—
128C2×C3×C42—22no—
129C2×C3×C42—22no—
130C2×#217—22no—
131C2×#217—22no—
132C2×#217—22no—
133C2×#217—22no—
134C2×#217—41no—
135C2×#217—41no—
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—22no—
142C2×(C2×D3)⋊C4—22no—
143C2×(C2×D3)⋊C4—22no—
144C2×(C2×D3)⋊C4—22no—
145C2×(C2×D3)⋊C4—22no—
146C2×(C2×D3)⋊C4—22no—
147C2×(C2×D3)⋊C4—22no—
148C2×(C2×D3)⋊C4—22no—
149C2×(C2×D3)⋊C4—22no—
150C2×(C2×D3)⋊C4—22no—
151C2×(C2×D3)⋊C4—22no—
152C2×(C2×D3)⋊C4—22no—
153C2×(C2×D3)⋊C4—22no—
154C2×(C2×D3)⋊C4—41no—
155C2×(C2×D3)⋊C4—41no—
156C2×(C2×D3)⋊C4—41no—
157C2×(C2×D3)⋊C4—41no—
158C2×(C2×D3)⋊C4—41no—
159C2×(C2×D3)⋊C4—41no—
160C2×(C2×D3)⋊C4—41no—
161C2×(C2×D3)⋊C4—41no—
162C2×(C2×D3)⋊C4—41no—
163C2×(C2×D3)⋊C4—41no—
164C2×(C2×D3)⋊C4D414yescomplemented
165C2×(C2×D3)⋊C4D414yescomplemented
166C2×Dic3⋊C4—22no—
167C2×Dic3⋊C4—22no—
168C2×Dic3⋊C4—22no—
169C2×Dic3⋊C4—22no—
170C2×Dic3⋊C4—41no—
171C2×Dic3⋊C4—41no—
172C2×C4×Dic3—22no—
173C2×C4×Dic3—22no—
174C2×C4×Dic3—41no—
175#875—232no—
176C3×#95—22no—
177C3×#95—41no—
178C3×#95—41no—
179C3⋊#95—22no—
180C3⋊#95—22no—
181C3⋊#95—22no—
182C3⋊#95—22no—
183C3⋊#95—22no—
184C3⋊#95—22no—
185C3⋊#95—22no—
186C3⋊#95—41no—
187C3⋊#95D414yes—
188C23×Q8—31no—
189C23×D4—31no—
190C23×D4—31no—
191C23×D4—31no—
192C2×#124—64no—
193C2×#124—64no—
194C2×#124—64no—
195C22×C4⋊C4—31no—
196C22×C4⋊C4—31no—
197C22×C22⋊C4—31no—
198C22×C22⋊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⋊C4—31no—
208C22×C22⋊C4—31no—
209C22×C22⋊C4C2×D311yescharacteristic
210C22×C22⋊C4C2×D311yescharacteristic
211C22×C22⋊C4C2×D311yescharacteristic
212C22×C42—31no—
213C22×C42C2×D311yescharacteristic
214#394—64no—
215#393—64no—
216#392—64no—
217#391—64no—
218#390—64no—
219C2×#95—31no—
220C2×#95—31no—
221C2×#95—31no—
222C2×#95—31no—
223C2×#95—31no—
224C2×#95—31no—
225C2×#95—31no—
226C2×#95—31no—
227C2×#95—31no—
228C2×#95C2×D311yescharacteristic
229C2×#95C2×D311yescharacteristic
230C2×#95C2×D311yescharacteristic
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×C3—21no—
241C24×C3—21no—
242C24×C3—21no—
243C24×C3—21no—
244C24×C3—21no—
245C24×C3#4112yes—
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×D3C2×D412yes—
276C23×D3C2×D412yes—
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×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×C4C2×D412yes—
314C22×C3×C4C2×D412yes—
315C22×C3×C4C2×D412yes—
316C22×C3×C4C2×D412yes—
317C22×C3×C4#4112yes—
318C22×C3×C4#4112yes—
319C2×#67—28no—
320C2×#67—44no—
321C2×#67—44no—
322C2×#67—44no—
323C2×#67—44no—
324C2×#67—44no—
325C2×#67—44no—
326C2×#67—44no—
327C2×#67—44no—
328C2×#67—44no—
329C2×#67—44no—
330C2×#67—44no—
331C2×#67—44no—
332C2×#67—44no—
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×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×Dic3C2×D412yes—
368C22×Dic3C2×D412yes—
369C22×Dic3C2×D412yes—
370C22×Dic3C2×D412yes—
371C22×Dic3C2×D412yes—
372C22×Dic3C2×D412yes—
373C22×Dic3#4112yes—
374C22×Dic3#4112yes—
375C2×D12—28no—
376C2×D12—44no—
377C2×D12—44no—
378C2×D12—44no—
379C2×D12—44no—
380C2×D12—44no—
381C2×D12—44no—
382C2×Dic6—28no—
383C2×Dic6—28no—
384C2×Dic6—44no—
385C2×Dic6—44no—
386C2×Dic6—44no—
387C2×Dic6—44no—
388C2×Dic6—44no—
389C3×C22⋊C4—44no—
390C3×C22⋊C4—44no—
391C3×C22⋊C4—44no—
392C3×C42—28no—
393#217—44no—
394#217—44no—
395(C2×D3)⋊C4—28no—
396(C2×D3)⋊C4—28no—
397(C2×D3)⋊C4—28no—
398(C2×D3)⋊C4—28no—
399(C2×D3)⋊C4—44no—
400(C2×D3)⋊C4—44no—
401(C2×D3)⋊C4—44no—
402(C2×D3)⋊C4—44no—
403(C2×D3)⋊C4—44no—
404(C2×D3)⋊C4—44no—
405Dic3⋊C4—44no—
406Dic3⋊C4—44no—
407C4×Dic3—44no—
408C25—31no—
409C25—31no—
410C25C22×D311yescharacteristic
411C22×Q8—34no—
412C22×Q8—62no—
413C22×Q8—62no—
414C22×Q8—62no—
415C22×Q8—62no—
416C22×Q8—121no—
417C22×Q8—121no—
418C22×D4—62no—
419C22×D4—62no—
420C22×D4—62no—
421C22×D4—62no—
422C22×D4—62no—
423C22×D4—62no—
424C22×D4—62no—
425C22×D4—62no—
426C22×D4—62no—
427C22×D4—62no—
428C22×D4—62no—
429C22×D4—62no—
430C22×D4—62no—
431C22×D4—121no—
432C22×D4—121no—
433C22×D4—121no—
434C22×D4—121no—
435C22×D4—121no—
436C22×D4—121no—
437C22×D4—121no—
438C22×D4—121no—
439C23×C4—31no—
440C23×C4—31no—
441C23×C4—31no—
442C23×C4—31no—
443C23×C4—31no—
444C23×C4—31no—
445C23×C4C22×D311yescharacteristic
446C23×C4C22×D311yescharacteristic
447C23×C4C22×D311yescharacteristic
448C23×C4C22×D311yescharacteristic
449C23×C4C22×D311yescharacteristic
450C23×C4C22×D311yescharacteristic
451#124—632no—
452C2×C4⋊C4—62no—
453C2×C4⋊C4—62no—
454C2×C4⋊C4—62no—
455C2×C4⋊C4—62no—
456C2×C4⋊C4—121no—
457C2×C4⋊C4—121no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4—22no—
462C2×C22⋊C4—22no—
463C2×C22⋊C4—22no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—34no—
466C2×C22⋊C4—34no—
467C2×C22⋊C4—41no—
468C2×C22⋊C4—41no—
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—62no—
476C2×C22⋊C4—62no—
477C2×C22⋊C4—62no—
478C2×C22⋊C4—62no—
479C2×C22⋊C4—62no—
480C2×C22⋊C4—62no—
481C2×C22⋊C4—62no—
482C2×C22⋊C4—62no—
483C2×C22⋊C4—62no—
484C2×C22⋊C4—62no—
485C2×C22⋊C4—62no—
486C2×C22⋊C4—62no—
487C2×C22⋊C4—62no—
488C2×C22⋊C4—62no—
489C2×C22⋊C4—62no—
490C2×C22⋊C4—62no—
491C2×C22⋊C4—121no—
492C2×C22⋊C4—121no—
493C2×C22⋊C4—121no—
494C2×C22⋊C4—121no—
495C2×C22⋊C4—121no—
496C2×C22⋊C4—121no—
497C2×C22⋊C4—121no—
498C2×C22⋊C4—121no—
499C2×C22⋊C4—121no—
500C2×C22⋊C4—121no—
501C2×C22⋊C4—121no—
502C2×C22⋊C4—121no—
503C2×C42—22no—
504C2×C42—22no—
505C2×C42—22no—
506C2×C42—62no—
507C2×C42—62no—
508C2×C42—121no—
509#95—22no—
510#95—34no—
511#95—41no—
512#95—41no—
513#95—62no—
514#95—62no—
515#95—62no—
516#95—62no—
517#95—62no—
518#95—62no—
519#95—62no—
520#95—121no—
521C23×C3—22no—
522C23×C3—22no—
523C23×C3—22no—
524C23×C3—22no—
525C23×C3—22no—
526C23×C3—22no—
527C23×C3—22no—
528C23×C3—41no—
529C23×C3—41no—
530C23×C3—41no—
531C23×C3—41no—
532C23×C3—41no—
533C23×C3—41no—
534C23×C3—41no—
535C23×C3—41no—
536C23×C3—41no—
537C23×C3—41no—
538C23×C3—41no—
539C23×C3—41no—
540C23×C3—41no—
541C23×C3—41no—
542C23×C3—41no—
543C23×C3—41no—
544C23×C3—41no—
545C23×C3—41no—
546C23×C3—41no—
547C23×C3—41no—
548C23×C3—41no—
549C23×C3—41no—
550C23×C3—41no—
551C23×C3—41no—
552C23×C3—41no—
553C23×C3—41no—
554C23×C3—41no—
555C23×C3—41no—
556C23×C3C22×D411yescharacteristic
557C23×C3C22×D411yescharacteristic
558C23×C3C22×D411yescharacteristic
559C23×C3C22×D411yescharacteristic
560C23×C3C2×#4111yescharacteristic
561C23×C3C2×#4111yescharacteristic
562C23×C3C2×#4111yescharacteristic
563C23×C3C2×#4111yescharacteristic
564C23×C3C2×#4111yescharacteristic
565C23×C3H(5,𝔽2)11yescharacteristic
566C23×C3H(5,𝔽2)11yescharacteristic
567C23×C3H(5,𝔽2)11yescharacteristic
568C23×C3H(5,𝔽2)11yescharacteristic
569C23×C3H(5,𝔽2)11yescharacteristic
570C23×C32−1+411yescharacteristic
571C22×D3—22no—
572C22×D3—22no—
573C22×D3—22no—
574C22×D3—22no—
575C22×D3—22no—
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—41no—
586C22×D3—41no—
587C22×D3—41no—
588C22×D3—41no—
589C22×D3—41no—
590C22×D3—41no—
591C22×D3—41no—
592C22×D3—41no—
593C22×D3—41no—
594C22×D3—41no—
595C22×D3—41no—
596C22×D3—41no—
597C22×D3—41no—
598C22×D3—41no—
599C22×D3—41no—
600C22×D3—41no—
601C22×D3—41no—
602C22×D3—41no—
603C22×D3—41no—
604C22×D3—41no—
605C22×D3—41no—
606C22×D3—41no—
607C22×D3—41no—
608C22×D3—41no—
609C22×D3—41no—
610C22×D3—41no—
611C22×D3—41no—
612C22×D3—41no—
613C22×D3—41no—
614C22×D3—41no—
615C22×D3—41no—
616C22×D3—41no—
617C22×D3—41no—
618C22×D3—41no—
619C22×D3—41no—
620C22×D3—41no—
621C22×D3—41no—
622C22×D3—41no—
623C22×D3—41no—
624C22×D3—41no—
625C22×D3—41no—
626C22×D3—41no—
627C22×D3—41no—
628C22×D3—41no—
629C22×D3—41no—
630C22×D3—41no—
631C22×D3—41no—
632C22×D3—41no—
633C22×D3—41no—
634C22×D3—41no—
635C22×D3—41no—
636C22×D3—41no—
637C22×D3—41no—
638C22×D3—41no—
639C22×D3—41no—
640C22×D3—41no—
641C2×C3×C4—22no—
642C2×C3×C4—22no—
643C2×C3×C4—22no—
644C2×C3×C4—22no—
645C2×C3×C4—22no—
646C2×C3×C4—22no—
647C2×C3×C4—22no—
648C2×C3×C4—22no—
649C2×C3×C4—22no—
650C2×C3×C4—22no—
651C2×C3×C4—22no—
652C2×C3×C4—22no—
653C2×C3×C4—22no—
654C2×C3×C4—22no—
655C2×C3×C4—22no—
656C2×C3×C4—41no—
657C2×C3×C4—41no—
658C2×C3×C4—41no—
659C2×C3×C4—41no—
660C2×C3×C4—41no—
661C2×C3×C4—41no—
662C2×C3×C4—41no—
663C2×C3×C4—41no—
664C2×C3×C4—41no—
665C2×C3×C4—41no—
666C2×C3×C4—41no—
667C2×C3×C4—41no—
668C2×C3×C4—41no—
669C2×C3×C4—41no—
670C2×C3×C4—41no—
671C2×C3×C4—41no—
672C2×C3×C4—41no—
673C2×C3×C4—41no—
674C2×C3×C4—41no—
675C2×C3×C4—41no—
676C2×C3×C4—41no—
677C2×C3×C4—41no—
678C2×C3×C4—41no—
679C2×C3×C4—41no—
680C2×C3×C4—41no—
681C2×C3×C4—41no—
682C2×C3×C4#12114yes—
683#67—416no—
684#67—416no—
685C2×Dic3—22no—
686C2×Dic3—22no—
687C2×Dic3—22no—
688C2×Dic3—22no—
689C2×Dic3—22no—
690C2×Dic3—22no—
691C2×Dic3—22no—
692C2×Dic3—22no—
693C2×Dic3—22no—
694C2×Dic3—22no—
695C2×Dic3—22no—
696C2×Dic3—22no—
697C2×Dic3—22no—
698C2×Dic3—22no—
699C2×Dic3—22no—
700C2×Dic3—22no—
701C2×Dic3—22no—
702C2×Dic3—22no—
703C2×Dic3—41no—
704C2×Dic3—41no—
705C2×Dic3—41no—
706C2×Dic3—41no—
707C2×Dic3—41no—
708C2×Dic3—41no—
709C2×Dic3—41no—
710C2×Dic3—41no—
711C2×Dic3—41no—
712C2×Dic3—41no—
713C2×Dic3—41no—
714C2×Dic3—41no—
715C2×Dic3—41no—
716C2×Dic3—41no—
717C2×Dic3—41no—
718C2×Dic3—41no—
719C2×Dic3—41no—
720C2×Dic3—41no—
721C2×Dic3—41no—
722C2×Dic3—41no—
723C2×Dic3—41no—
724C2×Dic3—41no—
725C2×Dic3#12014yes—
726C2×Dic3#12414yescomplemented
727D12—416no—
728Dic6—416no—
729C24—21no—
730C24—21no—
731C24—21no—
732C24—21no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—21no—
743C24—32no—
744C24—32no—
745C24—61no—
746C24—61no—
747C24—61no—
748C24—61no—
749C24—61no—
750C24—61no—
751C24—61no—
752C24—61no—
753C24—61no—
754C24—61no—
755C24—61no—
756C24—61no—
757C24—61no—
758C24—61no—
759C24—61no—
760C24—61no—
761C24—61no—
762C24—61no—
763C24—61no—
764C24—61no—
765C24—61no—
766C24—61no—
767C24—61no—
768C24—61no—
769C24—61no—
770C24—61no—
771C24—61no—
772C24—61no—
773C24#23512yes—
774C24C23×D311yescharacteristic
775C2×Q8—68no—
776C2×Q8—68no—
777C2×Q8—124no—
778C2×Q8—124no—
779C2×Q8—124no—
780C2×Q8—124no—
781C2×Q8—124no—
782C2×D4—68no—
783C2×D4—68no—
784C2×D4—124no—
785C2×D4—124no—
786C2×D4—124no—
787C2×D4—124no—
788C2×D4—124no—
789C2×D4—124no—
790C2×D4—124no—
791C2×D4—124no—
792C2×D4—124no—
793C2×D4—124no—
794C2×D4—124no—
795C2×D4—124no—
796C2×D4—124no—
797C2×D4—124no—
798C2×D4—124no—
799C2×D4—124no—
800C2×D4—124no—
801C2×D4—124no—
802C2×D4—124no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—32no—
840C22×C4—32no—
841C22×C4—32no—
842C22×C4—32no—
843C22×C4—32no—
844C22×C4—32no—
845C22×C4—32no—
846C22×C4—32no—
847C22×C4—61no—
848C22×C4—61no—
849C22×C4—61no—
850C22×C4—61no—
851C22×C4—61no—
852C22×C4—61no—
853C22×C4—61no—
854C22×C4—61no—
855C22×C4—61no—
856C22×C4—61no—
857C22×C4—61no—
858C22×C4—61no—
859C22×C4—61no—
860C22×C4—61no—
861C22×C4—61no—
862C22×C4—61no—
863C22×C4—61no—
864C22×C4—61no—
865C22×C4—61no—
866C22×C4—61no—
867C22×C4—61no—
868C22×C4—61no—
869C22×C4—61no—
870C22×C4—61no—
871C22×C4—61no—
872C22×C4—61no—
873C22×C4—61no—
874C22×C4—61no—
875C22×C4—61no—
876C22×C4—61no—
877C22×C4—61no—
878C22×C4—61no—
879C22×C4—61no—
880C22×C4—61no—
881C22×C4#23512yes—
882C22×C4#23512yes—
883C22×C4D3×D412yes—
884C22×C4D3×D412yes—
885C22×C4D3×D412yes—
886C22×C4D3×D412yes—
887C4⋊C4—124no—
888C4⋊C4—124no—
889C22⋊C4—44no—
890C22⋊C4—44no—
891C22⋊C4—44no—
892C22⋊C4—68no—
893C22⋊C4—68no—
894C22⋊C4—68no—
895C22⋊C4—68no—
896C22⋊C4—124no—
897C22⋊C4—124no—
898C22⋊C4—124no—
899C22⋊C4—124no—
900C22⋊C4—124no—
901C22⋊C4—124no—
902C22⋊C4—124no—
903C22⋊C4—124no—
904C42—28no—
905C42—124no—
906C22×C3—42no—
907C22×C3—42no—
908C22×C3—42no—
909C22×C3—42no—
910C22×C3—42no—
911C22×C3—42no—
912C22×C3—42no—
913C22×C3—81no—
914C22×C3—81no—
915C22×C3—81no—
916C22×C3—81no—
917C22×C3—81no—
918C22×C3—81no—
919C22×C3—81no—
920C22×C3—81no—
921C22×C3C2×#12011yescharacteristic
922C22×C3C2×#12111yescharacteristic
923C22×C3#52511yescharacteristic
924C22×C3C2×#12411yescharacteristic
925C22×C3#52911yescharacteristic
926C22×C3#53211yescharacteristic
927C22×C3#53411yescharacteristic
928C22×C3#53511yescharacteristic
929C22×C3#53511yescharacteristic
930C22×C3#53711yescharacteristic
931C22×C3#53811yescharacteristic
932C22×C3#53811yescharacteristic
933C22×C3#53811yescharacteristic
934C22×C3#54211yescharacteristic
935C22×C3#54211yescharacteristic
936C22×C3D4211yescharacteristic
937C22×C3D4211yescharacteristic
938C22×C3#54611yescharacteristic
939C22×C3#54611yescharacteristic
940C22×C3#54611yescharacteristic
941C22×C3#54611yescharacteristic
942C22×C3#54611yescharacteristic
943C22×C3#54611yescharacteristic
944C22×C3#54711yescharacteristic
945C22×C3#54811yescharacteristic
946C22×C3#54811yescharacteristic
947C22×C3#55011yescharacteristic
948C22×C3#55011yescharacteristic
949C22×C3#55011yescharacteristic
950C22×C3#55111yescharacteristic
951C22×C3#55511yescharacteristic
952C22×C3#55911yescharacteristic
953C22×C3#55911yescharacteristic
954C22×C3H(3,𝔽4)11yescharacteristic
955C22×C3#56211yescharacteristic
956C2×D3—42no—
957C2×D3—42no—
958C2×D3—42no—
959C2×D3—42no—
960C2×D3—42no—
961C2×D3—42no—
962C2×D3—42no—
963C2×D3—42no—
964C2×D3—42no—
965C2×D3—42no—
966C2×D3—42no—
967C2×D3—42no—
968C2×D3—42no—
969C2×D3—42no—
970C2×D3—81no—
971C2×D3—81no—
972C2×D3—81no—
973C2×D3—81no—
974C2×D3—81no—
975C2×D3—81no—
976C2×D3—81no—
977C2×D3—81no—
978C2×D3—81no—
979C2×D3—81no—
980C2×D3—81no—
981C2×D3—81no—
982C2×D3—81no—
983C2×D3—81no—
984C2×D3—81no—
985C2×D3—81no—
986C3×C4—24no—
987C3×C4—42no—
988C3×C4—42no—
989C3×C4—42no—
990C3×C4—81no—
991C3×C4—81no—
992Dic3—24no—
993Dic3—24no—
994Dic3—42no—
995Dic3—42no—
996Dic3—81no—
997Dic3—81no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—62no—
1034C23—62no—
1035C23—62no—
1036C23—62no—
1037C23—62no—
1038C23—62no—
1039C23—62no—
1040C23—62no—
1041C23—62no—
1042C23—62no—
1043C23—62no—
1044C23—62no—
1045C23—62no—
1046C23—62no—
1047C23—121no—
1048C23—121no—
1049C23—121no—
1050C23—121no—
1051C23—121no—
1052C23—121no—
1053C23—121no—
1054C23—121no—
1055C23—121no—
1056C23—121no—
1057C23—121no—
1058C23—121no—
1059C23—121no—
1060C23—121no—
1061C23—121no—
1062C23—121no—
1063C23—121no—
1064C23—121no—
1065C23—121no—
1066C23—121no—
1067C23—121no—
1068C23—121no—
1069C23—121no—
1070C23—121no—
1071C23—121no—
1072C23—121no—
1073C23—121no—
1074C23—121no—
1075C23—121no—
1076C23—121no—
1077C23—121no—
1078C23—121no—
1079C23—121no—
1080C23—121no—
1081C23—121no—
1082C23—121no—
1083C23—121no—
1084C23—121no—
1085C23—121no—
1086C23—121no—
1087C23—121no—
1088C23—121no—
1089C23—121no—
1090C23—121no—
1091C23—121no—
1092C23—121no—
1093C23—121no—
1094C23—121no—
1095C23—121no—
1096C23—121no—
1097C23—121no—
1098C23—121no—
1099C23—121no—
1100C23—121no—
1101C23—121no—
1102C23—121no—
1103C23C2×#23511yescharacteristic
1104C23C2×#23511yescharacteristic
1105C23C2×#23511yescharacteristic
1106C23C2×D3×D411yescharacteristic
1107C23C2×D3×D411yescharacteristic
1108C23C2×D3×D411yescharacteristic
1109C23C2×D3×D411yescharacteristic
1110C23#100411yescharacteristic
1111C23#100411yescharacteristic
1112C23D3×#4111yescharacteristic
1113C23D3×#4111yescharacteristic
1114C23#100911yescharacteristic
1115C23#100911yescharacteristic
1116C23#100911yescharacteristic
1117C23#101011yescharacteristic
1118Q8—1216no—
1119D4—1216no—
1120D4—1216no—
1121D4—1216no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—34no—
1138C2×C4—34no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—62no—
1166C2×C4—62no—
1167C2×C4—62no—
1168C2×C4—62no—
1169C2×C4—62no—
1170C2×C4—62no—
1171C2×C4—62no—
1172C2×C4—62no—
1173C2×C4—62no—
1174C2×C4—62no—
1175C2×C4—62no—
1176C2×C4—62no—
1177C2×C4—62no—
1178C2×C4—62no—
1179C2×C4—62no—
1180C2×C4—62no—
1181C2×C4—62no—
1182C2×C4—62no—
1183C2×C4—121no—
1184C2×C4—121no—
1185C2×C4—121no—
1186C2×C4—121no—
1187C2×C4—121no—
1188C2×C4—121no—
1189C2×C4—121no—
1190C2×C4—121no—
1191C2×C4—121no—
1192C2×C4—121no—
1193C2×C4—121no—
1194C2×C4—121no—
1195C2×C4—121no—
1196C2×C4—121no—
1197C2×C4—121no—
1198C2×C4—121no—
1199C2×C4—121no—
1200C2×C4—121no—
1201C2×C4—121no—
1202C2×C4—121no—
1203C2×C4—121no—
1204C2×C4—121no—
1205C2×C4#88414yes—
1206C2×C3—82no—
1207C2×C3#240711yescharacteristic
1208C2×C3#241011yescharacteristic
1209C2×C3#242611yescharacteristic
1210C2×C3#243111yescharacteristic
1211C2×C3#245911yescharacteristic
1212C2×C3#247211yescharacteristic
1213C2×C3#249111yescharacteristic
1214C2×C3#254811yescharacteristic
1215C2×C3#255711yescharacteristic
1216C2×C3#267011yescharacteristic
1217C2×C3#267611yescharacteristic
1218C2×C3#271011yescharacteristic
1219C2×C3#271211yescharacteristic
1220C2×C3#273011yescharacteristic
1221C2×C3#273311yescharacteristic
1222D3—82no—
1223D3—82no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22—81no—
1235C22—81no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—122no—
1240C22—122no—
1241C22—122no—
1242C22—122no—
1243C22—122no—
1244C22—122no—
1245C22—122no—
1246C22—122no—
1247C22—122no—
1248C22—122no—
1249C22—122no—
1250C22—122no—
1251C22—122no—
1252C22—122no—
1253C22—241no—
1254C22—241no—
1255C22—241no—
1256C22—241no—
1257C22—241no—
1258C22—241no—
1259C22—241no—
1260C22—241no—
1261C22—241no—
1262C22—241no—
1263C22—241no—
1264C22—241no—
1265C22—241no—
1266C22—241no—
1267C22—241no—
1268C22—241no—
1269C22#547911yescharacteristic
1270C22C2×#88411yescharacteristic
1271C22#549011yescharacteristic
1272C22#549011yescharacteristic
1273C22#552711yescharacteristic
1274C22#553211yescharacteristic
1275C22#553411yescharacteristic
1276C22#554711yescharacteristic
1277C22#554811yescharacteristic
1278C22#555011yescharacteristic
1279C22#555011yescharacteristic
1280C22#555011yescharacteristic
1281C22#555211yescharacteristic
1282C22#555211yescharacteristic
1283C22#555311yescharacteristic
1284C22#555911yescharacteristic
1285C22#555911yescharacteristic
1286C22#556011yescharacteristic
1287C22#556011yescharacteristic
1288C22D3×#12011yescharacteristic
1289C22#559911yescharacteristic
1290C22#559911yescharacteristic
1291C22#560711yescharacteristic
1292C22#560811yescharacteristic
1293C22#560911yescharacteristic
1294C22#560911yescharacteristic
1295C22#565311yescharacteristic
1296C22#565411yescharacteristic
1297C22#565511yescharacteristic
1298C22D3×#12411yescharacteristic
1299C22#568311yescharacteristic
1300C22#568411yescharacteristic
1301C22#570411yescharacteristic
1302C22#571011yescharacteristic
1303C22#571511yescharacteristic
1304C4—24no—
1305C4—42no—
1306C4—42no—
1307C4—42no—
1308C4—64no—
1309C4—64no—
1310C4—81no—
1311C4—81no—
1312C4—122no—
1313C4—122no—
1314C4—241no—
1315C4—241no—
1316C3#1531711yescharacteristic, complemented, Sylow
1317C2—82no—
1318C2—242no—
1319C2—242no—
1320C2#7348511yescharacteristic
1321C2#7359011yescharacteristic
1322C2#7360111yescharacteristic
1323C2#7468811yescharacteristic
1324C2#7470011yescharacteristic
1325C2#7488711yescharacteristic
1326C2#7552611yescharacteristic
1327C2#7554611yescharacteristic
1328C2#7569211yescharacteristic
1329C2#7570811yescharacteristic
1330C2#7571211yescharacteristic
1331C2#7592811yescharacteristic
1332C2#7635211yescharacteristic
1333C2#7637811yescharacteristic
1334C2#7646111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1437C2
prime radicalC2×#4960C2
hypercenter#1437D3
hypocenterC3#15317
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
1. C22×#875C2semidirect
2. C2×#4959C2semidirect
4. C2×#4947C2semidirect
5. C2×#4957C2semidirect
6. C2×#4646C2semidirect
7. C3×#1437C2semidirect
8. #71550C2semidirect
9. #71550C2semidirect
10. #71536C2semidirect
11. #69429C2semidirect
12. #69428C2semidirect
13. #69428C2semidirect
14. #69426C2semidirect
15. #69408C2semidirect
73. #1437D3semidirect
117. C22×Dic6D4semidirect
164. C2×(C2×D3)⋊C4D4semidirect
165. C2×(C2×D3)⋊C4D4semidirect
726. C2×Dic3#124semidirect
1316. C3#15317semidirect

Maximal subgroups

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

subgroupindex
C22×#8752
C2×#49592
C2×#49602
C2×#49472
C2×#49572
C2×#46462
C3×#14372
#715502
#715362
#694292
#694282
#694262
#694082
#153173