Finite Group Databasebeta

← #10750392

Subgroups — #10750392

Order 768.

2266 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×#885C211yesmaximal, characteristic, complemented
2C2×#5223C211yesmaximal, characteristic
3C2×#5222C211yesmaximal, characteristic, complemented
4C2×#4959C211yesmaximal, characteristic, complemented
5C2×#4947C211yesmaximal, characteristic, complemented
6C2×#4945C211yesmaximal, characteristic, complemented
7C3×#1438C211yesmaximal, characteristic, complemented
8#71550C211yesmaximal, characteristic, complemented
9#71550C211yesmaximal, characteristic, complemented
10#71547C211yesmaximal, characteristic, complemented
11#71547C211yesmaximal, characteristic, complemented
12#69428C211yesmaximal, characteristic, complemented
13#69428C211yesmaximal, characteristic, complemented
14#69424C211yesmaximal, characteristic, complemented
15Dic3⋊#95C211yesmaximal, characteristic, complemented
16#16504—31nomaximal, Sylow
17C23×C3×D4C2211yescharacteristic
18C23×#67C2211yescharacteristic
19C23×#67C2211yescharacteristic
20C23×Dic6C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×#217C2211yescharacteristic
26C22×#217C2211yescharacteristic
27C22×#217C2211yescharacteristic
28C22×#217C2211yescharacteristic
29C22×#217C2211yescharacteristic
30C22×#217C2211yescharacteristic
31C22×(C2×D3)⋊C4C2211yescharacteristic
32C22×(C2×D3)⋊C4C2211yescharacteristic
33C22×(C2×D3)⋊C4C2211yescharacteristic
34C22×(C2×D3)⋊C4C2211yescharacteristic
35C22×(C2×D3)⋊C4C2211yescharacteristic
36C22×Dic3⋊C4C2211yescharacteristic
37C22×Dic3⋊C4C2211yescharacteristic
38C22×Dic3⋊C4C2211yescharacteristic
39C22×C4×Dic3C2211yescharacteristic
40C2×#885—24no—
41C2×#885—24no—
42C2×#885—24no—
43C2×C3×#95C2211yescharacteristic
44C2×C3×#95C2211yescharacteristic
45#5223—24no—
46#5222—24no—
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
57#4959—24no—
58#4947—24no—
59#4945—24no—
60C22×#124—31no—
61C2×#394—31no—
62C2×#394—31no—
63C2×#393—31no—
64C2×#392—31no—
65C2×#388—31no—
66#1446—31no—
67#1439—31no—
68#1439—31no—
69#1439—31no—
70#1439—31no—
71#1438—31no—
72#1438—31no—
73#1438D311yescharacteristic, complemented
74C4⋊#95—31no—
75C25×C3C2311yescharacteristic
76C25×C3C2311yescharacteristic
77C24×D3C2311yescharacteristic
78C22×C3×D4—22no—
79C22×C3×D4—22no—
80C22×C3×D4—22no—
81C22×C3×D4—41no—
82C22×C3×D4—41no—
83C22×C3×D4—41no—
84C22×C3×D4—41no—
85C23×C3×C4C2311yescharacteristic
86C23×C3×C4C2311yescharacteristic
87C23×C3×C4C2311yescharacteristic
88C23×C3×C4C2311yescharacteristic
89C23×C3×C4C2311yescharacteristic
90C22×#67—22no—
91C22×#67—22no—
92C22×#67—22no—
93C22×#67—22no—
94C22×#67—22no—
95C22×#67—22no—
96C22×#67—22no—
97C22×#67—22no—
98C22×#67—41no—
99C22×#67—41no—
100C22×#67—41no—
101C22×#67—41no—
102C22×#67—41no—
103C22×#67—41no—
104C23×Dic3C2311yescharacteristic
105C23×Dic3C2311yescharacteristic
106C23×Dic3C2311yescharacteristic
107C23×Dic3C2311yescharacteristic
108C23×Dic3C2311yescharacteristic
109C23×Dic3C2311yescharacteristic
110C23×Dic3C2311yescharacteristic
111C22×Dic6—22no—
112C22×Dic6—22no—
113C22×Dic6—22no—
114C22×Dic6—22no—
115C22×Dic6—22no—
116C22×Dic6—41no—
117C22×Dic6—41no—
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—41no—
125C2×C3×C22⋊C4—41no—
126C2×C3×C22⋊C4—41no—
127C2×C3×C22⋊C4—41no—
128C2×C3×C22⋊C4—41no—
129C2×C3×C22⋊C4—41no—
130C2×#217—22no—
131C2×#217—22no—
132C2×#217—22no—
133C2×#217—22no—
134C2×#217—22no—
135C2×#217—22no—
136C2×#217—22no—
137C2×#217—22no—
138C2×#217—22no—
139C2×#217—22no—
140C2×#217—22no—
141C2×#217—22no—
142C2×#217—41no—
143C2×#217—41no—
144C2×#217—41no—
145C2×#217—41no—
146C2×#217D414yes—
147C2×#217D414yescomplemented
148C2×(C2×D3)⋊C4—22no—
149C2×(C2×D3)⋊C4—22no—
150C2×(C2×D3)⋊C4—22no—
151C2×(C2×D3)⋊C4—22no—
152C2×(C2×D3)⋊C4—22no—
153C2×(C2×D3)⋊C4—22no—
154C2×(C2×D3)⋊C4—22no—
155C2×(C2×D3)⋊C4—22no—
156C2×(C2×D3)⋊C4—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)⋊C4D414yescomplemented
163C2×Dic3⋊C4—22no—
164C2×Dic3⋊C4—22no—
165C2×Dic3⋊C4—22no—
166C2×Dic3⋊C4—22no—
167C2×Dic3⋊C4—22no—
168C2×Dic3⋊C4—41no—
169C2×Dic3⋊C4—41no—
170C2×Dic3⋊C4—41no—
171C2×Dic3⋊C4—41no—
172C2×C4×Dic3—22no—
173C2×C4×Dic3—22no—
174C2×C4×Dic3D414yescomplemented
175#885—232no—
176C3×#95—41no—
177C3×#95—41no—
178C3⋊#95—22no—
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⋊#95—41no—
188C23×Q8—31no—
189C23×D4—31no—
190C23×D4—31no—
191C23×D4C2×D311yescharacteristic
192C2×#124—64no—
193C2×#124—64no—
194C2×#124—64no—
195C22×C4⋊C4—31no—
196C22×C4⋊C4—31no—
197C22×C4⋊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×C22⋊C4C2×D311yescharacteristic
213C22×C42—31no—
214#394—64no—
215#394—64no—
216#393—64no—
217#392—64no—
218#388—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×#95—31no—
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—21no—
246C24×C3—21no—
247C24×C3—21no—
248C24×C3—21no—
249C24×C3—21no—
250C24×C3—21no—
251C24×C3—21no—
252C24×C3—21no—
253C24×C3—21no—
254C24×C3—21no—
255C24×C3—21no—
256C24×C3—21no—
257C24×C3—21no—
258C24×C3—21no—
259C24×C3C2×D412yes—
260C24×C3C2×D412yes—
261C24×C3C2411yescharacteristic
262C23×D3—21no—
263C23×D3—21no—
264C23×D3—21no—
265C23×D3—21no—
266C23×D3—21no—
267C23×D3—21no—
268C23×D3—21no—
269C23×D3—21no—
270C23×D3—21no—
271C23×D3—21no—
272C23×D3—21no—
273C23×D3—21no—
274C23×D3—21no—
275C23×D3—21no—
276C23×D3C2×D412yes—
277C2×C3×D4—44no—
278C2×C3×D4—44no—
279C2×C3×D4—44no—
280C2×C3×D4—44no—
281C2×C3×D4—44no—
282C2×C3×D4—44no—
283C2×C3×D4—44no—
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×C4—21no—
314C22×C3×C4—21no—
315C22×C3×C4—21no—
316C22×C3×C4C2×D412yes—
317C22×C3×C4C2×D412yes—
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×Dic3—21no—
368C22×Dic3—21no—
369C22×Dic3—21no—
370C22×Dic3—21no—
371C22×Dic3—21no—
372C22×Dic3—21no—
373C22×Dic3C2×D412yes—
374C22×Dic3C2×D412yes—
375C22×Dic3C2×D412yes—
376C22×Dic3C2×D412yes—
377C22×Dic3C2×D412yes—
378C22×Dic3C2×D412yes—
379C22×Dic3C2×D412yes—
380C22×Dic3#4112yes—
381C22×Dic3#4112yes—
382C2×Dic6—28no—
383C2×Dic6—44no—
384C2×Dic6—44no—
385C2×Dic6—44no—
386C2×Dic6—44no—
387C2×Dic6—44no—
388C2×Dic6—44no—
389C3×C22⋊C4—28no—
390C3×C22⋊C4—44no—
391C3×C22⋊C4—44no—
392C3×C22⋊C4—44no—
393#217—28no—
394#217—28no—
395#217—44no—
396#217—44no—
397#217—44no—
398#217—44no—
399(C2×D3)⋊C4—28no—
400(C2×D3)⋊C4—28no—
401(C2×D3)⋊C4—44no—
402(C2×D3)⋊C4—44no—
403(C2×D3)⋊C4—44no—
404Dic3⋊C4—44no—
405Dic3⋊C4—44no—
406Dic3⋊C4—44no—
407C4×Dic3—28no—
408C25—31no—
409C25C22×D311yescharacteristic
410C25C22×D311yescharacteristic
411C22×Q8—62no—
412C22×Q8—62no—
413C22×Q8—62no—
414C22×Q8—62no—
415C22×Q8—62no—
416C22×Q8—121no—
417C22×Q8—121no—
418C22×D4—22no—
419C22×D4—22no—
420C22×D4—22no—
421C22×D4—41no—
422C22×D4—41no—
423C22×D4—41no—
424C22×D4—41no—
425C22×D4—62no—
426C22×D4—62no—
427C22×D4—62no—
428C22×D4—62no—
429C22×D4—62no—
430C22×D4—62no—
431C22×D4—62no—
432C22×D4—62no—
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×C4—31no—
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—62no—
457C2×C4⋊C4—121no—
458C2×C4⋊C4—121no—
459C2×C4⋊C4—121no—
460C2×C4⋊C4—121no—
461C2×C22⋊C4—22no—
462C2×C22⋊C4—22no—
463C2×C22⋊C4—22no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—34no—
468C2×C22⋊C4—34no—
469C2×C22⋊C4—34no—
470C2×C22⋊C4—41no—
471C2×C22⋊C4—41no—
472C2×C22⋊C4—41no—
473C2×C22⋊C4—41no—
474C2×C22⋊C4—41no—
475C2×C22⋊C4—41no—
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—62no—
492C2×C22⋊C4—62no—
493C2×C22⋊C4—62no—
494C2×C22⋊C4—62no—
495C2×C22⋊C4—62no—
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×C22⋊C4—121no—
504C2×C22⋊C4—121no—
505C2×C22⋊C4—121no—
506C2×C42—34no—
507C2×C42—62no—
508C2×C42—62no—
509#95—41no—
510#95—41no—
511#95—62no—
512#95—62no—
513#95—62no—
514#95—62no—
515#95—62no—
516#95—62no—
517#95—62no—
518#95—62no—
519#95—121no—
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—22no—
529C23×C3—22no—
530C23×C3—22no—
531C23×C3—22no—
532C23×C3—22no—
533C23×C3—22no—
534C23×C3—22no—
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×C3—41no—
557C23×C3—41no—
558C23×C3—41no—
559C23×C3—41no—
560C23×C3—41no—
561C23×C3—41no—
562C23×C3—41no—
563C23×C3—41no—
564C23×C3—41no—
565C23×C3—41no—
566C23×C3—41no—
567C23×C3—41no—
568C23×C3—41no—
569C23×C3—41no—
570C23×C3—41no—
571C23×C3—41no—
572C23×C3—41no—
573C23×C3—41no—
574C23×C3—41no—
575C23×C3—41no—
576C23×C3—41no—
577C23×C3—41no—
578C23×C3—41no—
579C23×C3—41no—
580C23×C3—41no—
581C23×C3—41no—
582C23×C3—41no—
583C23×C3—41no—
584C23×C3—41no—
585C23×C3—41no—
586C23×C3—41no—
587C23×C3—41no—
588C23×C3—41no—
589C23×C3—41no—
590C23×C3—41no—
591C23×C3C22×D411yescharacteristic
592C23×C3C22×D411yescharacteristic
593C23×C3C22×D411yescharacteristic
594C23×C3C22×D411yescharacteristic
595C23×C3C2×#4111yescharacteristic
596C23×C3C2×#4111yescharacteristic
597C23×C3C2×#4111yescharacteristic
598C23×C3H(5,𝔽2)11yescharacteristic
599C23×C3H(5,𝔽2)11yescharacteristic
600C23×C3H(5,𝔽2)11yescharacteristic
601C23×C3H(5,𝔽2)11yescharacteristic
602C23×C3H(5,𝔽2)11yescharacteristic
603C23×C3H(5,𝔽2)11yescharacteristic
604C23×C32−1+411yescharacteristic
605C23×C32−1+411yescharacteristic
606C22×D3—22no—
607C22×D3—22no—
608C22×D3—22no—
609C22×D3—22no—
610C22×D3—22no—
611C22×D3—22no—
612C22×D3—22no—
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—
641C3×D4—416no—
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—41no—
652C2×C3×C4—41no—
653C2×C3×C4—41no—
654C2×C3×C4—41no—
655C2×C3×C4—41no—
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—
677#67—416no—
678#67—416no—
679C2×Dic3—22no—
680C2×Dic3—22no—
681C2×Dic3—22no—
682C2×Dic3—22no—
683C2×Dic3—22no—
684C2×Dic3—22no—
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—41no—
701C2×Dic3—41no—
702C2×Dic3—41no—
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—41no—
726C2×Dic3#12014yes—
727C2×Dic3#12114yes—
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—21no—
744C24—21no—
745C24—21no—
746C24—21no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—32no—
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—
772C24D3×D412yes—
773C24D3×D412yes—
774C24C23×D311yescharacteristic
775C2×Q8—68no—
776C2×Q8—124no—
777C2×Q8—124no—
778C2×Q8—124no—
779C2×Q8—124no—
780C2×Q8—124no—
781C2×Q8—124no—
782C2×D4—44no—
783C2×D4—44no—
784C2×D4—44no—
785C2×D4—44no—
786C2×D4—44no—
787C2×D4—44no—
788C2×D4—44no—
789C2×D4—68no—
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—32no—
836C22×C4—32no—
837C22×C4—32no—
838C22×C4—32no—
839C22×C4—32no—
840C22×C4—32no—
841C22×C4—32no—
842C22×C4—32no—
843C22×C4—32no—
844C22×C4—61no—
845C22×C4—61no—
846C22×C4—61no—
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—61no—
882C22×C4—61no—
883C22×C4—61no—
884C22×C4#23512yes—
885C22×C4D3×D412yes—
886C22×C4D3×D412yes—
887C4⋊C4—124no—
888C4⋊C4—124no—
889C4⋊C4—124no—
890C22⋊C4—28no—
891C22⋊C4—44no—
892C22⋊C4—44no—
893C22⋊C4—44no—
894C22⋊C4—68no—
895C22⋊C4—68no—
896C22⋊C4—68no—
897C22⋊C4—68no—
898C22⋊C4—124no—
899C22⋊C4—124no—
900C22⋊C4—124no—
901C22⋊C4—124no—
902C22⋊C4—124no—
903C22⋊C4—124no—
904C22⋊C4—124no—
905C42—68no—
906C22×C3—42no—
907C22×C3—42no—
908C22×C3—42no—
909C22×C3—42no—
910C22×C3—42no—
911C22×C3—42no—
912C22×C3—42no—
913C22×C3—42no—
914C22×C3—42no—
915C22×C3—42no—
916C22×C3—42no—
917C22×C3—42no—
918C22×C3—42no—
919C22×C3—42no—
920C22×C3—81no—
921C22×C3—81no—
922C22×C3—81no—
923C22×C3—81no—
924C22×C3—81no—
925C22×C3—81no—
926C22×C3—81no—
927C22×C3—81no—
928C22×C3—81no—
929C22×C3—81no—
930C22×C3—81no—
931C22×C3—81no—
932C22×C3—81no—
933C22×C3—81no—
934C22×C3—81no—
935C22×C3—81no—
936C22×C3C2×#12011yescharacteristic
937C22×C3C2×#12111yescharacteristic
938C22×C3#53211yescharacteristic
939C22×C3#53511yescharacteristic
940C22×C3#53511yescharacteristic
941C22×C3#53511yescharacteristic
942C22×C3#53511yescharacteristic
943C22×C3#53511yescharacteristic
944C22×C3#53611yescharacteristic
945C22×C3#53711yescharacteristic
946C22×C3#53711yescharacteristic
947C22×C3#53711yescharacteristic
948C22×C3#53711yescharacteristic
949C22×C3#53811yescharacteristic
950C22×C3#53811yescharacteristic
951C22×C3#54211yescharacteristic
952C22×C3#54211yescharacteristic
953C22×C3#54211yescharacteristic
954C22×C3#54211yescharacteristic
955C22×C3D4211yescharacteristic
956C22×C3D4211yescharacteristic
957C22×C3#54611yescharacteristic
958C22×C3#54611yescharacteristic
959C22×C3#54611yescharacteristic
960C22×C3#54611yescharacteristic
961C22×C3#54611yescharacteristic
962C22×C3#54611yescharacteristic
963C22×C3#54711yescharacteristic
964C22×C3#54711yescharacteristic
965C22×C3#55911yescharacteristic
966C22×C3#55911yescharacteristic
967C22×C3H(3,𝔽4)11yescharacteristic
968C22×C3H(3,𝔽4)11yescharacteristic
969C22×C3#56211yescharacteristic
970C22×C3#56211yescharacteristic
971C2×D3—42no—
972C2×D3—42no—
973C2×D3—42no—
974C2×D3—42no—
975C2×D3—42no—
976C2×D3—42no—
977C2×D3—42no—
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—42no—
987C3×C4—42no—
988C3×C4—42no—
989C3×C4—81no—
990C3×C4—81no—
991Dic3—24no—
992Dic3—24no—
993Dic3—42no—
994Dic3—42no—
995Dic3—42no—
996Dic3—81no—
997Dic3—81no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
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—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—62no—
1069C23—62no—
1070C23—62no—
1071C23—62no—
1072C23—62no—
1073C23—62no—
1074C23—62no—
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×D3×D411yescharacteristic
1105C23C2×D3×D411yescharacteristic
1106C23C2×D3×D411yescharacteristic
1107C23C2×D3×D411yescharacteristic
1108C23#100411yescharacteristic
1109C23#100411yescharacteristic
1110C23#100411yescharacteristic
1111C23#100411yescharacteristic
1112C23#100411yescharacteristic
1113C23#100411yescharacteristic
1114C23D3×#4111yescharacteristic
1115C23D3×#4111yescharacteristic
1116C23#101011yescharacteristic
1117C23#101011yescharacteristic
1118Q8—1216no—
1119D4—416no—
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—34no—
1132C2×C4—34no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
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—62no—
1160C2×C4—62no—
1161C2×C4—62no—
1162C2×C4—62no—
1163C2×C4—62no—
1164C2×C4—62no—
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—121no—
1181C2×C4—121no—
1182C2×C4—121no—
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—121no—
1206C2×C3—82no—
1207C2×C3—82no—
1208C2×C3#240811yescharacteristic
1209C2×C3#243011yescharacteristic
1210C2×C3#254411yescharacteristic
1211C2×C3#261511yescharacteristic
1212C2×C3#262011yescharacteristic
1213C2×C3#266211yescharacteristic
1214C2×C3#267011yescharacteristic
1215C2×C3#267011yescharacteristic
1216C2×C3#267211yescharacteristic
1217C2×C3#267211yescharacteristic
1218C2×C3#271011yescharacteristic
1219C2×C3#271011yescharacteristic
1220C2×C3#271211yescharacteristic
1221C2×C3#271211yescharacteristic
1222C2×C3#281911yescharacteristic
1223D3—82no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—42no—
1235C22—42no—
1236C22—42no—
1237C22—42no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22—81no—
1252C22—81no—
1253C22—81no—
1254C22—122no—
1255C22—122no—
1256C22—122no—
1257C22—122no—
1258C22—122no—
1259C22—122no—
1260C22—122no—
1261C22—241no—
1262C22—241no—
1263C22—241no—
1264C22—241no—
1265C22—241no—
1266C22—241no—
1267C22—241no—
1268C22—241no—
1269C22#549011yescharacteristic
1270C22#549011yescharacteristic
1271C22#549411yescharacteristic
1272C22#554811yescharacteristic
1273C22#555111yescharacteristic
1274C22#555911yescharacteristic
1275C22#556111yescharacteristic
1276C22D3×#12011yescharacteristic
1277C22#559011yescharacteristic
1278C22#559011yescharacteristic
1279C22#559211yescharacteristic
1280C22#559211yescharacteristic
1281C22#559211yescharacteristic
1282C22#559411yescharacteristic
1283C22#559411yescharacteristic
1284C22#559711yescharacteristic
1285C22#559711yescharacteristic
1286C22D3×#12111yescharacteristic
1287C22#560811yescharacteristic
1288C22#560811yescharacteristic
1289C22#561011yescharacteristic
1290C22#561011yescharacteristic
1291C22#561011yescharacteristic
1292C22#561211yescharacteristic
1293C22#561311yescharacteristic
1294C22#562111yescharacteristic
1295C22#562111yescharacteristic
1296C22#564811yescharacteristic
1297C22#565511yescharacteristic
1298C22#566211yescharacteristic
1299C22#566411yescharacteristic
1300C22#566911yescharacteristic
1301C22#566911yescharacteristic
1302C22#571511yescharacteristic
1303C22#571511yescharacteristic
1304C4—42no—
1305C4—42no—
1306C4—42no—
1307C4—64no—
1308C4—64no—
1309C4—81no—
1310C4—81no—
1311C4—122no—
1312C4—122no—
1313C4—122no—
1314C4—241no—
1315C4—241no—
1316C3#1650411yescharacteristic, complemented, Sylow
1317C2—82no—
1318C2—82no—
1319C2—242no—
1320C2#7383711yescharacteristic
1321C2#7475311yescharacteristic
1322C2#7482211yescharacteristic
1323C2#7489611yescharacteristic
1324C2#7491411yescharacteristic
1325C2#7637711yescharacteristic
1326C2#7647011yescharacteristic
1327C2#7666911yescharacteristic
1328C2#7669711yescharacteristic
1329C2#7674511yescharacteristic
1330C2#7676611yescharacteristic
1331C2#7697211yescharacteristic
1332C2#7700011yescharacteristic
1333C2#7703011yescharacteristic
1334C2#7703511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1438C2
prime radicalC2×#5223C2
hypercenter#1438D3
hypocenterC3#16504
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
1. C22×#885C2semidirect
3. C2×#5222C2semidirect
4. C2×#4959C2semidirect
5. C2×#4947C2semidirect
6. C2×#4945C2semidirect
7. C3×#1438C2semidirect
8. #71550C2semidirect
9. #71550C2semidirect
10. #71547C2semidirect
11. #71547C2semidirect
12. #69428C2semidirect
13. #69428C2semidirect
14. #69424C2semidirect
15. Dic3⋊#95C2semidirect
73. #1438D3semidirect
147. C2×#217D4semidirect
162. C2×(C2×D3)⋊C4D4semidirect
174. C2×C4×Dic3D4semidirect
1316. C3#16504semidirect

Maximal subgroups

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

subgroupindex
C22×#8852
C2×#52232
C2×#52222
C2×#49592
C2×#49472
C2×#49452
C3×#14382
#715502
#715472
#694282
#694242
Dic3⋊#952
#165043