Finite Group Databasebeta

← #10733672

Subgroups — #10733672

Order 768.

2442 conjugacy classes of subgroups.

The subgroup lattice has 1352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#930C211yesmaximal, characteristic
2C2×C3×#385C211yesmaximal, characteristic, complemented
3C2×#4994C211yesmaximal, characteristic, complemented
4C2×#4991C211yesmaximal, characteristic, complemented
5C2×#4984C211yesmaximal, characteristic, complemented
6C2×#4961C211yesmaximal, characteristic, complemented
7C2×#4961C211yesmaximal, characteristic, complemented
8C2×#4957C211yesmaximal, characteristic, complemented
9#72127C211yesmaximal, characteristic, complemented
10#71570C211yesmaximal, characteristic, complemented
11#71550C211yesmaximal, characteristic, complemented
12#69427C211yesmaximal, characteristic, complemented
13#69426C211yesmaximal, characteristic, complemented
14#69411C211yesmaximal, characteristic, complemented
15#69408C211yesmaximal, characteristic, complemented
16#15316—31nomaximal, Sylow
17C24×C3×C4C2211yescharacteristic
18C23×#67C2211yescharacteristic
19C23×#67C2211yescharacteristic
20C23×D12C2211yescharacteristic
21C22×C3×C4⋊C4C2211yescharacteristic
22C22×C3×C4⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×#217C2211yescharacteristic
26C22×#217C2211yescharacteristic
27C2×#930—24no—
28C2×#930—24no—
29C2×#930—24no—
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×(C2×D3)⋊C4C2211yescharacteristic
38C22×(C2×D3)⋊C4C2211yescharacteristic
39C22×(C2×D3)⋊C4C2211yescharacteristic
40C22×C4⋊Dic3C2211yescharacteristic
41C22×C4⋊Dic3C2211yescharacteristic
42C22×C4⋊Dic3C2211yescharacteristic
43C22×Dic3⋊C4C2211yescharacteristic
44C22×C4×Dic3C2211yescharacteristic
45C3×#385—24no—
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
56#4994—24no—
57#4991—24no—
58#4984—24no—
59#4961—24no—
60#4961—24no—
61#4957—24no—
62C22×#121—31no—
63C2×#396—31no—
64C2×#394—31no—
65C2×#394—31no—
66C2×#394—31no—
67C2×#390—31no—
68C2×#389—31no—
69C2×#385D311yescharacteristic, complemented
70#1441—31no—
71#1439—31no—
72#1439—31no—
73#1438—31no—
74#1438—31no—
75#1437—31no—
76C22⋊#95—31no—
77C25×C3C2311yescharacteristic
78C24×D3C2311yescharacteristic
79C24×D3C2311yescharacteristic
80C23×C3×C4—22no—
81C23×C3×C4—22no—
82C23×C3×C4—22no—
83C23×C3×C4—22no—
84C23×C3×C4—22no—
85C23×C3×C4—41no—
86C23×C3×C4—41no—
87C23×C3×C4C2311yescharacteristic
88C23×C3×C4C2311yescharacteristic
89C23×C3×C4C2311yescharacteristic
90C23×C3×C4C2311yescharacteristic
91C23×C3×C4C2311yescharacteristic
92C23×C3×C4C2311yescharacteristic
93C22×#67—22no—
94C22×#67—22no—
95C22×#67—22no—
96C22×#67—22no—
97C22×#67—22no—
98C22×#67—22no—
99C22×#67—22no—
100C22×#67—22no—
101C22×#67—22no—
102C22×#67—41no—
103C22×#67—41no—
104C22×#67—41no—
105C22×#67—41no—
106C22×#67D414yes—
107C23×Dic3C2311yescharacteristic
108C23×Dic3C2311yescharacteristic
109C23×Dic3C2311yescharacteristic
110C23×Dic3C2311yescharacteristic
111C23×Dic3C2311yescharacteristic
112C23×Dic3C2311yescharacteristic
113C22×D12—22no—
114C22×D12—22no—
115C22×D12—22no—
116C22×D12—22no—
117C22×D12—22no—
118C22×D12—41no—
119C22×D12—41no—
120C2×C3×C4⋊C4—22no—
121C2×C3×C4⋊C4—22no—
122C2×C3×C4⋊C4—22no—
123C2×C3×C4⋊C4—22no—
124C2×C3×C4⋊C4—41no—
125C2×C3×C4⋊C4D414yescomplemented
126C2×C3×C22⋊C4—22no—
127C2×C3×C22⋊C4—22no—
128C2×C3×C22⋊C4—22no—
129C2×C3×C22⋊C4—22no—
130C2×C3×C22⋊C4—41no—
131C2×C3×C22⋊C4D414yescomplemented
132C2×#217—22no—
133C2×#217—22no—
134C2×#217—22no—
135C2×#217—22no—
136C2×#217—22no—
137C2×#217—41no—
138#930—232no—
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—22no—
155C2×(C2×D3)⋊C4—22no—
156C2×(C2×D3)⋊C4—22no—
157C2×(C2×D3)⋊C4—22no—
158C2×(C2×D3)⋊C4—22no—
159C2×(C2×D3)⋊C4—22no—
160C2×(C2×D3)⋊C4—41no—
161C2×(C2×D3)⋊C4—41no—
162C2×(C2×D3)⋊C4—41no—
163C2×(C2×D3)⋊C4—41no—
164C2×(C2×D3)⋊C4—41no—
165C2×(C2×D3)⋊C4—41no—
166C2×(C2×D3)⋊C4—41no—
167C2×(C2×D3)⋊C4—41no—
168C2×(C2×D3)⋊C4D414yes—
169C2×C4⋊Dic3—22no—
170C2×C4⋊Dic3—22no—
171C2×C4⋊Dic3—22no—
172C2×C4⋊Dic3—22no—
173C2×C4⋊Dic3—22no—
174C2×C4⋊Dic3—22no—
175C2×C4⋊Dic3—22no—
176C2×C4⋊Dic3—41no—
177C2×C4⋊Dic3D414yes—
178C2×Dic3⋊C4—22no—
179C2×Dic3⋊C4—22no—
180C2×Dic3⋊C4—41no—
181C2×C4×Dic3—22no—
182C2×C4×Dic3—22no—
183C2×C4×Dic3—41no—
184C3×#95—22no—
185C3×#95—22no—
186C3⋊#95—22no—
187C3⋊#95—22no—
188C3⋊#95—22no—
189C3⋊#95—22no—
190C3⋊#95—22no—
191C3⋊#95—22no—
192C3⋊#95—41no—
193C3⋊#95—41no—
194C23×D4—31no—
195C23×D4—31no—
196C23×D4—31no—
197C24×C4C2×D311yescharacteristic
198C2×#121—64no—
199C2×#121—64no—
200C2×#121—64no—
201C22×C4⋊C4—31no—
202C22×C4⋊C4—31no—
203C22×C4⋊C4—31no—
204C22×C4⋊C4—31no—
205C22×C4⋊C4C2×D311yescharacteristic
206C22×C4⋊C4C2×D311yescharacteristic
207C22×C22⋊C4—31no—
208C22×C22⋊C4—31no—
209C22×C22⋊C4—31no—
210C22×C22⋊C4—31no—
211C22×C22⋊C4—31no—
212C22×C22⋊C4—31no—
213C22×C22⋊C4—31no—
214C22×C22⋊C4—31no—
215C22×C22⋊C4—31no—
216C22×C22⋊C4—31no—
217C22×C22⋊C4—31no—
218C22×C22⋊C4—31no—
219C22×C22⋊C4C2×D311yescharacteristic
220C22×C22⋊C4C2×D311yescharacteristic
221C22×C42—31no—
222#396—64no—
223#394—64no—
224#394—64no—
225#394—64no—
226#390—64no—
227#389—64no—
228#385—24no—
229C2×#95—31no—
230C2×#95—31no—
231C2×#95—31no—
232C2×#95—31no—
233C2×#95—31no—
234C2×#95—31no—
235C2×#95—31no—
236C2×#95—31no—
237C2×#95C2×D311yescharacteristic
238C2×#95C2×D311yescharacteristic
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×C3C2×D412yes—
252C24×C3C2×D412yes—
253C24×C3#4112yes—
254C24×C3C2411yescharacteristic
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×D3—21no—
276C23×D3—21no—
277C23×D3—21no—
278C23×D3—21no—
279C23×D3—21no—
280C23×D3—21no—
281C23×D3—21no—
282C23×D3—21no—
283C23×D3C2×D412yes—
284C23×D3C2×D412yes—
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—28no—
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×C4—21no—
317C22×C3×C4—21no—
318C22×C3×C4—21no—
319C22×C3×C4—44no—
320C22×C3×C4—44no—
321C22×C3×C4—44no—
322C22×C3×C4—44no—
323C22×C3×C4—44no—
324C22×C3×C4—44no—
325C22×C3×C4C2×D412yes—
326C22×C3×C4C2×D412yes—
327C22×C3×C4C2×D412yes—
328C22×C3×C4C2×D412yes—
329C22×C3×C4C2×D412yes—
330C22×C3×C4C2×D412yes—
331C22×C3×C4C2×D412yes—
332C22×C3×C4#4112yes—
333C22×C3×C4#4112yes—
334C2×#67—28no—
335C2×#67—28no—
336C2×#67—28no—
337C2×#67—44no—
338C2×#67—44no—
339C2×#67—44no—
340C2×#67—44no—
341C2×#67—44no—
342C2×#67—44no—
343C2×#67—44no—
344C2×#67—44no—
345C2×#67—44no—
346C2×#67—44no—
347C2×#67—44no—
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×Dic3—21no—
374C22×Dic3—21no—
375C22×Dic3—21no—
376C22×Dic3—21no—
377C22×Dic3—21no—
378C22×Dic3—21no—
379C22×Dic3—21no—
380C22×Dic3—21no—
381C22×Dic3—21no—
382C22×Dic3—21no—
383C22×Dic3—21no—
384C22×Dic3—21no—
385C22×Dic3C2×D412yes—
386C22×Dic3C2×D412yes—
387C22×Dic3C2×D412yes—
388C22×Dic3C2×D412yes—
389C22×Dic3#4112yes—
390C2×D12—28no—
391C2×D12—44no—
392C2×D12—44no—
393C2×D12—44no—
394C2×D12—44no—
395C2×D12—44no—
396C2×D12—44no—
397C3×C4⋊C4—28no—
398C3×C4⋊C4—44no—
399C3×C22⋊C4—28no—
400C3×C22⋊C4—44no—
401#217—44no—
402#217—44no—
403(C2×D3)⋊C4—28no—
404(C2×D3)⋊C4—28no—
405(C2×D3)⋊C4—44no—
406(C2×D3)⋊C4—44no—
407(C2×D3)⋊C4—44no—
408(C2×D3)⋊C4—44no—
409(C2×D3)⋊C4—44no—
410(C2×D3)⋊C4—44no—
411(C2×D3)⋊C4—44no—
412(C2×D3)⋊C4—44no—
413C4⋊Dic3—28no—
414C4⋊Dic3—44no—
415C4⋊Dic3—44no—
416Dic3⋊C4—44no—
417C4×Dic3—44no—
418C25—31no—
419C25—31no—
420C25C22×D311yescharacteristic
421C22×D4—34no—
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—62no—
432C22×D4—62no—
433C22×D4—62no—
434C22×D4—62no—
435C22×D4—62no—
436C22×D4—121no—
437C22×D4—121no—
438C22×D4—121no—
439C22×D4—121no—
440C22×D4—121no—
441C22×D4—121no—
442C23×C4—22no—
443C23×C4—22no—
444C23×C4—22no—
445C23×C4—22no—
446C23×C4—22no—
447C23×C4—31no—
448C23×C4—31no—
449C23×C4—31no—
450C23×C4—31no—
451C23×C4—31no—
452C23×C4—31no—
453C23×C4—41no—
454C23×C4—41no—
455C23×C4C22×D311yescharacteristic
456C23×C4C22×D311yescharacteristic
457C23×C4C22×D311yescharacteristic
458C23×C4C22×D311yescharacteristic
459C23×C4C22×D311yescharacteristic
460C23×C4C22×D311yescharacteristic
461#121—632no—
462C2×C4⋊C4—22no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4—22no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—34no—
467C2×C4⋊C4—41no—
468C2×C4⋊C4—62no—
469C2×C4⋊C4—62no—
470C2×C4⋊C4—62no—
471C2×C4⋊C4—62no—
472C2×C4⋊C4—62no—
473C2×C4⋊C4—62no—
474C2×C4⋊C4—62no—
475C2×C4⋊C4—62no—
476C2×C4⋊C4—62no—
477C2×C4⋊C4—121no—
478C2×C4⋊C4—121no—
479C2×C4⋊C4#6714yescomplemented
480C2×C22⋊C4—22no—
481C2×C22⋊C4—22no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—34no—
485C2×C22⋊C4—41no—
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—62no—
497C2×C22⋊C4—62no—
498C2×C22⋊C4—62no—
499C2×C22⋊C4—62no—
500C2×C22⋊C4—62no—
501C2×C22⋊C4—62no—
502C2×C22⋊C4—62no—
503C2×C22⋊C4—62no—
504C2×C22⋊C4—62no—
505C2×C22⋊C4—62no—
506C2×C22⋊C4—62no—
507C2×C22⋊C4—62no—
508C2×C22⋊C4—62no—
509C2×C22⋊C4—62no—
510C2×C22⋊C4—62no—
511C2×C22⋊C4—62no—
512C2×C22⋊C4—121no—
513C2×C22⋊C4—121no—
514C2×C22⋊C4—121no—
515C2×C22⋊C4—121no—
516C2×C22⋊C4—121no—
517C2×C22⋊C4—121no—
518C2×C22⋊C4—121no—
519C2×C22⋊C4—121no—
520C2×C22⋊C4—121no—
521C2×C22⋊C4D1214yescomplemented
522C2×C42—62no—
523C2×C42—62no—
524C2×C42—121no—
525#95—22no—
526#95—22no—
527#95—62no—
528#95—62no—
529#95—62no—
530#95—62no—
531#95—62no—
532#95—62no—
533#95—121no—
534#95—121no—
535C23×C3—22no—
536C23×C3—22no—
537C23×C3—22no—
538C23×C3—22no—
539C23×C3—22no—
540C23×C3—22no—
541C23×C3—22no—
542C23×C3—22no—
543C23×C3—22no—
544C23×C3—22no—
545C23×C3—22no—
546C23×C3—22no—
547C23×C3—22no—
548C23×C3—22no—
549C23×C3—22no—
550C23×C3—22no—
551C23×C3—22no—
552C23×C3—22no—
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#12114yes—
570C23×C3C22×D411yescharacteristic
571C23×C3C22×D411yescharacteristic
572C23×C3C22×D411yescharacteristic
573C23×C3C22×D411yescharacteristic
574C23×C3C22×D411yescharacteristic
575C23×C3C2×#4111yescharacteristic
576C23×C3C2×#4111yescharacteristic
577C23×C3C2×#4111yescharacteristic
578C23×C3C2×#4111yescharacteristic
579C23×C3H(5,𝔽2)11yescharacteristic
580C23×C3H(5,𝔽2)11yescharacteristic
581C23×C3H(5,𝔽2)11yescharacteristic
582C23×C3H(5,𝔽2)11yescharacteristic
583C23×C32−1+411yescharacteristic
584C23×C32−1+411yescharacteristic
585C22×D3—22no—
586C22×D3—22no—
587C22×D3—22no—
588C22×D3—22no—
589C22×D3—22no—
590C22×D3—22no—
591C22×D3—22no—
592C22×D3—22no—
593C22×D3—22no—
594C22×D3—22no—
595C22×D3—22no—
596C22×D3—22no—
597C22×D3—22no—
598C22×D3—22no—
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—
641C22×D3—41no—
642C22×D3—41no—
643C22×D3—41no—
644C22×D3—41no—
645C22×D3—41no—
646C22×D3—41no—
647C22×D3—41no—
648C22×D3—41no—
649C22×D3—41no—
650C22×D3—41no—
651C22×D3—41no—
652C22×D3—41no—
653C22×D3—41no—
654C22×D3—41no—
655C2×C3×C4—22no—
656C2×C3×C4—22no—
657C2×C3×C4—22no—
658C2×C3×C4—22no—
659C2×C3×C4—22no—
660C2×C3×C4—22no—
661C2×C3×C4—22no—
662C2×C3×C4—22no—
663C2×C3×C4—22no—
664C2×C3×C4—22no—
665C2×C3×C4—22no—
666C2×C3×C4—22no—
667C2×C3×C4—22no—
668C2×C3×C4—22no—
669C2×C3×C4—22no—
670C2×C3×C4—22no—
671C2×C3×C4—22no—
672C2×C3×C4—22no—
673C2×C3×C4—22no—
674C2×C3×C4—22no—
675C2×C3×C4—22no—
676C2×C3×C4—416no—
677C2×C3×C4—41no—
678C2×C3×C4—41no—
679C2×C3×C4—41no—
680C2×C3×C4—41no—
681C2×C3×C4—41no—
682C2×C3×C4—41no—
683C2×C3×C4—41no—
684C2×C3×C4—41no—
685C2×C3×C4—41no—
686C2×C3×C4—41no—
687C2×C3×C4—41no—
688C2×C3×C4—41no—
689C2×C3×C4—41no—
690C2×C3×C4—41no—
691C2×C3×C4—41no—
692C2×C3×C4—41no—
693C2×C3×C4—41no—
694C2×C3×C4—41no—
695C2×C3×C4—41no—
696C2×C3×C4#12114yes—
697C2×C3×C4#12114yescomplemented
698#67—416no—
699#67—416no—
700C2×Dic3—22no—
701C2×Dic3—22no—
702C2×Dic3—22no—
703C2×Dic3—22no—
704C2×Dic3—22no—
705C2×Dic3—22no—
706C2×Dic3—22no—
707C2×Dic3—22no—
708C2×Dic3—22no—
709C2×Dic3—22no—
710C2×Dic3—22no—
711C2×Dic3—22no—
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—41no—
727C2×Dic3—41no—
728C2×Dic3—41no—
729C2×Dic3—41no—
730C2×Dic3—41no—
731C2×Dic3—41no—
732C2×Dic3—41no—
733C2×Dic3—41no—
734C2×Dic3—41no—
735C2×Dic3—41no—
736C2×Dic3—41no—
737C2×Dic3—41no—
738C2×Dic3—41no—
739C2×Dic3—41no—
740C2×Dic3—41no—
741C2×Dic3#12014yes—
742D12—416no—
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—32no—
756C24—32no—
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—61no—
774C24—61no—
775C24—61no—
776C24—61no—
777C24—61no—
778C24—61no—
779C24—61no—
780C24—61no—
781C24—61no—
782C24—61no—
783C24—61no—
784C24—61no—
785C24C2×D1212yes—
786C24D3×D412yes—
787C24#23912yes—
788C24C23×D311yescharacteristic
789C2×D4—68no—
790C2×D4—68no—
791C2×D4—68no—
792C2×D4—68no—
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—
803C2×D4—124no—
804C2×D4—124no—
805C2×D4—124no—
806C2×D4—124no—
807C2×D4—124no—
808C2×D4—124no—
809C2×D4—124no—
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—28no—
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—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—32no—
845C22×C4—32no—
846C22×C4—32no—
847C22×C4—32no—
848C22×C4—32no—
849C22×C4—44no—
850C22×C4—44no—
851C22×C4—44no—
852C22×C4—44no—
853C22×C4—44no—
854C22×C4—44no—
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—61no—
885C22×C4—61no—
886C22×C4—61no—
887C22×C4—61no—
888C22×C4—61no—
889C22×C4—61no—
890C22×C4—61no—
891C22×C4—61no—
892C22×C4C2×D1212yes—
893C22×C4C2×D1212yes—
894C22×C4#23512yes—
895C22×C4D3×D412yes—
896C22×C4D3×D412yes—
897C22×C4#23712yes—
898C22×C4C2×#6712yes—
899C22×C4C2×#6712yes—
900C22×C4C2×#6712yes—
901C4⋊C4—28no—
902C4⋊C4—44no—
903C4⋊C4—68no—
904C4⋊C4—124no—
905C4⋊C4—124no—
906C4⋊C4—124no—
907C22⋊C4—28no—
908C22⋊C4—44no—
909C22⋊C4—68no—
910C22⋊C4—68no—
911C22⋊C4—124no—
912C22⋊C4—124no—
913C22⋊C4—124no—
914C22⋊C4—124no—
915C22⋊C4—124no—
916C22⋊C4—124no—
917C22⋊C4—124no—
918C22⋊C4—124no—
919C22⋊C4—124no—
920C22⋊C4—124no—
921C42—124no—
922C22×C3—24no—
923C22×C3—24no—
924C22×C3—24no—
925C22×C3—42no—
926C22×C3—42no—
927C22×C3—42no—
928C22×C3—42no—
929C22×C3—42no—
930C22×C3—42no—
931C22×C3—42no—
932C22×C3—42no—
933C22×C3—42no—
934C22×C3—42no—
935C22×C3—42no—
936C22×C3—42no—
937C22×C3C2×#12011yescharacteristic
938C22×C3C2×#12111yescharacteristic
939C22×C3C2×#12111yescharacteristic
940C22×C3C2×#12111yescharacteristic
941C22×C3#52911yescharacteristic
942C22×C3#53211yescharacteristic
943C22×C3#53411yescharacteristic
944C22×C3#53511yescharacteristic
945C22×C3#53611yescharacteristic
946C22×C3#53711yescharacteristic
947C22×C3#53711yescharacteristic
948C22×C3#53811yescharacteristic
949C22×C3#53911yescharacteristic
950C22×C3#54011yescharacteristic
951C22×C3#54211yescharacteristic
952C22×C3D4211yescharacteristic
953C22×C3D4211yescharacteristic
954C22×C3D4211yescharacteristic
955C22×C3D4211yescharacteristic
956C22×C3#54611yescharacteristic
957C22×C3#54611yescharacteristic
958C22×C3#54611yescharacteristic
959C22×C3#54611yescharacteristic
960C22×C3#54611yescharacteristic
961C22×C3#54711yescharacteristic
962C22×C3#54711yescharacteristic
963C22×C3#54711yescharacteristic
964C22×C3#54811yescharacteristic
965C22×C3#54811yescharacteristic
966C22×C3#54811yescharacteristic
967C22×C3#55011yescharacteristic
968C22×C3#55311yescharacteristic
969C22×C3#55311yescharacteristic
970C22×C3#56211yescharacteristic
971C22×C3#56211yescharacteristic
972C2×D3—42no—
973C2×D3—42no—
974C2×D3—42no—
975C2×D3—42no—
976C2×D3—42no—
977C2×D3—42no—
978C2×D3—42no—
979C2×D3—42no—
980C2×D3—42no—
981C2×D3—42no—
982C2×D3—42no—
983C2×D3—42no—
984C2×D3—42no—
985C2×D3—42no—
986C2×D3—81no—
987C2×D3—81no—
988C2×D3—81no—
989C2×D3—81no—
990C2×D3—81no—
991C2×D3—81no—
992C2×D3—81no—
993C2×D3—81no—
994C2×D3—81no—
995C2×D3—81no—
996C2×D3—81no—
997C2×D3—81no—
998C2×D3—81no—
999C2×D3—81no—
1000C2×D3—81no—
1001C2×D3—81no—
1002C3×C4—24no—
1003C3×C4—24no—
1004C3×C4—42no—
1005C3×C4—42no—
1006C3×C4—42no—
1007C3×C4—81no—
1008Dic3—24no—
1009Dic3—42no—
1010Dic3—42no—
1011Dic3—81no—
1012Dic3—81no—
1013Dic3—81no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
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—62no—
1049C23—62no—
1050C23—62no—
1051C23—62no—
1052C23—62no—
1053C23—62no—
1054C23—62no—
1055C23—62no—
1056C23—62no—
1057C23—62no—
1058C23—62no—
1059C23—62no—
1060C23—62no—
1061C23—62no—
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—
1103C23—121no—
1104C23—121no—
1105C23—121no—
1106C23—121no—
1107C23—121no—
1108C23—121no—
1109C23—121no—
1110C23—121no—
1111C23—121no—
1112C23—121no—
1113C23—121no—
1114C23—121no—
1115C23—121no—
1116C23—121no—
1117C23—121no—
1118C23#89514yes—
1119C23C22×D1211yescharacteristic
1120C23C2×#23511yescharacteristic
1121C23C2×D3×D411yescharacteristic
1122C23C2×D3×D411yescharacteristic
1123C23C2×D3×D411yescharacteristic
1124C23C2×#23711yescharacteristic
1125C23#100411yescharacteristic
1126C23#100411yescharacteristic
1127C23C2×#23911yescharacteristic
1128C23#100711yescharacteristic
1129C23D3×#4111yescharacteristic
1130C23#100911yescharacteristic
1131C23#100911yescharacteristic
1132C23#101011yescharacteristic
1133C23C22×#6711yescharacteristic
1134D4—1216no—
1135D4—1216no—
1136D4—1216no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—34no—
1159C2×C4—416no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—62no—
1180C2×C4—62no—
1181C2×C4—62no—
1182C2×C4—62no—
1183C2×C4—62no—
1184C2×C4—62no—
1185C2×C4—62no—
1186C2×C4—62no—
1187C2×C4—62no—
1188C2×C4—62no—
1189C2×C4—62no—
1190C2×C4—62no—
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×C4—121no—
1207C2×C4—121no—
1208C2×C4—121no—
1209C2×C4—121no—
1210C2×C4—121no—
1211C2×C4—121no—
1212C2×C4—121no—
1213C2×C4—121no—
1214C2×C4—121no—
1215C2×C4—121no—
1216C2×C4—121no—
1217C2×C4—121no—
1218C2×C4—121no—
1219C2×C4—121no—
1220C2×C4#93014yescomplemented
1221C2×C4#93914yes—
1222C2×C3—44no—
1223C2×C3#240811yescharacteristic
1224C2×C3#241011yescharacteristic
1225C2×C3#241611yescharacteristic
1226C2×C3#241611yescharacteristic
1227C2×C3#242511yescharacteristic
1228C2×C3#242611yescharacteristic
1229C2×C3#242811yescharacteristic
1230C2×C3#243211yescharacteristic
1231C2×C3#255911yescharacteristic
1232C2×C3#267211yescharacteristic
1233C2×C3#267611yescharacteristic
1234C2×C3#268111yescharacteristic
1235C2×C3#268211yescharacteristic
1236C2×C3#270111yescharacteristic
1237C2×C3#271111yescharacteristic
1238D3—82no—
1239D3—82no—
1240C22—24no—
1241C22—24no—
1242C22—24no—
1243C22—42no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—42no—
1251C22—42no—
1252C22—42no—
1253C22—42no—
1254C22—42no—
1255C22—122no—
1256C22—122no—
1257C22—122no—
1258C22—122no—
1259C22—122no—
1260C22—122no—
1261C22—122no—
1262C22—122no—
1263C22—122no—
1264C22—122no—
1265C22—122no—
1266C22—122no—
1267C22—122no—
1268C22—122no—
1269C22—241no—
1270C22—241no—
1271C22—241no—
1272C22—241no—
1273C22—241no—
1274C22—241no—
1275C22—241no—
1276C22—241no—
1277C22—241no—
1278C22—241no—
1279C22—241no—
1280C22—241no—
1281C22—241no—
1282C22—241no—
1283C22—241no—
1284C22—241no—
1285C22C2×#89511yescharacteristic
1286C22#550711yescharacteristic
1287C22#551011yescharacteristic
1288C22#551411yescharacteristic
1289C22#554811yescharacteristic
1290C22D4×D1211yescharacteristic
1291C22D4×D1211yescharacteristic
1292C22#555211yescharacteristic
1293C22#555411yescharacteristic
1294C22#555511yescharacteristic
1295C22#556211yescharacteristic
1296C22#556511yescharacteristic
1297C22D3×#12011yescharacteristic
1298C22#559111yescharacteristic
1299C22#559111yescharacteristic
1300C22#559211yescharacteristic
1301C22#562411yescharacteristic
1302C22#562811yescharacteristic
1303C22#563011yescharacteristic
1304C22#563011yescharacteristic
1305C22#563311yescharacteristic
1306C22#564311yescharacteristic
1307C22#564511yescharacteristic
1308C22#564711yescharacteristic
1309C22#565311yescharacteristic
1310C22#565511yescharacteristic
1311C22#565711yescharacteristic
1312C22#566711yescharacteristic
1313C22C2×#93011yescharacteristic
1314C22D4×#6711yescharacteristic
1315C22D4×#6711yescharacteristic
1316C22C2×#93911yescharacteristic
1317C22#581711yescharacteristic
1318C22#583311yescharacteristic
1319C22#583411yescharacteristic
1320C4—24no—
1321C4—24no—
1322C4—42no—
1323C4—42no—
1324C4—42no—
1325C4—64no—
1326C4—81no—
1327C4—122no—
1328C4—122no—
1329C4—241no—
1330C4—241no—
1331C4—241no—
1332C3#1531611yescharacteristic, complemented, Sylow
1333C2—44no—
1334C2—242no—
1335C2—242no—
1336C2#7441011yescharacteristic
1337C2#7441111yescharacteristic
1338C2#7447611yescharacteristic
1339C2#7450911yescharacteristic
1340C2#7452211yescharacteristic
1341C2#7452711yescharacteristic
1342C2#7460111yescharacteristic
1343C2#7462911yescharacteristic
1344C2#8219311yescharacteristic
1345C2#8235211yescharacteristic
1346C2#8240911yescharacteristic
1347C2#8258211yescharacteristic
1348C2#8275511yescharacteristic
1349C2#8282911yescharacteristic
1350C2#8287311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#385C2
prime radicalC22×#930C2
hypercenterC2×#385D3
hypocenterC3#15316
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. C2×C3×#385C2semidirect
3. C2×#4994C2semidirect
4. C2×#4991C2semidirect
5. C2×#4984C2semidirect
6. C2×#4961C2semidirect
7. C2×#4961C2semidirect
8. C2×#4957C2semidirect
9. #72127C2semidirect
10. #71570C2semidirect
11. #71550C2semidirect
12. #69427C2semidirect
13. #69426C2semidirect
14. #69411C2semidirect
15. #69408C2semidirect
69. C2×#385D3semidirect
125. C2×C3×C4⋊C4D4semidirect
131. C2×C3×C22⋊C4D4semidirect
479. C2×C4⋊C4#67semidirect
521. C2×C22⋊C4D12semidirect
697. C2×C3×C4#121semidirect
1220. C2×C4#930semidirect
1332. C3#15316semidirect

Maximal subgroups

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

subgroupindex
C22×#9302
C2×C3×#3852
C2×#49942
C2×#49912
C2×#49842
C2×#49612
C2×#49572
#721272
#715702
#715502
#694272
#694262
#694112
#694082
#153163