Finite Group Databasebeta

← #10735667

Subgroups — #10735667

Order 768.

2506 conjugacy classes of subgroups.

The subgroup lattice has 1362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#946C211yesmaximal, characteristic, complemented
2C2×C3×#393C211yesmaximal, characteristic, complemented
3C2×#5231C211yesmaximal, characteristic, complemented
4C2×#4960C211yesmaximal, characteristic
5C2×#4956C211yesmaximal, characteristic, complemented
6C2×#4961C211yesmaximal, characteristic, complemented
7C2×#4957C211yesmaximal, characteristic, complemented
8C2×#4665C211yesmaximal, characteristic, complemented
9#71550C211yesmaximal, characteristic, complemented
10#71547C211yesmaximal, characteristic, complemented
11#69428C211yesmaximal, characteristic, complemented
12#69426C211yesmaximal, characteristic, complemented
13#69421C211yesmaximal, characteristic, complemented
14#69408C211yesmaximal, characteristic, complemented
15#69407C211yesmaximal, characteristic, complemented
16#15453—31nomaximal, Sylow
17C23×C3×Q8C2211yescharacteristic
18C23×#67C2211yescharacteristic
19C23×#67C2211yescharacteristic
20C23×D12C2211yescharacteristic
21C23×C4×D3C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×#217C2211yescharacteristic
26C22×#217C2211yescharacteristic
27C2×#946—24no—
28C2×#946—24no—
29C2×#946—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×C4⋊Dic3C2211yescharacteristic
40C22×Dic3⋊C4C2211yescharacteristic
41C22×Dic3⋊C4C2211yescharacteristic
42C22×C4×Dic3C2211yescharacteristic
43C3×#393—24no—
44C2×C3×#95C2211yescharacteristic
45C2×C3×#95C2211yescharacteristic
46C2×C3×#95C2211yescharacteristic
47#5231—24no—
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#4961—24no—
58#4960—24no—
59#4957—24no—
60#4956—24no—
61#4665—24no—
62C22×C22⋊Q8—31no—
63C2×#394—31no—
64C2×#393—31no—
65C2×#393D311yescharacteristic, complemented
66C2×#392—31no—
67C2×#390—31no—
68C2×#386—31no—
69C2×#386—31no—
70#1445—31no—
71#1439—31no—
72#1439—31no—
73#1438—31no—
74#1438—31no—
75#1437—31no—
76#1436—31no—
77C25×C3C2311yescharacteristic
78C24×D3C2311yescharacteristic
79C24×D3C2311yescharacteristic
80C22×C3×Q8—22no—
81C22×C3×Q8—22no—
82C22×C3×Q8—22no—
83C22×C3×Q8—22no—
84C22×C3×Q8—22no—
85C22×C3×Q8—41no—
86C22×C3×Q8—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—22no—
103C22×#67—41no—
104C22×#67—41no—
105C22×#67—41no—
106C22×#67—41no—
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—
120C22×C4×D3—22no—
121C22×C4×D3—22no—
122C22×C4×D3—22no—
123C22×C4×D3—22no—
124C22×C4×D3—22no—
125C22×C4×D3—41no—
126C22×C4×D3—41no—
127C2×C3×C22⋊C4—22no—
128C2×C3×C22⋊C4—22no—
129C2×C3×C22⋊C4—22no—
130C2×C3×C22⋊C4—22no—
131C2×C3×C22⋊C4—22no—
132C2×C3×C22⋊C4—22no—
133C2×C3×C22⋊C4—22no—
134C2×C3×C22⋊C4—41no—
135C2×C3×C22⋊C4—41no—
136C2×#217—22no—
137C2×#217—22no—
138C2×#217—22no—
139C2×#217—22no—
140C2×#217—41no—
141C2×#217—41no—
142#946—232no—
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—22no—
161C2×(C2×D3)⋊C4—22no—
162C2×(C2×D3)⋊C4—22no—
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)⋊C4—41no—
169C2×(C2×D3)⋊C4D414yes—
170C2×C4⋊Dic3—22no—
171C2×C4⋊Dic3—22no—
172C2×C4⋊Dic3D414yescomplemented
173C2×Dic3⋊C4—22no—
174C2×Dic3⋊C4—22no—
175C2×Dic3⋊C4—22no—
176C2×Dic3⋊C4—22no—
177C2×Dic3⋊C4—22no—
178C2×Dic3⋊C4D414yescomplemented
179C2×C4×Dic3—22no—
180C2×C4×Dic3—41no—
181C2×C4×Dic3—41no—
182C3×#95—22no—
183C3×#95—22no—
184C3×#95D414yescomplemented
185C3⋊#95—22no—
186C3⋊#95—22no—
187C3⋊#95—22no—
188C3⋊#95—22no—
189C3⋊#95—22no—
190C3⋊#95—22no—
191C3⋊#95—41no—
192C3⋊#95—41no—
193C3⋊#95D414yescomplemented
194C23×Q8C2×D311yescharacteristic
195C23×D4—31no—
196C23×D4—31no—
197C23×D4—31no—
198C24×C4—31no—
199C2×C22⋊Q8—64no—
200C2×C22⋊Q8—64no—
201C2×C22⋊Q8—64no—
202C22×C4⋊C4—31no—
203C22×C4⋊C4—31no—
204C22×C4⋊C4—31no—
205C22×C22⋊C4—31no—
206C22×C22⋊C4—31no—
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⋊C4C2×D311yescharacteristic
217C22×C22⋊C4C2×D311yescharacteristic
218C22×C22⋊C4C2×D311yescharacteristic
219C22×C42—31no—
220#394—64no—
221#393—24no—
222#393—64no—
223#392—64no—
224#390—64no—
225#386—64no—
226#386—64no—
227C2×#95—31no—
228C2×#95—31no—
229C2×#95—31no—
230C2×#95—31no—
231C2×#95—31no—
232C2×#95—31no—
233C2×#95—31no—
234C2×#95—31no—
235C2×#95—31no—
236C2×#95C2×D311yescharacteristic
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×C3—21no—
252C24×C3—21no—
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×D3C2×D412yes—
282C23×D3#4112yes—
283C23×D3#4112yes—
284C23×D3#4112yes—
285C2×C3×Q8—28no—
286C2×C3×Q8—44no—
287C2×C3×Q8—44no—
288C2×C3×Q8—44no—
289C2×C3×Q8—44no—
290C2×C3×Q8—44no—
291C2×C3×Q8—44no—
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×C4—21no—
317C22×C3×C4—21no—
318C22×C3×C4—21no—
319C22×C3×C4—21no—
320C22×C3×C4—21no—
321C22×C3×C4—21no—
322C22×C3×C4—21no—
323C22×C3×C4—21no—
324C22×C3×C4—21no—
325C22×C3×C4—21no—
326C22×C3×C4—21no—
327C22×C3×C4C2×D412yes—
328C22×C3×C4C2×D412yes—
329C22×C3×C4C2×D412yes—
330C22×C3×C4C2×D412yes—
331C22×C3×C4C2×D412yes—
332C22×C3×C4C2×D412yes—
333C22×C3×C4C2×D412yes—
334C2×#67—28no—
335C2×#67—28no—
336C2×#67—44no—
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×Dic3C2×D412yes—
384C22×Dic3C2×D412yes—
385C22×Dic3C2×D412yes—
386C22×Dic3C2×D412yes—
387C22×Dic3C2×D412yes—
388C22×Dic3C2×D412yes—
389C22×Dic3C2×D412yes—
390C2×D12—28no—
391C2×D12—44no—
392C2×D12—44no—
393C2×D12—44no—
394C2×D12—44no—
395C2×D12—44no—
396C2×D12—44no—
397C2×C4×D3—28no—
398C2×C4×D3—44no—
399C2×C4×D3—44no—
400C2×C4×D3—44no—
401C2×C4×D3—44no—
402C2×C4×D3—44no—
403C2×C4×D3—44no—
404C3×C22⋊C4—44no—
405C3×C22⋊C4—44no—
406C3×C22⋊C4—44no—
407#217—44no—
408#217—44no—
409(C2×D3)⋊C4—28no—
410(C2×D3)⋊C4—28no—
411(C2×D3)⋊C4—44no—
412(C2×D3)⋊C4—44no—
413(C2×D3)⋊C4—44no—
414(C2×D3)⋊C4—44no—
415(C2×D3)⋊C4—44no—
416(C2×D3)⋊C4—44no—
417(C2×D3)⋊C4—44no—
418C4⋊Dic3—28no—
419Dic3⋊C4—28no—
420Dic3⋊C4—28no—
421C4×Dic3—44no—
422C25—31no—
423C25—31no—
424C25C22×D311yescharacteristic
425C22×Q8—22no—
426C22×Q8—22no—
427C22×Q8—22no—
428C22×Q8—22no—
429C22×Q8—22no—
430C22×Q8—41no—
431C22×Q8—41no—
432C22×D4—62no—
433C22×D4—62no—
434C22×D4—62no—
435C22×D4—62no—
436C22×D4—62no—
437C22×D4—62no—
438C22×D4—62no—
439C22×D4—62no—
440C22×D4—62no—
441C22×D4—62no—
442C22×D4—62no—
443C22×D4—62no—
444C22×D4—62no—
445C22×D4—62no—
446C22×D4—62no—
447C22×D4—121no—
448C22×D4—121no—
449C22×D4—121no—
450C22×D4—121no—
451C22×D4—121no—
452C22×D4—121no—
453C23×C4—31no—
454C23×C4—31no—
455C23×C4—31no—
456C23×C4—31no—
457C23×C4—31no—
458C23×C4—31no—
459C23×C4—62no—
460C23×C4—62no—
461C23×C4—62no—
462C23×C4—62no—
463C23×C4—62no—
464C23×C4—121no—
465C23×C4—121no—
466C23×C4C22×D311yescharacteristic
467C23×C4C22×D311yescharacteristic
468C23×C4C22×D311yescharacteristic
469C23×C4C22×D311yescharacteristic
470C23×C4C22×D311yescharacteristic
471C23×C4C22×D311yescharacteristic
472C22⋊Q8—632no—
473C2×C4⋊C4—34no—
474C2×C4⋊C4—34no—
475C2×C4⋊C4—62no—
476C2×C4⋊C4—62no—
477C2×C4⋊C4—62no—
478C2×C4⋊C4—62no—
479C2×C4⋊C4—62no—
480C2×C4⋊C4—62no—
481C2×C4⋊C4—62no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—22no—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—22no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—34no—
490C2×C22⋊C4—41no—
491C2×C22⋊C4—41no—
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—62no—
513C2×C22⋊C4—62no—
514C2×C22⋊C4—62no—
515C2×C22⋊C4—62no—
516C2×C22⋊C4—121no—
517C2×C22⋊C4—121no—
518C2×C22⋊C4—121no—
519C2×C22⋊C4—121no—
520C2×C22⋊C4—121no—
521C2×C22⋊C4—121no—
522C2×C22⋊C4—121no—
523C2×C22⋊C4—121no—
524C2×C42—62no—
525C2×C42—121no—
526C2×C42—121no—
527#95—22no—
528#95—22no—
529#95—34no—
530#95—62no—
531#95—62no—
532#95—62no—
533#95—62no—
534#95—62no—
535#95—62no—
536#95—121no—
537#95—121no—
538#95#6714yescomplemented
539C23×C3—22no—
540C23×C3—22no—
541C23×C3—22no—
542C23×C3—22no—
543C23×C3—22no—
544C23×C3—22no—
545C23×C3—22no—
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×C3C22×D411yescharacteristic
575C23×C3C22×D411yescharacteristic
576C23×C3C22×D411yescharacteristic
577C23×C3C22×D411yescharacteristic
578C23×C3C22×D411yescharacteristic
579C23×C3C2×#4111yescharacteristic
580C23×C3C2×#4111yescharacteristic
581C23×C3C2×#4111yescharacteristic
582C23×C3C2×#4111yescharacteristic
583C23×C3H(5,𝔽2)11yescharacteristic
584C23×C3H(5,𝔽2)11yescharacteristic
585C23×C3H(5,𝔽2)11yescharacteristic
586C23×C3H(5,𝔽2)11yescharacteristic
587C23×C32−1+411yescharacteristic
588C23×C32−1+411yescharacteristic
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—22no—
600C22×D3—22no—
601C22×D3—22no—
602C22×D3—22no—
603C22×D3—22no—
604C22×D3—22no—
605C22×D3—22no—
606C22×D3—22no—
607C22×D3—22no—
608C22×D3—22no—
609C22×D3—22no—
610C22×D3—22no—
611C22×D3—22no—
612C22×D3—22no—
613C22×D3—22no—
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—
655C22×D3—41no—
656C22×D3—41no—
657C22×D3—41no—
658C22×D3#12414yes—
659C3×Q8—416no—
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—22no—
677C2×C3×C4—22no—
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—41no—
697C2×C3×C4—41no—
698C2×C3×C4—41no—
699C2×C3×C4—41no—
700C2×C3×C4—41no—
701C2×C3×C4#12714yes—
702#67—416no—
703#67—416no—
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—22no—
713C2×Dic3—22no—
714C2×Dic3—22no—
715C2×Dic3—22no—
716C2×Dic3—22no—
717C2×Dic3—22no—
718C2×Dic3—22no—
719C2×Dic3—22no—
720C2×Dic3—22no—
721C2×Dic3—22no—
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—41no—
742C2×Dic3—41no—
743C2×Dic3—41no—
744C2×Dic3—41no—
745C2×Dic3#12014yes—
746D12—416no—
747C4×D3—416no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—32no—
763C24—32no—
764C24—32no—
765C24—32no—
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—
785C24—61no—
786C24—61no—
787C24—61no—
788C24—61no—
789C24—61no—
790C24—61no—
791C24—61no—
792C24#23912yes—
793C24C23×D311yescharacteristic
794C2×Q8—28no—
795C2×Q8—44no—
796C2×Q8—44no—
797C2×Q8—44no—
798C2×Q8—44no—
799C2×Q8—44no—
800C2×Q8—44no—
801C2×D4—68no—
802C2×D4—68no—
803C2×D4—68no—
804C2×D4—124no—
805C2×D4—124no—
806C2×D4—124no—
807C2×D4—124no—
808C2×D4—124no—
809C2×D4—124no—
810C2×D4—124no—
811C2×D4—124no—
812C2×D4—124no—
813C2×D4—124no—
814C2×D4—124no—
815C2×D4—124no—
816C2×D4—124no—
817C2×D4—124no—
818C2×D4—124no—
819C2×D4—124no—
820C2×D4—124no—
821C2×D4—124no—
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—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—32no—
858C22×C4—32no—
859C22×C4—32no—
860C22×C4—32no—
861C22×C4—32no—
862C22×C4—32no—
863C22×C4—32no—
864C22×C4—68no—
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×C4—61no—
893C22×C4—61no—
894C22×C4—61no—
895C22×C4—61no—
896C22×C4—61no—
897C22×C4—61no—
898C22×C4—61no—
899C22×C4—61no—
900C22×C4—124no—
901C22×C4—124no—
902C22×C4—124no—
903C22×C4—124no—
904C22×C4—124no—
905C22×C4—124no—
906C22×C4D3×D412yes—
907C22×C4D3×D412yes—
908C22×C4D3×D412yes—
909C22×C4D3×D412yes—
910C22×C4C2×#6712yes—
911C22×C4C2×#6712yes—
912C22×C4C2×#6712yes—
913C4⋊C4—68no—
914C4⋊C4—68no—
915C4⋊C4—68no—
916C22⋊C4—44no—
917C22⋊C4—44no—
918C22⋊C4—44no—
919C22⋊C4—68no—
920C22⋊C4—68no—
921C22⋊C4—124no—
922C22⋊C4—124no—
923C22⋊C4—124no—
924C22⋊C4—124no—
925C22⋊C4—124no—
926C22⋊C4—124no—
927C22⋊C4—124no—
928C22⋊C4—124no—
929C22⋊C4—124no—
930C42—124no—
931C22×C3—42no—
932C22×C3—42no—
933C22×C3—42no—
934C22×C3—42no—
935C22×C3—42no—
936C22×C3—42no—
937C22×C3—42no—
938C22×C3—81no—
939C22×C3—81no—
940C22×C3—81no—
941C22×C3—81no—
942C22×C3—81no—
943C22×C3—81no—
944C22×C3—81no—
945C22×C3—81no—
946C22×C3C2×#12011yescharacteristic
947C22×C3#52511yescharacteristic
948C22×C3#52511yescharacteristic
949C22×C3#52511yescharacteristic
950C22×C3C2×#12411yescharacteristic
951C22×C3C2×#12711yescharacteristic
952C22×C3#53511yescharacteristic
953C22×C3#53511yescharacteristic
954C22×C3#53611yescharacteristic
955C22×C3#53711yescharacteristic
956C22×C3#53711yescharacteristic
957C22×C3#53811yescharacteristic
958C22×C3#53811yescharacteristic
959C22×C3#53911yescharacteristic
960C22×C3#53911yescharacteristic
961C22×C3D4211yescharacteristic
962C22×C3D4211yescharacteristic
963C22×C3D4211yescharacteristic
964C22×C3D4211yescharacteristic
965C22×C3#54611yescharacteristic
966C22×C3#54611yescharacteristic
967C22×C3#54611yescharacteristic
968C22×C3#54611yescharacteristic
969C22×C3#54611yescharacteristic
970C22×C3#54611yescharacteristic
971C22×C3#54811yescharacteristic
972C22×C3#54811yescharacteristic
973C22×C3#54811yescharacteristic
974C22×C3#54811yescharacteristic
975C22×C3#54811yescharacteristic
976C22×C3#54811yescharacteristic
977C22×C3#55111yescharacteristic
978C22×C3#55111yescharacteristic
979C22×C3#56211yescharacteristic
980C22×C3#56211yescharacteristic
981C2×D3—24no—
982C2×D3—24no—
983C2×D3—24no—
984C2×D3—42no—
985C2×D3—42no—
986C2×D3—42no—
987C2×D3—42no—
988C2×D3—42no—
989C2×D3—42no—
990C2×D3—42no—
991C2×D3—42no—
992C2×D3—42no—
993C2×D3—42no—
994C2×D3—42no—
995C2×D3—42no—
996C2×D3—42no—
997C2×D3—42no—
998C2×D3—42no—
999C2×D3—42no—
1000C2×D3—42no—
1001C2×D3—42no—
1002C2×D3—42no—
1003C2×D3—81no—
1004C2×D3—81no—
1005C2×D3—81no—
1006C2×D3—81no—
1007C2×D3—81no—
1008C2×D3—81no—
1009C2×D3—81no—
1010C2×D3—81no—
1011C3×C4—24no—
1012C3×C4—42no—
1013C3×C4—42no—
1014C3×C4—42no—
1015C3×C4—42no—
1016C3×C4—81no—
1017Dic3—24no—
1018Dic3—42no—
1019Dic3—42no—
1020Dic3—42no—
1021Dic3—42no—
1022Dic3—81no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—34no—
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—62no—
1060C23—62no—
1061C23—62no—
1062C23—62no—
1063C23—62no—
1064C23—62no—
1065C23—62no—
1066C23—62no—
1067C23—62no—
1068C23—62no—
1069C23—62no—
1070C23—62no—
1071C23—62no—
1072C23—62no—
1073C23—62no—
1074C23—62no—
1075C23—62no—
1076C23—62no—
1077C23—62no—
1078C23—62no—
1079C23—62no—
1080C23—62no—
1081C23—62no—
1082C23—62no—
1083C23—62no—
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—121no—
1119C23—121no—
1120C23—121no—
1121C23—121no—
1122C23—121no—
1123C23—121no—
1124C23—121no—
1125C23—121no—
1126C23—121no—
1127C23—121no—
1128C23C2×D3×D411yescharacteristic
1129C23C2×D3×D411yescharacteristic
1130C23C2×D3×D411yescharacteristic
1131C23C2×D3×D411yescharacteristic
1132C23#100411yescharacteristic
1133C23#100411yescharacteristic
1134C23C2×#23911yescharacteristic
1135C23#100711yescharacteristic
1136C23D3×#4111yescharacteristic
1137C23D3×#4111yescharacteristic
1138C23D3×#4111yescharacteristic
1139C23#100911yescharacteristic
1140C23#100911yescharacteristic
1141C23#101011yescharacteristic
1142C23C22×#6711yescharacteristic
1143Q8—416no—
1144D4—1216no—
1145D4—1216no—
1146D4—1216no—
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—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—34no—
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—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—62no—
1190C2×C4—62no—
1191C2×C4—62no—
1192C2×C4—62no—
1193C2×C4—62no—
1194C2×C4—62no—
1195C2×C4—62no—
1196C2×C4—62no—
1197C2×C4—62no—
1198C2×C4—62no—
1199C2×C4—62no—
1200C2×C4—62no—
1201C2×C4—62no—
1202C2×C4—62no—
1203C2×C4—62no—
1204C2×C4—62no—
1205C2×C4—62no—
1206C2×C4—62no—
1207C2×C4—1216no—
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—121no—
1221C2×C4—121no—
1222C2×C4—121no—
1223C2×C4—121no—
1224C2×C4—121no—
1225C2×C4—121no—
1226C2×C4—121no—
1227C2×C4—121no—
1228C2×C4—121no—
1229C2×C4—121no—
1230C2×C4—121no—
1231C2×C4#94014yes—
1232C2×C3—82no—
1233C2×C3#240411yescharacteristic
1234C2×C3#243311yescharacteristic
1235C2×C3#243611yescharacteristic
1236C2×C3#246311yescharacteristic
1237C2×C3#246311yescharacteristic
1238C2×C3#247211yescharacteristic
1239C2×C3#247211yescharacteristic
1240C2×C3#254011yescharacteristic
1241C2×C3#254011yescharacteristic
1242C2×C3#267611yescharacteristic
1243C2×C3#267611yescharacteristic
1244C2×C3#268111yescharacteristic
1245C2×C3#268111yescharacteristic
1246C2×C3#269611yescharacteristic
1247C2×C3#269611yescharacteristic
1248D3—44no—
1249D3—82no—
1250C22—42no—
1251C22—42no—
1252C22—42no—
1253C22—42no—
1254C22—42no—
1255C22—42no—
1256C22—42no—
1257C22—64no—
1258C22—64no—
1259C22—64no—
1260C22—81no—
1261C22—81no—
1262C22—81no—
1263C22—81no—
1264C22—81no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22—122no—
1269C22—122no—
1270C22—122no—
1271C22—122no—
1272C22—122no—
1273C22—122no—
1274C22—122no—
1275C22—122no—
1276C22—122no—
1277C22—122no—
1278C22—122no—
1279C22—122no—
1280C22—122no—
1281C22—122no—
1282C22—122no—
1283C22—122no—
1284C22—122no—
1285C22—122no—
1286C22—122no—
1287C22—241no—
1288C22—241no—
1289C22—241no—
1290C22—241no—
1291C22—241no—
1292C22—241no—
1293C22—241no—
1294C22—241no—
1295C22D3×#12011yescharacteristic
1296C22#559011yescharacteristic
1297C22#559011yescharacteristic
1298C22#559211yescharacteristic
1299C22#562711yescharacteristic
1300C22#562711yescharacteristic
1301C22#562811yescharacteristic
1302C22#562911yescharacteristic
1303C22#563011yescharacteristic
1304C22#563011yescharacteristic
1305C22#563311yescharacteristic
1306C22#563311yescharacteristic
1307C22#563711yescharacteristic
1308C22#563811yescharacteristic
1309C22#564511yescharacteristic
1310C22#564711yescharacteristic
1311C22D3×#12411yescharacteristic
1312C22#567411yescharacteristic
1313C22#567611yescharacteristic
1314C22#567611yescharacteristic
1315C22#567611yescharacteristic
1316C22#567711yescharacteristic
1317C22#567711yescharacteristic
1318C22#567711yescharacteristic
1319C22#567811yescharacteristic
1320C22#567811yescharacteristic
1321C22#567911yescharacteristic
1322C22#568411yescharacteristic
1323C22D4×#6711yescharacteristic
1324C22D4×#6711yescharacteristic
1325C22C2×#94011yescharacteristic
1326C22#581711yescharacteristic
1327C22#582811yescharacteristic
1328C22#582911yescharacteristic
1329C22#583311yescharacteristic
1330C4—24no—
1331C4—42no—
1332C4—42no—
1333C4—42no—
1334C4—42no—
1335C4—64no—
1336C4—81no—
1337C4—122no—
1338C4—122no—
1339C4—122no—
1340C4—122no—
1341C4—241no—
1342C3#1545311yescharacteristic, complemented, Sylow
1343C2—82no—
1344C2—124no—
1345C2—242no—
1346C2#7678111yescharacteristic
1347C2#7678711yescharacteristic
1348C2#7679011yescharacteristic
1349C2#7682211yescharacteristic
1350C2#7682611yescharacteristic
1351C2#7682711yescharacteristic
1352C2#7686311yescharacteristic
1353C2#7687511yescharacteristic
1354C2#8258811yescharacteristic
1355C2#8277911yescharacteristic
1356C2#8281811yescharacteristic
1357C2#8282911yescharacteristic
1358C2#8296511yescharacteristic
1359C2#8298311yescharacteristic
1360C2#8299811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#393C2
prime radicalC2×#4960C2
hypercenterC2×#393D3
hypocenterC3#15453
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#393

Complements

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

NH ≅ G/Ntype
1. C22×#946C2semidirect
2. C2×C3×#393C2semidirect
3. C2×#5231C2semidirect
5. C2×#4956C2semidirect
6. C2×#4961C2semidirect
7. C2×#4957C2semidirect
8. C2×#4665C2semidirect
9. #71550C2semidirect
10. #71547C2semidirect
11. #69428C2semidirect
12. #69426C2semidirect
13. #69421C2semidirect
14. #69408C2semidirect
15. #69407C2semidirect
65. C2×#393D3semidirect
172. C2×C4⋊Dic3D4semidirect
178. C2×Dic3⋊C4D4semidirect
184. C3×#95D4semidirect
193. C3⋊#95D4semidirect
538. #95#67semidirect
1342. C3#15453semidirect

Maximal subgroups

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

subgroupindex
C22×#9462
C2×C3×#3932
C2×#52312
C2×#49602
C2×#49562
C2×#49612
C2×#49572
C2×#46652
#715502
#715472
#694282
#694262
#694212
#694082
#694072
#154533