Finite Group Databasebeta

← #10726749

Subgroups — #10726749

Order 768.

2662 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×#893C211yesmaximal, characteristic, complemented
2C2×C3×#396C211yesmaximal, characteristic, complemented
3C2×#4991C211yesmaximal, characteristic, complemented
4C2×#4987C211yesmaximal, characteristic, complemented
5C2×#4960C211yesmaximal, characteristic
6C2×#4956C211yesmaximal, characteristic, complemented
7C2×#4956C211yesmaximal, characteristic, complemented
8C2×#4961C211yesmaximal, characteristic, complemented
9#71570C211yesmaximal, characteristic, complemented
10#71565C211yesmaximal, characteristic, complemented
11#71564C211yesmaximal, characteristic, complemented
12#71550C211yesmaximal, characteristic, complemented
13#71545C211yesmaximal, characteristic, complemented
14#69429C211yesmaximal, characteristic, complemented
15(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
16#14732—31nomaximal, Sylow
17C23×#67C2211yescharacteristic
18C23×#67C2211yescharacteristic
19C23×D12C2211yescharacteristic
20C23×C4×D3C2211yescharacteristic
21C23×C4×D3C2211yescharacteristic
22C22×C3×C4⋊C4C2211yescharacteristic
23C22×C3×C4⋊C4C2211yescharacteristic
24C22×C3×C4⋊C4C2211yescharacteristic
25C22×C3×C22⋊C4C2211yescharacteristic
26C22×C3×C22⋊C4C2211yescharacteristic
27C22×C3×C22⋊C4C2211yescharacteristic
28C22×#217C2211yescharacteristic
29C22×#217C2211yescharacteristic
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×C4⋊Dic3C2211yescharacteristic
39C22×C4×Dic3C2211yescharacteristic
40C2×#893—24no—
41C2×#893—24no—
42C2×#893—24no—
43C3×#396—24no—
44C2×C3×#95C2211yescharacteristic
45C2×C3⋊#95C2211yescharacteristic
46C2×C3⋊#95C2211yescharacteristic
47C2×C3⋊#95C2211yescharacteristic
48C2×C3⋊#95C2211yescharacteristic
49C2×C3⋊#95C2211yescharacteristic
50C2×C3⋊#95C2211yescharacteristic
51C2×C3⋊#95C2211yescharacteristic
52C2×C3⋊#95C2211yescharacteristic
53C2×C3⋊#95C2211yescharacteristic
54C2×C3⋊#95C2211yescharacteristic
55C2×C3⋊#95C2211yescharacteristic
56#4991—24no—
57#4987—24no—
58#4961—24no—
59#4960—24no—
60#4956—24no—
61#4956—24no—
62C22×C4×D4—31no—
63C2×#396D311yescharacteristic, complemented
64C2×#394—31no—
65C2×#394—31no—
66C2×#392—31no—
67C2×#386—31no—
68C2×#386—31no—
69C2×#380—31no—
70#1441—31no—
71#1440—31no—
72#1439—31no—
73#1438—31no—
74#1437—31no—
75#1436—31no—
76C22⋊#95—31no—
77C25×C3C2311yescharacteristic
78C24×D3C2311yescharacteristic
79C24×D3C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C22×#67—22no—
87C22×#67—22no—
88C22×#67—22no—
89C22×#67—22no—
90C22×#67—22no—
91C22×#67—22no—
92C22×#67—22no—
93C22×#67—22no—
94C22×#67—22no—
95C22×#67—22no—
96C22×#67—41no—
97C22×#67—41no—
98C22×#67—41no—
99C22×#67—41no—
100C23×Dic3C2311yescharacteristic
101C23×Dic3C2311yescharacteristic
102C23×Dic3C2311yescharacteristic
103C23×Dic3C2311yescharacteristic
104C23×Dic3C2311yescharacteristic
105C23×Dic3C2311yescharacteristic
106C22×D12—22no—
107C22×D12—22no—
108C22×D12—22no—
109C22×D12—22no—
110C22×D12—22no—
111C22×D12—22no—
112C22×D12D414yes—
113C22×C4×D3—22no—
114C22×C4×D3—22no—
115C22×C4×D3—22no—
116C22×C4×D3—22no—
117C22×C4×D3—22no—
118C22×C4×D3—22no—
119C22×C4×D3—22no—
120C22×C4×D3—22no—
121C22×C4×D3—22no—
122C22×C4×D3—41no—
123C22×C4×D3—41no—
124C22×C4×D3—41no—
125C22×C4×D3—41no—
126C22×C4×D3D414yescomplemented
127C2×C3×C4⋊C4—22no—
128C2×C3×C4⋊C4—22no—
129C2×C3×C4⋊C4—22no—
130C2×C3×C4⋊C4—22no—
131C2×C3×C4⋊C4—22no—
132C2×C3×C4⋊C4—22no—
133C2×C3×C4⋊C4—22no—
134C2×C3×C4⋊C4—41no—
135C2×C3×C4⋊C4D414yescomplemented
136C2×C3×C22⋊C4—22no—
137C2×C3×C22⋊C4—22no—
138C2×C3×C22⋊C4—22no—
139C2×C3×C22⋊C4—22no—
140C2×C3×C22⋊C4—22no—
141C2×C3×C22⋊C4—22no—
142C2×C3×C22⋊C4—22no—
143C2×C3×C22⋊C4—22no—
144C2×C3×C22⋊C4—41no—
145C2×#217—22no—
146C2×#217—22no—
147C2×#217—22no—
148C2×#217—22no—
149C2×#217—22no—
150C2×#217—41no—
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—22no—
164C2×(C2×D3)⋊C4—22no—
165C2×(C2×D3)⋊C4—22no—
166C2×(C2×D3)⋊C4—22no—
167C2×(C2×D3)⋊C4—22no—
168C2×(C2×D3)⋊C4—22no—
169C2×(C2×D3)⋊C4—22no—
170C2×(C2×D3)⋊C4—41no—
171C2×(C2×D3)⋊C4—41no—
172C2×(C2×D3)⋊C4—41no—
173C2×(C2×D3)⋊C4—41no—
174C2×(C2×D3)⋊C4D414yescomplemented
175C2×C4⋊Dic3—22no—
176C2×C4⋊Dic3—22no—
177C2×C4⋊Dic3—41no—
178C2×C4×Dic3—22no—
179C2×C4×Dic3—22no—
180C2×C4×Dic3—22no—
181#893—232no—
182C3×#95—22no—
183C3⋊#95—22no—
184C3⋊#95—22no—
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×D4—31no—
195C23×D4—31no—
196C23×D4—31no—
197C24×C4—31no—
198C24×C4—31no—
199C2×C4×D4—64no—
200C2×C4×D4—64no—
201C2×C4×D4—64no—
202C22×C4⋊C4—31no—
203C22×C4⋊C4C2×D311yescharacteristic
204C22×C4⋊C4C2×D311yescharacteristic
205C22×C4⋊C4C2×D311yescharacteristic
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#396—24no—
221#394—64no—
222#394—64no—
223#392—64no—
224#386—64no—
225#386—64no—
226#380—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×#95—31no—
237C2×#95—31no—
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×D3C2×D412yes—
280C23×D3C2×D412yes—
281C23×D3C2×D412yes—
282C23×D3C2×D412yes—
283C23×D3#4112yes—
284C23×D3#4112yes—
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×C4—21no—
317C22×C3×C4—21no—
318C22×C3×C4—21no—
319C22×C3×C4C2×D412yes—
320C22×C3×C4C2×D412yes—
321C22×C3×C4C2×D412yes—
322C22×C3×C4C2×D412yes—
323C22×C3×C4C2×D412yes—
324C22×C3×C4C2×D412yes—
325C22×C3×C4C2×D412yes—
326C22×C3×C4#4112yes—
327C2×#67—28no—
328C2×#67—28no—
329C2×#67—44no—
330C2×#67—44no—
331C2×#67—44no—
332C2×#67—44no—
333C2×#67—44no—
334C2×#67—44no—
335C2×#67—44no—
336C2×#67—44no—
337C2×#67—44no—
338C2×#67—44no—
339C2×#67—44no—
340C2×#67—44no—
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×Dic3—21no—
374C22×Dic3—21no—
375C22×Dic3—21no—
376C22×Dic3—21no—
377C22×Dic3C2×D412yes—
378C22×Dic3C2×D412yes—
379C22×Dic3C2×D412yes—
380C22×Dic3C2×D412yes—
381C22×Dic3#4112yes—
382C22×Dic3#4112yes—
383C2×D12—28no—
384C2×D12—28no—
385C2×D12—28no—
386C2×D12—28no—
387C2×D12—28no—
388C2×D12—28no—
389C2×D12—28no—
390C2×C4×D3—28no—
391C2×C4×D3—28no—
392C2×C4×D3—28no—
393C2×C4×D3—44no—
394C2×C4×D3—44no—
395C2×C4×D3—44no—
396C2×C4×D3—44no—
397C2×C4×D3—44no—
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×C4⋊C4—28no—
405C3×C4⋊C4—44no—
406C3×C4⋊C4—44no—
407C3×C22⋊C4—44no—
408C3×C22⋊C4—44no—
409C3×C22⋊C4—44no—
410#217—44no—
411#217—44no—
412(C2×D3)⋊C4—28no—
413(C2×D3)⋊C4—28no—
414(C2×D3)⋊C4—44no—
415(C2×D3)⋊C4—44no—
416(C2×D3)⋊C4—44no—
417(C2×D3)⋊C4—44no—
418(C2×D3)⋊C4—44no—
419(C2×D3)⋊C4—44no—
420C4⋊Dic3—44no—
421C4×Dic3—28no—
422C25—31no—
423C25—31no—
424C25C22×D311yescharacteristic
425C22×D4—34no—
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—62no—
437C22×D4—62no—
438C22×D4—62no—
439C22×D4—62no—
440C22×D4—62no—
441C22×D4—62no—
442C22×D4—121no—
443C22×D4—121no—
444C22×D4—121no—
445C22×D4—121no—
446C23×C4—31no—
447C23×C4—31no—
448C23×C4—31no—
449C23×C4—31no—
450C23×C4—34no—
451C23×C4—31no—
452C23×C4—31no—
453C23×C4—62no—
454C23×C4—62no—
455C23×C4—62no—
456C23×C4—62no—
457C23×C4—62no—
458C23×C4—62no—
459C23×C4—62no—
460C23×C4—62no—
461C23×C4—62no—
462C23×C4—121no—
463C23×C4—121no—
464C23×C4—121no—
465C23×C4—121no—
466C23×C4C22×D311yescharacteristic
467C23×C4C22×D311yescharacteristic
468C23×C4C22×D311yescharacteristic
469C23×C4C22×D311yescharacteristic
470C23×C4C22×D311yescharacteristic
471C23×C4C22×D311yescharacteristic
472C4×D4—632no—
473C2×C4⋊C4—22no—
474C2×C4⋊C4—22no—
475C2×C4⋊C4—22no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—22no—
478C2×C4⋊C4—22no—
479C2×C4⋊C4—22no—
480C2×C4⋊C4—41no—
481C2×C4⋊C4—62no—
482C2×C4⋊C4—62no—
483C2×C4⋊C4—121no—
484C2×C4⋊C4#6714yescomplemented
485C2×C22⋊C4—22no—
486C2×C22⋊C4—22no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—22no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—34no—
494C2×C22⋊C4—41no—
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—62no—
517C2×C22⋊C4—62no—
518C2×C22⋊C4—62no—
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—62no—
526C2×C42—62no—
527#95—22no—
528#95—34no—
529#95—62no—
530#95—62no—
531#95—62no—
532#95—62no—
533#95—62no—
534#95—62no—
535#95—62no—
536#95—62no—
537#95—121no—
538#95—121no—
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×C3C2×#4111yescharacteristic
584C23×C3C2×#4111yescharacteristic
585C23×C3H(5,𝔽2)11yescharacteristic
586C23×C3H(5,𝔽2)11yescharacteristic
587C23×C3H(5,𝔽2)11yescharacteristic
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—22no—
615C22×D3—22no—
616C22×D3—22no—
617C22×D3—22no—
618C22×D3—22no—
619C22×D3—22no—
620C22×D3—22no—
621C22×D3—22no—
622C22×D3—22no—
623C22×D3—22no—
624C22×D3—22no—
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#12114yes—
658C22×D3#12114yes—
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—22no—
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—41no—
697C2×C3×C4—41no—
698C2×C3×C4—41no—
699C2×C3×C4#12014yes—
700C2×C3×C4#12114yes—
701#67—416no—
702#67—416no—
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—22no—
713C2×Dic3—22no—
714C2×Dic3—22no—
715C2×Dic3—22no—
716C2×Dic3—22no—
717C2×Dic3—22no—
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—41no—
742C2×Dic3—41no—
743C2×Dic3—41no—
744C2×Dic3#12114yes—
745D12—232no—
746C4×D3—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—32no—
767C24—32no—
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×D4—68no—
795C2×D4—68no—
796C2×D4—68no—
797C2×D4—68no—
798C2×D4—68no—
799C2×D4—68no—
800C2×D4—68no—
801C2×D4—68no—
802C2×D4—68no—
803C2×D4—124no—
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—
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—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—32no—
850C22×C4—32no—
851C22×C4—32no—
852C22×C4—32no—
853C22×C4—32no—
854C22×C4—32no—
855C22×C4—68no—
856C22×C4—68no—
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—68no—
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—124no—
895C22×C4—124no—
896C22×C4—124no—
897C22×C4—124no—
898C22×C4—124no—
899C22×C4—124no—
900C22×C4—124no—
901C22×C4—124no—
902C22×C4—124no—
903C22×C4—124no—
904C22×C4—124no—
905C22×C4D3×D412yes—
906C22×C4D3×D412yes—
907C22×C4D3×D412yes—
908C22×C4D3×D412yes—
909C22×C4#23712yes—
910C22×C4C2×#6712yes—
911C22×C4C2×#6712yes—
912C22×C4C2×#6712yes—
913C4⋊C4—28no—
914C4⋊C4—44no—
915C4⋊C4—44no—
916C4⋊C4—124no—
917C22⋊C4—44no—
918C22⋊C4—44no—
919C22⋊C4—44no—
920C22⋊C4—68no—
921C22⋊C4—68no—
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—68no—
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×C3C2×#12111yescharacteristic
948C22×C3C2×#12111yescharacteristic
949C22×C3C2×#12111yescharacteristic
950C22×C3C2×#12111yescharacteristic
951C22×C3#52511yescharacteristic
952C22×C3#52511yescharacteristic
953C22×C3#52511yescharacteristic
954C22×C3#52511yescharacteristic
955C22×C3#52511yescharacteristic
956C22×C3#52911yescharacteristic
957C22×C3#52911yescharacteristic
958C22×C3#53211yescharacteristic
959C22×C3#53411yescharacteristic
960C22×C3#53711yescharacteristic
961C22×C3#53811yescharacteristic
962C22×C3#53911yescharacteristic
963C22×C3#54011yescharacteristic
964C22×C3#54211yescharacteristic
965C22×C3D4211yescharacteristic
966C22×C3D4211yescharacteristic
967C22×C3D4211yescharacteristic
968C22×C3#54611yescharacteristic
969C22×C3#54611yescharacteristic
970C22×C3#54611yescharacteristic
971C22×C3#54611yescharacteristic
972C22×C3#54611yescharacteristic
973C22×C3#54711yescharacteristic
974C22×C3#54711yescharacteristic
975C22×C3#54811yescharacteristic
976C22×C3#54811yescharacteristic
977C22×C3#55011yescharacteristic
978C22×C3#55111yescharacteristic
979C22×C3#55111yescharacteristic
980C22×C3#55311yescharacteristic
981C2×D3—24no—
982C2×D3—24no—
983C2×D3—24no—
984C2×D3—24no—
985C2×D3—24no—
986C2×D3—24no—
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—42no—
1004C2×D3—42no—
1005C2×D3—42no—
1006C2×D3—42no—
1007C2×D3—42no—
1008C2×D3—42no—
1009C2×D3—42no—
1010C2×D3—42no—
1011C3×C4—24no—
1012C3×C4—24no—
1013C3×C4—42no—
1014C3×C4—42no—
1015C3×C4—81no—
1016C3×C4—81no—
1017Dic3—24no—
1018Dic3—42no—
1019Dic3—42no—
1020Dic3—42no—
1021Dic3—81no—
1022Dic3—81no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—34no—
1031C23—34no—
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—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—62no—
1085C23—62no—
1086C23—62no—
1087C23—62no—
1088C23—62no—
1089C23—62no—
1090C23—62no—
1091C23—62no—
1092C23—62no—
1093C23—62no—
1094C23—62no—
1095C23—62no—
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
1132C23C2×#23711yescharacteristic
1133C23#100411yescharacteristic
1134C23C2×#23911yescharacteristic
1135C23#100711yescharacteristic
1136C23D3×#4111yescharacteristic
1137C23D3×#4111yescharacteristic
1138C23D3×#4111yescharacteristic
1139C23D3×#4111yescharacteristic
1140C23#100911yescharacteristic
1141C23#100911yescharacteristic
1142C23C22×#6711yescharacteristic
1143D4—632no—
1144D4—1216no—
1145D4—1216no—
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—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—34no—
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—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—62no—
1188C2×C4—62no—
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—1216no—
1203C2×C4—1216no—
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—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#93714yes—
1231C2×C4#93814yes—
1232C2×C3—82no—
1233C2×C3#239211yescharacteristic
1234C2×C3#240711yescharacteristic
1235C2×C3#241011yescharacteristic
1236C2×C3#241611yescharacteristic
1237C2×C3#242411yescharacteristic
1238C2×C3#242511yescharacteristic
1239C2×C3#242711yescharacteristic
1240C2×C3#242811yescharacteristic
1241C2×C3#245711yescharacteristic
1242C2×C3#246111yescharacteristic
1243C2×C3#246311yescharacteristic
1244C2×C3#246711yescharacteristic
1245C2×C3#253411yescharacteristic
1246C2×C3#263011yescharacteristic
1247C2×C3#284711yescharacteristic
1248D3—44no—
1249D3—44no—
1250C22—42no—
1251C22—42no—
1252C22—42no—
1253C22—42no—
1254C22—42no—
1255C22—42no—
1256C22—42no—
1257C22—64no—
1258C22—64no—
1259C22—64no—
1260C22—64no—
1261C22—64no—
1262C22—64no—
1263C22—81no—
1264C22—81no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22—81no—
1269C22—81no—
1270C22—81no—
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—122no—
1288C22—122no—
1289C22—122no—
1290C22—122no—
1291C22—122no—
1292C22—122no—
1293C22—122no—
1294C22—122no—
1295C22#559611yescharacteristic
1296C22D3×#12111yescharacteristic
1297C22D3×#12111yescharacteristic
1298C22D3×#12111yescharacteristic
1299C22#560511yescharacteristic
1300C22#560611yescharacteristic
1301C22#560611yescharacteristic
1302C22#560911yescharacteristic
1303C22#560911yescharacteristic
1304C22#561011yescharacteristic
1305C22#561211yescharacteristic
1306C22#561911yescharacteristic
1307C22#562411yescharacteristic
1308C22#562711yescharacteristic
1309C22#562711yescharacteristic
1310C22#562911yescharacteristic
1311C22#563011yescharacteristic
1312C22#563011yescharacteristic
1313C22#563111yescharacteristic
1314C22#563111yescharacteristic
1315C22#563311yescharacteristic
1316C22#563711yescharacteristic
1317C22#563811yescharacteristic
1318C22#564311yescharacteristic
1319C22#570411yescharacteristic
1320C22#570511yescharacteristic
1321C22#570611yescharacteristic
1322C22#570911yescharacteristic
1323C22C2×#93711yescharacteristic
1324C22C2×#93811yescharacteristic
1325C22D4×#6711yescharacteristic
1326C22#581711yescharacteristic
1327C22#582811yescharacteristic
1328C22#582911yescharacteristic
1329C22#583411yescharacteristic
1330C4—24no—
1331C4—24no—
1332C4—42no—
1333C4—42no—
1334C4—64no—
1335C4—81no—
1336C4—81no—
1337C4—122no—
1338C4—122no—
1339C4—122no—
1340C4—241no—
1341C4—241no—
1342C3#1473211yescharacteristic, complemented, Sylow
1343C2—82no—
1344C2—124no—
1345C2—124no—
1346C2#7728111yescharacteristic
1347C2#7728411yescharacteristic
1348C2#7729311yescharacteristic
1349C2#7729511yescharacteristic
1350C2#7733311yescharacteristic
1351C2#7741611yescharacteristic
1352C2#7741711yescharacteristic
1353C2#7742111yescharacteristic
1354C2#8264811yescharacteristic
1355C2#8270211yescharacteristic
1356C2#8272311yescharacteristic
1357C2#8275611yescharacteristic
1358C2#8281211yescharacteristic
1359C2#8281811yescharacteristic
1360C2#8310611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#396C2
prime radicalC2×#4960C2
hypercenterC2×#396D3
hypocenterC3#14732
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. C22×#893C2semidirect
2. C2×C3×#396C2semidirect
3. C2×#4991C2semidirect
4. C2×#4987C2semidirect
6. C2×#4956C2semidirect
7. C2×#4956C2semidirect
8. C2×#4961C2semidirect
9. #71570C2semidirect
10. #71565C2semidirect
11. #71564C2semidirect
12. #71550C2semidirect
13. #71545C2semidirect
14. #69429C2semidirect
15. (C2×D3)⋊#95C2semidirect
63. C2×#396D3semidirect
126. C22×C4×D3D4semidirect
135. C2×C3×C4⋊C4D4semidirect
174. C2×(C2×D3)⋊C4D4semidirect
193. C3⋊#95D4semidirect
484. C2×C4⋊C4#67semidirect
1342. C3#14732semidirect

Maximal subgroups

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

subgroupindex
C22×#8932
C2×C3×#3962
C2×#49912
C2×#49872
C2×#49602
C2×#49562
C2×#49612
#715702
#715652
#715642
#715502
#715452
#694292
(C2×D3)⋊#952
#147323