Finite Group Databasebeta

← #10726621

Subgroups — #10726621

Order 768.

2774 conjugacy classes of subgroups.

The subgroup lattice has 1364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×#67C211yesmaximal, characteristic, complemented
2C22×#894C211yesmaximal, characteristic, complemented
3C2×C3×#385C211yesmaximal, characteristic, complemented
4C2×#5213C211yesmaximal, characteristic, complemented
5C2×#4991C211yesmaximal, characteristic, complemented
6C2×#4960C211yesmaximal, characteristic
7#71568C211yesmaximal, characteristic, complemented
8#71564C211yesmaximal, characteristic, complemented
9#71550C211yesmaximal, characteristic, complemented
10#71550C211yesmaximal, characteristic, complemented
11#71547C211yesmaximal, characteristic, complemented
12#69429C211yesmaximal, characteristic, complemented
13#69428C211yesmaximal, characteristic, complemented
14(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
15#69408C211yesmaximal, characteristic, complemented
16#14721—31nomaximal, Sylow
17C24×C3×C4C2211yescharacteristic
18C23×#67C2211yescharacteristic
19C23×#67C2211yescharacteristic
20C23×D12C2211yescharacteristic
21C23×C4×D3C2211yescharacteristic
22C22×C3×C4⋊C4C2211yescharacteristic
23C22×C3×C4⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×C3×C22⋊C4C2211yescharacteristic
26C22×#217C2211yescharacteristic
27C22×#217C2211yescharacteristic
28C2×C4×#67—24no—
29C2×C4×#67—24no—
30C2×C4×#67—24no—
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×Dic3⋊C4C2211yescharacteristic
41C22×Dic3⋊C4C2211yescharacteristic
42C22×C4×Dic3C2211yescharacteristic
43C2×#894—24no—
44C2×#894—24no—
45C2×#894—24no—
46C3×#385—24no—
47C2×C3×#95C2211yescharacteristic
48C2×C3×#95C2211yescharacteristic
49#5213—24no—
50C2×C3⋊#95C2211yescharacteristic
51C2×C3⋊#95C2211yescharacteristic
52C2×C3⋊#95C2211yescharacteristic
53C2×C3⋊#95C2211yescharacteristic
54C2×C3⋊#95C2211yescharacteristic
55C2×C3⋊#95C2211yescharacteristic
56C2×C3⋊#95C2211yescharacteristic
57C2×C3⋊#95C2211yescharacteristic
58C2×C3⋊#95C2211yescharacteristic
59C2×C3⋊#95C2211yescharacteristic
60#4991—24no—
61#4960—24no—
62C22×#123—31no—
63C22×C4×D4—31no—
64C2×#394—31no—
65C2×#392—31no—
66C2×#386—31no—
67C2×#385D311yescharacteristic, complemented
68#1444—31no—
69#1440—31no—
70#1439—31no—
71#1439—31no—
72#1438—31no—
73#1438—31no—
74#1437—31no—
75#1436—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—22no—
103C22×#67—22no—
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—
120C22×C4×D3—22no—
121C22×C4×D3—22no—
122C22×C4×D3—22no—
123C22×C4×D3—22no—
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—41no—
132C2×C3×C4⋊C4D414yescomplemented
133C2×C3×C22⋊C4—22no—
134C2×C3×C22⋊C4—22no—
135C2×C3×C22⋊C4—22no—
136C2×C3×C22⋊C4—22no—
137C2×C3×C22⋊C4—22no—
138C2×C3×C22⋊C4—41no—
139C2×#217—22no—
140C2×#217—22no—
141C2×#217—22no—
142C2×#217—22no—
143C2×#217—22no—
144C2×#217—41no—
145C4×#67—232no—
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—22no—
164C2×(C2×D3)⋊C4—22no—
165C2×(C2×D3)⋊C4—22no—
166C2×(C2×D3)⋊C4—22no—
167C2×(C2×D3)⋊C4—41no—
168C2×(C2×D3)⋊C4—41no—
169C2×(C2×D3)⋊C4—41no—
170C2×(C2×D3)⋊C4—41no—
171C2×(C2×D3)⋊C4D414yescomplemented
172C2×(C2×D3)⋊C4D414yescomplemented
173C2×Dic3⋊C4—22no—
174C2×Dic3⋊C4—22no—
175C2×Dic3⋊C4—22no—
176C2×Dic3⋊C4—22no—
177C2×Dic3⋊C4—22no—
178C2×Dic3⋊C4—22no—
179C2×C4×Dic3—22no—
180C2×C4×Dic3—22no—
181C2×C4×Dic3—22no—
182#894—232no—
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—22no—
192C3⋊#95—41no—
193C3⋊#95—41no—
194C3⋊#95—41no—
195C23×D4—31no—
196C23×D4—31no—
197C23×D4—31no—
198C24×C4—31no—
199C24×C4C2×D311yescharacteristic
200C2×#123—64no—
201C2×#123—64no—
202C2×#123—64no—
203C2×C4×D4—64no—
204C2×C4×D4—64no—
205C2×C4×D4—64no—
206C22×C4⋊C4—31no—
207C22×C4⋊C4—31no—
208C22×C4⋊C4C2×D311yescharacteristic
209C22×C4⋊C4C2×D311yescharacteristic
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⋊C4—31no—
220C22×C22⋊C4—31no—
221C22×C22⋊C4C2×D311yescharacteristic
222C22×C22⋊C4C2×D311yescharacteristic
223C22×C42—31no—
224#394—64no—
225#392—64no—
226#386—64no—
227#385—24no—
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
239C2×#95C2×D311yescharacteristic
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×C3C2×D412yes—
253C24×C3#4112yes—
254C24×C3#4112yes—
255C24×C3C2411yescharacteristic
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×D3C2×D412yes—
283C23×D3C2×D412yes—
284C23×D3C2×D412yes—
285C23×D3C2×D412yes—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—28no—
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×C4—21no—
320C22×C3×C4—21no—
321C22×C3×C4—21no—
322C22×C3×C4—44no—
323C22×C3×C4—44no—
324C22×C3×C4—44no—
325C22×C3×C4—44no—
326C22×C3×C4—44no—
327C22×C3×C4—44no—
328C22×C3×C4C2×D412yes—
329C22×C3×C4C2×D412yes—
330C22×C3×C4C2×D412yes—
331C22×C3×C4C2×D412yes—
332C22×C3×C4C2×D412yes—
333C22×C3×C4C2×D412yes—
334C22×C3×C4#4112yes—
335C2×#67—28no—
336C2×#67—28no—
337C2×#67—28no—
338C2×#67—28no—
339C2×#67—28no—
340C2×#67—28no—
341C2×#67—28no—
342C2×#67—28no—
343C2×#67—44no—
344C2×#67—44no—
345C2×#67—44no—
346C2×#67—44no—
347C2×#67—44no—
348C2×#67—44no—
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×Dic3C2×D412yes—
385C22×Dic3C2×D412yes—
386C22×Dic3C2×D412yes—
387C22×Dic3C2×D412yes—
388C22×Dic3#4112yes—
389C22×Dic3#4112yes—
390C22×Dic3#4112yes—
391C2×D12—28no—
392C2×D12—44no—
393C2×D12—44no—
394C2×D12—44no—
395C2×D12—44no—
396C2×D12—44no—
397C2×D12—44no—
398C2×C4×D3—28no—
399C2×C4×D3—28no—
400C2×C4×D3—44no—
401C2×C4×D3—44no—
402C2×C4×D3—44no—
403C2×C4×D3—44no—
404C2×C4×D3—44no—
405C3×C4⋊C4—28no—
406C3×C4⋊C4—44no—
407C3×C22⋊C4—28no—
408C3×C22⋊C4—44no—
409#217—28no—
410#217—44no—
411(C2×D3)⋊C4—28no—
412(C2×D3)⋊C4—28no—
413(C2×D3)⋊C4—28no—
414(C2×D3)⋊C4—28no—
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—
420Dic3⋊C4—28no—
421Dic3⋊C4—28no—
422C4×Dic3—28no—
423C25—31no—
424C25—31no—
425C25C22×D311yescharacteristic
426C22×D4—34no—
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—62no—
443C22×D4—121no—
444C22×D4—121no—
445C22×D4—121no—
446C22×D4—121no—
447C23×C4—22no—
448C23×C4—22no—
449C23×C4—22no—
450C23×C4—22no—
451C23×C4—22no—
452C23×C4—31no—
453C23×C4—31no—
454C23×C4—31no—
455C23×C4—31no—
456C23×C4—31no—
457C23×C4—34no—
458C23×C4—31no—
459C23×C4—41no—
460C23×C4—41no—
461C23×C4—62no—
462C23×C4—62no—
463C23×C4—62no—
464C23×C4—62no—
465C23×C4—121no—
466C23×C4—121no—
467C23×C4C22×D311yescharacteristic
468C23×C4C22×D311yescharacteristic
469C23×C4C22×D311yescharacteristic
470C23×C4C22×D311yescharacteristic
471C23×C4C22×D311yescharacteristic
472C23×C4C22×D311yescharacteristic
473#123—632no—
474C4×D4—632no—
475C2×C4⋊C4—22no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—22no—
478C2×C4⋊C4—22no—
479C2×C4⋊C4—41no—
480C2×C4⋊C4—62no—
481C2×C4⋊C4—62no—
482C2×C4⋊C4—62no—
483C2×C4⋊C4—62no—
484C2×C4⋊C4—62no—
485C2×C4⋊C4—62no—
486C2×C4⋊C4#6714yescomplemented
487C2×C22⋊C4—22no—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—22no—
492C2×C22⋊C4—34no—
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—62no—
520C2×C22⋊C4—62no—
521C2×C22⋊C4—121no—
522C2×C22⋊C4—121no—
523C2×C22⋊C4—121no—
524C2×C22⋊C4—121no—
525C2×C22⋊C4—121no—
526C2×C42—62no—
527C2×C42—62no—
528C2×C42—62no—
529#95—22no—
530#95—22no—
531#95—62no—
532#95—62no—
533#95—62no—
534#95—62no—
535#95—62no—
536#95—62no—
537#95—62no—
538#95—121no—
539#95—121no—
540#95—121no—
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—22no—
554C23×C3—22no—
555C23×C3—22no—
556C23×C3—22no—
557C23×C3—22no—
558C23×C3—22no—
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#12314yescomplemented
576C23×C3C22×D411yescharacteristic
577C23×C3C22×D411yescharacteristic
578C23×C3C22×D411yescharacteristic
579C23×C3C22×D411yescharacteristic
580C23×C3C22×D411yescharacteristic
581C23×C3C2×#4111yescharacteristic
582C23×C3C2×#4111yescharacteristic
583C23×C3C2×#4111yescharacteristic
584C23×C3C2×#4111yescharacteristic
585C23×C3C2×#4111yescharacteristic
586C23×C3C2×#4111yescharacteristic
587C23×C3H(5,𝔽2)11yescharacteristic
588C23×C3H(5,𝔽2)11yescharacteristic
589C23×C3H(5,𝔽2)11yescharacteristic
590C23×C32−1+411yescharacteristic
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—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—41no—
659C22×D3—41no—
660C22×D3#12014yes—
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—22no—
679C2×C3×C4—416no—
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—41no—
702C2×C3×C4—41no—
703C2×C3×C4#12014yes—
704#67—232no—
705#67—416no—
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—22no—
723C2×Dic3—22no—
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—41no—
746C2×Dic3—41no—
747C2×Dic3#12314yescomplemented
748D12—416no—
749C4×D3—416no—
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#23512yes—
793C24D3×D412yes—
794C24#23912yes—
795C24C23×D311yescharacteristic
796C2×D4—68no—
797C2×D4—68no—
798C2×D4—68no—
799C2×D4—68no—
800C2×D4—68no—
801C2×D4—68no—
802C2×D4—68no—
803C2×D4—68no—
804C2×D4—68no—
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—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—28no—
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—32no—
854C22×C4—32no—
855C22×C4—32no—
856C22×C4—32no—
857C22×C4—32no—
858C22×C4—32no—
859C22×C4—32no—
860C22×C4—44no—
861C22×C4—44no—
862C22×C4—44no—
863C22×C4—44no—
864C22×C4—44no—
865C22×C4—44no—
866C22×C4—68no—
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—68no—
896C22×C4—61no—
897C22×C4—61no—
898C22×C4—61no—
899C22×C4—61no—
900C22×C4—61no—
901C22×C4—61no—
902C22×C4—61no—
903C22×C4—124no—
904C22×C4—124no—
905C22×C4—124no—
906C22×C4—124no—
907C22×C4—124no—
908C22×C4#23512yes—
909C22×C4D3×D412yes—
910C22×C4D3×D412yes—
911C22×C4D3×D412yes—
912C22×C4C2×#6712yes—
913C22×C4C2×#6712yes—
914C22×C4C2×#6712yes—
915C4⋊C4—28no—
916C4⋊C4—44no—
917C4⋊C4—68no—
918C4⋊C4—68no—
919C22⋊C4—28no—
920C22⋊C4—44no—
921C22⋊C4—68no—
922C22⋊C4—68no—
923C22⋊C4—68no—
924C22⋊C4—68no—
925C22⋊C4—68no—
926C22⋊C4—124no—
927C22⋊C4—124no—
928C22⋊C4—124no—
929C22⋊C4—124no—
930C22⋊C4—124no—
931C22⋊C4—124no—
932C42—68no—
933C22×C3—24no—
934C22×C3—24no—
935C22×C3—24no—
936C22×C3—42no—
937C22×C3—42no—
938C22×C3—42no—
939C22×C3—42no—
940C22×C3—42no—
941C22×C3—42no—
942C22×C3—42no—
943C22×C3—42no—
944C22×C3—42no—
945C22×C3—42no—
946C22×C3—42no—
947C22×C3—42no—
948C22×C3C2×#12011yescharacteristic
949C22×C3C2×#12011yescharacteristic
950C22×C3C2×#12311yescharacteristic
951C22×C3C2×#12311yescharacteristic
952C22×C3#52511yescharacteristic
953C22×C3#52511yescharacteristic
954C22×C3#52511yescharacteristic
955C22×C3#52511yescharacteristic
956C22×C3#52511yescharacteristic
957C22×C3#52511yescharacteristic
958C22×C3#53211yescharacteristic
959C22×C3#53211yescharacteristic
960C22×C3#53211yescharacteristic
961C22×C3#53411yescharacteristic
962C22×C3#53711yescharacteristic
963C22×C3#53811yescharacteristic
964C22×C3#53911yescharacteristic
965C22×C3#54011yescharacteristic
966C22×C3#54211yescharacteristic
967C22×C3D4211yescharacteristic
968C22×C3D4211yescharacteristic
969C22×C3D4211yescharacteristic
970C22×C3D4211yescharacteristic
971C22×C3#54611yescharacteristic
972C22×C3#54611yescharacteristic
973C22×C3#54611yescharacteristic
974C22×C3#54711yescharacteristic
975C22×C3#54711yescharacteristic
976C22×C3#54711yescharacteristic
977C22×C3#54811yescharacteristic
978C22×C3#55011yescharacteristic
979C22×C3#55111yescharacteristic
980C22×C3#55311yescharacteristic
981C22×C3#55311yescharacteristic
982C22×C3#55911yescharacteristic
983C2×D3—24no—
984C2×D3—24no—
985C2×D3—24no—
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—42no—
1004C2×D3—42no—
1005C2×D3—81no—
1006C2×D3—81no—
1007C2×D3—81no—
1008C2×D3—81no—
1009C2×D3—81no—
1010C2×D3—81no—
1011C2×D3—81no—
1012C2×D3—81no—
1013C3×C4—24no—
1014C3×C4—42no—
1015C3×C4—42no—
1016C3×C4—42no—
1017C3×C4—42no—
1018C3×C4—81no—
1019Dic3—24no—
1020Dic3—42no—
1021Dic3—42no—
1022Dic3—42no—
1023Dic3—42no—
1024Dic3—81no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—34no—
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—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—
1128C23—121no—
1129C23#89414yescomplemented
1130C23C2×#23511yescharacteristic
1131C23C2×#23511yescharacteristic
1132C23C2×D3×D411yescharacteristic
1133C23C2×D3×D411yescharacteristic
1134C23C2×D3×D411yescharacteristic
1135C23C2×D3×D411yescharacteristic
1136C23#100411yescharacteristic
1137C23#100411yescharacteristic
1138C23C2×#23911yescharacteristic
1139C23#100711yescharacteristic
1140C23D3×#4111yescharacteristic
1141C23D3×#4111yescharacteristic
1142C23D3×#4111yescharacteristic
1143C23#100911yescharacteristic
1144C23C22×#6711yescharacteristic
1145D4—632no—
1146D4—1216no—
1147D4—1216no—
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—22no—
1166C2×C4—34no—
1167C2×C4—416no—
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—41no—
1190C2×C4—41no—
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—62no—
1208C2×C4—62no—
1209C2×C4—1216no—
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—121no—
1232C2×C4—121no—
1233C2×C4#93714yes—
1234C2×C3—44no—
1235C2×C3#238811yescharacteristic
1236C2×C3#240311yescharacteristic
1237C2×C3#240711yescharacteristic
1238C2×C3#241811yescharacteristic
1239C2×C3#242211yescharacteristic
1240C2×C3#243011yescharacteristic
1241C2×C3#244311yescharacteristic
1242C2×C3#244511yescharacteristic
1243C2×C3#245511yescharacteristic
1244C2×C3#245611yescharacteristic
1245C2×C3#246111yescharacteristic
1246C2×C3#246411yescharacteristic
1247C2×C3#260211yescharacteristic
1248C2×C3#263011yescharacteristic
1249C2×C3#284911yescharacteristic
1250D3—44no—
1251D3—82no—
1252C22—24no—
1253C22—24no—
1254C22—24no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—64no—
1268C22—64no—
1269C22—64no—
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—122no—
1288C22—122no—
1289C22—241no—
1290C22—241no—
1291C22—241no—
1292C22—241no—
1293C22—241no—
1294C22—241no—
1295C22—241no—
1296C22—241no—
1297C22C2×#89411yescharacteristic
1298C22#550711yescharacteristic
1299C22#551411yescharacteristic
1300C22#551511yescharacteristic
1301C22#554011yescharacteristic
1302C22#554711yescharacteristic
1303C22#554711yescharacteristic
1304C22#554711yescharacteristic
1305C22#554811yescharacteristic
1306C22#554811yescharacteristic
1307C22#555011yescharacteristic
1308C22#556011yescharacteristic
1309C22D3×#12011yescharacteristic
1310C22#558911yescharacteristic
1311C22#559011yescharacteristic
1312C22#559011yescharacteristic
1313C22#562711yescharacteristic
1314C22#562711yescharacteristic
1315C22#562911yescharacteristic
1316C22#563011yescharacteristic
1317C22#563111yescharacteristic
1318C22#563111yescharacteristic
1319C22#563711yescharacteristic
1320C22#564011yescharacteristic
1321C22D3×#12311yescharacteristic
1322C22#565411yescharacteristic
1323C22#566311yescharacteristic
1324C22#566411yescharacteristic
1325C22#579111yescharacteristic
1326C22C2×#93711yescharacteristic
1327C22D4×#6711yescharacteristic
1328C22D4×#6711yescharacteristic
1329C22#581711yescharacteristic
1330C22#583211yescharacteristic
1331C22#583411yescharacteristic
1332C4—24no—
1333C4—42no—
1334C4—42no—
1335C4—42no—
1336C4—42no—
1337C4—64no—
1338C4—81no—
1339C4—122no—
1340C4—122no—
1341C4—122no—
1342C4—122no—
1343C4—241no—
1344C3#1472111yescharacteristic, complemented, Sylow
1345C2—44no—
1346C2—124no—
1347C2—242no—
1348C2#7440911yescharacteristic
1349C2#7443211yescharacteristic
1350C2#7460311yescharacteristic
1351C2#7460611yescharacteristic
1352C2#7461211yescharacteristic
1353C2#7461811yescharacteristic
1354C2#7462211yescharacteristic
1355C2#7465611yescharacteristic
1356C2#8219511yescharacteristic
1357C2#8240011yescharacteristic
1358C2#8241111yescharacteristic
1359C2#8260411yescharacteristic
1360C2#8276711yescharacteristic
1361C2#8281211yescharacteristic
1362C2#8284911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#385C2
prime radicalC2×#4960C2
hypercenterC2×#385D3
hypocenterC3#14721
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C22×C4×#67C2semidirect
2. C22×#894C2semidirect
3. C2×C3×#385C2semidirect
4. C2×#5213C2semidirect
5. C2×#4991C2semidirect
7. #71568C2semidirect
8. #71564C2semidirect
9. #71550C2semidirect
10. #71550C2semidirect
11. #71547C2semidirect
12. #69429C2semidirect
13. #69428C2semidirect
14. (C2×D3)⋊#95C2semidirect
15. #69408C2semidirect
67. C2×#385D3semidirect
126. C22×C4×D3D4semidirect
132. C2×C3×C4⋊C4D4semidirect
171. C2×(C2×D3)⋊C4D4semidirect
172. C2×(C2×D3)⋊C4D4semidirect
486. C2×C4⋊C4#67semidirect
575. C23×C3#123semidirect
747. C2×Dic3#123semidirect
1129. C23#894semidirect
1344. C3#14721semidirect

Maximal subgroups

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

subgroupindex
C22×C4×#672
C22×#8942
C2×C3×#3852
C2×#52132
C2×#49912
C2×#49602
#715682
#715642
#715502
#715472
#694292
#694282
(C2×D3)⋊#952
#694082
#147213