Finite Group Databasebeta

← C2×#73600 #10965254

Subgroups — C2×#73600 #10965254

Order 768.

4110 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#930C211yesmaximal, characteristic, complemented
2C22×#884C211yesmaximal, characteristic, complemented
3C22×#885C211yesmaximal, characteristic, complemented
4C22×#875C211yesmaximal, characteristic, complemented
5C2×C3×C4×C22⋊C4C211yesmaximal, characteristic, complemented
6C2×#5213C211yesmaximal, characteristic, complemented
7C2×#4960C211yesmaximal, characteristic, complemented
8C2×#4961C211yesmaximal, characteristic, complemented
9C2×#4939C211yesmaximal, characteristic, complemented
10C2×#4940C211yesmaximal, characteristic, complemented
11C2×C4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
12#73600C2116yesmaximal, direct product factor
13C2×#4671C211yesmaximal, characteristic, complemented
14C2×#4665C211yesmaximal, characteristic, complemented
15C2×#4656C211yesmaximal, characteristic, complemented
16C2×#4670C211yesmaximal, characteristic, complemented
17C2×#2555—31nomaximal, Sylow
18C24×C3×C4C2211yescharacteristic
19C23×#67C2211yescharacteristic
20C23×#67C2211yescharacteristic
21C23×#67C2211yescharacteristic
22C23×D12C2211yescharacteristic
23C23×D12C2211yescharacteristic
24C23×D12C2211yescharacteristic
25C23×C4×D3C2211yescharacteristic
26C23×Dic6C2211yescharacteristic
27C22×C3×C22⋊C4C2211yescharacteristic
28C22×C3×C22⋊C4C2211yescharacteristic
29C22×C3×C42C2211yescharacteristic
30C22×C3×C42C2211yescharacteristic
31C22×#217C2211yescharacteristic
32C2×#930—28no—
33C2×#930C2218yescomplemented
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×(C2×D3)⋊C4C2211yescharacteristic
41C22×(C2×D3)⋊C4C2211yescharacteristic
42C22×(C2×D3)⋊C4C2211yescharacteristic
43C22×(C2×D3)⋊C4C2211yescharacteristic
44C22×(C2×D3)⋊C4C2211yescharacteristic
45C22×C4⋊Dic3C2211yescharacteristic
46C22×C4⋊Dic3C2211yescharacteristic
47C22×Dic3⋊C4C2211yescharacteristic
48C22×C4×Dic3C2211yescharacteristic
49C2×#885—28no—
50C2×#885C2218yescomplemented
51C2×#884—28no—
52C2×#884C2218yescomplemented
53C2×#875—28no—
54C2×#875C2218yescomplemented
55C3×C4×C22⋊C4C2218yescomplemented
56C2×C3×#95C2211yescharacteristic
57C2×C3×#95C2211yescharacteristic
58#5213C2218yescomplemented
59C2×C3⋊#95C2211yescharacteristic
60C2×C3⋊#95C2211yescharacteristic
61C2×C3⋊#95C2211yescharacteristic
62C2×C3⋊#95C2211yescharacteristic
63#4961C2218yescomplemented
64#4960C2218yescomplemented
65#4940C2218yescomplemented
66#4939C2218yescomplemented
67C4×(C2×D3)⋊C4C2218yescomplemented
68#4671C2218yescomplemented
69#4670C2218yescomplemented
70#4665C2218yescomplemented
71#4656C2218yescomplemented
72C22×#124—31no—
73C22×#124—31no—
74C22×#121—31no—
75C22×#121—31no—
76#2555—316no—
77C2×#395—31no—
78C2×#394—31no—
79C2×#392—31no—
80C2×#392—31no—
81C2×#390—31no—
82C2×#388—31no—
83C2×#388—31no—
84C2×#386—31no—
85C2×#386—31no—
86C2×C4×C22⋊C4—31no—
87C2×C4×C22⋊C4D311yescharacteristic, complemented
88C25×C3C2311yescharacteristic
89C24×D3C2311yescharacteristic
90C24×D3C2311yescharacteristic
91C24×D3C2311yescharacteristic
92C23×C3×C4—24no—
93C23×C3×C4—24no—
94C23×C3×C4—42no—
95C23×C3×C4C2311yescharacteristic
96C23×C3×C4C2314yes—
97C23×C3×C4C2311yescharacteristic
98C23×C3×C4C2311yescharacteristic
99C23×C3×C4C2311yescharacteristic
100C23×C3×C4C2311yescharacteristic
101C23×C3×C4C2311yescharacteristic
102C22×#67—24no—
103C22×#67—24no—
104C22×#67—24no—
105C22×#67—24no—
106C22×#67—24no—
107C22×#67—24no—
108C22×#67—42no—
109C22×#67—42no—
110C22×#67—42no—
111C22×#67C2314yes—
112C22×#67C2314yes—
113C22×#67C2314yes—
114C23×Dic3C2311yescharacteristic
115C23×Dic3C2311yescharacteristic
116C23×Dic3C2311yescharacteristic
117C23×Dic3C2311yescharacteristic
118C23×Dic3C2311yescharacteristic
119C22×D12—24no—
120C22×D12—24no—
121C22×D12—24no—
122C22×D12—24no—
123C22×D12—24no—
124C22×D12—42no—
125C22×D12—42no—
126C22×D12—42no—
127C22×D12—42no—
128C22×D12C2314yes—
129C22×D12C2314yes—
130C22×D12C2314yes—
131C22×C4×D3—24no—
132C22×C4×D3—24no—
133C22×C4×D3—42no—
134C22×C4×D3C2314yes—
135C22×Dic6—24no—
136C22×Dic6—24no—
137C22×Dic6—42no—
138C22×Dic6C2314yes—
139C2×C3×C22⋊C4—24no—
140C2×C3×C22⋊C4D418yescomplemented
141C2×C3×C22⋊C4C2314yes—
142C2×C3×C22⋊C4C2314yes—
143C2×C3×C42—24no—
144C2×C3×C42—42no—
145C2×C3×C42C2314yes—
146C2×C3×C42C2314yes—
147C2×#217—24no—
148C2×#217C2314yes—
149#930—232no—
150C2×(C2×D3)⋊C4—24no—
151C2×(C2×D3)⋊C4—24no—
152C2×(C2×D3)⋊C4—24no—
153C2×(C2×D3)⋊C4—24no—
154C2×(C2×D3)⋊C4—24no—
155C2×(C2×D3)⋊C4—24no—
156C2×(C2×D3)⋊C4—24no—
157C2×(C2×D3)⋊C4—24no—
158C2×(C2×D3)⋊C4—24no—
159C2×(C2×D3)⋊C4—24no—
160C2×(C2×D3)⋊C4D418yescomplemented
161C2×(C2×D3)⋊C4C2314yes—
162C2×(C2×D3)⋊C4C2314yes—
163C2×(C2×D3)⋊C4C2314yes—
164C2×(C2×D3)⋊C4C2314yes—
165C2×(C2×D3)⋊C4C2314yes—
166C2×(C2×D3)⋊C4C2314yes—
167C2×(C2×D3)⋊C4C2314yes—
168C2×(C2×D3)⋊C4C2314yes—
169C2×(C2×D3)⋊C4C2314yes—
170C2×(C2×D3)⋊C4C2314yes—
171C2×(C2×D3)⋊C4C2314yes—
172C2×C4⋊Dic3—24no—
173C2×C4⋊Dic3—42no—
174C2×C4⋊Dic3C2314yes—
175C2×C4⋊Dic3C2314yes—
176C2×Dic3⋊C4—24no—
177C2×Dic3⋊C4C2314yes—
178C2×C4×Dic3—24no—
179C2×C4×Dic3C2314yes—
180#885—232no—
181#884—232no—
182#875—232no—
183C3×#95C2314yes—
184C3×#95C2314yes—
185C3⋊#95C2314yes—
186C3⋊#95C2314yes—
187C3⋊#95C2314yes—
188C3⋊#95C2314yes—
189C23×Q8—31no—
190C23×D4—31no—
191C23×D4—31no—
192C23×D4—31no—
193C23×D4—31no—
194C23×D4—31no—
195C23×D4—31no—
196C24×C4—31no—
197C24×C4C2×D311yescharacteristic
198C2×#124—38no—
199C2×#124—38no—
200C2×#124—68no—
201C2×#124—68no—
202C2×#121—38no—
203C2×#121—38no—
204C2×#121—68no—
205C2×#121—68no—
206C22×C4⋊C4—31no—
207C22×C4⋊C4—31no—
208C22×C4⋊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⋊C4—31no—
220C22×C22⋊C4—31no—
221C22×C22⋊C4C2×D311yescharacteristic
222C22×C22⋊C4C2×D311yescharacteristic
223C22×C42—31no—
224C22×C42C2×D311yescharacteristic
225C22×C42C2×D311yescharacteristic
226#395—38no—
227#394—38no—
228#392—38no—
229#392—38no—
230#390—38no—
231#388—38no—
232#388—38no—
233#386—38no—
234#386—38no—
235C4×C22⋊C4—38no—
236C4×C22⋊C4C2×D318yescomplemented
237C2×#95—31no—
238C2×#95—31no—
239C2×#95—31no—
240C2×#95—31no—
241C2×#95C2×D311yescharacteristic
242C2×#95C2×D311yescharacteristic
243C24×C3—22no—
244C24×C3—22no—
245C24×C3—22no—
246C24×C3—22no—
247C24×C3—22no—
248C24×C3—22no—
249C24×C3C2×D414yes—
250C24×C3C2412yes—
251C24×C3C2411yescharacteristic
252C23×D3—22no—
253C23×D3—22no—
254C23×D3—22no—
255C23×D3—22no—
256C23×D3—22no—
257C23×D3—22no—
258C23×D3—22no—
259C23×D3—22no—
260C23×D3—22no—
261C23×D3—22no—
262C23×D3—22no—
263C23×D3—22no—
264C23×D3—22no—
265C23×D3—22no—
266C23×D3—22no—
267C23×D3—22no—
268C23×D3—22no—
269C23×D3—22no—
270C23×D3—22no—
271C23×D3—22no—
272C23×D3C2×D414yes—
273C23×D3C2412yes—
274C23×D3C2412yes—
275C23×D3C2412yes—
276C22×C3×C4—22no—
277C22×C3×C4—22no—
278C22×C3×C4—22no—
279C22×C3×C4—22no—
280C22×C3×C4—22no—
281C22×C3×C4—22no—
282C22×C3×C4—22no—
283C22×C3×C4—22no—
284C22×C3×C4—22no—
285C22×C3×C4—22no—
286C22×C3×C4—22no—
287C22×C3×C4—22no—
288C22×C3×C4—22no—
289C22×C3×C4—28no—
290C22×C3×C4—28no—
291C22×C3×C4—44no—
292C22×C3×C4—416no—
293C22×C3×C4C2×D414yes—
294C22×C3×C4C2×D414yes—
295C22×C3×C4C2×D414yes—
296C22×C3×C4#4114yes—
297C22×C3×C4#4114yes—
298C22×C3×C4C2412yes—
299C22×C3×C4C2412yes—
300C22×C3×C4C2412yes—
301C22×C3×C4C2412yes—
302C22×C3×C4C2412yes—
303C22×C3×C4C2412yes—
304C2×#67—28no—
305C2×#67—28no—
306C2×#67—28no—
307C2×#67—28no—
308C2×#67—28no—
309C2×#67—28no—
310C2×#67—44no—
311C2×#67—44no—
312C2×#67—44no—
313C2×#67—416no—
314C2×#67—416no—
315C2×#67—416no—
316C22×Dic3—22no—
317C22×Dic3—22no—
318C22×Dic3—22no—
319C22×Dic3—22no—
320C22×Dic3—22no—
321C22×Dic3—22no—
322C22×Dic3—22no—
323C22×Dic3—22no—
324C22×Dic3—22no—
325C22×Dic3—22no—
326C22×Dic3—22no—
327C22×Dic3—22no—
328C22×Dic3—22no—
329C22×Dic3C2×D414yes—
330C22×Dic3#4114yes—
331C22×Dic3C2412yes—
332C22×Dic3C2412yes—
333C22×Dic3C2412yes—
334C22×Dic3C2412yes—
335C22×Dic3C2412yes—
336C2×D12—28no—
337C2×D12—28no—
338C2×D12—28no—
339C2×D12—28no—
340C2×D12—28no—
341C2×D12—44no—
342C2×D12—44no—
343C2×D12—44no—
344C2×D12—44no—
345C2×D12—416no—
346C2×D12—416no—
347C2×D12—416no—
348C2×C4×D3—28no—
349C2×C4×D3—28no—
350C2×C4×D3—44no—
351C2×C4×D3—416no—
352C2×Dic6—28no—
353C2×Dic6—28no—
354C2×Dic6—44no—
355C2×Dic6—416no—
356C3×C22⋊C4—28no—
357C3×C22⋊C4C2×D4116yescomplemented
358C3×C42—28no—
359C3×C42—44no—
360#217—28no—
361(C2×D3)⋊C4—28no—
362(C2×D3)⋊C4—28no—
363(C2×D3)⋊C4—28no—
364(C2×D3)⋊C4—28no—
365(C2×D3)⋊C4—28no—
366(C2×D3)⋊C4—28no—
367(C2×D3)⋊C4—28no—
368(C2×D3)⋊C4—28no—
369(C2×D3)⋊C4—28no—
370(C2×D3)⋊C4—28no—
371(C2×D3)⋊C4C2×D4116yescomplemented
372C4⋊Dic3—28no—
373C4⋊Dic3—44no—
374Dic3⋊C4—28no—
375C4×Dic3—28no—
376C25—31no—
377C25—31no—
378C25—31no—
379C25C22×D311yescharacteristic
380C22×Q8—34no—
381C22×Q8—64no—
382C22×Q8—64no—
383C22×Q8—122no—
384C22×D4—34no—
385C22×D4—34no—
386C22×D4—34no—
387C22×D4—34no—
388C22×D4—34no—
389C22×D4—34no—
390C22×D4—64no—
391C22×D4—64no—
392C22×D4—64no—
393C22×D4—64no—
394C22×D4—64no—
395C22×D4—64no—
396C22×D4—64no—
397C22×D4—64no—
398C22×D4—64no—
399C22×D4—64no—
400C22×D4—64no—
401C22×D4—122no—
402C22×D4—122no—
403C22×D4—122no—
404C22×D4—122no—
405C22×D4—122no—
406C22×D4—122no—
407C22×D4—122no—
408C23×C4—24no—
409C23×C4—24no—
410C23×C4—31no—
411C23×C4—31no—
412C23×C4—31no—
413C23×C4—31no—
414C23×C4—31no—
415C23×C4—34no—
416C23×C4—42no—
417C23×C4—64no—
418C23×C4—64no—
419C23×C4—122no—
420C23×C4C22×D311yescharacteristic
421C23×C4C22×D314yes—
422C23×C4C22×D311yescharacteristic
423C23×C4C22×D311yescharacteristic
424C23×C4C22×D311yescharacteristic
425C23×C4C22×D311yescharacteristic
426C23×C4C22×D311yescharacteristic
427#124—632no—
428#124—632no—
429#121—632no—
430#121—632no—
431C2×C4⋊C4—34no—
432C2×C4⋊C4—34no—
433C2×C4⋊C4—34no—
434C2×C4⋊C4—64no—
435C2×C4⋊C4—64no—
436C2×C4⋊C4—122no—
437C2×C22⋊C4—24no—
438C2×C22⋊C4—38no—
439C2×C22⋊C4—34no—
440C2×C22⋊C4—34no—
441C2×C22⋊C4—34no—
442C2×C22⋊C4—34no—
443C2×C22⋊C4—34no—
444C2×C22⋊C4—34no—
445C2×C22⋊C4—34no—
446C2×C22⋊C4—34no—
447C2×C22⋊C4—34no—
448C2×C22⋊C4—34no—
449C2×C22⋊C4—34no—
450C2×C22⋊C4—34no—
451C2×C22⋊C4—64no—
452C2×C22⋊C4—64no—
453C2×C22⋊C4—64no—
454C2×C22⋊C4—64no—
455C2×C22⋊C4—64no—
456C2×C22⋊C4—64no—
457C2×C22⋊C4—64no—
458C2×C22⋊C4—64no—
459C2×C22⋊C4—64no—
460C2×C22⋊C4—64no—
461C2×C22⋊C4—64no—
462C2×C22⋊C4D1218yescomplemented
463C2×C22⋊C4C22×D314yes—
464C2×C22⋊C4C22×D314yes—
465C2×C42—24no—
466C2×C42—34no—
467C2×C42—42no—
468C2×C42—64no—
469C2×C42C22×D314yes—
470C2×C42C22×D314yes—
471#95—34no—
472#95—34no—
473#95—34no—
474#95—34no—
475#95C22×D314yes—
476#95C22×D314yes—
477C23×C3—28no—
478C23×C3—28no—
479C23×C3—28no—
480C23×C3—22no—
481C23×C3—22no—
482C23×C3—22no—
483C23×C3—22no—
484C23×C3—22no—
485C23×C3—22no—
486C23×C3—44no—
487C23×C3—44no—
488C23×C3—44no—
489C23×C3—44no—
490C23×C3C22×D414yes—
491C23×C3C22×D412yes—
492C23×C3C22×D412yes—
493C23×C3C2×#4112yes—
494C23×C3C2×#4112yes—
495C23×C3C2×#4112yes—
496C23×C3H(5,𝔽2)12yes—
497C23×C3H(5,𝔽2)12yes—
498C23×C3C2511yescharacteristic
499C22×D3—28no—
500C22×D3—28no—
501C22×D3—28no—
502C22×D3—22no—
503C22×D3—22no—
504C22×D3—22no—
505C22×D3—22no—
506C22×D3—22no—
507C22×D3—22no—
508C22×D3—22no—
509C22×D3—22no—
510C22×D3—22no—
511C22×D3—22no—
512C22×D3—22no—
513C22×D3—22no—
514C22×D3—22no—
515C22×D3—22no—
516C22×D3—22no—
517C22×D3—22no—
518C22×D3—22no—
519C22×D3—22no—
520C22×D3—22no—
521C22×D3—22no—
522C22×D3—44no—
523C22×D3—44no—
524C22×D3—44no—
525C22×D3—44no—
526C22×D3—44no—
527C22×D3—44no—
528C22×D3—44no—
529C22×D3—44no—
530C22×D3—44no—
531C22×D3—44no—
532C22×D3—44no—
533C22×D3—44no—
534C22×D3—44no—
535C22×D3—44no—
536C22×D3—44no—
537C22×D3—44no—
538C22×D3—44no—
539C22×D3—44no—
540C22×D3C22×D414yes—
541C2×C3×C4—28no—
542C2×C3×C4—28no—
543C2×C3×C4—28no—
544C2×C3×C4—28no—
545C2×C3×C4—28no—
546C2×C3×C4—22no—
547C2×C3×C4—22no—
548C2×C3×C4—22no—
549C2×C3×C4—22no—
550C2×C3×C4—22no—
551C2×C3×C4—22no—
552C2×C3×C4—22no—
553C2×C3×C4—22no—
554C2×C3×C4—22no—
555C2×C3×C4—22no—
556C2×C3×C4—22no—
557C2×C3×C4—22no—
558C2×C3×C4—22no—
559C2×C3×C4—416no—
560C2×C3×C4—44no—
561C2×C3×C4C22×D414yes—
562C2×C3×C4C22×D414yes—
563C2×C3×C4C22×D414yes—
564C2×C3×C4C2×#4114yes—
565C2×C3×C4C2×#4114yes—
566#67—416no—
567#67—416no—
568#67—416no—
569C2×Dic3—28no—
570C2×Dic3—28no—
571C2×Dic3—22no—
572C2×Dic3—22no—
573C2×Dic3—22no—
574C2×Dic3—22no—
575C2×Dic3—22no—
576C2×Dic3—22no—
577C2×Dic3—22no—
578C2×Dic3—22no—
579C2×Dic3—22no—
580C2×Dic3—22no—
581C2×Dic3—22no—
582C2×Dic3—22no—
583C2×Dic3—22no—
584C2×Dic3—44no—
585C2×Dic3—44no—
586C2×Dic3—44no—
587C2×Dic3C22×D414yes—
588C2×Dic3C2×#4114yes—
589D12—416no—
590D12—416no—
591D12—416no—
592C4×D3—416no—
593Dic6—416no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24—22no—
599C24—22no—
600C24—34no—
601C24—32no—
602C24—32no—
603C24—32no—
604C24—62no—
605C24—62no—
606C24—62no—
607C24—62no—
608C24—62no—
609C24—62no—
610C24—62no—
611C24—62no—
612C24—62no—
613C24—62no—
614C24—62no—
615C24—62no—
616C24—62no—
617C24—62no—
618C24—62no—
619C24—62no—
620C24—62no—
621C24—62no—
622C24—62no—
623C24—62no—
624C24C2×D1214yes—
625C24C23×D312yes—
626C24C23×D311yescharacteristic
627C2×Q8—68no—
628C2×Q8—68no—
629C2×Q8—124no—
630C2×Q8—1216no—
631C2×D4—68no—
632C2×D4—68no—
633C2×D4—68no—
634C2×D4—68no—
635C2×D4—68no—
636C2×D4—68no—
637C2×D4—68no—
638C2×D4—68no—
639C2×D4—68no—
640C2×D4—68no—
641C2×D4—68no—
642C2×D4—124no—
643C2×D4—124no—
644C2×D4—124no—
645C2×D4—124no—
646C2×D4—1216no—
647C2×D4—1216no—
648C2×D4—1216no—
649C2×D4—124no—
650C2×D4—124no—
651C2×D4—124no—
652C2×D4—1216no—
653C2×D4—1216no—
654C2×D4—1216no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—28no—
669C22×C4—28no—
670C22×C4—34no—
671C22×C4—34no—
672C22×C4—32no—
673C22×C4—32no—
674C22×C4—32no—
675C22×C4—32no—
676C22×C4—32no—
677C22×C4—44no—
678C22×C4—416no—
679C22×C4—68no—
680C22×C4—62no—
681C22×C4—62no—
682C22×C4—62no—
683C22×C4—62no—
684C22×C4—62no—
685C22×C4—62no—
686C22×C4—62no—
687C22×C4—62no—
688C22×C4—62no—
689C22×C4—62no—
690C22×C4—62no—
691C22×C4—62no—
692C22×C4—62no—
693C22×C4—68no—
694C22×C4—124no—
695C22×C4—1216no—
696C22×C4C2×D1214yes—
697C22×C4C2×D1214yes—
698C22×C4#23514yes—
699C22×C4#23514yes—
700C22×C4D3×D414yes—
701C22×C4C23×D312yes—
702C22×C4C23×D312yes—
703C22×C4C23×D312yes—
704C22×C4C23×D312yes—
705C22×C4C23×D312yes—
706C22×C4C23×D312yes—
707C4⋊C4—68no—
708C4⋊C4—68no—
709C4⋊C4—124no—
710C22⋊C4—28no—
711C22⋊C4—316no—
712C22⋊C4—68no—
713C22⋊C4—68no—
714C22⋊C4—68no—
715C22⋊C4—68no—
716C22⋊C4—68no—
717C22⋊C4—68no—
718C22⋊C4—68no—
719C22⋊C4—68no—
720C22⋊C4—68no—
721C22⋊C4—68no—
722C22⋊C4—68no—
723C22⋊C4C2×D12116yescomplemented
724C42—28no—
725C42—44no—
726C42—68no—
727C22×C3—24no—
728C22×C3—24no—
729C22×C3—24no—
730C22×C3—42no—
731C22×C3—42no—
732C22×C3—42no—
733C22×C3—42no—
734C22×C3—416no—
735C22×C3#53214yes—
736C22×C3#53214yes—
737C22×C3#53814yes—
738C22×C3D4214yes—
739C22×C3#54614yes—
740C22×C3#54614yes—
741C22×C3#55514yes—
742C22×C3C23×D411yescharacteristic
743C22×C3C23×D411yescharacteristic
744C22×C3C22×#4111yescharacteristic
745C22×C3C22×#4111yescharacteristic
746C22×C3C22×#4111yescharacteristic
747C22×C3C2×H(5,𝔽2)11yescharacteristic
748C22×C3C2×H(5,𝔽2)11yescharacteristic
749C2×D3—24no—
750C2×D3—24no—
751C2×D3—24no—
752C2×D3—42no—
753C2×D3—42no—
754C2×D3—42no—
755C2×D3—42no—
756C2×D3—416no—
757C2×D3—42no—
758C2×D3—42no—
759C2×D3—42no—
760C2×D3—42no—
761C2×D3—42no—
762C2×D3—42no—
763C2×D3—42no—
764C2×D3—42no—
765C2×D3—42no—
766C2×D3—42no—
767C2×D3—42no—
768C2×D3—42no—
769C2×D3—42no—
770C2×D3—42no—
771C2×D3—88no—
772C2×D3—88no—
773C3×C4—24no—
774C3×C4—24no—
775C3×C4—24no—
776C3×C4—24no—
777C3×C4—24no—
778C3×C4—42no—
779Dic3—24no—
780Dic3—24no—
781Dic3—42no—
782Dic3—42no—
783Dic3—42no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—28no—
791C23—28no—
792C23—28no—
793C23—34no—
794C23—44no—
795C23—44no—
796C23—44no—
797C23—44no—
798C23—62no—
799C23—62no—
800C23—62no—
801C23—62no—
802C23—62no—
803C23—62no—
804C23—68no—
805C23—68no—
806C23—68no—
807C23—62no—
808C23—62no—
809C23—62no—
810C23—62no—
811C23—62no—
812C23—62no—
813C23—62no—
814C23—62no—
815C23—62no—
816C23—62no—
817C23—62no—
818C23—62no—
819C23—62no—
820C23—62no—
821C23—124no—
822C23—124no—
823C23—124no—
824C23—124no—
825C23—124no—
826C23—124no—
827C23—124no—
828C23—124no—
829C23—124no—
830C23—124no—
831C23—124no—
832C23—124no—
833C23—124no—
834C23—124no—
835C23—124no—
836C23—124no—
837C23—124no—
838C23—124no—
839C23C22×D1214yes—
840C23C22×D1212yes—
841C23C2×#23512yes—
842C23C2×#23512yes—
843C23C2×D3×D412yes—
844C23#100412yes—
845C23D3×#4112yes—
846C23#100912yes—
847C23C24×D311yescharacteristic
848Q8—1216no—
849D4—1216no—
850D4—1216no—
851D4—1216no—
852D4—1216no—
853D4—1216no—
854D4—1216no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—28no—
866C2×C4—28no—
867C2×C4—28no—
868C2×C4—28no—
869C2×C4—28no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—34no—
874C2×C4—34no—
875C2×C4—416no—
876C2×C4—44no—
877C2×C4—62no—
878C2×C4—62no—
879C2×C4—62no—
880C2×C4—62no—
881C2×C4—68no—
882C2×C4—68no—
883C2×C4—62no—
884C2×C4—62no—
885C2×C4—62no—
886C2×C4—62no—
887C2×C4—62no—
888C2×C4—62no—
889C2×C4—62no—
890C2×C4—62no—
891C2×C4—62no—
892C2×C4—1216no—
893C2×C4—124no—
894C2×C4—124no—
895C2×C4—124no—
896C2×C4C22×D1214yes—
897C2×C4C22×D1214yes—
898C2×C4C2×#23514yes—
899C2×C4C2×#23514yes—
900C2×C4C2×D3×D414yes—
901C2×C3—44no—
902C2×C3#255518yescomplemented
903C2×C3C2×#53211yescharacteristic
904C2×C3C2×#53211yescharacteristic
905C2×C3C2×#53811yescharacteristic
906C2×C3C2×D4211yescharacteristic
907C2×C3C2×#54611yescharacteristic
908C2×C3C2×#54611yescharacteristic
909C2×C3C2×#55511yescharacteristic
910D3—44no—
911D3—82no—
912D3—82no—
913C22—24no—
914C22—24no—
915C22—24no—
916C22—42no—
917C22—42no—
918C22—416no—
919C22—42no—
920C22—42no—
921C22—64no—
922C22—64no—
923C22—64no—
924C22—122no—
925C22—122no—
926C22—1216no—
927C22—122no—
928C22—122no—
929C22—122no—
930C22—122no—
931C22—122no—
932C22—122no—
933C22—122no—
934C22—122no—
935C22—122no—
936C22—122no—
937C22—122no—
938C22—122no—
939C22—122no—
940C22—122no—
941C22—122no—
942C22—122no—
943C22—248no—
944C22—248no—
945C22#547714yes—
946C22#549014yes—
947C22#553214yes—
948C22#554814yes—
949C22D4×D1214yes—
950C22#555414yes—
951C22#556014yes—
952C22C23×D1211yescharacteristic
953C22C22×#23511yescharacteristic
954C22C22×#23511yescharacteristic
955C22C22×D3×D411yescharacteristic
956C22C2×#100411yescharacteristic
957C22C2×D3×#4111yescharacteristic
958C22C2×#100911yescharacteristic
959C4—24no—
960C4—24no—
961C4—24no—
962C4—24no—
963C4—24no—
964C4—42no—
965C4—64no—
966C4—64no—
967C4—122no—
968C4—122no—
969C4—122no—
970C3C2×#255511yescharacteristic, complemented, Sylow
971C2—44no—
972C2—124no—
973C2—242no—
974C2—242no—
975C2#7360018yesdirect product factor
976C2C2×#547711yescharacteristic
977C2C2×#549011yescharacteristic
978C2C2×#553211yescharacteristic
979C2C2×#554811yescharacteristic
980C2C2×#556011yescharacteristic
981C2C2×D4×D1211yescharacteristic
982C2C2×#555411yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC2×C3×C4×C22⋊C4C2
socleC24×C3C24
hypercenterC2×C4×C22⋊C4D3
hypocenterC3C2×#2555
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#930C2semidirect
2. C22×#884C2semidirect
3. C22×#885C2semidirect
4. C22×#875C2semidirect
5. C2×C3×C4×C22⋊C4C2semidirect
6. C2×#5213C2semidirect
7. C2×#4960C2semidirect
8. C2×#4961C2semidirect
9. C2×#4939C2semidirect
10. C2×#4940C2semidirect
11. C2×C4×(C2×D3)⋊C4C2semidirect
12. #73600C2direct (N × H)
13. C2×#4671C2semidirect
14. C2×#4665C2semidirect
15. C2×#4656C2semidirect
16. C2×#4670C2semidirect
33. C2×#930C22semidirect
50. C2×#885C22semidirect
52. C2×#884C22semidirect
54. C2×#875C22semidirect
55. C3×C4×C22⋊C4C22semidirect
58. #5213C22semidirect
63. #4961C22semidirect
64. #4960C22semidirect
65. #4940C22semidirect
66. #4939C22semidirect
67. C4×(C2×D3)⋊C4C22semidirect
68. #4671C22semidirect
69. #4670C22semidirect
70. #4665C22semidirect
71. #4656C22semidirect
87. C2×C4×C22⋊C4D3semidirect
140. C2×C3×C22⋊C4D4semidirect
160. C2×(C2×D3)⋊C4D4semidirect
236. C4×C22⋊C4C2×D3semidirect
357. C3×C22⋊C4C2×D4semidirect
371. (C2×D3)⋊C4C2×D4semidirect
462. C2×C22⋊C4D12semidirect
723. C22⋊C4C2×D12semidirect
902. C2×C3#2555semidirect
970. C3C2×#2555semidirect
975. C2#73600direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#9302
C22×#8842
C22×#8852
C22×#8752
C2×C3×C4×C22⋊C42
C2×#52132
C2×#49602
C2×#49612
C2×#49392
C2×#49402
C2×C4×(C2×D3)⋊C42
#736002
C2×#46712
C2×#46652
C2×#46562
C2×#46702
C2×#25553