Finite Group Databasebeta

← D4×#935 #10990524

Subgroups — D4×#935 #10990524

Order 768.

3742 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D42C211yesmaximal, characteristic
2C22×#935C212yesmaximal, complemented
3C22×D4×Dic3C211yesmaximal, characteristic, complemented
4#84047C212yesmaximal, complemented
5D4×#217C212yesmaximal, complemented
6D4×#217C211yesmaximal, characteristic, complemented
7#83176C212yesmaximal, complemented
8#82699C211yesmaximal, characteristic, complemented
9#82664C211yesmaximal, characteristic, complemented
10#82655C214yesmaximal, complemented
11#82644C212yesmaximal, complemented
12#82602C212yesmaximal, complemented
13#82585C214yesmaximal, complemented
14#82584C212yesmaximal, complemented
15#82373C211yesmaximal, characteristic, complemented
16D4×Dic3⋊C4C212yesmaximal, complemented
17C4×#935C211yesmaximal, characteristic, complemented
18D4×#123—31nomaximal, Sylow
19C23×C3×D4C2211yescharacteristic
20C23×C3×D4C2212yes—
21C23×C3×D4C2211yescharacteristic
22C24×Dic3C2212yescomplemented
23C3×D42—28no—
24C2×C3×#127C2211yescharacteristic
25C2×C3×#121C2211yescharacteristic
26C2×C3×#121C2211yescharacteristic
27C2×C3×#121C2212yes—
28C2×C3×#120C2212yes—
29C2×C3×#120C2212yes—
30C2×C3×C4×D4C2211yescharacteristic
31C2×C3×C4×D4C2211yescharacteristic
32C22×#217C2212yescomplemented
33C22×#217C2214yescomplemented
34C22×#217C2212yescomplemented
35C2×#935—216no—
36C2×#935C2212yes—
37C2×#935C2211yescharacteristic
38C2×#935C2212yescomplemented
39C2×#935C2212yescomplemented
40C2×#935C2214yescomplemented
41C2×#935C2214yescomplemented
42C2×#935C2212yescomplemented
43C2×D4×Dic3—28no—
44C2×D4×Dic3C2212yes—
45C2×D4×Dic3C2212yes—
46C2×D4×Dic3C2214yescomplemented
47C2×D4×Dic3C2212yescomplemented
48C22×C4⋊Dic3C2211yescharacteristic, complemented
49C22×Dic3⋊C4C2214yescomplemented
50C22×C4×Dic3C2211yescharacteristic, complemented
51#5247C2214yescomplemented
52#5247C2212yescomplemented
53#5222C2214yescomplemented
54#5222C2214yescomplemented
55#5222C2214yescomplemented
56#5221C2212yescomplemented
57#5221C2212yescomplemented
58#5221C2212yescomplemented
59#5220C2211yescharacteristic
60#5220C2212yescomplemented
61#5220C2214yescomplemented
62#5220C2214yescomplemented
63#5220C2214yescomplemented
64#5220C2214yescomplemented
65#5212C2211yescharacteristic, complemented
66#5212C2212yescomplemented
67#5210C2214yescomplemented
68C4×#217C2212yescomplemented
69C4×#217C2211yescharacteristic, complemented
70#4981C2212yescomplemented
71#4978C2212yescomplemented
72#4975C2212yescomplemented
73#4972C2212yescomplemented
74#4953C2212yescomplemented
75#4952C2214yescomplemented
76#4949C2214yescomplemented
77#4946C2211yescharacteristic, complemented
78#4946C2214yescomplemented
79#4946C2214yescomplemented
80#4944C2214yescomplemented
81#4944C2212yescomplemented
82#4943C2211yescharacteristic, complemented
83#4943C2212yescomplemented
84#4942C2214yescomplemented
85C4×Dic3⋊C4C2212yescomplemented
86#4928C2212yescomplemented
87C2×D42D311yescharacteristic
88C22×#123—32no—
89C22×C4×D4—31no—
90#2854—31no—
91#2849—32no—
92#2501—31no—
93#2486—31no—
94#2445—32no—
95#2443—34no—
96#2422—32no—
97#2418—34no—
98#2412—32no—
99#2405—32no—
100D4×C4⋊C4—32no—
101D4×C22⋊C4—31no—
102D4×C22⋊C4—32no—
103C4×#123—31no—
104C25×C3C2312yes—
105C25×C3C2312yes—
106C22×C3×D4—28no—
107C22×C3×D4—28no—
108C22×C3×D4—28no—
109C22×C3×D4—24no—
110C22×C3×D4—28no—
111C22×C3×D4—44no—
112C22×C3×D4D418yes—
113C22×C3×D4C2312yes—
114C22×C3×D4C2312yes—
115C22×C3×D4C2311yescharacteristic
116C22×C3×D4C2312yes—
117C22×C3×D4C2312yes—
118C22×C3×D4C2311yescharacteristic
119C22×C3×D4C2312yes—
120C22×C3×D4C2311yescharacteristic
121C22×C3×D4C2312yes—
122C22×C3×D4C2311yescharacteristic
123C23×C3×C4C2311yescharacteristic
124C23×C3×C4C2312yes—
125C23×C3×C4C2311yescharacteristic
126C23×Dic3—28no—
127C23×Dic3—28no—
128C23×Dic3—44no—
129C23×Dic3C2312yes—
130C23×Dic3C2314yes—
131C23×Dic3C2314yes—
132C23×Dic3C2314yes—
133C23×Dic3C2311yescharacteristic
134C23×Dic3C2311yescharacteristic
135C3×#127—24no—
136C3×#121—24no—
137C3×#121—28no—
138C3×#121—24no—
139C3×#120—28no—
140C3×#120—28no—
141C3×C4×D4—24no—
142C3×C4×D4—24no—
143C2×C3×C4⋊C4C2311yescharacteristic
144C2×C3×C4⋊C4C2311yescharacteristic
145C2×C3×C22⋊C4C2312yes—
146C2×C3×C22⋊C4C2311yescharacteristic
147C2×C3×C22⋊C4C2312yes—
148C2×C3×C22⋊C4C2311yescharacteristic
149C2×C3×C22⋊C4C2312yes—
150C2×C3×C42C2311yescharacteristic
151C2×#217—28no—
152C2×#217—28no—
153C2×#217—216no—
154C2×#217C2314yes—
155C2×#217C2311yescharacteristic
156C2×#217C2312yes—
157C2×#217C2314yes—
158C2×#217C2314yes—
159C2×#217C2314yes—
160C2×#217C2314yes—
161C2×#217C2314yes—
162C2×#217C2314yes—
163C2×#217C2312yes—
164C2×#217C2314yes—
165C2×#217C2314yes—
166C2×#217C2314yes—
167C2×#217C2312yes—
168C2×#217C2311yescharacteristic
169#935—28no—
170#935—28no—
171#935—216no—
172#935—28no—
173#935—216no—
174#935—44no—
175#935D418yesdirect product factor
176D4×Dic3—28no—
177D4×Dic3—216no—
178D4×Dic3—28no—
179D4×Dic3—28no—
180C2×C4⋊Dic3—24no—
181C2×C4⋊Dic3C2312yes—
182C2×C4⋊Dic3C2312yes—
183C2×C4⋊Dic3C2312yes—
184C2×Dic3⋊C4—216no—
185C2×Dic3⋊C4C2314yes—
186C2×Dic3⋊C4C2314yes—
187C2×Dic3⋊C4C2314yes—
188C2×Dic3⋊C4C2312yes—
189C2×Dic3⋊C4C2314yes—
190C2×Dic3⋊C4C2312yes—
191C2×C4×Dic3—24no—
192C2×C4×Dic3C2312yes—
193C2×C4×Dic3C2312yes—
194C2×C4×Dic3C2312yes—
195C3⋊#95C2314yes—
196C3⋊#95C2312yes—
197C3⋊#95C2312yes—
198C3⋊#95C2314yes—
199C3⋊#95C2312yes—
200C3⋊#95C2314yes—
201C3⋊#95C2312yes—
202C3⋊#95C2312yes—
203C3⋊#95C2312yes—
204C23×D4C2×D311yescharacteristic
205C23×D4C2×D312yes—
206C23×D4C2×D311yescharacteristic
207C24×C4—32no—
208D42—28no—
209C2×#127C2×D311yescharacteristic
210C2×#123—31no—
211C2×#123—32no—
212C2×#123—32no—
213C2×#123—32no—
214C2×#123—34no—
215C2×#123—34no—
216C2×#123—32no—
217C2×#123—616no—
218C2×#121C2×D311yescharacteristic
219C2×#121C2×D311yescharacteristic
220C2×#121C2×D312yes—
221C2×#120C2×D312yes—
222C2×#120C2×D312yes—
223C2×C4×D4—32no—
224C2×C4×D4—32no—
225C2×C4×D4—34no—
226C2×C4×D4—32no—
227C2×C4×D4—68no—
228C2×C4×D4C2×D311yescharacteristic
229C2×C4×D4C2×D311yescharacteristic
230C22×C4⋊C4—34no—
231C22×C4⋊C4—31no—
232C22×C22⋊C4—32no—
233C22×C22⋊C4—34no—
234C22×C22⋊C4—32no—
235C22×C42—31no—
236#399—34no—
237#398—32no—
238#397—34no—
239#397—32no—
240#394—34no—
241#394—34no—
242#394—34no—
243#390—32no—
244#390—32no—
245#390—32no—
246#389—32no—
247#389—32no—
248#388—34no—
249#388—32no—
250#387—32no—
251#386—34no—
252#386—34no—
253#386—34no—
254#386—34no—
255#386—32no—
256#386—31no—
257#385—34no—
258#385—34no—
259#385—34no—
260#385—31no—
261#384—32no—
262#381—31no—
263#381—32no—
264#380—31no—
265#380—32no—
266#380—34no—
267#379—32no—
268#379—34no—
269C4×C4⋊C4—32no—
270C4×C22⋊C4—32no—
271C4×C22⋊C4—31no—
272C24×C3—24no—
273C24×C3—28no—
274C24×C3—24no—
275C24×C3—24no—
276C24×C3—24no—
277C24×C3—28no—
278C24×C3—44no—
279C24×C3—44no—
280C24×C3—42no—
281C24×C3C2×D418yes—
282C24×C3C2412yes—
283C24×C3C2411yescharacteristic
284C24×C3C2412yes—
285C24×C3C2411yescharacteristic
286C24×C3C2412yes—
287C2×C3×D4—22no—
288C2×C3×D4—28no—
289C2×C3×D4—22no—
290C2×C3×D4—232no—
291C2×C3×D4—24no—
292C2×C3×D4—24no—
293C2×C3×D4—24no—
294C2×C3×D4—24no—
295C2×C3×D4—24no—
296C2×C3×D4—24no—
297C2×C3×D4—28no—
298C2×C3×D4—24no—
299C2×C3×D4—24no—
300C2×C3×D4—24no—
301C2×C3×D4—22no—
302C2×C3×D4—24no—
303C2×C3×D4—24no—
304C2×C3×D4—42no—
305C2×C3×D4—42no—
306C2×C3×D4—44no—
307C2×C3×D4—432no—
308C2×C3×D4—416no—
309C2×C3×D4C2×D414yes—
310C2×C3×D4C2×D418yes—
311C2×C3×D4C2×D414yes—
312C2×C3×D4C2×D414yes—
313C2×C3×D4#4118yes—
314C22×C3×C4—24no—
315C22×C3×C4—24no—
316C22×C3×C4—24no—
317C22×C3×C4—22no—
318C22×C3×C4—24no—
319C22×C3×C4—42no—
320C22×C3×C4C2×D414yes—
321C22×C3×C4C2411yescharacteristic
322C22×C3×C4C2411yescharacteristic
323C22×C3×C4C2412yes—
324C22×C3×C4C2411yescharacteristic
325C22×C3×C4C2411yescharacteristic
326C22×C3×C4C2411yescharacteristic
327C22×Dic3—22no—
328C22×Dic3—22no—
329C22×Dic3—22no—
330C22×Dic3—24no—
331C22×Dic3—28no—
332C22×Dic3—28no—
333C22×Dic3—24no—
334C22×Dic3—28no—
335C22×Dic3—24no—
336C22×Dic3—28no—
337C22×Dic3—28no—
338C22×Dic3—28no—
339C22×Dic3—44no—
340C22×Dic3—44no—
341C22×Dic3—44no—
342C22×Dic3—42no—
343C22×Dic3—432no—
344C22×Dic3C2×D414yescomplemented
345C22×Dic3C2412yes—
346C22×Dic3C2412yes—
347C22×Dic3C2414yes—
348C22×Dic3C2414yes—
349C22×Dic3C2412yes—
350C22×Dic3C2412yes—
351C3×C4⋊C4—22no—
352C3×C4⋊C4—22no—
353C3×C22⋊C4—24no—
354C3×C22⋊C4—22no—
355C3×C22⋊C4—24no—
356C3×C22⋊C4—22no—
357C3×C22⋊C4—24no—
358C3×C42—22no—
359#217—28no—
360#217—28no—
361#217—24no—
362#217—28no—
363#217—28no—
364#217—22no—
365#217—28no—
366#217—28no—
367#217—28no—
368#217—44no—
369#217—42no—
370#217—44no—
371#217—44no—
372#217C2×D414yescomplemented
373#217C2×D418yescomplemented
374C4⋊Dic3—24no—
375C4⋊Dic3—24no—
376C4⋊Dic3—24no—
377Dic3⋊C4—28no—
378Dic3⋊C4—28no—
379Dic3⋊C4—28no—
380Dic3⋊C4—42no—
381Dic3⋊C4—44no—
382Dic3⋊C4C2×D418yescomplemented
383C4×Dic3—24no—
384C4×Dic3—24no—
385C4×Dic3—24no—
386C25C22×D312yes—
387C25C22×D312yes—
388C22×D4—28no—
389C22×D4—28no—
390C22×D4—28no—
391C22×D4—28no—
392C22×D4—24no—
393C22×D4—44no—
394C22×D4#6718yes—
395C22×D4C22×D312yes—
396C22×D4C22×D312yes—
397C22×D4C22×D311yescharacteristic
398C22×D4C22×D312yes—
399C22×D4C22×D312yes—
400C22×D4C22×D311yescharacteristic
401C22×D4C22×D312yes—
402C22×D4C22×D311yescharacteristic
403C22×D4C22×D312yes—
404C22×D4C22×D311yescharacteristic
405C23×C4—31no—
406C23×C4—32no—
407C23×C4—34no—
408C23×C4—34no—
409C23×C4—34no—
410C23×C4—31no—
411C23×C4—68no—
412C23×C4—68no—
413C23×C4—124no—
414C23×C4C22×D311yescharacteristic
415C23×C4C22×D312yes—
416C23×C4C22×D311yescharacteristic
417#127—24no—
418#123—38no—
419#123—68no—
420#123—616no—
421#123—616no—
422#123—68no—
423#123—68no—
424#123—124no—
425#121—24no—
426#121—28no—
427#121—24no—
428#120—28no—
429#120—28no—
430C4×D4—24no—
431C4×D4—24no—
432C4×D4—68no—
433C4×D4—616no—
434C4×D4—68no—
435C4×D4—68no—
436C2×C4⋊C4—32no—
437C2×C4⋊C4—32no—
438C2×C4⋊C4—32no—
439C2×C4⋊C4—34no—
440C2×C4⋊C4—34no—
441C2×C4⋊C4—34no—
442C2×C4⋊C4—32no—
443C2×C4⋊C4—34no—
444C2×C4⋊C4—32no—
445C2×C4⋊C4—616no—
446C2×C4⋊C4—64no—
447C2×C4⋊C4C22×D311yescharacteristic
448C2×C4⋊C4C22×D311yescharacteristic
449C2×C22⋊C4—31no—
450C2×C22⋊C4—32no—
451C2×C22⋊C4—34no—
452C2×C22⋊C4—34no—
453C2×C22⋊C4—32no—
454C2×C22⋊C4—34no—
455C2×C22⋊C4—34no—
456C2×C22⋊C4—34no—
457C2×C22⋊C4—34no—
458C2×C22⋊C4—34no—
459C2×C22⋊C4—31no—
460C2×C22⋊C4—34no—
461C2×C22⋊C4—32no—
462C2×C22⋊C4—34no—
463C2×C22⋊C4—34no—
464C2×C22⋊C4—68no—
465C2×C22⋊C4—616no—
466C2×C22⋊C4—68no—
467C2×C22⋊C4C22×D312yes—
468C2×C22⋊C4C22×D311yescharacteristic
469C2×C22⋊C4C22×D311yescharacteristic
470C2×C22⋊C4C22×D312yes—
471C2×C22⋊C4C22×D312yes—
472C2×C42—32no—
473C2×C42—32no—
474C2×C42—32no—
475C2×C42—64no—
476C2×C42C22×D311yescharacteristic
477#95—32no—
478#95—32no—
479#95—32no—
480#95—32no—
481#95—32no—
482#95—34no—
483#95—34no—
484#95—34no—
485#95—32no—
486C23×C3—22no—
487C23×C3—22no—
488C23×C3—22no—
489C23×C3—24no—
490C23×C3—22no—
491C23×C3—216no—
492C23×C3—216no—
493C23×C3—22no—
494C23×C3—21no—
495C23×C3—22no—
496C23×C3—24no—
497C23×C3—22no—
498C23×C3—21no—
499C23×C3—24no—
500C23×C3—22no—
501C23×C3—22no—
502C23×C3—22no—
503C23×C3—24no—
504C23×C3—22no—
505C23×C3—24no—
506C23×C3—48no—
507C23×C3—416no—
508C23×C3—416no—
509C23×C3—48no—
510C23×C3—416no—
511C23×C3—48no—
512C23×C3—84no—
513C23×C3—88no—
514C23×C3C22×D412yes—
515C23×C3C22×D412yes—
516C23×C3C22×D414yes—
517C23×C3C22×D414yes—
518C23×C3C22×D412yes—
519C23×C3C2×#4118yes—
520C23×C3H(5,𝔽2)12yes—
521C23×C3C2511yescharacteristic
522C3×D4—216no—
523C3×D4—28no—
524C3×D4—28no—
525C3×D4—48no—
526C3×D4—48no—
527C3×D4—48no—
528C3×D4—48no—
529C3×D4—44no—
530C3×D4—84no—
531C3×D4#123116yescomplemented
532C2×C3×C4—21no—
533C2×C3×C4—22no—
534C2×C3×C4—21no—
535C2×C3×C4—28no—
536C2×C3×C4—22no—
537C2×C3×C4—21no—
538C2×C3×C4—21no—
539C2×C3×C4—22no—
540C2×C3×C4—22no—
541C2×C3×C4—22no—
542C2×C3×C4—22no—
543C2×C3×C4—48no—
544C2×C3×C4—44no—
545C2×C3×C4C22×D412yes—
546C2×C3×C4C22×D412yes—
547C2×C3×C4C22×D412yes—
548C2×C3×C4C2×#4114yes—
549C2×Dic3—28no—
550C2×Dic3—22no—
551C2×Dic3—22no—
552C2×Dic3—22no—
553C2×Dic3—22no—
554C2×Dic3—22no—
555C2×Dic3—24no—
556C2×Dic3—24no—
557C2×Dic3—24no—
558C2×Dic3—22no—
559C2×Dic3—24no—
560C2×Dic3—22no—
561C2×Dic3—24no—
562C2×Dic3—22no—
563C2×Dic3—22no—
564C2×Dic3—24no—
565C2×Dic3—22no—
566C2×Dic3—416no—
567C2×Dic3—416no—
568C2×Dic3—416no—
569C2×Dic3—44no—
570C2×Dic3—48no—
571C2×Dic3C22×D414yes—
572C2×Dic3C22×D414yes—
573C24—24no—
574C24—28no—
575C24—24no—
576C24—24no—
577C24—28no—
578C24—24no—
579C24—44no—
580C24—42no—
581C24—44no—
582C24C2×#6718yes—
583C24C23×D312yes—
584C24C23×D311yescharacteristic
585C24C23×D312yes—
586C24C23×D311yescharacteristic
587C24C23×D312yes—
588C2×D4—28no—
589C2×D4—22no—
590C2×D4—22no—
591C2×D4—232no—
592C2×D4—24no—
593C2×D4—24no—
594C2×D4—28no—
595C2×D4—24no—
596C2×D4—24no—
597C2×D4—24no—
598C2×D4—24no—
599C2×D4—24no—
600C2×D4—24no—
601C2×D4—24no—
602C2×D4—24no—
603C2×D4—24no—
604C2×D4—22no—
605C2×D4—42no—
606C2×D4—42no—
607C2×D4—44no—
608C2×D4—432no—
609C2×D4—416no—
610C2×D4D3×D414yes—
611C2×D4#23718yes—
612C2×D4C2×#6718yes—
613C2×D4C2×#6714yes—
614C2×D4C2×#6714yes—
615C22×C4—24no—
616C22×C4—24no—
617C22×C4—24no—
618C22×C4—24no—
619C22×C4—22no—
620C22×C4—34no—
621C22×C4—32no—
622C22×C4—32no—
623C22×C4—32no—
624C22×C4—32no—
625C22×C4—34no—
626C22×C4—34no—
627C22×C4—42no—
628C22×C4—68no—
629C22×C4—68no—
630C22×C4—68no—
631C22×C4—62no—
632C22×C4—62no—
633C22×C4—64no—
634C22×C4—68no—
635C22×C4—64no—
636C22×C4—62no—
637C22×C4—64no—
638C22×C4—68no—
639C22×C4—68no—
640C22×C4—124no—
641C22×C4—124no—
642C22×C4—124no—
643C22×C4—122no—
644C22×C4—1232no—
645C22×C4C2×#6714yes—
646C22×C4C23×D311yescharacteristic
647C22×C4C23×D311yescharacteristic
648C22×C4C23×D312yes—
649C22×C4C23×D311yescharacteristic
650C22×C4C23×D311yescharacteristic
651C22×C4C23×D311yescharacteristic
652C4⋊C4—22no—
653C4⋊C4—22no—
654C4⋊C4—38no—
655C4⋊C4—68no—
656C4⋊C4—68no—
657C4⋊C4—68no—
658C4⋊C4—64no—
659C4⋊C4—64no—
660C4⋊C4—64no—
661C4⋊C4—124no—
662C4⋊C4—122no—
663C22⋊C4—24no—
664C22⋊C4—22no—
665C22⋊C4—24no—
666C22⋊C4—22no—
667C22⋊C4—24no—
668C22⋊C4—34no—
669C22⋊C4—38no—
670C22⋊C4—68no—
671C22⋊C4—68no—
672C22⋊C4—68no—
673C22⋊C4—64no—
674C22⋊C4—68no—
675C22⋊C4—68no—
676C22⋊C4—62no—
677C22⋊C4—68no—
678C22⋊C4—68no—
679C22⋊C4—124no—
680C22⋊C4—124no—
681C22⋊C4—122no—
682C22⋊C4—124no—
683C42—22no—
684C42—64no—
685C42—64no—
686C42—64no—
687C22×C3—22no—
688C22×C3—24no—
689C22×C3—28no—
690C22×C3—24no—
691C22×C3—22no—
692C22×C3—24no—
693C22×C3—24no—
694C22×C3—28no—
695C22×C3—24no—
696C22×C3—24no—
697C22×C3—22no—
698C22×C3—24no—
699C22×C3—24no—
700C22×C3—432no—
701C22×C3—41no—
702C22×C3—44no—
703C22×C3—41no—
704C22×C3—44no—
705C22×C3—42no—
706C22×C3—42no—
707C22×C3—42no—
708C22×C3—44no—
709C22×C3—42no—
710C22×C3—44no—
711C22×C3—816no—
712C22×C3C2×#12318yescomplemented
713C22×C3D4214yes—
714C22×C3C23×D411yescharacteristic
715C22×C3C23×D411yescharacteristic
716C22×C3C22×#4112yes—
717C22×C3C2×H(5,𝔽2)11yescharacteristic
718C22×C3#58512yes—
719C3×C4—22no—
720C3×C4—22no—
721C3×C4—41no—
722C3×C4—42no—
723C3×C4—41no—
724C3×C4C2×#12314yescomplemented
725Dic3—24no—
726Dic3—24no—
727Dic3—44no—
728Dic3—44no—
729Dic3—42no—
730Dic3—42no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—24no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—24no—
739C23—22no—
740C23—21no—
741C23—24no—
742C23—22no—
743C23—21no—
744C23—216no—
745C23—216no—
746C23—22no—
747C23—24no—
748C23—22no—
749C23—24no—
750C23—22no—
751C23—48no—
752C23—416no—
753C23—416no—
754C23—48no—
755C23—416no—
756C23—48no—
757C23—88no—
758C23—84no—
759C23C2×D3×D412yes—
760C23C2×D3×D412yes—
761C23C2×#23718yes—
762C23#100412yes—
763C23C22×#6714yes—
764C23C22×#6714yes—
765C23C22×#6712yes—
766C23C24×D311yescharacteristic
767D4—216no—
768D4—28no—
769D4—28no—
770D4—48no—
771D4—48no—
772D4—48no—
773D4—48no—
774D4—44no—
775D4—84no—
776D4#935116yesdirect product factor
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—28no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—22no—
788C2×C4—34no—
789C2×C4—34no—
790C2×C4—48no—
791C2×C4—44no—
792C2×C4—62no—
793C2×C4—62no—
794C2×C4—62no—
795C2×C4—62no—
796C2×C4—68no—
797C2×C4—64no—
798C2×C4—64no—
799C2×C4—62no—
800C2×C4—64no—
801C2×C4—62no—
802C2×C4—64no—
803C2×C4—62no—
804C2×C4—64no—
805C2×C4—62no—
806C2×C4—62no—
807C2×C4—62no—
808C2×C4—64no—
809C2×C4—1216no—
810C2×C4—1216no—
811C2×C4—1216no—
812C2×C4—124no—
813C2×C4—128no—
814C2×C4C2×D3×D412yes—
815C2×C4C2×#23714yes—
816C2×C4C22×#6712yes—
817C2×C4C22×#6712yes—
818C2×C3—24no—
819C2×C3—28no—
820C2×C3—44no—
821C2×C3—42no—
822C2×C3—82no—
823C2×C3C22×#12311yescharacteristic
824C2×C3C2×D4211yescharacteristic
825C2×C3D4×#4112yes—
826C2×C3#348511yescharacteristic
827C2×C3#351312yes—
828C22—28no—
829C22—24no—
830C22—24no—
831C22—28no—
832C22—22no—
833C22—24no—
834C22—22no—
835C22—24no—
836C22—24no—
837C22—24no—
838C22—24no—
839C22—22no—
840C22—24no—
841C22—432no—
842C22—44no—
843C22—44no—
844C22—42no—
845C22—41no—
846C22—41no—
847C22—44no—
848C22—44no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—816no—
853C22C2×#93518yescomplemented
854C22D4×#6714yes—
855C22C22×D3×D411yescharacteristic
856C22C22×#23712yes—
857C22C2×#100411yescharacteristic
858C22#596612yes—
859C22C23×#6711yescharacteristic
860C4—22no—
861C4—22no—
862C4—41no—
863C4—42no—
864C4—41no—
865C4—64no—
866C4—64no—
867C4—124no—
868C4—122no—
869C4—124no—
870C4—122no—
871C4C2×#93514yescomplemented
872C3D4×#12311yescharacteristic, complemented, Sylow
873C2—24no—
874C2—28no—
875C2—44no—
876C2—42no—
877C2—82no—
878C2D4×#23712yes—
879C2#8660912yes—
880C2C22×#93511yescharacteristic
881C2C2×D4×#6711yescharacteristic
882C2#8728011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
Fitting, prime radicalC2×C3×D42C2
hypercenterC2×D42D3
hypocenterC3D4×#123
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×D42

Complements

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

NH ≅ G/Ntype
2. C22×#935C2semidirect
3. C22×D4×Dic3C2semidirect
4. #84047C2semidirect
5. D4×#217C2semidirect
6. D4×#217C2semidirect
7. #83176C2semidirect
8. #82699C2semidirect
9. #82664C2semidirect
10. #82655C2semidirect
11. #82644C2semidirect
12. #82602C2semidirect
13. #82585C2semidirect
14. #82584C2semidirect
15. #82373C2semidirect
16. D4×Dic3⋊C4C2semidirect
17. C4×#935C2semidirect
22. C24×Dic3C22semidirect
32. C22×#217C22semidirect
33. C22×#217C22semidirect
34. C22×#217C22semidirect
38. C2×#935C22semidirect
39. C2×#935C22semidirect
40. C2×#935C22semidirect
41. C2×#935C22semidirect
42. C2×#935C22semidirect
46. C2×D4×Dic3C22semidirect
47. C2×D4×Dic3C22semidirect
48. C22×C4⋊Dic3C22semidirect
49. C22×Dic3⋊C4C22semidirect
50. C22×C4×Dic3C22semidirect
51. #5247C22semidirect
52. #5247C22semidirect
53. #5222C22semidirect
54. #5222C22semidirect
55. #5222C22semidirect
56. #5221C22semidirect
57. #5221C22semidirect
58. #5221C22semidirect
60. #5220C22semidirect
61. #5220C22semidirect
62. #5220C22semidirect
63. #5220C22semidirect
64. #5220C22semidirect
65. #5212C22semidirect
66. #5212C22semidirect
67. #5210C22semidirect
68. C4×#217C22semidirect
69. C4×#217C22semidirect
70. #4981C22semidirect
71. #4978C22semidirect
72. #4975C22semidirect
73. #4972C22semidirect
74. #4953C22semidirect
75. #4952C22semidirect
76. #4949C22semidirect
77. #4946C22semidirect
78. #4946C22semidirect
79. #4946C22semidirect
80. #4944C22semidirect
81. #4944C22semidirect
82. #4943C22semidirect
83. #4943C22semidirect
84. #4942C22semidirect
85. C4×Dic3⋊C4C22semidirect
86. #4928C22semidirect
175. #935D4direct (N × H)
344. C22×Dic3C2×D4semidirect
372. #217C2×D4semidirect
373. #217C2×D4semidirect
382. Dic3⋊C4C2×D4semidirect
531. C3×D4#123semidirect
712. C22×C3C2×#123semidirect
724. C3×C4C2×#123semidirect
776. D4#935direct (N × H)
853. C22C2×#935semidirect
871. C4C2×#935semidirect
872. C3D4×#123semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D422
C22×#9352
C22×D4×Dic32
#840472
D4×#2172
#831762
#826992
#826642
#826552
#826442
#826022
#825852
#825842
#823732
D4×Dic3⋊C42
C4×#9352
D4×#1233