Finite Group Databasebeta

← C2×#83888 #11670232

Subgroups — C2×#83888 #11670232

Order 768.

2742 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×Q16C211yesmaximal, characteristic, complemented
2C2×#5817C211yesmaximal, characteristic
3C2×Q8×#67C211yesmaximal, characteristic, complemented
4C22×#918C211yesmaximal, characteristic, complemented
5C2×#5228C211yesmaximal, characteristic, complemented
6C2×#5227C211yesmaximal, characteristic, complemented
7#83888C2116yesmaximal, direct product factor
8C2×#5189C211yesmaximal, characteristic, complemented
9C2×#5187C211yesmaximal, characteristic, complemented
10C2×#5186C211yesmaximal, characteristic, complemented
11C2×#5190C211yesmaximal, characteristic, complemented
12C2×#5185C211yesmaximal, characteristic, complemented
13C2×#5182C211yesmaximal, characteristic, complemented
14C2×#5184C211yesmaximal, characteristic, complemented
15C2×#5114C211yesmaximal, characteristic, complemented
16C2×#5111C211yesmaximal, characteristic, complemented
17C2×#3270—31nomaximal, Sylow
18C23×C3×Q8C2211yescharacteristic
19C23×C3×Q8C2211yescharacteristic
20C22×#239C2211yescharacteristic
21C22×D3×Q8C2211yescharacteristic
22C22×C3×Q16—28no—
23C22×C3×Q16C2211yescharacteristic
24C22×C3×Q16C2211yescharacteristic
25C22×C3×Q16C2211yescharacteristic
26C22×C3×Q16C2211yescharacteristic
27C22×C3×Q16C2218yescomplemented
28C23×C3×C8C2211yescharacteristic
29#5817—24no—
30#5817C2218yes—
31Q8×#67—24no—
32Q8×#67C2218yescomplemented
33C2×#947—21no—
34C2×#947C2211yescharacteristic
35C2×#946—21no—
36C2×#946—21no—
37C2×#946C2211yescharacteristic
38C2×#946C2211yescharacteristic
39C2×Q8×Dic3C2211yescharacteristic
40C2×Q8×Dic3C2211yescharacteristic
41C2×#944—21no—
42C2×#944C2211yescharacteristic
43C22×#216C2211yescharacteristic
44C22×#216C2211yescharacteristic
45C22×#215C2211yescharacteristic
46C22×#215C2211yescharacteristic
47C2×#930—21no—
48C2×#930C2211yescharacteristic
49C2×C4×#67—21no—
50C2×C4×#67—21no—
51C2×C4×#67C2211yescharacteristic
52C2×#924—21no—
53C2×#924C2211yescharacteristic
54C2×#918—28no—
55C2×#918C2218yescomplemented
56C22×#204C2211yescharacteristic
57C22×ΓL(1,𝔽25)C2211yescharacteristic
58#5228C2218yescomplemented
59#5227C2218yescomplemented
60C2×#835C2211yescharacteristic
61C2×#835C2211yescharacteristic
62C2×#835C2211yescharacteristic
63C2×#835C2211yescharacteristic
64C2×#830C2211yescharacteristic
65#5190C2218yescomplemented
66#5189C2218yescomplemented
67#5187C2218yescomplemented
68#5186C2218yescomplemented
69#5185C2218yescomplemented
70#5184C2218yescomplemented
71#5182C2218yescomplemented
72#5114C2218yescomplemented
73C2×#821C2211yescharacteristic
74#5111C2218yescomplemented
75C2×(C2×D3)⋊C8C2211yescharacteristic
76C2×#817C2211yescharacteristic
77C2×#816C2211yescharacteristic
78C2×#815C2211yescharacteristic
79C2×Dic3⋊C8C2211yescharacteristic
80C22×#137—31no—
81C23×Q16D311yescharacteristic, complemented
82C2×D4×Q8—31no—
83C2×#548—31no—
84#3270—316no—
85C2×#497—31no—
86C2×#470—31no—
87C2×#465—31no—
88C2×#464—31no—
89C2×#462—31no—
90C2×#452—31no—
91C2×#451—31no—
92C2×#451—31no—
93C2×#448—31no—
94C2×#441—31no—
95C2×#435—31no—
96C22×C3×Q8—21no—
97C22×C3×Q8—21no—
98C22×C3×Q8—22no—
99C22×C3×Q8—22no—
100C22×C3×Q8—24no—
101C22×C3×Q8—24no—
102C22×C3×Q8—42no—
103C22×C3×Q8—42no—
104C22×C3×Q8C2311yescharacteristic
105C22×C3×Q8C2311yescharacteristic
106C22×C3×Q8C2314yes—
107C22×C3×Q8C2314yes—
108C22×C3×Q8C2311yescharacteristic
109C22×C3×Q8C2311yescharacteristic
110C23×C3×C4—21no—
111C23×C3×C4—21no—
112C23×C3×C4C2311yescharacteristic
113C22×#67—21no—
114C22×#67D411yescharacteristic
115C2×#239—22no—
116C2×#239—24no—
117C2×#239—42no—
118C2×#239C2314yes—
119C2×D3×Q8—22no—
120C2×D3×Q8—24no—
121C2×D3×Q8—42no—
122C2×D3×Q8C2314yes—
123C22×D12—21no—
124C22×D12C2311yescharacteristic
125C22×C4×D3—21no—
126C22×C4×D3—21no—
127C22×C4×D3C2311yescharacteristic
128C22×Dic6—21no—
129C22×Dic6C2311yescharacteristic
130C2×C3×Q16—24no—
131C2×C3×Q16—24no—
132C2×C3×Q16—232no—
133C2×C3×Q16—24no—
134C2×C3×Q16D418yescomplemented
135C2×C3×Q16C2314yes—
136C2×C3×Q16C2314yes—
137C2×C3×Q16C2314yes—
138C2×C3×Q16C2314yes—
139C22×C3×C8—24no—
140C22×C3×C8C2311yescharacteristic
141C22×C3×C8C2314yes—
142C22×C3×C8C2311yescharacteristic
143C2×#217—21no—
144C2×#217D411yescharacteristic
145#947—28no—
146#947—22no—
147#947C2314yes—
148#946—22no—
149#946—22no—
150#946—28no—
151#946—28no—
152#946C2314yes—
153#946C2314yes—
154Q8×Dic3—22no—
155Q8×Dic3—22no—
156Q8×Dic3C2314yes—
157Q8×Dic3C2314yes—
158#944—28no—
159#944—22no—
160#944C2314yes—
161C2×#216—24no—
162C2×#216—42no—
163C2×#216C2314yes—
164C2×#216C2314yes—
165C2×#215—24no—
166C2×#215—42no—
167C2×#215C2314yes—
168C2×#215C2314yes—
169#930—22no—
170#930—28no—
171#930C2314yes—
172C4×#67—28no—
173C4×#67—28no—
174C4×#67D414yes—
175C4×#67C2314yes—
176C2×(C2×D3)⋊C4—21no—
177C2×(C2×D3)⋊C4—21no—
178C2×(C2×D3)⋊C4—21no—
179C2×(C2×D3)⋊C4—21no—
180C2×(C2×D3)⋊C4—21no—
181C2×(C2×D3)⋊C4D411yescharacteristic
182C2×C4⋊Dic3—21no—
183C2×C4⋊Dic3—21no—
184C2×C4⋊Dic3C2311yescharacteristic
185C2×C4⋊Dic3C2311yescharacteristic
186#924—22no—
187#924—28no—
188#924C2314yes—
189C2×Dic3⋊C4—21no—
190C2×Dic3⋊C4—21no—
191C2×Dic3⋊C4—21no—
192C2×Dic3⋊C4—21no—
193C2×Dic3⋊C4—21no—
194C2×Dic3⋊C4D411yescharacteristic
195C2×C4×Dic3—21no—
196C2×C4×Dic3—21no—
197C2×C4×Dic3C2311yescharacteristic
198C22×C3⋊C8C2311yescharacteristic
199C22×C3⋊C8C2311yescharacteristic
200#918—232no—
201C2×#204—24no—
202C2×#204C2314yes—
203C2×ΓL(1,𝔽25)—24no—
204C2×ΓL(1,𝔽25)C2314yes—
205#835C2314yes—
206#835C2314yes—
207#835C2314yes—
208#835C2314yes—
209#830C2314yes—
210#821C2314yes—
211(C2×D3)⋊C8C2314yes—
212#817C2314yes—
213#816C2314yes—
214#815C2314yes—
215Dic3⋊C8C2314yes—
216C22×#41—31no—
217C23×Q8—31no—
218C23×Q8C2×D311yescharacteristic
219C23×Q8C2×D311yescharacteristic
220C2×#137—38no—
221C2×#137—68no—
222C22×Q16—28no—
223C22×Q16—31no—
224C22×Q16—31no—
225C22×Q16C2×D311yescharacteristic
226C22×Q16C2×D311yescharacteristic
227C22×Q16C2×D311yescharacteristic
228C22×Q16C2×D311yescharacteristic
229C22×Q16C2×D318yescomplemented
230C22×SD16—31no—
231C22×SD16—31no—
232C22×SD16—31no—
233C22×M16—31no—
234C23×C8C2×D311yescharacteristic
235D4×Q8—38no—
236D4×Q8—64no—
237#548—38no—
238#548—64no—
239C2×C4⋊Q8—31no—
240C2×C4⋊Q8—61no—
241C2×#124—31no—
242C2×#124—61no—
243C2×C22⋊Q8—31no—
244C2×C22⋊Q8—31no—
245C2×C22⋊Q8—31no—
246C2×C22⋊Q8—61no—
247C2×C22⋊Q8—61no—
248C2×C22⋊Q8—61no—
249C2×#121—31no—
250C2×#121—61no—
251C2×C4×Q8—31no—
252C2×C4×Q8—31no—
253C2×C4×D4—31no—
254C2×C4×D4—61no—
255C2×C4×D4—61no—
256#497—38no—
257#470—38no—
258#465—38no—
259#464—38no—
260#462—38no—
261#452—38no—
262#451—38no—
263#451—38no—
264#448—38no—
265#441—38no—
266#435—38no—
267C2×#106—31no—
268C2×C4⋊C8—31no—
269C2×#103—31no—
270C2×#103—31no—
271C2×#103—31no—
272C2×#103—31no—
273C2×#103—31no—
274C2×#102—31no—
275C2×C22⋊C8—31no—
276C2×C22⋊C8—31no—
277C2×#97—31no—
278C24×C3C2×D411yescharacteristic
279C23×D3—21no—
280C23×D3C2×D411yescharacteristic
281C2×C3×Q8—21no—
282C2×C3×Q8—21no—
283C2×C3×Q8—24no—
284C2×C3×Q8—21no—
285C2×C3×Q8—24no—
286C2×C3×Q8—21no—
287C2×C3×Q8—22no—
288C2×C3×Q8—22no—
289C2×C3×Q8—28no—
290C2×C3×Q8—28no—
291C2×C3×Q8—22no—
292C2×C3×Q8—22no—
293C2×C3×Q8—22no—
294C2×C3×Q8—22no—
295C2×C3×Q8—44no—
296C2×C3×Q8—44no—
297C2×C3×Q8—44no—
298C2×C3×Q8—44no—
299C2×C3×Q8—48no—
300C2×C3×Q8—48no—
301C2×C3×Q8C2×D414yes—
302C2×C3×Q8C2×D414yes—
303C2×C3×Q8C2412yes—
304C2×C3×Q8C2412yes—
305C2×C3×Q8C2412yes—
306C2×C3×Q8C2412yes—
307C22×C3×C4—21no—
308C22×C3×C4—21no—
309C22×C3×C4—22no—
310C22×C3×C4—22no—
311C22×C3×C4—21no—
312C22×C3×C4—21no—
313C22×C3×C4—24no—
314C22×C3×C4—24no—
315C22×C3×C4—44no—
316C22×C3×C4—44no—
317C22×C3×C4C2×D411yescharacteristic
318C22×C3×C4C2×D412yes—
319C22×C3×C4C2412yes—
320C22×C3×C4C2411yescharacteristic
321C2×#67—24no—
322C2×#67—24no—
323C2×#67—44no—
324C2×#67C2×D414yes—
325C22×Dic3—21no—
326C22×Dic3—21no—
327C22×Dic3—21no—
328C22×Dic3C2×D411yescharacteristic
329C22×Dic3C2×D411yescharacteristic
330C22×Dic3C2×D411yescharacteristic
331#239—28no—
332#239—44no—
333#239—48no—
334D3×Q8—28no—
335D3×Q8—44no—
336D3×Q8—48no—
337C2×D12—22no—
338C2×D12—22no—
339C2×D12—24no—
340C2×D12—21no—
341C2×D12—44no—
342C2×D12C2412yes—
343C2×C4×D3—22no—
344C2×C4×D3—22no—
345C2×C4×D3—24no—
346C2×C4×D3—24no—
347C2×C4×D3—44no—
348C2×C4×D3—44no—
349C2×C4×D3C2×D412yes—
350C2×C4×D3C2412yes—
351C2×Dic6—22no—
352C2×Dic6—22no—
353C2×Dic6—21no—
354C2×Dic6—24no—
355C2×Dic6—44no—
356C2×Dic6C2412yes—
357C3×Q16—28no—
358C3×Q16—28no—
359C3×Q16—28no—
360C3×Q16C2×D4116yescomplemented
361C2×C3×C8—22no—
362C2×C3×C8—28no—
363C2×C3×C8C2×D414yes—
364C2×C3×C8C2412yes—
365C2×C3×C8C2412yes—
366#217—24no—
367#217C2×D414yes—
368#216—28no—
369#216—44no—
370#215—28no—
371#215—44no—
372(C2×D3)⋊C4—24no—
373(C2×D3)⋊C4—24no—
374(C2×D3)⋊C4—24no—
375(C2×D3)⋊C4—24no—
376(C2×D3)⋊C4—24no—
377(C2×D3)⋊C4C2×D414yes—
378C4⋊Dic3—21no—
379C4⋊Dic3—21no—
380C4⋊Dic3—24no—
381C4⋊Dic3—24no—
382C4⋊Dic3C2412yes—
383C4⋊Dic3C2412yes—
384Dic3⋊C4—24no—
385Dic3⋊C4—24no—
386Dic3⋊C4—24no—
387Dic3⋊C4—24no—
388Dic3⋊C4—24no—
389Dic3⋊C4C2×D414yes—
390C4×Dic3—24no—
391C4×Dic3—24no—
392C4×Dic3C2×D412yes—
393C4×Dic3C2412yes—
394C2×C3⋊C8—22no—
395C2×C3⋊C8—22no—
396C2×C3⋊C8C2412yes—
397C2×C3⋊C8C2412yes—
398#204—28no—
399ΓL(1,𝔽25)—28no—
400C2×#41—34no—
401C2×#41—62no—
402C2×#41—64no—
403C2×#41—122no—
404C22×Q8—21no—
405C22×Q8—21no—
406C22×Q8—22no—
407C22×Q8—22no—
408C22×Q8—24no—
409C22×Q8—24no—
410C22×Q8—34no—
411C22×Q8—31no—
412C22×Q8—42no—
413C22×Q8—42no—
414C22×Q8—61no—
415C22×Q8—62no—
416C22×Q8—64no—
417C22×Q8—122no—
418C22×Q8C22×D311yescharacteristic
419C22×Q8C22×D311yescharacteristic
420C22×Q8C22×D314yes—
421C22×Q8C22×D314yes—
422C22×Q8C22×D311yescharacteristic
423C22×Q8C22×D311yescharacteristic
424C22×D4—31no—
425C22×D4—31no—
426C22×D4—61no—
427C22×D4—61no—
428C23×C4—21no—
429C23×C4—21no—
430C23×C4—31no—
431C23×C4—61no—
432C23×C4—61no—
433C23×C4C22×D311yescharacteristic
434#137—632no—
435C2×Q16—24no—
436C2×Q16—24no—
437C2×Q16—232no—
438C2×Q16—24no—
439C2×Q16—34no—
440C2×Q16—34no—
441C2×Q16—64no—
442C2×Q16—122no—
443C2×Q16#6718yescomplemented
444C2×Q16C22×D314yes—
445C2×Q16C22×D314yes—
446C2×Q16C22×D314yes—
447C2×Q16C22×D314yes—
448C2×SD16—34no—
449C2×SD16—34no—
450C2×SD16—34no—
451C2×SD16—64no—
452C2×SD16—64no—
453C2×SD16—122no—
454C2×M16—34no—
455C2×M16—64no—
456C22×C8—24no—
457C22×C8—31no—
458C22×C8—31no—
459C22×C8C22×D311yescharacteristic
460C22×C8C22×D314yes—
461C22×C8C22×D311yescharacteristic
462C4⋊Q8—34no—
463C4⋊Q8—62no—
464C4⋊Q8—68no—
465#124—34no—
466#124—62no—
467#124—68no—
468C22⋊Q8—34no—
469C22⋊Q8—34no—
470C22⋊Q8—34no—
471C22⋊Q8—68no—
472C22⋊Q8—68no—
473C22⋊Q8—68no—
474C22⋊Q8—62no—
475C22⋊Q8—62no—
476C22⋊Q8—62no—
477#121—34no—
478#121—68no—
479#121—62no—
480C4×Q8—34no—
481C4×Q8—34no—
482C4×Q8—62no—
483C4×Q8—62no—
484C4×D4—34no—
485C4×D4—34no—
486C4×D4—68no—
487C4×D4—68no—
488C2×C4⋊C4—31no—
489C2×C4⋊C4—31no—
490C2×C4⋊C4—31no—
491C2×C4⋊C4—61no—
492C2×C4⋊C4—61no—
493C2×C4⋊C4—61no—
494C2×C4⋊C4—61no—
495C2×C4⋊C4—61no—
496C2×C4⋊C4—61no—
497C2×C4⋊C4—61no—
498C2×C22⋊C4—31no—
499C2×C22⋊C4—31no—
500C2×C22⋊C4—61no—
501C2×C22⋊C4—61no—
502C2×C22⋊C4—61no—
503C2×C22⋊C4—61no—
504C2×C22⋊C4—61no—
505C2×C22⋊C4—61no—
506C2×C42—31no—
507C2×C42—61no—
508C2×C42—61no—
509#106—34no—
510C4⋊C8—34no—
511#103—34no—
512#103—34no—
513#103—34no—
514#103—34no—
515#103—34no—
516#102—34no—
517C22⋊C8—34no—
518C22⋊C8—34no—
519#97—34no—
520C23×C3—22no—
521C23×C3—22no—
522C23×C3#13714yescomplemented
523C23×C3C22×D412yes—
524C23×C3C22×D411yescharacteristic
525C22×D3—22no—
526C22×D3—22no—
527C22×D3—22no—
528C22×D3—22no—
529C22×D3—42no—
530C22×D3—42no—
531C22×D3—42no—
532C22×D3C22×D412yes—
533C3×Q8—24no—
534C3×Q8—24no—
535C3×Q8—22no—
536C3×Q8—22no—
537C3×Q8—22no—
538C3×Q8—22no—
539C3×Q8—22no—
540C3×Q8—22no—
541C3×Q8—48no—
542C3×Q8—48no—
543C3×Q8—42no—
544C3×Q8—42no—
545C3×Q8C22×D414yes—
546C3×Q8C22×D414yes—
547C2×C3×C4—24no—
548C2×C3×C4—24no—
549C2×C3×C4—22no—
550C2×C3×C4—22no—
551C2×C3×C4—22no—
552C2×C3×C4—24no—
553C2×C3×C4—22no—
554C2×C3×C4—22no—
555C2×C3×C4—22no—
556C2×C3×C4—22no—
557C2×C3×C4—48no—
558C2×C3×C4—48no—
559C2×C3×C4—42no—
560C2×C3×C4—42no—
561C2×C3×C4C22×D412yes—
562C2×C3×C4C22×D411yescharacteristic
563C2×C3×C4C22×D412yes—
564C2×C3×C4H(5,𝔽2)12yes—
565C2×C3×C4C2511yescharacteristic
566#67—28no—
567#67—48no—
568C2×Dic3—22no—
569C2×Dic3—22no—
570C2×Dic3—22no—
571C2×Dic3—22no—
572C2×Dic3—22no—
573C2×Dic3—22no—
574C2×Dic3—42no—
575C2×Dic3—42no—
576C2×Dic3—42no—
577C2×Dic3C22×D412yes—
578C2×Dic3C22×D412yes—
579C2×Dic3C22×D412yes—
580D12—22no—
581D12—22no—
582D12—48no—
583D12—42no—
584C4×D3—24no—
585C4×D3—22no—
586C4×D3—22no—
587C4×D3—48no—
588C4×D3—48no—
589Dic6—22no—
590Dic6—22no—
591Dic6—48no—
592Dic6—42no—
593C3×C8—22no—
594C3×C8C22×D414yes—
595C3⋊C8—22no—
596C3⋊C8—22no—
597C24—31no—
598C24—61no—
599C24D3×D411yescharacteristic
600#41—68no—
601#41—124no—
602#41—128no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—24no—
606C2×Q8—21no—
607C2×Q8—24no—
608C2×Q8—21no—
609C2×Q8—22no—
610C2×Q8—22no—
611C2×Q8—28no—
612C2×Q8—28no—
613C2×Q8—22no—
614C2×Q8—22no—
615C2×Q8—22no—
616C2×Q8—22no—
617C2×Q8—32no—
618C2×Q8—44no—
619C2×Q8—44no—
620C2×Q8—44no—
621C2×Q8—44no—
622C2×Q8—48no—
623C2×Q8—48no—
624C2×Q8—64no—
625C2×Q8—61no—
626C2×Q8—68no—
627C2×Q8—62no—
628C2×Q8—62no—
629C2×Q8—124no—
630C2×Q8—124no—
631C2×Q8—128no—
632C2×Q8C2×#6714yes—
633C2×Q8C2×#6714yes—
634C2×Q8C23×D312yes—
635C2×Q8C23×D312yes—
636C2×Q8C23×D312yes—
637C2×Q8C23×D312yes—
638C2×D4—34no—
639C2×D4—32no—
640C2×D4—64no—
641C2×D4—64no—
642C2×D4—64no—
643C2×D4—61no—
644C2×D4—62no—
645C2×D4—62no—
646C2×D4—124no—
647C2×D4—124no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—24no—
653C22×C4—24no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—31no—
657C22×C4—31no—
658C22×C4—31no—
659C22×C4—32no—
660C22×C4—32no—
661C22×C4—44no—
662C22×C4—44no—
663C22×C4—64no—
664C22×C4—64no—
665C22×C4—62no—
666C22×C4—62no—
667C22×C4—61no—
668C22×C4—61no—
669C22×C4—61no—
670C22×C4—124no—
671C22×C4—124no—
672C22×C4D3×D412yes—
673C22×C4D3×D411yescharacteristic
674C22×C4C23×D312yes—
675C22×C4C23×D311yescharacteristic
676Q16—28no—
677Q16—28no—
678Q16—28no—
679Q16—68no—
680Q16—124no—
681Q16C2×#67116yescomplemented
682SD16—68no—
683SD16—68no—
684SD16—124no—
685M16—68no—
686C2×C8—22no—
687C2×C8—28no—
688C2×C8—32no—
689C2×C8—32no—
690C2×C8—62no—
691C2×C8—62no—
692C2×C8C2×#6714yes—
693C2×C8C23×D312yes—
694C2×C8C23×D312yes—
695C4⋊C4—34no—
696C4⋊C4—32no—
697C4⋊C4—32no—
698C4⋊C4—64no—
699C4⋊C4—64no—
700C4⋊C4—64no—
701C4⋊C4—64no—
702C4⋊C4—64no—
703C4⋊C4—64no—
704C4⋊C4—61no—
705C4⋊C4—61no—
706C4⋊C4—64no—
707C22⋊C4—34no—
708C22⋊C4—34no—
709C22⋊C4—64no—
710C22⋊C4—64no—
711C22⋊C4—64no—
712C22⋊C4—64no—
713C22⋊C4—64no—
714C22⋊C4—64no—
715C42—32no—
716C42—32no—
717C42—64no—
718C42—64no—
719C22×C3—22no—
720C22×C3—28no—
721C22×C3—22no—
722C22×C3D4212yes—
723C22×C3C2×#13712yes—
724C22×C3C2×#13714yescomplemented
725C22×C3#57812yes—
726C22×C3C23×D411yescharacteristic
727C2×D3—22no—
728C2×D3—22no—
729C2×D3—22no—
730C2×D3—44no—
731C2×D3—42no—
732C2×D3—42no—
733C2×D3—42no—
734C2×D3—84no—
735C3×C4—24no—
736C3×C4—24no—
737C3×C4—22no—
738C3×C4—42no—
739C3×C4—42no—
740C3×C4D4212yes—
741C3×C4C23×D411yescharacteristic
742C3×C4C2×H(5,𝔽2)11yescharacteristic
743Dic3—22no—
744Dic3—22no—
745Dic3—22no—
746Dic3—42no—
747Dic3—42no—
748Dic3—42no—
749C23—22no—
750C23—22no—
751C23—32no—
752C23—62no—
753C23—62no—
754C23—62no—
755C23—62no—
756C23—122no—
757C23—122no—
758C23—122no—
759C23#91814yescomplemented
760C23C2×D3×D412yes—
761C23C2×D3×D411yescharacteristic
762Q8—22no—
763Q8—22no—
764Q8—24no—
765Q8—24no—
766Q8—22no—
767Q8—22no—
768Q8—22no—
769Q8—22no—
770Q8—48no—
771Q8—48no—
772Q8—42no—
773Q8—42no—
774Q8—62no—
775Q8—62no—
776Q8—128no—
777Q8—122no—
778Q8C22×#6714yes—
779Q8C22×#6714yes—
780D4—68no—
781D4—62no—
782D4—62no—
783D4—128no—
784D4—128no—
785D4—122no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—24no—
790C2×C4—24no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—24no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—32no—
797C2×C4—32no—
798C2×C4—32no—
799C2×C4—48no—
800C2×C4—48no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—62no—
804C2×C4—62no—
805C2×C4—62no—
806C2×C4—62no—
807C2×C4—62no—
808C2×C4—64no—
809C2×C4—62no—
810C2×C4—62no—
811C2×C4—62no—
812C2×C4—128no—
813C2×C4—128no—
814C2×C4—122no—
815C2×C4—122no—
816C2×C4—122no—
817C2×C4C2×D3×D412yes—
818C2×C4C2×D3×D411yescharacteristic
819C2×C4#100412yes—
820C2×C4C22×#6712yes—
821C2×C4C24×D311yescharacteristic
822C8—22no—
823C8—62no—
824C8—62no—
825C8C22×#6714yes—
826C2×C3—24no—
827C2×C3#327014yescomplemented
828C2×C3C2×D4211yescharacteristic
829C2×C3C22×#13711yescharacteristic
830C2×C3C2×#57811yescharacteristic
831D3—42no—
832D3—82no—
833C22—22no—
834C22—28no—
835C22—22no—
836C22—62no—
837C22—62no—
838C22—62no—
839C22—124no—
840C22—122no—
841C22—122no—
842C22—122no—
843C22—244no—
844C22C2×#91812yes—
845C22C2×#91814yescomplemented
846C22#576612yes—
847C22D4×#6712yes—
848C22C22×D3×D411yescharacteristic
849C4—22no—
850C4—24no—
851C4—24no—
852C4—42no—
853C4—42no—
854C4—62no—
855C4—62no—
856C4—62no—
857C4—122no—
858C4—122no—
859C4—122no—
860C4D4×#6712yes—
861C4C2×#100411yescharacteristic
862C4C23×#6711yescharacteristic
863C3C2×#327011yescharacteristic, complemented, Sylow
864C2—24no—
865C2—122no—
866C2—242no—
867C2#8388814yesdirect product factor
868C2C22×#91811yescharacteristic
869C2C2×#576611yescharacteristic
870C2C2×D4×#6711yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC23×C3×Q16C2
socleC23×C3C22×D4
prime radicalC2×#5817C2
hypercenterC23×Q16D3
hypocenterC3C2×#3270
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×Q16

Complements

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

NH ≅ G/Ntype
1. C23×C3×Q16C2semidirect
3. C2×Q8×#67C2semidirect
4. C22×#918C2semidirect
5. C2×#5228C2semidirect
6. C2×#5227C2semidirect
7. #83888C2direct (N × H)
8. C2×#5189C2semidirect
9. C2×#5187C2semidirect
10. C2×#5186C2semidirect
11. C2×#5190C2semidirect
12. C2×#5185C2semidirect
13. C2×#5182C2semidirect
14. C2×#5184C2semidirect
15. C2×#5114C2semidirect
16. C2×#5111C2semidirect
27. C22×C3×Q16C22semidirect
32. Q8×#67C22semidirect
55. C2×#918C22semidirect
58. #5228C22semidirect
59. #5227C22semidirect
65. #5190C22semidirect
66. #5189C22semidirect
67. #5187C22semidirect
68. #5186C22semidirect
69. #5185C22semidirect
70. #5184C22semidirect
71. #5182C22semidirect
72. #5114C22semidirect
74. #5111C22semidirect
81. C23×Q16D3semidirect
134. C2×C3×Q16D4semidirect
229. C22×Q16C2×D3semidirect
360. C3×Q16C2×D4semidirect
443. C2×Q16#67semidirect
522. C23×C3#137semidirect
681. Q16C2×#67semidirect
724. C22×C3C2×#137semidirect
759. C23#918semidirect
827. C2×C3#3270semidirect
845. C22C2×#918semidirect
863. C3C2×#3270semidirect
867. C2#83888direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×Q162
C2×#58172
C2×Q8×#672
C22×#9182
C2×#52282
C2×#52272
#838882
C2×#51892
C2×#51872
C2×#51862
C2×#51902
C2×#51852
C2×#51822
C2×#51842
C2×#51142
C2×#51112
C2×#32703