Finite Group Databasebeta

← C2×#83994 #11670339

Subgroups — C2×#83994 #11670339

Order 768.

2762 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#137C211yesmaximal, characteristic, complemented
2C2×#5831C211yesmaximal, characteristic, complemented
3C2×#5817C211yesmaximal, characteristic, complemented
4C22×#918C211yesmaximal, characteristic, complemented
5C2×#5238C211yesmaximal, characteristic, complemented
6C2×#5228C211yesmaximal, characteristic, complemented
7#83994C2116yesmaximal, direct product factor
8C2×#5186C211yesmaximal, characteristic, complemented
9C2×#5185C211yesmaximal, characteristic, complemented
10C2×Dic3×Q16C211yesmaximal, characteristic, complemented
11C2×#5174C211yesmaximal, characteristic, complemented
12C2×#5172C211yesmaximal, characteristic, complemented
13C2×#5168C211yesmaximal, characteristic, complemented
14C2×#5166C211yesmaximal, characteristic, complemented
15C2×#5134C211yesmaximal, characteristic, complemented
16C2×#5128C211yesmaximal, characteristic, complemented
17C2×#3277—31nomaximal, Sylow
18C22×C3×#41C2211yescharacteristic
19C23×C3×Q8C2211yescharacteristic
20C22×#239C2211yescharacteristic
21C22×D3×Q8C2211yescharacteristic
22C2×C3×#137—28no—
23C2×C3×#137C2218yescomplemented
24C22×C3×Q16C2211yescharacteristic
25C22×C3×Q16C2211yescharacteristic
26C22×C3×SD16C2211yescharacteristic
27C22×C3×SD16C2211yescharacteristic
28C22×C3×M16C2211yescharacteristic
29#5831—24no—
30#5831C2218yescomplemented
31#5817—24no—
32#5817C2218yescomplemented
33C2×#947—21no—
34C2×#947C2211yescharacteristic
35C2×#946—21no—
36C2×#946C2211yescharacteristic
37C2×Q8×Dic3C2211yescharacteristic
38C2×Q8×Dic3C2211yescharacteristic
39C22×#216C2211yescharacteristic
40C22×#216C2211yescharacteristic
41C22×#215C2211yescharacteristic
42C2×#938—21no—
43C2×#938C2211yescharacteristic
44C2×#936—21no—
45C2×#936C2211yescharacteristic
46C22×#213C2211yescharacteristic
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#5238C2218yescomplemented
59#5228C2218yescomplemented
60C2×#835C2211yescharacteristic
61C2×#835C2211yescharacteristic
62C2×#835C2211yescharacteristic
63C2×#832C2211yescharacteristic
64C2×#830C2211yescharacteristic
65#5186C2218yescomplemented
66#5185C2218yescomplemented
67Dic3×Q16C2218yescomplemented
68#5174C2218yescomplemented
69#5172C2218yescomplemented
70#5168C2218yescomplemented
71#5166C2218yescomplemented
72#5134C2218yescomplemented
73#5128C2218yescomplemented
74C2×#821C2211yescharacteristic
75C2×(C2×D3)⋊C8C2211yescharacteristic
76C2×#818C2211yescharacteristic
77C2×#816C2211yescharacteristic
78C2×Dic3⋊C8C2211yescharacteristic
79C2×C8×Dic3C2211yescharacteristic
80C22×#137—31no—
81C22×#137D311yescharacteristic, complemented
82C2×#548—31no—
83C2×#548—31no—
84#3277—316no—
85C2×#495—31no—
86C2×#468—31no—
87C2×#468—31no—
88C2×#464—31no—
89C2×#464—31no—
90C2×#449—31no—
91C2×#449—31no—
92C2×#451—31no—
93C2×#451—31no—
94C2×C4×Q16—31no—
95C2×#436—31no—
96C2×C3×#41—22no—
97C2×C3×#41—24no—
98C2×C3×#41—42no—
99C2×C3×#41C2314yes—
100C22×C3×Q8—21no—
101C22×C3×Q8—22no—
102C22×C3×Q8—24no—
103C22×C3×Q8—42no—
104C22×C3×Q8C2311yescharacteristic
105C22×C3×Q8C2314yes—
106C22×C3×Q8C2311yescharacteristic
107C22×C3×Q8C2311yescharacteristic
108C22×C3×D4—21no—
109C22×C3×D4C2311yescharacteristic
110C23×C3×C4—21no—
111C23×C3×C4—21no—
112C23×C3×C4C2311yescharacteristic
113C22×#67—21no—
114C22×#67—21no—
115C22×#67D411yescharacteristic
116C2×#239—22no—
117C2×#239—24no—
118C2×#239—42no—
119C2×#239C2314yes—
120C2×D3×Q8—22no—
121C2×D3×Q8—24no—
122C2×D3×Q8—42no—
123C2×D3×Q8C2314yes—
124C22×D12—21no—
125C22×D12C2311yescharacteristic
126C22×C4×D3—21no—
127C22×C4×D3—21no—
128C22×C4×D3C2311yescharacteristic
129C22×Dic6—21no—
130C22×Dic6C2311yescharacteristic
131C3×#137—232no—
132C2×C3×Q16—24no—
133C2×C3×Q16D418yescomplemented
134C2×C3×Q16C2314yes—
135C2×C3×Q16C2314yes—
136C2×C3×SD16—24no—
137C2×C3×SD16—24no—
138C2×C3×SD16C2314yes—
139C2×C3×SD16C2314yes—
140C2×C3×M16—24no—
141C2×C3×M16C2314yes—
142C22×C3×C8C2311yescharacteristic
143C22×C3×C8C2311yescharacteristic
144C2×#217—21no—
145C2×#217—21no—
146C2×#217—21no—
147C2×#217—21no—
148C2×#217D411yescharacteristic
149#947—28no—
150#947—22no—
151#947C2314yes—
152#946—22no—
153#946—28no—
154#946C2314yes—
155Q8×Dic3—22no—
156Q8×Dic3—22no—
157Q8×Dic3C2314yes—
158Q8×Dic3C2314yes—
159C2×#216—24no—
160C2×#216—42no—
161C2×#216C2314yes—
162C2×#216C2314yes—
163C2×#215—24no—
164C2×#215C2314yes—
165#938—28no—
166#938—22no—
167#938C2314yes—
168#936—28no—
169#936—22no—
170#936C2314yes—
171C2×#213—42no—
172C2×#213C2314yes—
173#930—22no—
174#930—28no—
175#930C2314yes—
176C4×#67—28no—
177C4×#67—28no—
178C4×#67D414yes—
179C4×#67C2314yes—
180C2×(C2×D3)⋊C4—21no—
181C2×(C2×D3)⋊C4—21no—
182C2×(C2×D3)⋊C4—21no—
183C2×(C2×D3)⋊C4—21no—
184C2×(C2×D3)⋊C4D411yescharacteristic
185C2×C4⋊Dic3—21no—
186C2×C4⋊Dic3—21no—
187C2×C4⋊Dic3C2311yescharacteristic
188C2×C4⋊Dic3C2311yescharacteristic
189#924—22no—
190#924—28no—
191#924C2314yes—
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#832C2314yes—
209#830C2314yes—
210#821C2314yes—
211(C2×D3)⋊C8C2314yes—
212#818C2314yes—
213#816C2314yes—
214Dic3⋊C8C2314yes—
215C8×Dic3C2314yes—
216C22×#41—31no—
217C22×#41C2×D311yescharacteristic
218C23×Q8—31no—
219C23×Q8C2×D311yescharacteristic
220C2×#137—28no—
221C2×#137—38no—
222C2×#137—68no—
223C2×#137C2×D318yescomplemented
224C22×Q16—31no—
225C22×Q16—31no—
226C22×Q16C2×D311yescharacteristic
227C22×Q16C2×D311yescharacteristic
228C22×SD16—31no—
229C22×SD16—31no—
230C22×SD16C2×D311yescharacteristic
231C22×SD16C2×D311yescharacteristic
232C22×D8—31no—
233C22×M16—31no—
234C22×M16C2×D311yescharacteristic
235#548—38no—
236#548—38no—
237#548—64no—
238#548—64no—
239C2×#124—31no—
240C2×#124—31no—
241C2×#124—61no—
242C2×#124—61no—
243C2×C22⋊Q8—31no—
244C2×C22⋊Q8—31no—
245C2×C22⋊Q8—61no—
246C2×C22⋊Q8—61no—
247C2×#121—31no—
248C2×#121—31no—
249C2×#121—61no—
250C2×#121—61no—
251C2×C4×Q8—31no—
252C2×C4×Q8—31no—
253C2×C4×D4—31no—
254C2×C4×D4—61no—
255C2×C4×D4—61no—
256#495—38no—
257#468—38no—
258#468—38no—
259#464—38no—
260#464—38no—
261#451—38no—
262#451—38no—
263#449—38no—
264#449—38no—
265C4×Q16—38no—
266#436—38no—
267C2×#107—31no—
268C2×C4⋊C8—31no—
269C2×#103—31no—
270C2×#103—31no—
271C2×#103—31no—
272C2×#103—31no—
273C2×#102—31no—
274C2×#102—31no—
275C2×C22⋊C8—31no—
276C2×C22⋊C8—31no—
277C2×C4×C8—31no—
278C24×C3—21no—
279C24×C3C2×D411yescharacteristic
280C23×D3—21no—
281C23×D3C2×D411yescharacteristic
282C3×#41—28no—
283C3×#41—44no—
284C3×#41—48no—
285C2×C3×Q8—21no—
286C2×C3×Q8—21no—
287C2×C3×Q8—24no—
288C2×C3×Q8—21no—
289C2×C3×Q8—22no—
290C2×C3×Q8—22no—
291C2×C3×Q8—28no—
292C2×C3×Q8—22no—
293C2×C3×Q8—22no—
294C2×C3×Q8—44no—
295C2×C3×Q8—44no—
296C2×C3×Q8—48no—
297C2×C3×Q8C2×D414yes—
298C2×C3×Q8C2×D414yes—
299C2×C3×Q8C2412yes—
300C2×C3×Q8C2412yes—
301C2×C3×Q8C2412yes—
302C2×C3×D4—24no—
303C2×C3×D4—22no—
304C2×C3×D4—21no—
305C2×C3×D4—22no—
306C2×C3×D4—44no—
307C2×C3×D4C2412yes—
308C22×C3×C4—21no—
309C22×C3×C4—21no—
310C22×C3×C4—22no—
311C22×C3×C4—22no—
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—42no—
324C2×#67—44no—
325C2×#67—44no—
326C2×#67C2×D414yes—
327C22×Dic3—21no—
328C22×Dic3—21no—
329C22×Dic3—21no—
330C22×Dic3C2×D411yescharacteristic
331C22×Dic3C2×D411yescharacteristic
332C22×Dic3C2×D411yescharacteristic
333#239—28no—
334#239—44no—
335#239—48no—
336D3×Q8—28no—
337D3×Q8—44no—
338D3×Q8—48no—
339C2×D12—22no—
340C2×D12—22no—
341C2×D12—24no—
342C2×D12—21no—
343C2×D12—44no—
344C2×D12C2412yes—
345C2×C4×D3—22no—
346C2×C4×D3—22no—
347C2×C4×D3—24no—
348C2×C4×D3—24no—
349C2×C4×D3—44no—
350C2×C4×D3—44no—
351C2×C4×D3C2×D412yes—
352C2×C4×D3C2412yes—
353C2×Dic6—22no—
354C2×Dic6—22no—
355C2×Dic6—21no—
356C2×Dic6—24no—
357C2×Dic6—44no—
358C2×Dic6C2412yes—
359C3×Q16—28no—
360C3×Q16C2×D4116yescomplemented
361C3×SD16—28no—
362C3×SD16—28no—
363C3×M16—28no—
364C2×C3×C8—22no—
365C2×C3×C8C2×D414yes—
366C2×C3×C8C2412yes—
367C2×C3×C8C2412yes—
368#217—24no—
369#217—24no—
370#217—24no—
371#217—24no—
372#217C2×D414yes—
373#216—28no—
374#216—44no—
375#215—28no—
376#213—44no—
377(C2×D3)⋊C4—24no—
378(C2×D3)⋊C4—24no—
379(C2×D3)⋊C4—24no—
380(C2×D3)⋊C4—24no—
381(C2×D3)⋊C4C2×D414yes—
382C4⋊Dic3—21no—
383C4⋊Dic3—21no—
384C4⋊Dic3—24no—
385C4⋊Dic3—24no—
386C4⋊Dic3C2412yes—
387C4⋊Dic3C2412yes—
388Dic3⋊C4—24no—
389Dic3⋊C4—24no—
390Dic3⋊C4C2×D414yes—
391C4×Dic3—24no—
392C4×Dic3—24no—
393C4×Dic3C2×D412yes—
394C4×Dic3C2412yes—
395C2×C3⋊C8—22no—
396C2×C3⋊C8—22no—
397C2×C3⋊C8C2412yes—
398C2×C3⋊C8C2412yes—
399#204—28no—
400ΓL(1,𝔽25)—28no—
401C2×#41—22no—
402C2×#41—24no—
403C2×#41—34no—
404C2×#41—42no—
405C2×#41—62no—
406C2×#41—64no—
407C2×#41—122no—
408C2×#41C22×D314yes—
409C22×Q8—21no—
410C22×Q8—22no—
411C22×Q8—24no—
412C22×Q8—34no—
413C22×Q8—31no—
414C22×Q8—42no—
415C22×Q8—61no—
416C22×Q8—62no—
417C22×Q8—64no—
418C22×Q8—122no—
419C22×Q8C22×D311yescharacteristic
420C22×Q8C22×D314yes—
421C22×Q8C22×D311yescharacteristic
422C22×Q8C22×D311yescharacteristic
423C22×D4—21no—
424C22×D4—31no—
425C22×D4—31no—
426C22×D4—61no—
427C22×D4—61no—
428C22×D4—61no—
429C22×D4C22×D311yescharacteristic
430C23×C4—21no—
431C23×C4—21no—
432C23×C4—31no—
433C23×C4—61no—
434C23×C4—61no—
435C23×C4C22×D311yescharacteristic
436#137—232no—
437#137—632no—
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×SD16—24no—
447C2×SD16—24no—
448C2×SD16—34no—
449C2×SD16—34no—
450C2×SD16—64no—
451C2×SD16—64no—
452C2×SD16C22×D314yes—
453C2×SD16C22×D314yes—
454C2×D8—34no—
455C2×D8—122no—
456C2×M16—24no—
457C2×M16—34no—
458C2×M16—64no—
459C2×M16C22×D314yes—
460C22×C8—31no—
461C22×C8—31no—
462C22×C8C22×D311yescharacteristic
463C22×C8C22×D311yescharacteristic
464#124—34no—
465#124—34no—
466#124—62no—
467#124—62no—
468#124—68no—
469#124—68no—
470C22⋊Q8—34no—
471C22⋊Q8—34no—
472C22⋊Q8—68no—
473C22⋊Q8—68no—
474C22⋊Q8—62no—
475C22⋊Q8—62no—
476#121—34no—
477#121—34no—
478#121—68no—
479#121—62no—
480#121—68no—
481#121—62no—
482C4×Q8—34no—
483C4×Q8—34no—
484C4×Q8—62no—
485C4×Q8—62no—
486C4×D4—34no—
487C4×D4—34no—
488C4×D4—68no—
489C4×D4—68no—
490C2×C4⋊C4—31no—
491C2×C4⋊C4—31no—
492C2×C4⋊C4—31no—
493C2×C4⋊C4—61no—
494C2×C4⋊C4—61no—
495C2×C4⋊C4—61no—
496C2×C4⋊C4—61no—
497C2×C22⋊C4—31no—
498C2×C22⋊C4—31no—
499C2×C22⋊C4—61no—
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×C22⋊C4—61no—
507C2×C42—31no—
508C2×C42—61no—
509C2×C42—61no—
510#107—34no—
511C4⋊C8—34no—
512#103—34no—
513#103—34no—
514#103—34no—
515#103—34no—
516#102—34no—
517#102—34no—
518C22⋊C8—34no—
519C22⋊C8—34no—
520C4×C8—34no—
521C23×C3—22no—
522C23×C3—22no—
523C23×C3—22no—
524C23×C3—22no—
525C23×C3—42no—
526C23×C3—42no—
527C23×C3—42no—
528C23×C3C22×D412yes—
529C23×C3C22×D411yescharacteristic
530C22×D3—22no—
531C22×D3—22no—
532C22×D3—22no—
533C22×D3—22no—
534C22×D3—42no—
535C22×D3—42no—
536C22×D3—42no—
537C22×D3C22×D412yes—
538C3×Q8—24no—
539C3×Q8—24no—
540C3×Q8—22no—
541C3×Q8—22no—
542C3×Q8—22no—
543C3×Q8—22no—
544C3×Q8—48no—
545C3×Q8—42no—
546C3×Q8C22×D414yes—
547C3×Q8C22×D414yes—
548C3×D4—22no—
549C3×D4—22no—
550C3×D4—48no—
551C3×D4—42no—
552C2×C3×C4—24no—
553C2×C3×C4—24no—
554C2×C3×C4—22no—
555C2×C3×C4—22no—
556C2×C3×C4—22no—
557C2×C3×C4—24no—
558C2×C3×C4—22no—
559C2×C3×C4—22no—
560C2×C3×C4—22no—
561C2×C3×C4—48no—
562C2×C3×C4—48no—
563C2×C3×C4—42no—
564C2×C3×C4C22×D412yes—
565C2×C3×C4C22×D411yescharacteristic
566C2×C3×C4C22×D412yes—
567C2×C3×C4H(5,𝔽2)12yes—
568C2×C3×C4C2511yescharacteristic
569#67—44no—
570#67—48no—
571#67—48no—
572C2×Dic3—22no—
573C2×Dic3—22no—
574C2×Dic3—22no—
575C2×Dic3—22no—
576C2×Dic3—22no—
577C2×Dic3—22no—
578C2×Dic3—42no—
579C2×Dic3—42no—
580C2×Dic3—42no—
581C2×Dic3C22×D412yes—
582C2×Dic3C22×D412yes—
583C2×Dic3C22×D412yes—
584D12—22no—
585D12—22no—
586D12—48no—
587D12—42no—
588C4×D3—24no—
589C4×D3—22no—
590C4×D3—22no—
591C4×D3—48no—
592C4×D3—48no—
593Dic6—22no—
594Dic6—22no—
595Dic6—48no—
596Dic6—42no—
597C3×C8—22no—
598C3×C8C22×D414yes—
599C3⋊C8—22no—
600C3⋊C8—22no—
601C24—21no—
602C24—31no—
603C24—61no—
604C24D3×D411yescharacteristic
605#41—28no—
606#41—44no—
607#41—48no—
608#41—68no—
609#41—124no—
610#41—128no—
611C2×Q8—21no—
612C2×Q8—21no—
613C2×Q8—24no—
614C2×Q8—21no—
615C2×Q8—22no—
616C2×Q8—22no—
617C2×Q8—28no—
618C2×Q8—22no—
619C2×Q8—22no—
620C2×Q8—32no—
621C2×Q8—44no—
622C2×Q8—44no—
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×D4—24no—
638C2×D4—21no—
639C2×D4—22no—
640C2×D4—22no—
641C2×D4—34no—
642C2×D4—32no—
643C2×D4—44no—
644C2×D4—64no—
645C2×D4—64no—
646C2×D4—64no—
647C2×D4—61no—
648C2×D4—62no—
649C2×D4—62no—
650C2×D4—124no—
651C2×D4—122no—
652C2×D4—124no—
653C2×D4—124no—
654C2×D4C23×D312yes—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—24no—
660C22×C4—21no—
661C22×C4—24no—
662C22×C4—31no—
663C22×C4—31no—
664C22×C4—31no—
665C22×C4—32no—
666C22×C4—32no—
667C22×C4—44no—
668C22×C4—44no—
669C22×C4—64no—
670C22×C4—64no—
671C22×C4—62no—
672C22×C4—62no—
673C22×C4—61no—
674C22×C4—61no—
675C22×C4—61no—
676C22×C4—124no—
677C22×C4—124no—
678C22×C4D3×D412yes—
679C22×C4D3×D411yescharacteristic
680C22×C4C23×D312yes—
681C22×C4C23×D311yescharacteristic
682Q16—28no—
683Q16—68no—
684Q16—124no—
685Q16C2×#67116yescomplemented
686SD16—28no—
687SD16—28no—
688SD16—68no—
689SD16—68no—
690D8—124no—
691M16—28no—
692M16—68no—
693C2×C8—22no—
694C2×C8—32no—
695C2×C8—32no—
696C2×C8—62no—
697C2×C8—62no—
698C2×C8C2×#6714yes—
699C2×C8C23×D312yes—
700C2×C8C23×D312yes—
701C4⋊C4—34no—
702C4⋊C4—32no—
703C4⋊C4—32no—
704C4⋊C4—64no—
705C4⋊C4—64no—
706C4⋊C4—64no—
707C4⋊C4—61no—
708C4⋊C4—61no—
709C4⋊C4—64no—
710C22⋊C4—34no—
711C22⋊C4—34no—
712C22⋊C4—64no—
713C22⋊C4—64no—
714C22⋊C4—64no—
715C22⋊C4—64no—
716C22⋊C4—64no—
717C22⋊C4—64no—
718C22⋊C4—64no—
719C22⋊C4—64no—
720C42—32no—
721C42—32no—
722C42—64no—
723C42—64no—
724C22×C3—22no—
725C22×C3—22no—
726C22×C3—22no—
727C22×C3—44no—
728C22×C3—42no—
729C22×C3—42no—
730C22×C3—42no—
731C22×C3—84no—
732C22×C3D4212yes—
733C22×C3#57512yes—
734C22×C3#57812yes—
735C22×C3C23×D411yescharacteristic
736C2×D3—22no—
737C2×D3—22no—
738C2×D3—22no—
739C2×D3—44no—
740C2×D3—42no—
741C2×D3—42no—
742C2×D3—42no—
743C2×D3—84no—
744C3×C4—24no—
745C3×C4—24no—
746C3×C4—22no—
747C3×C4—42no—
748C3×C4D4212yes—
749C3×C4C23×D411yescharacteristic
750C3×C4C2×H(5,𝔽2)11yescharacteristic
751Dic3—22no—
752Dic3—22no—
753Dic3—22no—
754Dic3—42no—
755Dic3—42no—
756Dic3—42no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—32no—
762C23—42no—
763C23—42no—
764C23—42no—
765C23—62no—
766C23—62no—
767C23—62no—
768C23—62no—
769C23—122no—
770C23—122no—
771C23—122no—
772C23C2×D3×D412yes—
773C23C2×D3×D411yescharacteristic
774Q8—22no—
775Q8—22no—
776Q8—24no—
777Q8—24no—
778Q8—22no—
779Q8—22no—
780Q8—48no—
781Q8—42no—
782Q8—62no—
783Q8—62no—
784Q8—128no—
785Q8—122no—
786Q8C22×#6714yes—
787Q8C22×#6714yes—
788D4—22no—
789D4—22no—
790D4—48no—
791D4—42no—
792D4—62no—
793D4—62no—
794D4—128no—
795D4—124no—
796D4—128no—
797D4—128no—
798D4—122no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—24no—
803C2×C4—24no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—24no—
807C2×C4—22no—
808C2×C4—32no—
809C2×C4—32no—
810C2×C4—32no—
811C2×C4—48no—
812C2×C4—48no—
813C2×C4—42no—
814C2×C4—62no—
815C2×C4—62no—
816C2×C4—62no—
817C2×C4—62no—
818C2×C4—62no—
819C2×C4—64no—
820C2×C4—62no—
821C2×C4—62no—
822C2×C4—62no—
823C2×C4—128no—
824C2×C4—128no—
825C2×C4—122no—
826C2×C4—122no—
827C2×C4—122no—
828C2×C4C2×D3×D412yes—
829C2×C4C2×D3×D411yescharacteristic
830C2×C4#100412yes—
831C2×C4C22×#6712yes—
832C2×C4C24×D311yescharacteristic
833C8—22no—
834C8—62no—
835C8—62no—
836C8C22×#6714yes—
837C2×C3—42no—
838C2×C3—82no—
839C2×C3#327714yescomplemented
840C2×C3C2×D4211yescharacteristic
841C2×C3C2×#57511yescharacteristic
842C2×C3C2×#57811yescharacteristic
843D3—42no—
844D3—82no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—44no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—62no—
853C22—62no—
854C22—62no—
855C22—84no—
856C22—124no—
857C22—122no—
858C22—122no—
859C22—122no—
860C22—244no—
861C22#577712yes—
862C22#577912yes—
863C22D4×#6712yes—
864C22C22×D3×D411yescharacteristic
865C4—22no—
866C4—24no—
867C4—24no—
868C4—42no—
869C4—62no—
870C4—62no—
871C4—62no—
872C4—122no—
873C4—122no—
874C4—122no—
875C4D4×#6712yes—
876C4C2×#100411yescharacteristic
877C4C23×#6711yescharacteristic
878C3C2×#327711yescharacteristic, complemented, Sylow
879C2—42no—
880C2—82no—
881C2—122no—
882C2—242no—
883C2#8399414yesdirect product factor
884C2C2×#577711yescharacteristic
885C2C2×#577911yescharacteristic
886C2C2×D4×#6711yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC22×C3×#137C2
socleC23×C3C22×D4
hypercenterC22×#137D3
hypocenterC3C2×#3277
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#137

Complements

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

NH ≅ G/Ntype
1. C22×C3×#137C2semidirect
2. C2×#5831C2semidirect
3. C2×#5817C2semidirect
4. C22×#918C2semidirect
5. C2×#5238C2semidirect
6. C2×#5228C2semidirect
7. #83994C2direct (N × H)
8. C2×#5186C2semidirect
9. C2×#5185C2semidirect
10. C2×Dic3×Q16C2semidirect
11. C2×#5174C2semidirect
12. C2×#5172C2semidirect
13. C2×#5168C2semidirect
14. C2×#5166C2semidirect
15. C2×#5134C2semidirect
16. C2×#5128C2semidirect
23. C2×C3×#137C22semidirect
30. #5831C22semidirect
32. #5817C22semidirect
55. C2×#918C22semidirect
58. #5238C22semidirect
59. #5228C22semidirect
65. #5186C22semidirect
66. #5185C22semidirect
67. Dic3×Q16C22semidirect
68. #5174C22semidirect
69. #5172C22semidirect
70. #5168C22semidirect
71. #5166C22semidirect
72. #5134C22semidirect
73. #5128C22semidirect
81. C22×#137D3semidirect
133. C2×C3×Q16D4semidirect
223. C2×#137C2×D3semidirect
360. C3×Q16C2×D4semidirect
443. C2×Q16#67semidirect
685. Q16C2×#67semidirect
839. C2×C3#3277semidirect
878. C3C2×#3277semidirect
883. C2#83994direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#1372
C2×#58312
C2×#58172
C22×#9182
C2×#52382
C2×#52282
#839942
C2×#51862
C2×#51852
C2×Dic3×Q162
C2×#51742
C2×#51722
C2×#51682
C2×#51662
C2×#51342
C2×#51282
C2×#32773