Finite Group Databasebeta

← C2×#75960 #11001078

Subgroups — C2×#75960 #11001078

Order 768.

4070 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#894C211yesmaximal, characteristic, complemented
2C22×#883C211yesmaximal, characteristic, complemented
3C22×#884C211yesmaximal, characteristic
4C22×C42×D3C211yesmaximal, characteristic, complemented
5C2×C3×#388C211yesmaximal, characteristic, complemented
6C2×#4976C211yesmaximal, characteristic, complemented
7C2×#4956C211yesmaximal, characteristic, complemented
8C2×#4957C211yesmaximal, characteristic, complemented
9C2×#4957C211yesmaximal, characteristic, complemented
10C2×#4944C211yesmaximal, characteristic, complemented
11C2×#4940C211yesmaximal, characteristic, complemented
12#75960C2116yesmaximal, direct product factor
13C2×#4665C211yesmaximal, characteristic, complemented
14C2×#4667C211yesmaximal, characteristic, complemented
15C2×#4647C211yesmaximal, characteristic, complemented
16C2×#4670C211yesmaximal, characteristic, complemented
17C2×#2854—31nomaximal, Sylow
18C23×#67C2211yescharacteristic
19C23×#67C2211yescharacteristic
20C23×D12C2211yescharacteristic
21C23×C4×D3C2211yescharacteristic
22C23×C4×D3C2211yescharacteristic
23C23×C4×D3C2211yescharacteristic
24C22×C3×C4⋊C4C2211yescharacteristic
25C22×C3×C22⋊C4C2211yescharacteristic
26C22×C3×C22⋊C4C2211yescharacteristic
27C22×C3×C22⋊C4C2211yescharacteristic
28C22×C3×C42C2211yescharacteristic
29C22×#217C2211yescharacteristic
30C22×#217C2211yescharacteristic
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×C4⋊Dic3C2211yescharacteristic
39C22×Dic3⋊C4C2211yescharacteristic
40C22×Dic3⋊C4C2211yescharacteristic
41C22×Dic3⋊C4C2211yescharacteristic
42C22×Dic3⋊C4C2211yescharacteristic
43C22×Dic3⋊C4C2211yescharacteristic
44C22×C4×Dic3C2211yescharacteristic
45C22×C4×Dic3C2211yescharacteristic
46C22×C4×Dic3C2211yescharacteristic
47C2×#894—28no—
48C2×#894C2218yescomplemented
49C2×#884—28no—
50C2×#884C2218yes—
51C2×#883—28no—
52C2×#883C2218yescomplemented
53C2×C42×D3—28no—
54C2×C42×D3C2218yescomplemented
55C3×#388C2218yescomplemented
56C2×C3×#95C2211yescharacteristic
57C2×C3×#95C2211yescharacteristic
58C2×C3⋊#95C2211yescharacteristic
59C2×C3⋊#95C2211yescharacteristic
60C2×C3⋊#95C2211yescharacteristic
61C2×C3⋊#95C2211yescharacteristic
62#4976C2218yescomplemented
63#4957C2218yescomplemented
64#4957C2218yescomplemented
65#4956C2218yescomplemented
66#4944C2218yescomplemented
67#4940C2218yescomplemented
68#4670C2218yescomplemented
69#4667C2218yescomplemented
70#4665C2218yescomplemented
71#4647C2218yescomplemented
72C22×#123—31no—
73C22×#123—31no—
74C22×#121—31no—
75C23×C42—31no—
76#2854—316no—
77C2×#390—31no—
78C2×#390—31no—
79C2×#389—31no—
80C2×#389—31no—
81C2×#388—31no—
82C2×#388—31no—
83C2×#388—31no—
84C2×#388D311yescharacteristic, complemented
85C2×#386—31no—
86C2×#386—31no—
87C2×#380—31no—
88C25×C3C2311yescharacteristic
89C24×D3C2311yescharacteristic
90C24×D3C2311yescharacteristic
91C23×C3×C4C2311yescharacteristic
92C23×C3×C4C2311yescharacteristic
93C23×C3×C4C2311yescharacteristic
94C23×C3×C4C2311yescharacteristic
95C23×C3×C4C2311yescharacteristic
96C23×C3×C4C2311yescharacteristic
97C22×#67—24no—
98C22×#67—24no—
99C22×#67—24no—
100C22×#67—24no—
101C22×#67—24no—
102C22×#67—24no—
103C22×#67C2314yes—
104C22×#67C2314yes—
105C23×Dic3C2311yescharacteristic
106C23×Dic3C2311yescharacteristic
107C23×Dic3C2311yescharacteristic
108C23×Dic3C2311yescharacteristic
109C23×Dic3C2311yescharacteristic
110C23×Dic3C2311yescharacteristic
111C22×D12—24no—
112C22×D12—24no—
113C22×D12—24no—
114C22×D12C2314yes—
115C22×C4×D3—24no—
116C22×C4×D3—24no—
117C22×C4×D3—24no—
118C22×C4×D3—24no—
119C22×C4×D3—24no—
120C22×C4×D3—24no—
121C22×C4×D3—24no—
122C22×C4×D3D418yes—
123C22×C4×D3D418yescomplemented
124C22×C4×D3C2314yes—
125C22×C4×D3C2314yes—
126C22×C4×D3C2314yes—
127C2×C3×C4⋊C4—24no—
128C2×C3×C4⋊C4C2314yes—
129C2×C3×C22⋊C4—24no—
130C2×C3×C22⋊C4—24no—
131C2×C3×C22⋊C4—24no—
132C2×C3×C22⋊C4C2314yes—
133C2×C3×C22⋊C4C2314yes—
134C2×C3×C22⋊C4C2314yes—
135C2×C3×C42—24no—
136C2×C3×C42C2314yes—
137C2×#217—24no—
138C2×#217—24no—
139C2×#217C2314yes—
140C2×#217C2314yes—
141C2×(C2×D3)⋊C4—24no—
142C2×(C2×D3)⋊C4—24no—
143C2×(C2×D3)⋊C4—24no—
144C2×(C2×D3)⋊C4—24no—
145C2×(C2×D3)⋊C4—24no—
146C2×(C2×D3)⋊C4—24no—
147C2×(C2×D3)⋊C4—24no—
148C2×(C2×D3)⋊C4C2314yes—
149C2×(C2×D3)⋊C4C2314yes—
150C2×(C2×D3)⋊C4C2314yes—
151C2×(C2×D3)⋊C4C2314yes—
152C2×(C2×D3)⋊C4C2314yes—
153C2×(C2×D3)⋊C4C2314yes—
154C2×(C2×D3)⋊C4C2314yes—
155C2×C4⋊Dic3—24no—
156C2×C4⋊Dic3C2314yes—
157C2×Dic3⋊C4—24no—
158C2×Dic3⋊C4—24no—
159C2×Dic3⋊C4—24no—
160C2×Dic3⋊C4—24no—
161C2×Dic3⋊C4—24no—
162C2×Dic3⋊C4C2314yes—
163C2×Dic3⋊C4C2314yes—
164C2×Dic3⋊C4C2314yes—
165C2×Dic3⋊C4C2314yes—
166C2×Dic3⋊C4C2314yes—
167C2×C4×Dic3—24no—
168C2×C4×Dic3—24no—
169C2×C4×Dic3—24no—
170C2×C4×Dic3C2314yes—
171C2×C4×Dic3C2314yes—
172C2×C4×Dic3C2314yes—
173#894—232no—
174#884—232no—
175#883—232no—
176C42×D3—232no—
177C3×#95C2314yes—
178C3×#95C2314yes—
179C3⋊#95C2314yes—
180C3⋊#95C2314yes—
181C3⋊#95C2314yes—
182C3⋊#95C2314yes—
183C23×D4—31no—
184C23×D4—31no—
185C23×D4—31no—
186C24×C4—31no—
187C24×C4—31no—
188C24×C4—31no—
189C2×#123—38no—
190C2×#123—38no—
191C2×#123—68no—
192C2×#123—68no—
193C2×#121—38no—
194C2×#121—68no—
195C22×C4⋊C4—31no—
196C22×C4⋊C4—31no—
197C22×C4⋊C4—31no—
198C22×C4⋊C4—31no—
199C22×C4⋊C4—31no—
200C22×C4⋊C4—31no—
201C22×C4⋊C4C2×D311yescharacteristic
202C22×C22⋊C4—31no—
203C22×C22⋊C4—31no—
204C22×C22⋊C4—31no—
205C22×C22⋊C4—31no—
206C22×C22⋊C4—31no—
207C22×C22⋊C4—31no—
208C22×C22⋊C4—31no—
209C22×C22⋊C4—31no—
210C22×C22⋊C4—31no—
211C22×C22⋊C4C2×D311yescharacteristic
212C22×C22⋊C4C2×D311yescharacteristic
213C22×C22⋊C4C2×D311yescharacteristic
214C22×C42—31no—
215C22×C42—31no—
216C22×C42—31no—
217C22×C42—38no—
218C22×C42—68no—
219C22×C42C2×D311yescharacteristic
220#390—38no—
221#390—38no—
222#389—38no—
223#389—38no—
224#388—38no—
225#388—38no—
226#388—38no—
227#388C2×D318yescomplemented
228#386—38no—
229#386—38no—
230#380—38no—
231C2×#95—31no—
232C2×#95—31no—
233C2×#95—31no—
234C2×#95—31no—
235C2×#95C2×D311yescharacteristic
236C2×#95C2×D311yescharacteristic
237C24×C3—22no—
238C24×C3—22no—
239C24×C3—22no—
240C24×C3—22no—
241C24×C3—22no—
242C24×C3—22no—
243C24×C3—22no—
244C24×C3C2412yes—
245C24×C3C2411yescharacteristic
246C23×D3—22no—
247C23×D3—22no—
248C23×D3—22no—
249C23×D3—22no—
250C23×D3—22no—
251C23×D3—22no—
252C23×D3—22no—
253C23×D3—22no—
254C23×D3—22no—
255C23×D3—22no—
256C23×D3—22no—
257C23×D3C2×D414yes—
258C23×D3C2×D414yes—
259C23×D3#4114yes—
260C23×D3C2412yes—
261C23×D3C2412yes—
262C22×C3×C4—22no—
263C22×C3×C4—22no—
264C22×C3×C4—22no—
265C22×C3×C4—22no—
266C22×C3×C4—22no—
267C22×C3×C4—22no—
268C22×C3×C4—22no—
269C22×C3×C4—22no—
270C22×C3×C4—22no—
271C22×C3×C4—22no—
272C22×C3×C4—22no—
273C22×C3×C4—22no—
274C22×C3×C4—22no—
275C22×C3×C4—22no—
276C22×C3×C4—22no—
277C22×C3×C4C2×D414yes—
278C22×C3×C4C2×D414yes—
279C22×C3×C4#4114yes—
280C22×C3×C4C2412yes—
281C22×C3×C4C2412yes—
282C22×C3×C4C2412yes—
283C22×C3×C4C2412yes—
284C22×C3×C4C2412yes—
285C22×C3×C4C2412yes—
286C2×#67—28no—
287C2×#67—28no—
288C2×#67—28no—
289C2×#67—28no—
290C2×#67—28no—
291C2×#67—28no—
292C2×#67—416no—
293C2×#67—416no—
294C22×Dic3—22no—
295C22×Dic3—22no—
296C22×Dic3—22no—
297C22×Dic3—22no—
298C22×Dic3—22no—
299C22×Dic3—22no—
300C22×Dic3—22no—
301C22×Dic3—22no—
302C22×Dic3—22no—
303C22×Dic3—22no—
304C22×Dic3—22no—
305C22×Dic3—22no—
306C22×Dic3—22no—
307C22×Dic3C2×D414yes—
308C22×Dic3C2×D414yes—
309C22×Dic3#4114yes—
310C22×Dic3#4114yes—
311C22×Dic3#4114yes—
312C22×Dic3C2412yes—
313C22×Dic3C2412yes—
314C22×Dic3C2412yes—
315C22×Dic3C2412yes—
316C22×Dic3C2412yes—
317C22×Dic3C2412yes—
318C2×D12—28no—
319C2×D12—28no—
320C2×D12—28no—
321C2×D12—416no—
322C2×C4×D3—232no—
323C2×C4×D3—232no—
324C2×C4×D3—28no—
325C2×C4×D3—28no—
326C2×C4×D3—28no—
327C2×C4×D3—28no—
328C2×C4×D3—232no—
329C2×C4×D3—28no—
330C2×C4×D3—28no—
331C2×C4×D3—28no—
332C2×C4×D3C2×D4116yes—
333C2×C4×D3C2×D4116yescomplemented
334C3×C4⋊C4—28no—
335C3×C22⋊C4—28no—
336C3×C22⋊C4—28no—
337C3×C22⋊C4—28no—
338C3×C42—28no—
339#217—28no—
340#217—28no—
341(C2×D3)⋊C4—28no—
342(C2×D3)⋊C4—28no—
343(C2×D3)⋊C4—28no—
344(C2×D3)⋊C4—28no—
345(C2×D3)⋊C4—28no—
346(C2×D3)⋊C4—28no—
347(C2×D3)⋊C4—28no—
348C4⋊Dic3—28no—
349Dic3⋊C4—28no—
350Dic3⋊C4—28no—
351Dic3⋊C4—28no—
352Dic3⋊C4—28no—
353Dic3⋊C4—28no—
354C4×Dic3—28no—
355C4×Dic3—28no—
356C4×Dic3—28no—
357C25—31no—
358C25—31no—
359C25C22×D311yescharacteristic
360C22×D4—34no—
361C22×D4—34no—
362C22×D4—34no—
363C22×D4—64no—
364C22×D4—64no—
365C22×D4—64no—
366C22×D4—64no—
367C22×D4—64no—
368C22×D4—64no—
369C22×D4—64no—
370C22×D4—64no—
371C22×D4—64no—
372C23×C4—31no—
373C23×C4—31no—
374C23×C4—31no—
375C23×C4—38no—
376C23×C4—38no—
377C23×C4—34no—
378C23×C4—34no—
379C23×C4—31no—
380C23×C4—31no—
381C23×C4—31no—
382C23×C4—34no—
383C23×C4—64no—
384C23×C4—64no—
385C23×C4—64no—
386C23×C4—64no—
387C23×C4—64no—
388C23×C4—64no—
389C23×C4—64no—
390C23×C4C22×D311yescharacteristic
391C23×C4C22×D311yescharacteristic
392C23×C4C22×D311yescharacteristic
393C23×C4C22×D311yescharacteristic
394C23×C4C22×D311yescharacteristic
395C23×C4C22×D311yescharacteristic
396#123—632no—
397#123—632no—
398#121—632no—
399C2×C4⋊C4—24no—
400C2×C4⋊C4—34no—
401C2×C4⋊C4—34no—
402C2×C4⋊C4—34no—
403C2×C4⋊C4—34no—
404C2×C4⋊C4—34no—
405C2×C4⋊C4—34no—
406C2×C4⋊C4—64no—
407C2×C4⋊C4—64no—
408C2×C4⋊C4—64no—
409C2×C4⋊C4—64no—
410C2×C4⋊C4—64no—
411C2×C4⋊C4—64no—
412C2×C4⋊C4C22×D314yes—
413C2×C22⋊C4—24no—
414C2×C22⋊C4—24no—
415C2×C22⋊C4—24no—
416C2×C22⋊C4—34no—
417C2×C22⋊C4—34no—
418C2×C22⋊C4—34no—
419C2×C22⋊C4—34no—
420C2×C22⋊C4—34no—
421C2×C22⋊C4—34no—
422C2×C22⋊C4—34no—
423C2×C22⋊C4—34no—
424C2×C22⋊C4—34no—
425C2×C22⋊C4—64no—
426C2×C22⋊C4—64no—
427C2×C22⋊C4—64no—
428C2×C22⋊C4—64no—
429C2×C22⋊C4—64no—
430C2×C22⋊C4—64no—
431C2×C22⋊C4—64no—
432C2×C22⋊C4—64no—
433C2×C22⋊C4—64no—
434C2×C22⋊C4C22×D314yes—
435C2×C22⋊C4C22×D314yes—
436C2×C22⋊C4C22×D314yes—
437C2×C42—24no—
438C2×C42—34no—
439C2×C42—34no—
440C2×C42—34no—
441C2×C42—632no—
442C2×C42—64no—
443C2×C42—64no—
444C2×C42—64no—
445C2×C42C22×D314yes—
446#95—34no—
447#95—34no—
448#95—34no—
449#95—34no—
450#95C22×D314yes—
451#95C22×D314yes—
452C23×C3—22no—
453C23×C3—22no—
454C23×C3—22no—
455C23×C3—22no—
456C23×C3—22no—
457C23×C3—22no—
458C23×C3—22no—
459C23×C3—44no—
460C23×C3—44no—
461C23×C3—44no—
462C23×C3—44no—
463C23×C3—44no—
464C23×C3—44no—
465C23×C3—44no—
466C23×C3C22×D412yes—
467C23×C3C22×D412yes—
468C23×C3C2×#4112yes—
469C23×C3C2×#4112yes—
470C23×C3C2×#4112yes—
471C23×C3C2×#4112yes—
472C23×C3C2×#4112yes—
473C23×C3C2511yescharacteristic
474C22×D3—28no—
475C22×D3—28no—
476C22×D3—28no—
477C22×D3—28no—
478C22×D3—28no—
479C22×D3—28no—
480C22×D3—22no—
481C22×D3—22no—
482C22×D3—22no—
483C22×D3—22no—
484C22×D3—22no—
485C22×D3—22no—
486C22×D3—22no—
487C22×D3—22no—
488C22×D3—22no—
489C22×D3—22no—
490C22×D3—22no—
491C22×D3—44no—
492C22×D3—44no—
493C22×D3—44no—
494C22×D3—44no—
495C22×D3—44no—
496C22×D3—44no—
497C22×D3—44no—
498C22×D3#121116yes—
499C22×D3C22×D414yes—
500C22×D3C22×D414yes—
501C22×D3C2×#4114yes—
502C2×C3×C4—28no—
503C2×C3×C4—28no—
504C2×C3×C4—28no—
505C2×C3×C4—22no—
506C2×C3×C4—22no—
507C2×C3×C4—22no—
508C2×C3×C4—22no—
509C2×C3×C4—22no—
510C2×C3×C4—22no—
511C2×C3×C4—22no—
512C2×C3×C4—22no—
513C2×C3×C4—22no—
514C2×C3×C4—22no—
515C2×C3×C4—22no—
516C2×C3×C4—22no—
517C2×C3×C4—22no—
518C2×C3×C4—22no—
519C2×C3×C4—22no—
520C2×C3×C4—44no—
521C2×C3×C4—44no—
522C2×C3×C4—44no—
523C2×C3×C4C22×D414yes—
524C2×C3×C4C22×D414yes—
525C2×C3×C4C2×#4114yes—
526#67—416no—
527#67—416no—
528C2×Dic3—28no—
529C2×Dic3—28no—
530C2×Dic3—22no—
531C2×Dic3—22no—
532C2×Dic3—22no—
533C2×Dic3—22no—
534C2×Dic3—22no—
535C2×Dic3—22no—
536C2×Dic3—22no—
537C2×Dic3—22no—
538C2×Dic3—22no—
539C2×Dic3—22no—
540C2×Dic3—22no—
541C2×Dic3—22no—
542C2×Dic3—22no—
543C2×Dic3—44no—
544C2×Dic3—44no—
545C2×Dic3—44no—
546C2×Dic3#123116yescomplemented
547C2×Dic3C22×D414yes—
548C2×Dic3C22×D414yes—
549C2×Dic3C2×#4114yes—
550C2×Dic3C2×#4114yes—
551C2×Dic3C2×#4114yes—
552D12—416no—
553C4×D3—232no—
554C4×D3—232no—
555C4×D3—232no—
556C24—22no—
557C24—22no—
558C24—22no—
559C24—22no—
560C24—22no—
561C24—22no—
562C24—22no—
563C24—34no—
564C24—34no—
565C24—34no—
566C24—32no—
567C24—32no—
568C24—62no—
569C24—62no—
570C24—62no—
571C24—62no—
572C24—62no—
573C24—62no—
574C24—62no—
575C24—62no—
576C24—62no—
577C24—62no—
578C24—62no—
579C24C23×D312yes—
580C24C23×D311yescharacteristic
581C2×D4—68no—
582C2×D4—68no—
583C2×D4—68no—
584C2×D4—68no—
585C2×D4—68no—
586C2×D4—68no—
587C2×D4—68no—
588C2×D4—68no—
589C2×D4—68no—
590C2×D4—1216no—
591C2×D4—1216no—
592C2×D4—1216no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—34no—
609C22×C4—34no—
610C22×C4—34no—
611C22×C4—32no—
612C22×C4—34no—
613C22×C4—34no—
614C22×C4—32no—
615C22×C4—32no—
616C22×C4—316no—
617C22×C4—316no—
618C22×C4—32no—
619C22×C4—32no—
620C22×C4—32no—
621C22×C4—632no—
622C22×C4—68no—
623C22×C4—68no—
624C22×C4—68no—
625C22×C4—68no—
626C22×C4—68no—
627C22×C4—68no—
628C22×C4—632no—
629C22×C4—632no—
630C22×C4—62no—
631C22×C4—62no—
632C22×C4—62no—
633C22×C4—62no—
634C22×C4—68no—
635C22×C4—62no—
636C22×C4—62no—
637C22×C4—62no—
638C22×C4—62no—
639C22×C4—62no—
640C22×C4—62no—
641C22×C4—62no—
642C22×C4—62no—
643C22×C4—62no—
644C22×C4#23514yes—
645C22×C4D3×D414yes—
646C22×C4D3×D414yes—
647C22×C4C23×D312yes—
648C22×C4C23×D312yes—
649C22×C4C23×D312yes—
650C22×C4C23×D312yes—
651C22×C4C23×D312yes—
652C22×C4C23×D312yes—
653C4⋊C4—28no—
654C4⋊C4—68no—
655C4⋊C4—68no—
656C4⋊C4—68no—
657C4⋊C4—68no—
658C4⋊C4—68no—
659C4⋊C4—68no—
660C22⋊C4—28no—
661C22⋊C4—28no—
662C22⋊C4—28no—
663C22⋊C4—68no—
664C22⋊C4—68no—
665C22⋊C4—68no—
666C22⋊C4—68no—
667C22⋊C4—68no—
668C22⋊C4—68no—
669C22⋊C4—68no—
670C22⋊C4—68no—
671C22⋊C4—68no—
672C42—28no—
673C42—68no—
674C42—68no—
675C42—68no—
676C22×C3—42no—
677C22×C3—42no—
678C22×C3—42no—
679C22×C3—42no—
680C22×C3—42no—
681C22×C3—42no—
682C22×C3—42no—
683C22×C3—88no—
684C22×C3C2×#12114yes—
685C22×C3C2×#12314yes—
686C22×C3#52514yes—
687C22×C3#52914yes—
688C22×C3#52914yes—
689C22×C3#53214yes—
690C22×C3#53214yes—
691C22×C3C23×D411yescharacteristic
692C22×C3C23×D411yescharacteristic
693C22×C3C22×#4111yescharacteristic
694C22×C3C22×#4111yescharacteristic
695C22×C3C22×#4111yescharacteristic
696C22×C3C22×#4111yescharacteristic
697C22×C3C22×#4111yescharacteristic
698C2×D3—232no—
699C2×D3—24no—
700C2×D3—24no—
701C2×D3—24no—
702C2×D3—24no—
703C2×D3—24no—
704C2×D3—24no—
705C2×D3—42no—
706C2×D3—42no—
707C2×D3—42no—
708C2×D3—42no—
709C2×D3—42no—
710C2×D3—42no—
711C2×D3—42no—
712C2×D3—88no—
713C2×D3C2×#12118yes—
714C3×C4—24no—
715C3×C4—24no—
716C3×C4—24no—
717C3×C4—42no—
718C3×C4—42no—
719C3×C4—42no—
720Dic3—24no—
721Dic3—24no—
722Dic3—42no—
723Dic3—42no—
724Dic3—42no—
725Dic3C2×#12318yescomplemented
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—34no—
734C23—34no—
735C23—34no—
736C23—316no—
737C23—44no—
738C23—44no—
739C23—44no—
740C23—44no—
741C23—44no—
742C23—44no—
743C23—44no—
744C23—68no—
745C23—68no—
746C23—62no—
747C23—62no—
748C23—62no—
749C23—62no—
750C23—68no—
751C23—68no—
752C23—68no—
753C23—68no—
754C23—62no—
755C23—62no—
756C23—62no—
757C23—62no—
758C23—62no—
759C23—62no—
760C23—62no—
761C23—124no—
762C23—124no—
763C23—124no—
764C23—124no—
765C23—124no—
766C23—124no—
767C23—124no—
768C23C2×#23512yes—
769C23C2×D3×D412yes—
770C23C2×D3×D412yes—
771C23D3×#4112yes—
772C23D3×#4112yes—
773C23D3×#4112yes—
774C23D3×#4112yes—
775C23C24×D311yescharacteristic
776D4—1216no—
777D4—1216no—
778D4—1216no—
779C2×C4—28no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—28no—
787C2×C4—28no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—316no—
798C2×C4—34no—
799C2×C4—34no—
800C2×C4—34no—
801C2×C4—34no—
802C2×C4—34no—
803C2×C4—44no—
804C2×C4—44no—
805C2×C4—44no—
806C2×C4—632no—
807C2×C4—632no—
808C2×C4—632no—
809C2×C4—62no—
810C2×C4—62no—
811C2×C4—62no—
812C2×C4—62no—
813C2×C4—68no—
814C2×C4—68no—
815C2×C4—62no—
816C2×C4—62no—
817C2×C4—62no—
818C2×C4—62no—
819C2×C4—62no—
820C2×C4—62no—
821C2×C4—62no—
822C2×C4—62no—
823C2×C4—62no—
824C2×C4—124no—
825C2×C4—124no—
826C2×C4—124no—
827C2×C4C2×#23514yes—
828C2×C4C2×D3×D414yes—
829C2×C4C2×D3×D414yes—
830C2×C3—82no—
831C2×C3#285418yescomplemented
832C2×C3C22×#12111yescharacteristic
833C2×C3C22×#12311yescharacteristic
834C2×C3C2×#52511yescharacteristic
835C2×C3C2×#52911yescharacteristic
836C2×C3C2×#52911yescharacteristic
837C2×C3C2×#53211yescharacteristic
838C2×C3C2×#53211yescharacteristic
839D3—28no—
840D3—82no—
841C22—38no—
842C22—42no—
843C22—42no—
844C22—42no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—64no—
850C22—64no—
851C22—64no—
852C22—64no—
853C22—632no—
854C22—64no—
855C22—64no—
856C22—88no—
857C22—122no—
858C22—122no—
859C22—122no—
860C22—122no—
861C22—122no—
862C22—122no—
863C22—122no—
864C22—248no—
865C22#552814yes—
866C22#554714yes—
867C22#554814yes—
868C22D3×#12114yes—
869C22D3×#12314yes—
870C22#566814yes—
871C22#570614yes—
872C22C22×#23511yescharacteristic
873C22C22×D3×D411yescharacteristic
874C22C22×D3×D411yescharacteristic
875C22C2×D3×#4111yescharacteristic
876C22C2×D3×#4111yescharacteristic
877C22C2×D3×#4111yescharacteristic
878C22C2×D3×#4111yescharacteristic
879C4—24no—
880C4—24no—
881C4—24no—
882C4—38no—
883C4—42no—
884C4—42no—
885C4—42no—
886C4—64no—
887C4—64no—
888C4—122no—
889C4—122no—
890C4—122no—
891C3C2×#285411yescharacteristic, complemented, Sylow
892C2—68no—
893C2—82no—
894C2—242no—
895C2#7596018yesdirect product factor
896C2C2×#552811yescharacteristic
897C2C2×#554711yescharacteristic
898C2C2×#554811yescharacteristic
899C2C2×D3×#12111yescharacteristic
900C2C2×D3×#12311yescharacteristic
901C2C2×#566811yescharacteristic
902C2C2×#570611yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC2×C3×#388C2
socleC24×C3C24
prime radicalC22×#884C2
hypercenterC2×#388D3
hypocenterC3C2×#2854
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C22×#894C2semidirect
2. C22×#883C2semidirect
4. C22×C42×D3C2semidirect
5. C2×C3×#388C2semidirect
6. C2×#4976C2semidirect
7. C2×#4956C2semidirect
8. C2×#4957C2semidirect
9. C2×#4957C2semidirect
10. C2×#4944C2semidirect
11. C2×#4940C2semidirect
12. #75960C2direct (N × H)
13. C2×#4665C2semidirect
14. C2×#4667C2semidirect
15. C2×#4647C2semidirect
16. C2×#4670C2semidirect
48. C2×#894C22semidirect
52. C2×#883C22semidirect
54. C2×C42×D3C22semidirect
55. C3×#388C22semidirect
62. #4976C22semidirect
63. #4957C22semidirect
64. #4957C22semidirect
65. #4956C22semidirect
66. #4944C22semidirect
67. #4940C22semidirect
68. #4670C22semidirect
69. #4667C22semidirect
70. #4665C22semidirect
71. #4647C22semidirect
84. C2×#388D3semidirect
123. C22×C4×D3D4semidirect
227. #388C2×D3semidirect
333. C2×C4×D3C2×D4semidirect
546. C2×Dic3#123semidirect
725. Dic3C2×#123semidirect
831. C2×C3#2854semidirect
891. C3C2×#2854semidirect
895. C2#75960direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#8942
C22×#8832
C22×#8842
C22×C42×D32
C2×C3×#3882
C2×#49762
C2×#49562
C2×#49572
C2×#49442
C2×#49402
#759602
C2×#46652
C2×#46672
C2×#46472
C2×#46702
C2×#28543