Finite Group Databasebeta

← C2×#75866 #10964950

Subgroups — C2×#75866 #10964950

Order 768.

4166 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×C22⋊C4C211yesmaximal, characteristic
2C22×#872C211yesmaximal, characteristic, complemented
3C2×C3×#388C211yesmaximal, characteristic, complemented
4C2×#4993C211yesmaximal, characteristic, complemented
5C2×#4989C211yesmaximal, characteristic, complemented
6C2×#4955C211yesmaximal, characteristic
7C2×#4955C211yesmaximal, characteristic
8C2×#4949C211yesmaximal, characteristic, complemented
9C2×#4952C211yesmaximal, characteristic, complemented
10C2×#4944C211yesmaximal, characteristic, complemented
11C2×#4940C211yesmaximal, characteristic, complemented
12#75866C2116yesmaximal, direct product factor
13C2×#4675C211yesmaximal, characteristic, complemented
14C2×#4668C211yesmaximal, characteristic, complemented
15C2×#4664C211yesmaximal, characteristic, complemented
16C2×#4670C211yesmaximal, characteristic, complemented
17C2×#2482—31nomaximal, Sylow
18C25×D3C2211yescharacteristic
19C23×C4×D3C2211yescharacteristic
20C23×C4×D3C2211yescharacteristic
21C22×C3×C4⋊C4C2211yescharacteristic, complemented
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×C3×C42C2211yescharacteristic, complemented
26C22×#217C2211yescharacteristic
27C22×#217C2211yescharacteristic
28C22×#217C2211yescharacteristic
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×(C2×D3)⋊C4C2211yescharacteristic
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×(C2×D3)⋊C4C2211yescharacteristic
39C22×C4⋊Dic3C2211yescharacteristic, complemented
40C22×Dic3⋊C4C2211yescharacteristic, complemented
41C22×Dic3⋊C4C2211yescharacteristic, complemented
42C22×Dic3⋊C4C2211yescharacteristic, complemented
43C22×Dic3⋊C4C2211yescharacteristic, complemented
44C22×C4×Dic3C2211yescharacteristic, complemented
45C2×D3×C22⋊C4—28no—
46C2×D3×C22⋊C4C2218yes—
47C2×#872—28no—
48C2×#872C2218yescomplemented
49C3×#388C2218yescomplemented
50C2×C3×#95C2211yescharacteristic, complemented
51C2×C3×#95C2211yescharacteristic, complemented
52C2×C3⋊#95C2211yescharacteristic, complemented
53C2×C3⋊#95C2211yescharacteristic, complemented
54C2×C3⋊#95C2211yescharacteristic, complemented
55C2×C3⋊#95C2211yescharacteristic, complemented
56C2×C3⋊#95C2211yescharacteristic, complemented
57C2×C3⋊#95C2211yescharacteristic, complemented
58#4993C2218yescomplemented
59#4989C2218yescomplemented
60#4955C2218yes—
61#4955C2218yes—
62#4952C2218yescomplemented
63#4949C2218yescomplemented
64#4944C2218yescomplemented
65#4940C2218yescomplemented
66#4675C2218yescomplemented
67#4670C2218yescomplemented
68#4668C2218yescomplemented
69#4664C2218yescomplemented
70C22×#117—31no—
71C23×C22⋊C4—31no—
72#2482—316no—
73C2×#399—31no—
74C2×#399—31no—
75C2×#397—31no—
76C2×#397—31no—
77C2×#388—31no—
78C2×#388—31no—
79C2×#388—31no—
80C2×#388D311yescharacteristic, complemented
81C2×#385—31no—
82C2×#385—31no—
83C2×#381—31no—
84C2×#379—31no—
85C2×#379—31no—
86C25×C3C2311yescharacteristic
87C24×D3—24no—
88C24×D3—24no—
89C24×D3—24no—
90C24×D3—24no—
91C24×D3—24no—
92C24×D3—42no—
93C24×D3—42no—
94C24×D3C2311yescharacteristic
95C24×D3C2314yes—
96C24×D3C2311yescharacteristic
97C23×C3×C4C2311yescharacteristic
98C23×C3×C4C2311yescharacteristic
99C23×C3×C4C2311yescharacteristic
100C23×C3×C4C2311yescharacteristic
101C23×C3×C4C2311yescharacteristic
102C23×C3×C4C2311yescharacteristic
103C23×Dic3C2311yescharacteristic
104C23×Dic3C2311yescharacteristic
105C23×Dic3C2311yescharacteristic
106C23×Dic3C2311yescharacteristic
107C23×Dic3C2311yescharacteristic
108C23×Dic3C2311yescharacteristic
109C22×C4×D3—24no—
110C22×C4×D3—24no—
111C22×C4×D3—24no—
112C22×C4×D3—42no—
113C22×C4×D3—42no—
114C22×C4×D3D418yes—
115C22×C4×D3C2314yes—
116C22×C4×D3C2314yes—
117C2×C3×C4⋊C4—42no—
118C2×C3×C4⋊C4C2314yescomplemented
119C2×C3×C22⋊C4—24no—
120C2×C3×C22⋊C4—24no—
121C2×C3×C22⋊C4—42no—
122C2×C3×C22⋊C4C2314yes—
123C2×C3×C22⋊C4C2314yes—
124C2×C3×C22⋊C4C2314yes—
125C2×C3×C42—24no—
126C2×C3×C42C2314yescomplemented
127C2×#217—24no—
128C2×#217—24no—
129C2×#217—42no—
130C2×#217C2314yes—
131C2×#217C2314yes—
132C2×#217C2314yes—
133C2×(C2×D3)⋊C4—24no—
134C2×(C2×D3)⋊C4—24no—
135C2×(C2×D3)⋊C4—24no—
136C2×(C2×D3)⋊C4—24no—
137C2×(C2×D3)⋊C4—24no—
138C2×(C2×D3)⋊C4—24no—
139C2×(C2×D3)⋊C4—24no—
140C2×(C2×D3)⋊C4—24no—
141C2×(C2×D3)⋊C4—42no—
142C2×(C2×D3)⋊C4—42no—
143C2×(C2×D3)⋊C4C2314yes—
144C2×(C2×D3)⋊C4C2314yes—
145C2×(C2×D3)⋊C4C2314yes—
146C2×(C2×D3)⋊C4C2314yes—
147C2×(C2×D3)⋊C4C2314yes—
148C2×(C2×D3)⋊C4C2314yes—
149C2×(C2×D3)⋊C4C2314yes—
150C2×(C2×D3)⋊C4C2314yes—
151C2×(C2×D3)⋊C4C2314yes—
152C2×(C2×D3)⋊C4C2314yes—
153C2×C4⋊Dic3—42no—
154C2×C4⋊Dic3C2314yescomplemented
155C2×Dic3⋊C4—24no—
156C2×Dic3⋊C4—24no—
157C2×Dic3⋊C4—42no—
158C2×Dic3⋊C4—42no—
159C2×Dic3⋊C4C2314yescomplemented
160C2×Dic3⋊C4C2314yescomplemented
161C2×Dic3⋊C4C2314yescomplemented
162C2×Dic3⋊C4C2314yescomplemented
163C2×C4×Dic3—24no—
164C2×C4×Dic3C2314yescomplemented
165D3×C22⋊C4—232no—
166#872—232no—
167C3×#95C2314yescomplemented
168C3×#95C2314yescomplemented
169C3⋊#95C2314yescomplemented
170C3⋊#95C2314yescomplemented
171C3⋊#95C2314yescomplemented
172C3⋊#95C2314yescomplemented
173C3⋊#95C2314yescomplemented
174C3⋊#95C2314yescomplemented
175C26—31no—
176C24×C4—31no—
177C24×C4—31no—
178C2×#117—38no—
179C2×#117—68no—
180C22×C4⋊C4—31no—
181C22×C4⋊C4—31no—
182C22×C4⋊C4—31no—
183C22×C4⋊C4—31no—
184C22×C4⋊C4—31no—
185C22×C4⋊C4C2×D311yescharacteristic, complemented
186C22×C22⋊C4—31no—
187C22×C22⋊C4—31no—
188C22×C22⋊C4—31no—
189C22×C22⋊C4—31no—
190C22×C22⋊C4—31no—
191C22×C22⋊C4—31no—
192C22×C22⋊C4—31no—
193C22×C22⋊C4—31no—
194C22×C22⋊C4—31no—
195C22×C22⋊C4—31no—
196C22×C22⋊C4—31no—
197C22×C22⋊C4—31no—
198C22×C22⋊C4—31no—
199C22×C22⋊C4—38no—
200C22×C22⋊C4—68no—
201C22×C22⋊C4C2×D311yescharacteristic
202C22×C22⋊C4C2×D311yescharacteristic
203C22×C22⋊C4C2×D311yescharacteristic
204C22×C42—31no—
205C22×C42C2×D311yescharacteristic, complemented
206#399—38no—
207#399—38no—
208#397—38no—
209#397—38no—
210#388—38no—
211#388—38no—
212#388—38no—
213#388C2×D318yescomplemented
214#385—38no—
215#385—38no—
216#381—38no—
217#379—38no—
218#379—38no—
219C2×#95—31no—
220C2×#95—31no—
221C2×#95—31no—
222C2×#95—31no—
223C2×#95—31no—
224C2×#95—31no—
225C2×#95C2×D311yescharacteristic, complemented
226C2×#95C2×D311yescharacteristic, complemented
227C24×C3—22no—
228C24×C3—22no—
229C24×C3—22no—
230C24×C3—22no—
231C24×C3—22no—
232C24×C3—22no—
233C24×C3#4114yes—
234C24×C3C2412yes—
235C24×C3C2411yescharacteristic
236C23×D3—22no—
237C23×D3—22no—
238C23×D3—22no—
239C23×D3—22no—
240C23×D3—232no—
241C23×D3—22no—
242C23×D3—28no—
243C23×D3—22no—
244C23×D3—22no—
245C23×D3—22no—
246C23×D3—22no—
247C23×D3—22no—
248C23×D3—28no—
249C23×D3—28no—
250C23×D3—28no—
251C23×D3—28no—
252C23×D3—44no—
253C23×D3—44no—
254C23×D3—416no—
255C23×D3—416no—
256C23×D3—416no—
257C23×D3—416no—
258C23×D3—416no—
259C23×D3—416no—
260C23×D3C2×D414yes—
261C23×D3#4114yes—
262C23×D3#4114yes—
263C23×D3#4114yes—
264C23×D3C2412yes—
265C23×D3C2412yes—
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×C4—22no—
278C22×C3×C4—22no—
279C22×C3×C4—22no—
280C22×C3×C4—22no—
281C22×C3×C4—22no—
282C22×C3×C4—22no—
283C22×C3×C4C2×D414yes—
284C22×C3×C4C2412yes—
285C22×C3×C4C2412yes—
286C22×C3×C4C2412yes—
287C22×C3×C4C2412yes—
288C22×C3×C4C2412yes—
289C22×C3×C4C2412yes—
290C22×Dic3—22no—
291C22×Dic3—22no—
292C22×Dic3—22no—
293C22×Dic3—22no—
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×Dic3C2412yes—
309C22×Dic3C2412yes—
310C22×Dic3C2412yes—
311C22×Dic3C2412yes—
312C22×Dic3C2412yes—
313C22×Dic3C2412yes—
314C2×C4×D3—232no—
315C2×C4×D3—28no—
316C2×C4×D3—28no—
317C2×C4×D3—28no—
318C2×C4×D3—44no—
319C2×C4×D3—44no—
320C2×C4×D3—416no—
321C2×C4×D3C2×D4116yes—
322C3×C4⋊C4—44no—
323C3×C22⋊C4—28no—
324C3×C22⋊C4—28no—
325C3×C22⋊C4—44no—
326C3×C42—28no—
327#217—28no—
328#217—28no—
329#217—44no—
330(C2×D3)⋊C4—28no—
331(C2×D3)⋊C4—28no—
332(C2×D3)⋊C4—28no—
333(C2×D3)⋊C4—28no—
334(C2×D3)⋊C4—28no—
335(C2×D3)⋊C4—28no—
336(C2×D3)⋊C4—28no—
337(C2×D3)⋊C4—28no—
338(C2×D3)⋊C4—44no—
339(C2×D3)⋊C4—44no—
340C4⋊Dic3—44no—
341Dic3⋊C4—28no—
342Dic3⋊C4—28no—
343Dic3⋊C4—44no—
344Dic3⋊C4—44no—
345C4×Dic3—28no—
346C25—31no—
347C25—31no—
348C25—34no—
349C25—64no—
350C25—64no—
351C25—64no—
352C25—64no—
353C25—64no—
354C25—122no—
355C25—122no—
356C25C22×D311yescharacteristic
357C23×C4—31no—
358C23×C4—38no—
359C23×C4—34no—
360C23×C4—31no—
361C23×C4—31no—
362C23×C4—31no—
363C23×C4—31no—
364C23×C4—31no—
365C23×C4—34no—
366C23×C4—64no—
367C23×C4—64no—
368C23×C4—64no—
369C23×C4—122no—
370C23×C4—122no—
371C23×C4C22×D311yescharacteristic
372C23×C4C22×D311yescharacteristic
373C23×C4C22×D311yescharacteristic
374C23×C4C22×D311yescharacteristic
375C23×C4C22×D311yescharacteristic
376C23×C4C22×D311yescharacteristic
377#117—632no—
378C2×C4⋊C4—34no—
379C2×C4⋊C4—34no—
380C2×C4⋊C4—34no—
381C2×C4⋊C4—34no—
382C2×C4⋊C4—34no—
383C2×C4⋊C4—42no—
384C2×C4⋊C4—64no—
385C2×C4⋊C4—64no—
386C2×C4⋊C4—122no—
387C2×C4⋊C4—122no—
388C2×C4⋊C4—122no—
389C2×C4⋊C4C22×D314yescomplemented
390C2×C22⋊C4—24no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—34no—
393C2×C22⋊C4—34no—
394C2×C22⋊C4—34no—
395C2×C22⋊C4—34no—
396C2×C22⋊C4—34no—
397C2×C22⋊C4—34no—
398C2×C22⋊C4—34no—
399C2×C22⋊C4—34no—
400C2×C22⋊C4—34no—
401C2×C22⋊C4—34no—
402C2×C22⋊C4—34no—
403C2×C22⋊C4—34no—
404C2×C22⋊C4—34no—
405C2×C22⋊C4—42no—
406C2×C22⋊C4—632no—
407C2×C22⋊C4—64no—
408C2×C22⋊C4—64no—
409C2×C22⋊C4—64no—
410C2×C22⋊C4—64no—
411C2×C22⋊C4—64no—
412C2×C22⋊C4—64no—
413C2×C22⋊C4—64no—
414C2×C22⋊C4—64no—
415C2×C22⋊C4—64no—
416C2×C22⋊C4—64no—
417C2×C22⋊C4—122no—
418C2×C22⋊C4—122no—
419C2×C22⋊C4—122no—
420C2×C22⋊C4C22×D314yes—
421C2×C22⋊C4C22×D314yes—
422C2×C22⋊C4C22×D314yes—
423C2×C42—24no—
424C2×C42—34no—
425C2×C42—64no—
426C2×C42C22×D314yescomplemented
427#95—34no—
428#95—34no—
429#95—34no—
430#95—34no—
431#95—34no—
432#95—34no—
433#95C22×D314yescomplemented
434#95C22×D314yescomplemented
435C23×C3—28no—
436C23×C3—28no—
437C23×C3—28no—
438C23×C3—22no—
439C23×C3—22no—
440C23×C3—22no—
441C23×C3—22no—
442C23×C3—22no—
443C23×C3—22no—
444C23×C3—44no—
445C23×C3—44no—
446C23×C3—44no—
447C23×C3—44no—
448C23×C3C22×D412yes—
449C23×C3C2×#4114yes—
450C23×C3C2×#4112yes—
451C23×C3C2×#4112yes—
452C23×C3C2×#4112yes—
453C23×C3C2×#4112yes—
454C23×C3H(5,𝔽2)12yes—
455C23×C3H(5,𝔽2)12yes—
456C23×C3C2511yescharacteristic
457C22×D3—28no—
458C22×D3—28no—
459C22×D3—28no—
460C22×D3—28no—
461C22×D3—28no—
462C22×D3—28no—
463C22×D3—22no—
464C22×D3—22no—
465C22×D3—22no—
466C22×D3—22no—
467C22×D3—232no—
468C22×D3—28no—
469C22×D3—28no—
470C22×D3—28no—
471C22×D3—22no—
472C22×D3—22no—
473C22×D3—22no—
474C22×D3—22no—
475C22×D3—22no—
476C22×D3—22no—
477C22×D3—416no—
478C22×D3—416no—
479C22×D3—416no—
480C22×D3—416no—
481C22×D3—416no—
482C22×D3—4128no—
483C22×D3—44no—
484C22×D3—44no—
485C22×D3—44no—
486C22×D3—44no—
487C22×D3—416no—
488C22×D3#123116yes—
489C22×D3C22×D414yes—
490C22×D3C2×#4114yes—
491C22×D3C2×#4114yes—
492C22×D3C2×#4114yes—
493C2×C3×C4—28no—
494C2×C3×C4—22no—
495C2×C3×C4—22no—
496C2×C3×C4—22no—
497C2×C3×C4—22no—
498C2×C3×C4—22no—
499C2×C3×C4—22no—
500C2×C3×C4—22no—
501C2×C3×C4—22no—
502C2×C3×C4—22no—
503C2×C3×C4—22no—
504C2×C3×C4—22no—
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—44no—
512C2×C3×C4—44no—
513C2×C3×C4—44no—
514C2×C3×C4—44no—
515C2×C3×C4—44no—
516C2×C3×C4C22×D414yes—
517C2×Dic3—28no—
518C2×Dic3—22no—
519C2×Dic3—22no—
520C2×Dic3—22no—
521C2×Dic3—22no—
522C2×Dic3—22no—
523C2×Dic3—22no—
524C2×Dic3—22no—
525C2×Dic3—22no—
526C2×Dic3—22no—
527C2×Dic3—22no—
528C2×Dic3—22no—
529C2×Dic3—22no—
530C2×Dic3—22no—
531C2×Dic3—22no—
532C2×Dic3—22no—
533C2×Dic3—22no—
534C2×Dic3—22no—
535C2×Dic3—44no—
536C2×Dic3—44no—
537C2×Dic3—44no—
538C2×Dic3—44no—
539C2×Dic3—44no—
540C2×Dic3C22×D414yes—
541C4×D3—232no—
542C4×D3—416no—
543C24—22no—
544C24—22no—
545C24—22no—
546C24—22no—
547C24—22no—
548C24—22no—
549C24—34no—
550C24—34no—
551C24—34no—
552C24—32no—
553C24—34no—
554C24—32no—
555C24—68no—
556C24—68no—
557C24—68no—
558C24—68no—
559C24—632no—
560C24—62no—
561C24—62no—
562C24—62no—
563C24—62no—
564C24—68no—
565C24—62no—
566C24—62no—
567C24—62no—
568C24—62no—
569C24—62no—
570C24—62no—
571C24—124no—
572C24—124no—
573C24—1216no—
574C24—1216no—
575C24—1216no—
576C24—1216no—
577C24—1216no—
578C24—1216no—
579C24#23514yes—
580C24C23×D312yes—
581C24C23×D311yescharacteristic
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—34no—
600C22×C4—32no—
601C22×C4—316no—
602C22×C4—32no—
603C22×C4—32no—
604C22×C4—32no—
605C22×C4—32no—
606C22×C4—32no—
607C22×C4—632no—
608C22×C4—68no—
609C22×C4—68no—
610C22×C4—68no—
611C22×C4—62no—
612C22×C4—62no—
613C22×C4—62no—
614C22×C4—62no—
615C22×C4—62no—
616C22×C4—62no—
617C22×C4—62no—
618C22×C4—62no—
619C22×C4—62no—
620C22×C4—62no—
621C22×C4—62no—
622C22×C4—62no—
623C22×C4—62no—
624C22×C4—62no—
625C22×C4—62no—
626C22×C4—62no—
627C22×C4—62no—
628C22×C4—124no—
629C22×C4—124no—
630C22×C4—1216no—
631C22×C4D3×D414yes—
632C22×C4C23×D312yes—
633C22×C4C23×D312yes—
634C22×C4C23×D312yes—
635C22×C4C23×D312yes—
636C22×C4C23×D312yes—
637C22×C4C23×D312yes—
638C4⋊C4—44no—
639C4⋊C4—68no—
640C4⋊C4—68no—
641C4⋊C4—124no—
642C4⋊C4—124no—
643C4⋊C4—124no—
644C22⋊C4—28no—
645C22⋊C4—28no—
646C22⋊C4—44no—
647C22⋊C4—68no—
648C22⋊C4—68no—
649C22⋊C4—68no—
650C22⋊C4—68no—
651C22⋊C4—68no—
652C22⋊C4—68no—
653C22⋊C4—68no—
654C22⋊C4—68no—
655C22⋊C4—68no—
656C22⋊C4—68no—
657C22⋊C4—124no—
658C22⋊C4—124no—
659C22⋊C4—124no—
660C42—28no—
661C42—68no—
662C22×C3—24no—
663C22×C3—24no—
664C22×C3—24no—
665C22×C3—42no—
666C22×C3—42no—
667C22×C3—42no—
668C22×C3—42no—
669C22×C3—416no—
670C22×C3C2×#12314yes—
671C22×C3#52514yes—
672C22×C3#53514yes—
673C22×C3#55114yes—
674C22×C3#55114yes—
675C22×C3#55114yes—
676C22×C3#55114yes—
677C22×C3C23×D411yescharacteristic
678C22×C3C22×#4111yescharacteristic
679C22×C3C22×#4111yescharacteristic
680C22×C3C22×#4111yescharacteristic
681C22×C3C22×#4111yescharacteristic
682C22×C3C2×H(5,𝔽2)11yescharacteristic
683C22×C3C2×H(5,𝔽2)11yescharacteristic
684C2×D3—24no—
685C2×D3—24no—
686C2×D3—24no—
687C2×D3—24no—
688C2×D3—24no—
689C2×D3—24no—
690C2×D3—232no—
691C2×D3—24no—
692C2×D3—24no—
693C2×D3—24no—
694C2×D3—464no—
695C2×D3—42no—
696C2×D3—42no—
697C2×D3—42no—
698C2×D3—42no—
699C2×D3—416no—
700C2×D3C2×#12318yes—
701C3×C4—24no—
702C3×C4—42no—
703C3×C4—42no—
704C3×C4—42no—
705C3×C4—42no—
706C3×C4—42no—
707Dic3—24no—
708Dic3—42no—
709Dic3—42no—
710Dic3—42no—
711Dic3—42no—
712Dic3—42no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—28no—
720C23—28no—
721C23—28no—
722C23—316no—
723C23—34no—
724C23—34no—
725C23—34no—
726C23—34no—
727C23—44no—
728C23—44no—
729C23—44no—
730C23—44no—
731C23—632no—
732C23—68no—
733C23—62no—
734C23—62no—
735C23—68no—
736C23—62no—
737C23—62no—
738C23—68no—
739C23—68no—
740C23—68no—
741C23—68no—
742C23—68no—
743C23—62no—
744C23—62no—
745C23—62no—
746C23—68no—
747C23—62no—
748C23—62no—
749C23—62no—
750C23—68no—
751C23—1216no—
752C23—1216no—
753C23—1216no—
754C23—1216no—
755C23—1216no—
756C23—12128no—
757C23—1216no—
758C23—124no—
759C23—124no—
760C23—124no—
761C23—124no—
762C23C2×#23514yes—
763C23C2×#23512yes—
764C23C2×D3×D412yes—
765C23#100412yes—
766C23D3×#4112yes—
767C23D3×#4112yes—
768C23D3×#4112yes—
769C23#100912yes—
770C23C24×D311yescharacteristic
771C2×C4—28no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—34no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—44no—
794C2×C4—44no—
795C2×C4—632no—
796C2×C4—68no—
797C2×C4—62no—
798C2×C4—62no—
799C2×C4—62no—
800C2×C4—62no—
801C2×C4—62no—
802C2×C4—62no—
803C2×C4—62no—
804C2×C4—62no—
805C2×C4—62no—
806C2×C4—62no—
807C2×C4—62no—
808C2×C4—62no—
809C2×C4—62no—
810C2×C4—62no—
811C2×C4—62no—
812C2×C4—62no—
813C2×C4—62no—
814C2×C4—1216no—
815C2×C4—124no—
816C2×C4—124no—
817C2×C4—124no—
818C2×C4—124no—
819C2×C4—124no—
820C2×C4C2×D3×D414yes—
821C2×C3—44no—
822C2×C3#248218yescomplemented
823C2×C3C22×#12311yescharacteristic
824C2×C3C2×#52511yescharacteristic
825C2×C3C2×#53511yescharacteristic
826C2×C3C2×#55111yescharacteristic
827C2×C3C2×#55111yescharacteristic
828C2×C3C2×#55111yescharacteristic
829C2×C3C2×#55111yescharacteristic
830D3—28no—
831D3—44no—
832C22—24no—
833C22—24no—
834C22—24no—
835C22—38no—
836C22—42no—
837C22—416no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—64no—
842C22—64no—
843C22—64no—
844C22—632no—
845C22—64no—
846C22—64no—
847C22—64no—
848C22—64no—
849C22—64no—
850C22—64no—
851C22—1264no—
852C22—122no—
853C22—1216no—
854C22—122no—
855C22—122no—
856C22—122no—
857C22#552714yes—
858C22#554714yes—
859C22#555614yes—
860C22#560714yes—
861C22D3×#12314yes—
862C22#567914yes—
863C22#570514yes—
864C22C22×#23511yescharacteristic
865C22C22×D3×D411yescharacteristic
866C22C2×#100411yescharacteristic
867C22C2×D3×#4111yescharacteristic
868C22C2×D3×#4111yescharacteristic
869C22C2×D3×#4111yescharacteristic
870C22C2×#100911yescharacteristic
871C4—24no—
872C4—42no—
873C4—42no—
874C4—42no—
875C4—42no—
876C4—42no—
877C4—64no—
878C4—122no—
879C4—122no—
880C4—122no—
881C4—122no—
882C4—122no—
883C3C2×#248211yescharacteristic, complemented, Sylow
884C2—44no—
885C2—68no—
886C2—124no—
887C2#7586618yesdirect product factor
888C2C2×#552711yescharacteristic
889C2C2×#554711yescharacteristic
890C2C2×#555611yescharacteristic
891C2C2×#560711yescharacteristic
892C2C2×D3×#12311yescharacteristic
893C2C2×#567911yescharacteristic
894C2C2×#570511yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC2×C3×#388C2
socleC24×C3C24
prime radicalC25×D3C22
hypercenterC2×#388D3
hypocenterC3C2×#2482
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C22×#872C2semidirect
3. C2×C3×#388C2semidirect
4. C2×#4993C2semidirect
5. C2×#4989C2semidirect
8. C2×#4949C2semidirect
9. C2×#4952C2semidirect
10. C2×#4944C2semidirect
11. C2×#4940C2semidirect
12. #75866C2direct (N × H)
13. C2×#4675C2semidirect
14. C2×#4668C2semidirect
15. C2×#4664C2semidirect
16. C2×#4670C2semidirect
21. C22×C3×C4⋊C4C22semidirect
25. C22×C3×C42C22semidirect
39. C22×C4⋊Dic3C22semidirect
40. C22×Dic3⋊C4C22semidirect
41. C22×Dic3⋊C4C22semidirect
42. C22×Dic3⋊C4C22semidirect
43. C22×Dic3⋊C4C22semidirect
44. C22×C4×Dic3C22semidirect
48. C2×#872C22semidirect
49. C3×#388C22semidirect
50. C2×C3×#95C22semidirect
51. C2×C3×#95C22semidirect
52. C2×C3⋊#95C22semidirect
53. C2×C3⋊#95C22semidirect
54. C2×C3⋊#95C22semidirect
55. C2×C3⋊#95C22semidirect
56. C2×C3⋊#95C22semidirect
57. C2×C3⋊#95C22semidirect
58. #4993C22semidirect
59. #4989C22semidirect
62. #4952C22semidirect
63. #4949C22semidirect
64. #4944C22semidirect
65. #4940C22semidirect
66. #4675C22semidirect
67. #4670C22semidirect
68. #4668C22semidirect
69. #4664C22semidirect
80. C2×#388D3semidirect
118. C2×C3×C4⋊C4C23semidirect
126. C2×C3×C42C23semidirect
154. C2×C4⋊Dic3C23semidirect
159. C2×Dic3⋊C4C23semidirect
160. C2×Dic3⋊C4C23semidirect
161. C2×Dic3⋊C4C23semidirect
162. C2×Dic3⋊C4C23semidirect
164. C2×C4×Dic3C23semidirect
167. C3×#95C23semidirect
168. C3×#95C23semidirect
169. C3⋊#95C23semidirect
170. C3⋊#95C23semidirect
171. C3⋊#95C23semidirect
172. C3⋊#95C23semidirect
173. C3⋊#95C23semidirect
174. C3⋊#95C23semidirect
185. C22×C4⋊C4C2×D3semidirect
205. C22×C42C2×D3semidirect
213. #388C2×D3semidirect
225. C2×#95C2×D3semidirect
226. C2×#95C2×D3semidirect
389. C2×C4⋊C4C22×D3semidirect
426. C2×C42C22×D3semidirect
433. #95C22×D3semidirect
434. #95C22×D3semidirect
822. C2×C3#2482semidirect
883. C3C2×#2482semidirect
887. C2#75866direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D3×C22⋊C42
C22×#8722
C2×C3×#3882
C2×#49932
C2×#49892
C2×#49552
C2×#49492
C2×#49522
C2×#49442
C2×#49402
#758662
C2×#46752
C2×#46682
C2×#46642
C2×#46702
C2×#24823