Finite Group Databasebeta

← C2×#78241 #11430276

Subgroups — C2×#78241 #11430276

Order 768.

3542 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#894C211yesmaximal, characteristic, complemented
2C22×#895C211yesmaximal, characteristic, complemented
3C2×C3×#400C211yesmaximal, characteristic, complemented
4C2×#4988C211yesmaximal, characteristic, complemented
5C2×#4990C211yesmaximal, characteristic, complemented
6#78241C2116yesmaximal, direct product factor
7C2×#4675C211yesmaximal, characteristic, complemented
8C2×#4671C211yesmaximal, characteristic, complemented
9C2×#4671C211yesmaximal, characteristic, complemented
10C2×#4671C211yesmaximal, characteristic, complemented
11C2×#4665C211yesmaximal, characteristic, complemented
12C2×#4665C211yesmaximal, characteristic, complemented
13C2×#4665C211yesmaximal, characteristic, complemented
14C2×#4667C211yesmaximal, characteristic, complemented
15C2×#4672C211yesmaximal, characteristic, complemented
16C2×#4669C211yesmaximal, characteristic, complemented
17C2×#2703—31nomaximal, Sylow
18C23×D12C2211yescharacteristic
19C23×D12C2211yescharacteristic
20C23×D12C2211yescharacteristic
21C23×D12C2211yescharacteristic
22C23×D12C2211yescharacteristic
23C23×D12C2211yescharacteristic
24C23×C4×D3C2211yescharacteristic
25C23×C4×D3C2211yescharacteristic
26C22×C3×C4⋊C4C2211yescharacteristic
27C22×C3×C4⋊C4C2211yescharacteristic
28C22×(C2×D3)⋊C4C2211yescharacteristic
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×(C2×D3)⋊C4C2211yescharacteristic
40C22×(C2×D3)⋊C4C2211yescharacteristic
41C22×(C2×D3)⋊C4C2211yescharacteristic
42C22×Dic3⋊C4C2211yescharacteristic
43C22×Dic3⋊C4C2211yescharacteristic
44C22×C4×Dic3C2211yescharacteristic
45C2×#895—28no—
46C2×#895C2218yescomplemented
47C2×#894—28no—
48C2×#894C2218yescomplemented
49C3×#400C2218yescomplemented
50C2×C3×#95C2211yescharacteristic
51C2×C3×#95C2211yescharacteristic
52C2×C3×#95C2211yescharacteristic
53C2×C3×#95C2211yescharacteristic
54C2×C3×#95C2211yescharacteristic
55C2×C3⋊#95C2211yescharacteristic
56C2×C3⋊#95C2211yescharacteristic
57C2×C3⋊#95C2211yescharacteristic
58#4990C2218yescomplemented
59#4988C2218yescomplemented
60#4675C2218yescomplemented
61#4672C2218yescomplemented
62#4671C2218yescomplemented
63#4671C2218yescomplemented
64#4671C2218yescomplemented
65#4669C2218yescomplemented
66#4667C2218yescomplemented
67#4665C2218yescomplemented
68#4665C2218yescomplemented
69#4665C2218yescomplemented
70C22×#123—31no—
71C22×#121—31no—
72#2703—316no—
73C2×#400D311yescharacteristic, complemented
74C2×#397—31no—
75C2×#394—31no—
76C2×#392—31no—
77C2×#392—31no—
78C2×#392—31no—
79C2×#390—31no—
80C2×#388—31no—
81C2×#388—31no—
82C2×#386—31no—
83C2×#386—31no—
84C2×#386—31no—
85C2×#380—31no—
86C24×D3C2311yescharacteristic
87C24×D3C2311yescharacteristic
88C24×D3C2311yescharacteristic
89C24×D3C2311yescharacteristic
90C23×C3×C4C2311yescharacteristic
91C23×C3×C4C2311yescharacteristic
92C23×C3×C4C2311yescharacteristic
93C23×C3×C4C2311yescharacteristic
94C23×C3×C4C2311yescharacteristic
95C23×C3×C4C2311yescharacteristic
96C23×C3×C4C2311yescharacteristic
97C23×Dic3C2311yescharacteristic
98C23×Dic3C2311yescharacteristic
99C23×Dic3C2311yescharacteristic
100C23×Dic3C2311yescharacteristic
101C22×D12—24no—
102C22×D12—24no—
103C22×D12—24no—
104C22×D12—24no—
105C22×D12—24no—
106C22×D12—24no—
107C22×D12—24no—
108C22×D12—24no—
109C22×D12—42no—
110C22×D12—42no—
111C22×D12—42no—
112C22×D12—42no—
113C22×D12—42no—
114C22×D12—42no—
115C22×D12—42no—
116C22×D12—42no—
117C22×D12—42no—
118C22×D12—42no—
119C22×D12C2314yes—
120C22×D12C2314yes—
121C22×D12C2314yes—
122C22×D12C2314yes—
123C22×D12C2314yes—
124C22×D12C2314yes—
125C22×C4×D3—24no—
126C22×C4×D3—24no—
127C22×C4×D3—24no—
128C22×C4×D3—42no—
129C22×C4×D3—42no—
130C22×C4×D3—42no—
131C22×C4×D3C2314yes—
132C22×C4×D3C2314yes—
133C2×C3×C4⋊C4—24no—
134C2×C3×C4⋊C4—24no—
135C2×C3×C4⋊C4C2314yes—
136C2×C3×C4⋊C4C2314yes—
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)⋊C4—42no—
144C2×(C2×D3)⋊C4—42no—
145C2×(C2×D3)⋊C4—42no—
146C2×(C2×D3)⋊C4—42no—
147C2×(C2×D3)⋊C4—42no—
148C2×(C2×D3)⋊C4—42no—
149C2×(C2×D3)⋊C4—42no—
150C2×(C2×D3)⋊C4D418yescomplemented
151C2×(C2×D3)⋊C4C2314yes—
152C2×(C2×D3)⋊C4C2314yes—
153C2×(C2×D3)⋊C4C2314yes—
154C2×(C2×D3)⋊C4C2314yes—
155C2×(C2×D3)⋊C4C2314yes—
156C2×(C2×D3)⋊C4C2314yes—
157C2×(C2×D3)⋊C4C2314yes—
158C2×(C2×D3)⋊C4C2314yes—
159C2×(C2×D3)⋊C4C2314yes—
160C2×(C2×D3)⋊C4C2314yes—
161C2×(C2×D3)⋊C4C2314yes—
162C2×(C2×D3)⋊C4C2314yes—
163C2×(C2×D3)⋊C4C2314yes—
164C2×(C2×D3)⋊C4C2314yes—
165C2×Dic3⋊C4—24no—
166C2×Dic3⋊C4—42no—
167C2×Dic3⋊C4C2314yes—
168C2×Dic3⋊C4C2314yes—
169C2×C4×Dic3—42no—
170C2×C4×Dic3C2314yes—
171#895—232no—
172#894—232no—
173C3×#95C2314yes—
174C3×#95C2314yes—
175C3×#95C2314yes—
176C3×#95C2314yes—
177C3×#95C2314yes—
178C3⋊#95C2314yes—
179C3⋊#95C2314yes—
180C3⋊#95C2314yes—
181C23×D4—31no—
182C23×D4—31no—
183C23×D4—31no—
184C23×D4—31no—
185C23×D4—31no—
186C23×D4—31no—
187C24×C4—31no—
188C24×C4—31no—
189C2×#123—38no—
190C2×#123—68no—
191C2×#121—38no—
192C2×#121—68no—
193C22×C4⋊C4—31no—
194C22×C4⋊C4—31no—
195C22×C4⋊C4C2×D311yescharacteristic
196C22×C4⋊C4C2×D311yescharacteristic
197C22×C22⋊C4—31no—
198C22×C22⋊C4—31no—
199C22×C22⋊C4—31no—
200C22×C22⋊C4—31no—
201C22×C22⋊C4—31no—
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×C42—31no—
212#400C2×D318yescomplemented
213#397—38no—
214#394—38no—
215#392—38no—
216#392—38no—
217#392—38no—
218#390—38no—
219#388—38no—
220#388—38no—
221#386—38no—
222#386—38no—
223#386—38no—
224#380—38no—
225C2×#95—31no—
226C2×#95—31no—
227C2×#95—31no—
228C2×#95C2×D311yescharacteristic
229C2×#95C2×D311yescharacteristic
230C2×#95C2×D311yescharacteristic
231C2×#95C2×D311yescharacteristic
232C2×#95C2×D311yescharacteristic
233C24×C3C2411yescharacteristic
234C23×D3—22no—
235C23×D3—22no—
236C23×D3—22no—
237C23×D3—22no—
238C23×D3—22no—
239C23×D3—22no—
240C23×D3—22no—
241C23×D3—22no—
242C23×D3—22no—
243C23×D3—22no—
244C23×D3—22no—
245C23×D3—22no—
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×D3—22no—
258C23×D3—22no—
259C23×D3—22no—
260C23×D3C2×D414yes—
261C23×D3#4114yes—
262C23×D3C2412yes—
263C23×D3C2412yes—
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×C4—22no—
284C22×C3×C4—22no—
285C22×C3×C4C2×D414yes—
286C22×C3×C4#4114yes—
287C22×C3×C4C2412yes—
288C22×C3×C4C2412yes—
289C22×C3×C4C2412yes—
290C22×C3×C4C2412yes—
291C22×C3×C4C2412yes—
292C22×C3×C4C2412yes—
293C22×C3×C4C2412yes—
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×Dic3C2×D414yes—
306C22×Dic3C2412yes—
307C22×Dic3C2412yes—
308C22×Dic3C2412yes—
309C22×Dic3C2412yes—
310C2×D12—28no—
311C2×D12—28no—
312C2×D12—28no—
313C2×D12—28no—
314C2×D12—28no—
315C2×D12—28no—
316C2×D12—28no—
317C2×D12—28no—
318C2×D12—44no—
319C2×D12—44no—
320C2×D12—44no—
321C2×D12—44no—
322C2×D12—44no—
323C2×D12—44no—
324C2×D12—44no—
325C2×D12—44no—
326C2×D12—44no—
327C2×D12—44no—
328C2×D12—416no—
329C2×D12—416no—
330C2×D12—416no—
331C2×D12—416no—
332C2×D12—416no—
333C2×D12—416no—
334C2×C4×D3—28no—
335C2×C4×D3—28no—
336C2×C4×D3—28no—
337C2×C4×D3—44no—
338C2×C4×D3—44no—
339C2×C4×D3—44no—
340C2×C4×D3—416no—
341C2×C4×D3—416no—
342C3×C4⋊C4—28no—
343C3×C4⋊C4—28no—
344(C2×D3)⋊C4—28no—
345(C2×D3)⋊C4—28no—
346(C2×D3)⋊C4—28no—
347(C2×D3)⋊C4—28no—
348(C2×D3)⋊C4—44no—
349(C2×D3)⋊C4—44no—
350(C2×D3)⋊C4—44no—
351(C2×D3)⋊C4—44no—
352(C2×D3)⋊C4—44no—
353(C2×D3)⋊C4—44no—
354(C2×D3)⋊C4—44no—
355(C2×D3)⋊C4—44no—
356(C2×D3)⋊C4—44no—
357(C2×D3)⋊C4C2×D4116yescomplemented
358Dic3⋊C4—28no—
359Dic3⋊C4—44no—
360C4×Dic3—44no—
361C25—31no—
362C25—31no—
363C25—31no—
364C25—31no—
365C22×D4—34no—
366C22×D4—34no—
367C22×D4—34no—
368C22×D4—34no—
369C22×D4—34no—
370C22×D4—34no—
371C22×D4—64no—
372C22×D4—64no—
373C22×D4—64no—
374C22×D4—64no—
375C22×D4—64no—
376C22×D4—64no—
377C22×D4—64no—
378C22×D4—64no—
379C22×D4—122no—
380C22×D4—122no—
381C22×D4—122no—
382C22×D4—122no—
383C22×D4—122no—
384C22×D4—122no—
385C22×D4—122no—
386C22×D4—122no—
387C22×D4—122no—
388C22×D4—122no—
389C23×C4—31no—
390C23×C4—31no—
391C23×C4—31no—
392C23×C4—31no—
393C23×C4—34no—
394C23×C4—34no—
395C23×C4—64no—
396C23×C4—64no—
397C23×C4—64no—
398C23×C4—122no—
399C23×C4—122no—
400C23×C4—122no—
401C23×C4C22×D311yescharacteristic
402C23×C4C22×D311yescharacteristic
403C23×C4C22×D311yescharacteristic
404C23×C4C22×D311yescharacteristic
405C23×C4C22×D311yescharacteristic
406C23×C4C22×D311yescharacteristic
407C23×C4C22×D311yescharacteristic
408#123—632no—
409#121—632no—
410C2×C4⋊C4—24no—
411C2×C4⋊C4—24no—
412C2×C4⋊C4—34no—
413C2×C4⋊C4—34no—
414C2×C4⋊C4—64no—
415C2×C4⋊C4—122no—
416C2×C4⋊C4C22×D314yes—
417C2×C4⋊C4C22×D314yes—
418C2×C22⋊C4—38no—
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—34no—
426C2×C22⋊C4—34no—
427C2×C22⋊C4—34no—
428C2×C22⋊C4—34no—
429C2×C22⋊C4—34no—
430C2×C22⋊C4—34no—
431C2×C22⋊C4—34no—
432C2×C22⋊C4—34no—
433C2×C22⋊C4—64no—
434C2×C22⋊C4—64no—
435C2×C22⋊C4—64no—
436C2×C22⋊C4—64no—
437C2×C22⋊C4—122no—
438C2×C22⋊C4—122no—
439C2×C22⋊C4—122no—
440C2×C22⋊C4—122no—
441C2×C22⋊C4—122no—
442C2×C22⋊C4—122no—
443C2×C22⋊C4—122no—
444C2×C22⋊C4—122no—
445C2×C22⋊C4—122no—
446C2×C42—34no—
447C2×C42—122no—
448#95—34no—
449#95—34no—
450#95—34no—
451#95C22×D314yes—
452#95C22×D314yes—
453#95C22×D314yes—
454#95C22×D314yes—
455#95C22×D314yes—
456C23×C3C22×D412yes—
457C23×C3C2×#4112yes—
458C23×C3C2×#4112yes—
459C23×C3H(5,𝔽2)12yes—
460C23×C3H(5,𝔽2)12yes—
461C23×C3H(5,𝔽2)12yes—
462C23×C3H(5,𝔽2)12yes—
463C23×C3C2511yescharacteristic
464C22×D3—28no—
465C22×D3—28no—
466C22×D3—28no—
467C22×D3—28no—
468C22×D3—28no—
469C22×D3—28no—
470C22×D3—22no—
471C22×D3—22no—
472C22×D3—22no—
473C22×D3—22no—
474C22×D3—22no—
475C22×D3—22no—
476C22×D3—22no—
477C22×D3—22no—
478C22×D3—22no—
479C22×D3—22no—
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—22no—
492C22×D3—22no—
493C22×D3—22no—
494C22×D3—22no—
495C22×D3—22no—
496C22×D3—44no—
497C22×D3—44no—
498C22×D3—44no—
499C22×D3—44no—
500C22×D3—44no—
501C22×D3—44no—
502C22×D3—44no—
503C22×D3—44no—
504C22×D3—44no—
505C22×D3—44no—
506C22×D3—44no—
507C22×D3—44no—
508C22×D3—44no—
509C22×D3—44no—
510C22×D3—44no—
511C22×D3—44no—
512C22×D3—44no—
513C22×D3—44no—
514C22×D3—44no—
515C22×D3—44no—
516C22×D3—44no—
517C22×D3—44no—
518C22×D3C22×D414yes—
519C22×D3C2×#4114yes—
520C2×C3×C4—28no—
521C2×C3×C4—28no—
522C2×C3×C4—22no—
523C2×C3×C4—22no—
524C2×C3×C4—22no—
525C2×C3×C4—22no—
526C2×C3×C4—22no—
527C2×C3×C4—22no—
528C2×C3×C4—22no—
529C2×C3×C4—22no—
530C2×C3×C4—22no—
531C2×C3×C4—22no—
532C2×C3×C4—22no—
533C2×C3×C4—22no—
534C2×C3×C4—22no—
535C2×C3×C4—22no—
536C2×C3×C4—22no—
537C2×C3×C4—22no—
538C2×C3×C4—22no—
539C2×C3×C4—22no—
540C2×C3×C4—22no—
541C2×C3×C4—44no—
542C2×C3×C4—44no—
543C2×C3×C4—44no—
544C2×C3×C4—44no—
545C2×C3×C4—44no—
546C2×C3×C4C22×D414yes—
547C2×C3×C4C2×#4114yes—
548C2×Dic3—28no—
549C2×Dic3—22no—
550C2×Dic3—22no—
551C2×Dic3—22no—
552C2×Dic3—22no—
553C2×Dic3—22no—
554C2×Dic3—22no—
555C2×Dic3—22no—
556C2×Dic3—22no—
557C2×Dic3—22no—
558C2×Dic3—22no—
559C2×Dic3—22no—
560C2×Dic3—44no—
561C2×Dic3—44no—
562C2×Dic3—44no—
563C2×Dic3C22×D414yes—
564D12—416no—
565D12—416no—
566D12—416no—
567D12—416no—
568D12—416no—
569D12—416no—
570C4×D3—416no—
571C4×D3—416no—
572C24—34no—
573C24—34no—
574C24—32no—
575C24—32no—
576C24—32no—
577C24—32no—
578C24—62no—
579C24—62no—
580C24—62no—
581C24—62no—
582C24—62no—
583C24—62no—
584C24—62no—
585C24—62no—
586C24—62no—
587C24—62no—
588C24—62no—
589C24—62no—
590C24—62no—
591C24—62no—
592C24—62no—
593C24—62no—
594C24—62no—
595C24—62no—
596C24—62no—
597C24—62no—
598C24—62no—
599C24—62no—
600C24—62no—
601C24—62no—
602C24—62no—
603C24—62no—
604C24C23×D311yescharacteristic
605C2×D4—68no—
606C2×D4—68no—
607C2×D4—68no—
608C2×D4—68no—
609C2×D4—68no—
610C2×D4—68no—
611C2×D4—68no—
612C2×D4—68no—
613C2×D4—124no—
614C2×D4—124no—
615C2×D4—124no—
616C2×D4—124no—
617C2×D4—124no—
618C2×D4—124no—
619C2×D4—124no—
620C2×D4—124no—
621C2×D4—124no—
622C2×D4—124no—
623C2×D4—1216no—
624C2×D4—1216no—
625C2×D4—1216no—
626C2×D4—1216no—
627C2×D4—1216no—
628C2×D4—1216no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—34no—
649C22×C4—32no—
650C22×C4—32no—
651C22×C4—32no—
652C22×C4—32no—
653C22×C4—68no—
654C22×C4—68no—
655C22×C4—62no—
656C22×C4—62no—
657C22×C4—62no—
658C22×C4—62no—
659C22×C4—62no—
660C22×C4—62no—
661C22×C4—62no—
662C22×C4—62no—
663C22×C4—62no—
664C22×C4—62no—
665C22×C4—62no—
666C22×C4—68no—
667C22×C4—124no—
668C22×C4—124no—
669C22×C4—124no—
670C22×C4—1216no—
671C22×C4—1216no—
672C22×C4D3×D414yes—
673C22×C4#23914yes—
674C22×C4C23×D312yes—
675C22×C4C23×D312yes—
676C22×C4C23×D312yes—
677C22×C4C23×D312yes—
678C22×C4C23×D312yes—
679C22×C4C23×D312yes—
680C22×C4C23×D312yes—
681C4⋊C4—28no—
682C4⋊C4—28no—
683C4⋊C4—68no—
684C4⋊C4—124no—
685C22⋊C4—316no—
686C22⋊C4—68no—
687C22⋊C4—68no—
688C22⋊C4—68no—
689C22⋊C4—68no—
690C22⋊C4—124no—
691C22⋊C4—124no—
692C22⋊C4—124no—
693C22⋊C4—124no—
694C22⋊C4—124no—
695C22⋊C4—124no—
696C22⋊C4—124no—
697C22⋊C4—124no—
698C22⋊C4—124no—
699C42—124no—
700C22×C3#53514yes—
701C22×C3#53814yes—
702C22×C3#54014yes—
703C22×C3#54614yes—
704C22×C3#54614yes—
705C22×C3#55314yes—
706C22×C3#56014yes—
707C22×C3C23×D411yescharacteristic
708C22×C3C22×#4111yescharacteristic
709C22×C3C22×#4111yescharacteristic
710C22×C3C2×H(5,𝔽2)11yescharacteristic
711C22×C3C2×H(5,𝔽2)11yescharacteristic
712C22×C3C2×H(5,𝔽2)11yescharacteristic
713C22×C3C2×H(5,𝔽2)11yescharacteristic
714C2×D3—24no—
715C2×D3—24no—
716C2×D3—24no—
717C2×D3—24no—
718C2×D3—24no—
719C2×D3—24no—
720C2×D3—42no—
721C2×D3—42no—
722C2×D3—42no—
723C2×D3—42no—
724C2×D3—42no—
725C2×D3—416no—
726C2×D3—416no—
727C2×D3—42no—
728C2×D3—42no—
729C2×D3—42no—
730C2×D3—42no—
731C2×D3—42no—
732C2×D3—42no—
733C2×D3—42no—
734C2×D3—42no—
735C2×D3—42no—
736C2×D3—42no—
737C2×D3—42no—
738C2×D3—42no—
739C2×D3—42no—
740C2×D3—42no—
741C2×D3—42no—
742C2×D3—42no—
743C2×D3—42no—
744C2×D3—88no—
745C2×D3—88no—
746C3×C4—24no—
747C3×C4—24no—
748C3×C4—42no—
749C3×C4—42no—
750C3×C4—42no—
751C3×C4—42no—
752C3×C4—42no—
753Dic3—24no—
754Dic3—42no—
755Dic3—42no—
756Dic3—42no—
757C23—34no—
758C23—34no—
759C23—68no—
760C23—68no—
761C23—68no—
762C23—68no—
763C23—62no—
764C23—62no—
765C23—62no—
766C23—68no—
767C23—62no—
768C23—62no—
769C23—62no—
770C23—62no—
771C23—62no—
772C23—62no—
773C23—62no—
774C23—62no—
775C23—62no—
776C23—68no—
777C23—62no—
778C23—62no—
779C23—62no—
780C23—62no—
781C23—62no—
782C23—62no—
783C23—62no—
784C23—62no—
785C23—62no—
786C23—62no—
787C23—62no—
788C23—62no—
789C23—62no—
790C23—62no—
791C23—124no—
792C23—124no—
793C23—124no—
794C23—124no—
795C23—124no—
796C23—124no—
797C23—124no—
798C23—124no—
799C23—124no—
800C23—124no—
801C23—124no—
802C23—124no—
803C23—124no—
804C23—124no—
805C23—124no—
806C23—124no—
807C23—124no—
808C23—124no—
809C23—124no—
810C23—124no—
811C23—124no—
812C23—124no—
813C23C2×D3×D412yes—
814C23C2×#23912yes—
815C23D3×#4112yes—
816C23#100912yes—
817C23#100912yes—
818C23#100912yes—
819C23#100912yes—
820C23C24×D311yescharacteristic
821D4—1216no—
822D4—1216no—
823D4—1216no—
824D4—1216no—
825D4—1216no—
826D4—1216no—
827C2×C4—28no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—28no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—34no—
849C2×C4—44no—
850C2×C4—44no—
851C2×C4—44no—
852C2×C4—44no—
853C2×C4—44no—
854C2×C4—62no—
855C2×C4—62no—
856C2×C4—68no—
857C2×C4—62no—
858C2×C4—62no—
859C2×C4—62no—
860C2×C4—62no—
861C2×C4—62no—
862C2×C4—62no—
863C2×C4—62no—
864C2×C4—62no—
865C2×C4—62no—
866C2×C4—1216no—
867C2×C4—1216no—
868C2×C4—124no—
869C2×C4—124no—
870C2×C4—124no—
871C2×C4C2×D3×D414yes—
872C2×C4C2×#23914yes—
873C2×C3#270318yescomplemented
874C2×C3C2×#53511yescharacteristic
875C2×C3C2×#53811yescharacteristic
876C2×C3C2×#54011yescharacteristic
877C2×C3C2×#54611yescharacteristic
878C2×C3C2×#54611yescharacteristic
879C2×C3C2×#55311yescharacteristic
880C2×C3C2×#56011yescharacteristic
881D3—44no—
882D3—44no—
883D3—82no—
884D3—82no—
885C22—64no—
886C22—64no—
887C22—64no—
888C22—64no—
889C22—64no—
890C22—64no—
891C22—122no—
892C22—122no—
893C22—122no—
894C22—122no—
895C22—122no—
896C22—122no—
897C22—122no—
898C22—1216no—
899C22—1216no—
900C22—122no—
901C22—122no—
902C22—122no—
903C22—122no—
904C22—122no—
905C22—122no—
906C22—122no—
907C22—122no—
908C22—122no—
909C22—122no—
910C22—122no—
911C22—122no—
912C22—122no—
913C22—122no—
914C22—122no—
915C22—248no—
916C22—248no—
917C22#563014yes—
918C22#565414yes—
919C22#567414yes—
920C22#569514yes—
921C22#569714yes—
922C22#570414yes—
923C22#571114yes—
924C22C22×D3×D411yescharacteristic
925C22C22×#23911yescharacteristic
926C22C2×D3×#4111yescharacteristic
927C22C2×#100911yescharacteristic
928C22C2×#100911yescharacteristic
929C22C2×#100911yescharacteristic
930C22C2×#100911yescharacteristic
931C4—24no—
932C4—24no—
933C4—42no—
934C4—42no—
935C4—42no—
936C4—42no—
937C4—42no—
938C4—64no—
939C4—122no—
940C4—122no—
941C4—122no—
942C3C2×#270311yescharacteristic, complemented, Sylow
943C2—124no—
944C2—124no—
945C2—242no—
946C2—242no—
947C2#7824118yesdirect product factor
948C2C2×#563011yescharacteristic
949C2C2×#565411yescharacteristic
950C2C2×#567411yescharacteristic
951C2C2×#569711yescharacteristic
952C2C2×#569511yescharacteristic
953C2C2×#570411yescharacteristic
954C2C2×#571111yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC2×C3×#400C2
socleC24×C3C24
hypercenterC2×#400D3
hypocenterC3C2×#2703
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#400

Complements

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

NH ≅ G/Ntype
1. C22×#894C2semidirect
2. C22×#895C2semidirect
3. C2×C3×#400C2semidirect
4. C2×#4988C2semidirect
5. C2×#4990C2semidirect
6. #78241C2direct (N × H)
7. C2×#4675C2semidirect
8. C2×#4671C2semidirect
9. C2×#4671C2semidirect
10. C2×#4671C2semidirect
11. C2×#4665C2semidirect
12. C2×#4665C2semidirect
13. C2×#4665C2semidirect
14. C2×#4667C2semidirect
15. C2×#4672C2semidirect
16. C2×#4669C2semidirect
46. C2×#895C22semidirect
48. C2×#894C22semidirect
49. C3×#400C22semidirect
58. #4990C22semidirect
59. #4988C22semidirect
60. #4675C22semidirect
61. #4672C22semidirect
62. #4671C22semidirect
63. #4671C22semidirect
64. #4671C22semidirect
65. #4669C22semidirect
66. #4667C22semidirect
67. #4665C22semidirect
68. #4665C22semidirect
69. #4665C22semidirect
73. C2×#400D3semidirect
150. C2×(C2×D3)⋊C4D4semidirect
212. #400C2×D3semidirect
357. (C2×D3)⋊C4C2×D4semidirect
873. C2×C3#2703semidirect
942. C3C2×#2703semidirect
947. C2#78241direct (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×#8952
C2×C3×#4002
C2×#49882
C2×#49902
#782412
C2×#46752
C2×#46712
C2×#46652
C2×#46672
C2×#46722
C2×#46692
C2×#27033