Finite Group Databasebeta

← C2×#75160 #11430470

Subgroups — C2×#75160 #11430470

Order 768.

3434 conjugacy classes of subgroups.

The subgroup lattice has 952 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#895C211yesmaximal, characteristic, complemented
2C22×#898C211yesmaximal, characteristic, complemented
3C2×C3×#387C211yesmaximal, characteristic, complemented
4C2×#4991C211yesmaximal, characteristic, complemented
5C2×#4988C211yesmaximal, characteristic, complemented
6C2×#4939C211yesmaximal, characteristic, complemented
7C2×#4939C211yesmaximal, characteristic, complemented
8#75160C2116yesmaximal, direct product factor
9C2×#4671C211yesmaximal, characteristic, complemented
10C2×#4671C211yesmaximal, characteristic, complemented
11C2×#4671C211yesmaximal, characteristic, complemented
12C2×#4665C211yesmaximal, characteristic, complemented
13C2×#4668C211yesmaximal, characteristic, complemented
14C2×#4674C211yesmaximal, characteristic, complemented
15C2×#4672C211yesmaximal, characteristic, complemented
16C2×#4670C211yesmaximal, characteristic, complemented
17C2×#2714—31nomaximal, Sylow
18C23×D12C2211yescharacteristic
19C23×D12C2211yescharacteristic
20C23×D12C2211yescharacteristic
21C23×D12C2211yescharacteristic
22C23×D12C2211yescharacteristic
23C23×D12C2211yescharacteristic
24C23×C4×D3C2211yescharacteristic
25C22×C3×C4⋊C4C2211yescharacteristic
26C22×C3×C4⋊C4C2211yescharacteristic
27C22×C3×C42C2211yescharacteristic
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×(C2×D3)⋊C4C2211yescharacteristic
43C22×C4⋊Dic3C2211yescharacteristic
44C22×C4⋊Dic3C2211yescharacteristic
45C22×Dic3⋊C4C2211yescharacteristic
46C22×C4×Dic3C2211yescharacteristic
47C2×#898—28no—
48C2×#898C2218yescomplemented
49C2×#895—28no—
50C2×#895C2218yescomplemented
51C3×#387C2218yescomplemented
52C2×C3×#95C2211yescharacteristic
53C2×C3×#95C2211yescharacteristic
54C2×C3×#95C2211yescharacteristic
55C2×C3×#95C2211yescharacteristic
56C2×C3⋊#95C2211yescharacteristic
57C2×C3⋊#95C2211yescharacteristic
58#4991C2218yescomplemented
59#4988C2218yescomplemented
60#4939C2218yescomplemented
61#4939C2218yescomplemented
62#4674C2218yescomplemented
63#4672C2218yescomplemented
64#4671C2218yescomplemented
65#4671C2218yescomplemented
66#4671C2218yescomplemented
67#4670C2218yescomplemented
68#4668C2218yescomplemented
69#4665C2218yescomplemented
70C22×#126—31no—
71C22×#121—31no—
72#2714—316no—
73C2×#397—31no—
74C2×#394—31no—
75C2×#394—31no—
76C2×#392—31no—
77C2×#392—31no—
78C2×#392—31no—
79C2×#390—31no—
80C2×#390—31no—
81C2×#390—31no—
82C2×#388—31no—
83C2×#387D311yescharacteristic, complemented
84C2×#386—31no—
85C2×#385—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—42no—
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—42no—
127C22×C4×D3—42no—
128C22×C4×D3C2314yes—
129C2×C3×C4⋊C4—42no—
130C2×C3×C4⋊C4D418yescomplemented
131C2×C3×C4⋊C4C2314yes—
132C2×C3×C4⋊C4C2314yes—
133C2×C3×C42—42no—
134C2×C3×C42C2314yes—
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—24no—
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)⋊C4C2314yes—
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×C4⋊Dic3—24no—
166C2×C4⋊Dic3—42no—
167C2×C4⋊Dic3C2314yes—
168C2×C4⋊Dic3C2314yes—
169C2×Dic3⋊C4—24no—
170C2×Dic3⋊C4C2314yes—
171C2×C4×Dic3—24no—
172C2×C4×Dic3C2314yes—
173#898—232no—
174#895—232no—
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—
188C2×#126—38no—
189C2×#126—68no—
190C2×#121—38no—
191C2×#121—68no—
192C22×C4⋊C4—31no—
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×C22⋊C4—31no—
212C22×C42—31no—
213C22×C42C2×D311yescharacteristic
214#397—38no—
215#394—38no—
216#394—38no—
217#392—38no—
218#392—38no—
219#392—38no—
220#390—38no—
221#390—38no—
222#390—38no—
223#388—38no—
224#387C2×D318yescomplemented
225#386—38no—
226#385—38no—
227C2×#95—31no—
228C2×#95—31no—
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×D3—22no—
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×C4C2×D414yes—
284C22×C3×C4C2×D414yes—
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×Dic3—22no—
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—44no—
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—44no—
336C2×C4×D3—44no—
337C2×C4×D3—416no—
338C3×C4⋊C4—44no—
339C3×C4⋊C4C2×D4116yescomplemented
340C3×C42—44no—
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—
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—
356C4⋊Dic3—28no—
357C4⋊Dic3—44no—
358Dic3⋊C4—28no—
359C4×Dic3—28no—
360C25—31no—
361C25—31no—
362C25—31no—
363C25—31no—
364C22×D4—34no—
365C22×D4—34no—
366C22×D4—34no—
367C22×D4—34no—
368C22×D4—34no—
369C22×D4—34no—
370C22×D4—64no—
371C22×D4—64no—
372C22×D4—64no—
373C22×D4—64no—
374C22×D4—64no—
375C22×D4—64no—
376C22×D4—64no—
377C22×D4—122no—
378C22×D4—122no—
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—
388C23×C4—31no—
389C23×C4—31no—
390C23×C4—31no—
391C23×C4—31no—
392C23×C4—34no—
393C23×C4—64no—
394C23×C4—122no—
395C23×C4—122no—
396C23×C4C22×D311yescharacteristic
397C23×C4C22×D311yescharacteristic
398C23×C4C22×D311yescharacteristic
399C23×C4C22×D311yescharacteristic
400C23×C4C22×D311yescharacteristic
401C23×C4C22×D311yescharacteristic
402C23×C4C22×D311yescharacteristic
403#126—632no—
404#121—632no—
405C2×C4⋊C4—34no—
406C2×C4⋊C4—34no—
407C2×C4⋊C4—34no—
408C2×C4⋊C4—42no—
409C2×C4⋊C4—64no—
410C2×C4⋊C4—64no—
411C2×C4⋊C4—122no—
412C2×C4⋊C4D1218yescomplemented
413C2×C4⋊C4C22×D314yes—
414C2×C4⋊C4C22×D314yes—
415C2×C22⋊C4—34no—
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—34no—
426C2×C22⋊C4—34no—
427C2×C22⋊C4—34no—
428C2×C22⋊C4—34no—
429C2×C22⋊C4—34no—
430C2×C22⋊C4—64no—
431C2×C22⋊C4—64no—
432C2×C22⋊C4—64no—
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×C42—34no—
446C2×C42—42no—
447C2×C42—64no—
448C2×C42C22×D314yes—
449#95—34no—
450#95—34no—
451#95C22×D314yes—
452#95C22×D314yes—
453#95C22×D314yes—
454#95C22×D314yes—
455C23×C3C22×D412yes—
456C23×C3C2×#4112yes—
457C23×C3C2×#4112yes—
458C23×C3H(5,𝔽2)12yes—
459C23×C3H(5,𝔽2)12yes—
460C23×C3H(5,𝔽2)12yes—
461C23×C3H(5,𝔽2)12yes—
462C23×C3C2511yescharacteristic
463C22×D3—28no—
464C22×D3—28no—
465C22×D3—28no—
466C22×D3—22no—
467C22×D3—22no—
468C22×D3—22no—
469C22×D3—22no—
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—44no—
494C22×D3—44no—
495C22×D3—44no—
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×D3C2×#4114yes—
519C2×C3×C4—28no—
520C2×C3×C4—28no—
521C2×C3×C4—28no—
522C2×C3×C4—28no—
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—44no—
541C2×C3×C4—44no—
542C2×C3×C4—44no—
543C2×C3×C4C22×D414yes—
544C2×C3×C4C22×D414yes—
545C2×C3×C4C22×D414yes—
546C2×C3×C4C2×#4114yes—
547C2×Dic3—22no—
548C2×Dic3—22no—
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—44no—
560C2×Dic3—44no—
561C2×Dic3—44no—
562C2×Dic3—44no—
563D12—416no—
564D12—416no—
565D12—416no—
566D12—416no—
567D12—416no—
568D12—416no—
569C4×D3—416no—
570C24—34no—
571C24—32no—
572C24—32no—
573C24—32no—
574C24—32no—
575C24—62no—
576C24—62no—
577C24—62no—
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—
602C24C23×D311yescharacteristic
603C2×D4—68no—
604C2×D4—68no—
605C2×D4—68no—
606C2×D4—68no—
607C2×D4—68no—
608C2×D4—68no—
609C2×D4—68no—
610C2×D4—124no—
611C2×D4—124no—
612C2×D4—124no—
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—1216no—
622C2×D4—1216no—
623C2×D4—1216no—
624C2×D4—1216no—
625C2×D4—1216no—
626C2×D4—1216no—
627C22×C4—22no—
628C22×C4—22no—
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—32no—
645C22×C4—32no—
646C22×C4—32no—
647C22×C4—32no—
648C22×C4—62no—
649C22×C4—62no—
650C22×C4—62no—
651C22×C4—62no—
652C22×C4—62no—
653C22×C4—62no—
654C22×C4—62no—
655C22×C4—62no—
656C22×C4—62no—
657C22×C4—62no—
658C22×C4—62no—
659C22×C4—62no—
660C22×C4—68no—
661C22×C4—124no—
662C22×C4—124no—
663C22×C4—1216no—
664C22×C4C2×D1214yes—
665C22×C4C2×D1214yes—
666C22×C4C2×D1214yes—
667C22×C4#23914yes—
668C22×C4C23×D312yes—
669C22×C4C23×D312yes—
670C22×C4C23×D312yes—
671C22×C4C23×D312yes—
672C22×C4C23×D312yes—
673C22×C4C23×D312yes—
674C22×C4C23×D312yes—
675C4⋊C4—44no—
676C4⋊C4—68no—
677C4⋊C4—68no—
678C4⋊C4—124no—
679C4⋊C4C2×D12116yescomplemented
680C22⋊C4—68no—
681C22⋊C4—68no—
682C22⋊C4—68no—
683C22⋊C4—68no—
684C22⋊C4—68no—
685C22⋊C4—68no—
686C22⋊C4—68no—
687C22⋊C4—124no—
688C22⋊C4—124no—
689C22⋊C4—124no—
690C22⋊C4—124no—
691C22⋊C4—124no—
692C22⋊C4—124no—
693C22⋊C4—124no—
694C22⋊C4—124no—
695C42—44no—
696C42—68no—
697C22×C3#53514yes—
698C22×C3#53814yes—
699C22×C3#53814yes—
700C22×C3#54614yes—
701C22×C3#55014yes—
702C22×C3#55314yes—
703C22×C3#56014yes—
704C22×C3C23×D411yescharacteristic
705C22×C3C22×#4111yescharacteristic
706C22×C3C22×#4111yescharacteristic
707C22×C3C2×H(5,𝔽2)11yescharacteristic
708C22×C3C2×H(5,𝔽2)11yescharacteristic
709C22×C3C2×H(5,𝔽2)11yescharacteristic
710C22×C3C2×H(5,𝔽2)11yescharacteristic
711C2×D3—24no—
712C2×D3—24no—
713C2×D3—24no—
714C2×D3—42no—
715C2×D3—42no—
716C2×D3—42no—
717C2×D3—416no—
718C2×D3—42no—
719C2×D3—42no—
720C2×D3—42no—
721C2×D3—42no—
722C2×D3—42no—
723C2×D3—42no—
724C2×D3—42no—
725C2×D3—42no—
726C2×D3—42no—
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—88no—
741C2×D3—88no—
742C2×D3—88no—
743C3×C4—24no—
744C3×C4—24no—
745C3×C4—24no—
746C3×C4—24no—
747C3×C4—42no—
748C3×C4—42no—
749C3×C4—42no—
750Dic3—42no—
751Dic3—42no—
752Dic3—42no—
753Dic3—42no—
754C23—34no—
755C23—68no—
756C23—62no—
757C23—62no—
758C23—62no—
759C23—68no—
760C23—62no—
761C23—62no—
762C23—62no—
763C23—68no—
764C23—62no—
765C23—62no—
766C23—62no—
767C23—62no—
768C23—62no—
769C23—62no—
770C23—62no—
771C23—62no—
772C23—62no—
773C23—62no—
774C23—62no—
775C23—62no—
776C23—62no—
777C23—62no—
778C23—62no—
779C23—62no—
780C23—62no—
781C23—62no—
782C23—62no—
783C23—62no—
784C23—62no—
785C23—124no—
786C23—124no—
787C23—124no—
788C23—124no—
789C23—124no—
790C23—124no—
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—
810C23C22×D1212yes—
811C23#100412yes—
812C23C2×#23912yes—
813C23D3×#4112yes—
814C23#100912yes—
815C23#100912yes—
816C23#100912yes—
817C23C24×D311yescharacteristic
818D4—1216no—
819D4—1216no—
820D4—1216no—
821D4—1216no—
822D4—1216no—
823D4—1216no—
824C2×C4—28no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—28no—
834C2×C4—28no—
835C2×C4—28no—
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—44no—
846C2×C4—44no—
847C2×C4—44no—
848C2×C4—62no—
849C2×C4—62no—
850C2×C4—62no—
851C2×C4—62no—
852C2×C4—62no—
853C2×C4—62no—
854C2×C4—62no—
855C2×C4—62no—
856C2×C4—62no—
857C2×C4—62no—
858C2×C4—62no—
859C2×C4—62no—
860C2×C4—1216no—
861C2×C4—124no—
862C2×C4—124no—
863C2×C4—124no—
864C2×C4—124no—
865C2×C4C22×D1214yes—
866C2×C4C22×D1214yes—
867C2×C4C22×D1214yes—
868C2×C4C2×#23914yes—
869C2×C3#271418yescomplemented
870C2×C3C2×#53511yescharacteristic
871C2×C3C2×#53811yescharacteristic
872C2×C3C2×#53811yescharacteristic
873C2×C3C2×#54611yescharacteristic
874C2×C3C2×#55011yescharacteristic
875C2×C3C2×#55311yescharacteristic
876C2×C3C2×#56011yescharacteristic
877D3—44no—
878D3—82no—
879D3—82no—
880D3—82no—
881C22—64no—
882C22—64no—
883C22—64no—
884C22—122no—
885C22—1216no—
886C22—122no—
887C22—122no—
888C22—122no—
889C22—122no—
890C22—122no—
891C22—122no—
892C22—122no—
893C22—122no—
894C22—122no—
895C22—122no—
896C22—122no—
897C22—122no—
898C22—122no—
899C22—122no—
900C22—122no—
901C22—122no—
902C22—122no—
903C22—122no—
904C22—122no—
905C22—122no—
906C22—122no—
907C22—122no—
908C22—122no—
909C22—122no—
910C22—248no—
911C22—248no—
912C22—248no—
913C22#552514yes—
914C22#555414yes—
915C22#557714yes—
916C22#564414yes—
917C22#566614yes—
918C22#569514yes—
919C22#570414yes—
920C22C23×D1211yescharacteristic
921C22C2×#100411yescharacteristic
922C22C22×#23911yescharacteristic
923C22C2×D3×#4111yescharacteristic
924C22C2×#100911yescharacteristic
925C22C2×#100911yescharacteristic
926C22C2×#100911yescharacteristic
927C4—24no—
928C4—24no—
929C4—24no—
930C4—24no—
931C4—42no—
932C4—42no—
933C4—42no—
934C4—122no—
935C4—122no—
936C4—122no—
937C4—122no—
938C3C2×#271411yescharacteristic, complemented, Sylow
939C2—124no—
940C2—242no—
941C2—242no—
942C2—242no—
943C2#7516018yesdirect product factor
944C2C2×#552511yescharacteristic
945C2C2×#555411yescharacteristic
946C2C2×#557711yescharacteristic
947C2C2×#564411yescharacteristic
948C2C2×#566611yescharacteristic
949C2C2×#569511yescharacteristic
950C2C2×#570411yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC2×C3×#387C2
socleC24×C3C24
hypercenterC2×#387D3
hypocenterC3C2×#2714
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
1. C22×#895C2semidirect
2. C22×#898C2semidirect
3. C2×C3×#387C2semidirect
4. C2×#4991C2semidirect
5. C2×#4988C2semidirect
6. C2×#4939C2semidirect
7. C2×#4939C2semidirect
8. #75160C2direct (N × H)
9. C2×#4671C2semidirect
10. C2×#4671C2semidirect
11. C2×#4671C2semidirect
12. C2×#4665C2semidirect
13. C2×#4668C2semidirect
14. C2×#4674C2semidirect
15. C2×#4672C2semidirect
16. C2×#4670C2semidirect
48. C2×#898C22semidirect
50. C2×#895C22semidirect
51. C3×#387C22semidirect
58. #4991C22semidirect
59. #4988C22semidirect
60. #4939C22semidirect
61. #4939C22semidirect
62. #4674C22semidirect
63. #4672C22semidirect
64. #4671C22semidirect
65. #4671C22semidirect
66. #4671C22semidirect
67. #4670C22semidirect
68. #4668C22semidirect
69. #4665C22semidirect
83. C2×#387D3semidirect
130. C2×C3×C4⋊C4D4semidirect
224. #387C2×D3semidirect
339. C3×C4⋊C4C2×D4semidirect
412. C2×C4⋊C4D12semidirect
679. C4⋊C4C2×D12semidirect
869. C2×C3#2714semidirect
938. C3C2×#2714semidirect
943. C2#75160direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#8952
C22×#8982
C2×C3×#3872
C2×#49912
C2×#49882
C2×#49392
#751602
C2×#46712
C2×#46652
C2×#46682
C2×#46742
C2×#46722
C2×#46702
C2×#27143