Finite Group Databasebeta

← C2×#75927 #11430275

Subgroups — C2×#75927 #11430275

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×#884C211yesmaximal, characteristic, complemented
2C22×#886C211yesmaximal, characteristic, complemented
3C2×C3×#388C211yesmaximal, characteristic, complemented
4C2×#4991C211yesmaximal, characteristic, complemented
5C2×#4987C211yesmaximal, characteristic, complemented
6C2×#4960C211yesmaximal, characteristic, complemented
7C2×#4960C211yesmaximal, characteristic, complemented
8C2×#4958C211yesmaximal, characteristic, complemented
9C2×#4958C211yesmaximal, characteristic, complemented
10C2×#4939C211yesmaximal, characteristic, complemented
11C2×#4940C211yesmaximal, characteristic, complemented
12#75927C2116yesmaximal, direct product factor
13C2×#4671C211yesmaximal, characteristic, complemented
14C2×#4665C211yesmaximal, characteristic, complemented
15C2×#4659C211yesmaximal, characteristic, complemented
16C2×#4674C211yesmaximal, characteristic, complemented
17C2×#2703—31nomaximal, Sylow
18C23×#67C2211yescharacteristic
19C23×#67C2211yescharacteristic
20C23×#67C2211yescharacteristic
21C24×Dic3C2211yescharacteristic
22C23×D12C2211yescharacteristic
23C23×D12C2211yescharacteristic
24C23×D12C2211yescharacteristic
25C23×C4×D3C2211yescharacteristic
26C22×C3×C4⋊C4C2211yescharacteristic
27C22×C3×C22⋊C4C2211yescharacteristic
28C22×C3×C22⋊C4C2211yescharacteristic
29C22×C3×C22⋊C4C2211yescharacteristic
30C22×C3×C42C2211yescharacteristic
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×C4⋊Dic3C2211yescharacteristic
43C22×C4⋊Dic3C2211yescharacteristic
44C22×Dic3⋊C4C2211yescharacteristic
45C2×#886—28no—
46C2×#886C2218yescomplemented
47C2×#884—28no—
48C2×#884C2218yescomplemented
49C3×#388C2218yescomplemented
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#4991C2218yescomplemented
59#4987C2218yescomplemented
60#4960C2218yescomplemented
61#4960C2218yescomplemented
62#4958C2218yescomplemented
63#4958C2218yescomplemented
64#4940C2218yescomplemented
65#4939C2218yescomplemented
66#4674C2218yescomplemented
67#4671C2218yescomplemented
68#4665C2218yescomplemented
69#4659C2218yescomplemented
70C22×#123—31no—
71C22×#121—31no—
72#2703—316no—
73C2×#400—31no—
74C2×#397—31no—
75C2×#394—31no—
76C2×#392—31no—
77C2×#392—31no—
78C2×#392—31no—
79C2×#390—31no—
80C2×#388—31no—
81C2×#388D311yescharacteristic, complemented
82C2×#386—31no—
83C2×#386—31no—
84C2×#386—31no—
85C2×#380—31no—
86C25×C3C2311yescharacteristic
87C24×D3C2311yescharacteristic
88C24×D3C2311yescharacteristic
89C24×D3C2311yescharacteristic
90C23×C3×C4C2311yescharacteristic
91C23×C3×C4C2311yescharacteristic
92C23×C3×C4C2311yescharacteristic
93C23×C3×C4C2311yescharacteristic
94C23×C3×C4C2311yescharacteristic
95C23×C3×C4C2311yescharacteristic
96C22×#67—24no—
97C22×#67—24no—
98C22×#67—24no—
99C22×#67—24no—
100C22×#67—24no—
101C22×#67—42no—
102C22×#67—42no—
103C22×#67—42no—
104C22×#67—42no—
105C22×#67C2314yes—
106C22×#67C2314yes—
107C22×#67C2314yes—
108C23×Dic3—24no—
109C23×Dic3—42no—
110C23×Dic3—42no—
111C23×Dic3C2311yescharacteristic
112C23×Dic3C2311yescharacteristic
113C23×Dic3C2311yescharacteristic
114C23×Dic3C2311yescharacteristic
115C23×Dic3C2311yescharacteristic
116C23×Dic3C2314yes—
117C22×D12—24no—
118C22×D12—24no—
119C22×D12—24no—
120C22×D12—42no—
121C22×D12—42no—
122C22×D12—42no—
123C22×D12—42no—
124C22×D12—42no—
125C22×D12—42no—
126C22×D12C2314yes—
127C22×D12C2314yes—
128C22×D12C2314yes—
129C22×C4×D3—24no—
130C22×C4×D3—24no—
131C22×C4×D3—42no—
132C22×C4×D3C2314yes—
133C2×C3×C4⋊C4—42no—
134C2×C3×C4⋊C4C2314yes—
135C2×C3×C22⋊C4—42no—
136C2×C3×C22⋊C4—42no—
137C2×C3×C22⋊C4D418yescomplemented
138C2×C3×C22⋊C4C2314yes—
139C2×C3×C22⋊C4C2314yes—
140C2×C3×C22⋊C4C2314yes—
141C2×C3×C42—42no—
142C2×C3×C42C2314yes—
143C2×(C2×D3)⋊C4—24no—
144C2×(C2×D3)⋊C4—24no—
145C2×(C2×D3)⋊C4—24no—
146C2×(C2×D3)⋊C4—24no—
147C2×(C2×D3)⋊C4—42no—
148C2×(C2×D3)⋊C4—42no—
149C2×(C2×D3)⋊C4—42no—
150C2×(C2×D3)⋊C4—42no—
151C2×(C2×D3)⋊C4—42no—
152C2×(C2×D3)⋊C4—42no—
153C2×(C2×D3)⋊C4—42no—
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—24no—
167C2×C4⋊Dic3C2314yes—
168C2×C4⋊Dic3C2314yes—
169C2×Dic3⋊C4—24no—
170C2×Dic3⋊C4C2314yes—
171#886—232no—
172#884—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⋊C4—31no—
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⋊C4C2×D311yescharacteristic
209C22×C22⋊C4C2×D311yescharacteristic
210C22×C22⋊C4C2×D311yescharacteristic
211C22×C42C2×D311yescharacteristic
212#400—38no—
213#397—38no—
214#394—38no—
215#392—38no—
216#392—38no—
217#392—38no—
218#390—38no—
219#388—38no—
220#388C2×D318yescomplemented
221#386—38no—
222#386—38no—
223#386—38no—
224#380—38no—
225C2×#95—31no—
226C2×#95—31no—
227C2×#95—31no—
228C2×#95—31no—
229C2×#95—31no—
230C2×#95—31no—
231C2×#95C2×D311yescharacteristic
232C2×#95C2×D311yescharacteristic
233C24×C3—22no—
234C24×C3—22no—
235C24×C3—22no—
236C24×C3—22no—
237C24×C3—22no—
238C24×C3—22no—
239C24×C3C2×D414yes—
240C24×C3C2412yes—
241C24×C3C2411yescharacteristic
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—22no—
262C23×D3#4114yes—
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×C4C2×D414yes—
283C22×C3×C4C2×D414yes—
284C22×C3×C4C2412yes—
285C22×C3×C4C2412yes—
286C22×C3×C4C2412yes—
287C22×C3×C4C2412yes—
288C22×C3×C4C2412yes—
289C22×C3×C4C2412yes—
290C2×#67—28no—
291C2×#67—28no—
292C2×#67—28no—
293C2×#67—28no—
294C2×#67—28no—
295C2×#67—44no—
296C2×#67—44no—
297C2×#67—44no—
298C2×#67—44no—
299C2×#67—416no—
300C2×#67—416no—
301C2×#67—416no—
302C22×Dic3—22no—
303C22×Dic3—22no—
304C22×Dic3—28no—
305C22×Dic3—22no—
306C22×Dic3—22no—
307C22×Dic3—22no—
308C22×Dic3—22no—
309C22×Dic3—22no—
310C22×Dic3—22no—
311C22×Dic3—22no—
312C22×Dic3—22no—
313C22×Dic3—22no—
314C22×Dic3—22no—
315C22×Dic3—22no—
316C22×Dic3—22no—
317C22×Dic3—44no—
318C22×Dic3—44no—
319C22×Dic3—416no—
320C22×Dic3#4114yes—
321C22×Dic3C2412yes—
322C22×Dic3C2412yes—
323C22×Dic3C2412yes—
324C22×Dic3C2412yes—
325C22×Dic3C2412yes—
326C2×D12—28no—
327C2×D12—28no—
328C2×D12—28no—
329C2×D12—44no—
330C2×D12—44no—
331C2×D12—44no—
332C2×D12—44no—
333C2×D12—44no—
334C2×D12—44no—
335C2×D12—416no—
336C2×D12—416no—
337C2×D12—416no—
338C2×C4×D3—28no—
339C2×C4×D3—28no—
340C2×C4×D3—44no—
341C2×C4×D3—416no—
342C3×C4⋊C4—44no—
343C3×C22⋊C4—44no—
344C3×C22⋊C4—44no—
345C3×C22⋊C4C2×D4116yescomplemented
346C3×C42—44no—
347(C2×D3)⋊C4—28no—
348(C2×D3)⋊C4—28no—
349(C2×D3)⋊C4—28no—
350(C2×D3)⋊C4—28no—
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)⋊C4—44no—
358C4⋊Dic3—28no—
359C4⋊Dic3—28no—
360Dic3⋊C4—28no—
361C25—31no—
362C25—31no—
363C25—31no—
364C25C22×D311yescharacteristic
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—31no—
394C23×C4—34no—
395C23×C4—34no—
396C23×C4—64no—
397C23×C4—64no—
398C23×C4—64no—
399C23×C4—122no—
400C23×C4—122no—
401C23×C4—122no—
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—34no—
411C2×C4⋊C4—34no—
412C2×C4⋊C4—34no—
413C2×C4⋊C4—42no—
414C2×C4⋊C4—64no—
415C2×C4⋊C4—64no—
416C2×C4⋊C4—64no—
417C2×C4⋊C4C22×D314yes—
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—42no—
430C2×C22⋊C4—42no—
431C2×C22⋊C4—64no—
432C2×C22⋊C4—64no—
433C2×C22⋊C4—64no—
434C2×C22⋊C4—64no—
435C2×C22⋊C4—122no—
436C2×C22⋊C4—122no—
437C2×C22⋊C4—122no—
438C2×C22⋊C4—122no—
439C2×C22⋊C4—122no—
440C2×C22⋊C4—122no—
441C2×C22⋊C4—122no—
442C2×C22⋊C4D1218yescomplemented
443C2×C22⋊C4C22×D314yes—
444C2×C22⋊C4C22×D314yes—
445C2×C22⋊C4C22×D314yes—
446C2×C42—42no—
447C2×C42C22×D314yes—
448#95—34no—
449#95—34no—
450#95—34no—
451#95—34no—
452#95—34no—
453#95—34no—
454#95C22×D314yes—
455#95C22×D314yes—
456C23×C3—28no—
457C23×C3—28no—
458C23×C3—28no—
459C23×C3—22no—
460C23×C3—22no—
461C23×C3—22no—
462C23×C3—22no—
463C23×C3—22no—
464C23×C3—22no—
465C23×C3—44no—
466C23×C3—44no—
467C23×C3—44no—
468C23×C3—44no—
469C23×C3C22×D414yes—
470C23×C3C22×D412yes—
471C23×C3C2×#4112yes—
472C23×C3C2×#4112yes—
473C23×C3H(5,𝔽2)12yes—
474C23×C3H(5,𝔽2)12yes—
475C23×C3H(5,𝔽2)12yes—
476C23×C3H(5,𝔽2)12yes—
477C23×C3C2511yescharacteristic
478C22×D3—28no—
479C22×D3—28no—
480C22×D3—28no—
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—22no—
497C22×D3—22no—
498C22×D3—22no—
499C22×D3—22no—
500C22×D3—22no—
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×D3—44no—
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—44no—
539C2×C3×C4—44no—
540C2×C3×C4—44no—
541C2×C3×C4—44no—
542C2×C3×C4C22×D414yes—
543C2×C3×C4C22×D414yes—
544#67—416no—
545#67—416no—
546#67—416no—
547C2×Dic3—28no—
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—22no—
560C2×Dic3—22no—
561C2×Dic3—22no—
562C2×Dic3—416no—
563C2×Dic3—44no—
564C2×Dic3—44no—
565C2×Dic3—44no—
566C2×Dic3—44no—
567C2×Dic3C2×#4114yes—
568D12—416no—
569D12—416no—
570D12—416no—
571C4×D3—416no—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—34no—
579C24—32no—
580C24—32no—
581C24—32no—
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—
602C24C2×D1214yes—
603C24C23×D312yes—
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—1216no—
620C2×D4—1216no—
621C2×D4—1216no—
622C2×D4—124no—
623C2×D4—124no—
624C2×D4—124no—
625C2×D4—124no—
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—34no—
646C22×C4—32no—
647C22×C4—32no—
648C22×C4—32no—
649C22×C4—32no—
650C22×C4—32no—
651C22×C4—68no—
652C22×C4—62no—
653C22×C4—62no—
654C22×C4—62no—
655C22×C4—62no—
656C22×C4—62no—
657C22×C4—62no—
658C22×C4—68no—
659C22×C4—62no—
660C22×C4—62no—
661C22×C4—62no—
662C22×C4—62no—
663C22×C4—62no—
664C22×C4—62no—
665C22×C4—62no—
666C22×C4—62no—
667C22×C4—68no—
668C22×C4—124no—
669C22×C4—1216no—
670C22×C4—124no—
671C22×C4—124no—
672C22×C4—1216no—
673C22×C4C2×D1214yes—
674C22×C4C2×D1214yes—
675C22×C4C23×D312yes—
676C22×C4C23×D312yes—
677C22×C4C23×D312yes—
678C22×C4C23×D312yes—
679C22×C4C23×D312yes—
680C22×C4C23×D312yes—
681C4⋊C4—44no—
682C4⋊C4—68no—
683C4⋊C4—68no—
684C4⋊C4—68no—
685C22⋊C4—44no—
686C22⋊C4—44no—
687C22⋊C4—68no—
688C22⋊C4—68no—
689C22⋊C4—68no—
690C22⋊C4—68no—
691C22⋊C4—124no—
692C22⋊C4—124no—
693C22⋊C4—124no—
694C22⋊C4—124no—
695C22⋊C4—124no—
696C22⋊C4—124no—
697C22⋊C4—124no—
698C22⋊C4C2×D12116yescomplemented
699C42—44no—
700C22×C3—24no—
701C22×C3—24no—
702C22×C3—24no—
703C22×C3—42no—
704C22×C3—42no—
705C22×C3—416no—
706C22×C3—42no—
707C22×C3—42no—
708C22×C3#53514yes—
709C22×C3#53814yes—
710C22×C3#54014yes—
711C22×C3#54614yes—
712C22×C3#54614yes—
713C22×C3#55314yes—
714C22×C3#56014yes—
715C22×C3C23×D411yescharacteristic
716C22×C3C22×#4111yescharacteristic
717C22×C3C22×#4111yescharacteristic
718C22×C3C2×H(5,𝔽2)11yescharacteristic
719C22×C3C2×H(5,𝔽2)11yescharacteristic
720C22×C3C2×H(5,𝔽2)11yescharacteristic
721C22×C3C2×H(5,𝔽2)11yescharacteristic
722C2×D3—24no—
723C2×D3—24no—
724C2×D3—24no—
725C2×D3—42no—
726C2×D3—42no—
727C2×D3—42no—
728C2×D3—416no—
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—
752Dic3—24no—
753Dic3—42no—
754Dic3—42no—
755Dic3—42no—
756Dic3—42no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—28no—
764C23—28no—
765C23—28no—
766C23—34no—
767C23—44no—
768C23—44no—
769C23—44no—
770C23—44no—
771C23—68no—
772C23—62no—
773C23—62no—
774C23—62no—
775C23—62no—
776C23—62no—
777C23—62no—
778C23—68no—
779C23—68no—
780C23—62no—
781C23—62no—
782C23—62no—
783C23—62no—
784C23—62no—
785C23—62no—
786C23—62no—
787C23—62no—
788C23—62no—
789C23—62no—
790C23—62no—
791C23—62no—
792C23—62no—
793C23—62no—
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—
812C23C22×D1214yes—
813C23C22×D1212yes—
814C23#100412yes—
815C23#100412yes—
816C23D3×#4112yes—
817C23D3×#4112yes—
818C23#100912yes—
819C23#100912yes—
820C23C24×D311yescharacteristic
821D4—1216no—
822D4—1216no—
823D4—1216no—
824D4—1216no—
825D4—1216no—
826D4—1216no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—28no—
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—34no—
846C2×C4—44no—
847C2×C4—44no—
848C2×C4—44no—
849C2×C4—44no—
850C2×C4—62no—
851C2×C4—62no—
852C2×C4—68no—
853C2×C4—62no—
854C2×C4—62no—
855C2×C4—62no—
856C2×C4—62no—
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—1216no—
866C2×C4—1216no—
867C2×C4—124no—
868C2×C4—124no—
869C2×C4—124no—
870C2×C4—124no—
871C2×C4C22×D1214yes—
872C2×C4C22×D1214yes—
873C2×C3—44no—
874C2×C3#270318yescomplemented
875C2×C3C2×#53511yescharacteristic
876C2×C3C2×#53811yescharacteristic
877C2×C3C2×#54011yescharacteristic
878C2×C3C2×#54611yescharacteristic
879C2×C3C2×#54611yescharacteristic
880C2×C3C2×#55311yescharacteristic
881C2×C3C2×#56011yescharacteristic
882D3—44no—
883D3—82no—
884D3—82no—
885C22—24no—
886C22—24no—
887C22—24no—
888C22—42no—
889C22—42no—
890C22—416no—
891C22—42no—
892C22—42no—
893C22—64no—
894C22—64no—
895C22—64no—
896C22—122no—
897C22—1216no—
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—122no—
911C22—122no—
912C22—122no—
913C22—122no—
914C22—122no—
915C22—248no—
916C22—248no—
917C22#552514yes—
918C22#555414yes—
919C22#555414yes—
920C22#562014yes—
921C22#566314yes—
922C22#567814yes—
923C22#570914yes—
924C22C23×D1211yescharacteristic
925C22C2×#100411yescharacteristic
926C22C2×#100411yescharacteristic
927C22C2×D3×#4111yescharacteristic
928C22C2×D3×#4111yescharacteristic
929C22C2×#100911yescharacteristic
930C22C2×#100911yescharacteristic
931C4—24no—
932C4—24no—
933C4—42no—
934C4—42no—
935C4—42no—
936C4—42no—
937C4—64no—
938C4—122no—
939C4—122no—
940C4—122no—
941C4—122no—
942C3C2×#270311yescharacteristic, complemented, Sylow
943C2—44no—
944C2—124no—
945C2—242no—
946C2—242no—
947C2#7592718yesdirect product factor
948C2C2×#552511yescharacteristic
949C2C2×#555411yescharacteristic
950C2C2×#555411yescharacteristic
951C2C2×#562011yescharacteristic
952C2C2×#566311yescharacteristic
953C2C2×#567811yescharacteristic
954C2C2×#570911yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC2×C3×#388C2
socleC24×C3C24
hypercenterC2×#388D3
hypocenterC3C2×#2703
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C22×#884C2semidirect
2. C22×#886C2semidirect
3. C2×C3×#388C2semidirect
4. C2×#4991C2semidirect
5. C2×#4987C2semidirect
6. C2×#4960C2semidirect
7. C2×#4960C2semidirect
8. C2×#4958C2semidirect
9. C2×#4958C2semidirect
10. C2×#4939C2semidirect
11. C2×#4940C2semidirect
12. #75927C2direct (N × H)
13. C2×#4671C2semidirect
14. C2×#4665C2semidirect
15. C2×#4659C2semidirect
16. C2×#4674C2semidirect
46. C2×#886C22semidirect
48. C2×#884C22semidirect
49. C3×#388C22semidirect
58. #4991C22semidirect
59. #4987C22semidirect
60. #4960C22semidirect
61. #4960C22semidirect
62. #4958C22semidirect
63. #4958C22semidirect
64. #4940C22semidirect
65. #4939C22semidirect
66. #4674C22semidirect
67. #4671C22semidirect
68. #4665C22semidirect
69. #4659C22semidirect
81. C2×#388D3semidirect
137. C2×C3×C22⋊C4D4semidirect
220. #388C2×D3semidirect
345. C3×C22⋊C4C2×D4semidirect
442. C2×C22⋊C4D12semidirect
698. C22⋊C4C2×D12semidirect
874. C2×C3#2703semidirect
942. C3C2×#2703semidirect
947. C2#75927direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#8842
C22×#8862
C2×C3×#3882
C2×#49912
C2×#49872
C2×#49602
C2×#49582
C2×#49392
C2×#49402
#759272
C2×#46712
C2×#46652
C2×#46592
C2×#46742
C2×#27033