Finite Group Databasebeta

← C2×#77693 #11430017

Subgroups — C2×#77693 #11430017

Order 768.

3650 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#884C211yesmaximal, characteristic, complemented
2C22×#884C211yesmaximal, characteristic, complemented
3C2×C3×#397C211yesmaximal, characteristic, complemented
4C2×#4991C211yesmaximal, characteristic, complemented
5C2×#4989C211yesmaximal, characteristic, complemented
6C2×#4960C211yesmaximal, characteristic, complemented
7C2×#4958C211yesmaximal, characteristic, complemented
8C2×#4958C211yesmaximal, characteristic, complemented
9C2×#4958C211yesmaximal, characteristic, complemented
10#77693C2116yesmaximal, direct product factor
11C2×#4675C211yesmaximal, characteristic, complemented
12C2×#4671C211yesmaximal, characteristic, complemented
13C2×#4665C211yesmaximal, characteristic, complemented
14C2×#4665C211yesmaximal, characteristic, complemented
15C2×#4664C211yesmaximal, characteristic, complemented
16C2×#4658C211yesmaximal, characteristic, complemented
17C2×#2688—31nomaximal, Sylow
18C23×#67C2211yescharacteristic
19C23×#67C2211yescharacteristic
20C23×#67C2211yescharacteristic
21C24×Dic3C2211yescharacteristic
22C23×D12C2211yescharacteristic
23C23×D12C2211yescharacteristic
24C23×D12C2211yescharacteristic
25C23×C4×D3C2211yescharacteristic
26C23×C4×D3C2211yescharacteristic
27C22×C3×C4⋊C4C2211yescharacteristic
28C22×C3×C22⋊C4C2211yescharacteristic
29C22×C3×C22⋊C4C2211yescharacteristic
30C22×C3×C22⋊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×Dic3⋊C4C2211yescharacteristic
42C22×Dic3⋊C4C2211yescharacteristic
43C2×#884—28no—
44C2×#884—28no—
45C2×#884C2218yescomplemented
46C2×#884C2218yescomplemented
47C3×#397C2218yescomplemented
48C2×C3×#95C2211yescharacteristic
49C2×C3×#95C2211yescharacteristic
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#4989C2218yescomplemented
60#4960C2218yescomplemented
61#4958C2218yescomplemented
62#4958C2218yescomplemented
63#4958C2218yescomplemented
64#4675C2218yescomplemented
65#4671C2218yescomplemented
66#4665C2218yescomplemented
67#4665C2218yescomplemented
68#4664C2218yescomplemented
69#4658C2218yescomplemented
70C22×#121—31no—
71C22×#121—31no—
72#2688—316no—
73C2×#400—31no—
74C2×#397—31no—
75C2×#397D311yescharacteristic, complemented
76C2×#394—31no—
77C2×#392—31no—
78C2×#392—31no—
79C2×#386—31no—
80C2×#386—31no—
81C2×#386—31no—
82C2×#386—31no—
83C2×#386—31no—
84C2×#385—31no—
85C2×#381—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—42no—
101C22×#67—42no—
102C22×#67—42no—
103C22×#67—42no—
104C22×#67D418yescomplemented
105C22×#67C2314yes—
106C22×#67C2314yes—
107C22×#67C2314yes—
108C23×Dic3—42no—
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—24no—
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—24no—
132C22×C4×D3—42no—
133C22×C4×D3—42no—
134C22×C4×D3—42no—
135C22×C4×D3C2314yes—
136C22×C4×D3C2314yes—
137C2×C3×C4⋊C4—42no—
138C2×C3×C4⋊C4C2314yes—
139C2×C3×C22⋊C4—24no—
140C2×C3×C22⋊C4—24no—
141C2×C3×C22⋊C4—42no—
142C2×C3×C22⋊C4C2314yes—
143C2×C3×C22⋊C4C2314yes—
144C2×C3×C22⋊C4C2314yes—
145C2×(C2×D3)⋊C4—24no—
146C2×(C2×D3)⋊C4—24no—
147C2×(C2×D3)⋊C4—24no—
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)⋊C4—42no—
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—24no—
167C2×Dic3⋊C4C2314yes—
168C2×Dic3⋊C4C2314yes—
169#884—232no—
170#884—232no—
171C3×#95C2314yes—
172C3×#95C2314yes—
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—
189C24×C4—31no—
190C2×#121—38no—
191C2×#121—38no—
192C2×#121—68no—
193C2×#121—68no—
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⋊C4C2×D311yescharacteristic
208C22×C22⋊C4C2×D311yescharacteristic
209C22×C22⋊C4C2×D311yescharacteristic
210#400—38no—
211#397—38no—
212#397C2×D318yescomplemented
213#394—38no—
214#392—38no—
215#392—38no—
216#386—38no—
217#386—38no—
218#386—38no—
219#386—38no—
220#386—38no—
221#385—38no—
222#381—38no—
223C2×#95—31no—
224C2×#95—31no—
225C2×#95—31no—
226C2×#95—31no—
227C2×#95—31no—
228C2×#95—31no—
229C2×#95—31no—
230C2×#95C2×D311yescharacteristic
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×D3C2×D414yes—
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×C4—22no—
283C22×C3×C4—22no—
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—416no—
295C2×#67—44no—
296C2×#67—44no—
297C2×#67—44no—
298C2×#67—44no—
299C2×#67—416no—
300C2×#67—416no—
301C2×#67C2×D4116yescomplemented
302C22×Dic3—22no—
303C22×Dic3—22no—
304C22×Dic3—22no—
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—44no—
316C22×Dic3—44no—
317C22×Dic3—44no—
318C22×Dic3—416no—
319C22×Dic3C2×D414yes—
320C22×Dic3#4114yes—
321C22×Dic3C2412yes—
322C22×Dic3C2412yes—
323C22×Dic3C2412yes—
324C22×Dic3C2412yes—
325C22×Dic3C2412yes—
326C2×D12—28no—
327C2×D12—28no—
328C2×D12—28no—
329C2×D12—28no—
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—28no—
341C2×C4×D3—44no—
342C2×C4×D3—44no—
343C2×C4×D3—44no—
344C2×C4×D3—416no—
345C2×C4×D3—416no—
346C3×C4⋊C4—44no—
347C3×C22⋊C4—28no—
348C3×C22⋊C4—28no—
349C3×C22⋊C4—44no—
350(C2×D3)⋊C4—28no—
351(C2×D3)⋊C4—28no—
352(C2×D3)⋊C4—28no—
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—
358(C2×D3)⋊C4—44no—
359(C2×D3)⋊C4—44no—
360Dic3⋊C4—28no—
361Dic3⋊C4—28no—
362C25—31no—
363C25—31no—
364C25—31no—
365C25C22×D311yescharacteristic
366C22×D4—38no—
367C22×D4—34no—
368C22×D4—34no—
369C22×D4—34no—
370C22×D4—34no—
371C22×D4—34no—
372C22×D4—34no—
373C22×D4—64no—
374C22×D4—64no—
375C22×D4—64no—
376C22×D4—64no—
377C22×D4—64no—
378C22×D4—64no—
379C22×D4—64no—
380C22×D4—64no—
381C22×D4—122no—
382C22×D4—122no—
383C22×D4—122no—
384C22×D4—122no—
385C22×D4—122no—
386C22×D4—122no—
387C22×D4—122no—
388C22×D4—122no—
389C22×D4—122no—
390C23×C4—31no—
391C23×C4—31no—
392C23×C4—31no—
393C23×C4—31no—
394C23×C4—31no—
395C23×C4—34no—
396C23×C4—34no—
397C23×C4—34no—
398C23×C4—64no—
399C23×C4—64no—
400C23×C4—64no—
401C23×C4—122no—
402C23×C4—122no—
403C23×C4—122no—
404C23×C4—122no—
405C23×C4—122no—
406C23×C4—122no—
407C23×C4C22×D311yescharacteristic
408C23×C4C22×D311yescharacteristic
409C23×C4C22×D311yescharacteristic
410C23×C4C22×D311yescharacteristic
411C23×C4C22×D311yescharacteristic
412C23×C4C22×D311yescharacteristic
413#121—632no—
414#121—632no—
415C2×C4⋊C4—34no—
416C2×C4⋊C4—34no—
417C2×C4⋊C4—42no—
418C2×C4⋊C4—64no—
419C2×C4⋊C4—64no—
420C2×C4⋊C4C22×D314yes—
421C2×C22⋊C4—24no—
422C2×C22⋊C4—24no—
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—42no—
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⋊C4C22×D314yes—
445C2×C22⋊C4C22×D314yes—
446C2×C22⋊C4C22×D314yes—
447#95—34no—
448#95—34no—
449#95—34no—
450#95—34no—
451#95—34no—
452#95—34no—
453#95—34no—
454#95C22×D314yes—
455#95C22×D314yes—
456#95C22×D314yes—
457C23×C3—28no—
458C23×C3—28no—
459C23×C3—28no—
460C23×C3—22no—
461C23×C3—22no—
462C23×C3—22no—
463C23×C3—22no—
464C23×C3—22no—
465C23×C3—22no—
466C23×C3—44no—
467C23×C3—44no—
468C23×C3—44no—
469C23×C3—44no—
470C23×C3C22×D414yes—
471C23×C3C22×D412yes—
472C23×C3C2×#4112yes—
473C23×C3C2×#4112yes—
474C23×C3H(5,𝔽2)12yes—
475C23×C3H(5,𝔽2)12yes—
476C23×C3H(5,𝔽2)12yes—
477C23×C3H(5,𝔽2)12yes—
478C23×C3C2511yescharacteristic
479C22×D3—28no—
480C22×D3—28no—
481C22×D3—28no—
482C22×D3—28no—
483C22×D3—28no—
484C22×D3—28no—
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—22no—
502C22×D3—22no—
503C22×D3—22no—
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×D3C22×D414yes—
520C22×D3C2×#4114yes—
521C2×C3×C4—22no—
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—44no—
540C2×C3×C4—44no—
541C2×C3×C4—44no—
542C2×C3×C4—44no—
543C2×C3×C4—44no—
544C2×C3×C4—44no—
545#67—416no—
546#67—416no—
547#67—416no—
548C2×Dic3—28no—
549C2×Dic3—28no—
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—22no—
563C2×Dic3—416no—
564C2×Dic3—44no—
565C2×Dic3—44no—
566C2×Dic3—44no—
567C2×Dic3C22×D414yes—
568C2×Dic3C2×#4114yes—
569D12—416no—
570D12—416no—
571D12—416no—
572C4×D3—416no—
573C4×D3—416no—
574C24—22no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—22no—
579C24—22no—
580C24—34no—
581C24—34no—
582C24—32no—
583C24—32no—
584C24—32no—
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—
604C24D3×D414yes—
605C24C23×D312yes—
606C24C23×D311yescharacteristic
607C2×D4—316no—
608C2×D4—68no—
609C2×D4—68no—
610C2×D4—68no—
611C2×D4—68no—
612C2×D4—68no—
613C2×D4—68no—
614C2×D4—68no—
615C2×D4—68no—
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—124no—
625C2×D4—124no—
626C2×D4—124no—
627C2×D4—1216no—
628C2×D4—124no—
629C2×D4—1216no—
630C2×D4—1216no—
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—22no—
649C22×C4—34no—
650C22×C4—34no—
651C22×C4—32no—
652C22×C4—32no—
653C22×C4—32no—
654C22×C4—32no—
655C22×C4—32no—
656C22×C4—68no—
657C22×C4—68no—
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—62no—
668C22×C4—62no—
669C22×C4—62no—
670C22×C4—62no—
671C22×C4—62no—
672C22×C4—124no—
673C22×C4—124no—
674C22×C4—124no—
675C22×C4—1216no—
676C22×C4—1216no—
677C22×C4—124no—
678C22×C4—124no—
679C22×C4—124no—
680C22×C4—1216no—
681C22×C4C23×D312yes—
682C22×C4C23×D312yes—
683C22×C4C23×D312yes—
684C22×C4C23×D312yes—
685C22×C4C23×D312yes—
686C22×C4C23×D312yes—
687C4⋊C4—44no—
688C4⋊C4—68no—
689C4⋊C4—68no—
690C22⋊C4—28no—
691C22⋊C4—28no—
692C22⋊C4—44no—
693C22⋊C4—68no—
694C22⋊C4—68no—
695C22⋊C4—68no—
696C22⋊C4—124no—
697C22⋊C4—124no—
698C22⋊C4—124no—
699C22⋊C4—124no—
700C22⋊C4—124no—
701C22⋊C4—124no—
702C22⋊C4—124no—
703C22×C3—24no—
704C22×C3—24no—
705C22×C3—24no—
706C22×C3—42no—
707C22×C3—42no—
708C22×C3—416no—
709C22×C3—42no—
710C22×C3—42no—
711C22×C3#53414yes—
712C22×C3#53814yes—
713C22×C3#54014yes—
714C22×C3#54614yes—
715C22×C3#54614yes—
716C22×C3#55314yes—
717C22×C3#56014yes—
718C22×C3C23×D411yescharacteristic
719C22×C3C22×#4111yescharacteristic
720C22×C3C22×#4111yescharacteristic
721C22×C3C2×H(5,𝔽2)11yescharacteristic
722C22×C3C2×H(5,𝔽2)11yescharacteristic
723C22×C3C2×H(5,𝔽2)11yescharacteristic
724C22×C3C2×H(5,𝔽2)11yescharacteristic
725C2×D3—24no—
726C2×D3—24no—
727C2×D3—24no—
728C2×D3—24no—
729C2×D3—24no—
730C2×D3—24no—
731C2×D3—42no—
732C2×D3—42no—
733C2×D3—42no—
734C2×D3—42no—
735C2×D3—416no—
736C2×D3—416no—
737C2×D3—42no—
738C2×D3—42no—
739C2×D3—42no—
740C2×D3—42no—
741C2×D3—42no—
742C2×D3—42no—
743C2×D3—42no—
744C2×D3—42no—
745C2×D3—42no—
746C2×D3—42no—
747C2×D3—42no—
748C2×D3—88no—
749C3×C4—42no—
750C3×C4—42no—
751C3×C4—42no—
752C3×C4—42no—
753C3×C4—42no—
754C3×C4—42no—
755Dic3—24no—
756Dic3—24no—
757Dic3—42no—
758Dic3—42no—
759Dic3—42no—
760C23—28no—
761C23—28no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—28no—
769C23—34no—
770C23—34no—
771C23—44no—
772C23—44no—
773C23—44no—
774C23—44no—
775C23—68no—
776C23—68no—
777C23—68no—
778C23—68no—
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—68no—
792C23—68no—
793C23—62no—
794C23—62no—
795C23—62no—
796C23—62no—
797C23—62no—
798C23—62no—
799C23—62no—
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—
813C23—124no—
814C23—124no—
815C23C2×D3×D414yes—
816C23C2×D3×D412yes—
817C23#100412yes—
818C23D3×#4112yes—
819C23D3×#4112yes—
820C23#100912yes—
821C23#100912yes—
822C23#100912yes—
823C23C24×D311yescharacteristic
824D4—1216no—
825D4—1216no—
826D4—1216no—
827D4—1216no—
828D4—1216no—
829D4—1216no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
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—34no—
850C2×C4—44no—
851C2×C4—44no—
852C2×C4—44no—
853C2×C4—44no—
854C2×C4—44no—
855C2×C4—44no—
856C2×C4—68no—
857C2×C4—62no—
858C2×C4—62no—
859C2×C4—62no—
860C2×C4—62no—
861C2×C4—68no—
862C2×C4—62no—
863C2×C4—62no—
864C2×C4—62no—
865C2×C4—62no—
866C2×C4—62no—
867C2×C4—62no—
868C2×C4—62no—
869C2×C4—62no—
870C2×C4—62no—
871C2×C4—1216no—
872C2×C4—1216no—
873C2×C4—1216no—
874C2×C4—124no—
875C2×C4—124no—
876C2×C4—124no—
877C2×C3—44no—
878C2×C3#268818yescomplemented
879C2×C3C2×#53411yescharacteristic
880C2×C3C2×#53811yescharacteristic
881C2×C3C2×#54011yescharacteristic
882C2×C3C2×#54611yescharacteristic
883C2×C3C2×#54611yescharacteristic
884C2×C3C2×#55311yescharacteristic
885C2×C3C2×#56011yescharacteristic
886D3—44no—
887D3—44no—
888D3—82no—
889C22—24no—
890C22—24no—
891C22—24no—
892C22—42no—
893C22—42no—
894C22—42no—
895C22—416no—
896C22—42no—
897C22—64no—
898C22—64no—
899C22—64no—
900C22—64no—
901C22—64no—
902C22—64no—
903C22—122no—
904C22—122no—
905C22—122no—
906C22—122no—
907C22—1216no—
908C22—1216no—
909C22—122no—
910C22—122no—
911C22—122no—
912C22—122no—
913C22—122no—
914C22—122no—
915C22—122no—
916C22—122no—
917C22—122no—
918C22—122no—
919C22—122no—
920C22—248no—
921C22#560514yes—
922C22#565414yes—
923C22#565414yes—
924C22#566314yes—
925C22#567814yes—
926C22#570914yes—
927C22#571114yes—
928C22C22×D3×D411yescharacteristic
929C22C2×#100411yescharacteristic
930C22C2×D3×#4111yescharacteristic
931C22C2×D3×#4111yescharacteristic
932C22C2×#100911yescharacteristic
933C22C2×#100911yescharacteristic
934C22C2×#100911yescharacteristic
935C4—42no—
936C4—42no—
937C4—42no—
938C4—42no—
939C4—42no—
940C4—42no—
941C4—64no—
942C4—64no—
943C4—122no—
944C4—122no—
945C4—122no—
946C3C2×#268811yescharacteristic, complemented, Sylow
947C2—44no—
948C2—124no—
949C2—124no—
950C2—242no—
951C2#7769318yesdirect product factor
952C2C2×#560511yescharacteristic
953C2C2×#566311yescharacteristic
954C2C2×#565411yescharacteristic
955C2C2×#565411yescharacteristic
956C2C2×#567811yescharacteristic
957C2C2×#570911yescharacteristic
958C2C2×#571111yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC2×C3×#397C2
socleC24×C3C24
hypercenterC2×#397D3
hypocenterC3C2×#2688
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
1. C22×#884C2semidirect
2. C22×#884C2semidirect
3. C2×C3×#397C2semidirect
4. C2×#4991C2semidirect
5. C2×#4989C2semidirect
6. C2×#4960C2semidirect
7. C2×#4958C2semidirect
8. C2×#4958C2semidirect
9. C2×#4958C2semidirect
10. #77693C2direct (N × H)
11. C2×#4675C2semidirect
12. C2×#4671C2semidirect
13. C2×#4665C2semidirect
14. C2×#4665C2semidirect
15. C2×#4664C2semidirect
16. C2×#4658C2semidirect
45. C2×#884C22semidirect
46. C2×#884C22semidirect
47. C3×#397C22semidirect
58. #4991C22semidirect
59. #4989C22semidirect
60. #4960C22semidirect
61. #4958C22semidirect
62. #4958C22semidirect
63. #4958C22semidirect
64. #4675C22semidirect
65. #4671C22semidirect
66. #4665C22semidirect
67. #4665C22semidirect
68. #4664C22semidirect
69. #4658C22semidirect
75. C2×#397D3semidirect
104. C22×#67D4semidirect
212. #397C2×D3semidirect
301. C2×#67C2×D4semidirect
878. C2×C3#2688semidirect
946. C3C2×#2688semidirect
951. C2#77693direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#8842
C2×C3×#3972
C2×#49912
C2×#49892
C2×#49602
C2×#49582
#776932
C2×#46752
C2×#46712
C2×#46652
C2×#46642
C2×#46582
C2×#26883