Finite Group Databasebeta

← C2×#77967 #11429782

Subgroups — C2×#77967 #11429782

Order 768.

4042 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#894C211yesmaximal, characteristic, complemented
2C22×#895C211yesmaximal, characteristic, complemented
3C22×#895C211yesmaximal, characteristic, complemented
4C22×#895C211yesmaximal, characteristic, complemented
5C2×C3×#398C211yesmaximal, characteristic, complemented
6C2×#4993C211yesmaximal, characteristic, complemented
7C2×#4991C211yesmaximal, characteristic, complemented
8C2×#4989C211yesmaximal, characteristic, complemented
9C2×#4989C211yesmaximal, characteristic, complemented
10#77967C2116yesmaximal, direct product factor
11C2×#4671C211yesmaximal, characteristic, complemented
12C2×#4665C211yesmaximal, characteristic, complemented
13C2×#4665C211yesmaximal, characteristic, complemented
14C2×#4667C211yesmaximal, characteristic, complemented
15C2×#4672C211yesmaximal, characteristic, complemented
16C2×#4672C211yesmaximal, characteristic, complemented
17C2×#2671—31nomaximal, Sylow
18C23×D12C2211yescharacteristic
19C23×D12C2211yescharacteristic
20C23×D12C2211yescharacteristic
21C23×D12C2211yescharacteristic
22C23×D12C2211yescharacteristic
23C23×D12C2211yescharacteristic
24C23×C4×D3C2211yescharacteristic
25C23×C4×D3C2211yescharacteristic
26C23×C4×D3C2211yescharacteristic
27C22×C3×C4⋊C4C2211yescharacteristic
28C22×C3×C4⋊C4C2211yescharacteristic
29C22×C3×C4⋊C4C2211yescharacteristic
30C22×C3×C4⋊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×(C2×D3)⋊C4C2211yescharacteristic
44C22×Dic3⋊C4C2211yescharacteristic
45C22×Dic3⋊C4C2211yescharacteristic
46C22×Dic3⋊C4C2211yescharacteristic
47C2×#895—28no—
48C2×#895—28no—
49C2×#895—28no—
50C2×#895C2218yescomplemented
51C2×#895C2218yescomplemented
52C2×#895C2218yescomplemented
53C2×#894—28no—
54C2×#894C2218yescomplemented
55C3×#398C2218yescomplemented
56C2×C3×#95C2211yescharacteristic
57C2×C3×#95C2211yescharacteristic
58C2×C3×#95C2211yescharacteristic
59C2×C3⋊#95C2211yescharacteristic
60C2×C3⋊#95C2211yescharacteristic
61C2×C3⋊#95C2211yescharacteristic
62#4993C2218yescomplemented
63#4991C2218yescomplemented
64#4989C2218yescomplemented
65#4989C2218yescomplemented
66#4672C2218yescomplemented
67#4672C2218yescomplemented
68#4671C2218yescomplemented
69#4667C2218yescomplemented
70#4665C2218yescomplemented
71#4665C2218yescomplemented
72C22×#123—31no—
73C22×#121—31no—
74C22×#121—31no—
75C22×#121—31no—
76#2671—316no—
77C2×#399—31no—
78C2×#398D311yescharacteristic, complemented
79C2×#394—31no—
80C2×#394—31no—
81C2×#394—31no—
82C2×#392—31no—
83C2×#386—31no—
84C2×#386—31no—
85C2×#385—31no—
86C2×#385—31no—
87C2×#380—31no—
88C24×D3C2311yescharacteristic
89C24×D3C2311yescharacteristic
90C24×D3C2311yescharacteristic
91C24×D3C2311yescharacteristic
92C23×C3×C4C2311yescharacteristic
93C23×C3×C4C2311yescharacteristic
94C23×C3×C4C2311yescharacteristic
95C23×C3×C4C2311yescharacteristic
96C23×C3×C4C2311yescharacteristic
97C23×C3×C4C2311yescharacteristic
98C23×C3×C4C2311yescharacteristic
99C23×Dic3C2311yescharacteristic
100C23×Dic3C2311yescharacteristic
101C23×Dic3C2311yescharacteristic
102C23×Dic3C2311yescharacteristic
103C22×D12—24no—
104C22×D12—24no—
105C22×D12—24no—
106C22×D12—24no—
107C22×D12—24no—
108C22×D12—24no—
109C22×D12—24no—
110C22×D12—24no—
111C22×D12—24no—
112C22×D12—42no—
113C22×D12—42no—
114C22×D12—42no—
115C22×D12—42no—
116C22×D12—42no—
117C22×D12—42no—
118C22×D12—42no—
119C22×D12—42no—
120C22×D12D418yescomplemented
121C22×D12C2314yes—
122C22×D12C2314yes—
123C22×D12C2314yes—
124C22×D12C2314yes—
125C22×D12C2314yes—
126C22×D12C2314yes—
127C22×C4×D3—24no—
128C22×C4×D3—24no—
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×D3—42no—
136C22×C4×D3C2314yes—
137C22×C4×D3C2314yes—
138C22×C4×D3C2314yes—
139C2×C3×C4⋊C4—24no—
140C2×C3×C4⋊C4—24no—
141C2×C3×C4⋊C4—24no—
142C2×C3×C4⋊C4—24no—
143C2×C3×C4⋊C4C2314yes—
144C2×C3×C4⋊C4C2314yes—
145C2×C3×C4⋊C4C2314yes—
146C2×C3×C4⋊C4C2314yes—
147C2×(C2×D3)⋊C4—24no—
148C2×(C2×D3)⋊C4—24no—
149C2×(C2×D3)⋊C4—24no—
150C2×(C2×D3)⋊C4—24no—
151C2×(C2×D3)⋊C4—24no—
152C2×(C2×D3)⋊C4—24no—
153C2×(C2×D3)⋊C4—24no—
154C2×(C2×D3)⋊C4—24no—
155C2×(C2×D3)⋊C4—42no—
156C2×(C2×D3)⋊C4—42no—
157C2×(C2×D3)⋊C4—42no—
158C2×(C2×D3)⋊C4—42no—
159C2×(C2×D3)⋊C4D418yescomplemented
160C2×(C2×D3)⋊C4C2314yes—
161C2×(C2×D3)⋊C4C2314yes—
162C2×(C2×D3)⋊C4C2314yes—
163C2×(C2×D3)⋊C4C2314yes—
164C2×(C2×D3)⋊C4C2314yes—
165C2×(C2×D3)⋊C4C2314yes—
166C2×(C2×D3)⋊C4C2314yes—
167C2×(C2×D3)⋊C4C2314yes—
168C2×(C2×D3)⋊C4C2314yes—
169C2×(C2×D3)⋊C4C2314yes—
170C2×(C2×D3)⋊C4C2314yes—
171C2×(C2×D3)⋊C4C2314yes—
172C2×(C2×D3)⋊C4C2314yes—
173C2×Dic3⋊C4—24no—
174C2×Dic3⋊C4—42no—
175C2×Dic3⋊C4—42no—
176C2×Dic3⋊C4C2314yes—
177C2×Dic3⋊C4C2314yes—
178C2×Dic3⋊C4C2314yes—
179#895—232no—
180#895—232no—
181#895—232no—
182#894—232no—
183C3×#95C2314yes—
184C3×#95C2314yes—
185C3×#95C2314yes—
186C3⋊#95C2314yes—
187C3⋊#95C2314yes—
188C3⋊#95C2314yes—
189C23×D4—31no—
190C23×D4—31no—
191C23×D4—31no—
192C23×D4—31no—
193C23×D4—31no—
194C23×D4—31no—
195C24×C4—31no—
196C24×C4—31no—
197C24×C4—31no—
198C2×#123—38no—
199C2×#123—68no—
200C2×#121—38no—
201C2×#121—38no—
202C2×#121—38no—
203C2×#121—68no—
204C2×#121—68no—
205C2×#121—68no—
206C22×C4⋊C4—31no—
207C22×C4⋊C4—31no—
208C22×C4⋊C4—31no—
209C22×C4⋊C4C2×D311yescharacteristic
210C22×C4⋊C4C2×D311yescharacteristic
211C22×C4⋊C4C2×D311yescharacteristic
212C22×C4⋊C4C2×D311yescharacteristic
213C22×C22⋊C4—31no—
214C22×C22⋊C4—31no—
215C22×C22⋊C4—31no—
216C22×C22⋊C4—31no—
217C22×C22⋊C4—31no—
218C22×C22⋊C4—31no—
219C22×C22⋊C4—31no—
220C22×C22⋊C4—31no—
221C22×C22⋊C4—31no—
222C22×C22⋊C4—31no—
223C22×C22⋊C4—31no—
224C22×C22⋊C4—31no—
225C22×C22⋊C4—31no—
226#399—38no—
227#398C2×D318yescomplemented
228#394—38no—
229#394—38no—
230#394—38no—
231#392—38no—
232#386—38no—
233#386—38no—
234#385—38no—
235#385—38no—
236#380—38no—
237C2×#95—31no—
238C2×#95—31no—
239C2×#95—31no—
240C2×#95C2×D311yescharacteristic
241C2×#95C2×D311yescharacteristic
242C2×#95C2×D311yescharacteristic
243C24×C3C2411yescharacteristic
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—22no—
263C23×D3—22no—
264C23×D3—22no—
265C23×D3—22no—
266C23×D3—22no—
267C23×D3—22no—
268C23×D3—22no—
269C23×D3C2×D414yes—
270C23×D3C2×D414yes—
271C23×D3C2×D414yes—
272C23×D3C2412yes—
273C23×D3C2412yes—
274C23×D3C2412yes—
275C23×D3C2412yes—
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×C4—22no—
286C22×C3×C4—22no—
287C22×C3×C4—22no—
288C22×C3×C4—22no—
289C22×C3×C4—22no—
290C22×C3×C4—22no—
291C22×C3×C4—22no—
292C22×C3×C4—22no—
293C22×C3×C4—22no—
294C22×C3×C4C2×D414yes—
295C22×C3×C4C2×D414yes—
296C22×C3×C4#4114yes—
297C22×C3×C4C2412yes—
298C22×C3×C4C2412yes—
299C22×C3×C4C2412yes—
300C22×C3×C4C2412yes—
301C22×C3×C4C2412yes—
302C22×C3×C4C2412yes—
303C22×C3×C4C2412yes—
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×Dic3C2×D414yes—
316C22×Dic3C2412yes—
317C22×Dic3C2412yes—
318C22×Dic3C2412yes—
319C22×Dic3C2412yes—
320C2×D12—28no—
321C2×D12—28no—
322C2×D12—28no—
323C2×D12—28no—
324C2×D12—28no—
325C2×D12—28no—
326C2×D12—28no—
327C2×D12—28no—
328C2×D12—28no—
329C2×D12—416no—
330C2×D12—44no—
331C2×D12—44no—
332C2×D12—44no—
333C2×D12—44no—
334C2×D12—44no—
335C2×D12—44no—
336C2×D12—44no—
337C2×D12—44no—
338C2×D12—416no—
339C2×D12—416no—
340C2×D12—416no—
341C2×D12—416no—
342C2×D12—416no—
343C2×D12C2×D4116yescomplemented
344C2×C4×D3—28no—
345C2×C4×D3—28no—
346C2×C4×D3—28no—
347C2×C4×D3—28no—
348C2×C4×D3—28no—
349C2×C4×D3—44no—
350C2×C4×D3—44no—
351C2×C4×D3—44no—
352C2×C4×D3—44no—
353C2×C4×D3—416no—
354C2×C4×D3—416no—
355C2×C4×D3—416no—
356C3×C4⋊C4—28no—
357C3×C4⋊C4—28no—
358C3×C4⋊C4—28no—
359C3×C4⋊C4—28no—
360(C2×D3)⋊C4—28no—
361(C2×D3)⋊C4—28no—
362(C2×D3)⋊C4—28no—
363(C2×D3)⋊C4—28no—
364(C2×D3)⋊C4—28no—
365(C2×D3)⋊C4—28no—
366(C2×D3)⋊C4—28no—
367(C2×D3)⋊C4—28no—
368(C2×D3)⋊C4—44no—
369(C2×D3)⋊C4—44no—
370(C2×D3)⋊C4—44no—
371(C2×D3)⋊C4—44no—
372(C2×D3)⋊C4C2×D4116yescomplemented
373Dic3⋊C4—28no—
374Dic3⋊C4—44no—
375Dic3⋊C4—44no—
376C25—31no—
377C25—31no—
378C25—31no—
379C25—31no—
380C22×D4—38no—
381C22×D4—34no—
382C22×D4—34no—
383C22×D4—34no—
384C22×D4—34no—
385C22×D4—34no—
386C22×D4—34no—
387C22×D4—64no—
388C22×D4—64no—
389C22×D4—64no—
390C22×D4—64no—
391C22×D4—64no—
392C22×D4—64no—
393C22×D4—64no—
394C22×D4—64no—
395C22×D4—64no—
396C22×D4—122no—
397C22×D4—122no—
398C22×D4—122no—
399C22×D4—122no—
400C22×D4—122no—
401C22×D4—122no—
402C22×D4—122no—
403C22×D4—122no—
404C23×C4—31no—
405C23×C4—31no—
406C23×C4—31no—
407C23×C4—31no—
408C23×C4—34no—
409C23×C4—34no—
410C23×C4—34no—
411C23×C4—64no—
412C23×C4—64no—
413C23×C4—64no—
414C23×C4—64no—
415C23×C4—64no—
416C23×C4—122no—
417C23×C4—122no—
418C23×C4—122no—
419C23×C4—122no—
420C23×C4C22×D311yescharacteristic
421C23×C4C22×D311yescharacteristic
422C23×C4C22×D311yescharacteristic
423C23×C4C22×D311yescharacteristic
424C23×C4C22×D311yescharacteristic
425C23×C4C22×D311yescharacteristic
426C23×C4C22×D311yescharacteristic
427#123—632no—
428#121—632no—
429#121—632no—
430#121—632no—
431C2×C4⋊C4—24no—
432C2×C4⋊C4—24no—
433C2×C4⋊C4—24no—
434C2×C4⋊C4—24no—
435C2×C4⋊C4—34no—
436C2×C4⋊C4—34no—
437C2×C4⋊C4—34no—
438C2×C4⋊C4—64no—
439C2×C4⋊C4—122no—
440C2×C4⋊C4—122no—
441C2×C4⋊C4C22×D314yes—
442C2×C4⋊C4C22×D314yes—
443C2×C4⋊C4C22×D314yes—
444C2×C4⋊C4C22×D314yes—
445C2×C22⋊C4—38no—
446C2×C22⋊C4—34no—
447C2×C22⋊C4—34no—
448C2×C22⋊C4—34no—
449C2×C22⋊C4—34no—
450C2×C22⋊C4—34no—
451C2×C22⋊C4—34no—
452C2×C22⋊C4—34no—
453C2×C22⋊C4—34no—
454C2×C22⋊C4—34no—
455C2×C22⋊C4—34no—
456C2×C22⋊C4—34no—
457C2×C22⋊C4—34no—
458C2×C22⋊C4—34no—
459C2×C22⋊C4—64no—
460C2×C22⋊C4—64no—
461C2×C22⋊C4—64no—
462C2×C22⋊C4—64no—
463C2×C22⋊C4—64no—
464C2×C22⋊C4—64no—
465C2×C22⋊C4—64no—
466C2×C22⋊C4—64no—
467C2×C22⋊C4—122no—
468C2×C22⋊C4—122no—
469C2×C22⋊C4—122no—
470C2×C22⋊C4—122no—
471#95—34no—
472#95—34no—
473#95—34no—
474#95C22×D314yes—
475#95C22×D314yes—
476#95C22×D314yes—
477C23×C3C22×D412yes—
478C23×C3C22×D412yes—
479C23×C3C2×#4112yes—
480C23×C3H(5,𝔽2)12yes—
481C23×C3H(5,𝔽2)12yes—
482C23×C3H(5,𝔽2)12yes—
483C23×C32−1+412yes—
484C23×C3C2511yescharacteristic
485C22×D3—28no—
486C22×D3—28no—
487C22×D3—28no—
488C22×D3—28no—
489C22×D3—28no—
490C22×D3—28no—
491C22×D3—28no—
492C22×D3—28no—
493C22×D3—28no—
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—22no—
505C22×D3—22no—
506C22×D3—22no—
507C22×D3—22no—
508C22×D3—22no—
509C22×D3—22no—
510C22×D3—22no—
511C22×D3—22no—
512C22×D3—22no—
513C22×D3—22no—
514C22×D3—22no—
515C22×D3—22no—
516C22×D3—22no—
517C22×D3—22no—
518C22×D3—22no—
519C22×D3—44no—
520C22×D3—44no—
521C22×D3—44no—
522C22×D3—44no—
523C22×D3—44no—
524C22×D3—44no—
525C22×D3—44no—
526C22×D3—44no—
527C22×D3—44no—
528C22×D3—44no—
529C22×D3—44no—
530C22×D3—44no—
531C22×D3—44no—
532C22×D3—44no—
533C22×D3—44no—
534C22×D3—44no—
535C22×D3—44no—
536C22×D3—44no—
537C22×D3—44no—
538C22×D3C22×D414yes—
539C22×D3C22×D414yes—
540C22×D3C22×D414yes—
541C2×C3×C4—28no—
542C2×C3×C4—28no—
543C2×C3×C4—28no—
544C2×C3×C4—22no—
545C2×C3×C4—22no—
546C2×C3×C4—22no—
547C2×C3×C4—22no—
548C2×C3×C4—22no—
549C2×C3×C4—22no—
550C2×C3×C4—22no—
551C2×C3×C4—22no—
552C2×C3×C4—22no—
553C2×C3×C4—22no—
554C2×C3×C4—22no—
555C2×C3×C4—22no—
556C2×C3×C4—22no—
557C2×C3×C4—22no—
558C2×C3×C4—22no—
559C2×C3×C4—22no—
560C2×C3×C4—22no—
561C2×C3×C4—22no—
562C2×C3×C4—44no—
563C2×C3×C4—44no—
564C2×C3×C4—44no—
565C2×C3×C4—44no—
566C2×C3×C4C22×D414yes—
567C2×C3×C4C22×D414yes—
568C2×C3×C4C2×#4114yes—
569C2×Dic3—28no—
570C2×Dic3—22no—
571C2×Dic3—22no—
572C2×Dic3—22no—
573C2×Dic3—22no—
574C2×Dic3—22no—
575C2×Dic3—22no—
576C2×Dic3—22no—
577C2×Dic3—22no—
578C2×Dic3—22no—
579C2×Dic3—22no—
580C2×Dic3—22no—
581C2×Dic3—44no—
582C2×Dic3—44no—
583C2×Dic3—44no—
584C2×Dic3C22×D414yes—
585D12—416no—
586D12—416no—
587D12—416no—
588D12—416no—
589D12—416no—
590D12—416no—
591C4×D3—416no—
592C4×D3—416no—
593C4×D3—416no—
594C24—34no—
595C24—34no—
596C24—34no—
597C24—32no—
598C24—32no—
599C24—32no—
600C24—32no—
601C24—62no—
602C24—62no—
603C24—62no—
604C24—62no—
605C24—62no—
606C24—62no—
607C24—62no—
608C24—62no—
609C24—62no—
610C24—62no—
611C24—62no—
612C24—62no—
613C24—62no—
614C24—62no—
615C24—62no—
616C24—62no—
617C24—62no—
618C24—62no—
619C24—62no—
620C24—62no—
621C24—62no—
622C24—62no—
623C24—62no—
624C24—62no—
625C24—62no—
626C24C23×D311yescharacteristic
627C2×D4—316no—
628C2×D4—68no—
629C2×D4—68no—
630C2×D4—68no—
631C2×D4—68no—
632C2×D4—68no—
633C2×D4—68no—
634C2×D4—68no—
635C2×D4—68no—
636C2×D4—68no—
637C2×D4—1216no—
638C2×D4—124no—
639C2×D4—124no—
640C2×D4—124no—
641C2×D4—124no—
642C2×D4—124no—
643C2×D4—124no—
644C2×D4—124no—
645C2×D4—124no—
646C2×D4—1216no—
647C2×D4—1216no—
648C2×D4—1216no—
649C2×D4—1216no—
650C2×D4—1216no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—34no—
670C22×C4—32no—
671C22×C4—32no—
672C22×C4—32no—
673C22×C4—32no—
674C22×C4—68no—
675C22×C4—68no—
676C22×C4—62no—
677C22×C4—62no—
678C22×C4—62no—
679C22×C4—62no—
680C22×C4—62no—
681C22×C4—62no—
682C22×C4—62no—
683C22×C4—62no—
684C22×C4—62no—
685C22×C4—62no—
686C22×C4—62no—
687C22×C4—68no—
688C22×C4—68no—
689C22×C4—68no—
690C22×C4—124no—
691C22×C4—124no—
692C22×C4—124no—
693C22×C4—124no—
694C22×C4—1216no—
695C22×C4—1216no—
696C22×C4—1216no—
697C22×C4D3×D414yes—
698C22×C4D3×D414yes—
699C22×C4#23914yes—
700C22×C4C23×D312yes—
701C22×C4C23×D312yes—
702C22×C4C23×D312yes—
703C22×C4C23×D312yes—
704C22×C4C23×D312yes—
705C22×C4C23×D312yes—
706C22×C4C23×D312yes—
707C4⋊C4—28no—
708C4⋊C4—28no—
709C4⋊C4—28no—
710C4⋊C4—28no—
711C4⋊C4—68no—
712C4⋊C4—124no—
713C4⋊C4—124no—
714C22⋊C4—316no—
715C22⋊C4—68no—
716C22⋊C4—68no—
717C22⋊C4—68no—
718C22⋊C4—68no—
719C22⋊C4—68no—
720C22⋊C4—68no—
721C22⋊C4—68no—
722C22⋊C4—68no—
723C22⋊C4—124no—
724C22⋊C4—124no—
725C22⋊C4—124no—
726C22⋊C4—124no—
727C22×C3#53414yes—
728C22×C3#53714yes—
729C22×C3#54014yes—
730C22×C3D4214yes—
731C22×C3#54614yes—
732C22×C3#54714yes—
733C22×C3#56214yes—
734C22×C3C23×D411yescharacteristic
735C22×C3C23×D411yescharacteristic
736C22×C3C22×#4111yescharacteristic
737C22×C3C2×H(5,𝔽2)11yescharacteristic
738C22×C3C2×H(5,𝔽2)11yescharacteristic
739C22×C3C2×H(5,𝔽2)11yescharacteristic
740C22×C3C2×2−1+411yescharacteristic
741C2×D3—24no—
742C2×D3—24no—
743C2×D3—24no—
744C2×D3—24no—
745C2×D3—24no—
746C2×D3—24no—
747C2×D3—24no—
748C2×D3—24no—
749C2×D3—24no—
750C2×D3—416no—
751C2×D3—416no—
752C2×D3—416no—
753C2×D3—42no—
754C2×D3—42no—
755C2×D3—42no—
756C2×D3—42no—
757C2×D3—42no—
758C2×D3—42no—
759C2×D3—42no—
760C2×D3—42no—
761C2×D3—42no—
762C2×D3—42no—
763C2×D3—42no—
764C2×D3—42no—
765C2×D3—42no—
766C2×D3—42no—
767C2×D3—42no—
768C2×D3—42no—
769C2×D3—42no—
770C2×D3—42no—
771C2×D3—42no—
772C2×D3—88no—
773C3×C4—24no—
774C3×C4—24no—
775C3×C4—24no—
776C3×C4—42no—
777C3×C4—42no—
778C3×C4—42no—
779C3×C4—42no—
780Dic3—24no—
781Dic3—42no—
782Dic3—42no—
783Dic3—42no—
784C23—34no—
785C23—34no—
786C23—34no—
787C23—68no—
788C23—68no—
789C23—62no—
790C23—62no—
791C23—62no—
792C23—62no—
793C23—62no—
794C23—62no—
795C23—62no—
796C23—62no—
797C23—62no—
798C23—62no—
799C23—62no—
800C23—62no—
801C23—62no—
802C23—62no—
803C23—62no—
804C23—62no—
805C23—62no—
806C23—62no—
807C23—68no—
808C23—68no—
809C23—68no—
810C23—68no—
811C23—68no—
812C23—68no—
813C23—68no—
814C23—62no—
815C23—62no—
816C23—62no—
817C23—62no—
818C23—62no—
819C23—62no—
820C23—62no—
821C23—124no—
822C23—124no—
823C23—124no—
824C23—124no—
825C23—124no—
826C23—124no—
827C23—124no—
828C23—124no—
829C23—124no—
830C23—124no—
831C23—124no—
832C23—124no—
833C23—124no—
834C23—124no—
835C23—124no—
836C23—124no—
837C23—124no—
838C23—124no—
839C23—124no—
840C23C2×D3×D412yes—
841C23C2×D3×D412yes—
842C23C2×#23912yes—
843C23#100712yes—
844C23#100912yes—
845C23#100912yes—
846C23#100912yes—
847C23C24×D311yescharacteristic
848D4—1216no—
849D4—1216no—
850D4—1216no—
851D4—1216no—
852D4—1216no—
853D4—1216no—
854C2×C4—28no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—28no—
862C2×C4—28no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—34no—
876C2×C4—44no—
877C2×C4—44no—
878C2×C4—44no—
879C2×C4—44no—
880C2×C4—62no—
881C2×C4—62no—
882C2×C4—68no—
883C2×C4—62no—
884C2×C4—62no—
885C2×C4—62no—
886C2×C4—62no—
887C2×C4—62no—
888C2×C4—62no—
889C2×C4—62no—
890C2×C4—62no—
891C2×C4—62no—
892C2×C4—1216no—
893C2×C4—1216no—
894C2×C4—1216no—
895C2×C4—124no—
896C2×C4—124no—
897C2×C4—124no—
898C2×C4C2×D3×D414yes—
899C2×C4C2×D3×D414yes—
900C2×C4C2×#23914yes—
901C2×C3#267118yescomplemented
902C2×C3C2×#53411yescharacteristic
903C2×C3C2×#53711yescharacteristic
904C2×C3C2×#54011yescharacteristic
905C2×C3C2×D4211yescharacteristic
906C2×C3C2×#54611yescharacteristic
907C2×C3C2×#54711yescharacteristic
908C2×C3C2×#56211yescharacteristic
909D3—44no—
910D3—44no—
911D3—44no—
912D3—82no—
913C22—64no—
914C22—64no—
915C22—64no—
916C22—64no—
917C22—64no—
918C22—64no—
919C22—64no—
920C22—64no—
921C22—64no—
922C22—122no—
923C22—122no—
924C22—122no—
925C22—122no—
926C22—122no—
927C22—122no—
928C22—1216no—
929C22—1216no—
930C22—1216no—
931C22—122no—
932C22—122no—
933C22—122no—
934C22—122no—
935C22—122no—
936C22—122no—
937C22—122no—
938C22—122no—
939C22—122no—
940C22—122no—
941C22—122no—
942C22—122no—
943C22—122no—
944C22—248no—
945C22#560914yes—
946C22#562914yes—
947C22#563014yes—
948C22#565314yes—
949C22#569714yes—
950C22#570014yes—
951C22#572614yes—
952C22C22×D3×D411yescharacteristic
953C22C22×D3×D411yescharacteristic
954C22C22×#23911yescharacteristic
955C22C2×#100711yescharacteristic
956C22C2×#100911yescharacteristic
957C22C2×#100911yescharacteristic
958C22C2×#100911yescharacteristic
959C4—24no—
960C4—24no—
961C4—24no—
962C4—42no—
963C4—42no—
964C4—42no—
965C4—42no—
966C4—64no—
967C4—122no—
968C4—122no—
969C4—122no—
970C3C2×#267111yescharacteristic, complemented, Sylow
971C2—124no—
972C2—124no—
973C2—124no—
974C2—242no—
975C2#7796718yesdirect product factor
976C2C2×#560911yescharacteristic
977C2C2×#562911yescharacteristic
978C2C2×#563011yescharacteristic
979C2C2×#565311yescharacteristic
980C2C2×#569711yescharacteristic
981C2C2×#570011yescharacteristic
982C2C2×#572611yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC2×C3×#398C2
socleC24×C3C24
hypercenterC2×#398D3
hypocenterC3C2×#2671
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
1. C22×#894C2semidirect
2. C22×#895C2semidirect
3. C22×#895C2semidirect
4. C22×#895C2semidirect
5. C2×C3×#398C2semidirect
6. C2×#4993C2semidirect
7. C2×#4991C2semidirect
8. C2×#4989C2semidirect
9. C2×#4989C2semidirect
10. #77967C2direct (N × H)
11. C2×#4671C2semidirect
12. C2×#4665C2semidirect
13. C2×#4665C2semidirect
14. C2×#4667C2semidirect
15. C2×#4672C2semidirect
16. C2×#4672C2semidirect
50. C2×#895C22semidirect
51. C2×#895C22semidirect
52. C2×#895C22semidirect
54. C2×#894C22semidirect
55. C3×#398C22semidirect
62. #4993C22semidirect
63. #4991C22semidirect
64. #4989C22semidirect
65. #4989C22semidirect
66. #4672C22semidirect
67. #4672C22semidirect
68. #4671C22semidirect
69. #4667C22semidirect
70. #4665C22semidirect
71. #4665C22semidirect
78. C2×#398D3semidirect
120. C22×D12D4semidirect
159. C2×(C2×D3)⋊C4D4semidirect
227. #398C2×D3semidirect
343. C2×D12C2×D4semidirect
372. (C2×D3)⋊C4C2×D4semidirect
901. C2×C3#2671semidirect
970. C3C2×#2671semidirect
975. C2#77967direct (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×#3982
C2×#49932
C2×#49912
C2×#49892
#779672
C2×#46712
C2×#46652
C2×#46672
C2×#46722
C2×#26713