Finite Group Databasebeta

← C2×#82905 #11429775

Subgroups — C2×#82905 #11429775

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×C3×#123C211yesmaximal, characteristic, complemented
2C22×#939C211yesmaximal, characteristic, complemented
3C22×#930C211yesmaximal, characteristic, complemented
4C22×#884C211yesmaximal, characteristic, complemented
5C2×#5223C211yesmaximal, characteristic, complemented
6C2×#5210C211yesmaximal, characteristic, complemented
7#82905C2116yesmaximal, direct product factor
8C2×#4993C211yesmaximal, characteristic, complemented
9C2×#4991C211yesmaximal, characteristic, complemented
10C2×#4987C211yesmaximal, characteristic, complemented
11C2×#4982C211yesmaximal, characteristic, complemented
12C2×#4959C211yesmaximal, characteristic, complemented
13C2×#4956C211yesmaximal, characteristic, complemented
14C2×#4961C211yesmaximal, characteristic, complemented
15C2×#4958C211yesmaximal, characteristic, complemented
16C2×#4950C211yesmaximal, characteristic, complemented
17C2×#2671—31nomaximal, Sylow
18C23×C3×D4C2211yescharacteristic
19C24×C3×C4C2211yescharacteristic
20C23×#67C2211yescharacteristic
21C23×#67C2211yescharacteristic
22C23×#67C2211yescharacteristic
23C23×#67C2211yescharacteristic
24C24×Dic3C2211yescharacteristic
25C23×D12C2211yescharacteristic
26C23×C4×D3C2211yescharacteristic
27C2×C3×#123—28no—
28C2×C3×#123C2218yescomplemented
29C22×C3×C4⋊C4C2211yescharacteristic
30C22×C3×C4⋊C4C2211yescharacteristic
31C22×C3×C22⋊C4C2211yescharacteristic
32C22×C3×C22⋊C4C2211yescharacteristic
33C22×C3×C22⋊C4C2211yescharacteristic
34C22×#217C2211yescharacteristic
35C22×#217C2211yescharacteristic
36C22×#217C2211yescharacteristic
37C2×#939—28no—
38C2×#939C2218yescomplemented
39C2×#930—28no—
40C2×#930C2218yescomplemented
41C22×(C2×D3)⋊C4C2211yescharacteristic
42C22×(C2×D3)⋊C4C2211yescharacteristic
43C22×(C2×D3)⋊C4C2211yescharacteristic
44C22×(C2×D3)⋊C4C2211yescharacteristic
45C22×(C2×D3)⋊C4C2211yescharacteristic
46C22×(C2×D3)⋊C4C2211yescharacteristic
47C22×(C2×D3)⋊C4C2211yescharacteristic
48C22×C4⋊Dic3C2211yescharacteristic
49C22×C4⋊Dic3C2211yescharacteristic
50C22×Dic3⋊C4C2211yescharacteristic
51C22×Dic3⋊C4C2211yescharacteristic
52C22×Dic3⋊C4C2211yescharacteristic
53C2×#884—28no—
54C2×#884C2218yescomplemented
55#5223C2218yescomplemented
56#5210C2218yescomplemented
57C2×C3⋊#95C2211yescharacteristic
58C2×C3⋊#95C2211yescharacteristic
59C2×C3⋊#95C2211yescharacteristic
60C2×C3⋊#95C2211yescharacteristic
61C2×C3⋊#95C2211yescharacteristic
62C2×C3⋊#95C2211yescharacteristic
63#4993C2218yescomplemented
64#4991C2218yescomplemented
65#4987C2218yescomplemented
66#4982C2218yescomplemented
67#4961C2218yescomplemented
68#4959C2218yescomplemented
69#4958C2218yescomplemented
70#4956C2218yescomplemented
71#4950C2218yescomplemented
72C22×#123D311yescharacteristic, complemented
73C22×#121—31no—
74C22×#121—31no—
75C22×#121—31no—
76#2671—316no—
77C2×#399—31no—
78C2×#398—31no—
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—
88C25×C3C2311yescharacteristic
89C25×C3C2311yescharacteristic
90C24×D3C2311yescharacteristic
91C24×D3C2311yescharacteristic
92C22×C3×D4—24no—
93C22×C3×D4—24no—
94C22×C3×D4—42no—
95C22×C3×D4C2314yes—
96C23×C3×C4—24no—
97C23×C3×C4—24no—
98C23×C3×C4—42no—
99C23×C3×C4C2311yescharacteristic
100C23×C3×C4C2311yescharacteristic
101C23×C3×C4C2311yescharacteristic
102C23×C3×C4C2314yes—
103C23×C3×C4C2311yescharacteristic
104C23×C3×C4C2311yescharacteristic
105C22×#67—24no—
106C22×#67—24no—
107C22×#67—24no—
108C22×#67—24no—
109C22×#67—24no—
110C22×#67—42no—
111C22×#67—42no—
112C22×#67—42no—
113C22×#67—42no—
114C22×#67—42no—
115C22×#67—42no—
116C22×#67D418yescomplemented
117C22×#67C2314yes—
118C22×#67C2314yes—
119C22×#67C2314yes—
120C22×#67C2314yes—
121C23×Dic3—24no—
122C23×Dic3—42no—
123C23×Dic3—42no—
124C23×Dic3C2311yescharacteristic
125C23×Dic3C2311yescharacteristic
126C23×Dic3C2311yescharacteristic
127C23×Dic3C2311yescharacteristic
128C23×Dic3C2311yescharacteristic
129C23×Dic3C2311yescharacteristic
130C23×Dic3C2314yes—
131C22×D12—24no—
132C22×D12—24no—
133C22×D12—42no—
134C22×D12C2314yes—
135C22×C4×D3—24no—
136C22×C4×D3—24no—
137C22×C4×D3—42no—
138C22×C4×D3C2314yes—
139C3×#123—232no—
140C2×C3×C4⋊C4—24no—
141C2×C3×C4⋊C4—24no—
142C2×C3×C4⋊C4C2314yes—
143C2×C3×C4⋊C4C2314yes—
144C2×C3×C22⋊C4—24no—
145C2×C3×C22⋊C4—24no—
146C2×C3×C22⋊C4D418yescomplemented
147C2×C3×C22⋊C4C2314yes—
148C2×C3×C22⋊C4C2314yes—
149C2×C3×C22⋊C4C2314yes—
150C2×#217—24no—
151C2×#217—24no—
152C2×#217—42no—
153C2×#217C2314yes—
154C2×#217C2314yes—
155C2×#217C2314yes—
156#939—232no—
157#930—232no—
158C2×(C2×D3)⋊C4—24no—
159C2×(C2×D3)⋊C4—24no—
160C2×(C2×D3)⋊C4—24no—
161C2×(C2×D3)⋊C4—24no—
162C2×(C2×D3)⋊C4—42no—
163C2×(C2×D3)⋊C4—42no—
164C2×(C2×D3)⋊C4—42no—
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×C4⋊Dic3—24no—
173C2×C4⋊Dic3—42no—
174C2×C4⋊Dic3C2314yes—
175C2×C4⋊Dic3C2314yes—
176C2×Dic3⋊C4—24no—
177C2×Dic3⋊C4—24no—
178C2×Dic3⋊C4—42no—
179C2×Dic3⋊C4C2314yes—
180C2×Dic3⋊C4C2314yes—
181C2×Dic3⋊C4C2314yes—
182#884—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×D4C2×D311yescharacteristic
195C24×C4—31no—
196C24×C4—31no—
197C24×C4C2×D311yescharacteristic
198C2×#123—28no—
199C2×#123C2×D318yescomplemented
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⋊C4—31no—
210C22×C4⋊C4—31no—
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⋊C4C2×D311yescharacteristic
224C22×C22⋊C4C2×D311yescharacteristic
225C22×C22⋊C4C2×D311yescharacteristic
226#399—38no—
227#398—38no—
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×#95—31no—
241C2×#95—31no—
242C2×#95—31no—
243C24×C3—22no—
244C24×C3—22no—
245C24×C3—22no—
246C24×C3—22no—
247C24×C3—22no—
248C24×C3—22no—
249C24×C3—22no—
250C24×C3—22no—
251C24×C3—22no—
252C24×C3—22no—
253C24×C3—22no—
254C24×C3—22no—
255C24×C3C2×D414yes—
256C24×C3C2×D414yes—
257C24×C3C2412yes—
258C24×C3C2412yes—
259C24×C3C2411yescharacteristic
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×D3—22no—
270C23×D3—22no—
271C23×D3—22no—
272C23×D3—22no—
273C23×D3C2×D414yes—
274C23×D3C2412yes—
275C23×D3C2412yes—
276C2×C3×D4—28no—
277C2×C3×D4—28no—
278C2×C3×D4—44no—
279C2×C3×D4—416no—
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—28no—
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×C4—28no—
295C22×C3×C4—44no—
296C22×C3×C4—416no—
297C22×C3×C4C2×D414yes—
298C22×C3×C4C2×D414yes—
299C22×C3×C4C2412yes—
300C22×C3×C4C2412yes—
301C22×C3×C4C2412yes—
302C22×C3×C4C2412yes—
303C22×C3×C4C2412yes—
304C2×#67—28no—
305C2×#67—28no—
306C2×#67—28no—
307C2×#67—28no—
308C2×#67—28no—
309C2×#67—416no—
310C2×#67—44no—
311C2×#67—44no—
312C2×#67—44no—
313C2×#67—44no—
314C2×#67—44no—
315C2×#67—44no—
316C2×#67—416no—
317C2×#67—416no—
318C2×#67—416no—
319C2×#67C2×D4116yescomplemented
320C22×Dic3—22no—
321C22×Dic3—22no—
322C22×Dic3—22no—
323C22×Dic3—22no—
324C22×Dic3—22no—
325C22×Dic3—22no—
326C22×Dic3—22no—
327C22×Dic3—22no—
328C22×Dic3—22no—
329C22×Dic3—22no—
330C22×Dic3—22no—
331C22×Dic3—22no—
332C22×Dic3—22no—
333C22×Dic3—22no—
334C22×Dic3—22no—
335C22×Dic3—22no—
336C22×Dic3—28no—
337C22×Dic3—44no—
338C22×Dic3—44no—
339C22×Dic3—416no—
340C22×Dic3C2×D414yes—
341C22×Dic3#4114yes—
342C22×Dic3C2412yes—
343C22×Dic3C2412yes—
344C22×Dic3C2412yes—
345C22×Dic3C2412yes—
346C22×Dic3C2412yes—
347C22×Dic3C2412yes—
348C2×D12—28no—
349C2×D12—28no—
350C2×D12—44no—
351C2×D12—416no—
352C2×C4×D3—28no—
353C2×C4×D3—28no—
354C2×C4×D3—44no—
355C2×C4×D3—416no—
356C3×C4⋊C4—28no—
357C3×C4⋊C4—28no—
358C3×C22⋊C4—28no—
359C3×C22⋊C4—28no—
360C3×C22⋊C4C2×D4116yescomplemented
361#217—28no—
362#217—28no—
363#217—44no—
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—
371C4⋊Dic3—28no—
372C4⋊Dic3—44no—
373Dic3⋊C4—28no—
374Dic3⋊C4—28no—
375Dic3⋊C4—44no—
376C25—31no—
377C25—31no—
378C25C22×D311yescharacteristic
379C25C22×D311yescharacteristic
380C22×D4—24no—
381C22×D4—24no—
382C22×D4—38no—
383C22×D4—34no—
384C22×D4—34no—
385C22×D4—34no—
386C22×D4—34no—
387C22×D4—34no—
388C22×D4—42no—
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×D4C22×D314yes—
404C23×C4—24no—
405C23×C4—24no—
406C23×C4—31no—
407C23×C4—31no—
408C23×C4—31no—
409C23×C4—31no—
410C23×C4—31no—
411C23×C4—31no—
412C23×C4—34no—
413C23×C4—34no—
414C23×C4—42no—
415C23×C4—64no—
416C23×C4—64no—
417C23×C4—64no—
418C23×C4—122no—
419C23×C4—122no—
420C23×C4—122no—
421C23×C4C22×D311yescharacteristic
422C23×C4C22×D311yescharacteristic
423C23×C4C22×D311yescharacteristic
424C23×C4C22×D314yes—
425C23×C4C22×D311yescharacteristic
426C23×C4C22×D311yescharacteristic
427#123—232no—
428#121—632no—
429#121—632no—
430#121—632no—
431C2×C4⋊C4—24no—
432C2×C4⋊C4—24no—
433C2×C4⋊C4—34no—
434C2×C4⋊C4—34no—
435C2×C4⋊C4—34no—
436C2×C4⋊C4—34no—
437C2×C4⋊C4—34no—
438C2×C4⋊C4—64no—
439C2×C4⋊C4—64no—
440C2×C4⋊C4—64no—
441C2×C4⋊C4—122no—
442C2×C4⋊C4—122no—
443C2×C4⋊C4C22×D314yes—
444C2×C4⋊C4C22×D314yes—
445C2×C22⋊C4—24no—
446C2×C22⋊C4—24no—
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—64no—
458C2×C22⋊C4—64no—
459C2×C22⋊C4—64no—
460C2×C22⋊C4—64no—
461C2×C22⋊C4—64no—
462C2×C22⋊C4—64no—
463C2×C22⋊C4—122no—
464C2×C22⋊C4—122no—
465C2×C22⋊C4—122no—
466C2×C22⋊C4—122no—
467C2×C22⋊C4#6718yescomplemented
468C2×C22⋊C4C22×D314yes—
469C2×C22⋊C4C22×D314yes—
470C2×C22⋊C4C22×D314yes—
471#95—34no—
472#95—34no—
473#95—34no—
474#95—34no—
475#95—34no—
476#95—34no—
477C23×C3—28no—
478C23×C3—28no—
479C23×C3—28no—
480C23×C3—28no—
481C23×C3—28no—
482C23×C3—28no—
483C23×C3—22no—
484C23×C3—22no—
485C23×C3—22no—
486C23×C3—22no—
487C23×C3—22no—
488C23×C3—22no—
489C23×C3—22no—
490C23×C3—22no—
491C23×C3—22no—
492C23×C3—22no—
493C23×C3—22no—
494C23×C3—22no—
495C23×C3—44no—
496C23×C3—44no—
497C23×C3—44no—
498C23×C3—44no—
499C23×C3—44no—
500C23×C3—44no—
501C23×C3—44no—
502C23×C3—44no—
503C23×C3C22×D414yes—
504C23×C3C22×D412yes—
505C23×C3C22×D414yes—
506C23×C3C22×D412yes—
507C23×C3C2×#4112yes—
508C23×C3H(5,𝔽2)12yes—
509C23×C3H(5,𝔽2)12yes—
510C23×C3H(5,𝔽2)12yes—
511C23×C32−1+412yes—
512C23×C3C2511yescharacteristic
513C22×D3—28no—
514C22×D3—28no—
515C22×D3—28no—
516C22×D3—22no—
517C22×D3—22no—
518C22×D3—22no—
519C22×D3—22no—
520C22×D3—22no—
521C22×D3—22no—
522C22×D3—22no—
523C22×D3—22no—
524C22×D3—22no—
525C22×D3—22no—
526C22×D3—22no—
527C22×D3—22no—
528C22×D3—22no—
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×D3—44no—
539C22×D3—44no—
540C22×D3C22×D414yes—
541C3×D4—416no—
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—416no—
558C2×C3×C4—44no—
559C2×C3×C4—44no—
560C2×C3×C4—44no—
561C2×C3×C4C22×D414yes—
562C2×C3×C4C22×D414yes—
563#67—416no—
564#67—416no—
565#67—416no—
566#67—416no—
567C2×Dic3—28no—
568C2×Dic3—28no—
569C2×Dic3—22no—
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—22no—
582C2×Dic3—22no—
583C2×Dic3—22no—
584C2×Dic3—22no—
585C2×Dic3—416no—
586C2×Dic3—44no—
587C2×Dic3—44no—
588C2×Dic3—44no—
589C2×Dic3—44no—
590C2×Dic3C22×D414yes—
591C2×Dic3C2×#4114yes—
592D12—416no—
593C4×D3—416no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24—22no—
599C24—22no—
600C24—22no—
601C24—22no—
602C24—22no—
603C24—22no—
604C24—22no—
605C24—22no—
606C24—34no—
607C24—32no—
608C24—32no—
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—
622C24D3×D414yes—
623C24C2×#6714yes—
624C24C23×D312yes—
625C24C23×D312yes—
626C24C23×D311yescharacteristic
627C2×D4—28no—
628C2×D4—28no—
629C2×D4—316no—
630C2×D4—44no—
631C2×D4—416no—
632C2×D4—68no—
633C2×D4—68no—
634C2×D4—68no—
635C2×D4—68no—
636C2×D4—68no—
637C2×D4—68no—
638C2×D4—68no—
639C2×D4—124no—
640C2×D4—1216no—
641C2×D4—1216no—
642C2×D4—124no—
643C2×D4—124no—
644C2×D4—124no—
645C2×D4—124no—
646C2×D4—124no—
647C2×D4—124no—
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—28no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—28no—
666C22×C4—34no—
667C22×C4—34no—
668C22×C4—32no—
669C22×C4—32no—
670C22×C4—32no—
671C22×C4—32no—
672C22×C4—32no—
673C22×C4—32no—
674C22×C4—44no—
675C22×C4—416no—
676C22×C4—68no—
677C22×C4—68no—
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—62no—
688C22×C4—62no—
689C22×C4—62no—
690C22×C4—62no—
691C22×C4—62no—
692C22×C4—62no—
693C22×C4—62no—
694C22×C4—68no—
695C22×C4—124no—
696C22×C4—1216no—
697C22×C4—124no—
698C22×C4—124no—
699C22×C4—1216no—
700C22×C4C2×#6714yes—
701C22×C4C2×#6714yes—
702C22×C4C23×D312yes—
703C22×C4C23×D312yes—
704C22×C4C23×D312yes—
705C22×C4C23×D312yes—
706C22×C4C23×D312yes—
707C4⋊C4—28no—
708C4⋊C4—28no—
709C4⋊C4—68no—
710C4⋊C4—68no—
711C4⋊C4—68no—
712C4⋊C4—124no—
713C4⋊C4—124no—
714C22⋊C4—28no—
715C22⋊C4—28no—
716C22⋊C4—68no—
717C22⋊C4—68no—
718C22⋊C4—68no—
719C22⋊C4—68no—
720C22⋊C4—68no—
721C22⋊C4—68no—
722C22⋊C4—124no—
723C22⋊C4—124no—
724C22⋊C4—124no—
725C22⋊C4—124no—
726C22⋊C4C2×#67116yescomplemented
727C22×C3—24no—
728C22×C3—24no—
729C22×C3—24no—
730C22×C3—24no—
731C22×C3—24no—
732C22×C3—24no—
733C22×C3—416no—
734C22×C3—416no—
735C22×C3—42no—
736C22×C3—42no—
737C22×C3—42no—
738C22×C3—42no—
739C22×C3—42no—
740C22×C3—42no—
741C22×C3—42no—
742C22×C3—42no—
743C22×C3#53414yes—
744C22×C3#53714yes—
745C22×C3#54014yes—
746C22×C3D4214yes—
747C22×C3#54614yes—
748C22×C3#54714yes—
749C22×C3#56214yes—
750C22×C3C23×D411yescharacteristic
751C22×C3C23×D411yescharacteristic
752C22×C3C22×#4111yescharacteristic
753C22×C3C2×H(5,𝔽2)11yescharacteristic
754C22×C3C2×H(5,𝔽2)11yescharacteristic
755C22×C3C2×H(5,𝔽2)11yescharacteristic
756C22×C3C2×2−1+411yescharacteristic
757C2×D3—24no—
758C2×D3—24no—
759C2×D3—24no—
760C2×D3—416no—
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—42no—
776C3×C4—42no—
777C3×C4—42no—
778Dic3—24no—
779Dic3—24no—
780Dic3—42no—
781Dic3—42no—
782Dic3—42no—
783Dic3—42no—
784C23—28no—
785C23—28no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—28no—
799C23—28no—
800C23—28no—
801C23—28no—
802C23—34no—
803C23—44no—
804C23—44no—
805C23—44no—
806C23—44no—
807C23—44no—
808C23—44no—
809C23—44no—
810C23—44no—
811C23—68no—
812C23—68no—
813C23—62no—
814C23—62no—
815C23—62no—
816C23—62no—
817C23—62no—
818C23—62no—
819C23—68no—
820C23—62no—
821C23—62no—
822C23—62no—
823C23—62no—
824C23—62no—
825C23—62no—
826C23—62no—
827C23—124no—
828C23—124no—
829C23—124no—
830C23—124no—
831C23—124no—
832C23—124no—
833C23—124no—
834C23—124no—
835C23—124no—
836C23—124no—
837C23—124no—
838C23C2×D3×D414yes—
839C23C2×D3×D412yes—
840C23#100412yes—
841C23D3×#4112yes—
842C23#100912yes—
843C23#100912yes—
844C23#101012yes—
845C23C22×#6714yes—
846C23C22×#6712yes—
847C23C24×D311yescharacteristic
848D4—416no—
849D4—1216no—
850D4—1216no—
851D4—1216no—
852D4—1216no—
853D4—1216no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—28no—
859C2×C4—28no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—34no—
870C2×C4—34no—
871C2×C4—416no—
872C2×C4—44no—
873C2×C4—44no—
874C2×C4—44no—
875C2×C4—68no—
876C2×C4—62no—
877C2×C4—62no—
878C2×C4—62no—
879C2×C4—62no—
880C2×C4—68no—
881C2×C4—62no—
882C2×C4—62no—
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—62no—
893C2×C4—1216no—
894C2×C4—1216no—
895C2×C4—124no—
896C2×C4—124no—
897C2×C4—124no—
898C2×C4—124no—
899C2×C4C22×#6714yes—
900C2×C4C22×#6714yes—
901C2×C3—44no—
902C2×C3—44no—
903C2×C3#267118yescomplemented
904C2×C3C2×#53411yescharacteristic
905C2×C3C2×#53711yescharacteristic
906C2×C3C2×#54011yescharacteristic
907C2×C3C2×D4211yescharacteristic
908C2×C3C2×#54611yescharacteristic
909C2×C3C2×#54711yescharacteristic
910C2×C3C2×#56211yescharacteristic
911D3—44no—
912D3—82no—
913C22—24no—
914C22—24no—
915C22—24no—
916C22—24no—
917C22—24no—
918C22—24no—
919C22—416no—
920C22—416no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22—42no—
929C22—64no—
930C22—64no—
931C22—64no—
932C22—1216no—
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#565314yes—
946C22#565514yes—
947C22#566314yes—
948C22#566714yes—
949C22D4×#6714yes—
950C22#582914yes—
951C22#583314yes—
952C22C22×D3×D411yescharacteristic
953C22C2×#100411yescharacteristic
954C22C2×D3×#4111yescharacteristic
955C22C2×#100911yescharacteristic
956C22C2×#100911yescharacteristic
957C22C2×#101011yescharacteristic
958C22C23×#6711yescharacteristic
959C4—24no—
960C4—24no—
961C4—42no—
962C4—42no—
963C4—42no—
964C4—64no—
965C4—64no—
966C4—122no—
967C4—122no—
968C4—122no—
969C4—122no—
970C3C2×#267111yescharacteristic, complemented, Sylow
971C2—44no—
972C2—44no—
973C2—124no—
974C2—242no—
975C2#8290518yesdirect product factor
976C2C2×#566311yescharacteristic
977C2C2×#565311yescharacteristic
978C2C2×#565511yescharacteristic
979C2C2×#566711yescharacteristic
980C2C2×D4×#6711yescharacteristic
981C2C2×#583311yescharacteristic
982C2C2×#582911yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC22×C3×#123C2
socleC24×C3C24
hypercenterC22×#123D3
hypocenterC3C2×#2671
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
1. C22×C3×#123C2semidirect
2. C22×#939C2semidirect
3. C22×#930C2semidirect
4. C22×#884C2semidirect
5. C2×#5223C2semidirect
6. C2×#5210C2semidirect
7. #82905C2direct (N × H)
8. C2×#4993C2semidirect
9. C2×#4991C2semidirect
10. C2×#4987C2semidirect
11. C2×#4982C2semidirect
12. C2×#4959C2semidirect
13. C2×#4956C2semidirect
14. C2×#4961C2semidirect
15. C2×#4958C2semidirect
16. C2×#4950C2semidirect
28. C2×C3×#123C22semidirect
38. C2×#939C22semidirect
40. C2×#930C22semidirect
54. C2×#884C22semidirect
55. #5223C22semidirect
56. #5210C22semidirect
63. #4993C22semidirect
64. #4991C22semidirect
65. #4987C22semidirect
66. #4982C22semidirect
67. #4961C22semidirect
68. #4959C22semidirect
69. #4958C22semidirect
70. #4956C22semidirect
71. #4950C22semidirect
72. C22×#123D3semidirect
116. C22×#67D4semidirect
146. C2×C3×C22⋊C4D4semidirect
199. C2×#123C2×D3semidirect
319. C2×#67C2×D4semidirect
360. C3×C22⋊C4C2×D4semidirect
467. C2×C22⋊C4#67semidirect
726. C22⋊C4C2×#67semidirect
903. C2×C3#2671semidirect
970. C3C2×#2671semidirect
975. C2#82905direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#1232
C22×#9392
C22×#9302
C22×#8842
C2×#52232
C2×#52102
#829052
C2×#49932
C2×#49912
C2×#49872
C2×#49822
C2×#49592
C2×#49562
C2×#49612
C2×#49582
C2×#49502
C2×#26713