Finite Group Databasebeta

← C2×#76461 #11429761

Subgroups — C2×#76461 #11429761

Order 768.

5006 conjugacy classes of subgroups.

The subgroup lattice has 1080 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#937C211yesmaximal, characteristic, complemented
2C22×#882C211yesmaximal, characteristic, complemented
3C22×#885C211yesmaximal, characteristic, complemented
4C22×#875C211yesmaximal, characteristic, complemented
5C2×C3×#390C211yesmaximal, characteristic, complemented
6C2×#5223C211yesmaximal, characteristic, complemented
7C2×#4991C211yesmaximal, characteristic, complemented
8C2×#4990C211yesmaximal, characteristic, complemented
9C2×#4959C211yesmaximal, characteristic, complemented
10C2×#4960C211yesmaximal, characteristic, complemented
11C2×#4960C211yesmaximal, characteristic, complemented
12C2×#4955C211yesmaximal, characteristic, complemented
13C2×#4947C211yesmaximal, characteristic, complemented
14C2×#4957C211yesmaximal, characteristic, complemented
15C2×#4940C211yesmaximal, characteristic, complemented
16#76461C2116yesmaximal, direct product factor
17C2×#2670—31nomaximal, Sylow
18C25×D3C2211yescharacteristic
19C23×C3×D4C2211yescharacteristic
20C23×#67C2211yescharacteristic
21C23×#67C2211yescharacteristic
22C23×#67C2211yescharacteristic
23C23×#67C2211yescharacteristic, complemented
24C23×D12C2211yescharacteristic
25C23×D12C2211yescharacteristic
26C23×Dic6C2211yescharacteristic, complemented
27C22×C3×C4⋊C4C2211yescharacteristic, complemented
28C22×C3×C22⋊C4C2211yescharacteristic
29C22×C3×C22⋊C4C2211yescharacteristic
30C22×C3×C22⋊C4C2211yescharacteristic, complemented
31C22×C3×C22⋊C4C2211yescharacteristic, complemented
32C22×C3×C42C2211yescharacteristic, complemented
33C22×#217C2211yescharacteristic
34C22×#217C2211yescharacteristic
35C22×#217C2211yescharacteristic, complemented
36C2×#937—28no—
37C2×#937C2218yescomplemented
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×(C2×D3)⋊C4C2211yescharacteristic
45C22×(C2×D3)⋊C4C2211yescharacteristic
46C22×(C2×D3)⋊C4C2211yescharacteristic, complemented
47C22×(C2×D3)⋊C4C2211yescharacteristic, complemented
48C22×(C2×D3)⋊C4C2211yescharacteristic, complemented
49C22×Dic3⋊C4C2211yescharacteristic, complemented
50C22×C4×Dic3C2211yescharacteristic, complemented
51C2×#885—28no—
52C2×#885C2218yescomplemented
53C2×#882—28no—
54C2×#882C2218yescomplemented
55C2×#875—28no—
56C2×#875C2218yescomplemented
57C3×#390C2218yescomplemented
58#5223C2218yescomplemented
59C2×C3⋊#95C2211yescharacteristic, complemented
60C2×C3⋊#95C2211yescharacteristic, complemented
61C2×C3⋊#95C2211yescharacteristic, complemented
62C2×C3⋊#95C2211yescharacteristic, complemented
63#4991C2218yescomplemented
64#4990C2218yescomplemented
65#4960C2218yescomplemented
66#4960C2218yescomplemented
67#4959C2218yescomplemented
68#4957C2218yescomplemented
69#4955C2218yescomplemented
70#4947C2218yescomplemented
71#4940C2218yescomplemented
72C22×#124—31no—
73C22×#124—31no—
74C22×#120—31no—
75C22×#120—31no—
76#2670—316no—
77C2×#394—31no—
78C2×#394—31no—
79C2×#393—31no—
80C2×#392—31no—
81C2×#392—31no—
82C2×#392—31no—
83C2×#390—31no—
84C2×#390D311yescharacteristic, complemented
85C2×#388—31no—
86C2×#388—31no—
87C2×#379—31no—
88C25×C3C2311yescharacteristic
89C25×C3C2311yescharacteristic
90C24×D3—24no—
91C24×D3—24no—
92C24×D3—24no—
93C24×D3—42no—
94C24×D3—42no—
95C24×D3—42no—
96C24×D3—42no—
97C24×D3C2311yescharacteristic
98C24×D3C2311yescharacteristic
99C24×D3C2311yescharacteristic
100C24×D3C2314yes—
101C22×C3×D4—24no—
102C22×C3×D4—24no—
103C22×C3×D4—42no—
104C22×C3×D4C2314yes—
105C23×C3×C4C2311yescharacteristic
106C23×C3×C4C2311yescharacteristic
107C23×C3×C4C2311yescharacteristic
108C23×C3×C4C2311yescharacteristic
109C23×C3×C4C2311yescharacteristic
110C22×#67—24no—
111C22×#67—24no—
112C22×#67—24no—
113C22×#67—24no—
114C22×#67—24no—
115C22×#67—42no—
116C22×#67—42no—
117C22×#67—42no—
118C22×#67—42no—
119C22×#67—42no—
120C22×#67—42no—
121C22×#67—42no—
122C22×#67C2314yes—
123C22×#67C2314yes—
124C22×#67C2314yes—
125C22×#67C2314yescomplemented
126C23×Dic3C2311yescharacteristic
127C23×Dic3C2311yescharacteristic
128C23×Dic3C2311yescharacteristic
129C23×Dic3C2311yescharacteristic
130C23×Dic3C2311yescharacteristic
131C22×D12—24no—
132C22×D12—24no—
133C22×D12—24no—
134C22×D12—42no—
135C22×D12—42no—
136C22×D12—42no—
137C22×D12C2314yes—
138C22×D12C2314yes—
139C22×Dic6—24no—
140C22×Dic6—24no—
141C22×Dic6—42no—
142C22×Dic6C2314yescomplemented
143C2×C3×C4⋊C4—42no—
144C2×C3×C4⋊C4C2314yescomplemented
145C2×C3×C22⋊C4—24no—
146C2×C3×C22⋊C4—24no—
147C2×C3×C22⋊C4—42no—
148C2×C3×C22⋊C4—42no—
149C2×C3×C22⋊C4C2314yes—
150C2×C3×C22⋊C4C2314yes—
151C2×C3×C22⋊C4C2314yescomplemented
152C2×C3×C22⋊C4C2314yescomplemented
153C2×C3×C42—24no—
154C2×C3×C42C2314yescomplemented
155C2×#217—24no—
156C2×#217—24no—
157C2×#217—42no—
158C2×#217C2314yes—
159C2×#217C2314yes—
160C2×#217C2314yescomplemented
161#937—232no—
162C2×(C2×D3)⋊C4—24no—
163C2×(C2×D3)⋊C4—24no—
164C2×(C2×D3)⋊C4—24no—
165C2×(C2×D3)⋊C4—24no—
166C2×(C2×D3)⋊C4—24no—
167C2×(C2×D3)⋊C4—24no—
168C2×(C2×D3)⋊C4—42no—
169C2×(C2×D3)⋊C4—42no—
170C2×(C2×D3)⋊C4—42no—
171C2×(C2×D3)⋊C4D418yescomplemented
172C2×(C2×D3)⋊C4D418yescomplemented
173C2×(C2×D3)⋊C4C2314yes—
174C2×(C2×D3)⋊C4C2314yes—
175C2×(C2×D3)⋊C4C2314yes—
176C2×(C2×D3)⋊C4C2314yes—
177C2×(C2×D3)⋊C4C2314yes—
178C2×(C2×D3)⋊C4C2314yes—
179C2×(C2×D3)⋊C4C2314yes—
180C2×(C2×D3)⋊C4C2314yes—
181C2×(C2×D3)⋊C4C2314yescomplemented
182C2×(C2×D3)⋊C4C2314yescomplemented
183C2×(C2×D3)⋊C4C2314yescomplemented
184C2×Dic3⋊C4—42no—
185C2×Dic3⋊C4C2314yescomplemented
186C2×C4×Dic3—24no—
187C2×C4×Dic3C2314yescomplemented
188#885—232no—
189#882—232no—
190#875—232no—
191C3⋊#95C2314yescomplemented
192C3⋊#95C2314yescomplemented
193C3⋊#95C2314yescomplemented
194C3⋊#95C2314yescomplemented
195C26—31no—
196C23×Q8—31no—
197C23×D4—31no—
198C23×D4—31no—
199C23×D4—31no—
200C23×D4—31no—
201C23×D4—31no—
202C23×D4—31no—
203C23×D4C2×D311yescharacteristic
204C2×#124—38no—
205C2×#124—38no—
206C2×#124—68no—
207C2×#124—68no—
208C2×#120—38no—
209C2×#120—38no—
210C2×#120—68no—
211C2×#120—68no—
212C22×C4⋊C4—31no—
213C22×C4⋊C4C2×D311yescharacteristic, complemented
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—
226C22×C22⋊C4—31no—
227C22×C22⋊C4—31no—
228C22×C22⋊C4C2×D311yescharacteristic
229C22×C22⋊C4C2×D311yescharacteristic
230C22×C22⋊C4C2×D311yescharacteristic, complemented
231C22×C22⋊C4C2×D311yescharacteristic, complemented
232C22×C42—31no—
233C22×C42C2×D311yescharacteristic, complemented
234#394—38no—
235#394—38no—
236#393—38no—
237#392—38no—
238#392—38no—
239#392—38no—
240#390—38no—
241#390C2×D318yescomplemented
242#388—38no—
243#388—38no—
244#379—38no—
245C2×#95—31no—
246C2×#95—31no—
247C2×#95—31no—
248C2×#95—31no—
249C24×C3—22no—
250C24×C3—22no—
251C24×C3—22no—
252C24×C3—22no—
253C24×C3—22no—
254C24×C3—22no—
255C24×C3—22no—
256C24×C3—22no—
257C24×C3—22no—
258C24×C3—22no—
259C24×C3—22no—
260C24×C3—22no—
261C24×C3—22no—
262C24×C3#4114yes—
263C24×C3C2412yes—
264C24×C3C2412yes—
265C24×C3C2411yescharacteristic
266C23×D3—22no—
267C23×D3—22no—
268C23×D3—22no—
269C23×D3—22no—
270C23×D3—22no—
271C23×D3—22no—
272C23×D3—22no—
273C23×D3—22no—
274C23×D3—22no—
275C23×D3—22no—
276C23×D3—22no—
277C23×D3—22no—
278C23×D3—22no—
279C23×D3—22no—
280C23×D3—22no—
281C23×D3—28no—
282C23×D3—22no—
283C23×D3—22no—
284C23×D3—22no—
285C23×D3—22no—
286C23×D3—28no—
287C23×D3—28no—
288C23×D3—44no—
289C23×D3—44no—
290C23×D3—44no—
291C23×D3—44no—
292C23×D3—416no—
293C23×D3—416no—
294C23×D3—416no—
295C23×D3—416no—
296C23×D3—416no—
297C23×D3—416no—
298C23×D3—416no—
299C23×D3C2×D414yes—
300C23×D3C2×D414yes—
301C23×D3C2412yes—
302C23×D3C2412yes—
303C23×D3C2412yes—
304C2×C3×D4—28no—
305C2×C3×D4—28no—
306C2×C3×D4—44no—
307C2×C3×D4—416no—
308C22×C3×C4—22no—
309C22×C3×C4—22no—
310C22×C3×C4—22no—
311C22×C3×C4—22no—
312C22×C3×C4—22no—
313C22×C3×C4—22no—
314C22×C3×C4—22no—
315C22×C3×C4—22no—
316C22×C3×C4—22no—
317C22×C3×C4—22no—
318C22×C3×C4—22no—
319C22×C3×C4—22no—
320C22×C3×C4—22no—
321C22×C3×C4C2×D414yes—
322C22×C3×C4C2×D414yes—
323C22×C3×C4C2412yes—
324C22×C3×C4C2412yes—
325C22×C3×C4C2412yes—
326C22×C3×C4C2412yes—
327C22×C3×C4C2412yes—
328C2×#67—28no—
329C2×#67—28no—
330C2×#67—28no—
331C2×#67—28no—
332C2×#67—28no—
333C2×#67—44no—
334C2×#67—44no—
335C2×#67—44no—
336C2×#67—44no—
337C2×#67—44no—
338C2×#67—44no—
339C2×#67—44no—
340C2×#67—416no—
341C2×#67—416no—
342C2×#67—416no—
343C2×#67—416no—
344C22×Dic3—22no—
345C22×Dic3—22no—
346C22×Dic3—22no—
347C22×Dic3—22no—
348C22×Dic3—22no—
349C22×Dic3—22no—
350C22×Dic3—22no—
351C22×Dic3—22no—
352C22×Dic3—22no—
353C22×Dic3—22no—
354C22×Dic3—22no—
355C22×Dic3—22no—
356C22×Dic3—22no—
357C22×Dic3C2×D414yes—
358C22×Dic3C2×D414yes—
359C22×Dic3C2412yes—
360C22×Dic3C2412yes—
361C22×Dic3C2412yes—
362C22×Dic3C2412yes—
363C22×Dic3C2412yes—
364C2×D12—28no—
365C2×D12—28no—
366C2×D12—28no—
367C2×D12—44no—
368C2×D12—44no—
369C2×D12—44no—
370C2×D12—416no—
371C2×D12—416no—
372C2×Dic6—28no—
373C2×Dic6—28no—
374C2×Dic6—44no—
375C2×Dic6—416no—
376C3×C4⋊C4—44no—
377C3×C22⋊C4—28no—
378C3×C22⋊C4—28no—
379C3×C22⋊C4—44no—
380C3×C22⋊C4—44no—
381C3×C42—28no—
382#217—28no—
383#217—28no—
384#217—44no—
385(C2×D3)⋊C4—28no—
386(C2×D3)⋊C4—28no—
387(C2×D3)⋊C4—28no—
388(C2×D3)⋊C4—28no—
389(C2×D3)⋊C4—28no—
390(C2×D3)⋊C4—28no—
391(C2×D3)⋊C4—44no—
392(C2×D3)⋊C4—44no—
393(C2×D3)⋊C4—44no—
394(C2×D3)⋊C4C2×D4116yescomplemented
395(C2×D3)⋊C4C2×D4116yescomplemented
396Dic3⋊C4—44no—
397C4×Dic3—28no—
398C25—31no—
399C25—31no—
400C25—31no—
401C25—34no—
402C25—64no—
403C25—64no—
404C25—64no—
405C25—122no—
406C25—122no—
407C25—122no—
408C25—122no—
409C25C22×D311yescharacteristic
410C25C22×D311yescharacteristic
411C22×Q8—34no—
412C22×Q8—64no—
413C22×Q8—64no—
414C22×Q8—122no—
415C22×D4—24no—
416C22×D4—24no—
417C22×D4—34no—
418C22×D4—34no—
419C22×D4—34no—
420C22×D4—34no—
421C22×D4—34no—
422C22×D4—34no—
423C22×D4—42no—
424C22×D4—64no—
425C22×D4—64no—
426C22×D4—64no—
427C22×D4—64no—
428C22×D4—64no—
429C22×D4—64no—
430C22×D4—64no—
431C22×D4—64no—
432C22×D4—122no—
433C22×D4—122no—
434C22×D4—122no—
435C22×D4—122no—
436C22×D4—122no—
437C22×D4—122no—
438C22×D4—122no—
439C22×D4—122no—
440C22×D4—122no—
441C22×D4—122no—
442C22×D4C22×D314yes—
443C23×C4—31no—
444C23×C4—31no—
445C23×C4—31no—
446C23×C4—31no—
447C23×C4—31no—
448C23×C4C22×D311yescharacteristic
449C23×C4C22×D311yescharacteristic
450C23×C4C22×D311yescharacteristic
451C23×C4C22×D311yescharacteristic
452C23×C4C22×D311yescharacteristic
453#124—632no—
454#124—632no—
455#120—632no—
456#120—632no—
457C2×C4⋊C4—34no—
458C2×C4⋊C4—42no—
459C2×C4⋊C4—122no—
460C2×C4⋊C4C22×D314yescomplemented
461C2×C22⋊C4—24no—
462C2×C22⋊C4—24no—
463C2×C22⋊C4—38no—
464C2×C22⋊C4—38no—
465C2×C22⋊C4—34no—
466C2×C22⋊C4—34no—
467C2×C22⋊C4—34no—
468C2×C22⋊C4—34no—
469C2×C22⋊C4—34no—
470C2×C22⋊C4—34no—
471C2×C22⋊C4—34no—
472C2×C22⋊C4—34no—
473C2×C22⋊C4—34no—
474C2×C22⋊C4—34no—
475C2×C22⋊C4—34no—
476C2×C22⋊C4—34no—
477C2×C22⋊C4—34no—
478C2×C22⋊C4—34no—
479C2×C22⋊C4—42no—
480C2×C22⋊C4—42no—
481C2×C22⋊C4—64no—
482C2×C22⋊C4—64no—
483C2×C22⋊C4—64no—
484C2×C22⋊C4—64no—
485C2×C22⋊C4—64no—
486C2×C22⋊C4—64no—
487C2×C22⋊C4—64no—
488C2×C22⋊C4—64no—
489C2×C22⋊C4—122no—
490C2×C22⋊C4—122no—
491C2×C22⋊C4—122no—
492C2×C22⋊C4—122no—
493C2×C22⋊C4C22×D314yes—
494C2×C22⋊C4C22×D314yes—
495C2×C22⋊C4C22×D314yescomplemented
496C2×C22⋊C4C22×D314yescomplemented
497C2×C42—24no—
498C2×C42—34no—
499C2×C42—64no—
500C2×C42C22×D314yescomplemented
501#95—34no—
502#95—34no—
503#95—34no—
504#95—34no—
505C23×C3—28no—
506C23×C3—28no—
507C23×C3—28no—
508C23×C3—22no—
509C23×C3—22no—
510C23×C3—22no—
511C23×C3—22no—
512C23×C3—22no—
513C23×C3—22no—
514C23×C3—22no—
515C23×C3—22no—
516C23×C3—22no—
517C23×C3—22no—
518C23×C3—22no—
519C23×C3—22no—
520C23×C3—22no—
521C23×C3—44no—
522C23×C3—44no—
523C23×C3—44no—
524C23×C3—44no—
525C23×C3—44no—
526C23×C3—44no—
527C23×C3—44no—
528C23×C3—44no—
529C23×C3—44no—
530C23×C3—44no—
531C23×C3—44no—
532C23×C3C22×D412yes—
533C23×C3C22×D412yes—
534C23×C3C2×#4114yes—
535C23×C3C2×#4112yes—
536C23×C3H(5,𝔽2)12yes—
537C23×C3H(5,𝔽2)12yes—
538C23×C3H(5,𝔽2)12yes—
539C23×C3H(5,𝔽2)12yes—
540C23×C3C2511yescharacteristic
541C22×D3—28no—
542C22×D3—28no—
543C22×D3—28no—
544C22×D3—28no—
545C22×D3—28no—
546C22×D3—28no—
547C22×D3—22no—
548C22×D3—22no—
549C22×D3—22no—
550C22×D3—22no—
551C22×D3—22no—
552C22×D3—22no—
553C22×D3—22no—
554C22×D3—22no—
555C22×D3—22no—
556C22×D3—22no—
557C22×D3—22no—
558C22×D3—22no—
559C22×D3—22no—
560C22×D3—22no—
561C22×D3—22no—
562C22×D3—22no—
563C22×D3—22no—
564C22×D3—22no—
565C22×D3—22no—
566C22×D3—416no—
567C22×D3—416no—
568C22×D3—416no—
569C22×D3—416no—
570C22×D3—416no—
571C22×D3—416no—
572C22×D3—4128no—
573C22×D3—416no—
574C22×D3—44no—
575C22×D3—44no—
576C22×D3—44no—
577C22×D3—44no—
578C22×D3—44no—
579C22×D3—44no—
580C22×D3—44no—
581C22×D3—44no—
582C22×D3—44no—
583C22×D3—44no—
584C22×D3—44no—
585C22×D3—44no—
586C22×D3—44no—
587C22×D3—44no—
588C22×D3—44no—
589C22×D3C22×D414yes—
590C22×D3C22×D414yes—
591C3×D4—416no—
592C2×C3×C4—28no—
593C2×C3×C4—28no—
594C2×C3×C4—22no—
595C2×C3×C4—22no—
596C2×C3×C4—22no—
597C2×C3×C4—22no—
598C2×C3×C4—22no—
599C2×C3×C4—22no—
600C2×C3×C4—22no—
601C2×C3×C4—22no—
602C2×C3×C4—22no—
603C2×C3×C4—22no—
604C2×C3×C4—22no—
605C2×C3×C4—22no—
606C2×C3×C4—22no—
607C2×C3×C4—44no—
608C2×C3×C4—44no—
609C2×C3×C4—44no—
610C2×C3×C4C22×D414yes—
611C2×C3×C4C22×D414yes—
612#67—416no—
613#67—416no—
614#67—416no—
615#67—416no—
616C2×Dic3—28no—
617C2×Dic3—28no—
618C2×Dic3—22no—
619C2×Dic3—22no—
620C2×Dic3—22no—
621C2×Dic3—22no—
622C2×Dic3—22no—
623C2×Dic3—22no—
624C2×Dic3—22no—
625C2×Dic3—22no—
626C2×Dic3—22no—
627C2×Dic3—22no—
628C2×Dic3—22no—
629C2×Dic3—22no—
630C2×Dic3—22no—
631C2×Dic3—44no—
632C2×Dic3—44no—
633C2×Dic3—44no—
634C2×Dic3C22×D414yes—
635C2×Dic3C22×D414yes—
636D12—416no—
637D12—416no—
638Dic6—416no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—34no—
653C24—34no—
654C24—32no—
655C24—32no—
656C24—32no—
657C24—68no—
658C24—68no—
659C24—62no—
660C24—62no—
661C24—62no—
662C24—62no—
663C24—62no—
664C24—62no—
665C24—62no—
666C24—62no—
667C24—62no—
668C24—62no—
669C24—62no—
670C24—62no—
671C24—62no—
672C24—68no—
673C24—62no—
674C24—62no—
675C24—62no—
676C24—62no—
677C24—62no—
678C24—62no—
679C24—124no—
680C24—124no—
681C24—124no—
682C24—124no—
683C24—1216no—
684C24—1216no—
685C24—1216no—
686C24—1216no—
687C24—1216no—
688C24—1216no—
689C24—1216no—
690C24#23514yes—
691C24C23×D312yes—
692C24C23×D312yes—
693C24C23×D311yescharacteristic
694C2×Q8—68no—
695C2×Q8—68no—
696C2×Q8—124no—
697C2×Q8—1216no—
698C2×D4—28no—
699C2×D4—28no—
700C2×D4—44no—
701C2×D4—416no—
702C2×D4—68no—
703C2×D4—68no—
704C2×D4—68no—
705C2×D4—68no—
706C2×D4—68no—
707C2×D4—68no—
708C2×D4—68no—
709C2×D4—68no—
710C2×D4—124no—
711C2×D4—124no—
712C2×D4—124no—
713C2×D4—1216no—
714C2×D4—1216no—
715C2×D4—124no—
716C2×D4—124no—
717C2×D4—124no—
718C2×D4—124no—
719C2×D4—124no—
720C2×D4—124no—
721C2×D4—124no—
722C2×D4—1216no—
723C2×D4—1216no—
724C2×D4—1216no—
725C2×D4—1216no—
726C22×C4—22no—
727C22×C4—22no—
728C22×C4—22no—
729C22×C4—22no—
730C22×C4—22no—
731C22×C4—22no—
732C22×C4—22no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—34no—
740C22×C4—34no—
741C22×C4—32no—
742C22×C4—32no—
743C22×C4—32no—
744C22×C4—32no—
745C22×C4—32no—
746C22×C4—62no—
747C22×C4—62no—
748C22×C4—62no—
749C22×C4—62no—
750C22×C4—62no—
751C22×C4—62no—
752C22×C4—62no—
753C22×C4—62no—
754C22×C4—62no—
755C22×C4—62no—
756C22×C4—62no—
757C22×C4—62no—
758C22×C4—62no—
759C22×C4D3×D414yes—
760C22×C4D3×D414yes—
761C22×C4C23×D312yes—
762C22×C4C23×D312yes—
763C22×C4C23×D312yes—
764C22×C4C23×D312yes—
765C22×C4C23×D312yes—
766C4⋊C4—44no—
767C4⋊C4—124no—
768C22⋊C4—28no—
769C22⋊C4—28no—
770C22⋊C4—316no—
771C22⋊C4—316no—
772C22⋊C4—44no—
773C22⋊C4—44no—
774C22⋊C4—68no—
775C22⋊C4—68no—
776C22⋊C4—68no—
777C22⋊C4—68no—
778C22⋊C4—68no—
779C22⋊C4—68no—
780C22⋊C4—68no—
781C22⋊C4—68no—
782C22⋊C4—124no—
783C22⋊C4—124no—
784C22⋊C4—124no—
785C22⋊C4—124no—
786C42—28no—
787C42—68no—
788C22×C3—24no—
789C22×C3—24no—
790C22×C3—24no—
791C22×C3—416no—
792C22×C3—42no—
793C22×C3—42no—
794C22×C3—42no—
795C22×C3—42no—
796C22×C3—42no—
797C22×C3—42no—
798C22×C3—42no—
799C22×C3—42no—
800C22×C3—42no—
801C22×C3—42no—
802C22×C3—42no—
803C22×C3—88no—
804C22×C3#53514yes—
805C22×C3#53514yes—
806C22×C3#53814yes—
807C22×C3D4214yes—
808C22×C3#54614yes—
809C22×C3#54614yes—
810C22×C3H(3,𝔽4)14yes—
811C22×C3C23×D411yescharacteristic
812C22×C3C23×D411yescharacteristic
813C22×C3C22×#4111yescharacteristic
814C22×C3C2×H(5,𝔽2)11yescharacteristic
815C22×C3C2×H(5,𝔽2)11yescharacteristic
816C22×C3C2×H(5,𝔽2)11yescharacteristic
817C22×C3C2×H(5,𝔽2)11yescharacteristic
818C2×D3—24no—
819C2×D3—24no—
820C2×D3—24no—
821C2×D3—24no—
822C2×D3—24no—
823C2×D3—24no—
824C2×D3—464no—
825C2×D3—416no—
826C2×D3—416no—
827C2×D3—42no—
828C2×D3—42no—
829C2×D3—42no—
830C2×D3—42no—
831C2×D3—42no—
832C2×D3—42no—
833C2×D3—42no—
834C2×D3—42no—
835C2×D3—42no—
836C2×D3—42no—
837C2×D3—42no—
838C2×D3—42no—
839C2×D3—42no—
840C2×D3—42no—
841C2×D3—42no—
842C2×D3—88no—
843C3×C4—24no—
844C3×C4—24no—
845C3×C4—42no—
846C3×C4—42no—
847C3×C4—42no—
848Dic3—24no—
849Dic3—24no—
850Dic3—42no—
851Dic3—42no—
852Dic3—42no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—28no—
860C23—28no—
861C23—28no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23—22no—
867C23—22no—
868C23—22no—
869C23—34no—
870C23—34no—
871C23—44no—
872C23—44no—
873C23—44no—
874C23—44no—
875C23—44no—
876C23—44no—
877C23—44no—
878C23—44no—
879C23—44no—
880C23—44no—
881C23—44no—
882C23—62no—
883C23—62no—
884C23—62no—
885C23—62no—
886C23—62no—
887C23—62no—
888C23—62no—
889C23—62no—
890C23—62no—
891C23—62no—
892C23—62no—
893C23—62no—
894C23—68no—
895C23—68no—
896C23—68no—
897C23—68no—
898C23—68no—
899C23—68no—
900C23—62no—
901C23—62no—
902C23—62no—
903C23—62no—
904C23—62no—
905C23—62no—
906C23—62no—
907C23—1216no—
908C23—1216no—
909C23—1216no—
910C23—1216no—
911C23—1216no—
912C23—1216no—
913C23—1216no—
914C23—12128no—
915C23—124no—
916C23—124no—
917C23—124no—
918C23—124no—
919C23—124no—
920C23—124no—
921C23—124no—
922C23—124no—
923C23—124no—
924C23—124no—
925C23—124no—
926C23—124no—
927C23—124no—
928C23—124no—
929C23—124no—
930C23C2×#23514yes—
931C23C2×#23512yes—
932C23C2×D3×D412yes—
933C23C2×D3×D412yes—
934C23#100412yes—
935C23#100412yes—
936C23#100912yes—
937C23#100912yes—
938C23C24×D311yescharacteristic
939Q8—1216no—
940D4—416no—
941D4—1216no—
942D4—1216no—
943D4—1216no—
944D4—1216no—
945D4—1216no—
946D4—1216no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—28no—
952C2×C4—28no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—34no—
963C2×C4—34no—
964C2×C4—44no—
965C2×C4—44no—
966C2×C4—44no—
967C2×C4—62no—
968C2×C4—62no—
969C2×C4—62no—
970C2×C4—62no—
971C2×C4—68no—
972C2×C4—68no—
973C2×C4—62no—
974C2×C4—62no—
975C2×C4—62no—
976C2×C4—62no—
977C2×C4—62no—
978C2×C4—62no—
979C2×C4—62no—
980C2×C4—62no—
981C2×C4—62no—
982C2×C4—124no—
983C2×C4—124no—
984C2×C4—124no—
985C2×C4C2×D3×D414yes—
986C2×C4C2×D3×D414yes—
987C2×C3—44no—
988C2×C3—82no—
989C2×C3#267018yescomplemented
990C2×C3C2×#53511yescharacteristic
991C2×C3C2×#53511yescharacteristic
992C2×C3C2×#53811yescharacteristic
993C2×C3C2×D4211yescharacteristic
994C2×C3C2×#54611yescharacteristic
995C2×C3C2×#54611yescharacteristic
996C2×C3C2×H(3,𝔽4)11yescharacteristic
997D3—44no—
998D3—44no—
999D3—82no—
1000C22—24no—
1001C22—24no—
1002C22—24no—
1003C22—42no—
1004C22—416no—
1005C22—42no—
1006C22—42no—
1007C22—42no—
1008C22—42no—
1009C22—42no—
1010C22—42no—
1011C22—42no—
1012C22—42no—
1013C22—42no—
1014C22—42no—
1015C22—64no—
1016C22—64no—
1017C22—64no—
1018C22—64no—
1019C22—64no—
1020C22—64no—
1021C22—88no—
1022C22—1264no—
1023C22—122no—
1024C22—122no—
1025C22—122no—
1026C22—122no—
1027C22—122no—
1028C22—1216no—
1029C22—1216no—
1030C22—122no—
1031C22—122no—
1032C22—122no—
1033C22—122no—
1034C22—122no—
1035C22—122no—
1036C22—122no—
1037C22—122no—
1038C22—122no—
1039C22—122no—
1040C22—248no—
1041C22#549014yes—
1042C22#555014yes—
1043C22#556014yes—
1044C22#560714yes—
1045C22#560914yes—
1046C22#568314yes—
1047C22#571514yes—
1048C22C22×#23511yescharacteristic
1049C22C22×D3×D411yescharacteristic
1050C22C22×D3×D411yescharacteristic
1051C22C2×#100411yescharacteristic
1052C22C2×#100411yescharacteristic
1053C22C2×#100911yescharacteristic
1054C22C2×#100911yescharacteristic
1055C4—24no—
1056C4—24no—
1057C4—42no—
1058C4—42no—
1059C4—42no—
1060C4—64no—
1061C4—64no—
1062C4—122no—
1063C4—122no—
1064C4—122no—
1065C3C2×#267011yescharacteristic, complemented, Sylow
1066C2—44no—
1067C2—82no—
1068C2—124no—
1069C2—124no—
1070C2—242no—
1071C2#7646118yesdirect product factor
1072C2C2×#549011yescharacteristic
1073C2C2×#556011yescharacteristic
1074C2C2×#555011yescharacteristic
1075C2C2×#560711yescharacteristic
1076C2C2×#560911yescharacteristic
1077C2C2×#568311yescharacteristic
1078C2C2×#571511yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC2×C3×#390C2
socleC24×C3C24
hypercenterC2×#390D3
hypocenterC3C2×#2670
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
1. C22×#937C2semidirect
2. C22×#882C2semidirect
3. C22×#885C2semidirect
4. C22×#875C2semidirect
5. C2×C3×#390C2semidirect
6. C2×#5223C2semidirect
7. C2×#4991C2semidirect
8. C2×#4990C2semidirect
9. C2×#4959C2semidirect
10. C2×#4960C2semidirect
11. C2×#4960C2semidirect
12. C2×#4955C2semidirect
13. C2×#4947C2semidirect
14. C2×#4957C2semidirect
15. C2×#4940C2semidirect
16. #76461C2direct (N × H)
23. C23×#67C22semidirect
26. C23×Dic6C22semidirect
27. C22×C3×C4⋊C4C22semidirect
30. C22×C3×C22⋊C4C22semidirect
31. C22×C3×C22⋊C4C22semidirect
32. C22×C3×C42C22semidirect
35. C22×#217C22semidirect
37. C2×#937C22semidirect
46. C22×(C2×D3)⋊C4C22semidirect
47. C22×(C2×D3)⋊C4C22semidirect
48. C22×(C2×D3)⋊C4C22semidirect
49. C22×Dic3⋊C4C22semidirect
50. C22×C4×Dic3C22semidirect
52. C2×#885C22semidirect
54. C2×#882C22semidirect
56. C2×#875C22semidirect
57. C3×#390C22semidirect
58. #5223C22semidirect
59. C2×C3⋊#95C22semidirect
60. C2×C3⋊#95C22semidirect
61. C2×C3⋊#95C22semidirect
62. C2×C3⋊#95C22semidirect
63. #4991C22semidirect
64. #4990C22semidirect
65. #4960C22semidirect
66. #4960C22semidirect
67. #4959C22semidirect
68. #4957C22semidirect
69. #4955C22semidirect
70. #4947C22semidirect
71. #4940C22semidirect
84. C2×#390D3semidirect
125. C22×#67C23semidirect
142. C22×Dic6C23semidirect
144. C2×C3×C4⋊C4C23semidirect
151. C2×C3×C22⋊C4C23semidirect
152. C2×C3×C22⋊C4C23semidirect
154. C2×C3×C42C23semidirect
160. C2×#217C23semidirect
171. C2×(C2×D3)⋊C4D4semidirect
172. C2×(C2×D3)⋊C4D4semidirect
181. C2×(C2×D3)⋊C4C23semidirect
182. C2×(C2×D3)⋊C4C23semidirect
183. C2×(C2×D3)⋊C4C23semidirect
185. C2×Dic3⋊C4C23semidirect
187. C2×C4×Dic3C23semidirect
191. C3⋊#95C23semidirect
192. C3⋊#95C23semidirect
193. C3⋊#95C23semidirect
194. C3⋊#95C23semidirect
213. C22×C4⋊C4C2×D3semidirect
230. C22×C22⋊C4C2×D3semidirect
231. C22×C22⋊C4C2×D3semidirect
233. C22×C42C2×D3semidirect
241. #390C2×D3semidirect
394. (C2×D3)⋊C4C2×D4semidirect
395. (C2×D3)⋊C4C2×D4semidirect
460. C2×C4⋊C4C22×D3semidirect
495. C2×C22⋊C4C22×D3semidirect
496. C2×C22⋊C4C22×D3semidirect
500. C2×C42C22×D3semidirect
989. C2×C3#2670semidirect
1065. C3C2×#2670semidirect
1071. C2#76461direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#9372
C22×#8822
C22×#8852
C22×#8752
C2×C3×#3902
C2×#52232
C2×#49912
C2×#49902
C2×#49592
C2×#49602
C2×#49552
C2×#49472
C2×#49572
C2×#49402
#764612
C2×#26703