Finite Group Databasebeta

← C2×#76766 #11429763

Subgroups — C2×#76766 #11429763

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×#937C211yesmaximal, characteristic, complemented
3C22×#936C211yesmaximal, characteristic, complemented
4C22×#885C211yesmaximal, characteristic, complemented
5C2×C3×#392C211yesmaximal, characteristic, complemented
6C2×#5223C211yesmaximal, characteristic, complemented
7C2×#5223C211yesmaximal, characteristic, complemented
8C2×#5222C211yesmaximal, characteristic, complemented
9C2×#4959C211yesmaximal, characteristic, complemented
10C2×#4955C211yesmaximal, characteristic, complemented
11C2×#4957C211yesmaximal, characteristic, complemented
12C2×#4957C211yesmaximal, characteristic, complemented
13C2×#4945C211yesmaximal, characteristic, complemented
14#76766C2116yesmaximal, direct product factor
15C2×#4673C211yesmaximal, characteristic, complemented
16C2×#4669C211yesmaximal, characteristic, complemented
17C2×#2670—31nomaximal, Sylow
18C25×D3C2211yescharacteristic
19C23×C3×D4C2211yescharacteristic
20C23×C3×D4C2211yescharacteristic
21C23×C3×D4C2211yescharacteristic, complemented
22C23×#67C2211yescharacteristic
23C23×#67C2211yescharacteristic
24C23×#67C2211yescharacteristic
25C23×#67C2211yescharacteristic
26C23×Dic6C2211yescharacteristic, complemented
27C22×C3×C22⋊C4C2211yescharacteristic
28C22×C3×C22⋊C4C2211yescharacteristic, complemented
29C22×C3×C22⋊C4C2211yescharacteristic, complemented
30C22×#217C2211yescharacteristic
31C22×#217C2211yescharacteristic
32C22×#217C2211yescharacteristic
33C22×#217C2211yescharacteristic, complemented
34C22×#217C2211yescharacteristic, complemented
35C22×#217C2211yescharacteristic, complemented
36C22×#217C2211yescharacteristic, complemented
37C2×#937—28no—
38C2×#937—28no—
39C2×#937C2218yescomplemented
40C2×#937C2218yescomplemented
41C2×#936—28no—
42C2×#936C2218yescomplemented
43C22×(C2×D3)⋊C4C2211yescharacteristic
44C22×(C2×D3)⋊C4C2211yescharacteristic
45C22×(C2×D3)⋊C4C2211yescharacteristic
46C22×(C2×D3)⋊C4C2211yescharacteristic
47C22×(C2×D3)⋊C4C2211yescharacteristic
48C22×(C2×D3)⋊C4C2211yescharacteristic
49C22×(C2×D3)⋊C4C2211yescharacteristic
50C22×(C2×D3)⋊C4C2211yescharacteristic
51C22×Dic3⋊C4C2211yescharacteristic, complemented
52C22×Dic3⋊C4C2211yescharacteristic, complemented
53C22×C4×Dic3C2211yescharacteristic, complemented
54C22×C4×Dic3C2211yescharacteristic, complemented
55C2×#885—28no—
56C2×#885C2218yescomplemented
57C3×#392C2218yescomplemented
58C2×C3×#95C2211yescharacteristic, complemented
59#5223C2218yescomplemented
60#5223C2218yescomplemented
61#5222C2218yescomplemented
62C2×C3⋊#95C2211yescharacteristic, complemented
63C2×C3⋊#95C2211yescharacteristic, complemented
64C2×C3⋊#95C2211yescharacteristic, complemented
65#4959C2218yescomplemented
66#4957C2218yescomplemented
67#4957C2218yescomplemented
68#4955C2218yescomplemented
69#4945C2218yescomplemented
70#4673C2218yescomplemented
71#4669C2218yescomplemented
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×#392D311yescharacteristic, complemented
83C2×#390—31no—
84C2×#390—31no—
85C2×#388—31no—
86C2×#388—31no—
87C2×#379—31no—
88C25×C3C2311yescharacteristic
89C25×C3C2311yescharacteristic
90C25×C3C2311yescharacteristic
91C24×D3—24no—
92C24×D3—24no—
93C24×D3—24no—
94C24×D3—42no—
95C24×D3—42no—
96C24×D3—42no—
97C24×D3—42no—
98C24×D3C2311yescharacteristic
99C24×D3C2311yescharacteristic
100C24×D3C2314yes—
101C22×C3×D4—24no—
102C22×C3×D4—24no—
103C22×C3×D4—24no—
104C22×C3×D4—42no—
105C22×C3×D4—42no—
106C22×C3×D4—42no—
107C22×C3×D4—42no—
108C22×C3×D4—42no—
109C22×C3×D4—42no—
110C22×C3×D4C2314yes—
111C22×C3×D4C2314yes—
112C22×C3×D4C2314yescomplemented
113C23×C3×C4C2311yescharacteristic
114C23×C3×C4C2311yescharacteristic
115C23×C3×C4C2311yescharacteristic
116C23×C3×C4C2311yescharacteristic
117C22×#67—24no—
118C22×#67—24no—
119C22×#67—24no—
120C22×#67—24no—
121C22×#67—24no—
122C22×#67—24no—
123C22×#67—24no—
124C22×#67—42no—
125C22×#67—42no—
126C22×#67—42no—
127C22×#67—42no—
128C22×#67—42no—
129C22×#67C2314yes—
130C22×#67C2314yes—
131C22×#67C2314yes—
132C22×#67C2314yes—
133C23×Dic3C2311yescharacteristic
134C23×Dic3C2311yescharacteristic
135C23×Dic3C2311yescharacteristic
136C23×Dic3C2311yescharacteristic
137C23×Dic3C2311yescharacteristic
138C23×Dic3C2311yescharacteristic
139C22×Dic6—24no—
140C22×Dic6—24no—
141C22×Dic6—42no—
142C22×Dic6C2314yescomplemented
143C2×C3×C22⋊C4—24no—
144C2×C3×C22⋊C4—42no—
145C2×C3×C22⋊C4—42no—
146C2×C3×C22⋊C4C2314yes—
147C2×C3×C22⋊C4C2314yescomplemented
148C2×C3×C22⋊C4C2314yescomplemented
149C2×#217—24no—
150C2×#217—24no—
151C2×#217—24no—
152C2×#217—24no—
153C2×#217—24no—
154C2×#217—42no—
155C2×#217D418yescomplemented
156C2×#217C2314yes—
157C2×#217C2314yes—
158C2×#217C2314yes—
159C2×#217C2314yescomplemented
160C2×#217C2314yescomplemented
161C2×#217C2314yescomplemented
162C2×#217C2314yescomplemented
163#937—232no—
164#937—232no—
165#936—232no—
166C2×(C2×D3)⋊C4—24no—
167C2×(C2×D3)⋊C4—24no—
168C2×(C2×D3)⋊C4—24no—
169C2×(C2×D3)⋊C4—24no—
170C2×(C2×D3)⋊C4—42no—
171C2×(C2×D3)⋊C4—42no—
172C2×(C2×D3)⋊C4—42no—
173C2×(C2×D3)⋊C4D418yescomplemented
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)⋊C4C2314yes—
182C2×Dic3⋊C4—42no—
183C2×Dic3⋊C4—42no—
184C2×Dic3⋊C4C2314yescomplemented
185C2×Dic3⋊C4C2314yescomplemented
186C2×C4×Dic3—24no—
187C2×C4×Dic3—24no—
188C2×C4×Dic3C2314yescomplemented
189C2×C4×Dic3C2314yescomplemented
190#885—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×D4C2×D311yescharacteristic
202C23×D4C2×D311yescharacteristic
203C23×D4C2×D311yescharacteristic, complemented
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⋊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—
226C22×C22⋊C4—31no—
227C22×C22⋊C4—31no—
228C22×C22⋊C4—31no—
229C22×C22⋊C4C2×D311yescharacteristic
230C22×C22⋊C4C2×D311yescharacteristic, complemented
231C22×C22⋊C4C2×D311yescharacteristic, complemented
232C22×C42—31no—
233C22×C42—31no—
234#394—38no—
235#394—38no—
236#393—38no—
237#392—38no—
238#392—38no—
239#392C2×D318yescomplemented
240#390—38no—
241#390—38no—
242#388—38no—
243#388—38no—
244#379—38no—
245C2×#95—31no—
246C2×#95—31no—
247C2×#95—31no—
248C2×#95C2×D311yescharacteristic, complemented
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—22no—
263C24×C3—22no—
264C24×C3—22no—
265C24×C3—22no—
266C24×C3—22no—
267C24×C3—22no—
268C24×C3—22no—
269C24×C3C2×D414yes—
270C24×C3C2412yes—
271C24×C3C2412yes—
272C24×C3C2412yes—
273C24×C3C2411yescharacteristic
274C23×D3—22no—
275C23×D3—22no—
276C23×D3—22no—
277C23×D3—22no—
278C23×D3—22no—
279C23×D3—22no—
280C23×D3—22no—
281C23×D3—22no—
282C23×D3—22no—
283C23×D3—22no—
284C23×D3—22no—
285C23×D3—22no—
286C23×D3—28no—
287C23×D3—28no—
288C23×D3—28no—
289C23×D3—44no—
290C23×D3—44no—
291C23×D3—44no—
292C23×D3—44no—
293C23×D3—416no—
294C23×D3—416no—
295C23×D3—416no—
296C23×D3—416no—
297C23×D3—416no—
298C23×D3—416no—
299C23×D3—416no—
300C23×D3C2×D414yes—
301C23×D3#4114yes—
302C23×D3C2412yes—
303C23×D3C2412yes—
304C2×C3×D4—28no—
305C2×C3×D4—28no—
306C2×C3×D4—28no—
307C2×C3×D4—44no—
308C2×C3×D4—44no—
309C2×C3×D4—44no—
310C2×C3×D4—44no—
311C2×C3×D4—44no—
312C2×C3×D4—44no—
313C2×C3×D4—416no—
314C2×C3×D4—416no—
315C2×C3×D4—416no—
316C22×C3×C4—22no—
317C22×C3×C4—22no—
318C22×C3×C4—22no—
319C22×C3×C4—22no—
320C22×C3×C4—22no—
321C22×C3×C4—22no—
322C22×C3×C4—22no—
323C22×C3×C4—22no—
324C22×C3×C4—22no—
325C22×C3×C4—22no—
326C22×C3×C4—22no—
327C22×C3×C4C2×D414yes—
328C22×C3×C4C2412yes—
329C22×C3×C4C2412yes—
330C22×C3×C4C2412yes—
331C22×C3×C4C2412yes—
332C2×#67—28no—
333C2×#67—28no—
334C2×#67—28no—
335C2×#67—28no—
336C2×#67—28no—
337C2×#67—28no—
338C2×#67—28no—
339C2×#67—44no—
340C2×#67—44no—
341C2×#67—44no—
342C2×#67—44no—
343C2×#67—44no—
344C2×#67—416no—
345C2×#67—416no—
346C2×#67—416no—
347C2×#67—416no—
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×Dic3—22no—
358C22×Dic3—22no—
359C22×Dic3—22no—
360C22×Dic3—22no—
361C22×Dic3—22no—
362C22×Dic3—22no—
363C22×Dic3C2×D414yes—
364C22×Dic3C2×D414yes—
365C22×Dic3C2×D414yes—
366C22×Dic3C2412yes—
367C22×Dic3C2412yes—
368C22×Dic3C2412yes—
369C22×Dic3C2412yes—
370C22×Dic3C2412yes—
371C22×Dic3C2412yes—
372C2×Dic6—28no—
373C2×Dic6—28no—
374C2×Dic6—44no—
375C2×Dic6—416no—
376C3×C22⋊C4—28no—
377C3×C22⋊C4—44no—
378C3×C22⋊C4—44no—
379#217—28no—
380#217—28no—
381#217—28no—
382#217—28no—
383#217—28no—
384#217—44no—
385#217C2×D4116yescomplemented
386(C2×D3)⋊C4—28no—
387(C2×D3)⋊C4—28no—
388(C2×D3)⋊C4—28no—
389(C2×D3)⋊C4—28no—
390(C2×D3)⋊C4—44no—
391(C2×D3)⋊C4—44no—
392(C2×D3)⋊C4—44no—
393(C2×D3)⋊C4C2×D4116yescomplemented
394Dic3⋊C4—44no—
395Dic3⋊C4—44no—
396C4×Dic3—28no—
397C4×Dic3—28no—
398C25—31no—
399C25—31no—
400C25—34no—
401C25—64no—
402C25—64no—
403C25—64no—
404C25—122no—
405C25—122no—
406C25—122no—
407C25—122no—
408C25C22×D311yescharacteristic
409C25C22×D311yescharacteristic
410C25C22×D311yescharacteristic
411C22×Q8—34no—
412C22×Q8—64no—
413C22×Q8—64no—
414C22×Q8—122no—
415C22×D4—24no—
416C22×D4—24no—
417C22×D4—24no—
418C22×D4—34no—
419C22×D4—34no—
420C22×D4—34no—
421C22×D4—34no—
422C22×D4—42no—
423C22×D4—42no—
424C22×D4—42no—
425C22×D4—42no—
426C22×D4—42no—
427C22×D4—42no—
428C22×D4—64no—
429C22×D4—64no—
430C22×D4—64no—
431C22×D4—64no—
432C22×D4—64no—
433C22×D4—64no—
434C22×D4—64no—
435C22×D4—122no—
436C22×D4—122no—
437C22×D4—122no—
438C22×D4—122no—
439C22×D4—122no—
440C22×D4C22×D314yes—
441C22×D4C22×D314yes—
442C22×D4C22×D314yescomplemented
443C23×C4—31no—
444C23×C4—31no—
445C23×C4—31no—
446C23×C4—31no—
447C23×C4—31no—
448C23×C4—31no—
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—34no—
459C2×C4⋊C4—122no—
460C2×C4⋊C4—122no—
461C2×C22⋊C4—24no—
462C2×C22⋊C4—38no—
463C2×C22⋊C4—34no—
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—64no—
490C2×C22⋊C4—122no—
491C2×C22⋊C4—122no—
492C2×C22⋊C4—122no—
493C2×C22⋊C4—122no—
494C2×C22⋊C4C22×D314yes—
495C2×C22⋊C4C22×D314yescomplemented
496C2×C22⋊C4C22×D314yescomplemented
497C2×C42—34no—
498C2×C42—34no—
499C2×C42—64no—
500C2×C42—64no—
501#95—34no—
502#95—34no—
503#95—34no—
504#95C22×D314yescomplemented
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—22no—
522C23×C3—22no—
523C23×C3—22no—
524C23×C3—22no—
525C23×C3—22no—
526C23×C3—22no—
527C23×C3—22no—
528C23×C3—44no—
529C23×C3—44no—
530C23×C3—44no—
531C23×C3—44no—
532C23×C3—44no—
533C23×C3—44no—
534C23×C3—44no—
535C23×C3—44no—
536C23×C3—44no—
537C23×C3—44no—
538C23×C3—44no—
539C23×C3—44no—
540C23×C3—44no—
541C23×C3—44no—
542C23×C3—44no—
543C23×C3—44no—
544C23×C3—44no—
545C23×C3—44no—
546C23×C3C22×D414yes—
547C23×C3C22×D412yes—
548C23×C3C22×D412yes—
549C23×C3C2×#4112yes—
550C23×C3H(5,𝔽2)12yes—
551C23×C3H(5,𝔽2)12yes—
552C23×C3H(5,𝔽2)12yes—
553C23×C3H(5,𝔽2)12yes—
554C23×C3C2511yescharacteristic
555C22×D3—28no—
556C22×D3—28no—
557C22×D3—28no—
558C22×D3—28no—
559C22×D3—28no—
560C22×D3—28no—
561C22×D3—22no—
562C22×D3—22no—
563C22×D3—22no—
564C22×D3—22no—
565C22×D3—22no—
566C22×D3—22no—
567C22×D3—22no—
568C22×D3—22no—
569C22×D3—22no—
570C22×D3—22no—
571C22×D3—22no—
572C22×D3—22no—
573C22×D3—416no—
574C22×D3—416no—
575C22×D3—416no—
576C22×D3—416no—
577C22×D3—416no—
578C22×D3—416no—
579C22×D3—4128no—
580C22×D3—416no—
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×D3C2×#4114yes—
591C3×D4—416no—
592C3×D4—416no—
593C3×D4—416no—
594C2×C3×C4—28no—
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—44no—
607C2×C3×C4—44no—
608C2×C3×C4—44no—
609C2×C3×C4C22×D414yes—
610#67—416no—
611#67—416no—
612#67—416no—
613#67—416no—
614C2×Dic3—28no—
615C2×Dic3—28no—
616C2×Dic3—28no—
617C2×Dic3—22no—
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—22no—
632C2×Dic3—44no—
633C2×Dic3—44no—
634C2×Dic3—44no—
635C2×Dic3C22×D414yes—
636C2×Dic3C22×D414yes—
637C2×Dic3C22×D414yes—
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—22no—
653C24—22no—
654C24—22no—
655C24—22no—
656C24—22no—
657C24—22no—
658C24—22no—
659C24—34no—
660C24—34no—
661C24—32no—
662C24—32no—
663C24—68no—
664C24—68no—
665C24—62no—
666C24—62no—
667C24—62no—
668C24—62no—
669C24—62no—
670C24—62no—
671C24—62no—
672C24—62no—
673C24—62no—
674C24—62no—
675C24—62no—
676C24—62no—
677C24—68no—
678C24—124no—
679C24—124no—
680C24—124no—
681C24—124no—
682C24—1216no—
683C24—1216no—
684C24—1216no—
685C24—1216no—
686C24—1216no—
687C24—1216no—
688C24—1216no—
689C24D3×D414yes—
690C24C23×D312yes—
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—28no—
701C2×D4—44no—
702C2×D4—44no—
703C2×D4—44no—
704C2×D4—44no—
705C2×D4—44no—
706C2×D4—44no—
707C2×D4—416no—
708C2×D4—416no—
709C2×D4—416no—
710C2×D4—68no—
711C2×D4—68no—
712C2×D4—68no—
713C2×D4—68no—
714C2×D4—68no—
715C2×D4—68no—
716C2×D4—68no—
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—34no—
738C22×C4—34no—
739C22×C4—34no—
740C22×C4—32no—
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×C4—62no—
760C22×C4—62no—
761C22×C4D3×D414yes—
762C22×C4C23×D312yes—
763C22×C4C23×D312yes—
764C22×C4C23×D312yes—
765C22×C4C23×D312yes—
766C4⋊C4—124no—
767C4⋊C4—124no—
768C22⋊C4—28no—
769C22⋊C4—316no—
770C22⋊C4—316no—
771C22⋊C4—44no—
772C22⋊C4—44no—
773C22⋊C4—68no—
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—68no—
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—42no—
804C22×C3—42no—
805C22×C3—42no—
806C22×C3—42no—
807C22×C3—42no—
808C22×C3—42no—
809C22×C3—42no—
810C22×C3—88no—
811C22×C3—88no—
812C22×C3#53514yes—
813C22×C3#53514yes—
814C22×C3#53814yes—
815C22×C3D4214yes—
816C22×C3#54614yes—
817C22×C3#54614yes—
818C22×C3H(3,𝔽4)14yes—
819C22×C3C23×D411yescharacteristic
820C22×C3C23×D411yescharacteristic
821C22×C3C22×#4111yescharacteristic
822C22×C3C2×H(5,𝔽2)11yescharacteristic
823C22×C3C2×H(5,𝔽2)11yescharacteristic
824C22×C3C2×H(5,𝔽2)11yescharacteristic
825C22×C3C2×H(5,𝔽2)11yescharacteristic
826C2×D3—24no—
827C2×D3—24no—
828C2×D3—24no—
829C2×D3—24no—
830C2×D3—24no—
831C2×D3—24no—
832C2×D3—464no—
833C2×D3—416no—
834C2×D3—416no—
835C2×D3—42no—
836C2×D3—42no—
837C2×D3—42no—
838C2×D3—42no—
839C2×D3—42no—
840C2×D3—42no—
841C2×D3—42no—
842C2×D3—42no—
843C3×C4—24no—
844C3×C4—42no—
845C3×C4—42no—
846C3×C4—42no—
847Dic3—24no—
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—22no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—22no—
874C23—22no—
875C23—22no—
876C23—34no—
877C23—34no—
878C23—44no—
879C23—44no—
880C23—44no—
881C23—44no—
882C23—44no—
883C23—44no—
884C23—44no—
885C23—44no—
886C23—44no—
887C23—44no—
888C23—44no—
889C23—44no—
890C23—44no—
891C23—44no—
892C23—44no—
893C23—44no—
894C23—44no—
895C23—44no—
896C23—62no—
897C23—62no—
898C23—62no—
899C23—62no—
900C23—62no—
901C23—62no—
902C23—62no—
903C23—62no—
904C23—62no—
905C23—62no—
906C23—62no—
907C23—62no—
908C23—68no—
909C23—68no—
910C23—68no—
911C23—68no—
912C23—68no—
913C23—68no—
914C23—1216no—
915C23—1216no—
916C23—1216no—
917C23—1216no—
918C23—1216no—
919C23—1216no—
920C23—1216no—
921C23—12128no—
922C23—124no—
923C23—124no—
924C23—124no—
925C23—124no—
926C23—124no—
927C23—124no—
928C23—124no—
929C23—124no—
930C23C2×D3×D414yes—
931C23C2×D3×D412yes—
932C23C2×D3×D412yes—
933C23#100412yes—
934C23#100412yes—
935C23#100412yes—
936C23#100412yes—
937C23D3×#4112yes—
938C23C24×D311yescharacteristic
939Q8—1216no—
940D4—416no—
941D4—416no—
942D4—416no—
943D4—1216no—
944D4—1216no—
945D4—1216no—
946D4—1216no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—28no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—34no—
960C2×C4—34no—
961C2×C4—34no—
962C2×C4—44no—
963C2×C4—44no—
964C2×C4—44no—
965C2×C4—62no—
966C2×C4—62no—
967C2×C4—62no—
968C2×C4—62no—
969C2×C4—62no—
970C2×C4—62no—
971C2×C4—68no—
972C2×C4—68no—
973C2×C4—68no—
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—62no—
983C2×C4—124no—
984C2×C4—124no—
985C2×C4—124no—
986C2×C4C2×D3×D414yes—
987C2×C3—44no—
988C2×C3—82no—
989C2×C3—82no—
990C2×C3#267018yescomplemented
991C2×C3C2×#53511yescharacteristic
992C2×C3C2×#53511yescharacteristic
993C2×C3C2×#53811yescharacteristic
994C2×C3C2×D4211yescharacteristic
995C2×C3C2×#54611yescharacteristic
996C2×C3C2×#54611yescharacteristic
997C2×C3C2×H(3,𝔽4)11yescharacteristic
998D3—44no—
999D3—44no—
1000C22—24no—
1001C22—24no—
1002C22—24no—
1003C22—42no—
1004C22—42no—
1005C22—42no—
1006C22—42no—
1007C22—416no—
1008C22—42no—
1009C22—42no—
1010C22—42no—
1011C22—42no—
1012C22—42no—
1013C22—42no—
1014C22—42no—
1015C22—42no—
1016C22—42no—
1017C22—42no—
1018C22—42no—
1019C22—42no—
1020C22—42no—
1021C22—42no—
1022C22—64no—
1023C22—64no—
1024C22—64no—
1025C22—64no—
1026C22—64no—
1027C22—64no—
1028C22—88no—
1029C22—88no—
1030C22—1264no—
1031C22—122no—
1032C22—122no—
1033C22—122no—
1034C22—122no—
1035C22—122no—
1036C22—122no—
1037C22—122no—
1038C22—122no—
1039C22—1216no—
1040C22—1216no—
1041C22#559014yes—
1042C22#559214yes—
1043C22#559414yes—
1044C22#561014yes—
1045C22#561214yes—
1046C22#561314yes—
1047C22#571514yes—
1048C22C22×D3×D411yescharacteristic
1049C22C22×D3×D411yescharacteristic
1050C22C2×#100411yescharacteristic
1051C22C2×#100411yescharacteristic
1052C22C2×#100411yescharacteristic
1053C22C2×#100411yescharacteristic
1054C22C2×D3×#4111yescharacteristic
1055C4—24no—
1056C4—42no—
1057C4—42no—
1058C4—42no—
1059C4—64no—
1060C4—64no—
1061C4—64no—
1062C4—122no—
1063C4—122no—
1064C4—122no—
1065C3C2×#267011yescharacteristic, complemented, Sylow
1066C2—44no—
1067C2—82no—
1068C2—82no—
1069C2—124no—
1070C2—124no—
1071C2#7676618yesdirect product factor
1072C2C2×#559211yescharacteristic
1073C2C2×#559411yescharacteristic
1074C2C2×#559011yescharacteristic
1075C2C2×#561311yescharacteristic
1076C2C2×#561011yescharacteristic
1077C2C2×#561211yescharacteristic
1078C2C2×#571511yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC2×C3×#392C2
socleC24×C3C24
hypercenterC2×#392D3
hypocenterC3C2×#2670
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. C22×#937C2semidirect
2. C22×#937C2semidirect
3. C22×#936C2semidirect
4. C22×#885C2semidirect
5. C2×C3×#392C2semidirect
6. C2×#5223C2semidirect
7. C2×#5223C2semidirect
8. C2×#5222C2semidirect
9. C2×#4959C2semidirect
10. C2×#4955C2semidirect
11. C2×#4957C2semidirect
12. C2×#4957C2semidirect
13. C2×#4945C2semidirect
14. #76766C2direct (N × H)
15. C2×#4673C2semidirect
16. C2×#4669C2semidirect
21. C23×C3×D4C22semidirect
26. C23×Dic6C22semidirect
28. C22×C3×C22⋊C4C22semidirect
29. C22×C3×C22⋊C4C22semidirect
33. C22×#217C22semidirect
34. C22×#217C22semidirect
35. C22×#217C22semidirect
36. C22×#217C22semidirect
39. C2×#937C22semidirect
40. C2×#937C22semidirect
42. C2×#936C22semidirect
51. C22×Dic3⋊C4C22semidirect
52. C22×Dic3⋊C4C22semidirect
53. C22×C4×Dic3C22semidirect
54. C22×C4×Dic3C22semidirect
56. C2×#885C22semidirect
57. C3×#392C22semidirect
58. C2×C3×#95C22semidirect
59. #5223C22semidirect
60. #5223C22semidirect
61. #5222C22semidirect
62. C2×C3⋊#95C22semidirect
63. C2×C3⋊#95C22semidirect
64. C2×C3⋊#95C22semidirect
65. #4959C22semidirect
66. #4957C22semidirect
67. #4957C22semidirect
68. #4955C22semidirect
69. #4945C22semidirect
70. #4673C22semidirect
71. #4669C22semidirect
82. C2×#392D3semidirect
112. C22×C3×D4C23semidirect
142. C22×Dic6C23semidirect
147. C2×C3×C22⋊C4C23semidirect
148. C2×C3×C22⋊C4C23semidirect
155. C2×#217D4semidirect
159. C2×#217C23semidirect
160. C2×#217C23semidirect
161. C2×#217C23semidirect
162. C2×#217C23semidirect
173. C2×(C2×D3)⋊C4D4semidirect
184. C2×Dic3⋊C4C23semidirect
185. C2×Dic3⋊C4C23semidirect
188. C2×C4×Dic3C23semidirect
189. C2×C4×Dic3C23semidirect
191. C3×#95C23semidirect
192. C3⋊#95C23semidirect
193. C3⋊#95C23semidirect
194. C3⋊#95C23semidirect
203. C23×D4C2×D3semidirect
230. C22×C22⋊C4C2×D3semidirect
231. C22×C22⋊C4C2×D3semidirect
239. #392C2×D3semidirect
248. C2×#95C2×D3semidirect
385. #217C2×D4semidirect
393. (C2×D3)⋊C4C2×D4semidirect
442. C22×D4C22×D3semidirect
495. C2×C22⋊C4C22×D3semidirect
496. C2×C22⋊C4C22×D3semidirect
504. #95C22×D3semidirect
990. C2×C3#2670semidirect
1065. C3C2×#2670semidirect
1071. C2#76766direct (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×#9362
C22×#8852
C2×C3×#3922
C2×#52232
C2×#52222
C2×#49592
C2×#49552
C2×#49572
C2×#49452
#767662
C2×#46732
C2×#46692
C2×#26703