Finite Group Databasebeta

← C2×#75913 #11429762

Subgroups — C2×#75913 #11429762

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×#882C211yesmaximal, characteristic, complemented
2C22×#882C211yesmaximal, characteristic, complemented
3C22×#885C211yesmaximal, characteristic, complemented
4C22×#875C211yesmaximal, characteristic, complemented
5C2×C3×#388C211yesmaximal, characteristic, complemented
6C2×#4991C211yesmaximal, characteristic, complemented
7C2×#4988C211yesmaximal, characteristic, complemented
8C2×#4960C211yesmaximal, characteristic, complemented
9C2×#4955C211yesmaximal, characteristic, complemented
10C2×#4961C211yesmaximal, characteristic, complemented
11C2×#4939C211yesmaximal, characteristic, complemented
12#75913C2116yesmaximal, direct product factor
13C2×#4673C211yesmaximal, characteristic, complemented
14C2×#4671C211yesmaximal, characteristic, complemented
15C2×#4671C211yesmaximal, characteristic, complemented
16C2×#4670C211yesmaximal, characteristic, complemented
17C2×#2670—31nomaximal, Sylow
18C25×D3C2211yescharacteristic
19C23×#67C2211yescharacteristic
20C23×#67C2211yescharacteristic
21C23×D12C2211yescharacteristic
22C23×D12C2211yescharacteristic
23C23×D12C2211yescharacteristic
24C23×D12C2211yescharacteristic
25C23×D12C2211yescharacteristic, complemented
26C23×Dic6C2211yescharacteristic, complemented
27C22×C3×C4⋊C4C2211yescharacteristic, complemented
28C22×C3×C22⋊C4C2211yescharacteristic
29C22×C3×C22⋊C4C2211yescharacteristic
30C22×C3×C22⋊C4C2211yescharacteristic
31C22×C3×C42C2211yescharacteristic, complemented
32C22×#217C2211yescharacteristic
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, complemented
42C22×(C2×D3)⋊C4C2211yescharacteristic, complemented
43C22×(C2×D3)⋊C4C2211yescharacteristic, complemented
44C22×(C2×D3)⋊C4C2211yescharacteristic, complemented
45C22×(C2×D3)⋊C4C2211yescharacteristic, complemented
46C22×(C2×D3)⋊C4C2211yescharacteristic, complemented
47C22×C4⋊Dic3C2211yescharacteristic, complemented
48C22×C4×Dic3C2211yescharacteristic, complemented
49C2×#885—28no—
50C2×#885C2218yescomplemented
51C2×#882—28no—
52C2×#882—28no—
53C2×#882C2218yescomplemented
54C2×#882C2218yescomplemented
55C2×#875—28no—
56C2×#875C2218yescomplemented
57C3×#388C2218yescomplemented
58C2×C3×#95C2211yescharacteristic, complemented
59C2×C3×#95C2211yescharacteristic, complemented
60C2×C3⋊#95C2211yescharacteristic, complemented
61C2×C3⋊#95C2211yescharacteristic, complemented
62#4991C2218yescomplemented
63#4988C2218yescomplemented
64#4961C2218yescomplemented
65#4960C2218yescomplemented
66#4955C2218yescomplemented
67#4939C2218yescomplemented
68#4673C2218yescomplemented
69#4671C2218yescomplemented
70#4671C2218yescomplemented
71#4670C2218yescomplemented
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×#390—31no—
85C2×#388—31no—
86C2×#388D311yescharacteristic, complemented
87C2×#379—31no—
88C25×C3C2311yescharacteristic
89C24×D3—24no—
90C24×D3—24no—
91C24×D3—24no—
92C24×D3—42no—
93C24×D3—42no—
94C24×D3—42no—
95C24×D3—42no—
96C24×D3C2311yescharacteristic
97C24×D3C2311yescharacteristic
98C24×D3C2311yescharacteristic
99C24×D3C2311yescharacteristic
100C24×D3C2314yes—
101C23×C3×C4C2311yescharacteristic
102C23×C3×C4C2311yescharacteristic
103C23×C3×C4C2311yescharacteristic
104C23×C3×C4C2311yescharacteristic
105C23×C3×C4C2311yescharacteristic
106C23×C3×C4C2311yescharacteristic
107C22×#67—24no—
108C22×#67—24no—
109C22×#67—24no—
110C22×#67—42no—
111C22×#67—42no—
112C22×#67—42no—
113C22×#67C2314yes—
114C22×#67C2314yes—
115C23×Dic3C2311yescharacteristic
116C23×Dic3C2311yescharacteristic
117C23×Dic3C2311yescharacteristic
118C23×Dic3C2311yescharacteristic
119C22×D12—24no—
120C22×D12—24no—
121C22×D12—24no—
122C22×D12—24no—
123C22×D12—24no—
124C22×D12—24no—
125C22×D12—24no—
126C22×D12—42no—
127C22×D12—42no—
128C22×D12—42no—
129C22×D12—42no—
130C22×D12—42no—
131C22×D12—42no—
132C22×D12—42no—
133C22×D12—42no—
134C22×D12C2314yes—
135C22×D12C2314yes—
136C22×D12C2314yes—
137C22×D12C2314yes—
138C22×D12C2314yescomplemented
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—42no—
147C2×C3×C22⋊C4D418yescomplemented
148C2×C3×C22⋊C4C2314yes—
149C2×C3×C22⋊C4C2314yes—
150C2×C3×C22⋊C4C2314yes—
151C2×C3×C42—24no—
152C2×C3×C42C2314yescomplemented
153C2×#217—24no—
154C2×#217C2314yes—
155C2×(C2×D3)⋊C4—24no—
156C2×(C2×D3)⋊C4—24no—
157C2×(C2×D3)⋊C4—24no—
158C2×(C2×D3)⋊C4—24no—
159C2×(C2×D3)⋊C4—24no—
160C2×(C2×D3)⋊C4—24no—
161C2×(C2×D3)⋊C4—24no—
162C2×(C2×D3)⋊C4—24no—
163C2×(C2×D3)⋊C4—42no—
164C2×(C2×D3)⋊C4—42no—
165C2×(C2×D3)⋊C4—42no—
166C2×(C2×D3)⋊C4—42no—
167C2×(C2×D3)⋊C4—42no—
168C2×(C2×D3)⋊C4D418yescomplemented
169C2×(C2×D3)⋊C4C2314yes—
170C2×(C2×D3)⋊C4C2314yes—
171C2×(C2×D3)⋊C4C2314yes—
172C2×(C2×D3)⋊C4C2314yes—
173C2×(C2×D3)⋊C4C2314yes—
174C2×(C2×D3)⋊C4C2314yes—
175C2×(C2×D3)⋊C4C2314yes—
176C2×(C2×D3)⋊C4C2314yes—
177C2×(C2×D3)⋊C4C2314yescomplemented
178C2×(C2×D3)⋊C4C2314yescomplemented
179C2×(C2×D3)⋊C4C2314yescomplemented
180C2×(C2×D3)⋊C4C2314yescomplemented
181C2×(C2×D3)⋊C4C2314yescomplemented
182C2×(C2×D3)⋊C4C2314yescomplemented
183C2×C4⋊Dic3—42no—
184C2×C4⋊Dic3C2314yescomplemented
185C2×C4×Dic3—24no—
186C2×C4×Dic3C2314yescomplemented
187#885—232no—
188#882—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×D4—31no—
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⋊C4—31no—
229C22×C22⋊C4C2×D311yescharacteristic
230C22×C22⋊C4C2×D311yescharacteristic
231C22×C22⋊C4C2×D311yescharacteristic
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#390—38no—
242#388—38no—
243#388C2×D318yescomplemented
244#379—38no—
245C2×#95—31no—
246C2×#95—31no—
247C2×#95C2×D311yescharacteristic, complemented
248C2×#95C2×D311yescharacteristic, complemented
249C24×C3—22no—
250C24×C3—22no—
251C24×C3—22no—
252C24×C3—22no—
253C24×C3—22no—
254C24×C3—22no—
255C24×C3C2×D414yes—
256C24×C3C2412yes—
257C24×C3C2411yescharacteristic
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×D3—22no—
270C23×D3—28no—
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—22no—
282C23×D3—22no—
283C23×D3—22no—
284C23×D3—22no—
285C23×D3—28no—
286C23×D3—28no—
287C23×D3—44no—
288C23×D3—44no—
289C23×D3—44no—
290C23×D3—44no—
291C23×D3—416no—
292C23×D3—416no—
293C23×D3—416no—
294C23×D3—416no—
295C23×D3—416no—
296C23×D3—416no—
297C23×D3—416no—
298C23×D3C2×D414yes—
299C23×D3#4114yes—
300C23×D3C2412yes—
301C23×D3C2412yes—
302C23×D3C2412yes—
303C23×D3C2412yes—
304C22×C3×C4—22no—
305C22×C3×C4—22no—
306C22×C3×C4—22no—
307C22×C3×C4—22no—
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×C4C2×D414yes—
320C22×C3×C4C2×D414yes—
321C22×C3×C4C2×D414yes—
322C22×C3×C4C2412yes—
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—44no—
332C2×#67—44no—
333C2×#67—44no—
334C2×#67—416no—
335C2×#67—416no—
336C22×Dic3—22no—
337C22×Dic3—22no—
338C22×Dic3—22no—
339C22×Dic3—22no—
340C22×Dic3—22no—
341C22×Dic3—22no—
342C22×Dic3—22no—
343C22×Dic3—22no—
344C22×Dic3—22no—
345C22×Dic3—22no—
346C22×Dic3—22no—
347C22×Dic3C2×D414yes—
348C22×Dic3C2412yes—
349C22×Dic3C2412yes—
350C22×Dic3C2412yes—
351C22×Dic3C2412yes—
352C2×D12—28no—
353C2×D12—28no—
354C2×D12—28no—
355C2×D12—28no—
356C2×D12—28no—
357C2×D12—28no—
358C2×D12—28no—
359C2×D12—44no—
360C2×D12—44no—
361C2×D12—44no—
362C2×D12—44no—
363C2×D12—44no—
364C2×D12—44no—
365C2×D12—44no—
366C2×D12—44no—
367C2×D12—416no—
368C2×D12—416no—
369C2×D12—416no—
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—44no—
379C3×C22⋊C4C2×D4116yescomplemented
380C3×C42—28no—
381#217—28no—
382(C2×D3)⋊C4—28no—
383(C2×D3)⋊C4—28no—
384(C2×D3)⋊C4—28no—
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—44no—
391(C2×D3)⋊C4—44no—
392(C2×D3)⋊C4—44no—
393(C2×D3)⋊C4—44no—
394(C2×D3)⋊C4—44no—
395(C2×D3)⋊C4C2×D4116yescomplemented
396C4⋊Dic3—44no—
397C4×Dic3—28no—
398C25—31no—
399C25—31no—
400C25—31no—
401C25—31no—
402C25—34no—
403C25—64no—
404C25—64no—
405C25—64no—
406C25—122no—
407C25—122no—
408C25—122no—
409C25—122no—
410C25C22×D311yescharacteristic
411C22×Q8—34no—
412C22×Q8—64no—
413C22×Q8—64no—
414C22×Q8—122no—
415C22×D4—34no—
416C22×D4—34no—
417C22×D4—34no—
418C22×D4—34no—
419C22×D4—34no—
420C22×D4—34no—
421C22×D4—34no—
422C22×D4—64no—
423C22×D4—64no—
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×D4—122no—
443C23×C4—31no—
444C23×C4—31no—
445C23×C4—31no—
446C23×C4—31no—
447C23×C4C22×D311yescharacteristic
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—38no—
463C2×C22⋊C4—34no—
464C2×C22⋊C4—34no—
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—42no—
479C2×C22⋊C4—64no—
480C2×C22⋊C4—64no—
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—122no—
489C2×C22⋊C4—122no—
490C2×C22⋊C4—122no—
491C2×C22⋊C4—122no—
492C2×C22⋊C4—122no—
493C2×C22⋊C4D1218yescomplemented
494C2×C22⋊C4C22×D314yes—
495C2×C22⋊C4C22×D314yes—
496C2×C22⋊C4C22×D314yes—
497C2×C42—24no—
498C2×C42—34no—
499C2×C42—64no—
500C2×C42C22×D314yescomplemented
501#95—34no—
502#95—34no—
503#95C22×D314yescomplemented
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—44no—
515C23×C3—44no—
516C23×C3—44no—
517C23×C3—44no—
518C23×C3C22×D414yes—
519C23×C3C22×D412yes—
520C23×C3C22×D412yes—
521C23×C3C2×#4112yes—
522C23×C3H(5,𝔽2)12yes—
523C23×C3H(5,𝔽2)12yes—
524C23×C3H(5,𝔽2)12yes—
525C23×C3H(5,𝔽2)12yes—
526C23×C3C2511yescharacteristic
527C22×D3—28no—
528C22×D3—28no—
529C22×D3—28no—
530C22×D3—28no—
531C22×D3—28no—
532C22×D3—28no—
533C22×D3—22no—
534C22×D3—22no—
535C22×D3—22no—
536C22×D3—22no—
537C22×D3—22no—
538C22×D3—22no—
539C22×D3—22no—
540C22×D3—22no—
541C22×D3—22no—
542C22×D3—22no—
543C22×D3—22no—
544C22×D3—22no—
545C22×D3—22no—
546C22×D3—22no—
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—416no—
560C22×D3—416no—
561C22×D3—416no—
562C22×D3—416no—
563C22×D3—416no—
564C22×D3—416no—
565C22×D3—4128no—
566C22×D3—416no—
567C22×D3—44no—
568C22×D3—44no—
569C22×D3—44no—
570C22×D3—44no—
571C22×D3—44no—
572C22×D3—44no—
573C22×D3—44no—
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×D3C2×#4114yes—
591C2×C3×C4—28no—
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—22no—
608C2×C3×C4—22no—
609C2×C3×C4—44no—
610C2×C3×C4—44no—
611C2×C3×C4—44no—
612C2×C3×C4C22×D414yes—
613C2×C3×C4C22×D414yes—
614C2×C3×C4C22×D414yes—
615#67—416no—
616#67—416no—
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—44no—
630C2×Dic3—44no—
631C2×Dic3—44no—
632C2×Dic3C22×D414yes—
633D12—416no—
634D12—416no—
635D12—416no—
636D12—416no—
637D12—416no—
638Dic6—416no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—34no—
646C24—34no—
647C24—32no—
648C24—32no—
649C24—32no—
650C24—32no—
651C24—68no—
652C24—68no—
653C24—62no—
654C24—62no—
655C24—62no—
656C24—62no—
657C24—62no—
658C24—62no—
659C24—62no—
660C24—62no—
661C24—62no—
662C24—62no—
663C24—62no—
664C24—62no—
665C24—62no—
666C24—68no—
667C24—62no—
668C24—62no—
669C24—62no—
670C24—62no—
671C24—62no—
672C24—62no—
673C24—62no—
674C24—62no—
675C24—62no—
676C24—62no—
677C24—62no—
678C24—62no—
679C24—62no—
680C24—124no—
681C24—124no—
682C24—124no—
683C24—124no—
684C24—1216no—
685C24—1216no—
686C24—1216no—
687C24—1216no—
688C24—1216no—
689C24—1216no—
690C24—1216no—
691C24C2×D1214yes—
692C24C23×D312yes—
693C24C23×D311yescharacteristic
694C2×Q8—68no—
695C2×Q8—68no—
696C2×Q8—124no—
697C2×Q8—1216no—
698C2×D4—68no—
699C2×D4—68no—
700C2×D4—68no—
701C2×D4—68no—
702C2×D4—68no—
703C2×D4—68no—
704C2×D4—68no—
705C2×D4—68no—
706C2×D4—68no—
707C2×D4—68no—
708C2×D4—124no—
709C2×D4—124no—
710C2×D4—124no—
711C2×D4—124no—
712C2×D4—124no—
713C2×D4—124no—
714C2×D4—124no—
715C2×D4—124no—
716C2×D4—1216no—
717C2×D4—1216no—
718C2×D4—1216no—
719C2×D4—1216no—
720C2×D4—1216no—
721C2×D4—124no—
722C2×D4—124no—
723C2×D4—124no—
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—22no—
740C22×C4—22no—
741C22×C4—34no—
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×C4C2×D1214yes—
758C22×C4C2×D1214yes—
759C22×C4D3×D414yes—
760C22×C4C23×D312yes—
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—316no—
770C22⋊C4—44no—
771C22⋊C4—68no—
772C22⋊C4—68no—
773C22⋊C4—68no—
774C22⋊C4—68no—
775C22⋊C4—68no—
776C22⋊C4—68no—
777C22⋊C4—68no—
778C22⋊C4—68no—
779C22⋊C4—68no—
780C22⋊C4—124no—
781C22⋊C4—124no—
782C22⋊C4—124no—
783C22⋊C4—124no—
784C22⋊C4—124no—
785C22⋊C4C2×D12116yescomplemented
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#53514yes—
797C22×C3#53514yes—
798C22×C3#53814yes—
799C22×C3D4214yes—
800C22×C3#54614yes—
801C22×C3#54614yes—
802C22×C3H(3,𝔽4)14yes—
803C22×C3C23×D411yescharacteristic
804C22×C3C23×D411yescharacteristic
805C22×C3C22×#4111yescharacteristic
806C22×C3C2×H(5,𝔽2)11yescharacteristic
807C22×C3C2×H(5,𝔽2)11yescharacteristic
808C22×C3C2×H(5,𝔽2)11yescharacteristic
809C22×C3C2×H(5,𝔽2)11yescharacteristic
810C2×D3—24no—
811C2×D3—24no—
812C2×D3—24no—
813C2×D3—24no—
814C2×D3—24no—
815C2×D3—24no—
816C2×D3—464no—
817C2×D3—416no—
818C2×D3—416no—
819C2×D3—42no—
820C2×D3—42no—
821C2×D3—42no—
822C2×D3—42no—
823C2×D3—42no—
824C2×D3—42no—
825C2×D3—42no—
826C2×D3—42no—
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—88no—
842C2×D3—88no—
843C3×C4—24no—
844C3×C4—24no—
845C3×C4—24no—
846C3×C4—42no—
847C3×C4—42no—
848C3×C4—42no—
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—34no—
863C23—34no—
864C23—44no—
865C23—44no—
866C23—44no—
867C23—44no—
868C23—68no—
869C23—68no—
870C23—62no—
871C23—62no—
872C23—62no—
873C23—62no—
874C23—62no—
875C23—68no—
876C23—62no—
877C23—62no—
878C23—62no—
879C23—62no—
880C23—62no—
881C23—62no—
882C23—62no—
883C23—68no—
884C23—68no—
885C23—68no—
886C23—62no—
887C23—62no—
888C23—62no—
889C23—62no—
890C23—62no—
891C23—62no—
892C23—62no—
893C23—62no—
894C23—62no—
895C23—62no—
896C23—62no—
897C23—62no—
898C23—62no—
899C23—62no—
900C23—1216no—
901C23—1216no—
902C23—1216no—
903C23—1216no—
904C23—1216no—
905C23—1216no—
906C23—1216no—
907C23—12128no—
908C23—124no—
909C23—124no—
910C23—124no—
911C23—124no—
912C23—124no—
913C23—124no—
914C23—124no—
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—
930C23C22×D1214yes—
931C23C22×D1212yes—
932C23C2×D3×D412yes—
933C23#100412yes—
934C23D3×#4112yes—
935C23#100912yes—
936C23#100912yes—
937C23#100912yes—
938C23C24×D311yescharacteristic
939Q8—1216no—
940D4—1216no—
941D4—1216no—
942D4—1216no—
943D4—1216no—
944D4—1216no—
945D4—1216no—
946D4—1216no—
947C2×C4—28no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—28no—
955C2×C4—28no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—34no—
966C2×C4—44no—
967C2×C4—44no—
968C2×C4—44no—
969C2×C4—62no—
970C2×C4—62no—
971C2×C4—68no—
972C2×C4—62no—
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—124no—
982C2×C4—124no—
983C2×C4—124no—
984C2×C4C22×D1214yes—
985C2×C4C22×D1214yes—
986C2×C4C2×D3×D414yes—
987C2×C3—44no—
988C2×C3#267018yescomplemented
989C2×C3C2×#53511yescharacteristic
990C2×C3C2×#53511yescharacteristic
991C2×C3C2×#53811yescharacteristic
992C2×C3C2×D4211yescharacteristic
993C2×C3C2×#54611yescharacteristic
994C2×C3C2×#54611yescharacteristic
995C2×C3C2×H(3,𝔽4)11yescharacteristic
996D3—44no—
997D3—44no—
998D3—82no—
999D3—82no—
1000C22—24no—
1001C22—24no—
1002C22—24no—
1003C22—42no—
1004C22—42no—
1005C22—416no—
1006C22—42no—
1007C22—42no—
1008C22—64no—
1009C22—64no—
1010C22—64no—
1011C22—64no—
1012C22—64no—
1013C22—64no—
1014C22—1264no—
1015C22—122no—
1016C22—122no—
1017C22—122no—
1018C22—122no—
1019C22—122no—
1020C22—1216no—
1021C22—1216no—
1022C22—122no—
1023C22—122no—
1024C22—122no—
1025C22—122no—
1026C22—122no—
1027C22—122no—
1028C22—122no—
1029C22—122no—
1030C22—122no—
1031C22—122no—
1032C22—122no—
1033C22—122no—
1034C22—122no—
1035C22—122no—
1036C22—122no—
1037C22—122no—
1038C22—122no—
1039C22—248no—
1040C22—248no—
1041C22#552514yes—
1042C22D4×D1214yes—
1043C22#555414yes—
1044C22#560714yes—
1045C22#565414yes—
1046C22#568314yes—
1047C22#570414yes—
1048C22C23×D1211yescharacteristic
1049C22C22×D3×D411yescharacteristic
1050C22C2×#100411yescharacteristic
1051C22C2×D3×#4111yescharacteristic
1052C22C2×#100911yescharacteristic
1053C22C2×#100911yescharacteristic
1054C22C2×#100911yescharacteristic
1055C4—24no—
1056C4—24no—
1057C4—24no—
1058C4—42no—
1059C4—42no—
1060C4—42no—
1061C4—64no—
1062C4—122no—
1063C4—122no—
1064C4—122no—
1065C3C2×#267011yescharacteristic, complemented, Sylow
1066C2—44no—
1067C2—124no—
1068C2—124no—
1069C2—242no—
1070C2—242no—
1071C2#7591318yesdirect product factor
1072C2C2×#552511yescharacteristic
1073C2C2×D4×D1211yescharacteristic
1074C2C2×#555411yescharacteristic
1075C2C2×#560711yescharacteristic
1076C2C2×#565411yescharacteristic
1077C2C2×#568311yescharacteristic
1078C2C2×#570411yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC2×C3×#388C2
socleC24×C3C24
hypercenterC2×#388D3
hypocenterC3C2×#2670
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C22×#882C2semidirect
2. C22×#882C2semidirect
3. C22×#885C2semidirect
4. C22×#875C2semidirect
5. C2×C3×#388C2semidirect
6. C2×#4991C2semidirect
7. C2×#4988C2semidirect
8. C2×#4960C2semidirect
9. C2×#4955C2semidirect
10. C2×#4961C2semidirect
11. C2×#4939C2semidirect
12. #75913C2direct (N × H)
13. C2×#4673C2semidirect
14. C2×#4671C2semidirect
15. C2×#4671C2semidirect
16. C2×#4670C2semidirect
25. C23×D12C22semidirect
26. C23×Dic6C22semidirect
27. C22×C3×C4⋊C4C22semidirect
31. C22×C3×C42C22semidirect
41. C22×(C2×D3)⋊C4C22semidirect
42. C22×(C2×D3)⋊C4C22semidirect
43. C22×(C2×D3)⋊C4C22semidirect
44. C22×(C2×D3)⋊C4C22semidirect
45. C22×(C2×D3)⋊C4C22semidirect
46. C22×(C2×D3)⋊C4C22semidirect
47. C22×C4⋊Dic3C22semidirect
48. C22×C4×Dic3C22semidirect
50. C2×#885C22semidirect
53. C2×#882C22semidirect
54. C2×#882C22semidirect
56. C2×#875C22semidirect
57. C3×#388C22semidirect
58. C2×C3×#95C22semidirect
59. C2×C3×#95C22semidirect
60. C2×C3⋊#95C22semidirect
61. C2×C3⋊#95C22semidirect
62. #4991C22semidirect
63. #4988C22semidirect
64. #4961C22semidirect
65. #4960C22semidirect
66. #4955C22semidirect
67. #4939C22semidirect
68. #4673C22semidirect
69. #4671C22semidirect
70. #4671C22semidirect
71. #4670C22semidirect
86. C2×#388D3semidirect
138. C22×D12C23semidirect
142. C22×Dic6C23semidirect
144. C2×C3×C4⋊C4C23semidirect
147. C2×C3×C22⋊C4D4semidirect
152. C2×C3×C42C23semidirect
168. C2×(C2×D3)⋊C4D4semidirect
177. C2×(C2×D3)⋊C4C23semidirect
178. C2×(C2×D3)⋊C4C23semidirect
179. C2×(C2×D3)⋊C4C23semidirect
180. C2×(C2×D3)⋊C4C23semidirect
181. C2×(C2×D3)⋊C4C23semidirect
182. C2×(C2×D3)⋊C4C23semidirect
184. C2×C4⋊Dic3C23semidirect
186. C2×C4×Dic3C23semidirect
191. C3×#95C23semidirect
192. C3×#95C23semidirect
193. C3⋊#95C23semidirect
194. C3⋊#95C23semidirect
213. C22×C4⋊C4C2×D3semidirect
233. C22×C42C2×D3semidirect
243. #388C2×D3semidirect
247. C2×#95C2×D3semidirect
248. C2×#95C2×D3semidirect
379. C3×C22⋊C4C2×D4semidirect
395. (C2×D3)⋊C4C2×D4semidirect
460. C2×C4⋊C4C22×D3semidirect
493. C2×C22⋊C4D12semidirect
500. C2×C42C22×D3semidirect
503. #95C22×D3semidirect
504. #95C22×D3semidirect
785. C22⋊C4C2×D12semidirect
988. C2×C3#2670semidirect
1065. C3C2×#2670semidirect
1071. C2#75913direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#8822
C22×#8852
C22×#8752
C2×C3×#3882
C2×#49912
C2×#49882
C2×#49602
C2×#49552
C2×#49612
C2×#49392
#759132
C2×#46732
C2×#46712
C2×#46702
C2×#26703