Finite Group Databasebeta

← C2×#78119 #11430828

Subgroups — C2×#78119 #11430828

Order 768.

2982 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#897C211yesmaximal, characteristic, complemented
2C22×#878C211yesmaximal, characteristic, complemented
3C2×C3×#399C211yesmaximal, characteristic, complemented
4C2×#4993C211yesmaximal, characteristic, complemented
5C2×#4994C211yesmaximal, characteristic, complemented
6C2×#4983C211yesmaximal, characteristic, complemented
7C2×#4982C211yesmaximal, characteristic, complemented
8C2×#4984C211yesmaximal, characteristic, complemented
9C2×#4956C211yesmaximal, characteristic
10C2×#4948C211yesmaximal, characteristic, complemented
11C2×#4957C211yesmaximal, characteristic
12C2×#4958C211yesmaximal, characteristic
13C2×#4950C211yesmaximal, characteristic, complemented
14#78119C2116yesmaximal, direct product factor
15C2×#4668C211yesmaximal, characteristic, complemented
16C2×#4646C211yesmaximal, characteristic, complemented
17C2×#2732—31nomaximal, Sylow
18C23×#67C2211yescharacteristic
19C24×Dic3C2211yescharacteristic
20C23×C4×D3C2211yescharacteristic
21C23×Dic6C2211yescharacteristic
22C22×C3×C4⋊C4C2211yescharacteristic
23C22×C3×C4⋊C4C2211yescharacteristic
24C22×C3×C4⋊C4C2211yescharacteristic
25C22×C3×C22⋊C4C2211yescharacteristic
26C22×C3×C22⋊C4C2211yescharacteristic
27C22×C3×C22⋊C4C2211yescharacteristic
28C22×#217C2211yescharacteristic
29C22×#217C2211yescharacteristic
30C22×(C2×D3)⋊C4C2211yescharacteristic
31C22×(C2×D3)⋊C4C2211yescharacteristic
32C22×(C2×D3)⋊C4C2211yescharacteristic
33C22×(C2×D3)⋊C4C2211yescharacteristic
34C22×(C2×D3)⋊C4C2211yescharacteristic
35C22×C4⋊Dic3C2211yescharacteristic
36C22×C4⋊Dic3C2211yescharacteristic
37C22×C4⋊Dic3C2211yescharacteristic
38C22×C4⋊Dic3C2211yescharacteristic
39C22×Dic3⋊C4C2211yescharacteristic
40C22×Dic3⋊C4C2211yescharacteristic
41C22×Dic3⋊C4C2211yescharacteristic
42C22×Dic3⋊C4C2211yescharacteristic
43C22×Dic3⋊C4C2211yescharacteristic
44C22×C4×Dic3C2211yescharacteristic
45C2×#897—28no—
46C2×#897C2218yescomplemented
47C2×#878—28no—
48C2×#878C2218yescomplemented
49C3×#399C2218yescomplemented
50C2×C3×#95C2211yescharacteristic
51C2×C3⋊#95C2211yescharacteristic
52C2×C3⋊#95C2211yescharacteristic
53C2×C3⋊#95C2211yescharacteristic
54C2×C3⋊#95C2211yescharacteristic
55C2×C3⋊#95C2211yescharacteristic
56C2×C3⋊#95C2211yescharacteristic
57C2×C3⋊#95C2211yescharacteristic
58#4994C2218yescomplemented
59#4993C2218yescomplemented
60#4984C2218yescomplemented
61#4983C2218yescomplemented
62#4982C2218yescomplemented
63#4958C2218yes—
64#4957C2218yes—
65#4956C2218yes—
66#4950C2218yescomplemented
67#4948C2218yescomplemented
68#4668C2218yescomplemented
69#4646C2218yescomplemented
70C22×C22⋊Q8—31no—
71C22×C22⋊Q8—31no—
72#2732—316no—
73C2×#399—31no—
74C2×#399D311yescharacteristic, complemented
75C2×#398—31no—
76C2×#398—31no—
77C2×#396—31no—
78C2×#396—31no—
79C2×#391—31no—
80C2×#390—31no—
81C2×#389—31no—
82C2×#386—31no—
83C2×#386—31no—
84C2×#385—31no—
85C2×#385—31no—
86C25×C3C2311yescharacteristic
87C24×D3C2311yescharacteristic
88C23×C3×C4C2311yescharacteristic
89C23×C3×C4C2311yescharacteristic
90C23×C3×C4C2311yescharacteristic
91C23×C3×C4C2311yescharacteristic
92C23×C3×C4C2311yescharacteristic
93C23×C3×C4C2311yescharacteristic
94C22×#67—42no—
95C22×#67—42no—
96C22×#67Q818yescomplemented
97C22×#67C2314yes—
98C23×Dic3—24no—
99C23×Dic3—42no—
100C23×Dic3—42no—
101C23×Dic3C2311yescharacteristic
102C23×Dic3C2311yescharacteristic
103C23×Dic3C2311yescharacteristic
104C23×Dic3C2311yescharacteristic
105C23×Dic3C2311yescharacteristic
106C23×Dic3C2311yescharacteristic
107C23×Dic3C2311yescharacteristic
108C23×Dic3C2314yes—
109C22×C4×D3—24no—
110C22×C4×D3—42no—
111C22×C4×D3—42no—
112C22×C4×D3C2314yes—
113C22×Dic6—42no—
114C22×Dic6—42no—
115C22×Dic6D418yescomplemented
116C22×Dic6C2314yes—
117C2×C3×C4⋊C4—24no—
118C2×C3×C4⋊C4—24no—
119C2×C3×C4⋊C4—42no—
120C2×C3×C4⋊C4C2314yes—
121C2×C3×C4⋊C4C2314yes—
122C2×C3×C4⋊C4C2314yes—
123C2×C3×C22⋊C4—24no—
124C2×C3×C22⋊C4—24no—
125C2×C3×C22⋊C4—42no—
126C2×C3×C22⋊C4C2314yes—
127C2×C3×C22⋊C4C2314yes—
128C2×C3×C22⋊C4C2314yes—
129C2×#217—24no—
130C2×#217—42no—
131C2×#217C2314yes—
132C2×#217C2314yes—
133C2×(C2×D3)⋊C4—24no—
134C2×(C2×D3)⋊C4—24no—
135C2×(C2×D3)⋊C4—24no—
136C2×(C2×D3)⋊C4—42no—
137C2×(C2×D3)⋊C4—42no—
138C2×(C2×D3)⋊C4C2314yes—
139C2×(C2×D3)⋊C4C2314yes—
140C2×(C2×D3)⋊C4C2314yes—
141C2×(C2×D3)⋊C4C2314yes—
142C2×(C2×D3)⋊C4C2314yes—
143C2×C4⋊Dic3—24no—
144C2×C4⋊Dic3—24no—
145C2×C4⋊Dic3—24no—
146C2×C4⋊Dic3—42no—
147C2×C4⋊Dic3C2314yes—
148C2×C4⋊Dic3C2314yes—
149C2×C4⋊Dic3C2314yes—
150C2×C4⋊Dic3C2314yes—
151C2×Dic3⋊C4—24no—
152C2×Dic3⋊C4—24no—
153C2×Dic3⋊C4—42no—
154C2×Dic3⋊C4—42no—
155C2×Dic3⋊C4—42no—
156C2×Dic3⋊C4C2314yes—
157C2×Dic3⋊C4C2314yes—
158C2×Dic3⋊C4C2314yes—
159C2×Dic3⋊C4C2314yes—
160C2×Dic3⋊C4C2314yes—
161C2×C4×Dic3—42no—
162C2×C4×Dic3C2314yes—
163#897—232no—
164#878—232no—
165C3×#95C2314yes—
166C3⋊#95C2314yes—
167C3⋊#95C2314yes—
168C3⋊#95C2314yes—
169C3⋊#95C2314yes—
170C3⋊#95C2314yes—
171C3⋊#95C2314yes—
172C3⋊#95C2314yes—
173C23×Q8—31no—
174C23×D4—31no—
175C24×C4—31no—
176C24×C4—31no—
177C2×C22⋊Q8—38no—
178C2×C22⋊Q8—38no—
179C2×C22⋊Q8—68no—
180C2×C22⋊Q8—68no—
181C22×C4⋊C4—31no—
182C22×C4⋊C4—31no—
183C22×C4⋊C4—31no—
184C22×C4⋊C4—31no—
185C22×C4⋊C4—31no—
186C22×C4⋊C4—31no—
187C22×C4⋊C4—31no—
188C22×C4⋊C4—31no—
189C22×C4⋊C4—31no—
190C22×C4⋊C4C2×D311yescharacteristic
191C22×C4⋊C4C2×D311yescharacteristic
192C22×C4⋊C4C2×D311yescharacteristic
193C22×C22⋊C4—31no—
194C22×C22⋊C4—31no—
195C22×C22⋊C4—31no—
196C22×C22⋊C4—31no—
197C22×C22⋊C4—31no—
198C22×C22⋊C4—31no—
199C22×C22⋊C4—31no—
200C22×C22⋊C4C2×D311yescharacteristic
201C22×C22⋊C4C2×D311yescharacteristic
202C22×C22⋊C4C2×D311yescharacteristic
203C22×C42—31no—
204#399—38no—
205#399C2×D318yescomplemented
206#398—38no—
207#398—38no—
208#396—38no—
209#396—38no—
210#391—38no—
211#390—38no—
212#389—38no—
213#386—38no—
214#386—38no—
215#385—38no—
216#385—38no—
217C2×#95—31no—
218C2×#95—31no—
219C2×#95—31no—
220C2×#95—31no—
221C2×#95—31no—
222C2×#95—31no—
223C2×#95—31no—
224C2×#95C2×D311yescharacteristic
225C24×C3—22no—
226C24×C3—22no—
227C24×C3—22no—
228C24×C3—22no—
229C24×C3—22no—
230C24×C3—22no—
231C24×C3C2×Q814yes—
232C24×C3C2412yes—
233C24×C3C2411yescharacteristic
234C23×D3—22no—
235C23×D3—22no—
236C23×D3—22no—
237C23×D3—22no—
238C23×D3—22no—
239C23×D3—22no—
240C23×D3C2×Q814yes—
241C23×D3C2412yes—
242C22×C3×C4—22no—
243C22×C3×C4—22no—
244C22×C3×C4—22no—
245C22×C3×C4—22no—
246C22×C3×C4—22no—
247C22×C3×C4—22no—
248C22×C3×C4—22no—
249C22×C3×C4—22no—
250C22×C3×C4—22no—
251C22×C3×C4—22no—
252C22×C3×C4—22no—
253C22×C3×C4—22no—
254C22×C3×C4—22no—
255C22×C3×C4—22no—
256C22×C3×C4—22no—
257C22×C3×C4—22no—
258C22×C3×C4C2×D414yes—
259C22×C3×C4#4114yes—
260C22×C3×C4C2412yes—
261C22×C3×C4C2412yes—
262C22×C3×C4C2412yes—
263C22×C3×C4C2412yes—
264C22×C3×C4C2412yes—
265C22×C3×C4C2412yes—
266C2×#67—416no—
267C2×#67—44no—
268C2×#67—44no—
269C2×#67C2×Q8116yescomplemented
270C22×Dic3—22no—
271C22×Dic3—22no—
272C22×Dic3—22no—
273C22×Dic3—22no—
274C22×Dic3—22no—
275C22×Dic3—22no—
276C22×Dic3—22no—
277C22×Dic3—22no—
278C22×Dic3—22no—
279C22×Dic3—22no—
280C22×Dic3—22no—
281C22×Dic3—22no—
282C22×Dic3—22no—
283C22×Dic3—22no—
284C22×Dic3—22no—
285C22×Dic3—22no—
286C22×Dic3—22no—
287C22×Dic3—22no—
288C22×Dic3—28no—
289C22×Dic3—44no—
290C22×Dic3—44no—
291C22×Dic3—416no—
292C22×Dic3C2×D414yes—
293C22×Dic3C2×D414yes—
294C22×Dic3C2×Q814yes—
295C22×Dic3C2412yes—
296C22×Dic3C2412yes—
297C22×Dic3C2412yes—
298C22×Dic3C2412yes—
299C22×Dic3C2412yes—
300C22×Dic3C2412yes—
301C22×Dic3C2412yes—
302C2×C4×D3—28no—
303C2×C4×D3—44no—
304C2×C4×D3—44no—
305C2×C4×D3—416no—
306C2×Dic6—416no—
307C2×Dic6—44no—
308C2×Dic6—44no—
309C2×Dic6C2×D4116yescomplemented
310C3×C4⋊C4—28no—
311C3×C4⋊C4—28no—
312C3×C4⋊C4—44no—
313C3×C22⋊C4—28no—
314C3×C22⋊C4—28no—
315C3×C22⋊C4—44no—
316#217—28no—
317#217—44no—
318(C2×D3)⋊C4—28no—
319(C2×D3)⋊C4—28no—
320(C2×D3)⋊C4—28no—
321(C2×D3)⋊C4—44no—
322(C2×D3)⋊C4—44no—
323C4⋊Dic3—28no—
324C4⋊Dic3—28no—
325C4⋊Dic3—28no—
326C4⋊Dic3—44no—
327Dic3⋊C4—28no—
328Dic3⋊C4—28no—
329Dic3⋊C4—44no—
330Dic3⋊C4—44no—
331Dic3⋊C4—44no—
332C4×Dic3—44no—
333C25—31no—
334C25C22×D311yescharacteristic
335C22×Q8—38no—
336C22×Q8—34no—
337C22×Q8—122no—
338C22×Q8—122no—
339C22×D4—38no—
340C22×D4—34no—
341C22×D4—122no—
342C22×D4—122no—
343C23×C4—31no—
344C23×C4—31no—
345C23×C4—31no—
346C23×C4—31no—
347C23×C4—31no—
348C23×C4—31no—
349C23×C4—31no—
350C23×C4—34no—
351C23×C4—34no—
352C23×C4—64no—
353C23×C4—64no—
354C23×C4—122no—
355C23×C4—122no—
356C23×C4—122no—
357C23×C4—122no—
358C23×C4C22×D311yescharacteristic
359C23×C4C22×D311yescharacteristic
360C23×C4C22×D311yescharacteristic
361C23×C4C22×D311yescharacteristic
362C23×C4C22×D311yescharacteristic
363C23×C4C22×D311yescharacteristic
364C22⋊Q8—632no—
365C22⋊Q8—632no—
366C2×C4⋊C4—24no—
367C2×C4⋊C4—24no—
368C2×C4⋊C4—34no—
369C2×C4⋊C4—34no—
370C2×C4⋊C4—34no—
371C2×C4⋊C4—34no—
372C2×C4⋊C4—34no—
373C2×C4⋊C4—34no—
374C2×C4⋊C4—34no—
375C2×C4⋊C4—34no—
376C2×C4⋊C4—34no—
377C2×C4⋊C4—42no—
378C2×C4⋊C4—64no—
379C2×C4⋊C4—64no—
380C2×C4⋊C4—64no—
381C2×C4⋊C4—64no—
382C2×C4⋊C4—64no—
383C2×C4⋊C4—122no—
384C2×C4⋊C4—122no—
385C2×C4⋊C4—122no—
386C2×C4⋊C4—122no—
387C2×C4⋊C4C22×D314yes—
388C2×C4⋊C4C22×D314yes—
389C2×C4⋊C4C22×D314yes—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—34no—
393C2×C22⋊C4—34no—
394C2×C22⋊C4—34no—
395C2×C22⋊C4—34no—
396C2×C22⋊C4—34no—
397C2×C22⋊C4—34no—
398C2×C22⋊C4—34no—
399C2×C22⋊C4—42no—
400C2×C22⋊C4—64no—
401C2×C22⋊C4—64no—
402C2×C22⋊C4—64no—
403C2×C22⋊C4—64no—
404C2×C22⋊C4—122no—
405C2×C22⋊C4—122no—
406C2×C22⋊C4—122no—
407C2×C22⋊C4C22×D314yes—
408C2×C22⋊C4C22×D314yes—
409C2×C22⋊C4C22×D314yes—
410C2×C42—34no—
411C2×C42—122no—
412#95—34no—
413#95—34no—
414#95—34no—
415#95—34no—
416#95—34no—
417#95—34no—
418#95—34no—
419#95C22×D314yes—
420C23×C3—28no—
421C23×C3—28no—
422C23×C3—28no—
423C23×C3—22no—
424C23×C3—22no—
425C23×C3—22no—
426C23×C3—22no—
427C23×C3—22no—
428C23×C3—22no—
429C23×C3—44no—
430C23×C3—44no—
431C23×C3—44no—
432C23×C3—44no—
433C23×C3C22×D412yes—
434C23×C3C22×Q814yes—
435C23×C3C22×Q812yes—
436C23×C3C2×#4112yes—
437C23×C3H(5,𝔽2)12yes—
438C23×C3H(5,𝔽2)12yes—
439C23×C3H(5,𝔽2)12yes—
440C23×C32−1+412yes—
441C23×C3C2511yescharacteristic
442C22×D3—28no—
443C22×D3—28no—
444C22×D3—28no—
445C22×D3—22no—
446C22×D3—22no—
447C22×D3—22no—
448C22×D3—22no—
449C22×D3—22no—
450C22×D3—22no—
451C22×D3—44no—
452C22×D3—44no—
453C22×D3—44no—
454C22×D3—44no—
455C22×D3C22×Q814yes—
456C2×C3×C4—28no—
457C2×C3×C4—28no—
458C2×C3×C4—22no—
459C2×C3×C4—22no—
460C2×C3×C4—22no—
461C2×C3×C4—22no—
462C2×C3×C4—22no—
463C2×C3×C4—22no—
464C2×C3×C4—22no—
465C2×C3×C4—22no—
466C2×C3×C4—22no—
467C2×C3×C4—22no—
468C2×C3×C4—22no—
469C2×C3×C4—22no—
470C2×C3×C4—22no—
471C2×C3×C4—22no—
472C2×C3×C4—22no—
473C2×C3×C4—22no—
474C2×C3×C4—44no—
475C2×C3×C4—44no—
476C2×C3×C4—44no—
477C2×C3×C4—44no—
478C2×C3×C4C22×D414yes—
479C2×C3×C4C2×#4114yes—
480#67—416no—
481C2×Dic3—28no—
482C2×Dic3—28no—
483C2×Dic3—28no—
484C2×Dic3—22no—
485C2×Dic3—22no—
486C2×Dic3—22no—
487C2×Dic3—22no—
488C2×Dic3—22no—
489C2×Dic3—22no—
490C2×Dic3—22no—
491C2×Dic3—22no—
492C2×Dic3—22no—
493C2×Dic3—22no—
494C2×Dic3—22no—
495C2×Dic3—22no—
496C2×Dic3—22no—
497C2×Dic3—22no—
498C2×Dic3—22no—
499C2×Dic3—22no—
500C2×Dic3—22no—
501C2×Dic3—22no—
502C2×Dic3—416no—
503C2×Dic3—44no—
504C2×Dic3—44no—
505C2×Dic3—44no—
506C2×Dic3—44no—
507C2×Dic3C22×D414yes—
508C2×Dic3C22×D414yes—
509C2×Dic3C22×Q814yes—
510C4×D3—416no—
511Dic6—416no—
512C24—22no—
513C24—22no—
514C24—22no—
515C24—22no—
516C24—22no—
517C24—22no—
518C24—34no—
519C24—32no—
520C24—62no—
521C24—62no—
522C24—62no—
523C24—62no—
524C24—62no—
525C24—62no—
526C24D3×Q814yes—
527C24C23×D312yes—
528C24C23×D311yescharacteristic
529C2×Q8—316no—
530C2×Q8—1216no—
531C2×Q8—124no—
532C2×Q8—124no—
533C2×D4—316no—
534C2×D4—1216no—
535C2×D4—124no—
536C2×D4—124no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—34no—
554C22×C4—34no—
555C22×C4—34no—
556C22×C4—32no—
557C22×C4—32no—
558C22×C4—32no—
559C22×C4—32no—
560C22×C4—32no—
561C22×C4—32no—
562C22×C4—32no—
563C22×C4—68no—
564C22×C4—62no—
565C22×C4—62no—
566C22×C4—62no—
567C22×C4—62no—
568C22×C4—62no—
569C22×C4—62no—
570C22×C4—62no—
571C22×C4—62no—
572C22×C4—62no—
573C22×C4—62no—
574C22×C4—62no—
575C22×C4—62no—
576C22×C4—62no—
577C22×C4—62no—
578C22×C4—62no—
579C22×C4—62no—
580C22×C4—62no—
581C22×C4—62no—
582C22×C4—68no—
583C22×C4—124no—
584C22×C4—124no—
585C22×C4—1216no—
586C22×C4—124no—
587C22×C4—124no—
588C22×C4—1216no—
589C22×C4D3×D414yes—
590C22×C4#23714yes—
591C22×C4C23×D312yes—
592C22×C4C23×D312yes—
593C22×C4C23×D312yes—
594C22×C4C23×D312yes—
595C22×C4C23×D312yes—
596C22×C4C23×D312yes—
597C4⋊C4—28no—
598C4⋊C4—28no—
599C4⋊C4—44no—
600C4⋊C4—68no—
601C4⋊C4—68no—
602C4⋊C4—68no—
603C4⋊C4—68no—
604C4⋊C4—68no—
605C4⋊C4—124no—
606C4⋊C4—124no—
607C4⋊C4—124no—
608C4⋊C4—124no—
609C22⋊C4—28no—
610C22⋊C4—28no—
611C22⋊C4—44no—
612C22⋊C4—68no—
613C22⋊C4—68no—
614C22⋊C4—68no—
615C22⋊C4—68no—
616C22⋊C4—124no—
617C22⋊C4—124no—
618C22⋊C4—124no—
619C42—124no—
620C22×C3—24no—
621C22×C3—24no—
622C22×C3—24no—
623C22×C3—42no—
624C22×C3—42no—
625C22×C3—42no—
626C22×C3—416no—
627C22×C3—42no—
628C22×C3#53414yes—
629C22×C3#53914yes—
630C22×C3#54314yes—
631C22×C3D4×Q814yes—
632C22×C3#55014yes—
633C22×C3#55414yes—
634C22×C3#56214yes—
635C22×C3C23×D411yescharacteristic
636C22×C3C23×Q811yescharacteristic
637C22×C3C22×#4111yescharacteristic
638C22×C3C2×H(5,𝔽2)11yescharacteristic
639C22×C3C2×H(5,𝔽2)11yescharacteristic
640C22×C3C2×H(5,𝔽2)11yescharacteristic
641C22×C3C2×2−1+411yescharacteristic
642C2×D3—24no—
643C2×D3—24no—
644C2×D3—24no—
645C2×D3—42no—
646C2×D3—42no—
647C2×D3—42no—
648C2×D3—416no—
649C2×D3—42no—
650C3×C4—24no—
651C3×C4—24no—
652C3×C4—42no—
653C3×C4—42no—
654C3×C4—42no—
655C3×C4—42no—
656Dic3—24no—
657Dic3—24no—
658Dic3—24no—
659Dic3—42no—
660Dic3—42no—
661Dic3—42no—
662Dic3—42no—
663C23—28no—
664C23—28no—
665C23—28no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—34no—
673C23—44no—
674C23—44no—
675C23—44no—
676C23—44no—
677C23—68no—
678C23—68no—
679C23—68no—
680C23—62no—
681C23—62no—
682C23—62no—
683C23—62no—
684C23—62no—
685C23—62no—
686C23—124no—
687C23—124no—
688C23—124no—
689C23—124no—
690C23C2×D3×D412yes—
691C23C2×#23712yes—
692C23#100412yes—
693C23C2×D3×Q814yes—
694C23C2×D3×Q812yes—
695C23#100912yes—
696C23#100912yes—
697C23#101012yes—
698C23C24×D311yescharacteristic
699Q8—1216no—
700D4—1216no—
701C2×C4—28no—
702C2×C4—28no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—34no—
720C2×C4—34no—
721C2×C4—34no—
722C2×C4—44no—
723C2×C4—44no—
724C2×C4—44no—
725C2×C4—44no—
726C2×C4—68no—
727C2×C4—68no—
728C2×C4—68no—
729C2×C4—62no—
730C2×C4—62no—
731C2×C4—62no—
732C2×C4—62no—
733C2×C4—62no—
734C2×C4—62no—
735C2×C4—62no—
736C2×C4—62no—
737C2×C4—62no—
738C2×C4—62no—
739C2×C4—62no—
740C2×C4—62no—
741C2×C4—62no—
742C2×C4—62no—
743C2×C4—62no—
744C2×C4—62no—
745C2×C4—62no—
746C2×C4—62no—
747C2×C4—1216no—
748C2×C4—1216no—
749C2×C4—124no—
750C2×C4—124no—
751C2×C4—124no—
752C2×C4—124no—
753C2×C4C2×D3×D414yes—
754C2×C4C2×#23714yes—
755C2×C3—44no—
756C2×C3#273218yescomplemented
757C2×C3C2×#53411yescharacteristic
758C2×C3C2×#53911yescharacteristic
759C2×C3C2×#54311yescharacteristic
760C2×C3C2×D4×Q811yescharacteristic
761C2×C3C2×#55011yescharacteristic
762C2×C3C2×#55411yescharacteristic
763C2×C3C2×#56211yescharacteristic
764D3—44no—
765C22—24no—
766C22—24no—
767C22—24no—
768C22—416no—
769C22—42no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—64no—
774C22—64no—
775C22—64no—
776C22—1216no—
777C22—122no—
778C22—122no—
779C22—122no—
780C22—122no—
781C22#563214yes—
782C22#563414yes—
783C22#563514yes—
784C22#565314yes—
785C22#566514yes—
786C22#566714yes—
787C22#571814yes—
788C22C22×D3×D411yescharacteristic
789C22C22×#23711yescharacteristic
790C22C2×#100411yescharacteristic
791C22C22×D3×Q811yescharacteristic
792C22C2×#100911yescharacteristic
793C22C2×#100911yescharacteristic
794C22C2×#101011yescharacteristic
795C4—24no—
796C4—24no—
797C4—42no—
798C4—42no—
799C4—42no—
800C4—42no—
801C4—64no—
802C4—64no—
803C4—64no—
804C4—122no—
805C4—122no—
806C4—122no—
807C4—122no—
808C3C2×#273211yescharacteristic, complemented, Sylow
809C2—44no—
810C2—124no—
811C2#7811918yesdirect product factor
812C2C2×#563211yescharacteristic
813C2C2×#563511yescharacteristic
814C2C2×#563411yescharacteristic
815C2C2×#566511yescharacteristic
816C2C2×#565311yescharacteristic
817C2C2×#566711yescharacteristic
818C2C2×#571811yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC2×C3×#399C2
socleC24×C3C24
prime radicalC23×#67C22
hypercenterC2×#399D3
hypocenterC3C2×#2732
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#399

Complements

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

NH ≅ G/Ntype
1. C22×#897C2semidirect
2. C22×#878C2semidirect
3. C2×C3×#399C2semidirect
4. C2×#4993C2semidirect
5. C2×#4994C2semidirect
6. C2×#4983C2semidirect
7. C2×#4982C2semidirect
8. C2×#4984C2semidirect
10. C2×#4948C2semidirect
13. C2×#4950C2semidirect
14. #78119C2direct (N × H)
15. C2×#4668C2semidirect
16. C2×#4646C2semidirect
46. C2×#897C22semidirect
48. C2×#878C22semidirect
49. C3×#399C22semidirect
58. #4994C22semidirect
59. #4993C22semidirect
60. #4984C22semidirect
61. #4983C22semidirect
62. #4982C22semidirect
66. #4950C22semidirect
67. #4948C22semidirect
68. #4668C22semidirect
69. #4646C22semidirect
74. C2×#399D3semidirect
96. C22×#67Q8semidirect
115. C22×Dic6D4semidirect
205. #399C2×D3semidirect
269. C2×#67C2×Q8semidirect
309. C2×Dic6C2×D4semidirect
756. C2×C3#2732semidirect
808. C3C2×#2732semidirect
811. C2#78119direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#8972
C22×#8782
C2×C3×#3992
C2×#49932
C2×#49942
C2×#49832
C2×#49822
C2×#49842
C2×#49562
C2×#49482
C2×#49572
C2×#49582
C2×#49502
#781192
C2×#46682
C2×#46462
C2×#27323