Finite Group Databasebeta

← C2×#78072 #11430715

Subgroups — C2×#78072 #11430715

Order 768.

2614 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#898C211yesmaximal, characteristic, complemented
2C22×#879C211yesmaximal, characteristic, complemented
3C2×C3×#399C211yesmaximal, characteristic, complemented
4C2×#4993C211yesmaximal, characteristic, complemented
5C2×#4994C211yesmaximal, characteristic, complemented
6C2×#4976C211yesmaximal, characteristic, complemented
7C2×#4984C211yesmaximal, characteristic, complemented
8C2×#4972C211yesmaximal, characteristic, complemented
9C2×#4959C211yesmaximal, characteristic
10C2×#4948C211yesmaximal, characteristic, complemented
11C2×#4961C211yesmaximal, characteristic
12C2×#4957C211yesmaximal, characteristic
13C2×#4951C211yesmaximal, characteristic, complemented
14#78072C2116yesmaximal, direct product factor
15C2×#4647C211yesmaximal, characteristic, complemented
16C2×#4670C211yesmaximal, characteristic, complemented
17C2×#2727—31nomaximal, Sylow
18C23×#67C2211yescharacteristic
19C22×C3×C4⋊C4C2211yescharacteristic
20C22×C3×C4⋊C4C2211yescharacteristic
21C22×C3×C4⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×#217C2211yescharacteristic
26C22×#217C2211yescharacteristic
27C22×#217C2211yescharacteristic
28C22×(C2×D3)⋊C4C2211yescharacteristic
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×(C2×D3)⋊C4C2211yescharacteristic
31C22×(C2×D3)⋊C4C2211yescharacteristic
32C22×(C2×D3)⋊C4C2211yescharacteristic
33C22×(C2×D3)⋊C4C2211yescharacteristic
34C22×C4⋊Dic3C2211yescharacteristic
35C22×C4⋊Dic3C2211yescharacteristic
36C22×C4⋊Dic3C2211yescharacteristic
37C22×C4⋊Dic3C2211yescharacteristic
38C22×Dic3⋊C4C2211yescharacteristic
39C22×Dic3⋊C4C2211yescharacteristic
40C22×Dic3⋊C4C2211yescharacteristic
41C22×Dic3⋊C4C2211yescharacteristic
42C22×Dic3⋊C4C2211yescharacteristic
43C22×Dic3⋊C4C2211yescharacteristic
44C22×C4×Dic3C2211yescharacteristic
45C22×C4×Dic3C2211yescharacteristic
46C22×C4×Dic3C2211yescharacteristic
47C2×#898—28no—
48C2×#898C2218yescomplemented
49C2×#879—28no—
50C2×#879C2218yescomplemented
51C3×#399C2218yescomplemented
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#4976C2218yescomplemented
62#4972C2218yescomplemented
63#4961C2218yes—
64#4959C2218yes—
65#4957C2218yes—
66#4951C2218yescomplemented
67#4948C2218yescomplemented
68#4670C2218yescomplemented
69#4647C2218yescomplemented
70C22×#126—31no—
71C22×#126—31no—
72#2727—316no—
73C2×#399—31no—
74C2×#399D311yescharacteristic, complemented
75C2×#396—31no—
76C2×#396—31no—
77C2×#394—31no—
78C2×#394—31no—
79C2×#390—31no—
80C2×#389—31no—
81C2×#389—31no—
82C2×#389—31no—
83C2×#389—31no—
84C2×#388—31no—
85C2×#388—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—24no—
95C22×#67—42no—
96C22×#67—42no—
97C22×#67C2314yes—
98C23×Dic3C2311yescharacteristic
99C23×Dic3C2311yescharacteristic
100C23×Dic3C2311yescharacteristic
101C23×Dic3C2311yescharacteristic
102C23×Dic3C2311yescharacteristic
103C23×Dic3C2311yescharacteristic
104C23×Dic3C2311yescharacteristic
105C2×C3×C4⋊C4—24no—
106C2×C3×C4⋊C4—24no—
107C2×C3×C4⋊C4—42no—
108C2×C3×C4⋊C4C2314yes—
109C2×C3×C4⋊C4C2314yes—
110C2×C3×C4⋊C4C2314yes—
111C2×C3×C22⋊C4—24no—
112C2×C3×C22⋊C4—24no—
113C2×C3×C22⋊C4—42no—
114C2×C3×C22⋊C4C2314yes—
115C2×C3×C22⋊C4C2314yes—
116C2×C3×C22⋊C4C2314yes—
117C2×#217—24no—
118C2×#217—24no—
119C2×#217—42no—
120C2×#217C2314yes—
121C2×#217C2314yes—
122C2×#217C2314yes—
123C2×(C2×D3)⋊C4—24no—
124C2×(C2×D3)⋊C4—24no—
125C2×(C2×D3)⋊C4—24no—
126C2×(C2×D3)⋊C4—24no—
127C2×(C2×D3)⋊C4—42no—
128C2×(C2×D3)⋊C4—42no—
129C2×(C2×D3)⋊C4C2314yes—
130C2×(C2×D3)⋊C4C2314yes—
131C2×(C2×D3)⋊C4C2314yes—
132C2×(C2×D3)⋊C4C2314yes—
133C2×(C2×D3)⋊C4C2314yes—
134C2×(C2×D3)⋊C4C2314yes—
135C2×C4⋊Dic3—24no—
136C2×C4⋊Dic3—24no—
137C2×C4⋊Dic3—24no—
138C2×C4⋊Dic3—42no—
139C2×C4⋊Dic3C2314yes—
140C2×C4⋊Dic3C2314yes—
141C2×C4⋊Dic3C2314yes—
142C2×C4⋊Dic3C2314yes—
143C2×Dic3⋊C4—24no—
144C2×Dic3⋊C4—24no—
145C2×Dic3⋊C4—42no—
146C2×Dic3⋊C4—42no—
147C2×Dic3⋊C4—42no—
148C2×Dic3⋊C4D418yescomplemented
149C2×Dic3⋊C4C2314yes—
150C2×Dic3⋊C4C2314yes—
151C2×Dic3⋊C4C2314yes—
152C2×Dic3⋊C4C2314yes—
153C2×Dic3⋊C4C2314yes—
154C2×Dic3⋊C4C2314yes—
155C2×C4×Dic3—24no—
156C2×C4×Dic3—24no—
157C2×C4×Dic3—42no—
158C2×C4×Dic3C2314yes—
159C2×C4×Dic3C2314yes—
160C2×C4×Dic3C2314yes—
161#898—232no—
162#879—232no—
163C3×#95C2314yes—
164C3⋊#95C2314yes—
165C3⋊#95C2314yes—
166C3⋊#95C2314yes—
167C3⋊#95C2314yes—
168C3⋊#95C2314yes—
169C23×D4—31no—
170C2×#126—38no—
171C2×#126—38no—
172C2×#126—68no—
173C2×#126—68no—
174C22×C4⋊C4—31no—
175C22×C4⋊C4—31no—
176C22×C4⋊C4—31no—
177C22×C4⋊C4—31no—
178C22×C4⋊C4—31no—
179C22×C4⋊C4—31no—
180C22×C4⋊C4—31no—
181C22×C4⋊C4—31no—
182C22×C4⋊C4—31no—
183C22×C4⋊C4—31no—
184C22×C4⋊C4C2×D311yescharacteristic
185C22×C4⋊C4C2×D311yescharacteristic
186C22×C4⋊C4C2×D311yescharacteristic
187C22×C22⋊C4—31no—
188C22×C22⋊C4—31no—
189C22×C22⋊C4—31no—
190C22×C22⋊C4—31no—
191C22×C22⋊C4—31no—
192C22×C22⋊C4—31no—
193C22×C22⋊C4—31no—
194C22×C22⋊C4—31no—
195C22×C22⋊C4—31no—
196C22×C22⋊C4C2×D311yescharacteristic
197C22×C22⋊C4C2×D311yescharacteristic
198C22×C22⋊C4C2×D311yescharacteristic
199C22×C42—31no—
200C22×C42—31no—
201C22×C42—31no—
202#399—38no—
203#399C2×D318yescomplemented
204#396—38no—
205#396—38no—
206#394—38no—
207#394—38no—
208#390—38no—
209#389—38no—
210#389—38no—
211#389—38no—
212#389—38no—
213#388—38no—
214#388—38no—
215C2×#95—31no—
216C2×#95—31no—
217C2×#95—31no—
218C2×#95—31no—
219C2×#95—31no—
220C2×#95C2×D311yescharacteristic
221C24×C3—22no—
222C24×C3—22no—
223C24×C3—22no—
224C24×C3—22no—
225C24×C3—22no—
226C24×C3—22no—
227C24×C3—22no—
228C24×C3C2412yes—
229C24×C3C2411yescharacteristic
230C23×D3—22no—
231C23×D3—22no—
232C23×D3—22no—
233C23×D3—22no—
234C23×D3—22no—
235C23×D3—22no—
236C23×D3—22no—
237C23×D3C2412yes—
238C22×C3×C4—22no—
239C22×C3×C4—22no—
240C22×C3×C4—22no—
241C22×C3×C4—22no—
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×C4C2×D414yes—
255C22×C3×C4#4114yes—
256C22×C3×C4C2412yes—
257C22×C3×C4C2412yes—
258C22×C3×C4C2412yes—
259C22×C3×C4C2412yes—
260C22×C3×C4C2412yes—
261C22×C3×C4C2412yes—
262C2×#67—28no—
263C2×#67—44no—
264C2×#67—44no—
265C2×#67—416no—
266C22×Dic3—22no—
267C22×Dic3—22no—
268C22×Dic3—22no—
269C22×Dic3—22no—
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×Dic3C2×D414yes—
285C22×Dic3C2×D414yes—
286C22×Dic3#4114yes—
287C22×Dic3C2412yes—
288C22×Dic3C2412yes—
289C22×Dic3C2412yes—
290C22×Dic3C2412yes—
291C22×Dic3C2412yes—
292C22×Dic3C2412yes—
293C22×Dic3C2412yes—
294C3×C4⋊C4—28no—
295C3×C4⋊C4—28no—
296C3×C4⋊C4—44no—
297C3×C22⋊C4—28no—
298C3×C22⋊C4—28no—
299C3×C22⋊C4—44no—
300#217—28no—
301#217—28no—
302#217—44no—
303(C2×D3)⋊C4—28no—
304(C2×D3)⋊C4—28no—
305(C2×D3)⋊C4—28no—
306(C2×D3)⋊C4—28no—
307(C2×D3)⋊C4—44no—
308(C2×D3)⋊C4—44no—
309C4⋊Dic3—28no—
310C4⋊Dic3—28no—
311C4⋊Dic3—28no—
312C4⋊Dic3—44no—
313Dic3⋊C4—28no—
314Dic3⋊C4—28no—
315Dic3⋊C4—44no—
316Dic3⋊C4—44no—
317Dic3⋊C4—44no—
318Dic3⋊C4C2×D4116yescomplemented
319C4×Dic3—28no—
320C4×Dic3—28no—
321C4×Dic3—44no—
322C25—31no—
323C25C22×D311yescharacteristic
324C22×D4—34no—
325C22×D4—64no—
326C22×D4—122no—
327C22×D4—122no—
328C23×C4—31no—
329C23×C4—31no—
330C23×C4—31no—
331C23×C4—31no—
332C23×C4—31no—
333C23×C4—31no—
334C23×C4—31no—
335C23×C4C22×D311yescharacteristic
336C23×C4C22×D311yescharacteristic
337C23×C4C22×D311yescharacteristic
338C23×C4C22×D311yescharacteristic
339C23×C4C22×D311yescharacteristic
340C23×C4C22×D311yescharacteristic
341#126—632no—
342#126—632no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—38no—
346C2×C4⋊C4—34no—
347C2×C4⋊C4—34no—
348C2×C4⋊C4—34no—
349C2×C4⋊C4—34no—
350C2×C4⋊C4—34no—
351C2×C4⋊C4—34no—
352C2×C4⋊C4—34no—
353C2×C4⋊C4—34no—
354C2×C4⋊C4—34no—
355C2×C4⋊C4—34no—
356C2×C4⋊C4—42no—
357C2×C4⋊C4—64no—
358C2×C4⋊C4—64no—
359C2×C4⋊C4—64no—
360C2×C4⋊C4—64no—
361C2×C4⋊C4—64no—
362C2×C4⋊C4—122no—
363C2×C4⋊C4—122no—
364C2×C4⋊C4—122no—
365C2×C4⋊C4—122no—
366C2×C4⋊C4C22×D314yes—
367C2×C4⋊C4C22×D314yes—
368C2×C4⋊C4C22×D314yes—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—34no—
372C2×C22⋊C4—34no—
373C2×C22⋊C4—34no—
374C2×C22⋊C4—34no—
375C2×C22⋊C4—34no—
376C2×C22⋊C4—34no—
377C2×C22⋊C4—34no—
378C2×C22⋊C4—34no—
379C2×C22⋊C4—34no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4—64no—
382C2×C22⋊C4—64no—
383C2×C22⋊C4—64no—
384C2×C22⋊C4—64no—
385C2×C22⋊C4—64no—
386C2×C22⋊C4—64no—
387C2×C22⋊C4—122no—
388C2×C22⋊C4—122no—
389C2×C22⋊C4—122no—
390C2×C22⋊C4C22×D314yes—
391C2×C22⋊C4C22×D314yes—
392C2×C22⋊C4C22×D314yes—
393C2×C42—34no—
394C2×C42—34no—
395C2×C42—34no—
396C2×C42—64no—
397C2×C42—64no—
398C2×C42—122no—
399#95—34no—
400#95—34no—
401#95—34no—
402#95—34no—
403#95—34no—
404#95C22×D314yes—
405C23×C3—22no—
406C23×C3—22no—
407C23×C3—22no—
408C23×C3—22no—
409C23×C3—22no—
410C23×C3—22no—
411C23×C3—22no—
412C23×C3—44no—
413C23×C3—44no—
414C23×C3—44no—
415C23×C3—44no—
416C23×C3—44no—
417C23×C3—44no—
418C23×C3—44no—
419C23×C3C22×D412yes—
420C23×C3C2×#4112yes—
421C23×C3C2×#4112yes—
422C23×C3H(5,𝔽2)12yes—
423C23×C3H(5,𝔽2)12yes—
424C23×C32−1+412yes—
425C23×C32−1+412yes—
426C23×C3C2511yescharacteristic
427C22×D3—22no—
428C22×D3—22no—
429C22×D3—22no—
430C22×D3—22no—
431C22×D3—22no—
432C22×D3—22no—
433C22×D3—22no—
434C22×D3—44no—
435C22×D3—44no—
436C22×D3—44no—
437C22×D3—44no—
438C22×D3—44no—
439C22×D3—44no—
440C22×D3—44no—
441C2×C3×C4—28no—
442C2×C3×C4—28no—
443C2×C3×C4—22no—
444C2×C3×C4—22no—
445C2×C3×C4—22no—
446C2×C3×C4—22no—
447C2×C3×C4—22no—
448C2×C3×C4—22no—
449C2×C3×C4—22no—
450C2×C3×C4—22no—
451C2×C3×C4—22no—
452C2×C3×C4—22no—
453C2×C3×C4—22no—
454C2×C3×C4—22no—
455C2×C3×C4—22no—
456C2×C3×C4—22no—
457C2×C3×C4—22no—
458C2×C3×C4—22no—
459C2×C3×C4—44no—
460C2×C3×C4—44no—
461C2×C3×C4—44no—
462C2×C3×C4—44no—
463C2×C3×C4C22×D414yes—
464C2×C3×C4C2×#4114yes—
465#67—416no—
466C2×Dic3—28no—
467C2×Dic3—28no—
468C2×Dic3—28no—
469C2×Dic3—22no—
470C2×Dic3—22no—
471C2×Dic3—22no—
472C2×Dic3—22no—
473C2×Dic3—22no—
474C2×Dic3—22no—
475C2×Dic3—22no—
476C2×Dic3—22no—
477C2×Dic3—22no—
478C2×Dic3—22no—
479C2×Dic3—22no—
480C2×Dic3—22no—
481C2×Dic3—22no—
482C2×Dic3—22no—
483C2×Dic3—22no—
484C2×Dic3—22no—
485C2×Dic3—22no—
486C2×Dic3—22no—
487C2×Dic3—44no—
488C2×Dic3—44no—
489C2×Dic3—44no—
490C2×Dic3—44no—
491C2×Dic3C22×D414yes—
492C2×Dic3C22×D414yes—
493C2×Dic3C2×#4114yes—
494C24—22no—
495C24—22no—
496C24—22no—
497C24—22no—
498C24—22no—
499C24—22no—
500C24—22no—
501C24—32no—
502C24—62no—
503C24—62no—
504C24—62no—
505C24—62no—
506C24—62no—
507C24—62no—
508C24—62no—
509C24C23×D312yes—
510C24C23×D311yescharacteristic
511C2×D4—68no—
512C2×D4—124no—
513C2×D4—124no—
514C2×D4—1216no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—34no—
532C22×C4—34no—
533C22×C4—34no—
534C22×C4—32no—
535C22×C4—32no—
536C22×C4—32no—
537C22×C4—32no—
538C22×C4—32no—
539C22×C4—32no—
540C22×C4—32no—
541C22×C4—62no—
542C22×C4—62no—
543C22×C4—62no—
544C22×C4—62no—
545C22×C4—62no—
546C22×C4—62no—
547C22×C4—62no—
548C22×C4—62no—
549C22×C4—62no—
550C22×C4—62no—
551C22×C4—62no—
552C22×C4—62no—
553C22×C4—62no—
554C22×C4—62no—
555C22×C4—62no—
556C22×C4—62no—
557C22×C4—62no—
558C22×C4—62no—
559C22×C4D3×D414yes—
560C22×C4#23714yes—
561C22×C4C23×D312yes—
562C22×C4C23×D312yes—
563C22×C4C23×D312yes—
564C22×C4C23×D312yes—
565C22×C4C23×D312yes—
566C22×C4C23×D312yes—
567C4⋊C4—28no—
568C4⋊C4—28no—
569C4⋊C4—316no—
570C4⋊C4—44no—
571C4⋊C4—68no—
572C4⋊C4—68no—
573C4⋊C4—68no—
574C4⋊C4—68no—
575C4⋊C4—68no—
576C4⋊C4—124no—
577C4⋊C4—124no—
578C4⋊C4—124no—
579C4⋊C4—124no—
580C22⋊C4—28no—
581C22⋊C4—28no—
582C22⋊C4—44no—
583C22⋊C4—68no—
584C22⋊C4—68no—
585C22⋊C4—68no—
586C22⋊C4—68no—
587C22⋊C4—68no—
588C22⋊C4—68no—
589C22⋊C4—124no—
590C22⋊C4—124no—
591C22⋊C4—124no—
592C42—68no—
593C42—68no—
594C42—124no—
595C22×C3—42no—
596C22×C3—42no—
597C22×C3—42no—
598C22×C3—42no—
599C22×C3—42no—
600C22×C3—42no—
601C22×C3—42no—
602C22×C3—88no—
603C22×C3#53714yes—
604C22×C3#53814yes—
605C22×C3#53914yes—
606C22×C3#54714yes—
607C22×C3#55014yes—
608C22×C3#55614yes—
609C22×C3#56314yes—
610C22×C3C23×D411yescharacteristic
611C22×C3C22×#4111yescharacteristic
612C22×C3C22×#4111yescharacteristic
613C22×C3C2×H(5,𝔽2)11yescharacteristic
614C22×C3C2×H(5,𝔽2)11yescharacteristic
615C22×C3C2×2−1+411yescharacteristic
616C22×C3C2×2−1+411yescharacteristic
617C2×D3—42no—
618C2×D3—42no—
619C2×D3—42no—
620C2×D3—42no—
621C2×D3—42no—
622C2×D3—42no—
623C2×D3—42no—
624C2×D3—88no—
625C3×C4—24no—
626C3×C4—24no—
627C3×C4—42no—
628C3×C4—42no—
629C3×C4—42no—
630C3×C4—42no—
631Dic3—24no—
632Dic3—24no—
633Dic3—24no—
634Dic3—42no—
635Dic3—42no—
636Dic3—42no—
637Dic3—42no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—44no—
646C23—44no—
647C23—44no—
648C23—44no—
649C23—44no—
650C23—44no—
651C23—44no—
652C23—62no—
653C23—62no—
654C23—62no—
655C23—62no—
656C23—62no—
657C23—62no—
658C23—62no—
659C23—124no—
660C23—124no—
661C23—124no—
662C23—124no—
663C23—124no—
664C23—124no—
665C23—124no—
666C23C2×D3×D412yes—
667C23C2×#23712yes—
668C23#100412yes—
669C23#100712yes—
670C23D3×#4112yes—
671C23#100912yes—
672C23#101012yes—
673C23C24×D311yescharacteristic
674D4—1216no—
675C2×C4—28no—
676C2×C4—28no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—34no—
694C2×C4—34no—
695C2×C4—34no—
696C2×C4—44no—
697C2×C4—44no—
698C2×C4—44no—
699C2×C4—44no—
700C2×C4—68no—
701C2×C4—68no—
702C2×C4—62no—
703C2×C4—62no—
704C2×C4—62no—
705C2×C4—62no—
706C2×C4—62no—
707C2×C4—62no—
708C2×C4—68no—
709C2×C4—62no—
710C2×C4—62no—
711C2×C4—62no—
712C2×C4—62no—
713C2×C4—62no—
714C2×C4—62no—
715C2×C4—62no—
716C2×C4—62no—
717C2×C4—62no—
718C2×C4—62no—
719C2×C4—62no—
720C2×C4—62no—
721C2×C4—124no—
722C2×C4—124no—
723C2×C4—124no—
724C2×C4—124no—
725C2×C4C2×D3×D414yes—
726C2×C4C2×#23714yes—
727C2×C3—82no—
728C2×C3#272718yescomplemented
729C2×C3C2×#53711yescharacteristic
730C2×C3C2×#53811yescharacteristic
731C2×C3C2×#53911yescharacteristic
732C2×C3C2×#54711yescharacteristic
733C2×C3C2×#55011yescharacteristic
734C2×C3C2×#55611yescharacteristic
735C2×C3C2×#56311yescharacteristic
736D3—82no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—88no—
745C22—122no—
746C22—122no—
747C22—122no—
748C22—122no—
749C22—122no—
750C22—122no—
751C22—122no—
752C22—248no—
753C22#562914yes—
754C22#564114yes—
755C22#564614yes—
756C22#565514yes—
757C22#565714yes—
758C22#566514yes—
759C22#571814yes—
760C22C22×D3×D411yescharacteristic
761C22C22×#23711yescharacteristic
762C22C2×#100411yescharacteristic
763C22C2×#100711yescharacteristic
764C22C2×D3×#4111yescharacteristic
765C22C2×#100911yescharacteristic
766C22C2×#101011yescharacteristic
767C4—24no—
768C4—24no—
769C4—42no—
770C4—42no—
771C4—42no—
772C4—42no—
773C4—64no—
774C4—64no—
775C4—64no—
776C4—122no—
777C4—122no—
778C4—122no—
779C4—122no—
780C3C2×#272711yescharacteristic, complemented, Sylow
781C2—82no—
782C2—242no—
783C2#7807218yesdirect product factor
784C2C2×#564111yescharacteristic
785C2C2×#564611yescharacteristic
786C2C2×#562911yescharacteristic
787C2C2×#566511yescharacteristic
788C2C2×#565711yescharacteristic
789C2C2×#565511yescharacteristic
790C2C2×#571811yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC2×C3×#399C2
socleC24×C3C24
prime radicalC23×#67C22
hypercenterC2×#399D3
hypocenterC3C2×#2727
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#399

Complements

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

NH ≅ G/Ntype
1. C22×#898C2semidirect
2. C22×#879C2semidirect
3. C2×C3×#399C2semidirect
4. C2×#4993C2semidirect
5. C2×#4994C2semidirect
6. C2×#4976C2semidirect
7. C2×#4984C2semidirect
8. C2×#4972C2semidirect
10. C2×#4948C2semidirect
13. C2×#4951C2semidirect
14. #78072C2direct (N × H)
15. C2×#4647C2semidirect
16. C2×#4670C2semidirect
48. C2×#898C22semidirect
50. C2×#879C22semidirect
51. C3×#399C22semidirect
58. #4994C22semidirect
59. #4993C22semidirect
60. #4984C22semidirect
61. #4976C22semidirect
62. #4972C22semidirect
66. #4951C22semidirect
67. #4948C22semidirect
68. #4670C22semidirect
69. #4647C22semidirect
74. C2×#399D3semidirect
148. C2×Dic3⋊C4D4semidirect
203. #399C2×D3semidirect
318. Dic3⋊C4C2×D4semidirect
728. C2×C3#2727semidirect
780. C3C2×#2727semidirect
783. C2#78072direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#8982
C22×#8792
C2×C3×#3992
C2×#49932
C2×#49942
C2×#49762
C2×#49842
C2×#49722
C2×#49592
C2×#49482
C2×#49612
C2×#49572
C2×#49512
#780722
C2×#46472
C2×#46702
C2×#27273