Finite Group Databasebeta

← C2×#75178 #11430784

Subgroups — C2×#75178 #11430784

Order 768.

2742 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#888C211yesmaximal, characteristic, complemented
2C22×#875C211yesmaximal, characteristic
3C2×C3×#387C211yesmaximal, characteristic, complemented
4C2×#4994C211yesmaximal, characteristic, complemented
5C2×#4991C211yesmaximal, characteristic
6C2×#4990C211yesmaximal, characteristic, complemented
7C2×#4933C211yesmaximal, characteristic, complemented
8#75178C2116yesmaximal, direct product factor
9C2×#4676C211yesmaximal, characteristic, complemented
10C2×#4673C211yesmaximal, characteristic, complemented
11C2×#4673C211yesmaximal, characteristic, complemented
12C2×#4672C211yesmaximal, characteristic
13C2×#4646C211yesmaximal, characteristic, complemented
14C2×#4670C211yesmaximal, characteristic, complemented
15C2×#4669C211yesmaximal, characteristic, complemented
16C2×#4669C211yesmaximal, characteristic, complemented
17C2×#2731—31nomaximal, Sylow
18C23×D12C2211yescharacteristic
19C23×Dic6C2211yescharacteristic
20C23×Dic6C2211yescharacteristic
21C22×C3×C4⋊C4C2211yescharacteristic
22C22×C3×C4⋊C4C2211yescharacteristic
23C22×C3×C42C2211yescharacteristic
24C22×(C2×D3)⋊C4C2211yescharacteristic
25C22×(C2×D3)⋊C4C2211yescharacteristic
26C22×(C2×D3)⋊C4C2211yescharacteristic
27C22×(C2×D3)⋊C4C2211yescharacteristic
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×(C2×D3)⋊C4C2211yescharacteristic
35C22×(C2×D3)⋊C4C2211yescharacteristic
36C22×C4⋊Dic3C2211yescharacteristic
37C22×Dic3⋊C4C2211yescharacteristic
38C22×Dic3⋊C4C2211yescharacteristic
39C22×Dic3⋊C4C2211yescharacteristic
40C22×Dic3⋊C4C2211yescharacteristic
41C22×C4×Dic3C2211yescharacteristic
42C22×C4×Dic3C2211yescharacteristic
43C2×#888—28no—
44C2×#888C2218yescomplemented
45C2×#875—28no—
46C2×#875C2218yes—
47C3×#387C2218yescomplemented
48C2×C3×#95C2211yescharacteristic
49C2×C3×#95C2211yescharacteristic
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#4991C2218yes—
60#4990C2218yescomplemented
61#4933C2218yescomplemented
62#4676C2218yescomplemented
63#4673C2218yescomplemented
64#4673C2218yescomplemented
65#4672C2218yes—
66#4670C2218yescomplemented
67#4669C2218yescomplemented
68#4669C2218yescomplemented
69#4646C2218yescomplemented
70C22×C4⋊Q8—31no—
71C22×#124—31no—
72#2731—316no—
73C2×#396—31no—
74C2×#396—31no—
75C2×#394—31no—
76C2×#394—31no—
77C2×#393—31no—
78C2×#393—31no—
79C2×#391—31no—
80C2×#388—31no—
81C2×#388—31no—
82C2×#388—31no—
83C2×#388—31no—
84C2×#387—31no—
85C2×#387D311yescharacteristic, complemented
86C24×D3C2311yescharacteristic
87C24×D3C2311yescharacteristic
88C23×C3×C4C2311yescharacteristic
89C23×C3×C4C2311yescharacteristic
90C23×C3×C4C2311yescharacteristic
91C23×C3×C4C2311yescharacteristic
92C23×C3×C4C2311yescharacteristic
93C23×C3×C4C2311yescharacteristic
94C23×C3×C4C2311yescharacteristic
95C23×Dic3C2311yescharacteristic
96C23×Dic3C2311yescharacteristic
97C23×Dic3C2311yescharacteristic
98C23×Dic3C2311yescharacteristic
99C23×Dic3C2311yescharacteristic
100C23×Dic3C2311yescharacteristic
101C22×D12—24no—
102C22×D12—42no—
103C22×D12—42no—
104C22×D12C2314yes—
105C22×Dic6—24no—
106C22×Dic6—42no—
107C22×Dic6—42no—
108C22×Dic6—42no—
109C22×Dic6—42no—
110C22×Dic6D418yes—
111C22×Dic6C2314yes—
112C22×Dic6C2314yes—
113C2×C3×C4⋊C4—24no—
114C2×C3×C4⋊C4—24no—
115C2×C3×C4⋊C4C2314yes—
116C2×C3×C4⋊C4C2314yes—
117C2×C3×C42—24no—
118C2×C3×C42C2314yes—
119C2×(C2×D3)⋊C4—24no—
120C2×(C2×D3)⋊C4—24no—
121C2×(C2×D3)⋊C4—24no—
122C2×(C2×D3)⋊C4—24no—
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)⋊C4—42no—
130C2×(C2×D3)⋊C4—42no—
131C2×(C2×D3)⋊C4C2314yes—
132C2×(C2×D3)⋊C4C2314yes—
133C2×(C2×D3)⋊C4C2314yes—
134C2×(C2×D3)⋊C4C2314yes—
135C2×(C2×D3)⋊C4C2314yes—
136C2×(C2×D3)⋊C4C2314yes—
137C2×(C2×D3)⋊C4C2314yes—
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⋊Dic3C2314yes—
145C2×Dic3⋊C4—24no—
146C2×Dic3⋊C4—24no—
147C2×Dic3⋊C4—24no—
148C2×Dic3⋊C4—42no—
149C2×Dic3⋊C4C2314yes—
150C2×Dic3⋊C4C2314yes—
151C2×Dic3⋊C4C2314yes—
152C2×Dic3⋊C4C2314yes—
153C2×C4×Dic3—24no—
154C2×C4×Dic3—42no—
155C2×C4×Dic3C2314yes—
156C2×C4×Dic3C2314yes—
157#888—232no—
158#875—232no—
159C3×#95C2314yes—
160C3×#95C2314yes—
161C3×#95C2314yes—
162C3×#95C2314yes—
163C3⋊#95C2314yes—
164C3⋊#95C2314yes—
165C3⋊#95C2314yes—
166C3⋊#95C2314yes—
167C3⋊#95C2314yes—
168C3⋊#95C2314yes—
169C23×Q8—31no—
170C23×Q8—31no—
171C23×D4—31no—
172C2×C4⋊Q8—38no—
173C2×C4⋊Q8—68no—
174C2×#124—38no—
175C2×#124—68no—
176C22×C4⋊C4—31no—
177C22×C4⋊C4—31no—
178C22×C4⋊C4—31no—
179C22×C4⋊C4—31no—
180C22×C4⋊C4—31no—
181C22×C4⋊C4C2×D311yescharacteristic
182C22×C4⋊C4C2×D311yescharacteristic
183C22×C22⋊C4—31no—
184C22×C22⋊C4—31no—
185C22×C22⋊C4—31no—
186C22×C22⋊C4—31no—
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×C42—31no—
196C22×C42—31no—
197C22×C42C2×D311yescharacteristic
198#396—38no—
199#396—38no—
200#394—38no—
201#394—38no—
202#393—38no—
203#393—38no—
204#391—38no—
205#388—38no—
206#388—38no—
207#388—38no—
208#388—38no—
209#387—38no—
210#387C2×D318yescomplemented
211C2×#95—31no—
212C2×#95—31no—
213C2×#95—31no—
214C2×#95—31no—
215C2×#95—31no—
216C2×#95—31no—
217C2×#95C2×D311yescharacteristic
218C2×#95C2×D311yescharacteristic
219C2×#95C2×D311yescharacteristic
220C2×#95C2×D311yescharacteristic
221C24×C3C2411yescharacteristic
222C23×D3—22no—
223C23×D3—22no—
224C23×D3—22no—
225C23×D3—22no—
226C23×D3—22no—
227C23×D3—22no—
228C23×D3—22no—
229C23×D3—22no—
230C23×D3—22no—
231C23×D3—22no—
232C23×D3—22no—
233C23×D3—22no—
234C23×D3—22no—
235C23×D3—22no—
236C23×D3C2412yes—
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×C4—22no—
255C22×C3×C4—22no—
256C22×C3×C4—22no—
257C22×C3×C4C2×D414yes—
258C22×C3×C4#4114yes—
259C22×C3×C4C2412yes—
260C22×C3×C4C2412yes—
261C22×C3×C4C2412yes—
262C22×C3×C4C2412yes—
263C22×C3×C4C2412yes—
264C22×C3×C4C2412yes—
265C22×C3×C4C2412yes—
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×Dic3C2×D414yes—
282C22×Dic3C2×D414yes—
283C22×Dic3#4114yes—
284C22×Dic3C2412yes—
285C22×Dic3C2412yes—
286C22×Dic3C2412yes—
287C22×Dic3C2412yes—
288C22×Dic3C2412yes—
289C22×Dic3C2412yes—
290C2×D12—28no—
291C2×D12—44no—
292C2×D12—44no—
293C2×D12—416no—
294C2×Dic6—28no—
295C2×Dic6—416no—
296C2×Dic6—44no—
297C2×Dic6—44no—
298C2×Dic6—44no—
299C2×Dic6—44no—
300C2×Dic6—416no—
301C2×Dic6C2×D4116yes—
302C3×C4⋊C4—28no—
303C3×C4⋊C4—28no—
304C3×C42—28no—
305(C2×D3)⋊C4—28no—
306(C2×D3)⋊C4—28no—
307(C2×D3)⋊C4—28no—
308(C2×D3)⋊C4—28no—
309(C2×D3)⋊C4—28no—
310(C2×D3)⋊C4—28no—
311(C2×D3)⋊C4—28no—
312(C2×D3)⋊C4—28no—
313(C2×D3)⋊C4—44no—
314(C2×D3)⋊C4—44no—
315(C2×D3)⋊C4—44no—
316(C2×D3)⋊C4—44no—
317C4⋊Dic3—28no—
318Dic3⋊C4—28no—
319Dic3⋊C4—28no—
320Dic3⋊C4—28no—
321Dic3⋊C4—44no—
322C4×Dic3—28no—
323C4×Dic3—44no—
324C25—31no—
325C25—31no—
326C22×Q8—38no—
327C22×Q8—34no—
328C22×Q8—34no—
329C22×Q8—64no—
330C22×Q8—122no—
331C22×Q8—122no—
332C22×Q8—122no—
333C22×Q8—122no—
334C22×D4—34no—
335C22×D4—64no—
336C22×D4—122no—
337C22×D4—122no—
338C23×C4—31no—
339C23×C4—31no—
340C23×C4—31no—
341C23×C4—31no—
342C23×C4—31no—
343C23×C4—31no—
344C23×C4C22×D311yescharacteristic
345C23×C4C22×D311yescharacteristic
346C23×C4C22×D311yescharacteristic
347C23×C4C22×D311yescharacteristic
348C23×C4C22×D311yescharacteristic
349C23×C4C22×D311yescharacteristic
350C23×C4C22×D311yescharacteristic
351C4⋊Q8—632no—
352#124—632no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—34no—
356C2×C4⋊C4—34no—
357C2×C4⋊C4—34no—
358C2×C4⋊C4—34no—
359C2×C4⋊C4—34no—
360C2×C4⋊C4—64no—
361C2×C4⋊C4—64no—
362C2×C4⋊C4—64no—
363C2×C4⋊C4—64no—
364C2×C4⋊C4—122no—
365C2×C4⋊C4C22×D314yes—
366C2×C4⋊C4C22×D314yes—
367C2×C22⋊C4—34no—
368C2×C22⋊C4—34no—
369C2×C22⋊C4—34no—
370C2×C22⋊C4—34no—
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—64no—
380C2×C22⋊C4—64no—
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⋊C4—122no—
391C2×C42—24no—
392C2×C42—34no—
393C2×C42—34no—
394C2×C42—64no—
395C2×C42—122no—
396C2×C42C22×D314yes—
397#95—34no—
398#95—34no—
399#95—34no—
400#95—34no—
401#95—34no—
402#95—34no—
403#95C22×D314yes—
404#95C22×D314yes—
405#95C22×D314yes—
406#95C22×D314yes—
407C23×C3C22×D412yes—
408C23×C3C2×#4112yes—
409C23×C3C2×#4112yes—
410C23×C3H(5,𝔽2)12yes—
411C23×C3H(5,𝔽2)12yes—
412C23×C32−1+412yes—
413C23×C32−1+412yes—
414C23×C3C2511yescharacteristic
415C22×D3—22no—
416C22×D3—22no—
417C22×D3—22no—
418C22×D3—22no—
419C22×D3—22no—
420C22×D3—22no—
421C22×D3—22no—
422C22×D3—22no—
423C22×D3—22no—
424C22×D3—22no—
425C22×D3—22no—
426C22×D3—22no—
427C22×D3—22no—
428C22×D3—22no—
429C22×D3—44no—
430C22×D3—44no—
431C22×D3—44no—
432C22×D3—44no—
433C22×D3—44no—
434C22×D3—44no—
435C22×D3—44no—
436C22×D3—44no—
437C22×D3—44no—
438C22×D3—44no—
439C22×D3—44no—
440C22×D3—44no—
441C22×D3—44no—
442C22×D3—44no—
443C2×C3×C4—28no—
444C2×C3×C4—28no—
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—22no—
460C2×C3×C4—22no—
461C2×C3×C4—22no—
462C2×C3×C4—22no—
463C2×C3×C4—22no—
464C2×C3×C4—44no—
465C2×C3×C4—44no—
466C2×C3×C4—44no—
467C2×C3×C4—44no—
468C2×C3×C4—44no—
469C2×C3×C4C22×D414yes—
470C2×C3×C4C2×#4114yes—
471C2×Dic3—28no—
472C2×Dic3—28no—
473C2×Dic3—28no—
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—22no—
488C2×Dic3—22no—
489C2×Dic3—44no—
490C2×Dic3—44no—
491C2×Dic3—44no—
492C2×Dic3C22×D414yes—
493C2×Dic3C22×D414yes—
494C2×Dic3C2×#4114yes—
495D12—416no—
496Dic6—416no—
497Dic6—416no—
498C24—32no—
499C24—32no—
500C24—62no—
501C24—62no—
502C24—62no—
503C24—62no—
504C24—62no—
505C24—62no—
506C24—62no—
507C24—62no—
508C24—62no—
509C24—62no—
510C24—62no—
511C24—62no—
512C24—62no—
513C24—62no—
514C24C23×D311yescharacteristic
515C2×Q8—316no—
516C2×Q8—68no—
517C2×Q8—1216no—
518C2×Q8—124no—
519C2×Q8—124no—
520C2×Q8—124no—
521C2×Q8—124no—
522C2×Q8—1216no—
523C2×D4—68no—
524C2×D4—124no—
525C2×D4—124no—
526C2×D4—1216no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
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—34no—
547C22×C4—34no—
548C22×C4—34no—
549C22×C4—32no—
550C22×C4—32no—
551C22×C4—32no—
552C22×C4—32no—
553C22×C4—32no—
554C22×C4—32no—
555C22×C4—62no—
556C22×C4—62no—
557C22×C4—62no—
558C22×C4—62no—
559C22×C4—62no—
560C22×C4—62no—
561C22×C4—62no—
562C22×C4—62no—
563C22×C4—62no—
564C22×C4—62no—
565C22×C4—62no—
566C22×C4—62no—
567C22×C4—62no—
568C22×C4—62no—
569C22×C4—62no—
570C22×C4#23514yes—
571C22×C4D3×D414yes—
572C22×C4C23×D312yes—
573C22×C4C23×D312yes—
574C22×C4C23×D312yes—
575C22×C4C23×D312yes—
576C22×C4C23×D312yes—
577C22×C4C23×D312yes—
578C22×C4C23×D312yes—
579C4⋊C4—28no—
580C4⋊C4—28no—
581C4⋊C4—68no—
582C4⋊C4—68no—
583C4⋊C4—68no—
584C4⋊C4—68no—
585C4⋊C4—124no—
586C22⋊C4—68no—
587C22⋊C4—68no—
588C22⋊C4—68no—
589C22⋊C4—68no—
590C22⋊C4—68no—
591C22⋊C4—68no—
592C22⋊C4—68no—
593C22⋊C4—68no—
594C22⋊C4—124no—
595C22⋊C4—124no—
596C22⋊C4—124no—
597C22⋊C4—124no—
598C42—28no—
599C42—68no—
600C42—124no—
601C22×C3#53414yes—
602C22×C3#54214yes—
603C22×C3#54214yes—
604C22×C3#54814yes—
605C22×C3#54814yes—
606C22×C3#55514yes—
607C22×C3#56314yes—
608C22×C3C23×D411yescharacteristic
609C22×C3C22×#4111yescharacteristic
610C22×C3C22×#4111yescharacteristic
611C22×C3C2×H(5,𝔽2)11yescharacteristic
612C22×C3C2×H(5,𝔽2)11yescharacteristic
613C22×C3C2×2−1+411yescharacteristic
614C22×C3C2×2−1+411yescharacteristic
615C2×D3—42no—
616C2×D3—42no—
617C2×D3—42no—
618C2×D3—42no—
619C2×D3—42no—
620C2×D3—42no—
621C2×D3—42no—
622C2×D3—42no—
623C2×D3—42no—
624C2×D3—42no—
625C2×D3—42no—
626C2×D3—42no—
627C2×D3—42no—
628C2×D3—42no—
629C2×D3—88no—
630C2×D3—88no—
631C3×C4—24no—
632C3×C4—24no—
633C3×C4—42no—
634C3×C4—42no—
635C3×C4—42no—
636C3×C4—42no—
637C3×C4—42no—
638Dic3—24no—
639Dic3—24no—
640Dic3—24no—
641Dic3—42no—
642Dic3—42no—
643Dic3—42no—
644C23—62no—
645C23—62no—
646C23—62no—
647C23—62no—
648C23—62no—
649C23—62no—
650C23—62no—
651C23—62no—
652C23—62no—
653C23—62no—
654C23—62no—
655C23—62no—
656C23—62no—
657C23—62no—
658C23—124no—
659C23—124no—
660C23—124no—
661C23—124no—
662C23—124no—
663C23—124no—
664C23—124no—
665C23—124no—
666C23—124no—
667C23—124no—
668C23—124no—
669C23—124no—
670C23—124no—
671C23—124no—
672C23C2×#23512yes—
673C23C2×D3×D412yes—
674C23#100712yes—
675C23D3×#4112yes—
676C23#100912yes—
677C23#100912yes—
678C23#101012yes—
679C23C24×D311yescharacteristic
680Q8—1216no—
681Q8—1216no—
682D4—1216no—
683C2×C4—28no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—28no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—34no—
705C2×C4—34no—
706C2×C4—34no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—44no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—68no—
713C2×C4—68no—
714C2×C4—68no—
715C2×C4—62no—
716C2×C4—62no—
717C2×C4—62no—
718C2×C4—62no—
719C2×C4—62no—
720C2×C4—62no—
721C2×C4—62no—
722C2×C4—62no—
723C2×C4—62no—
724C2×C4—62no—
725C2×C4—62no—
726C2×C4—62no—
727C2×C4—62no—
728C2×C4—62no—
729C2×C4—62no—
730C2×C4—124no—
731C2×C4—124no—
732C2×C4—124no—
733C2×C4C2×#23514yes—
734C2×C4C2×D3×D414yes—
735C2×C3#273118yescomplemented
736C2×C3C2×#53411yescharacteristic
737C2×C3C2×#54211yescharacteristic
738C2×C3C2×#54211yescharacteristic
739C2×C3C2×#54811yescharacteristic
740C2×C3C2×#54811yescharacteristic
741C2×C3C2×#55511yescharacteristic
742C2×C3C2×#56311yescharacteristic
743D3—82no—
744D3—82no—
745C22—122no—
746C22—122no—
747C22—122no—
748C22—122no—
749C22—122no—
750C22—122no—
751C22—122no—
752C22—122no—
753C22—122no—
754C22—122no—
755C22—122no—
756C22—122no—
757C22—122no—
758C22—122no—
759C22—248no—
760C22—248no—
761C22#553214yes—
762C22#555214yes—
763C22#558214yes—
764C22#563314yes—
765C22#565314yes—
766C22#569914yes—
767C22#571014yes—
768C22C22×#23511yescharacteristic
769C22C22×D3×D411yescharacteristic
770C22C2×#100711yescharacteristic
771C22C2×D3×#4111yescharacteristic
772C22C2×#100911yescharacteristic
773C22C2×#100911yescharacteristic
774C22C2×#101011yescharacteristic
775C4—24no—
776C4—24no—
777C4—42no—
778C4—42no—
779C4—42no—
780C4—42no—
781C4—42no—
782C4—64no—
783C4—64no—
784C4—64no—
785C4—122no—
786C4—122no—
787C4—122no—
788C3C2×#273111yescharacteristic, complemented, Sylow
789C2—242no—
790C2—242no—
791C2#7517818yesdirect product factor
792C2C2×#553211yescharacteristic
793C2C2×#555211yescharacteristic
794C2C2×#558211yescharacteristic
795C2C2×#563311yescharacteristic
796C2C2×#565311yescharacteristic
797C2C2×#569911yescharacteristic
798C2C2×#571011yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC2×C3×#387C2
socleC24×C3C24
prime radicalC23×D12C22
hypercenterC2×#387D3
hypocenterC3C2×#2731
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
1. C22×#888C2semidirect
3. C2×C3×#387C2semidirect
4. C2×#4994C2semidirect
6. C2×#4990C2semidirect
7. C2×#4933C2semidirect
8. #75178C2direct (N × H)
9. C2×#4676C2semidirect
10. C2×#4673C2semidirect
11. C2×#4673C2semidirect
13. C2×#4646C2semidirect
14. C2×#4670C2semidirect
15. C2×#4669C2semidirect
16. C2×#4669C2semidirect
44. C2×#888C22semidirect
47. C3×#387C22semidirect
58. #4994C22semidirect
60. #4990C22semidirect
61. #4933C22semidirect
62. #4676C22semidirect
63. #4673C22semidirect
64. #4673C22semidirect
66. #4670C22semidirect
67. #4669C22semidirect
68. #4669C22semidirect
69. #4646C22semidirect
85. C2×#387D3semidirect
210. #387C2×D3semidirect
735. C2×C3#2731semidirect
788. C3C2×#2731semidirect
791. C2#75178direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#8882
C22×#8752
C2×C3×#3872
C2×#49942
C2×#49912
C2×#49902
C2×#49332
#751782
C2×#46762
C2×#46732
C2×#46722
C2×#46462
C2×#46702
C2×#46692
C2×#27313