Finite Group Databasebeta

← C2×#19142699 #25302791

Subgroups — C2×#19142699 #25302791

Order 11008.

2218 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19142699C2116yesmaximal, direct product factor
2C2×#14582840C211yesmaximal, characteristic, complemented
3C2×#14582840C211yesmaximal, characteristic, complemented
4C2×#14582835C211yesmaximal, characteristic, complemented
5C2×#14582833C211yesmaximal, characteristic, complemented
6C2×#14582833C211yesmaximal, characteristic, complemented
7C2×#14582827C211yesmaximal, characteristic, complemented
8C2×#14582827C211yesmaximal, characteristic, complemented
9C2×#14582824C211yesmaximal, characteristic, complemented
10C2×#14582822C211yesmaximal, characteristic, complemented
11C2×#14582822C211yesmaximal, characteristic, complemented
12C2×#14582813C211yesmaximal, characteristic
13C2×#14582813C211yesmaximal, characteristic
14C2×#14582772C211yesmaximal, characteristic, complemented
15C2×#14582772C211yesmaximal, characteristic, complemented
16C2×C43×#386C211yesmaximal, characteristic
17C22×C4⋊Dic43C2211yescharacteristic
18C22×C4⋊Dic43C2211yescharacteristic
19C22×Dic43⋊C4C2211yescharacteristic
20C22×Dic43⋊C4C2211yescharacteristic
21C22×Dic43⋊C4C2211yescharacteristic
22C22×Dic43⋊C4C2211yescharacteristic
23C22×Dic43⋊C4C2211yescharacteristic
24C22×Dic43⋊C4C2211yescharacteristic
25C22×Dic43⋊C4C2211yescharacteristic
26C22×Dic43⋊C4C2211yescharacteristic
27C22×C22⋊Dic43C2211yescharacteristic
28C22×C22⋊Dic43C2211yescharacteristic
29C22×C22⋊Dic43C2211yescharacteristic
30C22×C22⋊Dic43C2211yescharacteristic
31C22×C22⋊Dic43C2211yescharacteristic
32C22×C22⋊Dic43C2211yescharacteristic
33C22×C22⋊Dic43C2211yescharacteristic
34C22×C22⋊Dic43C2211yescharacteristic
35#14582840C2218yescomplemented
36#14582840C2218yescomplemented
37#14582835C2218yescomplemented
38#14582833C2218yescomplemented
39#14582833C2218yescomplemented
40#14582827C2218yescomplemented
41#14582827C2218yescomplemented
42#14582824C2218yescomplemented
43#14582822C2218yescomplemented
44#14582822C2218yescomplemented
45#14582813C2218yes—
46#14582813C2218yes—
47#14582772C2218yescomplemented
48#14582772C2218yescomplemented
49C2×C43⋊#95C2211yescharacteristic
50C2×C43⋊#95C2211yescharacteristic
51C2×C43⋊#95C2211yescharacteristic
52C2×C43⋊#95C2211yescharacteristic
53C2×C43⋊#95C2211yescharacteristic
54C2×C43⋊#95C2211yescharacteristic
55C2×C43⋊#95C2211yescharacteristic
56C2×C43⋊#95C2211yescharacteristic
57C2×C43⋊#95C2211yescharacteristic
58C2×C43⋊#95C2211yescharacteristic
59C23×D4×C43C2211yescharacteristic
60C24×C4×C43C2211yescharacteristic
61C22×C22⋊C4×C43C2211yescharacteristic
62C22×C22⋊C4×C43C2211yescharacteristic
63C22×C22⋊C4×C43C2211yescharacteristic
64C43×#386C2218yes—
65C2×#95×C43C2211yescharacteristic
66C2×#95×C43C2211yescharacteristic
67C23×Dic43C2311yescharacteristic
68C23×Dic43C2311yescharacteristic
69C23×Dic43C2311yescharacteristic
70C23×Dic43C2311yescharacteristic
71C23×Dic43C2311yescharacteristic
72C23×Dic43C2311yescharacteristic
73C23×Dic43C2311yescharacteristic
74C23×Dic43C2311yescharacteristic
75C2×C4⋊Dic43—42no—
76C2×C4⋊Dic43—42no—
77C2×C4⋊Dic43C2314yes—
78C2×C4⋊Dic43C2314yes—
79C2×Dic43⋊C4—42no—
80C2×Dic43⋊C4—42no—
81C2×Dic43⋊C4—42no—
82C2×Dic43⋊C4—42no—
83C2×Dic43⋊C4—42no—
84C2×Dic43⋊C4—42no—
85C2×Dic43⋊C4—42no—
86C2×Dic43⋊C4—42no—
87C2×Dic43⋊C4C2314yes—
88C2×Dic43⋊C4C2314yes—
89C2×Dic43⋊C4C2314yes—
90C2×Dic43⋊C4C2314yes—
91C2×Dic43⋊C4C2314yes—
92C2×Dic43⋊C4C2314yes—
93C2×Dic43⋊C4C2314yes—
94C2×Dic43⋊C4C2314yes—
95C2×C22⋊Dic43—24no—
96C2×C22⋊Dic43—24no—
97C2×C22⋊Dic43—42no—
98C2×C22⋊Dic43—42no—
99C2×C22⋊Dic43—42no—
100C2×C22⋊Dic43—42no—
101C2×C22⋊Dic43—42no—
102C2×C22⋊Dic43—42no—
103C2×C22⋊Dic43C2314yes—
104C2×C22⋊Dic43C2314yes—
105C2×C22⋊Dic43C2314yes—
106C2×C22⋊Dic43C2314yes—
107C2×C22⋊Dic43C2314yes—
108C2×C22⋊Dic43C2314yes—
109C2×C22⋊Dic43C2314yes—
110C2×C22⋊Dic43C2314yes—
111C43⋊#95C2314yes—
112C43⋊#95C2314yes—
113C43⋊#95C2314yes—
114C43⋊#95C2314yes—
115C43⋊#95C2314yes—
116C43⋊#95C2314yes—
117C43⋊#95C2314yes—
118C43⋊#95C2314yes—
119C43⋊#95C2314yes—
120C43⋊#95C2314yes—
121C25×C43C2311yescharacteristic
122C25×C43C2311yescharacteristic
123C22×D4×C43—24no—
124C22×D4×C43—42no—
125C22×D4×C43—42no—
126C22×D4×C43C2314yes—
127C23×C4×C43—42no—
128C23×C4×C43—42no—
129C23×C4×C43—42no—
130C23×C4×C43C2311yescharacteristic
131C23×C4×C43C2311yescharacteristic
132C23×C4×C43C2311yescharacteristic
133C23×C4×C43C2311yescharacteristic
134C23×C4×C43C2311yescharacteristic
135C23×C4×C43C2314yes—
136C2×C22⋊C4×C43—42no—
137C2×C22⋊C4×C43—42no—
138C2×C22⋊C4×C43—42no—
139C2×C22⋊C4×C43C2314yes—
140C2×C22⋊C4×C43C2314yes—
141C2×C22⋊C4×C43C2314yes—
142#95×C43C2314yes—
143#95×C43C2314yes—
144C24×C43—22no—
145C24×C43—22no—
146C24×C43—22no—
147C24×C43—22no—
148C24×C43—22no—
149C24×C43—22no—
150C24×C43—22no—
151C24×C43—22no—
152C24×C43—22no—
153C24×C43—22no—
154C24×C43—22no—
155C24×C43—22no—
156C24×C43—22no—
157C24×C43#4114yes—
158C24×C43C2412yes—
159C24×C43C2412yes—
160C24×C43C2411yescharacteristic
161C2×D4×C43—28no—
162C2×D4×C43—44no—
163C2×D4×C43—44no—
164C2×D4×C43—416no—
165C22×C4×C43—22no—
166C22×C4×C43—22no—
167C22×C4×C43—22no—
168C22×C4×C43—22no—
169C22×C4×C43—22no—
170C22×C4×C43—22no—
171C22×C4×C43—22no—
172C22×C4×C43—22no—
173C22×C4×C43—22no—
174C22×C4×C43—22no—
175C22×C4×C43—22no—
176C22×C4×C43—22no—
177C22×C4×C43—22no—
178C22×C4×C43—22no—
179C22×C4×C43—22no—
180C22×C4×C43—44no—
181C22×C4×C43—44no—
182C22×C4×C43—44no—
183C22×C4×C43—416no—
184C22×C4×C43C2412yes—
185C22×C4×C43C2412yes—
186C22×C4×C43C2412yes—
187C22×C4×C43C2412yes—
188C22×C4×C43C2412yes—
189C22×Dic43—22no—
190C22×Dic43—22no—
191C22×Dic43—22no—
192C22×Dic43—22no—
193C22×Dic43—22no—
194C22×Dic43—22no—
195C22×Dic43—22no—
196C22×Dic43—22no—
197C22×Dic43—22no—
198C22×Dic43—22no—
199C22×Dic43—22no—
200C22×Dic43—22no—
201C22×Dic43—22no—
202C22×Dic43—22no—
203C22×Dic43—22no—
204C22×Dic43—22no—
205C22×Dic43—22no—
206C22×Dic43—22no—
207C22×Dic43—22no—
208C22×Dic43—22no—
209C22×Dic43—22no—
210C22×Dic43—22no—
211C22×Dic43—22no—
212C22×Dic43—22no—
213C22×Dic43C2412yes—
214C22×Dic43C2412yes—
215C22×Dic43C2412yes—
216C22×Dic43C2412yes—
217C22×Dic43C2412yes—
218C22×Dic43C2412yes—
219C22×Dic43C2412yes—
220C22×Dic43C2412yes—
221C22⋊C4×C43—44no—
222C22⋊C4×C43—44no—
223C22⋊C4×C43—44no—
224C22⋊Dic43—28no—
225C22⋊Dic43—28no—
226C22⋊Dic43—44no—
227C22⋊Dic43—44no—
228C22⋊Dic43—44no—
229C22⋊Dic43—44no—
230C22⋊Dic43—44no—
231C22⋊Dic43—44no—
232C4⋊Dic43—44no—
233C4⋊Dic43—44no—
234Dic43⋊C4—44no—
235Dic43⋊C4—44no—
236Dic43⋊C4—44no—
237Dic43⋊C4—44no—
238Dic43⋊C4—44no—
239Dic43⋊C4—44no—
240Dic43⋊C4—44no—
241Dic43⋊C4—44no—
242C23×C43—28no—
243C23×C43—28no—
244C23×C43—28no—
245C23×C43—22no—
246C23×C43—22no—
247C23×C43—22no—
248C23×C43—22no—
249C23×C43—22no—
250C23×C43—22no—
251C23×C43—22no—
252C23×C43—22no—
253C23×C43—22no—
254C23×C43—22no—
255C23×C43—22no—
256C23×C43—22no—
257C23×C43—22no—
258C23×C43—44no—
259C23×C43—44no—
260C23×C43—44no—
261C23×C43—44no—
262C23×C43—44no—
263C23×C43—44no—
264C23×C43—44no—
265C23×C43—44no—
266C23×C43—44no—
267C23×C43—44no—
268C23×C43—44no—
269C23×C43C2×#4114yes—
270C23×C43C2×#4112yes—
271C23×C43H(5,𝔽2)12yes—
272C23×C43H(5,𝔽2)12yes—
273C23×C43H(5,𝔽2)12yes—
274C23×C43H(5,𝔽2)12yes—
275C23×C432−1+412yes—
276C23×C432−1+412yes—
277C23×C43C2511yescharacteristic
278D4×C43—416no—
279C2×C4×C43—22no—
280C2×C4×C43—22no—
281C2×C4×C43—22no—
282C2×C4×C43—22no—
283C2×C4×C43—22no—
284C2×C4×C43—22no—
285C2×C4×C43—22no—
286C2×C4×C43—22no—
287C2×C4×C43—22no—
288C2×C4×C43—22no—
289C2×C4×C43—22no—
290C2×C4×C43—22no—
291C2×C4×C43—22no—
292C2×C4×C43—22no—
293C2×C4×C43—22no—
294C2×C4×C43—416no—
295C2×C4×C43—44no—
296C2×C4×C43—44no—
297C2×C4×C43—44no—
298C2×C4×C43—44no—
299C2×C4×C43—44no—
300C2×Dic43—22no—
301C2×Dic43—22no—
302C2×Dic43—22no—
303C2×Dic43—22no—
304C2×Dic43—22no—
305C2×Dic43—22no—
306C2×Dic43—22no—
307C2×Dic43—22no—
308C2×Dic43—22no—
309C2×Dic43—22no—
310C2×Dic43—22no—
311C2×Dic43—22no—
312C2×Dic43—22no—
313C2×Dic43—22no—
314C2×Dic43—22no—
315C2×Dic43—22no—
316C2×Dic43—22no—
317C2×Dic43—22no—
318C2×Dic43—22no—
319C2×Dic43—22no—
320C2×Dic43—22no—
321C2×Dic43—22no—
322C2×Dic43—22no—
323C2×Dic43—22no—
324C2×Dic43—44no—
325C2×Dic43—44no—
326C2×Dic43—44no—
327C2×Dic43—44no—
328C2×Dic43—44no—
329C2×Dic43—44no—
330C2×Dic43—44no—
331C2×Dic43—44no—
332C2×#2827—431nomaximal, Sylow
333C22×C43—24no—
334C22×C43—24no—
335C22×C43—24no—
336C22×C43—416no—
337C22×C43—42no—
338C22×C43—42no—
339C22×C43—42no—
340C22×C43—42no—
341C22×C43—42no—
342C22×C43—42no—
343C22×C43—42no—
344C22×C43—42no—
345C22×C43—42no—
346C22×C43—42no—
347C22×C43—42no—
348C22×C43—88no—
349C22×C43#53814yes—
350C22×C43#53914yes—
351C22×C43#53914yes—
352C22×C43#56014yes—
353C22×C43#56214yes—
354C22×C43#56214yes—
355C22×C43#56314yes—
356C22×C43C22×#4111yescharacteristic
357C22×C43C2×H(5,𝔽2)11yescharacteristic
358C22×C43C2×H(5,𝔽2)11yescharacteristic
359C22×C43C2×H(5,𝔽2)11yescharacteristic
360C22×C43C2×H(5,𝔽2)11yescharacteristic
361C22×C43C2×2−1+411yescharacteristic
362C22×C43C2×2−1+411yescharacteristic
363C4×C43—42no—
364C4×C43—42no—
365C4×C43—42no—
366C4×C43—42no—
367C4×C43—42no—
368Dic43—42no—
369Dic43—42no—
370Dic43—42no—
371Dic43—42no—
372Dic43—42no—
373Dic43—42no—
374Dic43—42no—
375Dic43—42no—
376#2827—4316no—
377C2×#400—431no—
378C2×#400—431no—
379C2×#399—431no—
380C2×#398—431no—
381C2×#398—431no—
382C2×#397—431no—
383C2×#397—431no—
384C2×#397—431no—
385C2×#396—431no—
386C2×#396—431no—
387C2×#394—431no—
388C2×#394—431no—
389C2×#386D4311yescharacteristic
390C2×#385—431no—
391C2×#385—431no—
392C2×C43—44no—
393C2×C43—82no—
394C2×C43#282718yescomplemented
395C2×C43C2×#53811yescharacteristic
396C2×C43C2×#53911yescharacteristic
397C2×C43C2×#53911yescharacteristic
398C2×C43C2×#56011yescharacteristic
399C2×C43C2×#56211yescharacteristic
400C2×C43C2×#56211yescharacteristic
401C2×C43C2×#56311yescharacteristic
402C23×D4C2×D4311yescharacteristic
403C24×C4C2×D4311yescharacteristic
404C22×C4⋊C4—431no—
405C22×C4⋊C4—431no—
406C22×C4⋊C4—431no—
407C22×C4⋊C4—431no—
408C22×C4⋊C4—431no—
409C22×C4⋊C4—431no—
410C22×C4⋊C4—431no—
411C22×C4⋊C4—431no—
412C22×C4⋊C4—431no—
413C22×C4⋊C4—431no—
414C22×C22⋊C4—431no—
415C22×C22⋊C4—431no—
416C22×C22⋊C4—431no—
417C22×C22⋊C4—431no—
418C22×C22⋊C4—431no—
419C22×C22⋊C4—431no—
420C22×C22⋊C4—431no—
421C22×C22⋊C4—431no—
422C22×C22⋊C4C2×D4311yescharacteristic
423C22×C22⋊C4C2×D4311yescharacteristic
424C22×C22⋊C4C2×D4311yescharacteristic
425#400—438no—
426#400—438no—
427#399—438no—
428#398—438no—
429#398—438no—
430#397—438no—
431#397—438no—
432#397—438no—
433#396—438no—
434#396—438no—
435#394—438no—
436#394—438no—
437#386C2×D4318yes—
438#385—438no—
439#385—438no—
440C2×#95—431no—
441C2×#95—431no—
442C2×#95—431no—
443C2×#95—431no—
444C2×#95—431no—
445C2×#95—431no—
446C2×#95—431no—
447C2×#95—431no—
448C2×#95—431no—
449C2×#95—431no—
450C2×#95C2×D4311yescharacteristic
451C2×#95C2×D4311yescharacteristic
452C43C2×#282711yescharacteristic, complemented, Sylow
453C25C22×D4311yescharacteristic
454C25C22×D4311yescharacteristic
455C22×D4—24no—
456C22×D4—42no—
457C22×D4—42no—
458C22×D4C22×D4314yes—
459C23×C4—42no—
460C23×C4—42no—
461C23×C4—42no—
462C23×C4—431no—
463C23×C4—431no—
464C23×C4—431no—
465C23×C4—431no—
466C23×C4—431no—
467C23×C4—431no—
468C23×C4—431no—
469C23×C4—431no—
470C23×C4C22×D4311yescharacteristic
471C23×C4C22×D4311yescharacteristic
472C23×C4C22×D4311yescharacteristic
473C23×C4C22×D4311yescharacteristic
474C23×C4C22×D4311yescharacteristic
475C23×C4C22×D4314yes—
476C2×C4⋊C4—434no—
477C2×C4⋊C4—434no—
478C2×C4⋊C4—434no—
479C2×C4⋊C4—434no—
480C2×C4⋊C4—434no—
481C2×C4⋊C4—434no—
482C2×C4⋊C4—434no—
483C2×C4⋊C4—434no—
484C2×C4⋊C4—434no—
485C2×C4⋊C4—434no—
486C2×C4⋊C4—1722no—
487C2×C4⋊C4—1722no—
488C2×C4⋊C4—1722no—
489C2×C4⋊C4—1722no—
490C2×C4⋊C4—1722no—
491C2×C4⋊C4—1722no—
492C2×C4⋊C4—1722no—
493C2×C4⋊C4—1722no—
494C2×C4⋊C4—1722no—
495C2×C4⋊C4—1722no—
496C2×C22⋊C4—42no—
497C2×C22⋊C4—42no—
498C2×C22⋊C4—42no—
499C2×C22⋊C4—434no—
500C2×C22⋊C4—434no—
501C2×C22⋊C4—434no—
502C2×C22⋊C4—434no—
503C2×C22⋊C4—434no—
504C2×C22⋊C4—434no—
505C2×C22⋊C4—434no—
506C2×C22⋊C4—434no—
507C2×C22⋊C4—864no—
508C2×C22⋊C4—864no—
509C2×C22⋊C4—1722no—
510C2×C22⋊C4—1722no—
511C2×C22⋊C4—1722no—
512C2×C22⋊C4—1722no—
513C2×C22⋊C4—1722no—
514C2×C22⋊C4—1722no—
515C2×C22⋊C4C22×D4314yes—
516C2×C22⋊C4C22×D4314yes—
517C2×C22⋊C4C22×D4314yes—
518#95—434no—
519#95—434no—
520#95—434no—
521#95—434no—
522#95—434no—
523#95—434no—
524#95—434no—
525#95—434no—
526#95—434no—
527#95—434no—
528#95C22×D4314yes—
529#95C22×D4314yes—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—22no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24—22no—
543C24#1062189814yes—
544C24C23×D4312yes—
545C24C23×D4312yes—
546C24C23×D4311yescharacteristic
547C2×D4—28no—
548C2×D4—44no—
549C2×D4—44no—
550C2×D4—416no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—44no—
567C22×C4—44no—
568C22×C4—44no—
569C22×C4—416no—
570C22×C4—432no—
571C22×C4—432no—
572C22×C4—432no—
573C22×C4—432no—
574C22×C4—432no—
575C22×C4—432no—
576C22×C4—432no—
577C22×C4—432no—
578C22×C4—862no—
579C22×C4—862no—
580C22×C4—862no—
581C22×C4—862no—
582C22×C4—862no—
583C22×C4—862no—
584C22×C4—862no—
585C22×C4—862no—
586C22×C4—862no—
587C22×C4—862no—
588C22×C4—862no—
589C22×C4—862no—
590C22×C4—862no—
591C22×C4—862no—
592C22×C4—862no—
593C22×C4—862no—
594C22×C4—862no—
595C22×C4—862no—
596C22×C4—862no—
597C22×C4—862no—
598C22×C4—862no—
599C22×C4—862no—
600C22×C4—862no—
601C22×C4—862no—
602C22×C4C23×D4312yes—
603C22×C4C23×D4312yes—
604C22×C4C23×D4312yes—
605C22×C4C23×D4312yes—
606C22×C4C23×D4312yes—
607C4⋊C4—1724no—
608C4⋊C4—1724no—
609C4⋊C4—1724no—
610C4⋊C4—1724no—
611C4⋊C4—1724no—
612C4⋊C4—1724no—
613C4⋊C4—1724no—
614C4⋊C4—1724no—
615C4⋊C4—1724no—
616C4⋊C4—1724no—
617C22⋊C4—44no—
618C22⋊C4—44no—
619C22⋊C4—44no—
620C22⋊C4—868no—
621C22⋊C4—868no—
622C22⋊C4—1724no—
623C22⋊C4—1724no—
624C22⋊C4—1724no—
625C22⋊C4—1724no—
626C22⋊C4—1724no—
627C22⋊C4—1724no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—28no—
635C23—28no—
636C23—28no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—44no—
645C23—44no—
646C23—44no—
647C23—44no—
648C23—44no—
649C23—44no—
650C23—44no—
651C23—44no—
652C23—44no—
653C23—44no—
654C23—44no—
655C23C2×#1062189814yes—
656C23C2×#1062189812yes—
657C23#1306337012yes—
658C23#1306337012yes—
659C23#1306337012yes—
660C23#1306337012yes—
661C23#1306337212yes—
662C23#1306337212yes—
663C23C24×D4311yescharacteristic
664D4—416no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—416no—
681C2×C4—44no—
682C2×C4—44no—
683C2×C4—44no—
684C2×C4—44no—
685C2×C4—44no—
686C2×C4—862no—
687C2×C4—862no—
688C2×C4—862no—
689C2×C4—862no—
690C2×C4—862no—
691C2×C4—862no—
692C2×C4—862no—
693C2×C4—862no—
694C2×C4—862no—
695C2×C4—862no—
696C2×C4—862no—
697C2×C4—862no—
698C2×C4—862no—
699C2×C4—862no—
700C2×C4—862no—
701C2×C4—862no—
702C2×C4—862no—
703C2×C4—862no—
704C2×C4—862no—
705C2×C4—862no—
706C2×C4—862no—
707C2×C4—862no—
708C2×C4—862no—
709C2×C4—862no—
710C2×C4—1724no—
711C2×C4—1724no—
712C2×C4—1724no—
713C2×C4—1724no—
714C2×C4—1724no—
715C2×C4—1724no—
716C2×C4—1724no—
717C2×C4—1724no—
718C22—24no—
719C22—24no—
720C22—24no—
721C22—416no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—42no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—88no—
734C22#1458348714yes—
735C22#1458349114yes—
736C22#1458349114yes—
737C22#1458363814yes—
738C22#1458364414yes—
739C22#1458364414yes—
740C22#1458365214yes—
741C22C22×#1062189811yescharacteristic
742C22C2×#1306337011yescharacteristic
743C22C2×#1306337011yescharacteristic
744C22C2×#1306337011yescharacteristic
745C22C2×#1306337011yescharacteristic
746C22C2×#1306337211yescharacteristic
747C22C2×#1306337211yescharacteristic
748C4—42no—
749C4—42no—
750C4—42no—
751C4—42no—
752C4—42no—
753C4—1722no—
754C4—1722no—
755C4—1722no—
756C4—1722no—
757C4—1722no—
758C4—1722no—
759C4—1722no—
760C4—1722no—
761C2—44no—
762C2—82no—
763C2#1914269918yesdirect product factor
764C2C2×#1458348711yescharacteristic
765C2C2×#1458349111yescharacteristic
766C2C2×#1458349111yescharacteristic
767C2C2×#1458363811yescharacteristic
768C2C2×#1458364411yescharacteristic
769C2C2×#1458364411yescharacteristic
770C2C2×#1458365211yescharacteristic
subgroupG/H
centerC24C23×D43
commutator, cosocleC23×C43C25
FrattiniC23C24×D43
FittingC2×C43×#386C2
socleC24×C43C24
prime radicalC23×D4×C43C22
hypercenterC2×#386D43
hypocenterC43C2×#2827
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. #19142699C2direct (N × H)
2. C2×#14582840C2semidirect
3. C2×#14582840C2semidirect
4. C2×#14582835C2semidirect
5. C2×#14582833C2semidirect
6. C2×#14582833C2semidirect
7. C2×#14582827C2semidirect
8. C2×#14582827C2semidirect
9. C2×#14582824C2semidirect
10. C2×#14582822C2semidirect
11. C2×#14582822C2semidirect
14. C2×#14582772C2semidirect
15. C2×#14582772C2semidirect
35. #14582840C22semidirect
36. #14582840C22semidirect
37. #14582835C22semidirect
38. #14582833C22semidirect
39. #14582833C22semidirect
40. #14582827C22semidirect
41. #14582827C22semidirect
42. #14582824C22semidirect
43. #14582822C22semidirect
44. #14582822C22semidirect
47. #14582772C22semidirect
48. #14582772C22semidirect
394. C2×C43#2827semidirect
452. C43C2×#2827semidirect
763. C2#19142699direct (N × H)

Maximal subgroups

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

subgroupindex
#191426992
C2×#145828402
C2×#145828352
C2×#145828332
C2×#145828272
C2×#145828242
C2×#145828222
C2×#145828132
C2×#145827722
C2×C43×#3862
C2×#282743