Finite Group Databasebeta

← C2×#19140664 #25263098

Subgroups — C2×#19140664 #25263098

Order 11008.

2394 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19140664C2116yesmaximal, direct product factor
2C2×C43⋊#401C211yesmaximal, characteristic, complemented
3C2×#14582832C211yesmaximal, characteristic, complemented
4C2×#14582828C211yesmaximal, characteristic, complemented
5C2×#14582826C211yesmaximal, characteristic, complemented
6C2×#14582817C211yesmaximal, characteristic
7C2×#14582816C211yesmaximal, characteristic
8C2×#14582810C211yesmaximal, characteristic, complemented
9C2×#14582810C211yesmaximal, characteristic, complemented
10C2×#14582790C211yesmaximal, characteristic, complemented
11C2×#14582788C211yesmaximal, characteristic, complemented
12C2×#14582781C211yesmaximal, characteristic, complemented
13C2×#14582777C211yesmaximal, characteristic
14C2×#14582773C211yesmaximal, characteristic, complemented
15C2×C4×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
16C2×C43×#391C211yesmaximal, characteristic, complemented
17C23×D172C2211yescharacteristic
18C23×C4×D43C2211yescharacteristic
19C22×C4⋊Dic43C2211yescharacteristic
20C22×Dic43⋊C4C2211yescharacteristic
21C22×Dic43⋊C4C2211yescharacteristic
22C22×Dic43⋊C4C2211yescharacteristic
23C22×(C2×D43)⋊C4C2211yescharacteristic
24C22×(C2×D43)⋊C4C2211yescharacteristic
25C22×(C2×D43)⋊C4C2211yescharacteristic
26C22×(C2×D43)⋊C4C2211yescharacteristic
27C22×(C2×D43)⋊C4C2211yescharacteristic
28C22×(C2×D43)⋊C4C2211yescharacteristic
29C22×(C2×D43)⋊C4C2211yescharacteristic
30C22×(C2×D43)⋊C4C2211yescharacteristic
31C22×(C2×D43)⋊C4C2211yescharacteristic
32C22×(C2×D43)⋊C4C2211yescharacteristic
33C22×(C2×D43)⋊C4C2211yescharacteristic
34C22×C4×Dic43C2211yescharacteristic
35C43⋊#401C2218yescomplemented
36#14582832C2218yescomplemented
37#14582828C2218yescomplemented
38#14582826C2218yescomplemented
39#14582817C2218yes—
40#14582816C2218yes—
41#14582810C2218yescomplemented
42#14582810C2218yescomplemented
43#14582790C2218yescomplemented
44#14582788C2218yescomplemented
45#14582781C2218yescomplemented
46#14582777C2218yes—
47#14582773C2218yescomplemented
48C4×(C2×D43)⋊C4C2218yescomplemented
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×Q8×C43C2211yescharacteristic
60C22×C4⋊C4×C43C2211yescharacteristic
61C22×C42×C43C2211yescharacteristic
62C43×#391C2218yescomplemented
63C2×#95×C43C2211yescharacteristic
64C2×#95×C43C2211yescharacteristic
65C2×#95×C43C2211yescharacteristic
66C2×#95×C43C2211yescharacteristic
67C24×D43C2311yescharacteristic
68C24×D43C2311yescharacteristic
69C22×D172—24no—
70C22×D172—42no—
71C22×D172—42no—
72C22×D172C2314yes—
73C23×Dic43C2311yescharacteristic
74C23×Dic43C2311yescharacteristic
75C23×Dic43C2311yescharacteristic
76C23×Dic43C2311yescharacteristic
77C23×Dic43C2311yescharacteristic
78C23×Dic43C2311yescharacteristic
79C22×C4×D43—24no—
80C22×C4×D43—42no—
81C22×C4×D43—42no—
82C22×C4×D43C2314yes—
83C2×C4⋊Dic43—42no—
84C2×C4⋊Dic43C2314yes—
85C2×Dic43⋊C4—24no—
86C2×Dic43⋊C4—42no—
87C2×Dic43⋊C4—42no—
88C2×Dic43⋊C4C2314yes—
89C2×Dic43⋊C4C2314yes—
90C2×Dic43⋊C4C2314yes—
91C2×(C2×D43)⋊C4—24no—
92C2×(C2×D43)⋊C4—24no—
93C2×(C2×D43)⋊C4—24no—
94C2×(C2×D43)⋊C4—24no—
95C2×(C2×D43)⋊C4—24no—
96C2×(C2×D43)⋊C4—42no—
97C2×(C2×D43)⋊C4—42no—
98C2×(C2×D43)⋊C4—42no—
99C2×(C2×D43)⋊C4—42no—
100C2×(C2×D43)⋊C4—42no—
101C2×(C2×D43)⋊C4—42no—
102C2×(C2×D43)⋊C4C2314yes—
103C2×(C2×D43)⋊C4C2314yes—
104C2×(C2×D43)⋊C4C2314yes—
105C2×(C2×D43)⋊C4C2314yes—
106C2×(C2×D43)⋊C4C2314yes—
107C2×(C2×D43)⋊C4C2314yes—
108C2×(C2×D43)⋊C4C2314yes—
109C2×(C2×D43)⋊C4C2314yes—
110C2×(C2×D43)⋊C4C2314yes—
111C2×(C2×D43)⋊C4C2314yes—
112C2×(C2×D43)⋊C4C2314yes—
113C2×C4×Dic43—42no—
114C2×C4×Dic43C2314yes—
115C43⋊#95C2314yes—
116C43⋊#95C2314yes—
117C43⋊#95C2314yes—
118C43⋊#95C2314yes—
119C43⋊#95C2314yes—
120C43⋊#95C2314yes—
121C43⋊#95C2314yes—
122C43⋊#95C2314yes—
123C43⋊#95C2314yes—
124C43⋊#95C2314yes—
125C22×Q8×C43—24no—
126C22×Q8×C43—42no—
127C22×Q8×C43—42no—
128C22×Q8×C43C2314yes—
129C23×C4×C43C2311yescharacteristic
130C23×C4×C43C2311yescharacteristic
131C23×C4×C43C2311yescharacteristic
132C23×C4×C43C2311yescharacteristic
133C23×C4×C43C2311yescharacteristic
134C23×C4×C43C2311yescharacteristic
135C23×C4×C43C2311yescharacteristic
136C2×C4⋊C4×C43—42no—
137C2×C4⋊C4×C43C2314yes—
138C2×C42×C43—42no—
139C2×C42×C43C2314yes—
140#95×C43C2314yes—
141#95×C43C2314yes—
142#95×C43C2314yes—
143#95×C43C2314yes—
144C24×C43C2411yescharacteristic
145C23×D43—22no—
146C23×D43—22no—
147C23×D43—22no—
148C23×D43—22no—
149C23×D43—22no—
150C23×D43—22no—
151C23×D43—22no—
152C23×D43—22no—
153C23×D43—22no—
154C23×D43—22no—
155C23×D43—22no—
156C23×D43—22no—
157C23×D43—22no—
158C23×D43#4114yes—
159C23×D43C2412yes—
160C23×D43C2412yes—
161C2×Q8×C43—28no—
162C2×Q8×C43—44no—
163C2×Q8×C43—44no—
164C2×Q8×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—22no—
181C22×C4×C43—22no—
182C22×C4×C43—22no—
183C22×C4×C43—22no—
184C22×C4×C43#4114yes—
185C22×C4×C43#4114yes—
186C22×C4×C43C2412yes—
187C22×C4×C43C2412yes—
188C22×C4×C43C2412yes—
189C22×C4×C43C2412yes—
190C22×C4×C43C2412yes—
191C22×C4×C43C2412yes—
192C22×C4×C43C2412yes—
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×Dic43C2412yes—
212C22×Dic43C2412yes—
213C22×Dic43C2412yes—
214C22×Dic43C2412yes—
215C22×Dic43C2412yes—
216C22×Dic43C2412yes—
217C2×D172—28no—
218C2×D172—44no—
219C2×D172—44no—
220C2×D172—416no—
221C2×C4×D43—28no—
222C2×C4×D43—44no—
223C2×C4×D43—44no—
224C2×C4×D43—416no—
225C4⋊C4×C43—44no—
226C42×C43—44no—
227(C2×D43)⋊C4—28no—
228(C2×D43)⋊C4—28no—
229(C2×D43)⋊C4—28no—
230(C2×D43)⋊C4—28no—
231(C2×D43)⋊C4—28no—
232(C2×D43)⋊C4—44no—
233(C2×D43)⋊C4—44no—
234(C2×D43)⋊C4—44no—
235(C2×D43)⋊C4—44no—
236(C2×D43)⋊C4—44no—
237(C2×D43)⋊C4—44no—
238C4⋊Dic43—44no—
239Dic43⋊C4—28no—
240Dic43⋊C4—44no—
241Dic43⋊C4—44no—
242C4×Dic43—44no—
243C23×C43C2×#4112yes—
244C23×C43C2×#4112yes—
245C23×C43C2×#4112yes—
246C23×C43H(5,𝔽2)12yes—
247C23×C43H(5,𝔽2)12yes—
248C23×C43H(5,𝔽2)12yes—
249C23×C432−1+412yes—
250C23×C43C2511yescharacteristic
251C22×D43—28no—
252C22×D43—28no—
253C22×D43—28no—
254C22×D43—22no—
255C22×D43—22no—
256C22×D43—22no—
257C22×D43—22no—
258C22×D43—22no—
259C22×D43—22no—
260C22×D43—22no—
261C22×D43—22no—
262C22×D43—22no—
263C22×D43—22no—
264C22×D43—22no—
265C22×D43—22no—
266C22×D43—22no—
267C22×D43—44no—
268C22×D43—44no—
269C22×D43—44no—
270C22×D43—44no—
271C22×D43—44no—
272C22×D43—44no—
273C22×D43—44no—
274C22×D43—44no—
275C22×D43—44no—
276C22×D43—44no—
277C22×D43—44no—
278C22×D43C2×#4114yes—
279Q8×C43—416no—
280C2×C4×C43—28no—
281C2×C4×C43—28no—
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—22no—
295C2×C4×C43—22no—
296C2×C4×C43—22no—
297C2×C4×C43—22no—
298C2×C4×C43—22no—
299C2×C4×C43—22no—
300C2×C4×C43—22no—
301C2×C4×C43—44no—
302C2×C4×C43—44no—
303C2×C4×C43—44no—
304C2×C4×C43—44no—
305C2×C4×C43—44no—
306C2×C4×C43C2×#4114yes—
307C2×C4×C43C2×#4114yes—
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—22no—
325C2×Dic43—22no—
326C2×Dic43—44no—
327C2×Dic43—44no—
328C2×Dic43—44no—
329C2×Dic43—44no—
330C2×Dic43—44no—
331C2×Dic43—44no—
332D172—416no—
333C4×D43—416no—
334C2×#2653—431nomaximal, Sylow
335C22×C43#52914yes—
336C22×C43#53814yes—
337C22×C43#53814yes—
338C22×C43#53814yes—
339C22×C43#53914yes—
340C22×C43#54214yes—
341C22×C43#54214yes—
342C22×C43C22×#4111yescharacteristic
343C22×C43C22×#4111yescharacteristic
344C22×C43C22×#4111yescharacteristic
345C22×C43C2×H(5,𝔽2)11yescharacteristic
346C22×C43C2×H(5,𝔽2)11yescharacteristic
347C22×C43C2×H(5,𝔽2)11yescharacteristic
348C22×C43C2×2−1+411yescharacteristic
349C2×D43—24no—
350C2×D43—24no—
351C2×D43—24no—
352C2×D43—416no—
353C2×D43—42no—
354C2×D43—42no—
355C2×D43—42no—
356C2×D43—42no—
357C2×D43—42no—
358C2×D43—42no—
359C2×D43—42no—
360C2×D43—42no—
361C2×D43—42no—
362C2×D43—42no—
363C2×D43—42no—
364C2×D43—88no—
365C4×C43—24no—
366C4×C43—24no—
367C4×C43—42no—
368C4×C43—42no—
369C4×C43—42no—
370C4×C43—42no—
371C4×C43—42no—
372Dic43—42no—
373Dic43—42no—
374Dic43—42no—
375Dic43—42no—
376Dic43—42no—
377Dic43—42no—
378#2653—4316no—
379C2×#401—431no—
380C2×#398—431no—
381C2×#397—431no—
382C2×#397—431no—
383C2×#394—431no—
384C2×#394—431no—
385C2×#393—431no—
386C2×#393—431no—
387C2×#391D4311yescharacteristic, complemented
388C2×#388—431no—
389C2×#388—431no—
390C2×#387—431no—
391C2×#386—431no—
392C2×#385—431no—
393C2×C4×C22⋊C4—431no—
394C2×C43#265318yescomplemented
395C2×C43C2×#52911yescharacteristic
396C2×C43C2×#53811yescharacteristic
397C2×C43C2×#53811yescharacteristic
398C2×C43C2×#53811yescharacteristic
399C2×C43C2×#53911yescharacteristic
400C2×C43C2×#54211yescharacteristic
401C2×C43C2×#54211yescharacteristic
402D43—44no—
403D43—82no—
404C23×Q8C2×D4311yescharacteristic
405C23×D4—431no—
406C24×C4—431no—
407C22×C4⋊C4—431no—
408C22×C4⋊C4—431no—
409C22×C4⋊C4—431no—
410C22×C4⋊C4—431no—
411C22×C4⋊C4C2×D4311yescharacteristic
412C22×C22⋊C4—431no—
413C22×C22⋊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⋊C4—431no—
423C22×C42—431no—
424C22×C42C2×D4311yescharacteristic
425#401—438no—
426#398—438no—
427#397—438no—
428#397—438no—
429#394—438no—
430#394—438no—
431#393—438no—
432#393—438no—
433#391C2×D4318yescomplemented
434#388—438no—
435#388—438no—
436#387—438no—
437#386—438no—
438#385—438no—
439C4×C22⋊C4—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
452C2×#95C2×D4311yescharacteristic
453C2×#95C2×D4311yescharacteristic
454C43C2×#265311yescharacteristic, complemented, Sylow
455C25—431no—
456C25—431no—
457C22×Q8—24no—
458C22×Q8—42no—
459C22×Q8—42no—
460C22×Q8C22×D4314yes—
461C22×D4—434no—
462C22×D4—864no—
463C22×D4—1722no—
464C22×D4—1722no—
465C23×C4—431no—
466C23×C4—431no—
467C23×C4—431no—
468C23×C4—431no—
469C23×C4—431no—
470C23×C4—431no—
471C23×C4—434no—
472C23×C4—864no—
473C23×C4—1722no—
474C23×C4—1722no—
475C23×C4C22×D4311yescharacteristic
476C23×C4C22×D4311yescharacteristic
477C23×C4C22×D4311yescharacteristic
478C23×C4C22×D4311yescharacteristic
479C23×C4C22×D4311yescharacteristic
480C23×C4C22×D4311yescharacteristic
481C23×C4C22×D4311yescharacteristic
482C2×C4⋊C4—42no—
483C2×C4⋊C4—434no—
484C2×C4⋊C4—434no—
485C2×C4⋊C4—434no—
486C2×C4⋊C4—434no—
487C2×C4⋊C4—864no—
488C2×C4⋊C4—1722no—
489C2×C4⋊C4—1722no—
490C2×C4⋊C4—1722no—
491C2×C4⋊C4C22×D4314yes—
492C2×C22⋊C4—434no—
493C2×C22⋊C4—434no—
494C2×C22⋊C4—434no—
495C2×C22⋊C4—434no—
496C2×C22⋊C4—434no—
497C2×C22⋊C4—434no—
498C2×C22⋊C4—434no—
499C2×C22⋊C4—434no—
500C2×C22⋊C4—434no—
501C2×C22⋊C4—434no—
502C2×C22⋊C4—434no—
503C2×C22⋊C4—864no—
504C2×C22⋊C4—864no—
505C2×C22⋊C4—864no—
506C2×C22⋊C4—864no—
507C2×C22⋊C4—864no—
508C2×C22⋊C4—1722no—
509C2×C22⋊C4—1722no—
510C2×C22⋊C4—1722no—
511C2×C22⋊C4—1722no—
512C2×C22⋊C4—1722no—
513C2×C22⋊C4—1722no—
514C2×C42—42no—
515C2×C42—434no—
516C2×C42—1722no—
517C2×C42C22×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—
530#95C22×D4314yes—
531#95C22×D4314yes—
532C24—434no—
533C24—432no—
534C24—432no—
535C24—862no—
536C24—862no—
537C24—862no—
538C24—862no—
539C24—862no—
540C24—862no—
541C24—862no—
542C24—862no—
543C24—862no—
544C24—862no—
545C24—862no—
546C24—862no—
547C24—862no—
548C24C23×D4311yescharacteristic
549C2×Q8—28no—
550C2×Q8—44no—
551C2×Q8—44no—
552C2×Q8—416no—
553C2×D4—868no—
554C2×D4—1724no—
555C2×D4—1724no—
556C2×D4—17216no—
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—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—432no—
577C22×C4—432no—
578C22×C4—432no—
579C22×C4—432no—
580C22×C4—432no—
581C22×C4—432no—
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—868no—
601C22×C4—1724no—
602C22×C4—1724no—
603C22×C4—17216no—
604C22×C4#1062189814yes—
605C22×C4#1062190214yes—
606C22×C4C23×D4312yes—
607C22×C4C23×D4312yes—
608C22×C4C23×D4312yes—
609C22×C4C23×D4312yes—
610C22×C4C23×D4312yes—
611C22×C4C23×D4312yes—
612C22×C4C23×D4312yes—
613C4⋊C4—44no—
614C4⋊C4—868no—
615C4⋊C4—1724no—
616C4⋊C4—1724no—
617C4⋊C4—1724no—
618C22⋊C4—868no—
619C22⋊C4—868no—
620C22⋊C4—868no—
621C22⋊C4—868no—
622C22⋊C4—868no—
623C22⋊C4—1724no—
624C22⋊C4—1724no—
625C22⋊C4—1724no—
626C22⋊C4—1724no—
627C22⋊C4—1724no—
628C22⋊C4—1724no—
629C42—44no—
630C42—1724no—
631C23—434no—
632C23—868no—
633C23—862no—
634C23—862no—
635C23—862no—
636C23—862no—
637C23—862no—
638C23—862no—
639C23—868no—
640C23—868no—
641C23—862no—
642C23—862no—
643C23—862no—
644C23—862no—
645C23—862no—
646C23—862no—
647C23—862no—
648C23—1724no—
649C23—1724no—
650C23—1724no—
651C23—1724no—
652C23—1724no—
653C23—1724no—
654C23—1724no—
655C23—1724no—
656C23—1724no—
657C23—1724no—
658C23—1724no—
659C23#41×D4312yes—
660C23C2×#1062189812yes—
661C23C2×#1062190212yes—
662C23#1306337012yes—
663C23#1306337012yes—
664C23#1306337112yes—
665C23#1306337312yes—
666C23C24×D4311yescharacteristic
667Q8—416no—
668D4—17216no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—28no—
674C2×C4—28no—
675C2×C4—22no—
676C2×C4—22no—
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—44no—
691C2×C4—44no—
692C2×C4—44no—
693C2×C4—44no—
694C2×C4—44no—
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—862no—
711C2×C4—862no—
712C2×C4—862no—
713C2×C4—17216no—
714C2×C4—1724no—
715C2×C4—1724no—
716C2×C4—1724no—
717C2×C4—1724no—
718C2×C4—1724no—
719C2×C4—1724no—
720C2×C4C2×#1062189814yes—
721C2×C4C2×#1062190214yes—
722C22—864no—
723C22—864no—
724C22—864no—
725C22—3448no—
726C22—1722no—
727C22—1722no—
728C22—1722no—
729C22—1722no—
730C22—1722no—
731C22—1722no—
732C22—1722no—
733C22—17216no—
734C22—1722no—
735C22—1722no—
736C22—1722no—
737C22—1722no—
738C22#1458343614yes—
739C22#1458348314yes—
740C22#1458348714yes—
741C22#1458348914yes—
742C22#1458349514yes—
743C22#1458352114yes—
744C22#1458352314yes—
745C22C2×#41×D4311yescharacteristic
746C22C22×#1062189811yescharacteristic
747C22C22×#1062190211yescharacteristic
748C22C2×#1306337011yescharacteristic
749C22C2×#1306337011yescharacteristic
750C22C2×#1306337111yescharacteristic
751C22C2×#1306337311yescharacteristic
752C4—24no—
753C4—24no—
754C4—42no—
755C4—42no—
756C4—42no—
757C4—42no—
758C4—42no—
759C4—1722no—
760C4—1722no—
761C4—1722no—
762C4—1722no—
763C4—1722no—
764C4—1722no—
765C2—3442no—
766C2—1724no—
767C2#1914066418yesdirect product factor
768C2C2×#1458343611yescharacteristic
769C2C2×#1458348311yescharacteristic
770C2C2×#1458348711yescharacteristic
771C2C2×#1458348911yescharacteristic
772C2C2×#1458349511yescharacteristic
773C2C2×#1458352111yescharacteristic
774C2C2×#1458352311yescharacteristic
subgroupG/H
centerC24C23×D43
commutator, cosocleC23×C43C25
FrattiniC23C24×D43
FittingC2×C43×#391C2
socleC24×C43C24
prime radicalC23×D172C22
hypercenterC2×#391D43
hypocenterC43C2×#2653
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
1. #19140664C2direct (N × H)
2. C2×C43⋊#401C2semidirect
3. C2×#14582832C2semidirect
4. C2×#14582828C2semidirect
5. C2×#14582826C2semidirect
8. C2×#14582810C2semidirect
9. C2×#14582810C2semidirect
10. C2×#14582790C2semidirect
11. C2×#14582788C2semidirect
12. C2×#14582781C2semidirect
14. C2×#14582773C2semidirect
15. C2×C4×(C2×D43)⋊C4C2semidirect
16. C2×C43×#391C2semidirect
35. C43⋊#401C22semidirect
36. #14582832C22semidirect
37. #14582828C22semidirect
38. #14582826C22semidirect
41. #14582810C22semidirect
42. #14582810C22semidirect
43. #14582790C22semidirect
44. #14582788C22semidirect
45. #14582781C22semidirect
47. #14582773C22semidirect
48. C4×(C2×D43)⋊C4C22semidirect
62. C43×#391C22semidirect
387. C2×#391D43semidirect
394. C2×C43#2653semidirect
433. #391C2×D43semidirect
454. C43C2×#2653semidirect
767. C2#19140664direct (N × H)

Maximal subgroups

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

subgroupindex
#191406642
C2×C43⋊#4012
C2×#145828322
C2×#145828282
C2×#145828262
C2×#145828172
C2×#145828162
C2×#145828102
C2×#145827902
C2×#145827882
C2×#145827812
C2×#145827772
C2×#145827732
C2×C4×(C2×D43)⋊C42
C2×C43×#3912
C2×#265343