Finite Group Databasebeta

← C2×#19140010 #25266880

Subgroups — C2×#19140010 #25266880

Order 11008.

2270 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19140010C2116yesmaximal, direct product factor
2C2×#14582841C211yesmaximal, characteristic, complemented
3C2×#14582833C211yesmaximal, characteristic, complemented
4C2×#14582822C211yesmaximal, characteristic
5C2×#14582822C211yesmaximal, characteristic
6C2×#14582797C211yesmaximal, characteristic, complemented
7C2×#14582797C211yesmaximal, characteristic, complemented
8C2×#14582796C211yesmaximal, characteristic, complemented
9C2×#14582792C211yesmaximal, characteristic
10C2×#14582792C211yesmaximal, characteristic
11C2×#14582786C211yesmaximal, characteristic, complemented
12C2×#14582783C211yesmaximal, characteristic, complemented
13C2×#14582772C211yesmaximal, characteristic
14C2×#14582772C211yesmaximal, characteristic
15C2×C4×Dic43⋊C4C211yesmaximal, characteristic, complemented
16C2×C4×C22⋊C4×C43C211yesmaximal, characteristic
17C22×C4⋊Dic43C2211yescharacteristic
18C22×C4⋊Dic43C2211yescharacteristic
19C22×C4⋊Dic43C2211yescharacteristic
20C22×C4⋊Dic43C2211yescharacteristic
21C22×Dic43⋊C4C2211yescharacteristic
22C22×Dic43⋊C4C2211yescharacteristic
23C22×Dic43⋊C4C2211yescharacteristic
24C22×Dic43⋊C4C2211yescharacteristic
25C22×Dic43⋊C4C2211yescharacteristic
26C22×Dic43⋊C4C2211yescharacteristic
27C22×Dic43⋊C4C2211yescharacteristic
28C22×Dic43⋊C4C2211yescharacteristic
29C22×C22⋊Dic43C2211yescharacteristic
30C22×C22⋊Dic43C2211yescharacteristic
31C22×C22⋊Dic43C2211yescharacteristic
32C22×C22⋊Dic43C2211yescharacteristic
33C22×C4×Dic43C2211yescharacteristic
34C22×C4×Dic43C2211yescharacteristic
35#14582841C2218yescomplemented
36#14582833C2218yescomplemented
37#14582822C2218yes—
38#14582822C2218yes—
39#14582797C2218yescomplemented
40#14582797C2218yescomplemented
41#14582796C2218yescomplemented
42#14582792C2218yes—
43#14582792C2218yes—
44#14582786C2218yescomplemented
45#14582783C2218yescomplemented
46#14582772C2218yes—
47#14582772C2218yes—
48C4×Dic43⋊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
59C24×C4×C43C2211yescharacteristic
60C22×C22⋊C4×C43C2211yescharacteristic
61C22×C22⋊C4×C43C2211yescharacteristic
62C22×C42×C43C2211yescharacteristic
63C22×C42×C43C2211yescharacteristic
64C4×C22⋊C4×C43C2218yes—
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—24no—
76C2×C4⋊Dic43—24no—
77C2×C4⋊Dic43—42no—
78C2×C4⋊Dic43—42no—
79C2×C4⋊Dic43C2314yes—
80C2×C4⋊Dic43C2314yes—
81C2×C4⋊Dic43C2314yes—
82C2×C4⋊Dic43C2314yes—
83C2×Dic43⋊C4—24no—
84C2×Dic43⋊C4—24no—
85C2×Dic43⋊C4—24no—
86C2×Dic43⋊C4—24no—
87C2×Dic43⋊C4—24no—
88C2×Dic43⋊C4—42no—
89C2×Dic43⋊C4—42no—
90C2×Dic43⋊C4—42no—
91C2×Dic43⋊C4C2314yes—
92C2×Dic43⋊C4C2314yes—
93C2×Dic43⋊C4C2314yes—
94C2×Dic43⋊C4C2314yes—
95C2×Dic43⋊C4C2314yes—
96C2×Dic43⋊C4C2314yes—
97C2×Dic43⋊C4C2314yes—
98C2×Dic43⋊C4C2314yes—
99C2×C22⋊Dic43—24no—
100C2×C22⋊Dic43—24no—
101C2×C22⋊Dic43—42no—
102C2×C22⋊Dic43—42no—
103C2×C22⋊Dic43C2314yes—
104C2×C22⋊Dic43C2314yes—
105C2×C22⋊Dic43C2314yes—
106C2×C22⋊Dic43C2314yes—
107C2×C4×Dic43—24no—
108C2×C4×Dic43—42no—
109C2×C4×Dic43C2314yes—
110C2×C4×Dic43C2314yes—
111C43⋊#95C2314yes—
112C43⋊#95C2314yes—
113C43⋊#95C2314yes—
114C43⋊#95C2314yes—
115C43⋊#95C2314yes—
116C43⋊#95C2314yes—
117C43⋊#95C2314yes—
118C43⋊#95C2314yes—
119C43⋊#95C2314yes—
120C43⋊#95C2314yes—
121C25×C43C2311yescharacteristic
122C23×C4×C43—24no—
123C23×C4×C43—42no—
124C23×C4×C43—42no—
125C23×C4×C43C2311yescharacteristic
126C23×C4×C43C2311yescharacteristic
127C23×C4×C43C2311yescharacteristic
128C23×C4×C43C2311yescharacteristic
129C23×C4×C43C2311yescharacteristic
130C23×C4×C43C2311yescharacteristic
131C23×C4×C43C2314yes—
132C2×C22⋊C4×C43—24no—
133C2×C22⋊C4×C43Q818yes—
134C2×C22⋊C4×C43C2314yes—
135C2×C22⋊C4×C43C2314yes—
136C2×C42×C43—42no—
137C2×C42×C43—42no—
138C2×C42×C43C2314yes—
139C2×C42×C43C2314yes—
140#95×C43C2314yes—
141#95×C43C2314yes—
142C24×C43—22no—
143C24×C43—22no—
144C24×C43—22no—
145C24×C43—22no—
146C24×C43—22no—
147C24×C43—22no—
148C24×C43C2×Q814yes—
149C24×C43C2412yes—
150C24×C43C2411yescharacteristic
151C22×C4×C43—28no—
152C22×C4×C43—22no—
153C22×C4×C43—22no—
154C22×C4×C43—22no—
155C22×C4×C43—22no—
156C22×C4×C43—22no—
157C22×C4×C43—22no—
158C22×C4×C43—22no—
159C22×C4×C43—22no—
160C22×C4×C43—22no—
161C22×C4×C43—22no—
162C22×C4×C43—22no—
163C22×C4×C43—22no—
164C22×C4×C43—22no—
165C22×C4×C43—22no—
166C22×C4×C43—44no—
167C22×C4×C43—44no—
168C22×C4×C43—416no—
169C22×C4×C43C2×Q814yes—
170C22×C4×C43C2×Q814yes—
171C22×C4×C43#4114yes—
172C22×C4×C43#4114yes—
173C22×C4×C43C2412yes—
174C22×C4×C43C2412yes—
175C22×C4×C43C2412yes—
176C22×C4×C43C2412yes—
177C22×C4×C43C2412yes—
178C22×C4×C43C2412yes—
179C22×Dic43—22no—
180C22×Dic43—22no—
181C22×Dic43—22no—
182C22×Dic43—22no—
183C22×Dic43—22no—
184C22×Dic43—22no—
185C22×Dic43—22no—
186C22×Dic43—22no—
187C22×Dic43—22no—
188C22×Dic43—22no—
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#4114yes—
202C22×Dic43#4114yes—
203C22×Dic43C2412yes—
204C22×Dic43C2412yes—
205C22×Dic43C2412yes—
206C22×Dic43C2412yes—
207C22×Dic43C2412yes—
208C22×Dic43C2412yes—
209C22×Dic43C2412yes—
210C22×Dic43C2412yes—
211C22⋊C4×C43—28no—
212C22⋊C4×C43C2×Q8116yes—
213C42×C43—44no—
214C42×C43—44no—
215C22⋊Dic43—28no—
216C22⋊Dic43—28no—
217C22⋊Dic43—44no—
218C22⋊Dic43—44no—
219C4⋊Dic43—28no—
220C4⋊Dic43—28no—
221C4⋊Dic43—44no—
222C4⋊Dic43—44no—
223Dic43⋊C4—28no—
224Dic43⋊C4—28no—
225Dic43⋊C4—28no—
226Dic43⋊C4—28no—
227Dic43⋊C4—28no—
228Dic43⋊C4—44no—
229Dic43⋊C4—44no—
230Dic43⋊C4—44no—
231C4×Dic43—28no—
232C4×Dic43—44no—
233C23×C43—28no—
234C23×C43—28no—
235C23×C43—28no—
236C23×C43—22no—
237C23×C43—22no—
238C23×C43—22no—
239C23×C43—22no—
240C23×C43—22no—
241C23×C43—22no—
242C23×C43—44no—
243C23×C43—44no—
244C23×C43—44no—
245C23×C43—44no—
246C23×C43C22×Q814yes—
247C23×C43C22×Q812yes—
248C23×C43C2×#4112yes—
249C23×C43C2×#4112yes—
250C23×C43C2×#4112yes—
251C23×C43C2×#4112yes—
252C23×C43H(5,𝔽2)12yes—
253C23×C43H(5,𝔽2)12yes—
254C23×C43C2511yescharacteristic
255C2×C4×C43—28no—
256C2×C4×C43—28no—
257C2×C4×C43—28no—
258C2×C4×C43—28no—
259C2×C4×C43—22no—
260C2×C4×C43—22no—
261C2×C4×C43—22no—
262C2×C4×C43—22no—
263C2×C4×C43—22no—
264C2×C4×C43—22no—
265C2×C4×C43—22no—
266C2×C4×C43—22no—
267C2×C4×C43—22no—
268C2×C4×C43—22no—
269C2×C4×C43—22no—
270C2×C4×C43—22no—
271C2×C4×C43—22no—
272C2×C4×C43—22no—
273C2×C4×C43—416no—
274C2×C4×C43—44no—
275C2×C4×C43—44no—
276C2×C4×C43C22×Q814yes—
277C2×C4×C43C22×Q814yes—
278C2×C4×C43C2×#4114yes—
279C2×C4×C43C2×#4114yes—
280C2×Dic43—28no—
281C2×Dic43—28no—
282C2×Dic43—22no—
283C2×Dic43—22no—
284C2×Dic43—22no—
285C2×Dic43—22no—
286C2×Dic43—22no—
287C2×Dic43—22no—
288C2×Dic43—22no—
289C2×Dic43—22no—
290C2×Dic43—22no—
291C2×Dic43—22no—
292C2×Dic43—22no—
293C2×Dic43—22no—
294C2×Dic43—22no—
295C2×Dic43—22no—
296C2×Dic43—22no—
297C2×Dic43—22no—
298C2×Dic43—22no—
299C2×Dic43—22no—
300C2×Dic43—22no—
301C2×Dic43—22no—
302C2×Dic43—22no—
303C2×Dic43—22no—
304C2×Dic43—44no—
305C2×Dic43—44no—
306C2×Dic43—44no—
307C2×Dic43—44no—
308C2×Dic43—44no—
309C2×Dic43—44no—
310C2×Dic43C2×#4114yes—
311C2×Dic43C2×#4114yes—
312C2×#2587—431nomaximal, Sylow
313C22×C43—24no—
314C22×C43—24no—
315C22×C43—24no—
316C22×C43—416no—
317C22×C43—42no—
318C22×C43—42no—
319C22×C43—42no—
320C22×C43—42no—
321C22×C43#52914yes—
322C22×C43#53314yes—
323C22×C43#53814yes—
324C22×C43#55314yes—
325C22×C43#55314yes—
326C22×C43#55414yes—
327C22×C43#55414yes—
328C22×C43C23×Q811yescharacteristic
329C22×C43C22×#4111yescharacteristic
330C22×C43C22×#4111yescharacteristic
331C22×C43C22×#4111yescharacteristic
332C22×C43C22×#4111yescharacteristic
333C22×C43C2×H(5,𝔽2)11yescharacteristic
334C22×C43C2×H(5,𝔽2)11yescharacteristic
335C4×C43—24no—
336C4×C43—24no—
337C4×C43—24no—
338C4×C43—24no—
339C4×C43—42no—
340C4×C43—42no—
341Dic43—24no—
342Dic43—24no—
343Dic43—42no—
344Dic43—42no—
345Dic43—42no—
346Dic43—42no—
347Dic43—42no—
348Dic43—42no—
349#2587—4316no—
350C2×#400—431no—
351C2×#398—431no—
352C2×#396—431no—
353C2×#396—431no—
354C2×#389—431no—
355C2×#389—431no—
356C2×#389—431no—
357C2×#388—431no—
358C2×#388—431no—
359C2×#387—431no—
360C2×#387—431no—
361C2×#385—431no—
362C2×#385—431no—
363C2×C4×C4⋊C4—431no—
364C2×C4×C22⋊C4D4311yescharacteristic
365C2×C43—44no—
366C2×C43#258718yescomplemented
367C2×C43C2×#52911yescharacteristic
368C2×C43C2×#53311yescharacteristic
369C2×C43C2×#53811yescharacteristic
370C2×C43C2×#55311yescharacteristic
371C2×C43C2×#55311yescharacteristic
372C2×C43C2×#55411yescharacteristic
373C2×C43C2×#55411yescharacteristic
374C24×C4C2×D4311yescharacteristic
375C22×C4⋊C4—431no—
376C22×C4⋊C4—431no—
377C22×C4⋊C4—431no—
378C22×C4⋊C4—431no—
379C22×C4⋊C4—431no—
380C22×C4⋊C4—431no—
381C22×C4⋊C4—431no—
382C22×C4⋊C4—431no—
383C22×C4⋊C4—431no—
384C22×C4⋊C4—431no—
385C22×C4⋊C4—431no—
386C22×C4⋊C4—431no—
387C22×C22⋊C4—431no—
388C22×C22⋊C4—431no—
389C22×C22⋊C4—431no—
390C22×C22⋊C4—431no—
391C22×C22⋊C4C2×D4311yescharacteristic
392C22×C22⋊C4C2×D4311yescharacteristic
393C22×C42—431no—
394C22×C42—431no—
395C22×C42C2×D4311yescharacteristic
396C22×C42C2×D4311yescharacteristic
397#400—438no—
398#398—438no—
399#396—438no—
400#396—438no—
401#389—438no—
402#389—438no—
403#389—438no—
404#388—438no—
405#388—438no—
406#387—438no—
407#387—438no—
408#385—438no—
409#385—438no—
410C4×C4⋊C4—438no—
411C4×C22⋊C4C2×D4318yes—
412C2×#95—431no—
413C2×#95—431no—
414C2×#95—431no—
415C2×#95—431no—
416C2×#95—431no—
417C2×#95—431no—
418C2×#95—431no—
419C2×#95—431no—
420C2×#95—431no—
421C2×#95—431no—
422C2×#95C2×D4311yescharacteristic
423C2×#95C2×D4311yescharacteristic
424C43C2×#258711yescharacteristic, complemented, Sylow
425C25C22×D4311yescharacteristic
426C23×C4—24no—
427C23×C4—42no—
428C23×C4—42no—
429C23×C4—431no—
430C23×C4—431no—
431C23×C4—431no—
432C23×C4—431no—
433C23×C4—431no—
434C23×C4—431no—
435C23×C4—431no—
436C23×C4—431no—
437C23×C4C22×D4311yescharacteristic
438C23×C4C22×D4311yescharacteristic
439C23×C4C22×D4311yescharacteristic
440C23×C4C22×D4311yescharacteristic
441C23×C4C22×D4311yescharacteristic
442C23×C4C22×D4311yescharacteristic
443C23×C4C22×D4314yes—
444C2×C4⋊C4—434no—
445C2×C4⋊C4—434no—
446C2×C4⋊C4—434no—
447C2×C4⋊C4—434no—
448C2×C4⋊C4—434no—
449C2×C4⋊C4—434no—
450C2×C4⋊C4—434no—
451C2×C4⋊C4—434no—
452C2×C4⋊C4—434no—
453C2×C4⋊C4—434no—
454C2×C4⋊C4—434no—
455C2×C4⋊C4—434no—
456C2×C4⋊C4—864no—
457C2×C4⋊C4—864no—
458C2×C4⋊C4—864no—
459C2×C4⋊C4—864no—
460C2×C4⋊C4—864no—
461C2×C4⋊C4—864no—
462C2×C4⋊C4—864no—
463C2×C4⋊C4—1722no—
464C2×C4⋊C4—1722no—
465C2×C4⋊C4—1722no—
466C2×C4⋊C4—1722no—
467C2×C4⋊C4—1722no—
468C2×C22⋊C4—24no—
469C2×C22⋊C4—434no—
470C2×C22⋊C4—434no—
471C2×C22⋊C4—434no—
472C2×C22⋊C4—434no—
473C2×C22⋊C4—864no—
474C2×C22⋊C4—864no—
475C2×C22⋊C4—1722no—
476C2×C22⋊C4—1722no—
477C2×C22⋊C4Dic8618yes—
478C2×C22⋊C4C22×D4314yes—
479C2×C22⋊C4C22×D4314yes—
480C2×C42—42no—
481C2×C42—42no—
482C2×C42—434no—
483C2×C42—434no—
484C2×C42—864no—
485C2×C42—1722no—
486C2×C42C22×D4314yes—
487C2×C42C22×D4314yes—
488#95—434no—
489#95—434no—
490#95—434no—
491#95—434no—
492#95—434no—
493#95—434no—
494#95—434no—
495#95—434no—
496#95—434no—
497#95—434no—
498#95C22×D4314yes—
499#95C22×D4314yes—
500C24—22no—
501C24—22no—
502C24—22no—
503C24—22no—
504C24—22no—
505C24—22no—
506C24C2×Dic8614yes—
507C24C23×D4312yes—
508C24C23×D4311yescharacteristic
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
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—28no—
524C22×C4—44no—
525C22×C4—44no—
526C22×C4—416no—
527C22×C4—434no—
528C22×C4—434no—
529C22×C4—432no—
530C22×C4—432no—
531C22×C4—432no—
532C22×C4—432no—
533C22×C4—432no—
534C22×C4—432no—
535C22×C4—432no—
536C22×C4—432no—
537C22×C4—862no—
538C22×C4—862no—
539C22×C4—862no—
540C22×C4—862no—
541C22×C4—862no—
542C22×C4—862no—
543C22×C4—862no—
544C22×C4—862no—
545C22×C4—862no—
546C22×C4—862no—
547C22×C4—862no—
548C22×C4—862no—
549C22×C4—862no—
550C22×C4—862no—
551C22×C4—862no—
552C22×C4—862no—
553C22×C4—862no—
554C22×C4—862no—
555C22×C4—862no—
556C22×C4—862no—
557C22×C4—862no—
558C22×C4—862no—
559C22×C4C2×Dic8614yes—
560C22×C4C2×Dic8614yes—
561C22×C4#1062189814yes—
562C22×C4#1062189814yes—
563C22×C4C23×D4312yes—
564C22×C4C23×D4312yes—
565C22×C4C23×D4312yes—
566C22×C4C23×D4312yes—
567C22×C4C23×D4312yes—
568C22×C4C23×D4312yes—
569C4⋊C4—868no—
570C4⋊C4—868no—
571C4⋊C4—868no—
572C4⋊C4—868no—
573C4⋊C4—868no—
574C4⋊C4—868no—
575C4⋊C4—868no—
576C4⋊C4—1724no—
577C4⋊C4—1724no—
578C4⋊C4—1724no—
579C4⋊C4—1724no—
580C4⋊C4—1724no—
581C22⋊C4—28no—
582C22⋊C4—868no—
583C22⋊C4—868no—
584C22⋊C4—1724no—
585C22⋊C4—1724no—
586C22⋊C4C2×Dic86116yes—
587C42—44no—
588C42—44no—
589C42—868no—
590C42—1724no—
591C23—28no—
592C23—28no—
593C23—28no—
594C23—22no—
595C23—22no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—44no—
601C23—44no—
602C23—44no—
603C23—44no—
604C23C22×Dic8614yes—
605C23C22×Dic8612yes—
606C23#41×D4312yes—
607C23#41×D4312yes—
608C23C2×#1062189812yes—
609C23C2×#1062189812yes—
610C23#1306337012yes—
611C23#1306337012yes—
612C23C24×D4311yescharacteristic
613C2×C4—28no—
614C2×C4—28no—
615C2×C4—28no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—28no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—416no—
632C2×C4—44no—
633C2×C4—44no—
634C2×C4—434no—
635C2×C4—434no—
636C2×C4—868no—
637C2×C4—868no—
638C2×C4—862no—
639C2×C4—862no—
640C2×C4—862no—
641C2×C4—862no—
642C2×C4—862no—
643C2×C4—862no—
644C2×C4—862no—
645C2×C4—862no—
646C2×C4—862no—
647C2×C4—862no—
648C2×C4—862no—
649C2×C4—862no—
650C2×C4—862no—
651C2×C4—862no—
652C2×C4—862no—
653C2×C4—862no—
654C2×C4—862no—
655C2×C4—862no—
656C2×C4—862no—
657C2×C4—862no—
658C2×C4—862no—
659C2×C4—862no—
660C2×C4—1724no—
661C2×C4—1724no—
662C2×C4—1724no—
663C2×C4—1724no—
664C2×C4—1724no—
665C2×C4—1724no—
666C2×C4C22×Dic8614yes—
667C2×C4C22×Dic8614yes—
668C2×C4C2×#1062189814yes—
669C2×C4C2×#1062189814yes—
670C22—24no—
671C22—24no—
672C22—24no—
673C22—42no—
674C22—42no—
675C22—42no—
676C22—42no—
677C22—416no—
678C22#1458342714yes—
679C22#1458345614yes—
680C22#1458348714yes—
681C22#1458359814yes—
682C22#1458359914yes—
683C22#1458360814yes—
684C22#1458360814yes—
685C22C23×Dic8611yescharacteristic
686C22C2×#41×D4311yescharacteristic
687C22C2×#41×D4311yescharacteristic
688C22C22×#1062189811yescharacteristic
689C22C22×#1062189811yescharacteristic
690C22C2×#1306337011yescharacteristic
691C22C2×#1306337011yescharacteristic
692C4—24no—
693C4—24no—
694C4—24no—
695C4—24no—
696C4—42no—
697C4—42no—
698C4—864no—
699C4—864no—
700C4—1722no—
701C4—1722no—
702C4—1722no—
703C4—1722no—
704C4—1722no—
705C4—1722no—
706C2—44no—
707C2#1914001018yesdirect product factor
708C2C2×#1458342711yescharacteristic
709C2C2×#1458345611yescharacteristic
710C2C2×#1458348711yescharacteristic
711C2C2×#1458359811yescharacteristic
712C2C2×#1458359911yescharacteristic
713C2C2×#1458360811yescharacteristic
714C2C2×#1458360811yescharacteristic
subgroupG/H
centerC24C23×D43
commutator, cosocleC23×C43C25
FrattiniC23C24×D43
FittingC2×C4×C22⋊C4×C43C2
socleC24×C43C24
prime radicalC25×C43C23
hypercenterC2×C4×C22⋊C4D43
hypocenterC43C2×#2587
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #19140010C2direct (N × H)
2. C2×#14582841C2semidirect
3. C2×#14582833C2semidirect
6. C2×#14582797C2semidirect
7. C2×#14582797C2semidirect
8. C2×#14582796C2semidirect
11. C2×#14582786C2semidirect
12. C2×#14582783C2semidirect
15. C2×C4×Dic43⋊C4C2semidirect
35. #14582841C22semidirect
36. #14582833C22semidirect
39. #14582797C22semidirect
40. #14582797C22semidirect
41. #14582796C22semidirect
44. #14582786C22semidirect
45. #14582783C22semidirect
48. C4×Dic43⋊C4C22semidirect
366. C2×C43#2587semidirect
424. C43C2×#2587semidirect
707. C2#19140010direct (N × H)

Maximal subgroups

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

subgroupindex
#191400102
C2×#145828412
C2×#145828332
C2×#145828222
C2×#145827972
C2×#145827962
C2×#145827922
C2×#145827862
C2×#145827832
C2×#145827722
C2×C4×Dic43⋊C42
C2×C4×C22⋊C4×C432
C2×#258743