Finite Group Databasebeta

← C2×#19138427 #25264638

Subgroups — C2×#19138427 #25264638

Order 11008.

2702 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063323C211yesmaximal, characteristic
2C22×#13063290C211yesmaximal, characteristic
3#19138427C2116yesmaximal, direct product factor
4C2×#14582832C211yesmaximal, characteristic
5C2×#14582830C211yesmaximal, characteristic
6C2×#14582819C211yesmaximal, characteristic
7C2×#14582806C211yesmaximal, characteristic
8C2×#14582803C211yesmaximal, characteristic
9C2×#14582803C211yesmaximal, characteristic
10C2×#14582803C211yesmaximal, characteristic
11C2×#14582796C211yesmaximal, characteristic
12C2×#14582794C211yesmaximal, characteristic
13C2×#14582784C211yesmaximal, characteristic
14C2×#14582782C211yesmaximal, characteristic
15C2×C4⋊C4×Dic43C211yesmaximal, characteristic
16C2×C43×#395C211yesmaximal, characteristic
17C23×Dic86C2211yescharacteristic
18C23×Dic86C2211yescharacteristic
19C2×#13063323—28no—
20C2×#13063323C2218yes—
21C2×#13063290—28no—
22C2×#13063290C2218yes—
23C22×C4⋊Dic43C2211yescharacteristic
24C22×C4⋊Dic43C2211yescharacteristic
25C22×Dic43⋊C4C2211yescharacteristic
26C22×Dic43⋊C4C2211yescharacteristic
27C22×Dic43⋊C4C2211yescharacteristic
28C22×Dic43⋊C4C2211yescharacteristic
29C22×Dic43⋊C4C2211yescharacteristic
30C22×Dic43⋊C4C2211yescharacteristic
31C22×Dic43⋊C4C2211yescharacteristic
32C22×Dic43⋊C4C2211yescharacteristic
33C22×C4×Dic43C2211yescharacteristic
34C22×C4×Dic43C2211yescharacteristic
35C22×C4×Dic43C2211yescharacteristic
36C22×C4×Dic43C2211yescharacteristic
37C22×C4×Dic43C2211yescharacteristic
38#14582832C2218yes—
39#14582830C2218yes—
40#14582819C2218yes—
41#14582806C2218yes—
42#14582803C2218yes—
43#14582803C2218yes—
44#14582803C2218yes—
45#14582796C2218yes—
46#14582794C2218yes—
47#14582784C2218yes—
48#14582782C2218yes—
49C4⋊C4×Dic43C2218yes—
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
59C2×C43⋊#95C2211yescharacteristic
60C2×C43⋊#95C2211yescharacteristic
61C23×Q8×C43C2211yescharacteristic
62C22×C4⋊C4×C43C2211yescharacteristic
63C22×C4⋊C4×C43C2211yescharacteristic
64C22×C4⋊C4×C43C2211yescharacteristic
65C43×#395C2218yes—
66C2×#95×C43C2211yescharacteristic
67C2×#95×C43C2211yescharacteristic
68C2×#95×C43C2211yescharacteristic
69C22×Dic86—24no—
70C22×Dic86—24no—
71C22×Dic86—24no—
72C22×Dic86—24no—
73C22×Dic86—42no—
74C22×Dic86Q818yescomplemented
75C22×Dic86C2314yes—
76C22×Dic86C2314yes—
77C23×Dic43C2311yescharacteristic
78C23×Dic43C2311yescharacteristic
79C23×Dic43C2311yescharacteristic
80C23×Dic43C2311yescharacteristic
81C23×Dic43C2311yescharacteristic
82C23×Dic43C2311yescharacteristic
83C23×Dic43C2311yescharacteristic
84C23×Dic43C2311yescharacteristic
85#13063323—232no—
86#13063290—232no—
87C2×C4⋊Dic43—42no—
88C2×C4⋊Dic43Q818yescomplemented
89C2×C4⋊Dic43C2314yes—
90C2×C4⋊Dic43C2314yes—
91C2×Dic43⋊C4—24no—
92C2×Dic43⋊C4—24no—
93C2×Dic43⋊C4—24no—
94C2×Dic43⋊C4—24no—
95C2×Dic43⋊C4—24no—
96C2×Dic43⋊C4—42no—
97C2×Dic43⋊C4—42no—
98C2×Dic43⋊C4D418yes—
99C2×Dic43⋊C4C2314yes—
100C2×Dic43⋊C4C2314yes—
101C2×Dic43⋊C4C2314yes—
102C2×Dic43⋊C4C2314yes—
103C2×Dic43⋊C4C2314yes—
104C2×Dic43⋊C4C2314yes—
105C2×Dic43⋊C4C2314yes—
106C2×Dic43⋊C4C2314yes—
107C2×C4×Dic43—24no—
108C2×C4×Dic43—24no—
109C2×C4×Dic43—24no—
110C2×C4×Dic43—24no—
111C2×C4×Dic43—24no—
112C2×C4×Dic43C2314yes—
113C2×C4×Dic43C2314yes—
114C2×C4×Dic43C2314yes—
115C2×C4×Dic43C2314yes—
116C2×C4×Dic43C2314yes—
117C43⋊#95C2314yes—
118C43⋊#95C2314yes—
119C43⋊#95C2314yes—
120C43⋊#95C2314yes—
121C43⋊#95C2314yes—
122C43⋊#95C2314yes—
123C43⋊#95C2314yes—
124C43⋊#95C2314yes—
125C43⋊#95C2314yes—
126C43⋊#95C2314yes—
127C43⋊#95C2314yes—
128C22×Q8×C43—24no—
129C22×Q8×C43—24no—
130C22×Q8×C43—42no—
131C22×Q8×C43C2314yes—
132C23×C4×C43C2311yescharacteristic
133C23×C4×C43C2311yescharacteristic
134C23×C4×C43C2311yescharacteristic
135C23×C4×C43C2311yescharacteristic
136C23×C4×C43C2311yescharacteristic
137C23×C4×C43C2311yescharacteristic
138C23×C4×C43C2311yescharacteristic
139C2×C4⋊C4×C43—24no—
140C2×C4⋊C4×C43—24no—
141C2×C4⋊C4×C43—42no—
142C2×C4⋊C4×C43C2314yes—
143C2×C4⋊C4×C43C2314yes—
144C2×C4⋊C4×C43C2314yes—
145#95×C43C2314yes—
146#95×C43C2314yes—
147#95×C43C2314yes—
148C24×C43C2411yescharacteristic
149C2×Q8×C43—28no—
150C2×Q8×C43—28no—
151C2×Q8×C43—44no—
152C2×Q8×C43—416no—
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—22no—
167C22×C4×C43—22no—
168C22×C4×C43—22no—
169C22×C4×C43—22no—
170C22×C4×C43C2×D414yes—
171C22×C4×C43C2×Q814yes—
172C22×C4×C43C2×Q814yes—
173C22×C4×C43#4114yes—
174C22×C4×C43C2412yes—
175C22×C4×C43C2412yes—
176C22×C4×C43C2412yes—
177C22×C4×C43C2412yes—
178C22×C4×C43C2412yes—
179C22×C4×C43C2412yes—
180C22×C4×C43C2412yes—
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×Dic43C2×D414yes—
199C22×Dic43C2×D414yes—
200C22×Dic43C2×Q814yes—
201C22×Dic43C2×Q814yes—
202C22×Dic43C2×Q814yes—
203C22×Dic43C2×Q814yes—
204C22×Dic43#4114yes—
205C22×Dic43C2412yes—
206C22×Dic43C2412yes—
207C22×Dic43C2412yes—
208C22×Dic43C2412yes—
209C22×Dic43C2412yes—
210C22×Dic43C2412yes—
211C22×Dic43C2412yes—
212C22×Dic43C2412yes—
213C2×Dic86—232no—
214C2×Dic86—28no—
215C2×Dic86—28no—
216C2×Dic86—28no—
217C2×Dic86—28no—
218C2×Dic86—44no—
219C2×Dic86—416no—
220C2×Dic86C2×Q8116yescomplemented
221C4⋊C4×C43—28no—
222C4⋊C4×C43—28no—
223C4⋊C4×C43—44no—
224C4⋊Dic43—44no—
225C4⋊Dic43C2×Q8116yescomplemented
226Dic43⋊C4—28no—
227Dic43⋊C4—28no—
228Dic43⋊C4—28no—
229Dic43⋊C4—28no—
230Dic43⋊C4—28no—
231Dic43⋊C4—44no—
232Dic43⋊C4—44no—
233Dic43⋊C4C2×D4116yes—
234C4×Dic43—28no—
235C4×Dic43—28no—
236C4×Dic43—28no—
237C4×Dic43—28no—
238C4×Dic43—28no—
239C23×C43C22×D412yes—
240C23×C43C22×Q812yes—
241C23×C43C22×Q812yes—
242C23×C43C2×#4112yes—
243C23×C43C2×#4112yes—
244C23×C43H(5,𝔽2)12yes—
245C23×C432−1+412yes—
246C23×C43C2511yescharacteristic
247Q8×C43—416no—
248C2×C4×C43—28no—
249C2×C4×C43—28no—
250C2×C4×C43—28no—
251C2×C4×C43—28no—
252C2×C4×C43—22no—
253C2×C4×C43—22no—
254C2×C4×C43—22no—
255C2×C4×C43—22no—
256C2×C4×C43—22no—
257C2×C4×C43—22no—
258C2×C4×C43—22no—
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—44no—
270C2×C4×C43—44no—
271C2×C4×C43—44no—
272C2×C4×C43C22×D414yes—
273C2×C4×C43C22×Q814yes—
274C2×C4×C43C22×Q814yes—
275C2×C4×C43C2×#4114yes—
276C2×Dic43—28no—
277C2×Dic43—28no—
278C2×Dic43—28no—
279C2×Dic43—28no—
280C2×Dic43—22no—
281C2×Dic43—22no—
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—44no—
298C2×Dic43—44no—
299C2×Dic43—44no—
300C2×Dic43C22⋊Q8116yes—
301C2×Dic43C22×D414yes—
302C2×Dic43C22×D414yes—
303C2×Dic43C22×Q814yes—
304C2×Dic43C22×Q814yes—
305C2×Dic43C22×Q814yes—
306C2×Dic43C22×Q814yes—
307C2×Dic43C2×#4114yes—
308Dic86—232no—
309Dic86—416no—
310C2×#2451—431nomaximal, Sylow
311C22×C43C2×C22⋊Q814yes—
312C22×C43#53314yes—
313C22×C43#54214yes—
314C22×C43#54614yes—
315C22×C43D4×Q814yes—
316C22×C43#55714yes—
317C22×C43Q8214yes—
318C22×C43C23×D411yescharacteristic
319C22×C43C23×Q811yescharacteristic
320C22×C43C23×Q811yescharacteristic
321C22×C43C22×#4111yescharacteristic
322C22×C43C22×#4111yescharacteristic
323C22×C43C2×H(5,𝔽2)11yescharacteristic
324C22×C43C2×2−1+411yescharacteristic
325C4×C43—24no—
326C4×C43—24no—
327C4×C43—24no—
328C4×C43—24no—
329C4×C43—42no—
330C4×C43—42no—
331C4×C43—42no—
332Dic43—24no—
333Dic43—24no—
334Dic43—24no—
335Dic43—24no—
336Dic43—42no—
337Dic43—42no—
338Dic43—42no—
339Dic43C2×C22⋊Q818yes—
340C22×C4⋊Q8—431no—
341C22×C4×Q8—431no—
342#2451—4316no—
343C2×#398—431no—
344C2×#398—431no—
345C2×#395—431no—
346C2×#395D4311yescharacteristic
347C2×#391—431no—
348C2×#391—431no—
349C2×#391—431no—
350C2×#391—431no—
351C2×#389—431no—
352C2×#389—431no—
353C2×#387—431no—
354C2×#387—431no—
355C2×C4×C4⋊C4—431no—
356C2×C43#245118yescomplemented
357C2×C43C22×C22⋊Q811yescharacteristic
358C2×C43C2×#53311yescharacteristic
359C2×C43C2×#54211yescharacteristic
360C2×C43C2×#54611yescharacteristic
361C2×C43C2×D4×Q811yescharacteristic
362C2×C43C2×#55711yescharacteristic
363C2×C43C2×Q8211yescharacteristic
364C23×Q8—431no—
365C23×Q8—431no—
366C23×Q8C2×D4311yescharacteristic
367C2×C4⋊Q8—438no—
368C2×C4⋊Q8—868no—
369C2×C4×Q8—438no—
370C2×C4×Q8—868no—
371C22×C4⋊C4—431no—
372C22×C4⋊C4—431no—
373C22×C4⋊C4—431no—
374C22×C4⋊C4—431no—
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⋊C4C2×D4311yescharacteristic
382C22×C4⋊C4C2×D4311yescharacteristic
383C22×C4⋊C4C2×D4311yescharacteristic
384C22×C42—431no—
385C22×C42—431no—
386C22×C42—431no—
387C22×C42—431no—
388C22×C42—431no—
389#398—438no—
390#398—438no—
391#395—438no—
392#395C2×D4318yes—
393#391—438no—
394#391—438no—
395#391—438no—
396#391—438no—
397#389—438no—
398#389—438no—
399#387—438no—
400#387—438no—
401C4×C4⋊C4—438no—
402C2×#95—431no—
403C2×#95—431no—
404C2×#95—431no—
405C2×#95—431no—
406C2×#95—431no—
407C2×#95—431no—
408C2×#95—431no—
409C2×#95—431no—
410C2×#95—431no—
411C2×#95—431no—
412C2×#95—431no—
413C2×#95C2×D4311yescharacteristic
414C2×#95C2×D4311yescharacteristic
415C2×#95C2×D4311yescharacteristic
416C43C2×#245111yescharacteristic, complemented, Sylow
417C22×Q8—24no—
418C22×Q8—24no—
419C22×Q8—42no—
420C22×Q8—438no—
421C22×Q8—434no—
422C22×Q8—434no—
423C22×Q8—864no—
424C22×Q8—864no—
425C22×Q8—864no—
426C22×Q8—864no—
427C22×Q8—1722no—
428C22×Q8C22×D4314yes—
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×D4311yescharacteristic
444C4⋊Q8—8632no—
445C4×Q8—8632no—
446C2×C4⋊C4—24no—
447C2×C4⋊C4—24no—
448C2×C4⋊C4—42no—
449C2×C4⋊C4—438no—
450C2×C4⋊C4—438no—
451C2×C4⋊C4—434no—
452C2×C4⋊C4—434no—
453C2×C4⋊C4—434no—
454C2×C4⋊C4—434no—
455C2×C4⋊C4—434no—
456C2×C4⋊C4—434no—
457C2×C4⋊C4—434no—
458C2×C4⋊C4—434no—
459C2×C4⋊C4—434no—
460C2×C4⋊C4—434no—
461C2×C4⋊C4—864no—
462C2×C4⋊C4—864no—
463C2×C4⋊C4—864no—
464C2×C4⋊C4—864no—
465C2×C4⋊C4—864no—
466C2×C4⋊C4—1722no—
467C2×C4⋊C4—1722no—
468C2×C4⋊C4—1722no—
469C2×C4⋊C4C22×D4314yes—
470C2×C4⋊C4C22×D4314yes—
471C2×C4⋊C4C22×D4314yes—
472C2×C42—434no—
473C2×C42—434no—
474C2×C42—434no—
475C2×C42—434no—
476C2×C42—434no—
477C2×C42—864no—
478C2×C42—864no—
479C2×C42—864no—
480C2×C42—864no—
481C2×C42—864no—
482#95—434no—
483#95—434no—
484#95—434no—
485#95—434no—
486#95—434no—
487#95—434no—
488#95—434no—
489#95—434no—
490#95—434no—
491#95—434no—
492#95—434no—
493#95C22×D4314yes—
494#95C22×D4314yes—
495#95C22×D4314yes—
496C24C23×D4311yescharacteristic
497C2×Q8—28no—
498C2×Q8—28no—
499C2×Q8—44no—
500C2×Q8—416no—
501C2×Q8—4316no—
502C2×Q8—868no—
503C2×Q8—8632no—
504C2×Q8—868no—
505C2×Q8—868no—
506C2×Q8—868no—
507C2×Q8—1724no—
508C2×Q8—17216no—
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—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—434no—
527C22×C4—434no—
528C22×C4—434no—
529C22×C4—432no—
530C22×C4—434no—
531C22×C4—434no—
532C22×C4—434no—
533C22×C4—434no—
534C22×C4—432no—
535C22×C4—432no—
536C22×C4—432no—
537C22×C4—432no—
538C22×C4—432no—
539C22×C4—432no—
540C22×C4—432no—
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×C4D4×D4314yes—
559C22×C4#1062190014yes—
560C22×C4Q8×D4314yes—
561C22×C4Q8×D4314yes—
562C22×C4C23×D4312yes—
563C22×C4C23×D4312yes—
564C22×C4C23×D4312yes—
565C22×C4C23×D4312yes—
566C22×C4C23×D4312yes—
567C22×C4C23×D4312yes—
568C22×C4C23×D4312yes—
569C4⋊C4—28no—
570C4⋊C4—28no—
571C4⋊C4—44no—
572C4⋊C4—4316no—
573C4⋊C4—4316no—
574C4⋊C4—868no—
575C4⋊C4—868no—
576C4⋊C4—868no—
577C4⋊C4—868no—
578C4⋊C4—868no—
579C4⋊C4—1724no—
580C4⋊C4—1724no—
581C4⋊C4—1724no—
582C42—868no—
583C42—868no—
584C42—868no—
585C42—868no—
586C42—868no—
587C23C2×D4×D4312yes—
588C23C2×Q8×D4312yes—
589C23C2×Q8×D4312yes—
590C23#41×D4312yes—
591C23C2×#1062190012yes—
592C23#1306337012yes—
593C23#1306337312yes—
594C23C24×D4311yescharacteristic
595Q8—416no—
596Q8—8632no—
597Q8—17216no—
598C2×C4—28no—
599C2×C4—28no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—28no—
609C2×C4—28no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—44no—
620C2×C4—44no—
621C2×C4—44no—
622C2×C4—4316no—
623C2×C4—434no—
624C2×C4—434no—
625C2×C4—434no—
626C2×C4—434no—
627C2×C4—434no—
628C2×C4—434no—
629C2×C4—434no—
630C2×C4—868no—
631C2×C4—868no—
632C2×C4—868no—
633C2×C4—862no—
634C2×C4—862no—
635C2×C4—862no—
636C2×C4—862no—
637C2×C4—862no—
638C2×C4—862no—
639C2×C4—862no—
640C2×C4—862no—
641C2×C4—868no—
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—1724no—
652C2×C4—1724no—
653C2×C4—1724no—
654C2×C4C2×D4×D4314yes—
655C2×C4C2×Q8×D4314yes—
656C2×C4C2×Q8×D4314yes—
657C2×C4C2×#1062190014yes—
658C22C22⋊Q8×D4314yes—
659C22#1458345114yes—
660C22#1458351914yes—
661C22#1458353614yes—
662C22#1458356414yes—
663C22#1458362414yes—
664C22#1458362914yes—
665C22C22×D4×D4311yescharacteristic
666C22C22×Q8×D4311yescharacteristic
667C22C22×Q8×D4311yescharacteristic
668C22C2×#41×D4311yescharacteristic
669C22C22×#1062190011yescharacteristic
670C22C2×#1306337011yescharacteristic
671C22C2×#1306337311yescharacteristic
672C4—24no—
673C4—24no—
674C4—24no—
675C4—24no—
676C4—42no—
677C4—42no—
678C4—42no—
679C4—438no—
680C4—864no—
681C4—864no—
682C4—864no—
683C4—864no—
684C4—1722no—
685C4—1722no—
686C4—1722no—
687C2#1913842718yesdirect product factor
688C2C2×C22⋊Q8×D4311yescharacteristic
689C2C2×#1458345111yescharacteristic
690C2C2×#1458351911yescharacteristic
691C2C2×#1458353611yescharacteristic
692C2C2×#1458356411yescharacteristic
693C2C2×#1458362411yescharacteristic
694C2C2×#1458362911yescharacteristic
subgroupG/H
centerC24C23×D43
commutator, cosocleC23×C43C25
FrattiniC23C24×D43
FittingC2×C43×#395C2
socle, prime radicalC24×C43C24
hypercenterC2×#395D43
hypocenterC43C2×#2451
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#395

Complements

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

NH ≅ G/Ntype
3. #19138427C2direct (N × H)
74. C22×Dic86Q8semidirect
88. C2×C4⋊Dic43Q8semidirect
220. C2×Dic86C2×Q8semidirect
225. C4⋊Dic43C2×Q8semidirect
356. C2×C43#2451semidirect
416. C43C2×#2451semidirect
687. C2#19138427direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633232
C22×#130632902
#191384272
C2×#145828322
C2×#145828302
C2×#145828192
C2×#145828062
C2×#145828032
C2×#145827962
C2×#145827942
C2×#145827842
C2×#145827822
C2×C4⋊C4×Dic432
C2×C43×#3952
C2×#245143