Finite Group Databasebeta

← C2×#19139981 #25267829

Subgroups — C2×#19139981 #25267829

Order 11008.

2574 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063315C211yesmaximal, characteristic
2C22×#13063290C211yesmaximal, characteristic
3#19139981C2116yesmaximal, direct product factor
4C2×#14582833C211yesmaximal, characteristic
5C2×#14582832C211yesmaximal, characteristic
6C2×#14582820C211yesmaximal, characteristic
7C2×#14582819C211yesmaximal, characteristic
8C2×#14582797C211yesmaximal, characteristic
9C2×#14582796C211yesmaximal, characteristic
10C2×#14582796C211yesmaximal, characteristic
11C2×#14582794C211yesmaximal, characteristic
12C2×#14582794C211yesmaximal, characteristic
13C2×#14582794C211yesmaximal, characteristic
14C2×#14582794C211yesmaximal, characteristic
15C2×C4×Dic43⋊C4C211yesmaximal, characteristic
16C2×C43×#389C211yesmaximal, characteristic
17C23×Dic86C2211yescharacteristic
18C2×#13063315—28no—
19C2×#13063315C2218yes—
20C2×#13063290—28no—
21C2×#13063290C2218yes—
22C22×C4⋊Dic43C2211yescharacteristic
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×Dic43⋊C4C2211yescharacteristic
34C22×Dic43⋊C4C2211yescharacteristic
35C22×Dic43⋊C4C2211yescharacteristic
36C22×Dic43⋊C4C2211yescharacteristic
37C22×C4×Dic43C2211yescharacteristic
38C22×C4×Dic43C2211yescharacteristic
39C22×C4×Dic43C2211yescharacteristic
40C22×C4×Dic43C2211yescharacteristic
41#14582833C2218yes—
42#14582832C2218yes—
43#14582820C2218yes—
44#14582819C2218yes—
45#14582797C2218yes—
46#14582796C2218yes—
47#14582796C2218yes—
48#14582794C2218yes—
49#14582794C2218yes—
50#14582794C2218yes—
51#14582794C2218yes—
52C4×Dic43⋊C4C2218yes—
53C2×C43⋊#95C2211yescharacteristic
54C2×C43⋊#95C2211yescharacteristic
55C2×C43⋊#95C2211yescharacteristic
56C2×C43⋊#95C2211yescharacteristic
57C2×C43⋊#95C2211yescharacteristic
58C2×C43⋊#95C2211yescharacteristic
59C2×C43⋊#95C2211yescharacteristic
60C2×C43⋊#95C2211yescharacteristic
61C22×C4⋊C4×C43C2211yescharacteristic
62C22×C4⋊C4×C43C2211yescharacteristic
63C22×C4⋊C4×C43C2211yescharacteristic
64C22×C4⋊C4×C43C2211yescharacteristic
65C22×C42×C43C2211yescharacteristic
66C43×#389C2218yes—
67C2×#95×C43C2211yescharacteristic
68C2×#95×C43C2211yescharacteristic
69C22×Dic86—24no—
70C22×Dic86—24no—
71C22×Dic86—24no—
72C22×Dic86C2314yes—
73C23×Dic43C2311yescharacteristic
74C23×Dic43C2311yescharacteristic
75C23×Dic43C2311yescharacteristic
76C23×Dic43C2311yescharacteristic
77C23×Dic43C2311yescharacteristic
78C23×Dic43C2311yescharacteristic
79C23×Dic43C2311yescharacteristic
80C23×Dic43C2311yescharacteristic
81#13063315—232no—
82#13063290—232no—
83C2×C4⋊Dic43—24no—
84C2×C4⋊Dic43—24no—
85C2×C4⋊Dic43—42no—
86C2×C4⋊Dic43C2314yes—
87C2×C4⋊Dic43C2314yes—
88C2×C4⋊Dic43C2314yes—
89C2×Dic43⋊C4—24no—
90C2×Dic43⋊C4—24no—
91C2×Dic43⋊C4—24no—
92C2×Dic43⋊C4—24no—
93C2×Dic43⋊C4—24no—
94C2×Dic43⋊C4—24no—
95C2×Dic43⋊C4—24no—
96C2×Dic43⋊C4—24no—
97C2×Dic43⋊C4—42no—
98C2×Dic43⋊C4—42no—
99C2×Dic43⋊C4Q818yescomplemented
100C2×Dic43⋊C4Q818yescomplemented
101C2×Dic43⋊C4C2314yes—
102C2×Dic43⋊C4C2314yes—
103C2×Dic43⋊C4C2314yes—
104C2×Dic43⋊C4C2314yes—
105C2×Dic43⋊C4C2314yes—
106C2×Dic43⋊C4C2314yes—
107C2×Dic43⋊C4C2314yes—
108C2×Dic43⋊C4C2314yes—
109C2×Dic43⋊C4C2314yes—
110C2×Dic43⋊C4C2314yes—
111C2×Dic43⋊C4C2314yes—
112C2×Dic43⋊C4C2314yes—
113C2×C4×Dic43—24no—
114C2×C4×Dic43—24no—
115C2×C4×Dic43—42no—
116C2×C4×Dic43D418yes—
117C2×C4×Dic43C2314yes—
118C2×C4×Dic43C2314yes—
119C2×C4×Dic43C2314yes—
120C2×C4×Dic43C2314yes—
121C43⋊#95C2314yes—
122C43⋊#95C2314yes—
123C43⋊#95C2314yes—
124C43⋊#95C2314yes—
125C43⋊#95C2314yes—
126C43⋊#95C2314yes—
127C43⋊#95C2314yes—
128C43⋊#95C2314yes—
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—24no—
137C2×C4⋊C4×C43—24no—
138C2×C4⋊C4×C43—24no—
139C2×C4⋊C4×C43—42no—
140C2×C4⋊C4×C43C2314yes—
141C2×C4⋊C4×C43C2314yes—
142C2×C4⋊C4×C43C2314yes—
143C2×C4⋊C4×C43C2314yes—
144C2×C42×C43—42no—
145C2×C42×C43C2314yes—
146#95×C43C2314yes—
147#95×C43C2314yes—
148C24×C43C2411yescharacteristic
149C22×C4×C43—22no—
150C22×C4×C43—22no—
151C22×C4×C43—22no—
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×C43C2×D414yes—
167C22×C4×C43C2×Q814yes—
168C22×C4×C43C2×Q814yes—
169C22×C4×C43#4114yes—
170C22×C4×C43C2412yes—
171C22×C4×C43C2412yes—
172C22×C4×C43C2412yes—
173C22×C4×C43C2412yes—
174C22×C4×C43C2412yes—
175C22×C4×C43C2412yes—
176C22×C4×C43C2412yes—
177C22×Dic43—22no—
178C22×Dic43—22no—
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×Dic43C2×D414yes—
195C22×Dic43C2×D414yes—
196C22×Dic43C2×Q814yes—
197C22×Dic43C2×Q814yes—
198C22×Dic43C2×Q814yes—
199C22×Dic43C2×Q814yes—
200C22×Dic43#4114yes—
201C22×Dic43C2412yes—
202C22×Dic43C2412yes—
203C22×Dic43C2412yes—
204C22×Dic43C2412yes—
205C22×Dic43C2412yes—
206C22×Dic43C2412yes—
207C22×Dic43C2412yes—
208C22×Dic43C2412yes—
209C2×Dic86—232no—
210C2×Dic86—28no—
211C2×Dic86—28no—
212C2×Dic86—28no—
213C4⋊C4×C43—28no—
214C4⋊C4×C43—28no—
215C4⋊C4×C43—28no—
216C4⋊C4×C43—44no—
217C42×C43—44no—
218C4⋊Dic43—28no—
219C4⋊Dic43—28no—
220C4⋊Dic43—44no—
221Dic43⋊C4—28no—
222Dic43⋊C4—28no—
223Dic43⋊C4—28no—
224Dic43⋊C4—28no—
225Dic43⋊C4—28no—
226Dic43⋊C4—28no—
227Dic43⋊C4—28no—
228Dic43⋊C4—28no—
229Dic43⋊C4—44no—
230Dic43⋊C4—44no—
231Dic43⋊C4C2×Q8116yescomplemented
232Dic43⋊C4C2×Q8116yescomplemented
233C4×Dic43—28no—
234C4×Dic43—28no—
235C4×Dic43—44no—
236C4×Dic43C2×D4116yes—
237C23×C43C22×D412yes—
238C23×C43C22×Q812yes—
239C23×C43C22×Q812yes—
240C23×C43C2×#4112yes—
241C23×C43C2×#4112yes—
242C23×C43H(5,𝔽2)12yes—
243C23×C432−1+412yes—
244C23×C43C2511yescharacteristic
245C2×C4×C43—28no—
246C2×C4×C43—28no—
247C2×C4×C43—28no—
248C2×C4×C43—28no—
249C2×C4×C43—22no—
250C2×C4×C43—22no—
251C2×C4×C43—22no—
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—44no—
267C2×C4×C43—44no—
268C2×C4×C43—44no—
269C2×C4×C43C22×D414yes—
270C2×C4×C43C22×Q814yes—
271C2×C4×C43C22×Q814yes—
272C2×C4×C43C2×#4114yes—
273C2×Dic43—28no—
274C2×Dic43—28no—
275C2×Dic43—28no—
276C2×Dic43—28no—
277C2×Dic43—22no—
278C2×Dic43—22no—
279C2×Dic43—22no—
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—44no—
295C2×Dic43—44no—
296C2×Dic43—44no—
297C2×Dic43C4⋊Q8116yes—
298C2×Dic43C22×D414yes—
299C2×Dic43C22×D414yes—
300C2×Dic43C22×Q814yes—
301C2×Dic43C22×Q814yes—
302C2×Dic43C22×Q814yes—
303C2×Dic43C22×Q814yes—
304C2×Dic43C2×#4114yes—
305Dic86—232no—
306C2×#2584—431nomaximal, Sylow
307C22×C43#52514yes—
308C22×C43C2×C4⋊Q814yes—
309C22×C43#53714yes—
310C22×C43#55414yes—
311C22×C43#55414yes—
312C22×C43#55714yes—
313C22×C43#55714yes—
314C22×C43C23×D411yescharacteristic
315C22×C43C23×Q811yescharacteristic
316C22×C43C23×Q811yescharacteristic
317C22×C43C22×#4111yescharacteristic
318C22×C43C22×#4111yescharacteristic
319C22×C43C2×H(5,𝔽2)11yescharacteristic
320C22×C43C2×2−1+411yescharacteristic
321C4×C43—24no—
322C4×C43—24no—
323C4×C43—24no—
324C4×C43—24no—
325C4×C43—42no—
326C4×C43—42no—
327C4×C43—42no—
328Dic43—24no—
329Dic43—24no—
330Dic43—24no—
331Dic43—24no—
332Dic43—42no—
333Dic43—42no—
334Dic43—42no—
335Dic43C2×C4⋊Q818yes—
336C22×#125—431no—
337C22×C4×Q8—431no—
338#2584—4316no—
339C2×#398—431no—
340C2×#398—431no—
341C2×#395—431no—
342C2×#395—431no—
343C2×#389—431no—
344C2×#389—431no—
345C2×#389—431no—
346C2×#389—431no—
347C2×#389—431no—
348C2×#389—431no—
349C2×#389—431no—
350C2×#389D4311yescharacteristic
351C2×C4×C4⋊C4—431no—
352C2×C43#258418yescomplemented
353C2×C43C2×#52511yescharacteristic
354C2×C43C22×C4⋊Q811yescharacteristic
355C2×C43C2×#53711yescharacteristic
356C2×C43C2×#55411yescharacteristic
357C2×C43C2×#55411yescharacteristic
358C2×C43C2×#55711yescharacteristic
359C2×C43C2×#55711yescharacteristic
360C23×Q8—431no—
361C2×#125—438no—
362C2×#125—868no—
363C2×C4×Q8—438no—
364C2×C4×Q8—868no—
365C22×C4⋊C4—431no—
366C22×C4⋊C4—431no—
367C22×C4⋊C4—431no—
368C22×C4⋊C4—431no—
369C22×C4⋊C4—431no—
370C22×C4⋊C4—431no—
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⋊C4C2×D4311yescharacteristic
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×C42C2×D4311yescharacteristic
389#398—438no—
390#398—438no—
391#395—438no—
392#395—438no—
393#389—438no—
394#389—438no—
395#389—438no—
396#389—438no—
397#389—438no—
398#389—438no—
399#389—438no—
400#389C2×D4318yes—
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×#95C2×D4311yescharacteristic
411C2×#95C2×D4311yescharacteristic
412C43C2×#258411yescharacteristic, complemented, Sylow
413C22×Q8—434no—
414C22×Q8—864no—
415C22×Q8—864no—
416C22×Q8—864no—
417C23×C4—431no—
418C23×C4—431no—
419C23×C4—431no—
420C23×C4—431no—
421C23×C4—431no—
422C23×C4—431no—
423C23×C4—431no—
424C23×C4—431no—
425C23×C4C22×D4311yescharacteristic
426C23×C4C22×D4311yescharacteristic
427C23×C4C22×D4311yescharacteristic
428C23×C4C22×D4311yescharacteristic
429C23×C4C22×D4311yescharacteristic
430C23×C4C22×D4311yescharacteristic
431C23×C4C22×D4311yescharacteristic
432#125—8632no—
433C4×Q8—8632no—
434C2×C4⋊C4—24no—
435C2×C4⋊C4—24no—
436C2×C4⋊C4—24no—
437C2×C4⋊C4—42no—
438C2×C4⋊C4—438no—
439C2×C4⋊C4—438no—
440C2×C4⋊C4—434no—
441C2×C4⋊C4—434no—
442C2×C4⋊C4—434no—
443C2×C4⋊C4—434no—
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—864no—
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—864no—
464C2×C4⋊C4—864no—
465C2×C4⋊C4—1722no—
466C2×C4⋊C4—1722no—
467C2×C4⋊C4—1722no—
468C2×C4⋊C4C22×D4314yes—
469C2×C4⋊C4C22×D4314yes—
470C2×C4⋊C4C22×D4314yes—
471C2×C4⋊C4C22×D4314yes—
472C2×C42—42no—
473C2×C42—438no—
474C2×C42—434no—
475C2×C42—434no—
476C2×C42—434no—
477C2×C42—434no—
478C2×C42—864no—
479C2×C42—864no—
480C2×C42—1722no—
481C2×C42C22×D4314yes—
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#95C22×D4314yes—
491#95C22×D4314yes—
492C24C23×D4311yescharacteristic
493C2×Q8—868no—
494C2×Q8—868no—
495C2×Q8—8632no—
496C2×Q8—868no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—434no—
515C22×C4—434no—
516C22×C4—434no—
517C22×C4—432no—
518C22×C4—434no—
519C22×C4—434no—
520C22×C4—434no—
521C22×C4—434no—
522C22×C4—432no—
523C22×C4—432no—
524C22×C4—432no—
525C22×C4—432no—
526C22×C4—432no—
527C22×C4—432no—
528C22×C4—432no—
529C22×C4—862no—
530C22×C4—862no—
531C22×C4—862no—
532C22×C4—862no—
533C22×C4—862no—
534C22×C4—862no—
535C22×C4—862no—
536C22×C4—862no—
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#1062189814yes—
547C22×C4D4×D4314yes—
548C22×C4Q8×D4314yes—
549C22×C4Q8×D4314yes—
550C22×C4C23×D4312yes—
551C22×C4C23×D4312yes—
552C22×C4C23×D4312yes—
553C22×C4C23×D4312yes—
554C22×C4C23×D4312yes—
555C22×C4C23×D4312yes—
556C22×C4C23×D4312yes—
557C4⋊C4—28no—
558C4⋊C4—28no—
559C4⋊C4—28no—
560C4⋊C4—44no—
561C4⋊C4—4316no—
562C4⋊C4—4316no—
563C4⋊C4—868no—
564C4⋊C4—868no—
565C4⋊C4—868no—
566C4⋊C4—868no—
567C4⋊C4—868no—
568C4⋊C4—868no—
569C4⋊C4—868no—
570C4⋊C4—868no—
571C4⋊C4—868no—
572C4⋊C4—868no—
573C4⋊C4—1724no—
574C4⋊C4—1724no—
575C4⋊C4—1724no—
576C42—44no—
577C42—4316no—
578C42—868no—
579C42—868no—
580C42—1724no—
581C23C2×D4×D4312yes—
582C23C2×Q8×D4312yes—
583C23C2×Q8×D4312yes—
584C23#41×D4312yes—
585C23C2×#1062189812yes—
586C23#1306337012yes—
587C23#1306337212yes—
588C23C24×D4311yescharacteristic
589Q8—8632no—
590C2×C4—28no—
591C2×C4—28no—
592C2×C4—28no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—28no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—44no—
612C2×C4—44no—
613C2×C4—44no—
614C2×C4—4316no—
615C2×C4—434no—
616C2×C4—434no—
617C2×C4—434no—
618C2×C4—434no—
619C2×C4—434no—
620C2×C4—434no—
621C2×C4—434no—
622C2×C4—868no—
623C2×C4—868no—
624C2×C4—868no—
625C2×C4—868no—
626C2×C4—862no—
627C2×C4—862no—
628C2×C4—862no—
629C2×C4—862no—
630C2×C4—862no—
631C2×C4—862no—
632C2×C4—862no—
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—862no—
642C2×C4—862no—
643C2×C4—1724no—
644C2×C4—1724no—
645C2×C4—1724no—
646C2×C4C2×D4×D4314yes—
647C2×C4C2×Q8×D4314yes—
648C2×C4C2×Q8×D4314yes—
649C2×C4C2×#1062189814yes—
650C22#1458340814yes—
651C22C4⋊Q8×D4314yes—
652C22#1458347614yes—
653C22#1458360314yes—
654C22#1458360414yes—
655C22#1458362614yes—
656C22#1458362714yes—
657C22C22×D4×D4311yescharacteristic
658C22C22×Q8×D4311yescharacteristic
659C22C22×Q8×D4311yescharacteristic
660C22C2×#41×D4311yescharacteristic
661C22C22×#1062189811yescharacteristic
662C22C2×#1306337011yescharacteristic
663C22C2×#1306337211yescharacteristic
664C4—24no—
665C4—24no—
666C4—24no—
667C4—24no—
668C4—42no—
669C4—42no—
670C4—42no—
671C4—438no—
672C4—864no—
673C4—864no—
674C4—864no—
675C4—864no—
676C4—1722no—
677C4—1722no—
678C4—1722no—
679C2#1913998118yesdirect product factor
680C2C2×#1458340811yescharacteristic
681C2C2×C4⋊Q8×D4311yescharacteristic
682C2C2×#1458347611yescharacteristic
683C2C2×#1458360311yescharacteristic
684C2C2×#1458360411yescharacteristic
685C2C2×#1458362611yescharacteristic
686C2C2×#1458362711yescharacteristic
subgroupG/H
centerC24C23×D43
commutator, cosocleC23×C43C25
FrattiniC23C24×D43
FittingC2×C43×#389C2
socle, prime radicalC24×C43C24
hypercenterC2×#389D43
hypocenterC43C2×#2584
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
3. #19139981C2direct (N × H)
99. C2×Dic43⋊C4Q8semidirect
100. C2×Dic43⋊C4Q8semidirect
231. Dic43⋊C4C2×Q8semidirect
232. Dic43⋊C4C2×Q8semidirect
352. C2×C43#2584semidirect
412. C43C2×#2584semidirect
679. C2#19139981direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633152
C22×#130632902
#191399812
C2×#145828332
C2×#145828322
C2×#145828202
C2×#145828192
C2×#145827972
C2×#145827962
C2×#145827942
C2×C4×Dic43⋊C42
C2×C43×#3892
C2×#258443