Finite Group Databasebeta

← C2×#19145790 #25968737

Subgroups — C2×#19145790 #25968737

Order 11008.

2038 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583452C211yesmaximal, characteristic, complemented
2C2×#14583444C211yesmaximal, characteristic
3#19145790C2116yesmaximal, direct product factor
4C2×#14583307C211yesmaximal, characteristic, complemented
5C2×#14583306C211yesmaximal, characteristic, complemented
6C2×#14583262C211yesmaximal, characteristic, complemented
7C2×#14583262C211yesmaximal, characteristic, complemented
8C2×#14583224C211yesmaximal, characteristic, complemented
9C2×#14583223C211yesmaximal, characteristic, complemented
10C2×#14583220C211yesmaximal, characteristic, complemented
11C2×#14583188C211yesmaximal, characteristic, complemented
12C2×#14583187C211yesmaximal, characteristic, complemented
13C2×#14583178C211yesmaximal, characteristic, complemented
14C2×#14583177C211yesmaximal, characteristic, complemented
15C2×#14582953C211yesmaximal, characteristic, complemented
16C2×C43×#482C211yesmaximal, characteristic, complemented
17C22×#10621900—21no—
18#14583452—24no—
19#14583452C2218yescomplemented
20#14583444—24no—
21#14583444C2218yes—
22C2×#13063324C2211yescharacteristic
23C2×#13063324C2211yescharacteristic
24C2×#13063324C2211yescharacteristic
25C2×#13063321C2211yescharacteristic
26C2×#13063316C2211yescharacteristic
27C2×#13063316C2211yescharacteristic
28C2×#13063311—21no—
29C2×#13063302—21no—
30C2×#13063302—21no—
31C2×#13063299C2211yescharacteristic
32C2×#13063297—21no—
33C2×C4×Dic86—21no—
34C2×C4×Dic86—21no—
35C2×D4×Dic43C2211yescharacteristic
36C2×#13063287C2211yescharacteristic
37C2×(C22⋊D43)⋊C4—21no—
38C2×#13063284C2211yescharacteristic
39C22×C4×Dic43C2211yescharacteristic
40#14583307C2218yescomplemented
41#14583306C2218yescomplemented
42#14583262C2218yescomplemented
43#14583262C2218yescomplemented
44#14583224C2218yescomplemented
45#14583223C2218yescomplemented
46#14583220C2218yescomplemented
47#14583188C2218yescomplemented
48#14583187C2218yescomplemented
49#14583178C2218yescomplemented
50#14583177C2218yescomplemented
51#14582953C2218yescomplemented
52C2×#13063259C2211yescharacteristic
53C2×#13063258C2211yescharacteristic
54C2×#13063258C2211yescharacteristic
55C2×#13063257C2211yescharacteristic
56C2×#13063256C2211yescharacteristic
57C2×#13063256C2211yescharacteristic
58C2×Dic43⋊C8C2211yescharacteristic
59C2×Dic43⋊C8C2211yescharacteristic
60C2×#13063247C2211yescharacteristic
61C2×#13063247C2211yescharacteristic
62C2×#13063246C2211yescharacteristic
63C2×#13063246C2211yescharacteristic
64C2×#13063245C2211yescharacteristic
65C2×#13063245C2211yescharacteristic
66C2×C22⋊(C43⋊C8)C2211yescharacteristic
67C2×#13063235C2211yescharacteristic
68C2×#13063235C2211yescharacteristic
69C2×#121×C43C2211yescharacteristic
70C2×#117×C43C2211yescharacteristic
71C43×#482C2218yescomplemented
72C2×#107×C43C2211yescharacteristic
73C2×#106×C43C2211yescharacteristic
74C2×#102×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×C22⋊C8×C43C2211yescharacteristic
77C2×#10621900—28no—
78C2×#10621900—48no—
79C22×Dic86—21no—
80C22×Dic86—21no—
81C22×Dic86—21no—
82C22×D172C2311yescharacteristic
83C22×C22⋊D43—21no—
84C22×C22⋊D43—21no—
85C22×C22⋊D43—21no—
86C23×Dic43—21no—
87C23×Dic43D411yescharacteristic
88C23×Dic43D411yescharacteristic
89C22×C4×D43—21no—
90C22×C43⋊C8C2311yescharacteristic
91C22×C43⋊C8C2311yescharacteristic
92#13063324—22no—
93#13063324—22no—
94#13063324—22no—
95#13063324C2314yes—
96#13063324C2314yes—
97#13063324C2314yes—
98#13063321—22no—
99#13063321C2314yes—
100#13063316—22no—
101#13063316—22no—
102#13063316C2314yes—
103#13063316C2314yes—
104#13063311—28no—
105#13063302—28no—
106#13063302—28no—
107#13063299—22no—
108#13063299C2314yes—
109#13063297—28no—
110C4×Dic86—28no—
111C4×Dic86—28no—
112D4×Dic43—22no—
113D4×Dic43C2314yes—
114#13063287—22no—
115#13063287C2314yes—
116(C22⋊D43)⋊C4—28no—
117#13063284—22no—
118#13063284C2314yes—
119C2×C4⋊Dic43—21no—
120C2×C4⋊Dic43—21no—
121C2×C4⋊Dic43C2311yescharacteristic
122C2×C4⋊Dic43C2311yescharacteristic
123C2×C4⋊Dic43C2311yescharacteristic
124C2×Dic43⋊C4—21no—
125C2×Dic43⋊C4—21no—
126C2×Dic43⋊C4—21no—
127C2×Dic43⋊C4—21no—
128C2×Dic43⋊C4—21no—
129C2×C22⋊Dic43—21no—
130C2×C22⋊Dic43—21no—
131C2×(C2×D43)⋊C4—21no—
132C2×(C2×D43)⋊C4—21no—
133C2×C4×Dic43—21no—
134C2×C4×Dic43D411yescharacteristic
135C2×C4×Dic43D411yescharacteristic
136C2×C4×Dic43D414yes—
137C2×C4×Dic43C2311yescharacteristic
138C2×C4×Dic43C2311yescharacteristic
139C2×C4×Dic43C2314yes—
140#13063259C2314yes—
141#13063258C2314yes—
142#13063258C2314yes—
143#13063257C2314yes—
144#13063256C2314yes—
145#13063256C2314yes—
146Dic43⋊C8C2314yes—
147Dic43⋊C8C2314yes—
148#13063247C2314yes—
149#13063247C2314yes—
150#13063246C2314yes—
151#13063246C2314yes—
152#13063245C2314yes—
153#13063245C2314yes—
154C22⋊(C43⋊C8)C2314yes—
155#13063235C2314yes—
156#13063235C2314yes—
157C22×D4×C43—21no—
158C22×D4×C43C2311yescharacteristic
159C23×C4×C43C2311yescharacteristic
160C22×C8×C43C2311yescharacteristic
161C22×C8×C43C2311yescharacteristic
162#121×C43—22no—
163#121×C43C2314yes—
164#117×C43—22no—
165#117×C43C2314yes—
166C2×C4⋊C4×C43C2311yescharacteristic
167C2×C4⋊C4×C43C2311yescharacteristic
168C2×C4⋊C4×C43C2311yescharacteristic
169C2×C22⋊C4×C43—21no—
170C2×C22⋊C4×C43—21no—
171C2×C42×C43—21no—
172#107×C43C2314yes—
173#106×C43C2314yes—
174#102×C43C2314yes—
175#102×C43C2314yes—
176C22⋊C8×C43C2314yes—
177C24×C43—21no—
178C24×C43C2×D411yescharacteristic
179C23×D43—21no—
180C2×D4×C43—21no—
181C2×D4×C43—24no—
182C2×D4×C43—22no—
183C2×D4×C43—22no—
184C2×D4×C43—44no—
185C2×D4×C43C2412yes—
186C22×C4×C43—22no—
187C22×C4×C43—22no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43—21no—
191C22×C4×C43C2×D411yescharacteristic
192C22×C4×C43C2×D412yes—
193C22×C4×C43C2412yes—
194C22×C4×C43C2411yescharacteristic
195C2×C22⋊D43—24no—
196C2×C22⋊D43—24no—
197C2×C22⋊D43—24no—
198C2×C22⋊D43—44no—
199C2×C22⋊D43—44no—
200C2×C22⋊D43—44no—
201C22×Dic43—24no—
202C22×Dic43—24no—
203C22×Dic43—21no—
204C22×Dic43—21no—
205C22×Dic43—21no—
206C22×Dic43—42no—
207C22×Dic43—44no—
208C22×Dic43C2×D411yescharacteristic
209C22×Dic43C2×D411yescharacteristic
210C22×Dic43C2×D411yescharacteristic
211C22×Dic43C2×D414yes—
212C22×Dic43C2×D414yes—
213C22×Dic43C2×D411yescharacteristic
214#10621900—432no—
215C2×D172—21no—
216C2×D172—22no—
217C2×D172—22no—
218C2×D172C2412yes—
219C2×C4×D43—24no—
220C2×C4×D43—44no—
221C2×Dic86—24no—
222C2×Dic86—24no—
223C2×Dic86—24no—
224C2×Dic86—44no—
225C2×Dic86—44no—
226C2×Dic86—44no—
227C2×C8×C43—22no—
228C2×C8×C43—22no—
229C2×C8×C43C2412yes—
230C2×C8×C43C2412yes—
231C4⋊C4×C43—21no—
232C4⋊C4×C43—21no—
233C4⋊C4×C43—21no—
234C4⋊C4×C43C2412yes—
235C4⋊C4×C43C2412yes—
236C4⋊C4×C43C2412yes—
237C22⋊C4×C43—24no—
238C22⋊C4×C43—24no—
239C42×C43—24no—
240C22⋊Dic43—24no—
241C22⋊Dic43—24no—
242(C2×D43)⋊C4—24no—
243(C2×D43)⋊C4—24no—
244C4⋊Dic43—21no—
245C4⋊Dic43—21no—
246C4⋊Dic43—21no—
247C4⋊Dic43—24no—
248C4⋊Dic43—24no—
249C4⋊Dic43C2412yes—
250C4⋊Dic43C2412yes—
251C4⋊Dic43C2412yes—
252Dic43⋊C4—24no—
253Dic43⋊C4—24no—
254Dic43⋊C4—24no—
255Dic43⋊C4—24no—
256Dic43⋊C4—24no—
257C4×Dic43—24no—
258C4×Dic43C2×D414yes—
259C4×Dic43C2×D412yes—
260C4×Dic43C2×D414yes—
261C4×Dic43C2×D412yes—
262C4×Dic43C2412yes—
263C4×Dic43C2412yes—
264C2×C43⋊C8—22no—
265C2×C43⋊C8—22no—
266C2×C43⋊C8C2412yes—
267C2×C43⋊C8C2412yes—
268C23×C43—22no—
269C23×C43—22no—
270C23×C43—22no—
271C23×C43—22no—
272C23×C43—42no—
273C23×C43—42no—
274C23×C43—42no—
275C23×C43C22×D412yes—
276C23×C43C22×D411yescharacteristic
277C22×D43—22no—
278C22×D43—42no—
279C22×D43—42no—
280C22×D43—42no—
281D4×C43—22no—
282D4×C43—22no—
283D4×C43—48no—
284D4×C43—42no—
285C2×C4×C43—22no—
286C2×C4×C43—24no—
287C2×C4×C43—22no—
288C2×C4×C43—22no—
289C2×C4×C43—22no—
290C2×C4×C43—22no—
291C2×C4×C43—22no—
292C2×C4×C43—42no—
293C2×C4×C43—42no—
294C2×C4×C43—42no—
295C2×C4×C43C22×D412yes—
296C2×C4×C43C22×D411yescharacteristic
297C2×C4×C432−1+412yes—
298C2×C4×C432−1+412yes—
299C2×C4×C43C2511yescharacteristic
300C22⋊D43—48no—
301C22⋊D43—48no—
302C22⋊D43—48no—
303C2×Dic43—22no—
304C2×Dic43—22no—
305C2×Dic43—22no—
306C2×Dic43—28no—
307C2×Dic43—22no—
308C2×Dic43—22no—
309C2×Dic43—22no—
310C2×Dic43—44no—
311C2×Dic43—42no—
312C2×Dic43—42no—
313C2×Dic43—42no—
314C2×Dic43—48no—
315C2×Dic43AGL(1,ℤ/8)14yes—
316C2×Dic43C22×D412yes—
317C2×Dic43C22×D412yes—
318C2×Dic43C22×D412yes—
319C2×Dic43C22×D412yes—
320D172—22no—
321D172—22no—
322D172—42no—
323C4×D43—48no—
324Dic86—48no—
325Dic86—48no—
326Dic86—48no—
327C8×C43—22no—
328C8×C43—22no—
329C43⋊C8—22no—
330C43⋊C8—22no—
331C2×#3235—431nomaximal, Sylow
332C22×C43—22no—
333C22×C43—22no—
334C22×C43—22no—
335C22×C43—44no—
336C22×C43—42no—
337C22×C43—42no—
338C22×C43—42no—
339C22×C43—84no—
340C22×C43#53612yes—
341C22×C43C2×AGL(1,ℤ/8)12yes—
342C22×C43#57512yes—
343C22×C43C23×D411yescharacteristic
344C2×D43—42no—
345C2×D43—42no—
346C2×D43—42no—
347C2×D43—84no—
348C4×C43—22no—
349C4×C43—42no—
350C4×C43—42no—
351C4×C43—42no—
352C4×C43#53612yes—
353C4×C43C2×2−1+411yescharacteristic
354C4×C43C2×2−1+411yescharacteristic
355Dic43—22no—
356Dic43—22no—
357Dic43—22no—
358Dic43—42no—
359Dic43—42no—
360Dic43—42no—
361Dic43C2×AGL(1,ℤ/8)14yes—
362C2×#533—431no—
363C2×#532—431no—
364#3235—4316no—
365C2×#501—431no—
366C2×#501—431no—
367C2×#490—431no—
368C2×#490—431no—
369C2×#482—431no—
370C2×#482—431no—
371C2×#482—431no—
372C2×#482D4311yescharacteristic, complemented
373C2×#476—431no—
374C2×#476—431no—
375C2×#474—431no—
376C2×#474—431no—
377C2×#432—431no—
378C2×C43—42no—
379C2×C43—82no—
380C2×C43#323514yescomplemented
381C2×C43C2×#53611yescharacteristic
382C2×C43C22×AGL(1,ℤ/8)11yescharacteristic
383C2×C43C2×#57511yescharacteristic
384D43—82no—
385C22×#41—861no—
386#533—438no—
387#533—864no—
388#532—438no—
389#532—864no—
390C2×C4⋊Q8—431no—
391C2×C4⋊Q8—431no—
392C2×C4⋊Q8—431no—
393C2×#127—431no—
394C2×#125—431no—
395C2×#125—431no—
396C2×#124—861no—
397C2×C22⋊Q8—861no—
398C2×C22⋊Q8—861no—
399C2×#121—431no—
400C2×#121—861no—
401C2×#121C2×D4311yescharacteristic
402C2×C4×Q8—861no—
403C2×C4×Q8—861no—
404C2×C4×D4—431no—
405C2×C4×D4—431no—
406C2×C4×D4—861no—
407C2×#117—431no—
408C2×#117C2×D4311yescharacteristic
409C22×C42—431no—
410#501—438no—
411#501—438no—
412#490—438no—
413#490—438no—
414#482—438no—
415#482—438no—
416#482—438no—
417#482C2×D4318yescomplemented
418#476—438no—
419#476—438no—
420#474—438no—
421#474—438no—
422#432—438no—
423C2×#107—431no—
424C2×#107—431no—
425C2×#107—431no—
426C2×#107C2×D4311yescharacteristic
427C2×#106—431no—
428C2×#106—431no—
429C2×#106—431no—
430C2×#106C2×D4311yescharacteristic
431C2×C4⋊C8—431no—
432C2×C4⋊C8—431no—
433C2×#102—431no—
434C2×#102—431no—
435C2×#102—431no—
436C2×#102—431no—
437C2×#102—431no—
438C2×#102—431no—
439C2×#102C2×D4311yescharacteristic
440C2×#102C2×D4311yescharacteristic
441C2×C22⋊C8—431no—
442C2×C22⋊C8C2×D4311yescharacteristic
443C2×#97—431no—
444C2×#97—431no—
445C43C2×#323511yescharacteristic, complemented, Sylow
446C2×#41—868no—
447C2×#41—1728no—
448C22×Q8—861no—
449C22×Q8—861no—
450C22×Q8—861no—
451C22×D4—21no—
452C22×D4—431no—
453C22×D4—861no—
454C22×D4—861no—
455C22×D4—861no—
456C22×D4C22×D4311yescharacteristic
457C23×C4—431no—
458C23×C4—431no—
459C23×C4—861no—
460C23×C4—861no—
461C23×C4C22×D4311yescharacteristic
462C22×C8—431no—
463C22×C8—431no—
464C22×C8C22×D4311yescharacteristic
465C22×C8C22×D4311yescharacteristic
466C4⋊Q8—434no—
467C4⋊Q8—434no—
468C4⋊Q8—434no—
469C4⋊Q8—862no—
470C4⋊Q8—862no—
471C4⋊Q8—862no—
472#127—434no—
473#127—862no—
474#125—434no—
475#125—434no—
476#125—862no—
477#125—862no—
478#124—868no—
479C22⋊Q8—868no—
480C22⋊Q8—868no—
481#121—22no—
482#121—434no—
483#121—868no—
484#121—862no—
485#121C22×D4314yes—
486C4×Q8—868no—
487C4×Q8—868no—
488C4×D4—434no—
489C4×D4—434no—
490C4×D4—868no—
491C4×D4—862no—
492C4×D4—862no—
493#117—22no—
494#117—434no—
495#117—862no—
496#117C22×D4314yes—
497C2×C4⋊C4—431no—
498C2×C4⋊C4—431no—
499C2×C4⋊C4—431no—
500C2×C4⋊C4—861no—
501C2×C4⋊C4—861no—
502C2×C4⋊C4—861no—
503C2×C4⋊C4—861no—
504C2×C4⋊C4—861no—
505C2×C4⋊C4—861no—
506C2×C4⋊C4—861no—
507C2×C4⋊C4C22×D4311yescharacteristic
508C2×C4⋊C4C22×D4311yescharacteristic
509C2×C4⋊C4C22×D4311yescharacteristic
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—861no—
513C2×C22⋊C4—861no—
514C2×C22⋊C4—861no—
515C2×C22⋊C4—861no—
516C2×C42—21no—
517C2×C42—431no—
518C2×C42—431no—
519C2×C42—434no—
520C2×C42—431no—
521C2×C42—431no—
522C2×C42—434no—
523C2×C42—861no—
524#107—434no—
525#107—434no—
526#107—434no—
527#107C22×D4314yes—
528#106—434no—
529#106—434no—
530#106—434no—
531#106C22×D4314yes—
532C4⋊C8—434no—
533C4⋊C8—434no—
534#102—434no—
535#102—434no—
536#102—434no—
537#102—434no—
538#102—434no—
539#102—434no—
540#102C22×D4314yes—
541#102C22×D4314yes—
542C22⋊C8—434no—
543C22⋊C8C22×D4314yes—
544#97—434no—
545#97—434no—
546C24—21no—
547C24—861no—
548C24D4×D4311yescharacteristic
549#41—17232no—
550C2×Q8—864no—
551C2×Q8—864no—
552C2×Q8—864no—
553C2×Q8—1724no—
554C2×Q8—1724no—
555C2×Q8—1724no—
556C2×D4—24no—
557C2×D4—21no—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—44no—
561C2×D4—432no—
562C2×D4—864no—
563C2×D4—864no—
564C2×D4—864no—
565C2×D4—861no—
566C2×D4—862no—
567C2×D4—862no—
568C2×D4—1724no—
569C2×D4—1724no—
570C2×D4—1724no—
571C2×D4C23×D4312yes—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—431no—
578C22×C4—434no—
579C22×C4—431no—
580C22×C4—431no—
581C22×C4—431no—
582C22×C4—434no—
583C22×C4—864no—
584C22×C4—864no—
585C22×C4—864no—
586C22×C4—861no—
587C22×C4—861no—
588C22×C4—861no—
589C22×C4—1724no—
590C22×C4—1724no—
591C22×C4—1722no—
592C22×C4D4×D4312yes—
593C22×C4D4×D4311yescharacteristic
594C22×C4C23×D4312yes—
595C22×C4C23×D4311yescharacteristic
596C2×C8—22no—
597C2×C8—22no—
598C2×C8—432no—
599C2×C8—432no—
600C2×C8—862no—
601C2×C8—862no—
602C2×C8C23×D4312yes—
603C2×C8C23×D4312yes—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—432no—
608C4⋊C4—432no—
609C4⋊C4—432no—
610C4⋊C4—864no—
611C4⋊C4—864no—
612C4⋊C4—864no—
613C4⋊C4—864no—
614C4⋊C4—864no—
615C4⋊C4—864no—
616C4⋊C4—864no—
617C4⋊C4—861no—
618C4⋊C4—861no—
619C4⋊C4—861no—
620C4⋊C4C23×D4312yes—
621C4⋊C4C23×D4312yes—
622C4⋊C4C23×D4312yes—
623C22⋊C4—24no—
624C22⋊C4—24no—
625C22⋊C4—864no—
626C22⋊C4—864no—
627C22⋊C4—864no—
628C22⋊C4—864no—
629C42—24no—
630C42—434no—
631C42—432no—
632C42—434no—
633C42—432no—
634C42—432no—
635C42—432no—
636C42—864no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—862no—
645C23—1722no—
646C23—1722no—
647C23—1722no—
648C23C2×D4×D4312yes—
649C23C2×D4×D4311yescharacteristic
650Q8—1728no—
651Q8—1728no—
652Q8—1728no—
653D4—22no—
654D4—22no—
655D4—48no—
656D4—42no—
657D4—862no—
658D4—862no—
659D4—1728no—
660D4—1728no—
661D4—1728no—
662D4—1722no—
663C2×C4—22no—
664C2×C4—24no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—434no—
674C2×C4—432no—
675C2×C4—432no—
676C2×C4—432no—
677C2×C4—432no—
678C2×C4—868no—
679C2×C4—862no—
680C2×C4—862no—
681C2×C4—862no—
682C2×C4—862no—
683C2×C4—862no—
684C2×C4—862no—
685C2×C4—1728no—
686C2×C4—1728no—
687C2×C4—1724no—
688C2×C4—1722no—
689C2×C4—1722no—
690C2×C4—1722no—
691C2×C4C2×D4×D4312yes—
692C2×C4C2×D4×D4311yescharacteristic
693C2×C4#1306337212yes—
694C2×C4#1306337212yes—
695C2×C4C24×D4311yescharacteristic
696C8—22no—
697C8—22no—
698C8—862no—
699C8—862no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—44no—
704C22—42no—
705C22—42no—
706C22—42no—
707C22—84no—
708C22—3444no—
709C22—1722no—
710C22—1722no—
711C22—1722no—
712C22#1458347112yes—
713C22AGL(1,ℤ/8)×D4312yes—
714C22#1458369612yes—
715C22C22×D4×D4311yescharacteristic
716C4—22no—
717C4—42no—
718C4—42no—
719C4—42no—
720C4—434no—
721C4—862no—
722C4—862no—
723C4—862no—
724C4—1722no—
725C4—1722no—
726C4—1722no—
727C4#1458347112yes—
728C4C2×#1306337211yescharacteristic
729C4C2×#1306337211yescharacteristic
730C2—42no—
731C2—82no—
732C2—3442no—
733C2#1914579014yesdirect product factor
734C2C2×#1458347111yescharacteristic
735C2C2×AGL(1,ℤ/8)×D4311yescharacteristic
736C2C2×#1458369611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#482C2
socleC23×C43C22×D4
prime radicalC2×#14583444C2
hypercenterC2×#482D43
hypocenterC43C2×#3235
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#482

Complements

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

NH ≅ G/Ntype
1. C2×#14583452C2semidirect
3. #19145790C2direct (N × H)
4. C2×#14583307C2semidirect
5. C2×#14583306C2semidirect
6. C2×#14583262C2semidirect
7. C2×#14583262C2semidirect
8. C2×#14583224C2semidirect
9. C2×#14583223C2semidirect
10. C2×#14583220C2semidirect
11. C2×#14583188C2semidirect
12. C2×#14583187C2semidirect
13. C2×#14583178C2semidirect
14. C2×#14583177C2semidirect
15. C2×#14582953C2semidirect
16. C2×C43×#482C2semidirect
19. #14583452C22semidirect
40. #14583307C22semidirect
41. #14583306C22semidirect
42. #14583262C22semidirect
43. #14583262C22semidirect
44. #14583224C22semidirect
45. #14583223C22semidirect
46. #14583220C22semidirect
47. #14583188C22semidirect
48. #14583187C22semidirect
49. #14583178C22semidirect
50. #14583177C22semidirect
51. #14582953C22semidirect
71. C43×#482C22semidirect
372. C2×#482D43semidirect
380. C2×C43#3235semidirect
417. #482C2×D43semidirect
445. C43C2×#3235semidirect
733. C2#19145790direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834522
C2×#145834442
#191457902
C2×#145833072
C2×#145833062
C2×#145832622
C2×#145832242
C2×#145832232
C2×#145832202
C2×#145831882
C2×#145831872
C2×#145831782
C2×#145831772
C2×#145829532
C2×C43×#4822
C2×#323543