Finite Group Databasebeta

← C2×#19147037 #25975130

Subgroups — C2×#19147037 #25975130

Order 11008.

2094 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583589C211yesmaximal, characteristic, complemented
2C2×#14583553C211yesmaximal, characteristic
3#19147037C2116yesmaximal, direct product factor
4C2×#14583308C211yesmaximal, characteristic, complemented
5C2×#14583235C211yesmaximal, characteristic, complemented
6C2×#14583224C211yesmaximal, characteristic, complemented
7C2×#14583230C211yesmaximal, characteristic, complemented
8C2×#14583213C211yesmaximal, characteristic, complemented
9C2×#14583195C211yesmaximal, characteristic, complemented
10C2×#14583200C211yesmaximal, characteristic, complemented
11C2×#14583145C211yesmaximal, characteristic, complemented
12C2×#14583128C211yesmaximal, characteristic, complemented
13C2×#14583001C211yesmaximal, characteristic, complemented
14C2×#14582941C211yesmaximal, characteristic, complemented
15C22×#13063259C211yesmaximal, characteristic, complemented
16C2×C43×#435C211yesmaximal, characteristic, complemented
17C22×#10621900—21no—
18C22×#10621873C2211yescharacteristic
19#14583589—24no—
20#14583589C2218yescomplemented
21#14583553—24no—
22#14583553C2218yes—
23C2×#13063325C2211yescharacteristic
24C2×#13063318—21no—
25C2×#13063317C2211yescharacteristic
26C2×#13063315—21no—
27C2×#13063309—21no—
28C2×#13063309—21no—
29C2×#13063306—21no—
30C2×#13063305—21no—
31C2×#13063304C2211yescharacteristic
32C2×#13063304C2211yescharacteristic
33C2×#13063299C2211yescharacteristic
34C2×#13063299C2211yescharacteristic
35C2×C4×Dic86C2211yescharacteristic
36C2×C4×D172C2211yescharacteristic
37C2×#13063284C2211yescharacteristic
38C2×#13063281—21no—
39C22×C4⋊Dic43C2211yescharacteristic
40C22×C4⋊Dic43C2211yescharacteristic
41C22×C4⋊Dic43C2211yescharacteristic
42#14583308C2218yescomplemented
43#14583235C2218yescomplemented
44#14583230C2218yescomplemented
45#14583224C2218yescomplemented
46#14583213C2218yescomplemented
47#14583200C2218yescomplemented
48#14583195C2218yescomplemented
49#14583145C2218yescomplemented
50#14583128C2218yescomplemented
51#14583001C2218yescomplemented
52#14582941C2218yescomplemented
53C2×#13063259C2211yescharacteristic
54C2×#13063259C2211yescharacteristic
55C2×#13063259C2211yescharacteristic
56C2×#13063259C2211yescharacteristic
57C2×#13063259C2211yescharacteristic
58C2×#13063259C2211yescharacteristic
59C2×#13063259C2218yescomplemented
60C2×#13063257C2211yescharacteristic
61C2×#13063257C2211yescharacteristic
62C2×#13063257C2211yescharacteristic
63C2×#13063250C2211yescharacteristic
64C2×#13063250C2211yescharacteristic
65C2×#13063250C2211yescharacteristic
66C2×#13063247C2211yescharacteristic
67C2×#13063247C2211yescharacteristic
68C2×#13063247C2211yescharacteristic
69C22×M16×C43C2211yescharacteristic
70C23×C8×C43C2211yescharacteristic
71C2×C4×D4×C43C2211yescharacteristic
72C43×#435C2218yescomplemented
73C2×C4⋊C8×C43C2211yescharacteristic
74C2×C22⋊C8×C43C2211yescharacteristic
75C2×C22⋊C8×C43C2211yescharacteristic
76C2×#97×C43C2211yescharacteristic
77C2×#10621900—28no—
78C2×#10621900—48no—
79C22×Dic86—21no—
80C22×Dic86C2311yescharacteristic
81C22×D172C2311yescharacteristic
82C22×C22⋊D43—21no—
83C22×C22⋊D43—21no—
84C23×Dic43—21no—
85C23×Dic43—21no—
86C23×Dic43—21no—
87C22×C4×D43—21no—
88C2×#10621873—24no—
89C2×#10621873C2314yes—
90#13063325—22no—
91#13063325C2314yes—
92#13063318—28no—
93#13063317—22no—
94#13063317C2314yes—
95#13063315—28no—
96#13063309—28no—
97#13063309—28no—
98#13063306—28no—
99#13063305—28no—
100#13063304—22no—
101#13063304—22no—
102#13063304C2314yes—
103#13063304C2314yes—
104#13063299—22no—
105#13063299—22no—
106#13063299C2314yes—
107#13063299C2314yes—
108C4×Dic86—22no—
109C4×Dic86C2314yes—
110C4×D172—22no—
111C4×D172C2314yes—
112#13063284—22no—
113#13063284C2314yes—
114#13063281—28no—
115C2×C4⋊Dic43—22no—
116C2×C4⋊Dic43—22no—
117C2×C4⋊Dic43—22no—
118C2×C4⋊Dic43—21no—
119C2×C4⋊Dic43—21no—
120C2×C4⋊Dic43—21no—
121C2×C4⋊Dic43—21no—
122C2×C4⋊Dic43C2314yes—
123C2×C4⋊Dic43C2314yes—
124C2×C4⋊Dic43C2314yes—
125C2×C4⋊Dic43C2311yescharacteristic
126C2×C4⋊Dic43C2311yescharacteristic
127C2×C4⋊Dic43C2311yescharacteristic
128C2×C4⋊Dic43C2311yescharacteristic
129C2×C4⋊Dic43C2311yescharacteristic
130C2×C4⋊Dic43C2311yescharacteristic
131C2×Dic43⋊C4—21no—
132C2×Dic43⋊C4—21no—
133C2×Dic43⋊C4—21no—
134C2×Dic43⋊C4—21no—
135C2×Dic43⋊C4—21no—
136C2×C22⋊Dic43—21no—
137C2×C22⋊Dic43—21no—
138C2×C22⋊Dic43—21no—
139C2×(C2×D43)⋊C4—21no—
140C2×(C2×D43)⋊C4—21no—
141C2×(C2×D43)⋊C4—21no—
142C2×C4×Dic43—21no—
143C2×C4×Dic43—21no—
144#13063259C2314yes—
145#13063259C2314yes—
146#13063259C2314yes—
147#13063259C2314yes—
148#13063259C2314yes—
149#13063259C2314yes—
150#13063257C2314yes—
151#13063257C2314yes—
152#13063257C2314yes—
153#13063250C2314yes—
154#13063250C2314yes—
155#13063250C2314yes—
156#13063247C2314yes—
157#13063247C2314yes—
158#13063247C2314yes—
159C22×D4×C43D411yescharacteristic
160C23×C4×C43C2311yescharacteristic
161C23×C4×C43C2311yescharacteristic
162C2×M16×C43—24no—
163C2×M16×C43C2314yes—
164C22×C8×C43—24no—
165C22×C8×C43C2314yes—
166C22×C8×C43C2311yescharacteristic
167C22×C8×C43C2311yescharacteristic
168C22×C8×C43C2311yescharacteristic
169C22×C8×C43C2311yescharacteristic
170C4×D4×C43D414yes—
171C4×D4×C43C2314yes—
172C2×C4⋊C4×C43D411yescharacteristic
173C2×C22⋊C4×C43D411yescharacteristic
174C2×C22⋊C4×C43D411yescharacteristic
175C2×C42×C43C2311yescharacteristic
176C4⋊C8×C43C2314yes—
177C22⋊C8×C43C2314yes—
178C22⋊C8×C43C2314yes—
179#97×C43C2314yes—
180C24×C43C2×D411yescharacteristic
181C24×C43C2×D411yescharacteristic
182C23×D43—21no—
183C2×D4×C43—24no—
184C2×D4×C43C2×D414yes—
185C22×C4×C43—22no—
186C22×C4×C43—22no—
187C22×C4×C43—22no—
188C22×C4×C43—22no—
189C22×C4×C43C2×D411yescharacteristic
190C22×C4×C43C2×D411yescharacteristic
191C22×C4×C43C2×D411yescharacteristic
192C22×C4×C43C2×D411yescharacteristic
193C22×C4×C43C2×D412yes—
194C22×C4×C43C2×D412yes—
195C22×C4×C43C2412yes—
196C22×C4×C43C2412yes—
197C22×C4×C43C2411yescharacteristic
198C2×C22⋊D43—24no—
199C2×C22⋊D43—24no—
200C2×C22⋊D43—44no—
201C2×C22⋊D43—44no—
202C22×Dic43—21no—
203C22×Dic43—21no—
204C22×Dic43—21no—
205C22×Dic43—21no—
206C22×Dic43—21no—
207C22×Dic43—21no—
208C22×Dic43—21no—
209C22×Dic43—24no—
210C22×Dic43—24no—
211C22×Dic43—24no—
212C22×Dic43—44no—
213C22×Dic43—44no—
214C22×Dic43—44no—
215#10621900—432no—
216C2×D172—21no—
217C2×D172—22no—
218C2×D172—22no—
219C2×D172C2412yes—
220C2×C4×D43—24no—
221C2×C4×D43—44no—
222C2×Dic86—22no—
223C2×Dic86—22no—
224C2×Dic86—21no—
225C2×Dic86—24no—
226C2×Dic86—44no—
227C2×Dic86C2412yes—
228M16×C43—28no—
229C2×C8×C43—22no—
230C2×C8×C43—22no—
231C2×C8×C43—22no—
232C2×C8×C43—28no—
233C2×C8×C43#4114yescomplemented
234C2×C8×C43C2412yes—
235C2×C8×C43C2412yes—
236C2×C8×C43C2412yes—
237C2×C8×C43C2412yes—
238C4⋊C4×C43C2×D414yes—
239C22⋊C4×C43C2×D414yes—
240C22⋊C4×C43C2×D414yes—
241C42×C43C2×D412yes—
242C42×C43C2412yes—
243C22⋊Dic43—24no—
244C22⋊Dic43—24no—
245C22⋊Dic43—24no—
246(C2×D43)⋊C4—24no—
247(C2×D43)⋊C4—24no—
248(C2×D43)⋊C4—24no—
249C4⋊Dic43—21no—
250C4⋊Dic43—21no—
251C4⋊Dic43—21no—
252C4⋊Dic43—21no—
253C4⋊Dic43—21no—
254C4⋊Dic43—24no—
255C4⋊Dic43—24no—
256C4⋊Dic43—24no—
257C4⋊Dic43—24no—
258C4⋊Dic43—21no—
259C4⋊Dic43C2412yes—
260C4⋊Dic43C2412yes—
261C4⋊Dic43C2412yes—
262C4⋊Dic43C2412yes—
263C4⋊Dic43C2412yes—
264C4⋊Dic43C2412yes—
265Dic43⋊C4—24no—
266Dic43⋊C4—24no—
267Dic43⋊C4—24no—
268Dic43⋊C4—24no—
269Dic43⋊C4—24no—
270C4×Dic43—24no—
271C4×Dic43—24no—
272#10621873—28no—
273C23×C43—22no—
274C23×C43—22no—
275C23×C43—22no—
276C23×C43—22no—
277C23×C43—22no—
278C23×C43AGL(1,ℤ/8)14yes—
279C23×C43C22×D412yes—
280C23×C43C22×D412yes—
281C23×C43C22×D411yescharacteristic
282C22×D43—22no—
283C22×D43—42no—
284C22×D43—42no—
285C22×D43—42no—
286D4×C43—28no—
287C2×C4×C43—22no—
288C2×C4×C43—22no—
289C2×C4×C43—22no—
290C2×C4×C43—22no—
291C2×C4×C43—24no—
292C2×C4×C43—24no—
293C2×C4×C43—22no—
294C2×C4×C43—22no—
295C2×C4×C43—22no—
296C2×C4×C43—22no—
297C2×C4×C43C22×D412yes—
298C2×C4×C43C22×D412yes—
299C2×C4×C43C22×D412yes—
300C2×C4×C43C22×D412yes—
301C2×C4×C43C22×D411yescharacteristic
302C2×C4×C43C2×#4112yes—
303C2×C4×C432−1+412yes—
304C2×C4×C43C2511yescharacteristic
305C22⋊D43—48no—
306C22⋊D43—48no—
307C2×Dic43—22no—
308C2×Dic43—22no—
309C2×Dic43—22no—
310C2×Dic43—22no—
311C2×Dic43—22no—
312C2×Dic43—22no—
313C2×Dic43—22no—
314C2×Dic43—48no—
315C2×Dic43—42no—
316C2×Dic43—42no—
317C2×Dic43—42no—
318C2×Dic43—42no—
319C2×Dic43—48no—
320C2×Dic43—48no—
321C2×Dic43—42no—
322C2×Dic43—42no—
323C2×Dic43—42no—
324D172—22no—
325D172—22no—
326D172—42no—
327C4×D43—48no—
328Dic86—22no—
329Dic86—22no—
330Dic86—48no—
331Dic86—42no—
332C8×C43—22no—
333C8×C43—22no—
334C8×C43—22no—
335C8×C43C2×#4114yescomplemented
336C2×#3343—431nomaximal, Sylow
337C22×C43—28no—
338C22×C43—22no—
339C22×C43—22no—
340C22×C43—22no—
341C22×C43—22no—
342C22×C43—22no—
343C22×C43—44no—
344C22×C43#54712yes—
345C22×C43C2×AGL(1,ℤ/8)14yes—
346C22×C43C2×AGL(1,ℤ/8)12yes—
347C22×C43#57812yes—
348C22×C43C23×D411yescharacteristic
349C2×D43—42no—
350C2×D43—42no—
351C2×D43—42no—
352C2×D43—84no—
353C4×C43—22no—
354C4×C43—22no—
355C4×C43—22no—
356C4×C43—22no—
357C4×C43#54712yes—
358C4×C43C22×#4111yescharacteristic
359C4×C43C2×2−1+411yescharacteristic
360Dic43—42no—
361Dic43—42no—
362Dic43—42no—
363Dic43—42no—
364Dic43—42no—
365Dic43—42no—
366Dic43—42no—
367C2×#552—431no—
368C2×#547—431no—
369#3343—4316no—
370C2×#501—431no—
371C2×#484—431no—
372C2×#482—431no—
373C2×#483—431no—
374C2×#480—431no—
375C2×#477—431no—
376C2×#478—431no—
377C2×#468—431no—
378C2×#465—431no—
379C2×#440—431no—
380C2×#435D4311yescharacteristic, complemented
381C2×#428—431no—
382C22×#107—431no—
383C2×C43—24no—
384C2×C43—42no—
385C2×C43#334314yescomplemented
386C2×C43C2×#54711yescharacteristic
387C2×C43C22×AGL(1,ℤ/8)11yescharacteristic
388C2×C43C2×#57811yescharacteristic
389D43—82no—
390C22×#41—861no—
391C22×SD16—431no—
392C22×M16C2×D4311yescharacteristic
393C23×C8C2×D4311yescharacteristic
394#552—438no—
395#552—864no—
396#547—438no—
397#547—864no—
398C2×C4⋊Q8—431no—
399C2×#126—861no—
400C2×#125—431no—
401C2×#125—861no—
402C2×#123—861no—
403C2×#123—861no—
404C2×#123—861no—
405C2×C22⋊Q8—431no—
406C2×C22⋊Q8—431no—
407C2×C22⋊Q8—861no—
408C2×#121—431no—
409C2×#121—431no—
410C2×C4×Q8—431no—
411C2×C4×D4—431no—
412C2×C4×D4C2×D4311yescharacteristic
413C2×#117—431no—
414C2×#117—861no—
415C22×C4⋊C4—431no—
416C22×C4⋊C4—431no—
417C22×C4⋊C4—431no—
418#501—438no—
419#484—438no—
420#483—438no—
421#482—438no—
422#480—438no—
423#478—438no—
424#477—438no—
425#468—438no—
426#465—438no—
427#440—438no—
428#435C2×D4318yescomplemented
429#428—438no—
430C2×#107—431no—
431C2×#107—431no—
432C2×#107—431no—
433C2×#107—431no—
434C2×#107—438no—
435C2×#107—431no—
436C2×#107—431no—
437C2×#106—431no—
438C2×#106—431no—
439C2×#106—431no—
440C2×C4⋊C8C2×D4311yescharacteristic
441C2×#103—431no—
442C2×#103—431no—
443C2×#103—431no—
444C2×#102—431no—
445C2×#102—431no—
446C2×#102—431no—
447C2×C22⋊C8C2×D4311yescharacteristic
448C2×C22⋊C8C2×D4311yescharacteristic
449C2×#97C2×D4311yescharacteristic
450C43C2×#334311yescharacteristic, complemented, Sylow
451C2×#41—868no—
452C2×#41—1728no—
453C22×Q8—431no—
454C22×Q8—861no—
455C22×D4—431no—
456C22×D4—861no—
457C22×D4—861no—
458C22×D4D17211yescharacteristic
459C23×C4—861no—
460C23×C4—861no—
461C23×C4—861no—
462C23×C4—861no—
463C23×C4C22×D4311yescharacteristic
464C23×C4C22×D4311yescharacteristic
465C2×SD16—434no—
466C2×SD16—864no—
467C2×M16—24no—
468C2×M16C22×D4314yes—
469C22×C8—24no—
470C22×C8C22×D4311yescharacteristic
471C22×C8C22×D4314yes—
472C22×C8C22×D4311yescharacteristic
473C22×C8C22×D4311yescharacteristic
474C22×C8C22×D4311yescharacteristic
475C4⋊Q8—434no—
476C4⋊Q8—862no—
477#126—868no—
478#125—434no—
479#125—868no—
480#125—862no—
481#123—868no—
482#123—868no—
483#123—868no—
484C22⋊Q8—434no—
485C22⋊Q8—434no—
486C22⋊Q8—862no—
487C22⋊Q8—862no—
488C22⋊Q8—868no—
489#121—434no—
490#121—434no—
491#121—862no—
492#121—862no—
493C4×Q8—434no—
494C4×Q8—862no—
495C4×D4—434no—
496C4×D4—862no—
497C4×D4D17214yes—
498C4×D4C22×D4314yes—
499#117—434no—
500#117—862no—
501#117—868no—
502C2×C4⋊C4—431no—
503C2×C4⋊C4—431no—
504C2×C4⋊C4—431no—
505C2×C4⋊C4—431no—
506C2×C4⋊C4—431no—
507C2×C4⋊C4—434no—
508C2×C4⋊C4—434no—
509C2×C4⋊C4—434no—
510C2×C4⋊C4—431no—
511C2×C4⋊C4—861no—
512C2×C4⋊C4—861no—
513C2×C4⋊C4—861no—
514C2×C4⋊C4—862no—
515C2×C4⋊C4—862no—
516C2×C4⋊C4—862no—
517C2×C4⋊C4—861no—
518C2×C4⋊C4—861no—
519C2×C4⋊C4—861no—
520C2×C4⋊C4—861no—
521C2×C4⋊C4—861no—
522C2×C4⋊C4—861no—
523C2×C4⋊C4D17211yescharacteristic
524C2×C22⋊C4—861no—
525C2×C22⋊C4—861no—
526C2×C22⋊C4—861no—
527C2×C22⋊C4—861no—
528C2×C22⋊C4—861no—
529C2×C22⋊C4—861no—
530C2×C22⋊C4D17211yescharacteristic
531C2×C22⋊C4D17211yescharacteristic
532C2×C42—861no—
533C2×C42—861no—
534C2×C42C22×D4311yescharacteristic
535#107—434no—
536#107—434no—
537#107—434no—
538#107—434no—
539#107—434no—
540#107—434no—
541#106—434no—
542#106—434no—
543#106—434no—
544C4⋊C8C22×D4314yes—
545#103—434no—
546#103—434no—
547#103—434no—
548#102—434no—
549#102—434no—
550#102—434no—
551C22⋊C8C22×D4314yes—
552C22⋊C8C22×D4314yes—
553#97C22×D4314yes—
554C24—861no—
555C24C2×D17211yescharacteristic
556C24C2×D17211yescharacteristic
557#41—17232no—
558C2×Q8—432no—
559C2×Q8—861no—
560C2×Q8—864no—
561C2×Q8—862no—
562C2×Q8—862no—
563C2×Q8—1724no—
564C2×D4—24no—
565C2×D4—432no—
566C2×D4—864no—
567C2×D4—864no—
568C2×D4—861no—
569C2×D4—862no—
570C2×D4—862no—
571C2×D4—1724no—
572C2×D4—1724no—
573C2×D4C2×D17214yes—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—864no—
579C22×C4—864no—
580C22×C4—864no—
581C22×C4—861no—
582C22×C4—861no—
583C22×C4—861no—
584C22×C4—861no—
585C22×C4—861no—
586C22×C4—861no—
587C22×C4—861no—
588C22×C4—864no—
589C22×C4—1724no—
590C22×C4—1724no—
591C22×C4—1724no—
592C22×C4—1724no—
593C22×C4C2×D17212yes—
594C22×C4C2×D17212yes—
595C22×C4C2×D17211yescharacteristic
596C22×C4C2×D17211yescharacteristic
597C22×C4C2×D17211yescharacteristic
598C22×C4C2×D17211yescharacteristic
599C22×C4C23×D4312yes—
600C22×C4C23×D4312yes—
601C22×C4C23×D4311yescharacteristic
602SD16—868no—
603M16—28no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—28no—
608C2×C8#1062190014yescomplemented
609C2×C8C23×D4312yes—
610C2×C8C23×D4312yes—
611C2×C8C23×D4312yes—
612C2×C8C23×D4312yes—
613C4⋊C4—432no—
614C4⋊C4—432no—
615C4⋊C4—432no—
616C4⋊C4—432no—
617C4⋊C4—432no—
618C4⋊C4—432no—
619C4⋊C4—861no—
620C4⋊C4—861no—
621C4⋊C4—861no—
622C4⋊C4—861no—
623C4⋊C4—864no—
624C4⋊C4—864no—
625C4⋊C4—861no—
626C4⋊C4—864no—
627C4⋊C4—861no—
628C4⋊C4—864no—
629C4⋊C4—864no—
630C4⋊C4—864no—
631C4⋊C4—864no—
632C4⋊C4—864no—
633C4⋊C4—864no—
634C4⋊C4C2×D17214yes—
635C22⋊C4—864no—
636C22⋊C4—864no—
637C22⋊C4—864no—
638C22⋊C4—864no—
639C22⋊C4—864no—
640C22⋊C4—864no—
641C22⋊C4C2×D17214yes—
642C22⋊C4C2×D17214yes—
643C42—864no—
644C42—864no—
645C42C2×D17212yes—
646C42C23×D4312yes—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—862no—
653C23—1722no—
654C23—1722no—
655C23—1722no—
656C23#1306335314yes—
657C23C22×D17212yes—
658C23C22×D17212yes—
659C23C22×D17211yescharacteristic
660Q8—862no—
661Q8—862no—
662Q8—1728no—
663Q8—1722no—
664D4—28no—
665D4—862no—
666D4—862no—
667D4—1728no—
668D4—1728no—
669D4—1722no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—862no—
681C2×C4—862no—
682C2×C4—862no—
683C2×C4—862no—
684C2×C4—862no—
685C2×C4—862no—
686C2×C4—862no—
687C2×C4—1728no—
688C2×C4—1728no—
689C2×C4—1722no—
690C2×C4—1722no—
691C2×C4—1722no—
692C2×C4—1722no—
693C2×C4—1728no—
694C2×C4—1728no—
695C2×C4—1722no—
696C2×C4—1722no—
697C2×C4—1722no—
698C2×C4C22×D17212yes—
699C2×C4C22×D17212yes—
700C2×C4C22×D17212yes—
701C2×C4C22×D17212yes—
702C2×C4C22×D17211yescharacteristic
703C2×C4C2×#1062190012yes—
704C2×C4#1306337212yes—
705C2×C4C24×D4311yescharacteristic
706C8—22no—
707C8—22no—
708C8—22no—
709C8C2×#1062190014yescomplemented
710C22—22no—
711C22—28no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—44no—
717C22—3444no—
718C22—1722no—
719C22—1722no—
720C22—1722no—
721C22#1458355312yes—
722C22C2×#1306335314yes—
723C22C2×#1306335312yes—
724C22#1458371612yes—
725C22C23×D17211yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—1722no—
731C4—1722no—
732C4—1722no—
733C4—1722no—
734C4—1722no—
735C4—1722no—
736C4—1722no—
737C4#1458355312yes—
738C4C22×#1062190011yescharacteristic
739C4C2×#1306337211yescharacteristic
740C2—24no—
741C2—42no—
742C2—3442no—
743C2#1914703714yesdirect product factor
744C2C2×#1458355311yescharacteristic
745C2C22×#1306335311yescharacteristic
746C2C2×#1458371611yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#435C2
socleC23×C43C22×D4
prime radicalC2×#14583553C2
hypercenterC2×#435D43
hypocenterC43C2×#3343
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#14583589C2semidirect
3. #19147037C2direct (N × H)
4. C2×#14583308C2semidirect
5. C2×#14583235C2semidirect
6. C2×#14583224C2semidirect
7. C2×#14583230C2semidirect
8. C2×#14583213C2semidirect
9. C2×#14583195C2semidirect
10. C2×#14583200C2semidirect
11. C2×#14583145C2semidirect
12. C2×#14583128C2semidirect
13. C2×#14583001C2semidirect
14. C2×#14582941C2semidirect
15. C22×#13063259C2semidirect
16. C2×C43×#435C2semidirect
20. #14583589C22semidirect
42. #14583308C22semidirect
43. #14583235C22semidirect
44. #14583230C22semidirect
45. #14583224C22semidirect
46. #14583213C22semidirect
47. #14583200C22semidirect
48. #14583195C22semidirect
49. #14583145C22semidirect
50. #14583128C22semidirect
51. #14583001C22semidirect
52. #14582941C22semidirect
59. C2×#13063259C22semidirect
72. C43×#435C22semidirect
233. C2×C8×C43#41semidirect
335. C8×C43C2×#41semidirect
380. C2×#435D43semidirect
385. C2×C43#3343semidirect
428. #435C2×D43semidirect
450. C43C2×#3343semidirect
608. C2×C8#10621900semidirect
709. C8C2×#10621900semidirect
743. C2#19147037direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835892
C2×#145835532
#191470372
C2×#145833082
C2×#145832352
C2×#145832242
C2×#145832302
C2×#145832132
C2×#145831952
C2×#145832002
C2×#145831452
C2×#145831282
C2×#145830012
C2×#145829412
C22×#130632592
C2×C43×#4352
C2×#334343