Finite Group Databasebeta

← C2×#19144812 #25964863

Subgroups — C2×#19144812 #25964863

Order 11008.

2070 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583509C211yesmaximal, characteristic, complemented
2C2×#14583380C211yesmaximal, characteristic
3#19144812C2116yesmaximal, direct product factor
4C2×#14583234C211yesmaximal, characteristic, complemented
5C2×#14583209C211yesmaximal, characteristic, complemented
6C2×#14583198C211yesmaximal, characteristic, complemented
7C2×#14583108C211yesmaximal, characteristic, complemented
8C2×#14583103C211yesmaximal, characteristic, complemented
9C2×#14583063C211yesmaximal, characteristic
10C2×#14583059C211yesmaximal, characteristic
11C2×#14583005C211yesmaximal, characteristic, complemented
12C2×#14583002C211yesmaximal, characteristic, complemented
13C2×#14582991C211yesmaximal, characteristic, complemented
14C2×#14582986C211yesmaximal, characteristic, complemented
15C2×#14582957C211yesmaximal, characteristic, complemented
16C2×C43×#483C211yesmaximal, characteristic, complemented
17C22×#10621898C2211yescharacteristic
18C22×Dic172C2211yescharacteristic
19C22×#10621885C2211yescharacteristic
20C22×#10621873C2211yescharacteristic
21C22×#10621884C2211yescharacteristic
22#14583509—24no—
23#14583509C2218yescomplemented
24C2×#13063323C2211yescharacteristic
25C2×#13063318—21no—
26C2×#13063318—21no—
27C2×#13063316—21no—
28C2×#13063316C2211yescharacteristic
29C2×#13063315—21no—
30C2×#13063304C2211yescharacteristic
31#14583380—24no—
32#14583380C2218yes—
33C2×Q8×Dic43C2211yescharacteristic
34C2×#13063290C2211yescharacteristic
35C2×#13063290C2211yescharacteristic
36C2×#13063290C2211yescharacteristic
37C2×#13063287C2211yescharacteristic
38C2×#13063287C2211yescharacteristic
39C2×C4×C22⋊D43—21no—
40C2×C4×C22⋊D43—21no—
41C2×#13063284C2211yescharacteristic
42C2×#13063283—21no—
43C2×C4⋊C4×D43—21no—
44#14583234C2218yescomplemented
45#14583209C2218yescomplemented
46#14583198C2218yescomplemented
47#14583108C2218yescomplemented
48#14583103C2218yescomplemented
49#14583063C2218yes—
50#14583059C2218yes—
51#14583005C2218yescomplemented
52#14583002C2218yescomplemented
53#14582991C2218yescomplemented
54#14582986C2218yescomplemented
55#14582957C2218yescomplemented
56C2×#13063258C2211yescharacteristic
57C2×#13063258C2211yescharacteristic
58C2×Dic43⋊C8C2211yescharacteristic
59C2×Dic43⋊C8C2211yescharacteristic
60C2×#13063250C2211yescharacteristic
61C2×#13063248C2211yescharacteristic
62C2×#13063248C2211yescharacteristic
63C2×#13063248C2211yescharacteristic
64C2×#13063247C2211yescharacteristic
65C2×#13063245C2211yescharacteristic
66C2×C22⋊(C43⋊C8)C2211yescharacteristic
67C2×#13063235C2211yescharacteristic
68C2×C8×Dic43C2211yescharacteristic
69C2×C22⋊Q8×C43C2211yescharacteristic
70C22×C4⋊C4×C43C2211yescharacteristic
71C43×#483C2218yescomplemented
72C2×#106×C43C2211yescharacteristic
73C2×#106×C43C2211yescharacteristic
74C2×#103×C43C2211yescharacteristic
75C2×#103×C43C2211yescharacteristic
76C2×C22⋊C8×C43C2211yescharacteristic
77C2×#10621898—22no—
78C2×#10621898—24no—
79C2×#10621898—24no—
80C2×#10621898C2314yes—
81C22×Dic86C2311yescharacteristic
82C22×Dic86C2311yescharacteristic
83C22×D172C2311yescharacteristic
84C22×C22⋊D43—21no—
85C22×C4×D43—21no—
86C22×C4×D43—21no—
87C22×C4×D43—21no—
88C2×Dic172—24no—
89C2×Dic172C2314yes—
90C2×#10621885—24no—
91C2×#10621885C2314yes—
92C2×#10621873—24no—
93C2×#10621873C2314yes—
94C2×#10621884—24no—
95C2×#10621884C2314yes—
96C22×C43⋊C8C2311yescharacteristic
97C22×C43⋊C8C2311yescharacteristic
98#13063323—22no—
99#13063323C2314yes—
100#13063318—28no—
101#13063318—28no—
102#13063316—28no—
103#13063316—22no—
104#13063316C2314yes—
105#13063315—28no—
106#13063304—22no—
107#13063304C2314yes—
108Q8×Dic43—22no—
109Q8×Dic43C2314yes—
110#13063290—22no—
111#13063290—22no—
112#13063290—22no—
113#13063290C2314yes—
114#13063290C2314yes—
115#13063290C2314yes—
116#13063287—22no—
117#13063287—22no—
118#13063287C2314yes—
119#13063287C2314yes—
120C4×C22⋊D43—28no—
121C4×C22⋊D43—28no—
122#13063284D414yes—
123#13063284C2314yes—
124#13063283—28no—
125C2×C4⋊Dic43—21no—
126C2×C4⋊Dic43—21no—
127C2×C4⋊Dic43D411yescharacteristic
128C2×C4⋊Dic43D411yescharacteristic
129C2×C4⋊Dic43C2311yescharacteristic
130C2×Dic43⋊C4—21no—
131C2×Dic43⋊C4—21no—
132C2×Dic43⋊C4—21no—
133C2×Dic43⋊C4—21no—
134C2×Dic43⋊C4—21no—
135C2×Dic43⋊C4—21no—
136C2×Dic43⋊C4—21no—
137C4⋊C4×D43—28no—
138C2×C22⋊Dic43—21no—
139C2×C22⋊Dic43D411yescharacteristic
140C2×C22⋊Dic43D411yescharacteristic
141C2×(C2×D43)⋊C4—21no—
142C2×(C2×D43)⋊C4—21no—
143C2×C4×Dic43—21no—
144C2×C4×Dic43—21no—
145C2×C4×Dic43—21no—
146C2×C4×Dic43—21no—
147C2×C4×Dic43C2311yescharacteristic
148C2×C4×Dic43C2311yescharacteristic
149#13063258C2314yes—
150#13063258C2314yes—
151Dic43⋊C8C2314yes—
152Dic43⋊C8C2314yes—
153#13063250C2314yes—
154#13063248C2314yes—
155#13063248C2314yes—
156#13063248C2314yes—
157#13063247C2314yes—
158#13063245C2314yes—
159C22⋊(C43⋊C8)C2314yes—
160#13063235C2314yes—
161C8×Dic43C2314yes—
162C22×Q8×C43C2311yescharacteristic
163C23×C4×C43—21no—
164C23×C4×C43C2311yescharacteristic
165C22×C8×C43C2311yescharacteristic
166C22×C8×C43C2311yescharacteristic
167C22⋊Q8×C43—22no—
168C22⋊Q8×C43C2314yes—
169C2×C4⋊C4×C43—21no—
170C2×C4⋊C4×C43—22no—
171C2×C4⋊C4×C43—21no—
172C2×C4⋊C4×C43C2311yescharacteristic
173C2×C4⋊C4×C43C2311yescharacteristic
174C2×C4⋊C4×C43C2314yes—
175C2×C4⋊C4×C43C2311yescharacteristic
176C2×C22⋊C4×C43—21no—
177#106×C43C2314yes—
178#106×C43C2314yes—
179#103×C43C2314yes—
180#103×C43C2314yes—
181C22⋊C8×C43C2314yes—
182C24×C43C2×D411yescharacteristic
183C23×D43—21no—
184C2×Q8×C43—21no—
185C2×Q8×C43—22no—
186C2×Q8×C43—22no—
187C2×Q8×C43C2412yes—
188C22×C4×C43—22no—
189C22×C4×C43—22no—
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43—21no—
194C22×C4×C43—24no—
195C22×C4×C43—82no—
196C22×C4×C43C2×D411yescharacteristic
197C22×C4×C43C2×D412yes—
198C22×C4×C43C2412yes—
199C22×C4×C43C2411yescharacteristic
200C2×C22⋊D43—28no—
201C2×C22⋊D43—24no—
202C22×Dic43—21no—
203C22×Dic43—21no—
204C22×Dic43—21no—
205C22×Dic43C2×D411yescharacteristic
206C22×Dic43C2×D411yescharacteristic
207C22×Dic43C2×D411yescharacteristic
208C22×Dic43C2×D411yescharacteristic
209#10621898—216no—
210#10621898—28no—
211#10621898—28no—
212C2×D172—21no—
213C2×D172—22no—
214C2×D172#4114yes—
215C2×D172C2412yes—
216C2×C4×D43—28no—
217C2×C4×D43—24no—
218C2×C4×D43—24no—
219C2×C4×D43—24no—
220C2×C4×D43—82no—
221C2×C4×D43—82no—
222C2×Dic86—21no—
223C2×Dic86—22no—
224C2×Dic86—22no—
225C2×Dic86—22no—
226C2×Dic86—21no—
227C2×Dic86#4114yes—
228C2×Dic86C2412yes—
229C2×Dic86C2412yes—
230C2×C8×C43—22no—
231C2×C8×C43—22no—
232C2×C8×C43C2412yes—
233C2×C8×C43C2412yes—
234C4⋊C4×C43—24no—
235C4⋊C4×C43—21no—
236C4⋊C4×C43—21no—
237C4⋊C4×C43—24no—
238C4⋊C4×C43—21no—
239C4⋊C4×C43C2412yes—
240C4⋊C4×C43C2412yes—
241C4⋊C4×C43C2412yes—
242C22⋊C4×C43—24no—
243C22⋊Dic43—24no—
244C22⋊Dic43C2×D414yes—
245C22⋊Dic43C2×D414yes—
246#10621885—28no—
247#10621884—28no—
248(C2×D43)⋊C4—24no—
249(C2×D43)⋊C4—24no—
250C4⋊Dic43—21no—
251C4⋊Dic43—24no—
252C4⋊Dic43—24no—
253C4⋊Dic43C2×D414yes—
254C4⋊Dic43C2×D414yes—
255C4⋊Dic43C2412yes—
256Dic43⋊C4—24no—
257Dic43⋊C4—24no—
258Dic43⋊C4—24no—
259Dic43⋊C4—24no—
260Dic43⋊C4—24no—
261Dic43⋊C4—24no—
262Dic43⋊C4—24no—
263C4×Dic43—24no—
264C4×Dic43—24no—
265C4×Dic43—24no—
266C4×Dic43—24no—
267C4×Dic43C2×D412yes—
268C4×Dic43C2×D412yes—
269C4×Dic43C2412yes—
270C4×Dic43C2412yes—
271C2×C43⋊C8—22no—
272C2×C43⋊C8—22no—
273C2×C43⋊C8C2412yes—
274C2×C43⋊C8C2412yes—
275Dic172—28no—
276#10621873—28no—
277C23×C43—22no—
278C23×C43—22no—
279C23×C43—22no—
280C23×C43C22×D412yes—
281C23×C43C22×D411yescharacteristic
282C22×D43—24no—
283C22×D43—22no—
284C22×D43—42no—
285C22×D43—42no—
286Q8×C43—22no—
287Q8×C43—22no—
288Q8×C43—42no—
289C2×C4×C43—22no—
290C2×C4×C43—24no—
291C2×C4×C43—22no—
292C2×C4×C43—22no—
293C2×C4×C43—22no—
294C2×C4×C43—22no—
295C2×C4×C43—22no—
296C2×C4×C43—22no—
297C2×C4×C43—42no—
298C2×C4×C43—42no—
299C2×C4×C43—42no—
300C2×C4×C43—42no—
301C2×C4×C43—84no—
302C2×C4×C43C22×D412yes—
303C2×C4×C43C22×D411yescharacteristic
304C2×C4×C43C2×#4112yes—
305C2×C4×C43C2×#4112yes—
306C2×C4×C43C2511yescharacteristic
307C22⋊D43—216no—
308C2×Dic43—24no—
309C2×Dic43—22no—
310C2×Dic43—22no—
311C2×Dic43—22no—
312C2×Dic43—22no—
313C2×Dic43—22no—
314C2×Dic43—22no—
315C2×Dic43—22no—
316C2×Dic43—42no—
317C2×Dic43—42no—
318C2×Dic43C22×D412yes—
319C2×Dic43C22×D412yes—
320C2×Dic43C22×D412yes—
321C2×Dic43C22×D412yes—
322D172—24no—
323D172—22no—
324D172C2×#4114yes—
325C4×D43—216no—
326C4×D43—84no—
327C4×D43—84no—
328Dic86—24no—
329Dic86—22no—
330Dic86—22no—
331Dic86—22no—
332Dic86—42no—
333Dic86C2×#4114yes—
334C8×C43—22no—
335C8×C43—22no—
336C43⋊C8—22no—
337C43⋊C8—22no—
338C2×#3120—431nomaximal, Sylow
339C22×C43—22no—
340C22×C43—22no—
341C22×C43—22no—
342C22×C43—44no—
343C22×C43#52512yes—
344C22×C43#57712yes—
345C22×C43#57812yes—
346C22×C43C23×D411yescharacteristic
347C2×D43—24no—
348C2×D43—48no—
349C2×D43—42no—
350C2×D43—42no—
351C4×C43—22no—
352C4×C43—42no—
353C4×C43—42no—
354C4×C43—42no—
355C4×C43—42no—
356C4×C43#52512yes—
357C4×C43C22×#4111yescharacteristic
358C4×C43C22×#4111yescharacteristic
359Dic43—24no—
360Dic43—22no—
361Dic43—22no—
362Dic43—22no—
363Dic43—22no—
364Dic43—42no—
365Dic43—42no—
366C2×#541—431no—
367C2×#520—431no—
368#3120—4316no—
369C2×#484—431no—
370C2×#483D4311yescharacteristic, complemented
371C2×#479—431no—
372C2×#478—431no—
373C2×#462—431no—
374C2×#461—431no—
375C2×#452—431no—
376C2×#452—431no—
377C2×#441—431no—
378C2×#440—431no—
379C2×C4×Q16—431no—
380C2×C4×SD16—431no—
381C2×#433—431no—
382C2×C43—42no—
383C2×C43#312014yescomplemented
384C2×C43C2×#52511yescharacteristic
385C2×C43C2×#57711yescharacteristic
386C2×C43C2×#57811yescharacteristic
387D43—44no—
388C22×#41—431no—
389C22×Q16—431no—
390C22×Q16—431no—
391C22×SD16—431no—
392C22×SD16—431no—
393#541—438no—
394#541—864no—
395C2×C4⋊Q8—431no—
396C2×#126—861no—
397C2×#126—861no—
398C2×#125—431no—
399C2×#125—861no—
400C2×#125—861no—
401C2×C22⋊Q8—431no—
402C2×C22⋊Q8C2×D4311yescharacteristic
403#520—438no—
404#520—864no—
405C2×C4×Q8—431no—
406C2×C4×Q8—431no—
407C2×C4×Q8—431no—
408C2×C4×Q8—431no—
409C2×C4×D4—431no—
410C2×C4×D4—431no—
411C2×C4×D4—861no—
412C2×C4×D4—861no—
413C2×#117—431no—
414C2×#117—861no—
415C22×C4⋊C4—861no—
416C22×C4⋊C4C2×D4311yescharacteristic
417#484—438no—
418#483C2×D4318yescomplemented
419#479—438no—
420#478—438no—
421#462—438no—
422#461—438no—
423#452—438no—
424#452—438no—
425#441—438no—
426#440—438no—
427C4×Q16—438no—
428C4×SD16—438no—
429#433—438no—
430C2×#107—431no—
431C2×#107—431no—
432C2×#106C2×D4311yescharacteristic
433C2×#106C2×D4311yescharacteristic
434C2×C4⋊C8—431no—
435C2×C4⋊C8—431no—
436C2×#103—431no—
437C2×#103—431no—
438C2×#103—431no—
439C2×#103—431no—
440C2×#103C2×D4311yescharacteristic
441C2×#103C2×D4311yescharacteristic
442C2×#102—431no—
443C2×#102—431no—
444C2×C22⋊C8—431no—
445C2×C22⋊C8C2×D4311yescharacteristic
446C2×#97—431no—
447C2×C4×C8—431no—
448C43C2×#312011yescharacteristic, complemented, Sylow
449C2×#41—434no—
450C2×#41—864no—
451C2×#41—864no—
452C2×#41—862no—
453C22×Q8—431no—
454C22×Q8—431no—
455C22×Q8C22×D4311yescharacteristic
456C22×D4—431no—
457C22×D4—861no—
458C23×C4—21no—
459C23×C4—861no—
460C23×C4—861no—
461C23×C4—861no—
462C23×C4C22×D4311yescharacteristic
463C2×Q16—434no—
464C2×Q16—434no—
465C2×Q16—864no—
466C2×Q16—864no—
467C2×SD16—434no—
468C2×SD16—434no—
469C2×SD16—864no—
470C2×SD16—864no—
471C22×C8—431no—
472C22×C8—431no—
473C22×C8C22×D4311yescharacteristic
474C22×C8C22×D4311yescharacteristic
475C4⋊Q8—434no—
476C4⋊Q8—862no—
477#126—868no—
478#126—868no—
479#125—434no—
480#125—862no—
481#125—868no—
482#125—868no—
483C22⋊Q8—22no—
484C22⋊Q8—434no—
485C22⋊Q8—862no—
486C22⋊Q8C22×D4314yes—
487C4×Q8—434no—
488C4×Q8—434no—
489C4×Q8—434no—
490C4×Q8—434no—
491C4×Q8—862no—
492C4×Q8—862no—
493C4×Q8—862no—
494C4×Q8—862no—
495C4×D4—434no—
496C4×D4—434no—
497C4×D4—862no—
498C4×D4—862no—
499C4×D4—868no—
500C4×D4—868no—
501#117—434no—
502#117—434no—
503#117—868no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—22no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—431no—
508C2×C4⋊C4—431no—
509C2×C4⋊C4—431no—
510C2×C4⋊C4—868no—
511C2×C4⋊C4—861no—
512C2×C4⋊C4—861no—
513C2×C4⋊C4—861no—
514C2×C4⋊C4—861no—
515C2×C4⋊C4—861no—
516C2×C4⋊C4—861no—
517C2×C4⋊C4—861no—
518C2×C4⋊C4—861no—
519C2×C4⋊C4—861no—
520C2×C4⋊C4C22×D4311yescharacteristic
521C2×C4⋊C4C22×D4311yescharacteristic
522C2×C4⋊C4C22×D4314yes—
523C2×C4⋊C4C22×D4311yescharacteristic
524C2×C22⋊C4—21no—
525C2×C22⋊C4—431no—
526C2×C22⋊C4—431no—
527C2×C22⋊C4—861no—
528C2×C22⋊C4—861no—
529C2×C22⋊C4—861no—
530C2×C42—431no—
531C2×C42—431no—
532C2×C42—861no—
533C2×C42—861no—
534C2×C42—861no—
535C2×C42—861no—
536#107—434no—
537#107—434no—
538#106C22×D4314yes—
539#106C22×D4314yes—
540C4⋊C8—434no—
541C4⋊C8—434no—
542#103—434no—
543#103—434no—
544#103—434no—
545#103—434no—
546#103C22×D4314yes—
547#103C22×D4314yes—
548#102—434no—
549#102—434no—
550C22⋊C8—434no—
551C22⋊C8C22×D4314yes—
552#97—434no—
553C4×C8—434no—
554C24—861no—
555C24D4×D4311yescharacteristic
556#41—868no—
557#41—868no—
558#41—8616no—
559C2×Q8—21no—
560C2×Q8—22no—
561C2×Q8—22no—
562C2×Q8—434no—
563C2×Q8—432no—
564C2×Q8—432no—
565C2×Q8—861no—
566C2×Q8—861no—
567C2×Q8—862no—
568C2×Q8—862no—
569C2×Q8—862no—
570C2×Q8C23×D4312yes—
571C2×D4—434no—
572C2×D4—432no—
573C2×D4—868no—
574C2×D4—864no—
575C2×D4—861no—
576C2×D4—862no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—24no—
584C22×C4—82no—
585C22×C4—431no—
586C22×C4—431no—
587C22×C4—431no—
588C22×C4—431no—
589C22×C4—864no—
590C22×C4—864no—
591C22×C4—868no—
592C22×C4—861no—
593C22×C4—864no—
594C22×C4—861no—
595C22×C4—861no—
596C22×C4—3442no—
597C22×C4—3442no—
598C22×C4D4×D4312yes—
599C22×C4D4×D4311yescharacteristic
600C22×C4C23×D4312yes—
601C22×C4C23×D4311yescharacteristic
602Q16—868no—
603Q16—868no—
604SD16—868no—
605SD16—868no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—432no—
609C2×C8—432no—
610C2×C8—862no—
611C2×C8—862no—
612C2×C8C23×D4312yes—
613C2×C8C23×D4312yes—
614C4⋊C4—24no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—24no—
618C4⋊C4—21no—
619C4⋊C4—434no—
620C4⋊C4—434no—
621C4⋊C4—432no—
622C4⋊C4—864no—
623C4⋊C4—864no—
624C4⋊C4—864no—
625C4⋊C4—864no—
626C4⋊C4—864no—
627C4⋊C4—864no—
628C4⋊C4—864no—
629C4⋊C4—864no—
630C4⋊C4—861no—
631C4⋊C4—864no—
632C4⋊C4C23×D4312yes—
633C4⋊C4C23×D4312yes—
634C4⋊C4C23×D4312yes—
635C22⋊C4—24no—
636C22⋊C4—434no—
637C22⋊C4—434no—
638C22⋊C4—864no—
639C22⋊C4—864no—
640C22⋊C4—864no—
641C42—432no—
642C42—432no—
643C42—432no—
644C42—432no—
645C42—864no—
646C42—864no—
647C42—864no—
648C42—864no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—864no—
653C23—862no—
654C23—1722no—
655C23—1722no—
656C23C2×D4×D4312yes—
657C23C2×D4×D4311yescharacteristic
658Q8—22no—
659Q8—22no—
660Q8—42no—
661Q8—434no—
662Q8—864no—
663Q8—862no—
664Q8—862no—
665Q8—862no—
666Q8—1722no—
667D4—434no—
668D4—8616no—
669D4—864no—
670D4—862no—
671C2×C4—22no—
672C2×C4—24no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—84no—
684C2×C4—432no—
685C2×C4—432no—
686C2×C4—432no—
687C2×C4—432no—
688C2×C4—8616no—
689C2×C4—864no—
690C2×C4—862no—
691C2×C4—862no—
692C2×C4—862no—
693C2×C4—862no—
694C2×C4—862no—
695C2×C4—862no—
696C2×C4—862no—
697C2×C4—3444no—
698C2×C4—3444no—
699C2×C4—1722no—
700C2×C4—1722no—
701C2×C4C2×D4×D4312yes—
702C2×C4C2×D4×D4311yescharacteristic
703C2×C4#41×D4312yes—
704C2×C4#41×D4312yes—
705C2×C4C24×D4311yescharacteristic
706C8—22no—
707C8—22no—
708C8—862no—
709C8—862no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—44no—
714C22—864no—
715C22—1722no—
716C22—1722no—
717C22—1728no—
718C22#1458340712yes—
719C22#1458370512yes—
720C22#1458371512yes—
721C22C22×D4×D4311yescharacteristic
722C4—22no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—42no—
727C4—862no—
728C4—862no—
729C4—862no—
730C4—862no—
731C4—864no—
732C4—1722no—
733C4—1722no—
734C4#1458340712yes—
735C4C2×#41×D4311yescharacteristic
736C4C2×#41×D4311yescharacteristic
737C2—42no—
738C2—1724no—
739C2#1914481214yesdirect product factor
740C2C2×#1458340711yescharacteristic
741C2C2×#1458370511yescharacteristic
742C2C2×#1458371511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#483C2
socleC23×C43C22×D4
prime radicalC22×#10621898C22
hypercenterC2×#483D43
hypocenterC43C2×#3120
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#483

Complements

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

NH ≅ G/Ntype
1. C2×#14583509C2semidirect
3. #19144812C2direct (N × H)
4. C2×#14583234C2semidirect
5. C2×#14583209C2semidirect
6. C2×#14583198C2semidirect
7. C2×#14583108C2semidirect
8. C2×#14583103C2semidirect
11. C2×#14583005C2semidirect
12. C2×#14583002C2semidirect
13. C2×#14582991C2semidirect
14. C2×#14582986C2semidirect
15. C2×#14582957C2semidirect
16. C2×C43×#483C2semidirect
23. #14583509C22semidirect
44. #14583234C22semidirect
45. #14583209C22semidirect
46. #14583198C22semidirect
47. #14583108C22semidirect
48. #14583103C22semidirect
51. #14583005C22semidirect
52. #14583002C22semidirect
53. #14582991C22semidirect
54. #14582986C22semidirect
55. #14582957C22semidirect
71. C43×#483C22semidirect
370. C2×#483D43semidirect
383. C2×C43#3120semidirect
418. #483C2×D43semidirect
448. C43C2×#3120semidirect
739. C2#19144812direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835092
C2×#145833802
#191448122
C2×#145832342
C2×#145832092
C2×#145831982
C2×#145831082
C2×#145831032
C2×#145830632
C2×#145830592
C2×#145830052
C2×#145830022
C2×#145829912
C2×#145829862
C2×#145829572
C2×C43×#4832
C2×#312043