Finite Group Databasebeta

← C2×#19147077 #25975173

Subgroups — C2×#19147077 #25975173

Order 11008.

1942 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×#14583610C211yesmaximal, characteristic, complemented
2C2×#14583599C211yesmaximal, characteristic
3#19147077C2116yesmaximal, direct product factor
4C2×#14583305C211yesmaximal, characteristic, complemented
5C2×#14583236C211yesmaximal, characteristic, complemented
6C2×#14583216C211yesmaximal, characteristic, complemented
7C2×#14583242C211yesmaximal, characteristic, complemented
8C2×#14583211C211yesmaximal, characteristic, complemented
9C2×#14583207C211yesmaximal, characteristic, complemented
10C2×#14583144C211yesmaximal, characteristic, complemented
11C2×#14583127C211yesmaximal, characteristic, complemented
12C2×#14582999C211yesmaximal, characteristic, complemented
13C2×#14582969C211yesmaximal, characteristic, complemented
14C2×#14582940C211yesmaximal, characteristic, complemented
15C2×#107×D43C211yesmaximal, characteristic, complemented
16C2×C43×#474C211yesmaximal, characteristic, complemented
17C22×#10621883C2211yescharacteristic
18C22×#10621872C2211yescharacteristic
19C22×C8×D43C2211yescharacteristic
20#14583610—24no—
21#14583610C2218yescomplemented
22#14583599—24no—
23#14583599C2218yes—
24C2×#13063318—21no—
25C2×#13063317C2211yescharacteristic
26C2×#13063316—21no—
27C2×#13063308—21no—
28C2×#13063305C2211yescharacteristic
29C2×#13063305C2211yescharacteristic
30C2×#13063301—21no—
31C2×#13063301—21no—
32C2×#13063298—21no—
33C2×#13063296C2211yescharacteristic
34C2×#13063296C2211yescharacteristic
35C2×C4×Dic86C2211yescharacteristic
36C2×C4×D172C2211yescharacteristic
37C2×#13063287—21no—
38C2×C4×C22⋊D43—21no—
39C2×#13063283C2211yescharacteristic
40C2×C4⋊C4×D43C2211yescharacteristic
41C2×C4⋊C4×D43C2211yescharacteristic
42C2×C4⋊C4×D43C2211yescharacteristic
43#14583305C2218yescomplemented
44#14583242C2218yescomplemented
45#14583236C2218yescomplemented
46#14583216C2218yescomplemented
47#14583211C2218yescomplemented
48#14583207C2218yescomplemented
49#14583144C2218yescomplemented
50#14583127C2218yescomplemented
51#14582999C2218yescomplemented
52#14582969C2218yescomplemented
53#14582940C2218yescomplemented
54C2×#13063259C2211yescharacteristic
55C2×#13063258C2211yescharacteristic
56C2×#13063258C2211yescharacteristic
57C2×#13063258C2211yescharacteristic
58#107×D43C2218yescomplemented
59C2×#13063257C2211yescharacteristic
60C2×#13063256C2211yescharacteristic
61C2×#13063256C2211yescharacteristic
62C2×#13063250C2211yescharacteristic
63C2×#13063250C2211yescharacteristic
64C2×#13063248C2211yescharacteristic
65C2×#13063246C2211yescharacteristic
66C2×(C2×D43)⋊C8C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×#13063236C2211yescharacteristic
69C2×C4⋊Q8×C43C2211yescharacteristic
70C2×C4×D4×C43C2211yescharacteristic
71C43×#474C2218yescomplemented
72C2×#107×C43C2211yescharacteristic
73C2×#107×C43C2211yescharacteristic
74C2×C4⋊C8×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×#102×C43C2211yescharacteristic
77C22×Dic86C2311yescharacteristic
78C22×D172D411yescharacteristic
79C22×C22⋊D43—21no—
80C22×C22⋊D43—21no—
81C22×C4×D43—21no—
82C22×C4×D43—21no—
83C22×C4×D43—21no—
84C22×C4×D43C2311yescharacteristic
85C22×C4×D43C2311yescharacteristic
86C2×#10621883—24no—
87C2×#10621883C2314yes—
88C2×#10621872—24no—
89C2×#10621872C2314yes—
90C22×C43⋊C8C2311yescharacteristic
91C22×C43⋊C8C2311yescharacteristic
92C2×C8×D43—24no—
93C2×C8×D43C2314yes—
94#13063318—28no—
95#13063317—22no—
96#13063317C2314yes—
97#13063316—28no—
98#13063308—28no—
99#13063305—22no—
100#13063305—22no—
101#13063305C2314yes—
102#13063305C2314yes—
103#13063301—28no—
104#13063301—28no—
105#13063298—28no—
106#13063296—22no—
107#13063296—22no—
108#13063296C2314yes—
109#13063296C2314yes—
110C4×Dic86—22no—
111C4×Dic86C2314yes—
112C4×D172D414yes—
113C4×D172C2314yes—
114#13063287—28no—
115C4×C22⋊D43—28no—
116#13063283—22no—
117#13063283C2314yes—
118C2×C4⋊Dic43—21no—
119C2×C4⋊Dic43—21no—
120C2×C4⋊Dic43D411yescharacteristic
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×Dic43⋊C4—21no—
130C4⋊C4×D43—22no—
131C4⋊C4×D43—22no—
132C4⋊C4×D43—22no—
133C4⋊C4×D43C2314yes—
134C4⋊C4×D43C2314yes—
135C4⋊C4×D43C2314yes—
136C2×C22⋊Dic43—21no—
137C2×C22⋊Dic43—21no—
138C2×(C2×D43)⋊C4—21no—
139C2×(C2×D43)⋊C4—21no—
140C2×(C2×D43)⋊C4—21no—
141C2×(C2×D43)⋊C4D411yescharacteristic
142C2×(C2×D43)⋊C4D411yescharacteristic
143C2×C4×Dic43—21no—
144C2×C4×Dic43—21no—
145#13063259C2314yes—
146#13063258C2314yes—
147#13063258C2314yes—
148#13063258C2314yes—
149#13063257C2314yes—
150#13063256C2314yes—
151#13063256C2314yes—
152#13063250C2314yes—
153#13063250C2314yes—
154#13063248C2314yes—
155#13063246C2314yes—
156(C2×D43)⋊C8C2314yes—
157(C2×D43)⋊C8C2314yes—
158#13063236C2314yes—
159C22×Q8×C43—21no—
160C22×D4×C43C2311yescharacteristic
161C23×C4×C43—21no—
162C22×C8×C43C2311yescharacteristic
163C22×C8×C43C2311yescharacteristic
164C4⋊Q8×C43—22no—
165C4⋊Q8×C43C2314yes—
166C4×D4×C43—22no—
167C4×D4×C43C2314yes—
168C2×C4⋊C4×C43—21no—
169C2×C4⋊C4×C43C2311yescharacteristic
170C2×C4⋊C4×C43C2311yescharacteristic
171C2×C4⋊C4×C43C2311yescharacteristic
172C2×C22⋊C4×C43—21no—
173C2×C42×C43C2311yescharacteristic
174#107×C43C2314yes—
175#107×C43C2314yes—
176C4⋊C8×C43C2314yes—
177#102×C43C2314yes—
178#102×C43C2314yes—
179C24×C43—21no—
180C23×D43C2×D411yescharacteristic
181C23×D43C2×D411yescharacteristic
182C2×Q8×C43—24no—
183C2×Q8×C43—82no—
184C2×D4×C43—21no—
185C2×D4×C43—22no—
186C2×D4×C43—22no—
187C2×D4×C43C2412yes—
188C22×C4×C43—24no—
189C22×C4×C43—21no—
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43—82no—
193C22×C4×C43C2×D411yescharacteristic
194C22×C4×C43C2×D411yescharacteristic
195C22×C4×C43C2411yescharacteristic
196C2×C22⋊D43—24no—
197C2×C22⋊D43—24no—
198C2×C22⋊D43—44no—
199C2×C22⋊D43—82no—
200C22×Dic43—21no—
201C22×Dic43—21no—
202C22×Dic43—21no—
203C22×Dic43—21no—
204C22×Dic43C2×D411yescharacteristic
205C22×Dic43C2×D411yescharacteristic
206C2×D172—24no—
207C2×D172C2×D414yes—
208C2×C4×D43—22no—
209C2×C4×D43—22no—
210C2×C4×D43—22no—
211C2×C4×D43—22no—
212C2×C4×D43—24no—
213C2×C4×D43—24no—
214C2×C4×D43—24no—
215C2×C4×D43—82no—
216C2×C4×D43—82no—
217C2×C4×D43—82no—
218C2×C4×D43C2×D412yes—
219C2×C4×D43C2×D412yes—
220C2×C4×D43C2412yes—
221C2×C4×D43C2412yes—
222C2×Dic86—22no—
223C2×Dic86—22no—
224C2×Dic86—21no—
225C2×Dic86C2412yes—
226C2×C8×C43—22no—
227C2×C8×C43—22no—
228C2×C8×C43C2412yes—
229C2×C8×C43C2412yes—
230C4⋊C4×C43—24no—
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—
238C42×C43C2×D412yes—
239C42×C43C2412yes—
240C22⋊Dic43—24no—
241C22⋊Dic43—24no—
242#10621883—28no—
243(C2×D43)⋊C4—24no—
244(C2×D43)⋊C4—24no—
245(C2×D43)⋊C4—24no—
246(C2×D43)⋊C4C2×D414yes—
247(C2×D43)⋊C4C2×D414yes—
248C4⋊Dic43—21no—
249C4⋊Dic43—21no—
250C4⋊Dic43—21no—
251C4⋊Dic43—24no—
252C4⋊Dic43—24no—
253C4⋊Dic43C2×D414yes—
254C4⋊Dic43C2412yes—
255C4⋊Dic43C2412yes—
256C4⋊Dic43C2412yes—
257Dic43⋊C4—24no—
258Dic43⋊C4—24no—
259Dic43⋊C4—24no—
260Dic43⋊C4—24no—
261Dic43⋊C4—24no—
262Dic43⋊C4—24no—
263C4×Dic43—24no—
264C4×Dic43—24no—
265C2×C43⋊C8—22no—
266C2×C43⋊C8#4114yes—
267C2×C43⋊C8C2412yes—
268C2×C43⋊C8C2412yes—
269#10621872—28no—
270C8×D43—28no—
271C23×C43—22no—
272C23×C43—42no—
273C23×C43—42no—
274C23×C43—42no—
275C23×C43C22×D411yescharacteristic
276C22×D43—22no—
277C22×D43—22no—
278C22×D43—22no—
279C22×D43—22no—
280C22×D43—22no—
281C22×D43#13714yes—
282C22×D43C22×D412yes—
283C22×D43C22×D412yes—
284Q8×C43—84no—
285D4×C43—22no—
286D4×C43—22no—
287D4×C43—42no—
288C2×C4×C43—22no—
289C2×C4×C43—22no—
290C2×C4×C43—22no—
291C2×C4×C43—22no—
292C2×C4×C43—22no—
293C2×C4×C43—42no—
294C2×C4×C43—42no—
295C2×C4×C43—42no—
296C2×C4×C43—84no—
297C2×C4×C43C22×D412yes—
298C2×C4×C43C22×D412yes—
299C2×C4×C43C22×D411yescharacteristic
300C2×C4×C43C2×#4112yes—
301C2×C4×C432−1+412yes—
302C2×C4×C43C2511yescharacteristic
303C22⋊D43—48no—
304C22⋊D43—84no—
305C2×Dic43—22no—
306C2×Dic43—22no—
307C2×Dic43—22no—
308C2×Dic43—22no—
309C2×Dic43—22no—
310C2×Dic43—22no—
311C2×Dic43—42no—
312C2×Dic43—42no—
313C2×Dic43—42no—
314C2×Dic43—42no—
315C2×Dic43C22×D412yes—
316C2×Dic43C22×D412yes—
317D172—28no—
318C4×D43—24no—
319C4×D43—24no—
320C4×D43—22no—
321C4×D43—22no—
322C4×D43—22no—
323C4×D43—22no—
324C4×D43—84no—
325C4×D43—84no—
326C4×D43—84no—
327Dic86—22no—
328Dic86—22no—
329Dic86—42no—
330C8×C43—22no—
331C8×C43—22no—
332C43⋊C8—22no—
333C43⋊C8C2×#4114yes—
334C2×#3346—431nomaximal, Sylow
335C22×C43—42no—
336C22×C43—42no—
337C22×C43—42no—
338C22×C43—84no—
339C22×C43#54712yes—
340C22×C43C2×#13712yes—
341C22×C43#57612yes—
342C22×C43C23×D411yescharacteristic
343C2×D43—28no—
344C2×D43—22no—
345C2×D43—22no—
346C2×D43—22no—
347C2×D43—22no—
348C2×D43—22no—
349C2×D43—44no—
350C2×D43C2×#13714yes—
351C4×C43—22no—
352C4×C43—22no—
353C4×C43—42no—
354C4×C43—42no—
355C4×C43—42no—
356C4×C43#54712yes—
357C4×C43C22×#4111yescharacteristic
358C4×C43C2×2−1+411yescharacteristic
359Dic43—22no—
360Dic43—22no—
361Dic43—42no—
362Dic43—42no—
363Dic43—42no—
364Dic43—42no—
365C2×#554—431no—
366C2×#553—431no—
367#3346—4316no—
368C2×#501—431no—
369C2×#484—431no—
370C2×#481—431no—
371C2×#485—431no—
372C2×#480—431no—
373C2×#479—431no—
374C2×#474D4311yescharacteristic, complemented
375C2×#468—431no—
376C2×#465—431no—
377C2×#440—431no—
378C2×#435—431no—
379C2×#428—431no—
380C22×#107—431no—
381C2×C43—82no—
382C2×C43#334614yescomplemented
383C2×C43C2×#54711yescharacteristic
384C2×C43C22×#13711yescharacteristic
385C2×C43C2×#57611yescharacteristic
386D43—24no—
387D43—42no—
388C22×SD16—431no—
389C22×M16—431no—
390C23×C8—431no—
391#554—438no—
392#554—864no—
393#553—438no—
394#553—864no—
395C2×C4⋊Q8C2×D4311yescharacteristic
396C2×#126—861no—
397C2×#125—431no—
398C2×#125—861no—
399C2×#123—861no—
400C2×C22⋊Q8—431no—
401C2×C22⋊Q8—431no—
402C2×C22⋊Q8—861no—
403C2×C22⋊Q8—861no—
404C2×#121—431no—
405C2×#121—431no—
406C2×#121—861no—
407C2×C4×Q8—431no—
408C2×C4×D4—431no—
409C2×C4×D4—861no—
410C2×C4×D4—861no—
411C2×C4×D4C2×D4311yescharacteristic
412C2×#117—431no—
413C22×C4⋊C4—431no—
414C22×C4⋊C4—431no—
415C22×C4⋊C4—431no—
416#501—438no—
417#485—438no—
418#484—438no—
419#481—438no—
420#480—438no—
421#479—438no—
422#474C2×D4318yescomplemented
423#468—438no—
424#465—438no—
425#440—438no—
426#435—438no—
427#428—438no—
428C2×#107—431no—
429C2×#107—431no—
430C2×#107—431no—
431C2×#107—431no—
432C2×#107—438no—
433C2×#107C2×D4311yescharacteristic
434C2×#107C2×D4311yescharacteristic
435C2×#106—431no—
436C2×#106—431no—
437C2×#106—431no—
438C2×C4⋊C8C2×D4311yescharacteristic
439C2×#103—431no—
440C2×#103—431no—
441C2×#103—431no—
442C2×#102—431no—
443C2×#102C2×D4311yescharacteristic
444C2×#102C2×D4311yescharacteristic
445C2×C22⋊C8—431no—
446C2×C22⋊C8—431no—
447C2×#97—431no—
448C43C2×#334611yescharacteristic, complemented, Sylow
449C22×Q8—21no—
450C22×Q8—431no—
451C22×D4—431no—
452C22×D4—861no—
453C22×D4—861no—
454C22×D4C22×D4311yescharacteristic
455C23×C4—21no—
456C23×C4—431no—
457C23×C4—431no—
458C23×C4—861no—
459C23×C4—861no—
460C23×C4—861no—
461C2×SD16—434no—
462C2×SD16—864no—
463C2×M16—434no—
464C2×M16—864no—
465C22×C8—431no—
466C22×C8—431no—
467C22×C8—434no—
468C22×C8—864no—
469C22×C8C22×D4311yescharacteristic
470C22×C8C22×D4311yescharacteristic
471C4⋊Q8—22no—
472C4⋊Q8C22×D4314yes—
473#126—868no—
474#125—434no—
475#125—868no—
476#125—862no—
477#123—868no—
478C22⋊Q8—434no—
479C22⋊Q8—434no—
480C22⋊Q8—868no—
481C22⋊Q8—868no—
482C22⋊Q8—862no—
483C22⋊Q8—862no—
484#121—434no—
485#121—434no—
486#121—868no—
487#121—862no—
488#121—862no—
489C4×Q8—434no—
490C4×Q8—862no—
491C4×D4—22no—
492C4×D4—434no—
493C4×D4—434no—
494C4×D4—868no—
495C4×D4—868no—
496C4×D4C22×D4314yes—
497#117—434no—
498#117—862no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—431no—
501C2×C4⋊C4—431no—
502C2×C4⋊C4—431no—
503C2×C4⋊C4—431no—
504C2×C4⋊C4—434no—
505C2×C4⋊C4—434no—
506C2×C4⋊C4—434no—
507C2×C4⋊C4—862no—
508C2×C4⋊C4—862no—
509C2×C4⋊C4—862no—
510C2×C4⋊C4—861no—
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⋊C4C22×D4311yescharacteristic
519C2×C4⋊C4C22×D4311yescharacteristic
520C2×C4⋊C4C22×D4311yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—431no—
523C2×C22⋊C4—431no—
524C2×C22⋊C4—861no—
525C2×C22⋊C4—861no—
526C2×C22⋊C4—861no—
527C2×C22⋊C4—861no—
528C2×C22⋊C4—861no—
529C2×C42—861no—
530C2×C42—861no—
531C2×C42C22×D4311yescharacteristic
532#107—434no—
533#107—434no—
534#107—434no—
535#107—434no—
536#107C22×D4314yes—
537#107C22×D4314yes—
538#106—434no—
539#106—434no—
540#106—434no—
541C4⋊C8C22×D4314yes—
542#103—434no—
543#103—434no—
544#103—434no—
545#102—434no—
546#102C22×D4314yes—
547#102C22×D4314yes—
548C22⋊C8—434no—
549C22⋊C8—434no—
550#97—434no—
551C24—21no—
552C24—431no—
553C24—431no—
554C2×Q8—24no—
555C2×Q8—82no—
556C2×Q8—432no—
557C2×Q8—861no—
558C2×Q8—862no—
559C2×Q8—862no—
560C2×D4—21no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—434no—
564C2×D4—864no—
565C2×D4—864no—
566C2×D4—864no—
567C2×D4—3442no—
568C2×D4—1724no—
569C2×D4C23×D4312yes—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—24no—
574C22×C4—82no—
575C22×C4—431no—
576C22×C4—431no—
577C22×C4—432no—
578C22×C4—432no—
579C22×C4—432no—
580C22×C4—432no—
581C22×C4—864no—
582C22×C4—864no—
583C22×C4—864no—
584C22×C4—862no—
585C22×C4—862no—
586C22×C4—862no—
587C22×C4—862no—
588C22×C4—861no—
589C22×C4—861no—
590C22×C4—861no—
591C22×C4—861no—
592C22×C4—3442no—
593C22×C4—3442no—
594C22×C4—3442no—
595C22×C4D4×D4311yescharacteristic
596C22×C4D4×D4311yescharacteristic
597C22×C4C23×D4311yescharacteristic
598SD16—868no—
599M16—868no—
600C2×C8—22no—
601C2×C8—22no—
602C2×C8—434no—
603C2×C8—432no—
604C2×C8—432no—
605C2×C8—868no—
606C2×C8—862no—
607C2×C8C23×D4312yes—
608C2×C8C23×D4312yes—
609C4⋊C4—24no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—434no—
614C4⋊C4—432no—
615C4⋊C4—432no—
616C4⋊C4—432no—
617C4⋊C4—864no—
618C4⋊C4—864no—
619C4⋊C4—864no—
620C4⋊C4—864no—
621C4⋊C4—864no—
622C4⋊C4—861no—
623C4⋊C4—861no—
624C4⋊C4—861no—
625C4⋊C4—864no—
626C4⋊C4—864no—
627C4⋊C4—864no—
628C4⋊C4C23×D4312yes—
629C4⋊C4C23×D4312yes—
630C4⋊C4C23×D4312yes—
631C22⋊C4—24no—
632C22⋊C4—434no—
633C22⋊C4—434no—
634C22⋊C4—864no—
635C22⋊C4—864no—
636C22⋊C4—864no—
637C22⋊C4—864no—
638C22⋊C4—864no—
639C42—864no—
640C42—864no—
641C42D4×D4312yes—
642C42C23×D4312yes—
643C23—22no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—434no—
648C23—432no—
649C23—432no—
650C23—862no—
651C23—862no—
652C23—862no—
653C23—862no—
654C23—862no—
655C23C2×D4×D4311yescharacteristic
656Q8—84no—
657Q8—862no—
658Q8—862no—
659Q8—1722no—
660D4—22no—
661D4—22no—
662D4—42no—
663D4—868no—
664D4—3444no—
665D4—1728no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—84no—
675C2×C4—432no—
676C2×C4—432no—
677C2×C4—862no—
678C2×C4—862no—
679C2×C4—862no—
680C2×C4—862no—
681C2×C4—862no—
682C2×C4—862no—
683C2×C4—864no—
684C2×C4—864no—
685C2×C4—862no—
686C2×C4—862no—
687C2×C4—862no—
688C2×C4—862no—
689C2×C4—3444no—
690C2×C4—3444no—
691C2×C4—3444no—
692C2×C4—1722no—
693C2×C4—1722no—
694C2×C4—1722no—
695C2×C4—1722no—
696C2×C4C2×D4×D4312yes—
697C2×C4C2×D4×D4312yes—
698C2×C4C2×D4×D4311yescharacteristic
699C2×C4#41×D4312yes—
700C2×C4#1306337312yes—
701C2×C4C24×D4311yescharacteristic
702C8—22no—
703C8—22no—
704C8—434no—
705C8—862no—
706C22—42no—
707C22—42no—
708C22—42no—
709C22—84no—
710C22—434no—
711C22—862no—
712C22—862no—
713C22—868no—
714C22—862no—
715C22—862no—
716C22—862no—
717C22—1724no—
718C22#1458355112yes—
719C22#137×D4312yes—
720C22#1458370012yes—
721C22C22×D4×D4311yescharacteristic
722C4—22no—
723C4—22no—
724C4—42no—
725C4—42no—
726C4—42no—
727C4—862no—
728C4—862no—
729C4—1722no—
730C4—1722no—
731C4—1722no—
732C4—1722no—
733C4#1458355112yes—
734C4C2×#41×D4311yescharacteristic
735C4C2×#1306337311yescharacteristic
736C2—82no—
737C2—864no—
738C2—1722no—
739C2#1914707714yesdirect product factor
740C2C2×#1458355111yescharacteristic
741C2C2×#137×D4311yescharacteristic
742C2C2×#1458370011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#474C2
socleC23×C43C22×D4
prime radicalC2×#14583599C2
hypercenterC2×#474D43
hypocenterC43C2×#3346
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. C2×#14583610C2semidirect
3. #19147077C2direct (N × H)
4. C2×#14583305C2semidirect
5. C2×#14583236C2semidirect
6. C2×#14583216C2semidirect
7. C2×#14583242C2semidirect
8. C2×#14583211C2semidirect
9. C2×#14583207C2semidirect
10. C2×#14583144C2semidirect
11. C2×#14583127C2semidirect
12. C2×#14582999C2semidirect
13. C2×#14582969C2semidirect
14. C2×#14582940C2semidirect
15. C2×#107×D43C2semidirect
16. C2×C43×#474C2semidirect
21. #14583610C22semidirect
43. #14583305C22semidirect
44. #14583242C22semidirect
45. #14583236C22semidirect
46. #14583216C22semidirect
47. #14583211C22semidirect
48. #14583207C22semidirect
49. #14583144C22semidirect
50. #14583127C22semidirect
51. #14582999C22semidirect
52. #14582969C22semidirect
53. #14582940C22semidirect
58. #107×D43C22semidirect
71. C43×#474C22semidirect
374. C2×#474D43semidirect
382. C2×C43#3346semidirect
422. #474C2×D43semidirect
448. C43C2×#3346semidirect
739. C2#19147077direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836102
C2×#145835992
#191470772
C2×#145833052
C2×#145832362
C2×#145832162
C2×#145832422
C2×#145832112
C2×#145832072
C2×#145831442
C2×#145831272
C2×#145829992
C2×#145829692
C2×#145829402
C2×#107×D432
C2×C43×#4742
C2×#334643