Finite Group Databasebeta

← C2×#19147217 #25975343

Subgroups — C2×#19147217 #25975343

Order 11008.

1930 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×#14583612C211yesmaximal, characteristic
2C2×#14583604C211yesmaximal, characteristic, complemented
3#19147217C2116yesmaximal, direct product factor
4C2×#14583303C211yesmaximal, characteristic, complemented
5C2×#14583243C211yesmaximal, characteristic, complemented
6C2×#14583240C211yesmaximal, characteristic, complemented
7C2×#14583214C211yesmaximal, characteristic, complemented
8C2×#14583212C211yesmaximal, characteristic, complemented
9C2×#14583193C211yesmaximal, characteristic, complemented
10C2×#14583188C211yesmaximal, characteristic, complemented
11C2×#14583146C211yesmaximal, characteristic, complemented
12C2×#14583145C211yesmaximal, characteristic, complemented
13C2×#14582986C211yesmaximal, characteristic, complemented
14C2×#14582975C211yesmaximal, characteristic, complemented
15C2×#14582938C211yesmaximal, characteristic, complemented
16C2×C43×#428C211yesmaximal, characteristic, complemented
17C22×#10621873C2211yescharacteristic
18C22×#10621872C2211yescharacteristic
19#14583612—24no—
20#14583612C2218yes—
21#14583604—24no—
22#14583604C2218yescomplemented
23C2×#13063324C2211yescharacteristic
24C2×#13063324C2211yescharacteristic
25C2×#13063315—21no—
26C2×#13063313—21no—
27C2×#13063311—21no—
28C2×#13063305C2211yescharacteristic
29C2×#13063304—21no—
30C2×#13063304C2211yescharacteristic
31C2×#13063303—21no—
32C2×#13063300C2211yescharacteristic
33C2×#13063299C2211yescharacteristic
34C2×#13063298—21no—
35C2×#13063290C2211yescharacteristic
36C2×#13063287C2211yescharacteristic
37C2×C4×C22⋊D43—21no—
38C2×C4×C22⋊D43C2211yescharacteristic
39C2×#13063283C2211yescharacteristic
40C2×#13063282—21no—
41C2×C4⋊C4×D43C2211yescharacteristic
42#14583303C2218yescomplemented
43#14583243C2218yescomplemented
44#14583240C2218yescomplemented
45#14583214C2218yescomplemented
46#14583212C2218yescomplemented
47#14583193C2218yescomplemented
48#14583188C2218yescomplemented
49#14583146C2218yescomplemented
50#14583145C2218yescomplemented
51#14582986C2218yescomplemented
52#14582975C2218yescomplemented
53#14582938C2218yescomplemented
54C2×#13063259C2211yescharacteristic
55C2×#13063258C2211yescharacteristic
56C2×#13063258C2211yescharacteristic
57C2×#13063258C2211yescharacteristic
58C2×#13063256C2211yescharacteristic
59C2×Dic43⋊C8C2211yescharacteristic
60C2×#13063250C2211yescharacteristic
61C2×#13063248C2211yescharacteristic
62C2×#13063248C2211yescharacteristic
63C2×#13063247C2211yescharacteristic
64C2×#13063245C2211yescharacteristic
65C2×#13063245C2211yescharacteristic
66C2×C22⋊(C43⋊C8)C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×C8×Dic43C2211yescharacteristic
69C22×M16×C43C2211yescharacteristic
70C2×#117×C43C2211yescharacteristic
71C22×C4⋊C4×C43C2211yescharacteristic
72C43×#428C2218yescomplemented
73C2×#107×C43C2211yescharacteristic
74C2×#107×C43C2211yescharacteristic
75C2×#106×C43C2211yescharacteristic
76C2×#106×C43C2211yescharacteristic
77C22×Dic86—21no—
78C22×Dic86—21no—
79C22×Dic86C2311yescharacteristic
80C22×D172—21no—
81C22×D172C2311yescharacteristic
82C22×C22⋊D43—21no—
83C22×C22⋊D43D411yescharacteristic
84C22×C4×D43—21no—
85C22×C4×D43—21no—
86C22×C4×D43C2311yescharacteristic
87C2×#10621873—24no—
88C2×#10621873C2314yes—
89C2×#10621872—24no—
90C2×#10621872C2314yes—
91C22×C43⋊C8C2311yescharacteristic
92C22×C43⋊C8C2311yescharacteristic
93#13063324—22no—
94#13063324—22no—
95#13063324C2314yes—
96#13063324C2314yes—
97#13063315—28no—
98#13063313—28no—
99#13063311—28no—
100#13063305—22no—
101#13063305C2314yes—
102#13063304—22no—
103#13063304—28no—
104#13063304C2314yes—
105#13063303—28no—
106#13063300—22no—
107#13063300C2314yes—
108#13063299—22no—
109#13063299C2314yes—
110#13063298—28no—
111#13063290—22no—
112#13063290C2314yes—
113#13063287—22no—
114#13063287C2314yes—
115C4×C22⋊D43—28no—
116C4×C22⋊D43D414yes—
117C4×C22⋊D43C2314yes—
118#13063283—22no—
119#13063283C2314yes—
120#13063282—28no—
121C2×C4⋊Dic43—21no—
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⋊C4D411yescharacteristic
130C4⋊C4×D43—22no—
131C4⋊C4×D43C2314yes—
132C2×C22⋊Dic43—21no—
133C2×C22⋊Dic43D411yescharacteristic
134C2×(C2×D43)⋊C4—21no—
135C2×(C2×D43)⋊C4—21no—
136C2×(C2×D43)⋊C4—21no—
137C2×(C2×D43)⋊C4—21no—
138C2×(C2×D43)⋊C4—21no—
139C2×(C2×D43)⋊C4D411yescharacteristic
140C2×C4×Dic43—21no—
141C2×C4×Dic43—21no—
142C2×C4×Dic43C2311yescharacteristic
143#13063259C2314yes—
144#13063258C2314yes—
145#13063258C2314yes—
146#13063258C2314yes—
147#13063256C2314yes—
148Dic43⋊C8C2314yes—
149#13063250C2314yes—
150#13063248C2314yes—
151#13063248C2314yes—
152#13063247C2314yes—
153#13063245C2314yes—
154#13063245C2314yes—
155C22⋊(C43⋊C8)C2314yes—
156(C2×D43)⋊C8C2314yes—
157C8×Dic43C2314yes—
158C23×C4×C43—21no—
159C23×C4×C43C2311yescharacteristic
160C2×M16×C43—24no—
161C2×M16×C43C2314yes—
162C22×C8×C43C2311yescharacteristic
163C22×C8×C43C2311yescharacteristic
164#117×C43—22no—
165#117×C43C2314yes—
166C2×C4⋊C4×C43—22no—
167C2×C4⋊C4×C43—21no—
168C2×C4⋊C4×C43C2311yescharacteristic
169C2×C4⋊C4×C43C2314yes—
170C2×C4⋊C4×C43C2311yescharacteristic
171C2×C4⋊C4×C43C2311yescharacteristic
172C2×C4⋊C4×C43C2311yescharacteristic
173C2×C22⋊C4×C43—21no—
174C2×C42×C43—21no—
175#107×C43C2314yes—
176#107×C43C2314yes—
177#106×C43C2314yes—
178#106×C43C2314yes—
179C24×C43C2×D411yescharacteristic
180C23×D43—21no—
181C23×D43C2×D411yescharacteristic
182C22×C4×C43—22no—
183C22×C4×C43—22no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—24no—
189C22×C4×C43—82no—
190C22×C4×C43C2×D411yescharacteristic
191C22×C4×C43C2×D412yes—
192C22×C4×C43C2412yes—
193C22×C4×C43C2411yescharacteristic
194C2×C22⋊D43—24no—
195C2×C22⋊D43—24no—
196C2×C22⋊D43—82no—
197C2×C22⋊D43C2×D414yes—
198C22×Dic43—21no—
199C22×Dic43—21no—
200C22×Dic43—21no—
201C22×Dic43C2×D411yescharacteristic
202C22×Dic43C2×D411yescharacteristic
203C22×Dic43C2×D411yescharacteristic
204C2×D172—21no—
205C2×D172—24no—
206C2×D172—22no—
207C2×D172—22no—
208C2×D172—82no—
209C2×D172C2412yes—
210C2×C4×D43—22no—
211C2×C4×D43—22no—
212C2×C4×D43—24no—
213C2×C4×D43—24no—
214C2×C4×D43—44no—
215C2×C4×D43—82no—
216C2×C4×D43C2×D412yes—
217C2×C4×D43C2412yes—
218C2×Dic86—22no—
219C2×Dic86—22no—
220C2×Dic86—21no—
221C2×Dic86—24no—
222C2×Dic86—24no—
223C2×Dic86—82no—
224C2×Dic86—82no—
225C2×Dic86C2412yes—
226M16×C43—28no—
227C2×C8×C43—22no—
228C2×C8×C43#4114yes—
229C2×C8×C43C2412yes—
230C2×C8×C43C2412yes—
231C4⋊C4×C43—21no—
232C4⋊C4×C43—24no—
233C4⋊C4×C43—21no—
234C4⋊C4×C43—21no—
235C4⋊C4×C43—21no—
236C4⋊C4×C43C2412yes—
237C4⋊C4×C43C2412yes—
238C4⋊C4×C43C2412yes—
239C4⋊C4×C43C2412yes—
240C22⋊C4×C43—24no—
241C42×C43—24no—
242C22⋊Dic43—24no—
243C22⋊Dic43C2×D414yes—
244(C2×D43)⋊C4—24no—
245(C2×D43)⋊C4—24no—
246(C2×D43)⋊C4—24no—
247(C2×D43)⋊C4—24no—
248(C2×D43)⋊C4—24no—
249(C2×D43)⋊C4C2×D414yes—
250C4⋊Dic43—21no—
251C4⋊Dic43—21no—
252C4⋊Dic43—24no—
253C4⋊Dic43C2412yes—
254C4⋊Dic43C2412yes—
255Dic43⋊C4—24no—
256Dic43⋊C4—24no—
257Dic43⋊C4—24no—
258Dic43⋊C4—24no—
259Dic43⋊C4—24no—
260Dic43⋊C4C2×D414yes—
261C4×Dic43—24no—
262C4×Dic43—24no—
263C4×Dic43C2×D412yes—
264C4×Dic43C2412yes—
265C2×C43⋊C8—22no—
266C2×C43⋊C8—22no—
267C2×C43⋊C8C2412yes—
268C2×C43⋊C8C2412yes—
269#10621873—28no—
270#10621872—28no—
271C23×C43—22no—
272C23×C43—22no—
273C23×C43—22no—
274C23×C43C22×D412yes—
275C23×C43C22×D411yescharacteristic
276C22×D43—22no—
277C22×D43—22no—
278C22×D43—22no—
279C22×D43—22no—
280C22×D43—42no—
281C22×D43—42no—
282C22×D43—42no—
283C22×D43C22×D412yes—
284C2×C4×C43—22no—
285C2×C4×C43—24no—
286C2×C4×C43—22no—
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×C43—42no—
296C2×C4×C43—84no—
297C2×C4×C43C22×D412yes—
298C2×C4×C43C22×D411yescharacteristic
299C2×C4×C43C2×#4112yes—
300C2×C4×C432−1+412yes—
301C2×C4×C43C2511yescharacteristic
302C22⋊D43—28no—
303C22⋊D43—84no—
304C2×Dic43—22no—
305C2×Dic43—22no—
306C2×Dic43—22no—
307C2×Dic43—22no—
308C2×Dic43—22no—
309C2×Dic43—42no—
310C2×Dic43—42no—
311C2×Dic43—42no—
312C2×Dic43#13714yes—
313C2×Dic43C22×D412yes—
314C2×Dic43C22×D412yes—
315C2×Dic43C22×D412yes—
316D172—22no—
317D172—22no—
318D172—42no—
319D172—84no—
320C4×D43—24no—
321C4×D43—22no—
322C4×D43—22no—
323C4×D43—48no—
324C4×D43—84no—
325Dic86—22no—
326Dic86—22no—
327Dic86—42no—
328Dic86—84no—
329Dic86—84no—
330C8×C43—22no—
331C8×C43C2×#4114yes—
332C43⋊C8—22no—
333C43⋊C8—22no—
334C2×#3357—431nomaximal, Sylow
335C22×C43—22no—
336C22×C43—22no—
337C22×C43—22no—
338C22×C43—44no—
339C22×C43#54712yes—
340C22×C43C2×#13712yes—
341C22×C43#57612yes—
342C22×C43C23×D411yescharacteristic
343C2×D43—22no—
344C2×D43—22no—
345C2×D43—22no—
346C2×D43—44no—
347C2×D43—42no—
348C2×D43—42no—
349C2×D43—42no—
350C2×D43—84no—
351C4×C43—22no—
352C4×C43—42no—
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—
364Dic43C2×#13714yes—
365C2×#555—431no—
366C2×#554—431no—
367#3357—4316no—
368C2×#500—431no—
369C2×#485—431no—
370C2×#485—431no—
371C2×#480—431no—
372C2×#480—431no—
373C2×#477—431no—
374C2×#476—431no—
375C2×#468—431no—
376C2×#468—431no—
377C2×C4×SD16—431no—
378C2×#436—431no—
379C2×#428—431no—
380C2×#428D4311yescharacteristic, complemented
381C2×C43—42no—
382C2×C43#335714yescomplemented
383C2×C43C2×#54711yescharacteristic
384C2×C43C22×#13711yescharacteristic
385C2×C43C2×#57611yescharacteristic
386D43—42no—
387D43—82no—
388C22×SD16—431no—
389C22×M16—431no—
390C22×M16C2×D4311yescharacteristic
391#555—438no—
392#555—864no—
393#554—438no—
394#554—864no—
395C2×C4⋊Q8—431no—
396C2×C4⋊Q8—431no—
397C2×#125—861no—
398C2×#124—861no—
399C2×#124—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—431no—
410C2×C4×D4—861no—
411C2×#117—431no—
412C2×#117—861no—
413C2×#117C2×D4311yescharacteristic
414C22×C4⋊C4—431no—
415C22×C4⋊C4C2×D4311yescharacteristic
416#500—438no—
417#485—438no—
418#485—438no—
419#480—438no—
420#480—438no—
421#477—438no—
422#476—438no—
423#468—438no—
424#468—438no—
425C4×SD16—438no—
426#436—438no—
427#428—438no—
428#428C2×D4318yescomplemented
429C2×#107—431no—
430C2×#107—431no—
431C2×#107—431no—
432C2×#107—431no—
433C2×#107C2×D4311yescharacteristic
434C2×#107C2×D4311yescharacteristic
435C2×#106—431no—
436C2×#106C2×D4311yescharacteristic
437C2×#106C2×D4311yescharacteristic
438C2×C4⋊C8—431no—
439C2×#103—431no—
440C2×#103—431no—
441C2×#103—431no—
442C2×#102—431no—
443C2×#102—431no—
444C2×#102—431no—
445C2×C22⋊C8—431no—
446C2×C22⋊C8—431no—
447C2×C4×C8—431no—
448C43C2×#335711yescharacteristic, complemented, Sylow
449C22×Q8—431no—
450C22×Q8—861no—
451C22×Q8—861no—
452C22×D4—431no—
453C22×D4—431no—
454C22×D4—861no—
455C22×D4—861no—
456C23×C4—21no—
457C23×C4—431no—
458C23×C4—861no—
459C23×C4—861no—
460C23×C4C22×D4311yescharacteristic
461C2×SD16—434no—
462C2×SD16—864no—
463C2×M16—24no—
464C2×M16—434no—
465C2×M16—864no—
466C2×M16C22×D4314yes—
467C22×C8—431no—
468C22×C8—431no—
469C22×C8C22×D4311yescharacteristic
470C22×C8C22×D4311yescharacteristic
471C4⋊Q8—434no—
472C4⋊Q8—434no—
473C4⋊Q8—862no—
474C4⋊Q8—862no—
475#125—868no—
476#124—868no—
477#124—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—434no—
492C4×D4—434no—
493C4×D4—434no—
494C4×D4—862no—
495C4×D4—868no—
496#117—22no—
497#117—434no—
498#117—868no—
499#117—862no—
500#117C22×D4314yes—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—22no—
503C2×C4⋊C4—431no—
504C2×C4⋊C4—431no—
505C2×C4⋊C4—431no—
506C2×C4⋊C4—434no—
507C2×C4⋊C4—862no—
508C2×C4⋊C4—861no—
509C2×C4⋊C4—861no—
510C2×C4⋊C4—861no—
511C2×C4⋊C4—861no—
512C2×C4⋊C4—861no—
513C2×C4⋊C4—861no—
514C2×C4⋊C4C22×D4311yescharacteristic
515C2×C4⋊C4C22×D4311yescharacteristic
516C2×C4⋊C4C22×D4314yes—
517C2×C4⋊C4C22×D4311yescharacteristic
518C2×C4⋊C4C22×D4311yescharacteristic
519C2×C22⋊C4—21no—
520C2×C22⋊C4—431no—
521C2×C22⋊C4—431no—
522C2×C22⋊C4—861no—
523C2×C22⋊C4—861no—
524C2×C22⋊C4—861no—
525C2×C22⋊C4—861no—
526C2×C22⋊C4—861no—
527C2×C22⋊C4—861no—
528C2×C42—21no—
529C2×C42—431no—
530C2×C42—861no—
531C2×C42—861no—
532#107—434no—
533#107—434no—
534#107—434no—
535#107—434no—
536#107C22×D4314yes—
537#107C22×D4314yes—
538#106—434no—
539#106C22×D4314yes—
540#106C22×D4314yes—
541C4⋊C8—434no—
542#103—434no—
543#103—434no—
544#103—434no—
545#102—434no—
546#102—434no—
547#102—434no—
548C22⋊C8—434no—
549C22⋊C8—434no—
550C4×C8—434no—
551C24—431no—
552C24—861no—
553C24D4×D4311yescharacteristic
554C2×Q8—432no—
555C2×Q8—864no—
556C2×Q8—864no—
557C2×Q8—861no—
558C2×Q8—862no—
559C2×Q8—862no—
560C2×Q8—3442no—
561C2×Q8—3442no—
562C2×D4—434no—
563C2×D4—432no—
564C2×D4—864no—
565C2×D4—864no—
566C2×D4—864no—
567C2×D4—861no—
568C2×D4—862no—
569C2×D4—862no—
570C2×D4—3442no—
571C2×D4—3442no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—24no—
579C22×C4—82no—
580C22×C4—431no—
581C22×C4—431no—
582C22×C4—431no—
583C22×C4—432no—
584C22×C4—432no—
585C22×C4—864no—
586C22×C4—864no—
587C22×C4—862no—
588C22×C4—862no—
589C22×C4—861no—
590C22×C4—861no—
591C22×C4—861no—
592C22×C4—3442no—
593C22×C4—1724no—
594C22×C4D4×D4312yes—
595C22×C4D4×D4311yescharacteristic
596C22×C4C23×D4312yes—
597C22×C4C23×D4311yescharacteristic
598SD16—868no—
599M16—28no—
600M16—868no—
601C2×C8—22no—
602C2×C8—432no—
603C2×C8—432no—
604C2×C8—862no—
605C2×C8—862no—
606C2×C8#1062189814yes—
607C2×C8C23×D4312yes—
608C2×C8C23×D4312yes—
609C4⋊C4—21no—
610C4⋊C4—24no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—434no—
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—864no—
625C4⋊C4C23×D4312yes—
626C4⋊C4C23×D4312yes—
627C4⋊C4C23×D4312yes—
628C4⋊C4C23×D4312yes—
629C22⋊C4—24no—
630C22⋊C4—434no—
631C22⋊C4—434no—
632C22⋊C4—864no—
633C22⋊C4—864no—
634C22⋊C4—864no—
635C22⋊C4—864no—
636C22⋊C4—864no—
637C22⋊C4—864no—
638C42—24no—
639C42—432no—
640C42—432no—
641C42—864no—
642C42—864no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—432no—
647C23—862no—
648C23—862no—
649C23—862no—
650C23—862no—
651C23—1722no—
652C23—1722no—
653C23—1722no—
654C23C2×D4×D4312yes—
655C23C2×D4×D4311yescharacteristic
656Q8—862no—
657Q8—862no—
658Q8—3444no—
659Q8—3444no—
660Q8—1722no—
661D4—868no—
662D4—862no—
663D4—862no—
664D4—3444no—
665D4—3444no—
666D4—1722no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—24no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—84no—
680C2×C4—434no—
681C2×C4—432no—
682C2×C4—432no—
683C2×C4—432no—
684C2×C4—862no—
685C2×C4—862no—
686C2×C4—862no—
687C2×C4—862no—
688C2×C4—864no—
689C2×C4—862no—
690C2×C4—862no—
691C2×C4—862no—
692C2×C4—3444no—
693C2×C4—1728no—
694C2×C4—1722no—
695C2×C4—1722no—
696C2×C4—1722no—
697C2×C4C2×D4×D4312yes—
698C2×C4C2×D4×D4311yescharacteristic
699C2×C4C2×#1062189812yes—
700C2×C4#1306337312yes—
701C2×C4C24×D4311yescharacteristic
702C8—22no—
703C8—862no—
704C8—862no—
705C8C2×#1062189814yes—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—44no—
710C22—862no—
711C22—862no—
712C22—862no—
713C22—3444no—
714C22—1722no—
715C22—1722no—
716C22—1722no—
717C22—1724no—
718C22#1458355012yes—
719C22#137×D4312yes—
720C22#1458370312yes—
721C22C22×D4×D4311yescharacteristic
722C4—22no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—42no—
727C4—434no—
728C4—862no—
729C4—862no—
730C4—1722no—
731C4—1722no—
732C4—1722no—
733C4#1458355012yes—
734C4C22×#1062189811yescharacteristic
735C4C2×#1306337311yescharacteristic
736C2—42no—
737C2—3442no—
738C2—1722no—
739C2#1914721714yesdirect product factor
740C2C2×#1458355011yescharacteristic
741C2C2×#137×D4311yescharacteristic
742C2C2×#1458370311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#428C2
socleC23×C43C22×D4
prime radicalC2×#14583612C2
hypercenterC2×#428D43
hypocenterC43C2×#3357
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
2. C2×#14583604C2semidirect
3. #19147217C2direct (N × H)
4. C2×#14583303C2semidirect
5. C2×#14583243C2semidirect
6. C2×#14583240C2semidirect
7. C2×#14583214C2semidirect
8. C2×#14583212C2semidirect
9. C2×#14583193C2semidirect
10. C2×#14583188C2semidirect
11. C2×#14583146C2semidirect
12. C2×#14583145C2semidirect
13. C2×#14582986C2semidirect
14. C2×#14582975C2semidirect
15. C2×#14582938C2semidirect
16. C2×C43×#428C2semidirect
22. #14583604C22semidirect
42. #14583303C22semidirect
43. #14583243C22semidirect
44. #14583240C22semidirect
45. #14583214C22semidirect
46. #14583212C22semidirect
47. #14583193C22semidirect
48. #14583188C22semidirect
49. #14583146C22semidirect
50. #14583145C22semidirect
51. #14582986C22semidirect
52. #14582975C22semidirect
53. #14582938C22semidirect
72. C43×#428C22semidirect
380. C2×#428D43semidirect
382. C2×C43#3357semidirect
428. #428C2×D43semidirect
448. C43C2×#3357semidirect
739. C2#19147217direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836122
C2×#145836042
#191472172
C2×#145833032
C2×#145832432
C2×#145832402
C2×#145832142
C2×#145832122
C2×#145831932
C2×#145831882
C2×#145831462
C2×#145831452
C2×#145829862
C2×#145829752
C2×#145829382
C2×C43×#4282
C2×#335743