Finite Group Databasebeta

← C2×#19144661 #25964665

Subgroups — C2×#19144661 #25964665

Order 11008.

2170 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583451C211yesmaximal, characteristic, complemented
2C2×#14583367C211yesmaximal, characteristic
3#19144661C2116yesmaximal, direct product factor
4C2×#14583240C211yesmaximal, characteristic, complemented
5C2×#14583183C211yesmaximal, characteristic, complemented
6C2×#14583178C211yesmaximal, characteristic, complemented
7C2×#14583108C211yesmaximal, characteristic, complemented
8C2×#14583103C211yesmaximal, characteristic, complemented
9C2×#14583063C211yesmaximal, characteristic
10C2×#14583059C211yesmaximal, characteristic
11C2×#14582993C211yesmaximal, characteristic, complemented
12C2×#14582991C211yesmaximal, characteristic, complemented
13C2×#14582986C211yesmaximal, characteristic, complemented
14C2×#14582984C211yesmaximal, characteristic, complemented
15C2×#14582949C211yesmaximal, characteristic, complemented
16C2×C43×#485C211yesmaximal, characteristic, complemented
17C22×#10621898C2211yescharacteristic
18C22×Dic172C2211yescharacteristic
19C22×#10621885C2211yescharacteristic
20C22×#10621873C2211yescharacteristic
21C22×#10621884C2211yescharacteristic
22#14583451—24no—
23#14583451C2218yescomplemented
24C2×#13063324C2211yescharacteristic
25C2×#13063323C2211yescharacteristic
26C2×#13063315—21no—
27C2×#13063304C2211yescharacteristic
28C2×#13063302—21no—
29#14583367—24no—
30#14583367C2218yes—
31C2×Q8×Dic43C2211yescharacteristic
32C2×#13063290—21no—
33C2×#13063290C2211yescharacteristic
34C2×#13063290C2211yescharacteristic
35C2×#13063290C2211yescharacteristic
36C2×#13063287C2211yescharacteristic
37C2×#13063287C2211yescharacteristic
38C2×(C22⋊D43)⋊C4—21no—
39C2×(C22⋊D43)⋊C4—21no—
40C2×#13063282—21no—
41C2×#13063281—21no—
42C22×C4×Dic43C2211yescharacteristic
43C2×C42×D43—21no—
44#14583240C2218yescomplemented
45#14583183C2218yescomplemented
46#14583178C2218yescomplemented
47#14583108C2218yescomplemented
48#14583103C2218yescomplemented
49#14583063C2218yes—
50#14583059C2218yes—
51#14582993C2218yescomplemented
52#14582991C2218yescomplemented
53#14582986C2218yescomplemented
54#14582984C2218yescomplemented
55#14582949C2218yescomplemented
56C2×#13063258C2211yescharacteristic
57C2×#13063256C2211yescharacteristic
58C2×Dic43⋊C8C2211yescharacteristic
59C2×Dic43⋊C8C2211yescharacteristic
60C2×#13063250C2211yescharacteristic
61C2×#13063248C2211yescharacteristic
62C2×#13063248C2211yescharacteristic
63C2×#13063248C2211yescharacteristic
64C2×#13063247C2211yescharacteristic
65C2×#13063245C2211yescharacteristic
66C2×C22⋊(C43⋊C8)C2211yescharacteristic
67C2×C8×Dic43C2211yescharacteristic
68C2×C8×Dic43C2211yescharacteristic
69C2×C22⋊Q8×C43C2211yescharacteristic
70C2×#117×C43C2211yescharacteristic
71C43×#485C2218yescomplemented
72C2×#107×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×Dic86—21no—
82C22×Dic86C2311yescharacteristic
83C22×Dic86C2311yescharacteristic
84C22×D172C2311yescharacteristic
85C22×C22⋊D43—21no—
86C23×Dic43D411yescharacteristic
87C23×Dic43D411yescharacteristic
88C22×C4×D43—21no—
89C22×C4×D43—21no—
90C22×C4×D43—21no—
91C2×Dic172—24no—
92C2×Dic172C2314yes—
93C2×#10621885—24no—
94C2×#10621885C2314yes—
95C2×#10621873—24no—
96C2×#10621873C2314yes—
97C2×#10621884—24no—
98C2×#10621884C2314yes—
99C22×C43⋊C8C2311yescharacteristic
100C22×C43⋊C8C2311yescharacteristic
101#13063324—22no—
102#13063324C2314yes—
103#13063323—22no—
104#13063323C2314yes—
105#13063315—28no—
106#13063304—22no—
107#13063304C2314yes—
108#13063302—28no—
109Q8×Dic43—22no—
110Q8×Dic43C2314yes—
111#13063290—28no—
112#13063290—22no—
113#13063290—22no—
114#13063290—22no—
115#13063290C2314yes—
116#13063290C2314yes—
117#13063290C2314yes—
118#13063287—22no—
119#13063287—22no—
120#13063287C2314yes—
121#13063287C2314yes—
122(C22⋊D43)⋊C4—28no—
123(C22⋊D43)⋊C4—28no—
124#13063282—28no—
125#13063281—28no—
126C2×C4⋊Dic43—21no—
127C2×C4⋊Dic43C2311yescharacteristic
128C2×Dic43⋊C4—21no—
129C2×Dic43⋊C4—21no—
130C2×Dic43⋊C4—21no—
131C2×Dic43⋊C4—21no—
132C2×Dic43⋊C4—21no—
133C2×Dic43⋊C4—21no—
134C2×Dic43⋊C4—21no—
135C2×C22⋊Dic43—21no—
136C2×(C2×D43)⋊C4—21no—
137C2×(C2×D43)⋊C4—21no—
138C2×C4×Dic43—21no—
139C2×C4×Dic43—21no—
140C2×C4×Dic43—21no—
141C2×C4×Dic43—21no—
142C2×C4×Dic43D411yescharacteristic
143C2×C4×Dic43D411yescharacteristic
144C2×C4×Dic43D414yes—
145C2×C4×Dic43C2311yescharacteristic
146C2×C4×Dic43C2311yescharacteristic
147C2×C4×Dic43C2314yes—
148C42×D43—28no—
149#13063258C2314yes—
150#13063256C2314yes—
151Dic43⋊C8C2314yes—
152Dic43⋊C8C2314yes—
153#13063250C2314yes—
154#13063248C2314yes—
155#13063248C2314yes—
156#13063248C2314yes—
157#13063247C2314yes—
158#13063245C2314yes—
159C22⋊(C43⋊C8)C2314yes—
160C8×Dic43C2314yes—
161C8×Dic43C2314yes—
162C22×Q8×C43C2311yescharacteristic
163C23×C4×C43C2311yescharacteristic
164C22×C8×C43C2311yescharacteristic
165C22×C8×C43C2311yescharacteristic
166C22⋊Q8×C43—22no—
167C22⋊Q8×C43C2314yes—
168#117×C43—22no—
169#117×C43C2314yes—
170C2×C4⋊C4×C43—21no—
171C2×C4⋊C4×C43C2311yescharacteristic
172C2×C4⋊C4×C43C2311yescharacteristic
173C2×C4⋊C4×C43C2311yescharacteristic
174C2×C22⋊C4×C43—21no—
175C2×C22⋊C4×C43—21no—
176C2×C42×C43—21no—
177#107×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×C43C2×D411yescharacteristic
195C22×C4×C43C2×D412yes—
196C22×C4×C43C2412yes—
197C22×C4×C43C2411yescharacteristic
198C2×C22⋊D43—28no—
199C2×C22⋊D43—24no—
200C22×Dic43—24no—
201C22×Dic43—24no—
202C22×Dic43—21no—
203C22×Dic43—21no—
204C22×Dic43—21no—
205C22×Dic43C2×D411yescharacteristic
206C22×Dic43C2×D411yescharacteristic
207C22×Dic43C2×D414yes—
208C22×Dic43C2×D414yes—
209C22×Dic43C2×D411yescharacteristic
210C22×Dic43C2×D411yescharacteristic
211#10621898—216no—
212#10621898—28no—
213#10621898—28no—
214C2×D172—21no—
215C2×D172—22no—
216C2×D172#4114yes—
217C2×D172C2412yes—
218C2×C4×D43—28no—
219C2×C4×D43—24no—
220C2×C4×D43—24no—
221C2×C4×D43—24no—
222C2×C4×D43—44no—
223C2×C4×D43—44no—
224C2×Dic86—21no—
225C2×Dic86—22no—
226C2×Dic86—22no—
227C2×Dic86—22no—
228C2×Dic86—21no—
229C2×Dic86—24no—
230C2×Dic86—44no—
231C2×Dic86#4114yes—
232C2×Dic86C2412yes—
233C2×Dic86C2412yes—
234C2×C8×C43—22no—
235C2×C8×C43—22no—
236C2×C8×C43C2412yes—
237C2×C8×C43C2412yes—
238C4⋊C4×C43—24no—
239C4⋊C4×C43—21no—
240C4⋊C4×C43—21no—
241C4⋊C4×C43—21no—
242C4⋊C4×C43C2412yes—
243C4⋊C4×C43C2412yes—
244C4⋊C4×C43C2412yes—
245C22⋊C4×C43—24no—
246C22⋊C4×C43—24no—
247C42×C43—24no—
248C22⋊Dic43—24no—
249#10621885—28no—
250#10621884—28no—
251(C2×D43)⋊C4—24no—
252(C2×D43)⋊C4—24no—
253C4⋊Dic43—21no—
254C4⋊Dic43—24no—
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×D414yes—
268C4×Dic43C2×D414yes—
269C4×Dic43C2×D412yes—
270C4×Dic43C2×D412yes—
271C4×Dic43C2412yes—
272C4×Dic43C2412yes—
273C2×C43⋊C8—22no—
274C2×C43⋊C8—22no—
275C2×C43⋊C8C2412yes—
276C2×C43⋊C8C2412yes—
277Dic172—28no—
278#10621873—28no—
279C23×C43—22no—
280C23×C43—22no—
281C23×C43—22no—
282C23×C43C22×D412yes—
283C23×C43C22×D411yescharacteristic
284C22×D43—24no—
285C22×D43—22no—
286C22×D43—42no—
287C22×D43—42no—
288Q8×C43—22no—
289Q8×C43—22no—
290Q8×C43—42no—
291C2×C4×C43—22no—
292C2×C4×C43—24no—
293C2×C4×C43—22no—
294C2×C4×C43—22no—
295C2×C4×C43—22no—
296C2×C4×C43—22no—
297C2×C4×C43—22no—
298C2×C4×C43—22no—
299C2×C4×C43—42no—
300C2×C4×C43—42no—
301C2×C4×C43—42no—
302C2×C4×C43—42no—
303C2×C4×C43C22×D412yes—
304C2×C4×C43C22×D411yescharacteristic
305C2×C4×C43C2×#4112yes—
306C2×C4×C43C2×#4112yes—
307C2×C4×C43C2511yescharacteristic
308C22⋊D43—216no—
309C2×Dic43—24no—
310C2×Dic43—22no—
311C2×Dic43—22no—
312C2×Dic43—22no—
313C2×Dic43—28no—
314C2×Dic43—28no—
315C2×Dic43—22no—
316C2×Dic43—22no—
317C2×Dic43—42no—
318C2×Dic43—42no—
319C2×Dic43#13514yes—
320C2×Dic43#13714yes—
321C2×Dic43C22×D412yes—
322C2×Dic43C22×D412yes—
323C2×Dic43C22×D412yes—
324C2×Dic43C22×D412yes—
325D172—24no—
326D172—22no—
327D172C2×#4114yes—
328C4×D43—216no—
329C4×D43—48no—
330C4×D43—48no—
331Dic86—24no—
332Dic86—22no—
333Dic86—22no—
334Dic86—22no—
335Dic86—42no—
336Dic86—48no—
337Dic86C2×#4114yes—
338C8×C43—22no—
339C8×C43—22no—
340C43⋊C8—22no—
341C43⋊C8—22no—
342C2×#3107—431nomaximal, Sylow
343C22×C43—22no—
344C22×C43—22no—
345C22×C43—22no—
346C22×C43—44no—
347C22×C43#52512yes—
348C22×C43C2×#13512yes—
349C22×C43C2×#13712yes—
350C22×C43C23×D411yescharacteristic
351C2×D43—24no—
352C2×D43—48no—
353C2×D43—42no—
354C2×D43—42no—
355C4×C43—22no—
356C4×C43—42no—
357C4×C43—42no—
358C4×C43—42no—
359C4×C43—42no—
360C4×C43#52512yes—
361C4×C43C22×#4111yescharacteristic
362C4×C43C22×#4111yescharacteristic
363Dic43—24no—
364Dic43—22no—
365Dic43—22no—
366Dic43—42no—
367Dic43—42no—
368Dic43C2×#13514yes—
369Dic43C2×#13714yes—
370C2×#533—431no—
371C2×C4×#41—431no—
372#3107—4316no—
373C2×#485—431no—
374C2×#485D4311yescharacteristic, complemented
375C2×#475—431no—
376C2×#474—431no—
377C2×#462—431no—
378C2×#461—431no—
379C2×#452—431no—
380C2×#452—431no—
381C2×C4×Q16—431no—
382C2×C4×Q16—431no—
383C2×C4×SD16—431no—
384C2×C4×SD16—431no—
385C2×#431—431no—
386C2×C43—42no—
387C2×C43#310714yescomplemented
388C2×C43C2×#52511yescharacteristic
389C2×C43C22×#13511yescharacteristic
390C2×C43C22×#13711yescharacteristic
391D43—44no—
392C22×#41—431no—
393C22×Q16—431no—
394C22×Q16—431no—
395C22×SD16—431no—
396C22×SD16—431no—
397#533—438no—
398#533—864no—
399C2×C4⋊Q8—431no—
400C2×C4⋊Q8—431no—
401C2×#125—861no—
402C2×C22⋊Q8—431no—
403C2×C22⋊Q8—861no—
404C2×C22⋊Q8C2×D4311yescharacteristic
405C4×#41—438no—
406C4×#41—864no—
407C2×C4×Q8—431no—
408C2×C4×Q8—431no—
409C2×C4×Q8—431no—
410C2×C4×Q8—431no—
411C2×C4×Q8—861no—
412C2×C4×D4—431no—
413C2×C4×D4—431no—
414C2×C4×D4—861no—
415C2×C4×D4—861no—
416C2×#117—861no—
417C2×#117—861no—
418C2×#117C2×D4311yescharacteristic
419C22×C42—431no—
420C22×C42—861no—
421#485—438no—
422#485C2×D4318yescomplemented
423#475—438no—
424#474—438no—
425#462—438no—
426#461—438no—
427#452—438no—
428#452—438no—
429C4×Q16—438no—
430C4×Q16—438no—
431C4×SD16—438no—
432C4×SD16—438no—
433#431—438no—
434C2×#107—431no—
435C2×#107C2×D4311yescharacteristic
436C2×#106—431no—
437C2×#106C2×D4311yescharacteristic
438C2×C4⋊C8—431no—
439C2×C4⋊C8—431no—
440C2×#103—431no—
441C2×#103—431no—
442C2×#103—431no—
443C2×#103—431no—
444C2×#103C2×D4311yescharacteristic
445C2×#103C2×D4311yescharacteristic
446C2×#102—431no—
447C2×#102—431no—
448C2×C22⋊C8—431no—
449C2×C22⋊C8C2×D4311yescharacteristic
450C2×C4×C8—431no—
451C2×C4×C8—431no—
452C43C2×#310711yescharacteristic, complemented, Sylow
453C2×#41—434no—
454C2×#41—864no—
455C2×#41—864no—
456C2×#41—862no—
457C22×Q8—431no—
458C22×Q8—431no—
459C22×Q8—861no—
460C22×Q8C22×D4311yescharacteristic
461C22×D4—431no—
462C22×D4—861no—
463C23×C4—431no—
464C23×C4—431no—
465C23×C4—861no—
466C23×C4—861no—
467C23×C4—861no—
468C23×C4C22×D4311yescharacteristic
469C2×Q16—434no—
470C2×Q16—434no—
471C2×Q16—864no—
472C2×Q16—864no—
473C2×SD16—434no—
474C2×SD16—434no—
475C2×SD16—864no—
476C2×SD16—864no—
477C22×C8—431no—
478C22×C8—431no—
479C22×C8C22×D4311yescharacteristic
480C22×C8C22×D4311yescharacteristic
481C4⋊Q8—434no—
482C4⋊Q8—434no—
483C4⋊Q8—862no—
484C4⋊Q8—862no—
485#125—868no—
486C22⋊Q8—22no—
487C22⋊Q8—434no—
488C22⋊Q8—868no—
489C22⋊Q8—862no—
490C22⋊Q8C22×D4314yes—
491C4×Q8—434no—
492C4×Q8—434no—
493C4×Q8—434no—
494C4×Q8—434no—
495C4×Q8—862no—
496C4×Q8—862no—
497C4×Q8—862no—
498C4×Q8—868no—
499C4×Q8—862no—
500C4×D4—434no—
501C4×D4—434no—
502C4×D4—862no—
503C4×D4—862no—
504C4×D4—868no—
505C4×D4—868no—
506#117—22no—
507#117—868no—
508#117—868no—
509#117C22×D4314yes—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—431no—
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×D4311yescharacteristic
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—861no—
526C2×C22⋊C4—861no—
527C2×C22⋊C4—861no—
528C2×C42—21no—
529C2×C42—431no—
530C2×C42—431no—
531C2×C42—434no—
532C2×C42—431no—
533C2×C42—431no—
534C2×C42—434no—
535C2×C42—868no—
536C2×C42—861no—
537C2×C42—861no—
538C2×C42—861no—
539C2×C42—861no—
540#107—434no—
541#107C22×D4314yes—
542#106—434no—
543#106C22×D4314yes—
544C4⋊C8—434no—
545C4⋊C8—434no—
546#103—434no—
547#103—434no—
548#103—434no—
549#103—434no—
550#103C22×D4314yes—
551#103C22×D4314yes—
552#102—434no—
553#102—434no—
554C22⋊C8—434no—
555C22⋊C8C22×D4314yes—
556C4×C8—434no—
557C4×C8—434no—
558C24—861no—
559C24D4×D4311yescharacteristic
560#41—868no—
561#41—868no—
562#41—8616no—
563C2×Q8—21no—
564C2×Q8—22no—
565C2×Q8—22no—
566C2×Q8—434no—
567C2×Q8—432no—
568C2×Q8—432no—
569C2×Q8—864no—
570C2×Q8—861no—
571C2×Q8—861no—
572C2×Q8—862no—
573C2×Q8—862no—
574C2×Q8—862no—
575C2×Q8—1724no—
576C2×Q8C23×D4312yes—
577C2×D4—434no—
578C2×D4—432no—
579C2×D4—868no—
580C2×D4—864no—
581C2×D4—861no—
582C2×D4—862no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—431no—
590C22×C4—431no—
591C22×C4—434no—
592C22×C4—434no—
593C22×C4—431no—
594C22×C4—431no—
595C22×C4—864no—
596C22×C4—864no—
597C22×C4—868no—
598C22×C4—864no—
599C22×C4—864no—
600C22×C4—861no—
601C22×C4—864no—
602C22×C4—861no—
603C22×C4—861no—
604C22×C4—1724no—
605C22×C4—1724no—
606C22×C4D4×D4312yes—
607C22×C4D4×D4311yescharacteristic
608C22×C4C23×D4312yes—
609C22×C4C23×D4311yescharacteristic
610Q16—868no—
611Q16—868no—
612SD16—868no—
613SD16—868no—
614C2×C8—22no—
615C2×C8—22no—
616C2×C8—432no—
617C2×C8—432no—
618C2×C8—862no—
619C2×C8—862no—
620C2×C8C23×D4312yes—
621C2×C8C23×D4312yes—
622C4⋊C4—24no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—432no—
627C4⋊C4—864no—
628C4⋊C4—864no—
629C4⋊C4—864no—
630C4⋊C4—864no—
631C4⋊C4—864no—
632C4⋊C4—864no—
633C4⋊C4—864no—
634C4⋊C4—861no—
635C4⋊C4—864no—
636C4⋊C4C23×D4312yes—
637C4⋊C4C23×D4312yes—
638C4⋊C4C23×D4312yes—
639C22⋊C4—24no—
640C22⋊C4—24no—
641C22⋊C4—864no—
642C22⋊C4—864no—
643C22⋊C4—864no—
644C42—24no—
645C42—434no—
646C42—434no—
647C42—432no—
648C42—432no—
649C42—432no—
650C42—432no—
651C42—864no—
652C42—864no—
653C42—864no—
654C42—864no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—864no—
659C23—862no—
660C23—1722no—
661C23—1722no—
662C23C2×D4×D4312yes—
663C23C2×D4×D4311yescharacteristic
664Q8—22no—
665Q8—22no—
666Q8—42no—
667Q8—434no—
668Q8—864no—
669Q8—862no—
670Q8—862no—
671Q8—862no—
672Q8—1728no—
673Q8—1722no—
674D4—434no—
675D4—8616no—
676D4—864no—
677D4—862no—
678C2×C4—22no—
679C2×C4—24no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—434no—
691C2×C4—434no—
692C2×C4—432no—
693C2×C4—432no—
694C2×C4—432no—
695C2×C4—432no—
696C2×C4—8616no—
697C2×C4—868no—
698C2×C4—868no—
699C2×C4—864no—
700C2×C4—862no—
701C2×C4—862no—
702C2×C4—862no—
703C2×C4—862no—
704C2×C4—862no—
705C2×C4—1728no—
706C2×C4—1728no—
707C2×C4—1722no—
708C2×C4—1722no—
709C2×C4C2×D4×D4312yes—
710C2×C4C2×D4×D4311yescharacteristic
711C2×C4#41×D4312yes—
712C2×C4#41×D4312yes—
713C2×C4C24×D4311yescharacteristic
714C8—22no—
715C8—22no—
716C8—862no—
717C8—862no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—44no—
722C22—864no—
723C22—1722no—
724C22—1722no—
725C22—1728no—
726C22#1458340712yes—
727C22#135×D4312yes—
728C22#137×D4312yes—
729C22C22×D4×D4311yescharacteristic
730C4—22no—
731C4—42no—
732C4—42no—
733C4—42no—
734C4—42no—
735C4—434no—
736C4—434no—
737C4—862no—
738C4—862no—
739C4—864no—
740C4—1722no—
741C4—1722no—
742C4#1458340712yes—
743C4C2×#41×D4311yescharacteristic
744C4C2×#41×D4311yescharacteristic
745C2—42no—
746C2—1724no—
747C2#1914466114yesdirect product factor
748C2C2×#1458340711yescharacteristic
749C2C2×#135×D4311yescharacteristic
750C2C2×#137×D4311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#485C2
socleC23×C43C22×D4
prime radicalC22×#10621898C22
hypercenterC2×#485D43
hypocenterC43C2×#3107
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
1. C2×#14583451C2semidirect
3. #19144661C2direct (N × H)
4. C2×#14583240C2semidirect
5. C2×#14583183C2semidirect
6. C2×#14583178C2semidirect
7. C2×#14583108C2semidirect
8. C2×#14583103C2semidirect
11. C2×#14582993C2semidirect
12. C2×#14582991C2semidirect
13. C2×#14582986C2semidirect
14. C2×#14582984C2semidirect
15. C2×#14582949C2semidirect
16. C2×C43×#485C2semidirect
23. #14583451C22semidirect
44. #14583240C22semidirect
45. #14583183C22semidirect
46. #14583178C22semidirect
47. #14583108C22semidirect
48. #14583103C22semidirect
51. #14582993C22semidirect
52. #14582991C22semidirect
53. #14582986C22semidirect
54. #14582984C22semidirect
55. #14582949C22semidirect
71. C43×#485C22semidirect
374. C2×#485D43semidirect
387. C2×C43#3107semidirect
422. #485C2×D43semidirect
452. C43C2×#3107semidirect
747. C2#19144661direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834512
C2×#145833672
#191446612
C2×#145832402
C2×#145831832
C2×#145831782
C2×#145831082
C2×#145831032
C2×#145830632
C2×#145830592
C2×#145829932
C2×#145829912
C2×#145829862
C2×#145829842
C2×#145829492
C2×C43×#4852
C2×#310743