Finite Group Databasebeta

← C2×#19146458 #25972978

Subgroups — C2×#19146458 #25972978

Order 11008.

2374 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583562C211yesmaximal, characteristic, complemented
2C2×#14583550C211yesmaximal, characteristic
3#19146458C2116yesmaximal, direct product factor
4C2×#14583248C211yesmaximal, characteristic, complemented
5C2×#14583231C211yesmaximal, characteristic, complemented
6C2×#14583183C211yesmaximal, characteristic, complemented
7C2×#14583130C211yesmaximal, characteristic, complemented
8C2×#14583129C211yesmaximal, characteristic, complemented
9C2×#14583103C211yesmaximal, characteristic, complemented
10C2×#14583040C211yesmaximal, characteristic, complemented
11C2×#14583039C211yesmaximal, characteristic, complemented
12C2×#14582986C211yesmaximal, characteristic, complemented
13C2×(C22⋊D43)⋊C8C211yesmaximal, characteristic, complemented
14C22×#13063248C211yesmaximal, characteristic, complemented
15C2×#103×D43C211yesmaximal, characteristic, complemented
16C2×C43×#483C211yesmaximal, characteristic, complemented
17C22×#10621898—21no—
18C23×Dic86C2211yescharacteristic
19C22×Q8×D43C2211yescharacteristic
20C22×#10621873C2211yescharacteristic
21C22×#10621873C2211yescharacteristic
22C22×#10621884C2211yescharacteristic
23C23×C43⋊C8C2211yescharacteristic
24C22×C8×D43C2211yescharacteristic
25#14583562—24no—
26#14583562C2218yescomplemented
27#14583550—24no—
28#14583550C2218yes—
29C2×#13063324—21no—
30C2×#13063324C2211yescharacteristic
31C2×#13063323C2211yescharacteristic
32C2×#13063310—21no—
33C2×#13063308—21no—
34C2×#13063305C2211yescharacteristic
35C2×#13063303—21no—
36C2×#13063303—21no—
37C2×#13063302—21no—
38C2×#13063300C2211yescharacteristic
39C2×#13063299C2211yescharacteristic
40C2×#13063290C2211yescharacteristic
41C2×#13063287C2211yescharacteristic
42C2×C4×C22⋊D43C2211yescharacteristic
43C2×(C22⋊D43)⋊C4—21no—
44C2×C4⋊C4×D43C2211yescharacteristic
45#14583248C2218yescomplemented
46#14583231C2218yescomplemented
47#14583183C2218yescomplemented
48#14583130C2218yescomplemented
49#14583129C2218yescomplemented
50#14583103C2218yescomplemented
51#14583040C2218yescomplemented
52#14583039C2218yescomplemented
53#14582986C2218yescomplemented
54(C22⋊D43)⋊C8C2218yescomplemented
55C2×#13063256C2211yescharacteristic
56C2×Dic43⋊C8C2211yescharacteristic
57C2×#13063250C2211yescharacteristic
58C2×#13063250C2211yescharacteristic
59C2×#13063249C2211yescharacteristic
60C2×#13063248C2211yescharacteristic
61C2×#13063248C2211yescharacteristic
62C2×#13063248C2211yescharacteristic
63C2×#13063248C2211yescharacteristic
64C2×#13063248C2218yescomplemented
65#103×D43C2218yescomplemented
66C2×#13063245C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
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—28no—
78C2×#10621898—48no—
79C22×Dic86—24no—
80C22×Dic86—22no—
81C22×Dic86—21no—
82C22×Dic86—21no—
83C22×Dic86—21no—
84C22×Dic86—42no—
85C22×Dic86C2311yescharacteristic
86C22×Dic86C2314yes—
87C22×Dic86C2311yescharacteristic
88C2×Q8×D43—22no—
89C2×Q8×D43—24no—
90C2×Q8×D43—42no—
91C2×Q8×D43C2314yes—
92C22×D172—21no—
93C22×D172C2311yescharacteristic
94C22×C22⋊D43—21no—
95C22×C22⋊D43D411yescharacteristic
96C23×Dic43—21no—
97C22×C4×D43—21no—
98C22×C4×D43—21no—
99C22×C4×D43—21no—
100C22×C4×D43C2311yescharacteristic
101C2×#10621873—24no—
102C2×#10621873—42no—
103C2×#10621873C2314yes—
104C2×#10621873C2314yes—
105C2×#10621884—42no—
106C2×#10621884C2314yes—
107C22×C43⋊C8—42no—
108C22×C43⋊C8C2311yescharacteristic
109C22×C43⋊C8C2311yescharacteristic
110C22×C43⋊C8C2314yes—
111C2×C8×D43—42no—
112C2×C8×D43C2314yes—
113#13063324—28no—
114#13063324—22no—
115#13063324C2314yes—
116#13063323—22no—
117#13063323C2314yes—
118#13063310—28no—
119#13063308—28no—
120#13063305—22no—
121#13063305C2314yes—
122#13063303—28no—
123#13063303—28no—
124#13063302—28no—
125#13063300—22no—
126#13063300C2314yes—
127#13063299—22no—
128#13063299C2314yes—
129#13063290—22no—
130#13063290C2314yes—
131#13063287—22no—
132#13063287C2314yes—
133C4×C22⋊D43D414yes—
134C4×C22⋊D43C2314yes—
135(C22⋊D43)⋊C4—28no—
136C2×C4⋊Dic43—21no—
137C2×C4⋊Dic43C2311yescharacteristic
138C2×Dic43⋊C4—21no—
139C2×Dic43⋊C4—21no—
140C2×Dic43⋊C4—21no—
141C2×Dic43⋊C4—21no—
142C2×Dic43⋊C4—21no—
143C2×Dic43⋊C4D411yescharacteristic
144C4⋊C4×D43—22no—
145C4⋊C4×D43C2314yes—
146C2×C22⋊Dic43D411yescharacteristic
147C2×(C2×D43)⋊C4—21no—
148C2×(C2×D43)⋊C4—21no—
149C2×(C2×D43)⋊C4—21no—
150C2×(C2×D43)⋊C4—21no—
151C2×(C2×D43)⋊C4D411yescharacteristic
152C2×C4×Dic43—21no—
153C2×C4×Dic43C2311yescharacteristic
154#13063256C2314yes—
155Dic43⋊C8C2314yes—
156#13063250C2314yes—
157#13063250C2314yes—
158#13063249C2314yes—
159#13063248C2314yes—
160#13063248C2314yes—
161#13063248C2314yes—
162#13063248C2314yes—
163#13063245C2314yes—
164(C2×D43)⋊C8C2314yes—
165C8×Dic43C2314yes—
166C22×Q8×C43C2311yescharacteristic
167C23×C4×C43—21no—
168C23×C4×C43C2311yescharacteristic
169C22×C8×C43C2311yescharacteristic
170C22×C8×C43C2311yescharacteristic
171C22⋊Q8×C43—22no—
172C22⋊Q8×C43C2314yes—
173C2×C4⋊C4×C43—21no—
174C2×C4⋊C4×C43—22no—
175C2×C4⋊C4×C43—21no—
176C2×C4⋊C4×C43C2311yescharacteristic
177C2×C4⋊C4×C43C2311yescharacteristic
178C2×C4⋊C4×C43C2314yes—
179C2×C4⋊C4×C43C2311yescharacteristic
180C2×C22⋊C4×C43—21no—
181#106×C43C2314yes—
182#106×C43C2314yes—
183#103×C43C2314yes—
184#103×C43C2314yes—
185C22⋊C8×C43C2314yes—
186C24×C43C2×D411yescharacteristic
187C23×D43—21no—
188C23×D43C2×D411yescharacteristic
189C2×Q8×C43—21no—
190C2×Q8×C43—22no—
191C2×Q8×C43—22no—
192C2×Q8×C43C2412yes—
193C22×C4×C43—22no—
194C22×C4×C43—22no—
195C22×C4×C43—21no—
196C22×C4×C43—21no—
197C22×C4×C43—21no—
198C22×C4×C43—21no—
199C22×C4×C43—24no—
200C22×C4×C43—44no—
201C22×C4×C43C2×D411yescharacteristic
202C22×C4×C43C2×D412yes—
203C22×C4×C43C2412yes—
204C22×C4×C43C2411yescharacteristic
205C2×C22⋊D43—24no—
206C2×C22⋊D43—44no—
207C2×C22⋊D43SD1618yescomplemented
208C2×C22⋊D43C2×D414yes—
209C22×Dic43—21no—
210C22×Dic43—21no—
211C22×Dic43—21no—
212C22×Dic43—24no—
213C22×Dic43—44no—
214C22×Dic43C2×D411yescharacteristic
215C22×Dic43C2×D411yescharacteristic
216C22×Dic43C2×D411yescharacteristic
217Q8×D43—28no—
218Q8×D43—44no—
219Q8×D43—48no—
220#10621898—432no—
221C2×D172—21no—
222C2×D172—24no—
223C2×D172—22no—
224C2×D172—22no—
225C2×D172—44no—
226C2×D172C2412yes—
227C2×C4×D43—22no—
228C2×C4×D43—22no—
229C2×C4×D43—24no—
230C2×C4×D43—24no—
231C2×C4×D43—24no—
232C2×C4×D43—44no—
233C2×C4×D43—44no—
234C2×C4×D43—44no—
235C2×C4×D43C2×D412yes—
236C2×C4×D43C2412yes—
237C2×Dic86—21no—
238C2×Dic86—22no—
239C2×Dic86—22no—
240C2×Dic86—22no—
241C2×Dic86—28no—
242C2×Dic86—24no—
243C2×Dic86—21no—
244C2×Dic86—24no—
245C2×Dic86—24no—
246C2×Dic86—44no—
247C2×Dic86—48no—
248C2×Dic86—44no—
249C2×Dic86—44no—
250C2×Dic86—44no—
251C2×Dic86#4114yescomplemented
252C2×Dic86C2412yes—
253C2×Dic86C2412yes—
254C2×C8×C43—22no—
255C2×C8×C43—22no—
256C2×C8×C43C2412yes—
257C2×C8×C43C2412yes—
258C4⋊C4×C43—21no—
259C4⋊C4×C43—21no—
260C4⋊C4×C43—24no—
261C4⋊C4×C43—24no—
262C4⋊C4×C43—21no—
263C4⋊C4×C43C2412yes—
264C4⋊C4×C43C2412yes—
265C4⋊C4×C43C2412yes—
266C22⋊C4×C43—24no—
267C22⋊Dic43C2×D414yes—
268#10621884—44no—
269(C2×D43)⋊C4—24no—
270(C2×D43)⋊C4—24no—
271(C2×D43)⋊C4—24no—
272(C2×D43)⋊C4—24no—
273(C2×D43)⋊C4C2×D414yes—
274C4⋊Dic43—21no—
275C4⋊Dic43—24no—
276C4⋊Dic43C2412yes—
277Dic43⋊C4—24no—
278Dic43⋊C4—24no—
279Dic43⋊C4—24no—
280Dic43⋊C4—24no—
281Dic43⋊C4—24no—
282Dic43⋊C4C2×D414yes—
283C4×Dic43—24no—
284C4×Dic43C2×D412yes—
285C4×Dic43C2412yes—
286C2×C43⋊C8—22no—
287C2×C43⋊C8—22no—
288C2×C43⋊C8—44no—
289C2×C43⋊C8C2412yes—
290C2×C43⋊C8C2412yes—
291#10621873—28no—
292#10621873—44no—
293C8×D43—44no—
294C23×C43—22no—
295C23×C43—22no—
296C23×C43C2×SD1614yes—
297C23×C43C22×D412yes—
298C23×C43C22×D411yescharacteristic
299C22×D43—22no—
300C22×D43—22no—
301C22×D43—22no—
302C22×D43—42no—
303C22×D43—42no—
304C22×D43—42no—
305C22×D43C2×SD1614yes—
306C22×D43C22×D412yes—
307Q8×C43—22no—
308Q8×C43—22no—
309Q8×C43—42no—
310C2×C4×C43—22no—
311C2×C4×C43—24no—
312C2×C4×C43—22no—
313C2×C4×C43—22no—
314C2×C4×C43—22no—
315C2×C4×C43—22no—
316C2×C4×C43—22no—
317C2×C4×C43—22no—
318C2×C4×C43—42no—
319C2×C4×C43—42no—
320C2×C4×C43—42no—
321C2×C4×C43—48no—
322C2×C4×C43—42no—
323C2×C4×C43C22×D412yes—
324C2×C4×C43C22×D411yescharacteristic
325C2×C4×C43C2×#4112yes—
326C2×C4×C43H(5,𝔽2)12yes—
327C2×C4×C43C2511yescharacteristic
328C22⋊D43—48no—
329C22⋊D43C2×SD16116yescomplemented
330C2×Dic43—24no—
331C2×Dic43—22no—
332C2×Dic43—22no—
333C2×Dic43—22no—
334C2×Dic43—22no—
335C2×Dic43—22no—
336C2×Dic43—48no—
337C2×Dic43—42no—
338C2×Dic43—42no—
339C2×Dic43C2×SD1614yes—
340C2×Dic43C22×D412yes—
341C2×Dic43C22×D412yes—
342C2×Dic43C22×D412yes—
343D172—22no—
344D172—22no—
345D172—48no—
346D172—42no—
347C4×D43—24no—
348C4×D43—22no—
349C4×D43—22no—
350C4×D43—48no—
351C4×D43—48no—
352C4×D43—48no—
353Dic86—24no—
354Dic86—22no—
355Dic86—22no—
356Dic86—22no—
357Dic86—48no—
358Dic86—48no—
359Dic86—42no—
360Dic86—48no—
361Dic86C2×#4114yescomplemented
362C8×C43—22no—
363C8×C43—22no—
364C43⋊C8—22no—
365C43⋊C8—22no—
366C2×#3298—431nomaximal, Sylow
367C22×C43—22no—
368C22×C43—28no—
369C22×C43—22no—
370C22×C43#54612yes—
371C22×C43C22×SD1614yes—
372C22×C43C22×SD1612yes—
373C22×C43#57812yes—
374C22×C43C23×D411yescharacteristic
375C2×D43—22no—
376C2×D43—28no—
377C2×D43—22no—
378C2×D43—42no—
379C2×D43—42no—
380C2×D43—42no—
381C2×D43—84no—
382C2×D43C22×SD1614yes—
383C4×C43—22no—
384C4×C43—42no—
385C4×C43—42no—
386C4×C43—42no—
387C4×C43—42no—
388C4×C43#54612yes—
389C4×C43C22×#4111yescharacteristic
390C4×C43C2×H(5,𝔽2)11yescharacteristic
391Dic43—24no—
392Dic43—22no—
393Dic43—22no—
394Dic43—42no—
395Dic43—42no—
396Dic43C22×SD1614yes—
397C2×D4×Q8—431no—
398C2×#547—431no—
399#3298—4316no—
400C2×#487—431no—
401C2×#483—431no—
402C2×#483D4311yescharacteristic, complemented
403C2×#475—431no—
404C2×#465—431no—
405C2×#465—431no—
406C2×#461—431no—
407C2×#448—431no—
408C2×#448—431no—
409C2×C4×SD16—431no—
410C2×C8×D4—431no—
411C22×#103—431no—
412C22×#103—431no—
413C2×C43—24no—
414C2×C43#329814yescomplemented
415C2×C43C2×#54611yescharacteristic
416C2×C43C23×SD1611yescharacteristic
417C2×C43C2×#57811yescharacteristic
418D43—24no—
419D43—82no—
420C22×#41—861no—
421C23×Q8—431no—
422C23×Q8—431no—
423C22×SD16—431no—
424C22×SD16—431no—
425C22×SD16—431no—
426C23×C8—431no—
427C23×C8—431no—
428D4×Q8—438no—
429D4×Q8—864no—
430#547—438no—
431#547—864no—
432C2×C4⋊Q8—431no—
433C2×C4⋊Q8—431no—
434C2×C4⋊Q8—861no—
435C2×#123—861no—
436C2×#123—861no—
437C2×C22⋊Q8—431no—
438C2×C22⋊Q8—861no—
439C2×C22⋊Q8—861no—
440C2×C22⋊Q8—861no—
441C2×C22⋊Q8C2×D4311yescharacteristic
442C2×#121—431no—
443C2×#121—431no—
444C2×C4×Q8—431no—
445C2×C4×D4—431no—
446C2×C4×D4—431no—
447C2×C4×D4—861no—
448C22×C4⋊C4—431no—
449C22×C4⋊C4C2×D4311yescharacteristic
450#487—438no—
451#483—438no—
452#483C2×D4318yescomplemented
453#475—438no—
454#465—438no—
455#465—438no—
456#461—438no—
457#448—438no—
458#448—438no—
459C4×SD16—438no—
460C8×D4—438no—
461C2×#106—431no—
462C2×#106C2×D4311yescharacteristic
463C2×#106C2×D4311yescharacteristic
464C2×C4⋊C8—431no—
465C2×#103—431no—
466C2×#103—431no—
467C2×#103—431no—
468C2×#103—431no—
469C2×#103—431no—
470C2×#103—431no—
471C2×#103—431no—
472C2×#103—438no—
473C2×#103—438no—
474C2×#103C2×D4311yescharacteristic
475C2×#103C2×D4311yescharacteristic
476C2×#102—431no—
477C2×C22⋊C8—431no—
478C2×C22⋊C8C2×D4311yescharacteristic
479C2×C4×C8—431no—
480C43C2×#329811yescharacteristic, complemented, Sylow
481C2×#41—868no—
482C2×#41—1728no—
483C22×Q8—434no—
484C22×Q8—431no—
485C22×Q8—431no—
486C22×Q8—434no—
487C22×Q8—861no—
488C22×Q8—861no—
489C22×Q8—864no—
490C22×Q8—862no—
491C22×Q8—861no—
492C22×Q8—862no—
493C22×Q8—864no—
494C22×Q8—1722no—
495C22×Q8—1722no—
496C22×Q8C22×D4311yescharacteristic
497C22×D4—431no—
498C22×D4—431no—
499C22×D4—861no—
500C22×D4—861no—
501C23×C4—21no—
502C23×C4—431no—
503C23×C4—861no—
504C23×C4—861no—
505C23×C4—861no—
506C23×C4—861no—
507C23×C4C22×D4311yescharacteristic
508C2×SD16—434no—
509C2×SD16—434no—
510C2×SD16—434no—
511C2×SD16—864no—
512C2×SD16—1722no—
513C2×SD16—1722no—
514C22×C8—431no—
515C22×C8—431no—
516C22×C8—434no—
517C22×C8—434no—
518C22×C8—1722no—
519C22×C8—1722no—
520C22×C8C22×D4311yescharacteristic
521C22×C8C22×D4311yescharacteristic
522C4⋊Q8—434no—
523C4⋊Q8—434no—
524C4⋊Q8—862no—
525C4⋊Q8—862no—
526C4⋊Q8—868no—
527#123—868no—
528#123—868no—
529C22⋊Q8—22no—
530C22⋊Q8—434no—
531C22⋊Q8—868no—
532C22⋊Q8—868no—
533C22⋊Q8—868no—
534C22⋊Q8—862no—
535C22⋊Q8C22×D4314yes—
536#121—434no—
537#121—434no—
538#121—862no—
539#121—862no—
540C4×Q8—434no—
541C4×Q8—862no—
542C4×D4—434no—
543C4×D4—434no—
544C4×D4—434no—
545C4×D4—862no—
546C4×D4—868no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—22no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—431no—
551C2×C4⋊C4—431no—
552C2×C4⋊C4—434no—
553C2×C4⋊C4—862no—
554C2×C4⋊C4—861no—
555C2×C4⋊C4—861no—
556C2×C4⋊C4—861no—
557C2×C4⋊C4—861no—
558C2×C4⋊C4—861no—
559C2×C4⋊C4—861no—
560C2×C4⋊C4C22×D4311yescharacteristic
561C2×C4⋊C4C22×D4311yescharacteristic
562C2×C4⋊C4C22×D4314yes—
563C2×C4⋊C4C22×D4311yescharacteristic
564C2×C22⋊C4—21no—
565C2×C22⋊C4—431no—
566C2×C22⋊C4—431no—
567C2×C22⋊C4—861no—
568C2×C22⋊C4—861no—
569C2×C22⋊C4—861no—
570C2×C22⋊C4—861no—
571C2×C42—431no—
572C2×C42—861no—
573#106—434no—
574#106C22×D4314yes—
575#106C22×D4314yes—
576C4⋊C8—434no—
577#103—434no—
578#103—434no—
579#103—434no—
580#103—434no—
581#103—434no—
582#103—434no—
583#103—434no—
584#103C22×D4314yes—
585#103C22×D4314yes—
586#102—434no—
587C22⋊C8—434no—
588C22⋊C8C22×D4314yes—
589C4×C8—434no—
590C24—431no—
591C24—861no—
592C24D4×D4311yescharacteristic
593#41—17232no—
594C2×Q8—21no—
595C2×Q8—22no—
596C2×Q8—22no—
597C2×Q8—434no—
598C2×Q8—432no—
599C2×Q8—432no—
600C2×Q8—864no—
601C2×Q8—864no—
602C2×Q8—868no—
603C2×Q8—861no—
604C2×Q8—864no—
605C2×Q8—861no—
606C2×Q8—862no—
607C2×Q8—868no—
608C2×Q8—862no—
609C2×Q8—862no—
610C2×Q8—1724no—
611C2×Q8—1724no—
612C2×Q8—1728no—
613C2×Q8—1724no—
614C2×Q8—1724no—
615C2×Q8—1724no—
616C2×Q8—1728no—
617C2×Q8C23×D4312yes—
618C2×D4—438no—
619C2×D4—434no—
620C2×D4—432no—
621C2×D4—864no—
622C2×D4—864no—
623C2×D4—861no—
624C2×D4—862no—
625C2×D4—862no—
626C2×D4—1724no—
627C2×D4—1724no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—24no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—44no—
636C22×C4—431no—
637C22×C4—431no—
638C22×C4—431no—
639C22×C4—432no—
640C22×C4—432no—
641C22×C4—864no—
642C22×C4—864no—
643C22×C4—864no—
644C22×C4—861no—
645C22×C4—862no—
646C22×C4—862no—
647C22×C4—864no—
648C22×C4—861no—
649C22×C4—861no—
650C22×C4—1724no—
651C22×C4—1724no—
652C22×C4—1724no—
653C22×C4—1724no—
654C22×C4D4×D4312yes—
655C22×C4D4×D4311yescharacteristic
656C22×C4C23×D4312yes—
657C22×C4C23×D4311yescharacteristic
658SD16—868no—
659SD16—1724no—
660SD16—1724no—
661C2×C8—22no—
662C2×C8—22no—
663C2×C8—432no—
664C2×C8—432no—
665C2×C8—862no—
666C2×C8—862no—
667C2×C8—1724no—
668C2×C8—1724no—
669C2×C8C23×D4312yes—
670C2×C8C23×D4312yes—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—24no—
674C4⋊C4—24no—
675C4⋊C4—21no—
676C4⋊C4—434no—
677C4⋊C4—432no—
678C4⋊C4—864no—
679C4⋊C4—864no—
680C4⋊C4—864no—
681C4⋊C4—864no—
682C4⋊C4—864no—
683C4⋊C4—864no—
684C4⋊C4—861no—
685C4⋊C4C23×D4312yes—
686C4⋊C4C23×D4312yes—
687C4⋊C4C23×D4312yes—
688C22⋊C4—24no—
689C22⋊C4—434no—
690C22⋊C4—434no—
691C22⋊C4—864no—
692C22⋊C4—864no—
693C22⋊C4—864no—
694C22⋊C4—864no—
695C42—432no—
696C42—432no—
697C42—864no—
698C23—22no—
699C23—22no—
700C23—434no—
701C23—432no—
702C23—862no—
703C23—862no—
704C23—862no—
705C23—1722no—
706C23—1722no—
707C23—1722no—
708C23SD16×D4314yes—
709C23C2×D4×D4312yes—
710C23C2×D4×D4311yescharacteristic
711Q8—22no—
712Q8—22no—
713Q8—42no—
714Q8—434no—
715Q8—862no—
716Q8—864no—
717Q8—862no—
718Q8—862no—
719Q8—1728no—
720Q8—1728no—
721Q8—1728no—
722Q8—1722no—
723D4—4316no—
724D4—862no—
725D4—862no—
726D4—1728no—
727D4—1728no—
728D4—1722no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—24no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—48no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—434no—
743C2×C4—432no—
744C2×C4—432no—
745C2×C4—432no—
746C2×C4—862no—
747C2×C4—862no—
748C2×C4—862no—
749C2×C4—864no—
750C2×C4—862no—
751C2×C4—862no—
752C2×C4—864no—
753C2×C4—862no—
754C2×C4—862no—
755C2×C4—1728no—
756C2×C4—1728no—
757C2×C4—1728no—
758C2×C4—1728no—
759C2×C4—1722no—
760C2×C4—1722no—
761C2×C4C2×D4×D4312yes—
762C2×C4C2×D4×D4311yescharacteristic
763C2×C4#41×D4312yes—
764C2×C4#1306337112yes—
765C2×C4C24×D4311yescharacteristic
766C8—22no—
767C8—22no—
768C8—862no—
769C8—862no—
770C22—22no—
771C22—22no—
772C22—28no—
773C22—434no—
774C22—862no—
775C22—862no—
776C22—868no—
777C22—3444no—
778C22—1722no—
779C22—1722no—
780C22—1722no—
781C22#1458354112yes—
782C22C2×SD16×D4314yes—
783C22C2×SD16×D4312yes—
784C22#1458371512yes—
785C22C22×D4×D4311yescharacteristic
786C4—22no—
787C4—42no—
788C4—42no—
789C4—42no—
790C4—42no—
791C4—434no—
792C4—862no—
793C4—864no—
794C4—862no—
795C4—1722no—
796C4—1722no—
797C4#1458354112yes—
798C4C2×#41×D4311yescharacteristic
799C4C2×#1306337111yescharacteristic
800C2—24no—
801C2—864no—
802C2—3442no—
803C2#1914645814yesdirect product factor
804C2C2×#1458354111yescharacteristic
805C2C22×SD16×D4311yescharacteristic
806C2C2×#1458371511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#483C2
socleC23×C43C22×D4
prime radicalC2×#14583550C2
hypercenterC2×#483D43
hypocenterC43C2×#3298
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×#14583562C2semidirect
3. #19146458C2direct (N × H)
4. C2×#14583248C2semidirect
5. C2×#14583231C2semidirect
6. C2×#14583183C2semidirect
7. C2×#14583130C2semidirect
8. C2×#14583129C2semidirect
9. C2×#14583103C2semidirect
10. C2×#14583040C2semidirect
11. C2×#14583039C2semidirect
12. C2×#14582986C2semidirect
13. C2×(C22⋊D43)⋊C8C2semidirect
14. C22×#13063248C2semidirect
15. C2×#103×D43C2semidirect
16. C2×C43×#483C2semidirect
26. #14583562C22semidirect
45. #14583248C22semidirect
46. #14583231C22semidirect
47. #14583183C22semidirect
48. #14583130C22semidirect
49. #14583129C22semidirect
50. #14583103C22semidirect
51. #14583040C22semidirect
52. #14583039C22semidirect
53. #14582986C22semidirect
54. (C22⋊D43)⋊C8C22semidirect
64. C2×#13063248C22semidirect
65. #103×D43C22semidirect
71. C43×#483C22semidirect
207. C2×C22⋊D43SD16semidirect
251. C2×Dic86#41semidirect
329. C22⋊D43C2×SD16semidirect
361. Dic86C2×#41semidirect
402. C2×#483D43semidirect
414. C2×C43#3298semidirect
452. #483C2×D43semidirect
480. C43C2×#3298semidirect
803. C2#19146458direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835622
C2×#145835502
#191464582
C2×#145832482
C2×#145832312
C2×#145831832
C2×#145831302
C2×#145831292
C2×#145831032
C2×#145830402
C2×#145830392
C2×#145829862
C2×(C22⋊D43)⋊C82
C22×#130632482
C2×#103×D432
C2×C43×#4832
C2×#329843