Finite Group Databasebeta

← C2×#19145488 #25967295

Subgroups — C2×#19145488 #25967295

Order 11008.

2122 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583473C211yesmaximal, characteristic
2C2×#14583472C211yesmaximal, characteristic
3#19145488C2116yesmaximal, direct product factor
4C2×#14583241C211yesmaximal, characteristic, complemented
5C2×#14583239C211yesmaximal, characteristic, complemented
6C2×#14583238C211yesmaximal, characteristic, complemented
7C2×#14583237C211yesmaximal, characteristic, complemented
8C2×#14583156C211yesmaximal, characteristic, complemented
9C2×#14583154C211yesmaximal, characteristic, complemented
10C2×#14583139C211yesmaximal, characteristic, complemented
11C2×#14583137C211yesmaximal, characteristic, complemented
12C2×#14583055C211yesmaximal, characteristic, complemented
13C2×#14583053C211yesmaximal, characteristic, complemented
14C2×#14583053C211yesmaximal, characteristic, complemented
15C2×#14582864C211yesmaximal, characteristic
16C2×C43×#451C211yesmaximal, characteristic, complemented
17C22×#10621898C2211yescharacteristic
18C22×Q8×D43C2211yescharacteristic
19C22×#10621885C2211yescharacteristic
20C22×#10621885C2211yescharacteristic
21C22×#10621872C2211yescharacteristic
22C22×C8×D43C2211yescharacteristic
23#14583473—24no—
24#14583473C2218yes—
25#14583472—24no—
26#14583472C2218yes—
27C2×#13063324—21no—
28C2×#13063323—21no—
29C2×#13063314—21no—
30C2×#13063311—21no—
31C2×#13063310—21no—
32C2×#13063308—21no—
33C2×#13063308—21no—
34C2×#13063307—21no—
35C2×#13063305C2211yescharacteristic
36C2×#13063304C2211yescharacteristic
37C2×#13063301C2211yescharacteristic
38C2×#13063301C2211yescharacteristic
39C2×#13063301C2211yescharacteristic
40C2×#13063301C2211yescharacteristic
41C2×#13063301C2211yescharacteristic
42C2×#13063284C2211yescharacteristic
43C2×#13063283C2211yescharacteristic
44#14583241C2218yescomplemented
45#14583239C2218yescomplemented
46#14583238C2218yescomplemented
47#14583237C2218yescomplemented
48#14583156C2218yescomplemented
49#14583154C2218yescomplemented
50#14583139C2218yescomplemented
51#14583137C2218yescomplemented
52#14583055C2218yescomplemented
53#14583053C2218yescomplemented
54#14583053C2218yescomplemented
55C2×#13063259C2211yescharacteristic
56C2×#13063258C2211yescharacteristic
57C2×#13063257C2211yescharacteristic
58C2×#13063256C2211yescharacteristic
59C2×#13063250C2211yescharacteristic
60C2×#13063250C2211yescharacteristic
61C2×#13063249C2211yescharacteristic
62C2×#13063249C2211yescharacteristic
63C2×#13063249C2211yescharacteristic
64C2×#13063249C2211yescharacteristic
65#14582864C2218yes—
66C2×C22⋊(C43⋊C8)C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×(C2×D43)⋊C8C2211yescharacteristic
69C23×Q8×C43C2211yescharacteristic
70C22×Q16×C43C2211yescharacteristic
71C22×Q16×C43C2211yescharacteristic
72C2×C22⋊Q8×C43C2211yescharacteristic
73C43×#451C2218yescomplemented
74C2×#103×C43C2211yescharacteristic
75C2×#103×C43C2211yescharacteristic
76C2×C22⋊C8×C43C2211yescharacteristic
77C2×#10621898—42no—
78C2×#10621898—42no—
79C2×#10621898D414yes—
80C2×#10621898C2314yes—
81C22×Dic86—21no—
82C22×Dic86D411yescharacteristic
83C22×Dic86C2311yescharacteristic
84C2×Q8×D43—22no—
85C2×Q8×D43—42no—
86C2×Q8×D43—42no—
87C2×Q8×D43C2314yes—
88C22×D172D411yescharacteristic
89C22×C22⋊D43D411yescharacteristic
90C22×C22⋊D43D411yescharacteristic
91C22×C4×D43—21no—
92C22×C4×D43C2311yescharacteristic
93C22×C4×D43C2311yescharacteristic
94C2×#10621885—42no—
95C2×#10621885—42no—
96C2×#10621885C2314yes—
97C2×#10621885C2314yes—
98C2×#10621872—42no—
99C2×#10621872C2314yes—
100C22×C43⋊C8C2311yescharacteristic
101C22×C43⋊C8C2311yescharacteristic
102C2×C8×D43—42no—
103C2×C8×D43C2314yes—
104#13063324—28no—
105#13063323—28no—
106#13063314—28no—
107#13063311—28no—
108#13063310—28no—
109#13063308—28no—
110#13063308—28no—
111#13063307—28no—
112#13063305—22no—
113#13063305C2314yes—
114#13063304—22no—
115#13063304C2314yes—
116#13063301—22no—
117#13063301—22no—
118#13063301—22no—
119#13063301—22no—
120#13063301—22no—
121#13063301C2314yes—
122#13063301C2314yes—
123#13063301C2314yes—
124#13063301C2314yes—
125#13063301C2314yes—
126#13063284—22no—
127#13063284C2314yes—
128#13063283—22no—
129#13063283C2314yes—
130C2×C4⋊Dic43—21no—
131C2×C4⋊Dic43C2311yescharacteristic
132C2×C4⋊Dic43C2311yescharacteristic
133C2×C4⋊Dic43C2311yescharacteristic
134C2×Dic43⋊C4—21no—
135C2×Dic43⋊C4—21no—
136C2×Dic43⋊C4—21no—
137C2×Dic43⋊C4—21no—
138C2×Dic43⋊C4—21no—
139C2×Dic43⋊C4—21no—
140C2×C22⋊Dic43—21no—
141C2×C22⋊Dic43—21no—
142C2×(C2×D43)⋊C4—21no—
143C2×(C2×D43)⋊C4—21no—
144C2×(C2×D43)⋊C4—21no—
145C2×(C2×D43)⋊C4—21no—
146C2×(C2×D43)⋊C4—21no—
147C2×(C2×D43)⋊C4—21no—
148C2×(C2×D43)⋊C4—21no—
149C2×C4×Dic43—21no—
150C2×C4×Dic43—21no—
151#13063259C2314yes—
152#13063258C2314yes—
153#13063257C2314yes—
154#13063256C2314yes—
155#13063250C2314yes—
156#13063250C2314yes—
157#13063249C2314yes—
158#13063249C2314yes—
159#13063249C2314yes—
160#13063249C2314yes—
161C22⋊(C43⋊C8)C2314yes—
162(C2×D43)⋊C8C2314yes—
163(C2×D43)⋊C8C2314yes—
164C22×Q8×C43—21no—
165C22×Q8×C43—22no—
166C22×Q8×C43—42no—
167C22×Q8×C43—42no—
168C22×Q8×C43C2311yescharacteristic
169C22×Q8×C43C2311yescharacteristic
170C22×Q8×C43C2311yescharacteristic
171C22×Q8×C43C2314yes—
172C23×C4×C43—21no—
173C23×C4×C43C2311yescharacteristic
174C2×Q16×C43—42no—
175C2×Q16×C43—42no—
176C2×Q16×C43C2314yes—
177C2×Q16×C43C2314yes—
178C22×C8×C43C2311yescharacteristic
179C22×C8×C43C2311yescharacteristic
180C22⋊Q8×C43—22no—
181C22⋊Q8×C43C2314yes—
182C2×C4⋊C4×C43—21no—
183C2×C4⋊C4×C43C2311yescharacteristic
184C2×C22⋊C4×C43—21no—
185#103×C43C2314yes—
186#103×C43C2314yes—
187C22⋊C8×C43C2314yes—
188C24×C43C2×D411yescharacteristic
189C23×D43C2×D411yescharacteristic
190C23×D43C2×D411yescharacteristic
191C2×Q8×C43—21no—
192C2×Q8×C43—21no—
193C2×Q8×C43—21no—
194C2×Q8×C43—24no—
195C2×Q8×C43—22no—
196C2×Q8×C43—22no—
197C2×Q8×C43—22no—
198C2×Q8×C43—22no—
199C2×Q8×C43—22no—
200C2×Q8×C43—22no—
201C2×Q8×C43—44no—
202C2×Q8×C43—44no—
203C2×Q8×C43—44no—
204C2×Q8×C43—48no—
205C2×Q8×C43C2412yes—
206C2×Q8×C43C2412yes—
207C2×Q8×C43C2412yes—
208C22×C4×C43—22no—
209C22×C4×C43—22no—
210C22×C4×C43—21no—
211C22×C4×C43—21no—
212C22×C4×C43—21no—
213C22×C4×C43—21no—
214C22×C4×C43—24no—
215C22×C4×C43—44no—
216C22×C4×C43C2×D411yescharacteristic
217C22×C4×C43C2×D412yes—
218C22×C4×C43C2412yes—
219C22×C4×C43C2411yescharacteristic
220C2×C22⋊D43—42no—
221C2×C22⋊D43—42no—
222C2×C22⋊D43C2×D414yes—
223C2×C22⋊D43C2×D414yes—
224C22×Dic43—21no—
225C22×Dic43—21no—
226C22×Dic43—21no—
227C22×Dic43—21no—
228C22×Dic43C2×D411yescharacteristic
229C22×Dic43C2×D411yescharacteristic
230Q8×D43—44no—
231Q8×D43—44no—
232Q8×D43—48no—
233#10621898—48no—
234#10621898—44no—
235#10621898—44no—
236C2×D172—42no—
237C2×D172C2×D414yes—
238C2×C4×D43—22no—
239C2×C4×D43—22no—
240C2×C4×D43—22no—
241C2×C4×D43—22no—
242C2×C4×D43—24no—
243C2×C4×D43—44no—
244C2×C4×D43C2×D412yes—
245C2×C4×D43C2×D412yes—
246C2×C4×D43C2412yes—
247C2×C4×D43C2412yes—
248C2×Dic86—22no—
249C2×Dic86—22no—
250C2×Dic86—21no—
251C2×Dic86—24no—
252C2×Dic86—42no—
253C2×Dic86—44no—
254C2×Dic86C2×D414yes—
255C2×Dic86C2412yes—
256Q16×C43—44no—
257Q16×C43—44no—
258C2×C8×C43—22no—
259C2×C8×C43—22no—
260C2×C8×C43C2412yes—
261C2×C8×C43C2412yes—
262C4⋊C4×C43—24no—
263C4⋊C4×C43—21no—
264C4⋊C4×C43C2412yes—
265C22⋊C4×C43—24no—
266C22⋊Dic43—24no—
267C22⋊Dic43—24no—
268#10621885—44no—
269#10621885—44no—
270(C2×D43)⋊C4—24no—
271(C2×D43)⋊C4—24no—
272(C2×D43)⋊C4—24no—
273(C2×D43)⋊C4—24no—
274(C2×D43)⋊C4—24no—
275(C2×D43)⋊C4—24no—
276(C2×D43)⋊C4—24no—
277C4⋊Dic43—21no—
278C4⋊Dic43—21no—
279C4⋊Dic43—21no—
280C4⋊Dic43—24no—
281C4⋊Dic43C2412yes—
282C4⋊Dic43C2412yes—
283C4⋊Dic43C2412yes—
284Dic43⋊C4—24no—
285Dic43⋊C4—24no—
286Dic43⋊C4—24no—
287Dic43⋊C4—24no—
288Dic43⋊C4—24no—
289Dic43⋊C4—24no—
290C4×Dic43—24no—
291C4×Dic43—24no—
292C2×C43⋊C8—22no—
293C2×C43⋊C8—22no—
294C2×C43⋊C8C2412yes—
295C2×C43⋊C8C2412yes—
296#10621872—44no—
297C8×D43—44no—
298C23×C43—22no—
299C23×C43—22no—
300C23×C43—22no—
301C23×C43C22×D412yes—
302C23×C43C22×D411yescharacteristic
303C22×D43—22no—
304C22×D43—22no—
305C22×D43—22no—
306C22×D43—22no—
307C22×D43—22no—
308C22×D43—22no—
309C22×D43C22×D412yes—
310C22×D43C22×D412yes—
311Q8×C43—22no—
312Q8×C43—22no—
313Q8×C43—22no—
314Q8×C43—22no—
315Q8×C43—22no—
316Q8×C43—22no—
317Q8×C43—48no—
318Q8×C43—42no—
319Q8×C43—42no—
320Q8×C43—42no—
321C2×C4×C43—22no—
322C2×C4×C43—24no—
323C2×C4×C43—22no—
324C2×C4×C43—22no—
325C2×C4×C43—22no—
326C2×C4×C43—22no—
327C2×C4×C43—22no—
328C2×C4×C43—22no—
329C2×C4×C43—48no—
330C2×C4×C43—42no—
331C2×C4×C43—42no—
332C2×C4×C43—42no—
333C2×C4×C43—42no—
334C2×C4×C43C22×D412yes—
335C2×C4×C43C22×D411yescharacteristic
336C2×C4×C43H(5,𝔽2)12yes—
337C2×C4×C43H(5,𝔽2)12yes—
338C2×C4×C43C2511yescharacteristic
339C22⋊D43—44no—
340C22⋊D43—44no—
341C2×Dic43—22no—
342C2×Dic43—22no—
343C2×Dic43—22no—
344C2×Dic43—22no—
345C2×Dic43—22no—
346C2×Dic43—22no—
347C2×Dic43—42no—
348C2×Dic43—42no—
349C2×Dic43—42no—
350C2×Dic43—42no—
351C2×Dic43C22×D412yes—
352C2×Dic43C22×D412yes—
353D172—44no—
354C4×D43—24no—
355C4×D43—24no—
356C4×D43—22no—
357C4×D43—22no—
358C4×D43—22no—
359C4×D43—22no—
360C4×D43—48no—
361Dic86—22no—
362Dic86—22no—
363Dic86—44no—
364Dic86—48no—
365Dic86—42no—
366C8×C43—22no—
367C8×C43—22no—
368C43⋊C8—22no—
369C43⋊C8—22no—
370C2×#3202—431nomaximal, Sylow
371C22×C43—22no—
372C22×C43—22no—
373C22×C43—22no—
374C22×C43—44no—
375C22×C43#53412yes—
376C22×C43#57812yes—
377C22×C43#57812yes—
378C22×C43C23×D411yescharacteristic
379C2×D43—22no—
380C2×D43—22no—
381C2×D43—22no—
382C2×D43—22no—
383C2×D43—22no—
384C2×D43—22no—
385C2×D43—44no—
386C2×D43—44no—
387C4×C43—22no—
388C4×C43—42no—
389C4×C43—42no—
390C4×C43—42no—
391C4×C43—42no—
392C4×C43#53412yes—
393C4×C43C2×H(5,𝔽2)11yescharacteristic
394C4×C43C2×H(5,𝔽2)11yescharacteristic
395Dic43—22no—
396Dic43—22no—
397Dic43—42no—
398Dic43—42no—
399Dic43—42no—
400Dic43—42no—
401C2×#536—431no—
402C2×#536—431no—
403#3202—4316no—
404C2×#485—431no—
405C2×#485—431no—
406C2×#485—431no—
407C2×#485—431no—
408C2×#470—431no—
409C2×#470—431no—
410C2×#467—431no—
411C2×#467—431no—
412C2×#451—431no—
413C2×#451—431no—
414C2×#451—431no—
415C2×#451D4311yescharacteristic, complemented
416C2×#408—431no—
417C2×C43—42no—
418C2×C43#320214yescomplemented
419C2×C43C2×#53411yescharacteristic
420C2×C43C2×#57811yescharacteristic
421C2×C43C2×#57811yescharacteristic
422D43—42no—
423D43—42no—
424C22×#41—431no—
425C23×Q8—431no—
426C23×Q8C2×D4311yescharacteristic
427C22×Q16—431no—
428C22×Q16—431no—
429C22×Q16C2×D4311yescharacteristic
430C22×Q16C2×D4311yescharacteristic
431C22×M16—431no—
432C23×C8—431no—
433#536—438no—
434#536—438no—
435#536—864no—
436#536—864no—
437C2×C4⋊Q8—861no—
438C2×C4⋊Q8—861no—
439C2×#124—861no—
440C2×#124—861no—
441C2×#123—861no—
442C2×#123—861no—
443C2×#123—861no—
444C2×#123—861no—
445C2×C22⋊Q8—431no—
446C2×C22⋊Q8—431no—
447C2×C22⋊Q8—431no—
448C2×C22⋊Q8—431no—
449C2×C22⋊Q8—431no—
450C2×C22⋊Q8—431no—
451C2×C22⋊Q8—431no—
452C2×C22⋊Q8C2×D4311yescharacteristic
453C2×#117—431no—
454C2×#117—431no—
455#485—438no—
456#485—438no—
457#485—438no—
458#485—438no—
459#470—438no—
460#470—438no—
461#467—438no—
462#467—438no—
463#451—438no—
464#451—438no—
465#451—438no—
466#451C2×D4318yescomplemented
467C2×#107—431no—
468C2×#107—431no—
469C2×#106—431no—
470C2×#106—431no—
471C2×#103—431no—
472C2×#103—431no—
473C2×#103—431no—
474C2×#103—431no—
475C2×#103—431no—
476C2×#103—431no—
477C2×#103C2×D4311yescharacteristic
478C2×#103C2×D4311yescharacteristic
479#408—438no—
480C2×C22⋊C8—431no—
481C2×C22⋊C8—431no—
482C2×C22⋊C8—431no—
483C2×C22⋊C8C2×D4311yescharacteristic
484C43C2×#320211yescharacteristic, complemented, Sylow
485C2×#41—434no—
486C2×#41—434no—
487C2×#41—1722no—
488C2×#41—1722no—
489C22×Q8—21no—
490C22×Q8—22no—
491C22×Q8—42no—
492C22×Q8—42no—
493C22×Q8—431no—
494C22×Q8—434no—
495C22×Q8—431no—
496C22×Q8—861no—
497C22×Q8—862no—
498C22×Q8—1722no—
499C22×Q8—1722no—
500C22×Q8C22×D4311yescharacteristic
501C22×Q8C22×D4311yescharacteristic
502C22×Q8C22×D4311yescharacteristic
503C22×Q8C22×D4314yes—
504C22×D4—431no—
505C22×D4—431no—
506C22×D4—431no—
507C23×C4—21no—
508C23×C4—431no—
509C23×C4—431no—
510C23×C4—861no—
511C23×C4C22×D4311yescharacteristic
512C2×Q16—42no—
513C2×Q16—42no—
514C2×Q16—434no—
515C2×Q16—434no—
516C2×Q16—1722no—
517C2×Q16—1722no—
518C2×Q16C22×D4314yes—
519C2×Q16C22×D4314yes—
520C2×M16—434no—
521C2×M16—1722no—
522C22×C8—431no—
523C22×C8—431no—
524C22×C8—434no—
525C22×C8—1722no—
526C22×C8C22×D4311yescharacteristic
527C22×C8C22×D4311yescharacteristic
528C4⋊Q8—868no—
529C4⋊Q8—868no—
530#124—868no—
531#124—868no—
532#123—868no—
533#123—868no—
534#123—868no—
535#123—868no—
536C22⋊Q8—22no—
537C22⋊Q8—434no—
538C22⋊Q8—434no—
539C22⋊Q8—434no—
540C22⋊Q8—434no—
541C22⋊Q8—434no—
542C22⋊Q8—434no—
543C22⋊Q8—434no—
544C22⋊Q8—862no—
545C22⋊Q8—862no—
546C22⋊Q8—862no—
547C22⋊Q8—862no—
548C22⋊Q8—862no—
549C22⋊Q8—862no—
550C22⋊Q8—862no—
551C22⋊Q8C22×D4314yes—
552#117—434no—
553#117—434no—
554#117—862no—
555#117—862no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—431no—
558C2×C4⋊C4—431no—
559C2×C4⋊C4—431no—
560C2×C4⋊C4—861no—
561C2×C4⋊C4—861no—
562C2×C4⋊C4—861no—
563C2×C4⋊C4—861no—
564C2×C4⋊C4—861no—
565C2×C4⋊C4—861no—
566C2×C4⋊C4—861no—
567C2×C4⋊C4C22×D4311yescharacteristic
568C2×C22⋊C4—21no—
569C2×C22⋊C4—861no—
570C2×C22⋊C4—861no—
571C2×C22⋊C4—861no—
572C2×C22⋊C4—861no—
573C2×C22⋊C4—861no—
574C2×C22⋊C4—861no—
575C2×C22⋊C4—861no—
576C2×C22⋊C4—861no—
577C2×C22⋊C4—861no—
578C2×C42—861no—
579C2×C42—861no—
580#107—434no—
581#107—434no—
582#106—434no—
583#106—434no—
584#103—434no—
585#103—434no—
586#103—434no—
587#103—434no—
588#103—434no—
589#103—434no—
590#103C22×D4314yes—
591#103C22×D4314yes—
592C22⋊C8—434no—
593C22⋊C8—434no—
594C22⋊C8—434no—
595C22⋊C8C22×D4314yes—
596C24—431no—
597C24—431no—
598C24D4×D4311yescharacteristic
599#41—1728no—
600#41—1724no—
601#41—1724no—
602C2×Q8—21no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—24no—
606C2×Q8—22no—
607C2×Q8—22no—
608C2×Q8—22no—
609C2×Q8—22no—
610C2×Q8—22no—
611C2×Q8—22no—
612C2×Q8—44no—
613C2×Q8—44no—
614C2×Q8—44no—
615C2×Q8—48no—
616C2×Q8—434no—
617C2×Q8—432no—
618C2×Q8—864no—
619C2×Q8—861no—
620C2×Q8—862no—
621C2×Q8—862no—
622C2×Q8—1722no—
623C2×Q8—1724no—
624C2×Q8—1724no—
625C2×Q8—1724no—
626C2×Q8—1728no—
627C2×Q8C23×D4312yes—
628C2×Q8C23×D4312yes—
629C2×Q8C23×D4312yes—
630C2×D4—434no—
631C2×D4—434no—
632C2×D4—434no—
633C2×D4—1722no—
634C2×D4—1722no—
635C2×D4—1722no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—24no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—44no—
644C22×C4—431no—
645C22×C4—431no—
646C22×C4—432no—
647C22×C4—432no—
648C22×C4—432no—
649C22×C4—432no—
650C22×C4—864no—
651C22×C4—862no—
652C22×C4—862no—
653C22×C4—862no—
654C22×C4—862no—
655C22×C4—861no—
656C22×C4—861no—
657C22×C4—861no—
658C22×C4—861no—
659C22×C4—1724no—
660C22×C4D4×D4312yes—
661C22×C4D4×D4311yescharacteristic
662C22×C4C23×D4312yes—
663C22×C4C23×D4311yescharacteristic
664Q16—44no—
665Q16—44no—
666Q16—1724no—
667Q16—1724no—
668M16—1724no—
669C2×C8—22no—
670C2×C8—22no—
671C2×C8—432no—
672C2×C8—432no—
673C2×C8—862no—
674C2×C8—862no—
675C2×C8—1724no—
676C2×C8C23×D4312yes—
677C2×C8C23×D4312yes—
678C4⋊C4—24no—
679C4⋊C4—21no—
680C4⋊C4—432no—
681C4⋊C4—432no—
682C4⋊C4—432no—
683C4⋊C4—864no—
684C4⋊C4—864no—
685C4⋊C4—864no—
686C4⋊C4—864no—
687C4⋊C4—864no—
688C4⋊C4—864no—
689C4⋊C4—861no—
690C4⋊C4—861no—
691C4⋊C4—861no—
692C4⋊C4—864no—
693C4⋊C4C23×D4312yes—
694C22⋊C4—24no—
695C22⋊C4—864no—
696C22⋊C4—864no—
697C22⋊C4—864no—
698C22⋊C4—864no—
699C22⋊C4—864no—
700C22⋊C4—864no—
701C22⋊C4—864no—
702C22⋊C4—864no—
703C22⋊C4—864no—
704C42—864no—
705C42—864no—
706C23—22no—
707C23—22no—
708C23—22no—
709C23—432no—
710C23—432no—
711C23—862no—
712C23—862no—
713C23—862no—
714C23—862no—
715C23—862no—
716C23—862no—
717C23C2×D4×D4312yes—
718C23C2×D4×D4311yescharacteristic
719Q8—22no—
720Q8—22no—
721Q8—22no—
722Q8—22no—
723Q8—22no—
724Q8—22no—
725Q8—48no—
726Q8—42no—
727Q8—42no—
728Q8—42no—
729Q8—862no—
730Q8—862no—
731Q8—1724no—
732Q8—1728no—
733Q8—1722no—
734D4—1724no—
735D4—1724no—
736D4—1724no—
737C2×C4—22no—
738C2×C4—24no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—48no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—432no—
751C2×C4—432no—
752C2×C4—862no—
753C2×C4—862no—
754C2×C4—864no—
755C2×C4—864no—
756C2×C4—862no—
757C2×C4—862no—
758C2×C4—862no—
759C2×C4—862no—
760C2×C4—862no—
761C2×C4—862no—
762C2×C4—862no—
763C2×C4—862no—
764C2×C4—1728no—
765C2×C4—1722no—
766C2×C4—1722no—
767C2×C4—1722no—
768C2×C4—1722no—
769C2×C4C2×D4×D4312yes—
770C2×C4C2×D4×D4311yescharacteristic
771C2×C4#1306337012yes—
772C2×C4#1306337012yes—
773C2×C4C24×D4311yescharacteristic
774C8—22no—
775C8—22no—
776C8—862no—
777C8—862no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—44no—
782C22—862no—
783C22—862no—
784C22—862no—
785C22—862no—
786C22—862no—
787C22—862no—
788C22—1724no—
789C22—1724no—
790C22#1458345912yes—
791C22#1458371212yes—
792C22#1458371512yes—
793C22C22×D4×D4311yescharacteristic
794C4—22no—
795C4—42no—
796C4—42no—
797C4—42no—
798C4—42no—
799C4—862no—
800C4—862no—
801C4—1722no—
802C4—1722no—
803C4—1722no—
804C4—1722no—
805C4#1458345912yes—
806C4C2×#1306337011yescharacteristic
807C4C2×#1306337011yescharacteristic
808C2—42no—
809C2—1722no—
810C2—1722no—
811C2#1914548814yesdirect product factor
812C2C2×#1458345911yescharacteristic
813C2C2×#1458371211yescharacteristic
814C2C2×#1458371511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#451C2
socleC23×C43C22×D4
prime radicalC22×#10621898C22
hypercenterC2×#451D43
hypocenterC43C2×#3202
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
3. #19145488C2direct (N × H)
4. C2×#14583241C2semidirect
5. C2×#14583239C2semidirect
6. C2×#14583238C2semidirect
7. C2×#14583237C2semidirect
8. C2×#14583156C2semidirect
9. C2×#14583154C2semidirect
10. C2×#14583139C2semidirect
11. C2×#14583137C2semidirect
12. C2×#14583055C2semidirect
13. C2×#14583053C2semidirect
14. C2×#14583053C2semidirect
16. C2×C43×#451C2semidirect
44. #14583241C22semidirect
45. #14583239C22semidirect
46. #14583238C22semidirect
47. #14583237C22semidirect
48. #14583156C22semidirect
49. #14583154C22semidirect
50. #14583139C22semidirect
51. #14583137C22semidirect
52. #14583055C22semidirect
53. #14583053C22semidirect
54. #14583053C22semidirect
73. C43×#451C22semidirect
415. C2×#451D43semidirect
418. C2×C43#3202semidirect
466. #451C2×D43semidirect
484. C43C2×#3202semidirect
811. C2#19145488direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834732
C2×#145834722
#191454882
C2×#145832412
C2×#145832392
C2×#145832382
C2×#145832372
C2×#145831562
C2×#145831542
C2×#145831392
C2×#145831372
C2×#145830552
C2×#145830532
C2×#145828642
C2×C43×#4512
C2×#320243