Finite Group Databasebeta

← C2×#19144423 #25964153

Subgroups — C2×#19144423 #25964153

Order 11008.

2234 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583529C211yesmaximal, characteristic, complemented
2C2×#14583371C211yesmaximal, characteristic
3#19144423C2116yesmaximal, direct product factor
4C2×#14583202C211yesmaximal, characteristic, complemented
5C2×#14583197C211yesmaximal, characteristic, complemented
6C2×#14583196C211yesmaximal, characteristic, complemented
7C2×#14583189C211yesmaximal, characteristic, complemented
8C2×#14583188C211yesmaximal, characteristic, complemented
9C2×#14583180C211yesmaximal, characteristic, complemented
10C2×#14583177C211yesmaximal, characteristic, complemented
11C2×#14582938C211yesmaximal, characteristic, complemented
12C2×#14582936C211yesmaximal, characteristic, complemented
13C2×#14582924C211yesmaximal, characteristic, complemented
14C2×#14582902C211yesmaximal, characteristic
15C2×#102×D43C211yesmaximal, characteristic
16C2×C43×#478C211yesmaximal, characteristic, complemented
17C22×D4×D43C2211yescharacteristic
18C22×#10621872C2211yescharacteristic
19C22×C8×D43C2211yescharacteristic
20#14583529—24no—
21#14583529C2218yescomplemented
22C2×#13063325C2211yescharacteristic, complemented
23C2×#13063324—21no—
24C2×#13063324C2211yescharacteristic, complemented
25C2×#13063316C2211yescharacteristic, complemented
26C2×#13063315—21no—
27C2×#13063305—21no—
28C2×#13063303—21no—
29#14583371—24no—
30#14583371C2218yes—
31C2×C4×D172C2211yescharacteristic
32C2×D4×Dic43C2211yescharacteristic
33C2×#13063287C2211yescharacteristic
34C2×C4×C22⋊D43—21no—
35C2×(C22⋊D43)⋊C4—21no—
36C2×#13063283C2211yescharacteristic
37C2×#13063283C2211yescharacteristic
38C2×#13063282C2211yescharacteristic
39C2×C4⋊C4×D43C2211yescharacteristic
40C22×(C2×D43)⋊C4—21no—
41C2×C22⋊C4×D43—21no—
42#14583202C2218yescomplemented
43#14583197C2218yescomplemented
44#14583196C2218yescomplemented
45#14583189C2218yescomplemented
46#14583188C2218yescomplemented
47#14583180C2218yescomplemented
48#14583177C2218yescomplemented
49#14582938C2218yescomplemented
50#14582936C2218yescomplemented
51C2×#13063259C2211yescharacteristic, complemented
52C2×#13063259C2211yescharacteristic, complemented
53C2×#13063258C2211yescharacteristic, complemented
54C2×#13063256C2211yescharacteristic, complemented
55C2×#13063256C2211yescharacteristic, complemented
56C2×#13063256C2211yescharacteristic, complemented
57#14582924C2218yescomplemented
58C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
59C2×Dic43⋊C8C2211yescharacteristic, complemented
60C2×Dic43⋊C8C2211yescharacteristic, complemented
61#14582902C2218yes—
62C2×#13063247C2211yescharacteristic
63C2×#13063247C2211yescharacteristic
64C2×#13063246C2211yescharacteristic
65C2×#13063246C2211yescharacteristic
66C2×#13063245C2211yescharacteristic
67C2×#13063245C2211yescharacteristic
68#102×D43C2218yes—
69C2×#125×C43C2211yescharacteristic, complemented
70C2×C4×D4×C43C2211yescharacteristic
71C43×#478C2218yescomplemented
72C2×#107×C43C2211yescharacteristic, complemented
73C2×#106×C43C2211yescharacteristic, complemented
74C2×C4⋊C8×C43C2211yescharacteristic, complemented
75C2×#102×C43C2211yescharacteristic
76C2×#102×C43C2211yescharacteristic
77C24×D43—21no—
78C22×Dic86—21no—
79C22×Dic86—21no—
80C22×D172C2311yescharacteristic
81C22×C22⋊D43—21no—
82C2×D4×D43—22no—
83C2×D4×D43—24no—
84C2×D4×D43Q818yescomplemented
85C2×D4×D43C2314yes—
86C23×Dic43—21no—
87C22×C4×D43—21no—
88C22×C4×D43—21no—
89C22×C4×D43—21no—
90C22×C4×D43C2311yescharacteristic
91C2×#10621872—24no—
92C2×#10621872C2314yes—
93C22×C43⋊C8C2311yescharacteristic
94C22×C43⋊C8C2311yescharacteristic
95C2×C8×D43—24no—
96C2×C8×D43C2314yes—
97#13063325—22no—
98#13063325C2314yescomplemented
99#13063324—28no—
100#13063324—22no—
101#13063324C2314yescomplemented
102#13063316—22no—
103#13063316C2314yescomplemented
104#13063315—28no—
105#13063305—28no—
106#13063303—28no—
107C4×D172—22no—
108C4×D172C2314yes—
109D4×Dic43—22no—
110D4×Dic43C2314yes—
111#13063287—22no—
112#13063287C2314yes—
113C4×C22⋊D43—28no—
114(C22⋊D43)⋊C4—28no—
115#13063283—22no—
116#13063283—22no—
117#13063283C2314yes—
118#13063283C2314yes—
119#13063282D414yes—
120#13063282C2314yes—
121C2×C4⋊Dic43—21no—
122C2×C4⋊Dic43—21no—
123C2×C4⋊Dic43C2311yescharacteristic
124C2×C4⋊Dic43C2311yescharacteristic
125C2×C4⋊Dic43C2311yescharacteristic
126C2×Dic43⋊C4—21no—
127C2×Dic43⋊C4—21no—
128C2×Dic43⋊C4—21no—
129C2×Dic43⋊C4D411yescharacteristic
130C2×Dic43⋊C4D411yescharacteristic
131C4⋊C4×D43—22no—
132C4⋊C4×D43C2314yes—
133C2×C22⋊Dic43—21no—
134C2×(C2×D43)⋊C4—21no—
135C2×(C2×D43)⋊C4—21no—
136C2×(C2×D43)⋊C4—21no—
137C2×(C2×D43)⋊C4—21no—
138C2×(C2×D43)⋊C4—28no—
139C2×(C2×D43)⋊C4D411yescharacteristic
140C2×(C2×D43)⋊C4D411yescharacteristic
141C22⋊C4×D43—28no—
142C2×C4×Dic43—21no—
143C2×C4×Dic43—21no—
144C2×C4×Dic43C2311yescharacteristic
145#13063259C2314yescomplemented
146#13063259C2314yescomplemented
147#13063258C2314yescomplemented
148#13063256C2314yescomplemented
149#13063256C2314yescomplemented
150#13063256C2314yescomplemented
151C4⋊(C43⋊C8)C2314yescomplemented
152Dic43⋊C8C2314yescomplemented
153Dic43⋊C8C2314yescomplemented
154#13063247C2314yes—
155#13063247C2314yes—
156#13063246C2314yes—
157#13063246C2314yes—
158#13063245C2314yes—
159#13063245C2314yes—
160C22×D4×C43C2311yescharacteristic
161C23×C4×C43—21no—
162C22×C8×C43C2311yescharacteristic
163C22×C8×C43C2311yescharacteristic
164#125×C43—22no—
165#125×C43C2314yescomplemented
166C4×D4×C43—22no—
167C4×D4×C43C2314yes—
168C2×C4⋊C4×C43—21no—
169C2×C4⋊C4×C43—21no—
170C2×C4⋊C4×C43C2311yescharacteristic
171C2×C4⋊C4×C43C2311yescharacteristic
172C2×C4⋊C4×C43C2311yescharacteristic
173C2×C22⋊C4×C43—21no—
174C2×C42×C43C2311yescharacteristic
175#107×C43C2314yescomplemented
176#106×C43C2314yescomplemented
177C4⋊C8×C43C2314yescomplemented
178#102×C43C2314yes—
179#102×C43C2314yes—
180C24×C43—21no—
181C23×D43—21no—
182C23×D43—28no—
183C23×D43—24no—
184C23×D43—82no—
185C23×D43—82no—
186C23×D43C2×D411yescharacteristic
187C2×D4×C43—21no—
188C2×D4×C43—22no—
189C2×D4×C43C2×Q814yes—
190C2×D4×C43C2412yes—
191C22×C4×C43—24no—
192C22×C4×C43—21no—
193C22×C4×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43—82no—
196C22×C4×C43C2×D411yescharacteristic
197C22×C4×C43C2×D411yescharacteristic
198C22×C4×C43C2411yescharacteristic
199C2×C22⋊D43—28no—
200C2×C22⋊D43—24no—
201C22×Dic43—24no—
202C22×Dic43—21no—
203C22×Dic43—21no—
204C22×Dic43—21no—
205C22×Dic43—82no—
206C22×Dic43C2×D411yescharacteristic
207C22×Dic43C2×D411yescharacteristic
208C22×Dic43C2×D411yescharacteristic
209D4×D43—216no—
210D4×D43—28no—
211D4×D43C2×Q8116yescomplemented
212C2×D172—21no—
213C2×D172—22no—
214C2×D172C2×Q814yes—
215C2×D172C2412yes—
216C2×C4×D43—24no—
217C2×C4×D43—24no—
218C2×C4×D43—24no—
219C2×C4×D43—82no—
220C2×C4×D43—82no—
221C2×C4×D43—82no—
222C2×C4×D43C2×D412yes—
223C2×C4×D43C2×Q814yes—
224C2×C4×D43#4114yes—
225C2×C4×D43C2412yes—
226C2×Dic86—24no—
227C2×Dic86—24no—
228C2×Dic86—82no—
229C2×Dic86—82no—
230C2×C8×C43—22no—
231C2×C8×C43—22no—
232C2×C8×C43C2412yes—
233C2×C8×C43C2412yes—
234C4⋊C4×C43—24no—
235C4⋊C4×C43—24no—
236C4⋊C4×C43—21no—
237C4⋊C4×C43—21no—
238C4⋊C4×C43—21no—
239C4⋊C4×C43C2412yes—
240C4⋊C4×C43C2412yes—
241C4⋊C4×C43C2412yes—
242C22⋊C4×C43—24no—
243C42×C43C2×D412yes—
244C42×C43C2412yes—
245C22⋊Dic43—24no—
246(C2×D43)⋊C4—24no—
247(C2×D43)⋊C4—24no—
248(C2×D43)⋊C4—24no—
249(C2×D43)⋊C4—24no—
250(C2×D43)⋊C4C2×D414yes—
251(C2×D43)⋊C4C2×D414yes—
252C4⋊Dic43—21no—
253C4⋊Dic43—24no—
254C4⋊Dic43—21no—
255C4⋊Dic43—21no—
256C4⋊Dic43—24no—
257C4⋊Dic43C2412yes—
258C4⋊Dic43C2412yes—
259C4⋊Dic43C2412yes—
260Dic43⋊C4—24no—
261Dic43⋊C4—24no—
262Dic43⋊C4—24no—
263Dic43⋊C4C2×D414yes—
264Dic43⋊C4C2×D414yes—
265C4×Dic43—24no—
266C4×Dic43—24no—
267C4×Dic43C2×D412yes—
268C4×Dic43C2412yes—
269C2×C43⋊C8—22no—
270C2×C43⋊C8—22no—
271C2×C43⋊C8C2412yes—
272C2×C43⋊C8C2412yes—
273#10621872—28no—
274C8×D43—28no—
275C23×C43—24no—
276C23×C43—22no—
277C23×C43—42no—
278C23×C43—42no—
279C23×C43C22×D411yescharacteristic
280C22×D43—22no—
281C22×D43—22no—
282C22×D43—24no—
283C22×D43—22no—
284C22×D43—216no—
285C22×D43—42no—
286C22×D43—42no—
287C22×D43—816no—
288C22×D43—84no—
289C22×D43—84no—
290C22×D43C22⋊Q814yes—
291C22×D43C22×D412yes—
292D4×C43—24no—
293D4×C43—22no—
294D4×C43C22×Q814yes—
295C2×C4×C43—22no—
296C2×C4×C43—22no—
297C2×C4×C43—22no—
298C2×C4×C43—22no—
299C2×C4×C43—22no—
300C2×C4×C43—42no—
301C2×C4×C43—42no—
302C2×C4×C43—42no—
303C2×C4×C43—84no—
304C2×C4×C43C22×D412yes—
305C2×C4×C43C22×D412yes—
306C2×C4×C43C22×D411yescharacteristic
307C2×C4×C43C22×Q812yes—
308C2×C4×C43C2×#4112yes—
309C2×C4×C43C2511yescharacteristic
310C22⋊D43—216no—
311C2×Dic43—22no—
312C2×Dic43—22no—
313C2×Dic43—22no—
314C2×Dic43—22no—
315C2×Dic43—22no—
316C2×Dic43—42no—
317C2×Dic43—42no—
318C2×Dic43—42no—
319C2×Dic43—84no—
320C2×Dic43C22⋊Q814yes—
321C2×Dic43C22×D412yes—
322C2×Dic43C22×D412yes—
323C2×Dic43C22×D412yes—
324D172—24no—
325D172—22no—
326D172C22×Q814yes—
327C4×D43—84no—
328C4×D43—84no—
329C4×D43—84no—
330C4×D43C22⋊Q818yes—
331C4×D43C22×Q814yes—
332C4×D43C2×#4114yes—
333Dic86—84no—
334Dic86—84no—
335C8×C43—22no—
336C8×C43—22no—
337C43⋊C8—22no—
338C43⋊C8—22no—
339C2×#3081—431nomaximal, Sylow
340C22×C43—24no—
341C22×C43—48no—
342C22×C43—42no—
343C22×C43—42no—
344C22×C43C2×C22⋊Q812yes—
345C22×C43#57612yes—
346C22×C43#57712yes—
347C22×C43C23×D411yescharacteristic
348C2×D43—28no—
349C2×D43—22no—
350C2×D43—22no—
351C2×D43—24no—
352C2×D43—48no—
353C2×D43—42no—
354C2×D43—42no—
355C2×D43—816no—
356C2×D43C2×C22⋊Q814yes—
357C4×C43—22no—
358C4×C43—22no—
359C4×C43—42no—
360C4×C43—42no—
361C4×C43—42no—
362C4×C43C2×C22⋊Q812yes—
363C4×C43C23×Q811yescharacteristic
364C4×C43C22×#4111yescharacteristic
365Dic43—22no—
366Dic43—22no—
367Dic43—42no—
368Dic43—42no—
369Dic43—42no—
370Dic43C2×C22⋊Q814yes—
371C2×#544—431no—
372C2×#518—431no—
373#3081—4316no—
374C2×#478—431no—
375C2×#478—431no—
376C2×#478—431no—
377C2×#478D4311yescharacteristic, complemented
378C2×#476—431no—
379C2×#476—431no—
380C2×#474—431no—
381C2×#474—431no—
382C2×#428—431no—
383C2×#427—431no—
384C2×#424—431no—
385C2×#418—431no—
386C22×#102—431no—
387C2×C43—44no—
388C2×C43#308114yescomplemented
389C2×C43C22×C22⋊Q811yescharacteristic
390C2×C43C2×#57611yescharacteristic
391C2×C43C2×#57711yescharacteristic
392D43—24no—
393D43—44no—
394C23×D4—431no—
395C22×M16—431no—
396C23×C8—431no—
397#544—438no—
398#544—864no—
399C2×C4⋊Q8—431no—
400C2×C4⋊Q8—431no—
401C2×C4⋊Q8—861no—
402C2×#125—431no—
403C2×#125—861no—
404C2×#125C2×D4311yescharacteristic, complemented
405C2×C22⋊Q8—861no—
406C2×C22⋊Q8—861no—
407#518—438no—
408#518—864no—
409C2×C4×D4—431no—
410C2×C4×D4—431no—
411C2×C4×D4—431no—
412C2×C4×D4—861no—
413C2×C4×D4—861no—
414C2×C4×D4C2×D4311yescharacteristic
415C2×#117—431no—
416C2×#117—431no—
417C2×#117—431no—
418C22×C4⋊C4—431no—
419C22×C22⋊C4—861no—
420C22×C22⋊C4—861no—
421#478—438no—
422#478—438no—
423#478—438no—
424#478C2×D4318yescomplemented
425#476—438no—
426#476—438no—
427#474—438no—
428#474—438no—
429#428—438no—
430#427—438no—
431C2×#107—431no—
432C2×#107—431no—
433C2×#107—431no—
434C2×#107C2×D4311yescharacteristic, complemented
435C2×#106—431no—
436C2×#106—431no—
437C2×#106—431no—
438C2×#106C2×D4311yescharacteristic, complemented
439#424—438no—
440C2×C4⋊C8—431no—
441C2×C4⋊C8—431no—
442C2×C4⋊C8—431no—
443C2×C4⋊C8C2×D4311yescharacteristic, complemented
444#418—438no—
445C2×#102—431no—
446C2×#102—431no—
447C2×#102—431no—
448C2×#102—431no—
449C2×#102—431no—
450C2×#102—431no—
451C2×#102—438no—
452C2×#102C2×D4311yescharacteristic
453C2×#102C2×D4311yescharacteristic
454C43C2×#308111yescharacteristic, complemented, Sylow
455C25—861no—
456C22×Q8—861no—
457C22×Q8—861no—
458C22×D4—438no—
459C22×D4—434no—
460C22×D4—431no—
461C22×D4—862no—
462C22×D4—864no—
463C22×D4—861no—
464C22×D4C22×D4311yescharacteristic
465C23×C4—21no—
466C23×C4—431no—
467C23×C4—861no—
468C23×C4—861no—
469C23×C4—861no—
470C23×C4—861no—
471C2×M16—434no—
472C2×M16—864no—
473C22×C8—431no—
474C22×C8—431no—
475C22×C8—434no—
476C22×C8—864no—
477C22×C8C22×D4311yescharacteristic
478C22×C8C22×D4311yescharacteristic
479C4⋊Q8—434no—
480C4⋊Q8—434no—
481C4⋊Q8—862no—
482C4⋊Q8—868no—
483C4⋊Q8—862no—
484#125—22no—
485#125—434no—
486#125—862no—
487#125—868no—
488#125C22×D4314yescomplemented
489C22⋊Q8—868no—
490C22⋊Q8—868no—
491C4×D4—22no—
492C4×D4—434no—
493C4×D4—434no—
494C4×D4—434no—
495C4×D4—862no—
496C4×D4—862no—
497C4×D4—868no—
498C4×D4—868no—
499C4×D4—862no—
500C4×D4C22×D4314yes—
501#117—434no—
502#117—434no—
503#117—434no—
504#117—434no—
505#117—862no—
506#117—862no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—431no—
510C2×C4⋊C4—431no—
511C2×C4⋊C4—431no—
512C2×C4⋊C4—431no—
513C2×C4⋊C4—431no—
514C2×C4⋊C4—434no—
515C2×C4⋊C4—862no—
516C2×C4⋊C4—861no—
517C2×C4⋊C4—861no—
518C2×C4⋊C4—861no—
519C2×C4⋊C4—861no—
520C2×C4⋊C4—861no—
521C2×C4⋊C4C22×D4311yescharacteristic
522C2×C4⋊C4C22×D4311yescharacteristic
523C2×C4⋊C4C22×D4311yescharacteristic
524C2×C22⋊C4—21no—
525C2×C22⋊C4—431no—
526C2×C22⋊C4—431no—
527C2×C22⋊C4—868no—
528C2×C22⋊C4—868no—
529C2×C22⋊C4—861no—
530C2×C22⋊C4—861no—
531C2×C22⋊C4—861no—
532C2×C22⋊C4—861no—
533C2×C22⋊C4—861no—
534C2×C42—431no—
535C2×C42—861no—
536C2×C42—861no—
537C2×C42C22×D4311yescharacteristic
538#107—434no—
539#107—434no—
540#107—434no—
541#107C22×D4314yescomplemented
542#106—434no—
543#106—434no—
544#106—434no—
545#106C22×D4314yescomplemented
546C4⋊C8—434no—
547C4⋊C8—434no—
548C4⋊C8—434no—
549C4⋊C8C22×D4314yescomplemented
550#102—434no—
551#102—434no—
552#102—434no—
553#102—434no—
554#102—434no—
555#102—434no—
556#102C22×D4314yes—
557#102C22×D4314yes—
558C24—21no—
559C24—431no—
560C24—864no—
561C24—868no—
562C24—861no—
563C24—3442no—
564C24—3442no—
565C2×Q8—864no—
566C2×Q8—864no—
567C2×Q8—3442no—
568C2×Q8—3442no—
569C2×D4—21no—
570C2×D4—22no—
571C2×D4—4316no—
572C2×D4—434no—
573C2×D4—432no—
574C2×D4—8616no—
575C2×D4—868no—
576C2×D4—864no—
577C2×D4—868no—
578C2×D4—861no—
579C2×D4—862no—
580C2×D4Q8×D4314yes—
581C2×D4C23×D4312yes—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—24no—
586C22×C4—82no—
587C22×C4—431no—
588C22×C4—432no—
589C22×C4—434no—
590C22×C4—434no—
591C22×C4—432no—
592C22×C4—431no—
593C22×C4—431no—
594C22×C4—864no—
595C22×C4—864no—
596C22×C4—864no—
597C22×C4—861no—
598C22×C4—861no—
599C22×C4—861no—
600C22×C4—864no—
601C22×C4—3442no—
602C22×C4—3442no—
603C22×C4—3442no—
604C22×C4—3442no—
605C22×C4D4×D4311yescharacteristic
606C22×C4D4×D4311yescharacteristic
607C22×C4C23×D4311yescharacteristic
608M16—868no—
609C2×C8—22no—
610C2×C8—22no—
611C2×C8—432no—
612C2×C8—432no—
613C2×C8—868no—
614C2×C8—862no—
615C2×C8—862no—
616C2×C8C23×D4312yes—
617C2×C8C23×D4312yes—
618C4⋊C4—24no—
619C4⋊C4—24no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—434no—
624C4⋊C4—434no—
625C4⋊C4—432no—
626C4⋊C4—432no—
627C4⋊C4—432no—
628C4⋊C4—864no—
629C4⋊C4—864no—
630C4⋊C4—864no—
631C4⋊C4—864no—
632C4⋊C4—861no—
633C4⋊C4—861no—
634C4⋊C4—861no—
635C4⋊C4—864no—
636C4⋊C4C23×D4312yes—
637C4⋊C4C23×D4312yes—
638C4⋊C4C23×D4312yes—
639C22⋊C4—24no—
640C22⋊C4—434no—
641C22⋊C4—434no—
642C22⋊C4—864no—
643C22⋊C4—864no—
644C22⋊C4—864no—
645C22⋊C4—864no—
646C22⋊C4—864no—
647C42—432no—
648C42—432no—
649C42—864no—
650C42—864no—
651C42D4×D4312yes—
652C42C23×D4312yes—
653C23—24no—
654C23—22no—
655C23—42no—
656C23—42no—
657C23—434no—
658C23—432no—
659C23—8616no—
660C23—862no—
661C23—862no—
662C23—864no—
663C23—862no—
664C23—3444no—
665C23—3444no—
666C23—34416no—
667C23—1722no—
668C23—1722no—
669C23C2×D4×D4311yescharacteristic
670Q8—3444no—
671Q8—3444no—
672D4—24no—
673D4—22no—
674D4—434no—
675D4—8616no—
676D4—864no—
677D4—862no—
678D4C2×Q8×D4314yes—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—84no—
688C2×C4—434no—
689C2×C4—432no—
690C2×C4—438no—
691C2×C4—434no—
692C2×C4—434no—
693C2×C4—432no—
694C2×C4—432no—
695C2×C4—862no—
696C2×C4—862no—
697C2×C4—862no—
698C2×C4—862no—
699C2×C4—862no—
700C2×C4—3444no—
701C2×C4—3444no—
702C2×C4—3444no—
703C2×C4—3444no—
704C2×C4—1722no—
705C2×C4—1722no—
706C2×C4—1722no—
707C2×C4C2×D4×D4312yes—
708C2×C4C2×D4×D4312yes—
709C2×C4C2×D4×D4311yescharacteristic
710C2×C4C2×Q8×D4312yes—
711C2×C4#41×D4312yes—
712C2×C4C24×D4311yescharacteristic
713C8—22no—
714C8—22no—
715C8—862no—
716C8—862no—
717C22—24no—
718C22—42no—
719C22—42no—
720C22—48no—
721C22—434no—
722C22—862no—
723C22—862no—
724C22—868no—
725C22—864no—
726C22—34416no—
727C22—1722no—
728C22—1722no—
729C22—1728no—
730C22C22⋊Q8×D4312yes—
731C22#1458370112yes—
732C22#1458370912yes—
733C22C22×D4×D4311yescharacteristic
734C4—22no—
735C4—22no—
736C4—42no—
737C4—42no—
738C4—42no—
739C4—434no—
740C4—862no—
741C4—862no—
742C4—1722no—
743C4—1722no—
744C4—1722no—
745C4C22⋊Q8×D4312yes—
746C4C22×Q8×D4311yescharacteristic
747C4C2×#41×D4311yescharacteristic
748C2—44no—
749C2—864no—
750C2—1724no—
751C2#1914442314yesdirect product factor
752C2C2×C22⋊Q8×D4311yescharacteristic
753C2C2×#1458370111yescharacteristic
754C2C2×#1458370911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#478C2
socleC23×C43C22×D4
prime radicalC22×D4×D43C22
hypercenterC2×#478D43
hypocenterC43C2×#3081
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. C2×#14583529C2semidirect
3. #19144423C2direct (N × H)
4. C2×#14583202C2semidirect
5. C2×#14583197C2semidirect
6. C2×#14583196C2semidirect
7. C2×#14583189C2semidirect
8. C2×#14583188C2semidirect
9. C2×#14583180C2semidirect
10. C2×#14583177C2semidirect
11. C2×#14582938C2semidirect
12. C2×#14582936C2semidirect
13. C2×#14582924C2semidirect
16. C2×C43×#478C2semidirect
21. #14583529C22semidirect
22. C2×#13063325C22semidirect
24. C2×#13063324C22semidirect
25. C2×#13063316C22semidirect
42. #14583202C22semidirect
43. #14583197C22semidirect
44. #14583196C22semidirect
45. #14583189C22semidirect
46. #14583188C22semidirect
47. #14583180C22semidirect
48. #14583177C22semidirect
49. #14582938C22semidirect
50. #14582936C22semidirect
51. C2×#13063259C22semidirect
52. C2×#13063259C22semidirect
53. C2×#13063258C22semidirect
54. C2×#13063256C22semidirect
55. C2×#13063256C22semidirect
56. C2×#13063256C22semidirect
57. #14582924C22semidirect
58. C2×C4⋊(C43⋊C8)C22semidirect
59. C2×Dic43⋊C8C22semidirect
60. C2×Dic43⋊C8C22semidirect
69. C2×#125×C43C22semidirect
71. C43×#478C22semidirect
72. C2×#107×C43C22semidirect
73. C2×#106×C43C22semidirect
74. C2×C4⋊C8×C43C22semidirect
84. C2×D4×D43Q8semidirect
98. #13063325C23semidirect
101. #13063324C23semidirect
103. #13063316C23semidirect
145. #13063259C23semidirect
146. #13063259C23semidirect
147. #13063258C23semidirect
148. #13063256C23semidirect
149. #13063256C23semidirect
150. #13063256C23semidirect
151. C4⋊(C43⋊C8)C23semidirect
152. Dic43⋊C8C23semidirect
153. Dic43⋊C8C23semidirect
165. #125×C43C23semidirect
175. #107×C43C23semidirect
176. #106×C43C23semidirect
177. C4⋊C8×C43C23semidirect
211. D4×D43C2×Q8semidirect
377. C2×#478D43semidirect
388. C2×C43#3081semidirect
404. C2×#125C2×D43semidirect
424. #478C2×D43semidirect
434. C2×#107C2×D43semidirect
438. C2×#106C2×D43semidirect
443. C2×C4⋊C8C2×D43semidirect
454. C43C2×#3081semidirect
488. #125C22×D43semidirect
541. #107C22×D43semidirect
545. #106C22×D43semidirect
549. C4⋊C8C22×D43semidirect
751. C2#19144423direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835292
C2×#145833712
#191444232
C2×#145832022
C2×#145831972
C2×#145831962
C2×#145831892
C2×#145831882
C2×#145831802
C2×#145831772
C2×#145829382
C2×#145829362
C2×#145829242
C2×#145829022
C2×#102×D432
C2×C43×#4782
C2×#308143